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An evaluation of rheological parameters for a model shear-thinning system with application to the diffusion… Haugen, Frances Patricia 1974

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AN EVALUATION OF RHEOLOGICAL PARAMETERS FOR A MODEL SHEAR-THINNING SYSTEM WITH APPLICATION TO THE DIFFUSION OF HYDROCORTISONE by FRANCES PATRICIA HAUGEN B.Sc. (Pharm), University of British Columbia, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Faculty of Pharmaceutical Sciences Division of Pharmaceutics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1974 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Depa rtment The University of British Columbia Vancouver 8, Canada r. i ABSTRACT Many pharmaceutical systems exhibit shear-thinning flow properties but the expression of these properties i n terms of meaningful r h e o l o g i c a l parameters remains a problem. To be us e f u l , the parameters must be rheometer-independent and eit h e r describe the f l u i d under a p p l i c a t i o n , processing and storage conditions, or speci f y the f l u i d structure and d i s p o s i t i o n of the molecules at n e g l i g i b l e shear rates. Interlinked with t h i s problem i s the correct s e l e c t i o n of r h e o l o g i c a l parameters and systems for applied studies, i . e . the determination of rh e o l o g i c a l e f f e c t s on drug d i f f u s i o n . The components of the model shear-thinning system, the nonionic c e l l u l o s e polymer, hydroxyethylcellulose (HEC, Natrosol 250G), and the nonionic surfactant, polyoxyethylene (4) dodecyl e t h e r . ( B r i j 30), were characterized, physicochemically. The addition of B r i j 30 to HEC dispersions provided a r e l i a b l e means of obtaining a series of systems showing predictable increments i n shear-thinning behaviour at each HEC concentration. Over a 5 year period, the r h e o l o g i c a l r e p r o d u c i b i l i t y and s t a b i l i t y of aqueous HEC dispersions were determined and compared with corresponding data for 2% methylcellulose (MC, 1500 cP) dispersions. For si m i l a r consistencies, HEC and MC dispersions showed comparable r e p r o d u c i b i l i t y and s t a b i l i t y . The power-law consistency index was observed to be rela t e d to both storage time and polymer concentration. Two methods of shear s t r e s s c a l i b r a t i o n were examined f o r the Rotovisko. The determination of a shear stress c a l i b r a t i o n constant for each shear rate provided a s i g n i f i c a n t improvement f o r non-Newtonian shear-thinning f l u i d s over the manufacturer's c a l i b r a t i o n method when both methods were compared with corresponding data generated with the i i cone-plate Weissenberg rheogoniometer. The l i m i t a t i o n s of shear rate equations and two Couette rheometers, Haake Rotovisko and Brookfield Synchro-lectric (with SC-4 spi n d l e s ) , to accurately represent shear stress-shear rate parameters were examined. The Krieger-Maron and the Mooney shear rate equations were found to y i e l d the widest range of rheometer-independent r e s u l t s for the Rotovisko and Br o o k f i e l d rheometers, r e s p e c t i v e l y , when separately compared with s i m i l a r data obtained with the rheogoniometer. Viscometric properties of polyoxyethylene (4) dodecyl ether i n HEC dispersions were evaluated over a concentration range of 2.0 -3.5% HEC and 0 - 16% B r i j 30. Three r h e o l o g i c a l models: the modified Shangraw structure equation, the Steiger-Trippi-Ory equation and the power-law model were.fitted to the data and found to describe accurately the flow behaviour of the dispersions at 30.0°C between shear rates of 8.5 - 685 s \ V a r i a t i o n of model parameters with surfactantcconcentration was computed for each HEC dispersion. A shear-sensitive i n t e r a c t i o n between the surfactant and the c e l l u l o s e polymer was noted. To determine the d i s p o s i t i o n of HEC i n s o l u t i o n and the nature of the viscous i n t e r a c t i o n noted for the HEC - B r i j 30 systems, low shear rate and dynamic measurements were made. From storage and loss moduli, dynamic v i s c o s i t i e s and loss tangents, HEC was determined to be a molecule with intermediate f l e x i b i l i t y and the HEC - B r i j 30 systems were composed of a loose three dimensional network. The e f f e c t of increased l i m i t i n g v i s c o s i t y at low shear rates was measured on the d i f f u s i o n of hydrocortisone through nylon membrane and human autopsy epidermis. The absence of drug-vehicle i n t e r a c t i o n s i i i was demonstrated and the s i m i l a r i t y i n the r e s u l t s f o r the two membranes indicated that the observed decrease i n steady state flux was due to the a l t e r a t i o n of v e h i c l e v i s c o s i t y . The s o l u b i l i t y , p a r t i t i o n c o e f f i c i e n t and d i f f u s i o n c o e f f i c i e n t s were measured for hydrocortisone. i v TABLE OF CONTENTS Page LIST OF TABLES . . x LIST OF FIGURES • . . . . . . x i i LIST OF MASS SPECTRAL FRAGMENT MAPS x v i i LIST OF SYMBOLS x v i i i INTRODUCTION 1 STATEMENT OF PROBLEM 4 SECTION I. A MODEL SHEAR-THINNING SYSTEM WITH RHEOLOGICAL FLEXIBILITY: MATERIAL SELECTION AND CHARACTER-IZATION 7. A. HYDROXYETHYLCELLULOSE 7 INTRODUCTION AND SELECTION 7 EXPERIMENTAL 10 1. Molecular Weight and Moisture Content- 10 2. Density and Apparent Molar Volume of'Aqueous Dispersions . . , 14 RESULTS AND DISCUSSION 16 1'; Characterization Data f o r Hydroxyethylcellulose . . * 16 2. Density- and Apparent Molar Volume-Temperature . Relationships f o r Aqueous Dispersions . . . . . . 19 B. POLYOXYETHYLENE $4) DODECYL ETHER . . . . . . . . . . 25 INTRODUCTION 25 EXPERIMENTAL 26 1. Surfactant Selection 26 2. Molecular Weight, C r i t i c a l M i c e l l e Concentration V Page and Infrared Spectrum . . . . . . 27 3. Component Analysis . . . . . . . 28 RESULTS AND DISCUSSION . 31 1. Surfactant Selection . . 31 2. Characterization Data for Polyoxyethylene (4) Dodecyl Ether 37 3. Polymerization Products I d e n t i f i e d . . . . . . 43 SECTION I I . RHEOMETRIC STUDIES OF A MODEL SHEAR-THINNING SYSTEM . . 76 A. STEADY SHEAR STUDIES OF PRACTICAL IMPORTANCE . . . 76 LITERATURE SURVEY . . . .-. . . . . . . . . . . . . . 77 1. Shear Stress/Shear Rate Determination i n Rotational Viscometry 77 a) Co-axial Cylinder,Geometry . . . . . . . . 77 b) Cone-Plate Geometry . . . . . . . 82 2. Errors i n Rotational Viscometry . 83 3. Flow Model Selection 85 EXPERIMENTAL . . . . . . . . . . . . 86 1. Rheometers and Methods . . • 86 2. Rheological Properties, R e p r o d u c i b i l i t y and S t a b i l i t y of Hydroxyethylcellulose and Methyl-c e l l u l o s e Dispersions . . . . . v 8^ 3. Rheological Properties of Hydroxyethylcellulose -Polyoxyethylene (4) Dodecyl Ether Systems . . . 90 4. Comparison of Rotovisko Shear Stress C a l i b r a t i o n 5. Evaluation of Non-Newtonian Rheograms Derived from Two Different Types of Rheometers . 6. Evaluation of Rheological Models for Shear-Thinning Systems RESULTS AND DISCUSSION . . . , . . . 1. Rheological Properties, Reproducibility and Stability of Hydroxyethylcellulose and Methyl-cellulose Dispersions . . . a) - Rheological Properties . . b) Reproducibility . . . . . . . . . . . . . . c) Stability 'i 2. Rheological Features of Hydroxyethylcellulose -Polyoxyethylene (4) Dodecyl Ether Systems . . . 3 . An Improved Rotovisko Shear Stress Calibration Method . 4. - Limitations of Couette Rheometers in Shear Stress/Shear Rate Determination of Non-Newtonian Shear-Thinning Systems . a) Haake Rotovisko - Weissenberg rheogonio- . meter comparison . . . . . . . . . . . . , b) Brookfield Synchro-lectric - Weissenberg rheogoniometer comparison . . 5. Rheological Models for Shear-Thinning v i i Page B. RHEOMETRIC STUDIES OF A FUNDAMENTAL NATURE: LOW SHEAR AND DYNAMIC MEASUREMENTS . . . . . . . . . . 142 INTRODUCTION 142 1. Lim i t i n g V i s c o s i t y at Low Shear Rates 142 2. V i s c o e l a s t i c Moduli . . . 144 3. Dynamic Testing . . . . . . . 145 EXPERIMENTAL . 147 1. Low Shear Rate Studies of Hydroxyethylcellulose and Hydroxyethylcellulose - Polyoxyethylene (4) Dodecyl Ether Systems 147 2. V i s c o e l a s t i c Studies: Rheometer and Methods . . . 147 3. V i s c o e l a s t i c Features of Hydroxyethylcellulose and Hydroxyethylcellulose - Polyoxyethylene (4) Dodecyl Ether Systems . . . . . . . 149 RESULTS AND DISCUSSION 150 1. Flow C h a r a c t e r i s t i c s of Hydroxyethylcellulose and Hydroxyethylcellulose - Polyoxyethylene (4) Dodecyl Ether Systems at Low Shear Rates . . . . . 150 2. V i s c o e l a s t i c Properties of Hydroxyethylcellulose Dispersions 154 3. V i s c o e l a s t i c Features of Hydroxyethylcellulose -Polyoxyethylene (4) Dodecyl Ether Systems . . . . . 160 SECTION I I I . LIMITING VISCOSITY AT LOW SHEAR RATES AND HYDROCORTISONE DIFFUSION . . . . . . . . . . . 168 INTRODUCTION 168 v i i i Page EXPERIMENTAL . 1 6 9 • 1. Determination of S o l u b i l i t y and P a r t i t i o n C o e f f i c i e n t f o r Hydrocortisone . . 169 2. The Interaction of Hydrocortisone with . Hydroxyethylcellulose . 172 a) Membrane Preparation and Selection . . . . . 172 b) Binding of•Hydrocortisone with Nylon Membrane . 175 c) Interaction of Hydrocortisone with Hydroxyethylcellulose . . . 175 3. Hydrocortisone - Hydroxyethylcellulose D i f f u s i o n Studies in.the Presence of a Membrane . . . . . . 176 RESULTS AND DISCUSSION 1. Hydrocortisone S o l u b i l i t y and P a r t i t i o n C o e f f i c i e n t . . . . . . . . . . . . . . . . . . . 178 2. Hydrocortisone - Hydroxyethylcellulose Interactions 179 3. Influence of Lim i t i n g V i s c o s i t y at Low Shear i Rates on the D i f f u s i o n of Hydrocortisone i n Hydroxyethylcellulose Dispersions 180 SECTION IV. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . 186 APPENDICES I, MATERIALS '. 193 I I . APPARATUS 202 i x Page III. COMPUTER PROGRAMS 2 0 6 REFERENCES 226 X LIST OF TABLES Table Page I. Sedimentation v e l o c i t y data f o r a 0.25% w/w HEC dispersion , 17 I I . Synthetic boundary data for a 0.25% w/w HEC dispersion 18 I I I . Density and apparent volume of aqueous HEC dispersions at 15, 20, 30, 35 and 40°C 20 —BT IV. Density-temperature r e l a t i o n s h i p , d = A e , for aqueous HEC dispersions . . . . . . . . . . . . 23 V. The subjective v i s c o s i t y and s t a b i l i t y of nonionic surfactants i n combination with a 2% w/w HEC dispersion: . . . . . . . . . . . 33 VI. Vapour pressure osmometer data for B r i j 30 and b e n z i l standard dissolved i n benzene 37 VII. Retention time, retention volume and degree of r e s o l u t i o n f or the major components of B r i j 30 . . . 46 VIII. Retention times and volumes for B r i j 30, the homologous serie s of alcohols and the B r i j 30 -alcohol se r i e s combination • . . . . 48 IX. Some positi o n s of i n i t i a l fragmentation of polyoxyethylene (n) .dodecyl and tetradecyl ethers . . . . . 73 X. Rheological r e p r o d u c i b i l i t y data for HEC and MC dispersions a f t e r 0.13 year storage . . . . . . . 101 XI. Rheological r e p r o d u c i b i l i t y data for HEC and MC dispersions a f t e r 1 and 5 years storage 102 XII. Shear stress c a l i b r a t i o n data for the Rotovisko rheometer f i t t e d with an MV1 spindle . . . 113 XIII. Comparison of the two Rotovisko shear stress c a l i b r a t i o n methods to data generated using the Weissenberg rheogoniometer 115 XIV. Power-law parameters f o r HEC - B r i j 30 systems measured with the Haake Rotovisko at 25 C . . . . . 117 LIST OF TABLES (Continued) x i Table Page XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. Power-law parameters for the HEC - B r i j 30 systems measured with the Weissenberg rheogoniometer at 25 C . . 118 Comparison of two shear rate c a l c u l a t i o n equations for the Rotovisko with r e s u l t s from the Weissenberg rheogoniometer for shear-thinning systems . . . . . . 119 Power-law parameters f o r the HEC - B r i j 30 systems measured with the Brookfield rheometer at 25 C. C a l i b r a t i o n and Krieger-Maron shear rate equations , . 121 Power-law parameters f o r the HEC - B r i j 30 systems measured with the Brookfield rheometer at 25 C. Krieger and Mooney shear rate equations • • • 122 Comparison of several shear rate equations for the Brookfield Synchro-lectric with r e s u l t s from the Weissenberg rheogoniometer for shear-thinning systems 124 Viscous i n t e r a c t i o n at low shear rates i n a 2.5% HEC di s p e r s i o n containing 16% B r i j 30 . . 141 S i g n i f i c a n t instrumental conditions i n HEC - B r i j 30 dispersion frequency curve generation . 151 Comparison of v e h i c l e v i s c o s i t y e f f e c t s on the d i f f u s i o n of HC through nylon membrane and human autopsy epidermis 181 V i s c o s i t y standardsuusedlinrr.heometer c a l i b r a t i o n . 197 XXIV. Blending time for HEC and MC dispersions x i i LIST OF FIGURES Figure Page 1. Ostwald's flow curve . 2 2. Idealized two-dimensional structure of HEC (Natrosol 250G) 8 3. Photographs of the HEC peak taken at 1.5 and 2.5 hours during the sedimentation v e l o c i t y run H 4. Density-temperature r e l a t i o n s h i p f o r aqueous HEC dispersions . . 21 5. T y p i c a l change i n c a r r i e r gas flow rate f o r B r i j 30 chromatographed i n the temperature programming mode . . . 29 6. T y p i c a l change i n c a r r i e r gas flow rate f o r the sol u t i o n of homologous alcohols chromatographed i n the temperature programming mode 32 7. Extrapolation of the vapour pressure osmometer data to zero concentration for the number-average molecular weight determination of B r i j 30 . . . . . . . . . . . . 38 8. Nuclear magnetic resonance spectrum of B r i j 30 i n CD C l ^ at 31°C. Sweep width, 1000 Hz; sweep time, 250 sec;, frequency response, 20 Hz . . . . . . . . . . . . . 41 9. Thin l i q u i d f i l m i n f r a r e d spectrum of B r i j 30 . . . . . . -42. 10. Relationship of surface tension to concentration of B r i j 30 i n d i s t i l l e d water at 22 ± 1°C . . . . . . ... . 44 11. Temperature programmed gas chromatogram of B r i j 30. T. = 110°C, T f = 250°C, dT/dt = 6°C/min 45 12. Temperature programmed gas chromatogram of the homologous.series of alcohols. T ± = 110°C, T = 220°C, dT/dt = 6°C/min . . . . . . . . . . . . . . . . . . . . . 4 9 13. Temperature programmed gas chromatogram of a 1:3 volume r a t i o of the homologous alcohols s o l u t i o n and B r i j 30. T ± = 110°C, T f = 250°C, dT/dt = 6°C/min . . . . 50 14. Mass spectra of dodecanol and B r i j 30 - peak A 52 15. Mass spectrum of B r i j 30 - peak C .. . . 54 16. . Mass spectrum of B r i j 30 - peak E . 57 X1X1 \ * C L95% ) 66 Figure Page 17. Mass spectrum of. Brij 30 - peak G. O ^ C ^ ) ^ CH^ + fragment pattern omitted . . . 60 18. Mass spectrum of Brij 30 - peak I. CR^CCH^)^ CH 2] + fragment pattern omitted . . 63 19. Mass spectra of tetradecanol and Brij 30 - peak B . . . 20. Laminar flow of an inelastic f l u i d in the gap between two concentric cylinders. A. the outer cylinder rotates with angular velocity P. and the inner one i s stationary, B. the inner cylinder rotates with angular velocity Q and the outer one is stationary (adapted from Lielmezs and Runikis, 1967) . 78 21. Rheograms for aqueous HEC dispersions (age =0.13 yr) measured with the Rotovisko rheometer (y = 8.5 -1370 s - 1 , T = 30.0 ± 0.5°C) 96 22. Shear stress - HEC concentration relationship for a selected range of shear rates.. . . . . 98 23. Rheograms for 2.0% w/w.MC in comparison with two HEC dispersions measured with the Rotovisko rheometer ' (y = 8.5 - 1370 s _ 1 , T = 30.0 ± 0,5°C, age =0.13 yr) . 99 24. Relationship of the power-law consistency index to storage time for aqueous MC and HEC dispersions (m + CL Q 5 %) 104 25. Effect of storage time on the apparent viscosity of 2.0% w/w HEC dispersions measured with a Rotovisko over a shear rate range of 8.5 - 685 s~^~ (T = 30.0 ± .0.5°C; age = 1 day, n o - range; age =47 and 365 days, a 106 26. Effect of storage time on the apparent viscosity of 3.0% w/w HEC dispersions measured with a Rotovisko over a shear rate range of 8.5 - 685 s--*- (T = 30.0 ± . 0.5°C; age = 1 day, n ,±.range; age =47 and 365 -.. days, n a ± CL 9 5 %) • • • • .107 27. Effect of storage time on the apparent viscosity of 2.0% w/w MC (1500 cP) dispersions measured with a , Rotovisko rheometer over a shear rate range of 8.5 -1370 s _ 1 (n ± CL Q.„, n = 9) 108 28. Flow behaviour of HEC.. dispersions containing 0 and 4% Brij 30 110 x i v Figure Page 29. Flow behaviour of 2.5% HEC dispersions containing d i f f e r e n t l e v e l s of -Brij 30 . . . . . . . . . . . . . 112 30. Consistency index - flow behaviour index r e l a t i o n -ship for the HEC - B r i j 30 systems measured with the rheogoniometer at 25°C over a 10.95 - 690 s _ 1 range i n shear rate 125 31. Consistency index - flow behaviour index r e l a t i o n -ship for the HEC - B r i j 30 systems measured with the rheogoniometer at 25°C over a 0.3 - 17. s~^~ range i n shear rate - 127 32. Flow behaviour of 2.5% HEC dispersions containing 16% B r i j 30. The modified Shangraw, S t e i g e r - T r i p p i -Ory and power-law models are shown f i t t e d to the data 129 33. V a r i a t i o n of the modified Shangraw parameter, a_, with HEC and B r i j 30 concentration . . . , . . . . .131 34. V a r i a t i o n of the modified Shangraw parameter, b_, with HEC and B r i j 30 concentration 132 35. V a r i a t i o n of the modified Shangraw parameter, c_, with HEC and B r i j 30 concentration 133 36. V a r i a t i o n of the Steiger-Trippi-Ory model parameter, a', with HEC and B r i j 30 concentration . . 134 37. • • V a r i a t i o n of the Steiger-Trippi-Ory model parameter, cj_, with HEC and B r i j 30 concentration . .135 38. V a r i a t i o n of the power-law model parameter, m, with HEC and B r i j 30 concentration . . . 137 39. V a r i a t i o n of the power-law model parameter, n, with HEC and B r i j 30 concentration . . . . . . . . . . 138 40. Apparent v i s c o s i t y of 2.5% HEC dispersions containing 0, 4, 8, 12 and 16% B r i j 30. The power-law model i s shown . . . . . 140 41. Viscosity-shear rate r e l a t i o n s h i p f o r the HEC dispersions showing the l i m i t i n g v i s c o s i t y region at low shear rates. Measured with the rheogoniometer at 23.0 ± 0.5°C . . . . . . . . . . . . . . . . . . . 152 42. Low shear rate l i m i t i n g v i s c o s i t y r e l a t i o n s h i p . . . . . . . . . . - HEC concentration . 153 XV Figure Page 43. V i s c o s i t y - shear rate r e l a t i o n s h i p for the 3% HEC plus 0, 8, 12 and 16% B r i j 30 dispersions showing the absence of a l i m i t i n g v i s c o s i t y region at low shear rates. Measured with the rheogonio-meter at 23.0 ± 0.5°C 1 5 5 44. Storage modulus as a function of o s c i l l a t o r y frequency for 1, 2, 3. and 4% w/w HEC dispersions (T = 23.0 ± 0.5°C) 156 45. Loss modulus as a function of o s c i l l a t o r y frequency for 1, 2, 3 and 4% w/w.HEC dispersions (T = 23.0 ± 0.5°C) . . . . . . . . . . . . . . . . . . 157 46. Storage - loss moduli r e l a t i o n s h i p for the 3 and 4% HEC dispersions . 159 47. Dynamic and steady shear v i s c o s i t y r e l a t i o n s h i p for 1, 2, 3 and 4% HEC dispersions (T = 23.0 ± 0.5°C) . . . . . . . . . . . . . . . . . 161 48. Storage modulus as a function of o s c i l l a t o r y frequency for 4% HEC plus 0, 8, 12 and 16% B r i j 30 (T = 23.0 ± 0.5°C) 162 49. Loss modulus as a function of o s c i l l a t o r y frequency for 4% HEC plus 0, 8, 12 and 16% B r i j 30 (T = 23.0 ± 0.5°C) . 1 6 4 50. Dynamic and.steady shear v i s c o s i t y r e l a t i o n s h i p for selected HEC and B r i j 30 systems . . . . . . . . . 165 51. Consistency spectrum or loss tangent of selected HEC and HEC - B r i j 30 systems 167 52. UV spectrophotometry standard curve f o r hydrocortisone . . . . . . . . . . 170 53. UV spectrophotometry standard curve for hydrocortisone i n octanol . . . . . . . 171 54. UV spectrophotometric, standard curve f o r hydroxyethylcellulose . . . . . . . . . . . 174 3 55. Quench cor r e c t i o n curve for (1, 2 H) C o r t i s o l . . . 177 56. Cumulative d i f f u s i o n of HC through, nylon membrane from a 11 ug/ml s o l u t i o n i n 1.0 and 4.0% w/w HEC dispersions and d i s t i l l e d water . . 182 x v i Figure Page 57. Cumulative d i f f u s i o n of HC through human autopsy epidermis from a 11 ug/ml so l u t i o n i n 1,0 and 4.0% w/w HEC dispersions and d i s t i l l e d water 184 3 58. Thin layer chromatogram o f ( l , 2 H)0Cortisol. Solvent system, chloroform/absolute ethanol 90:10 v/v) 195 3 59. Thin layer chromatogram of (1, 2 H) C o r t i s o l . Solvent system, chloroform/acetone/acetic acid {12:8:1 v/v) . . . . . . . . . . . . . . . . . . . . 196 x v i i LIST OF MASS SPECTRAL FRAGMENT MAPS Page 1. P r i n c i p a l fragments of B r i j 30 - peak A and dodecanol 53 2. P r i n c i p a l fragments of B r i j 30 - peak C, polyoxyethylene (1) dodecyl ether 56 3. P r i n c i p a l fragments of B r i j 30 - peak E, polyoxyethylene (2) dodecyl ether . . . . . . . . . 59 4. P r i n c i p a l fragments of B r i j 30 - peak G, polyoxyethylene (3) dodecyllether . . . . . . . . . 62 5. P r i n c i p a l fragments of B r i j 30 - peak I, polyoxyethylene (4) dodecyl ether . . .64 6. P r i n c i p a l fragments of B r i j 30 - peak B and tetradecanol . 67 7. P r i n c i p a l fragments of B r i j 30 - peak D, polyoxyethylene (1) tetradecyl ether . 69 8. P r i n c i p a l fragments of B r i j 30 - peak F, polyoxyethylene (2) tetr a d e c y l ether . 70 9. P r i n c i p a l fragments of B r i j 30 - peak H, polyoxyethylene (3) tetradecyl ether . . . . . . . 71 XVX11 LIST OF SYMBOLS modified Shangraw equation parameter Steiger-Trippi-Ory equation parameter a g UV a b s o r p t i v i t y b modified Shangraw equation parameter c concentration c modified Shangraw equation parameter c' Steiger-Trippi-Ory equation parameter 1 3 d density (g cm ) d diameter (cm) _3 d Q density of the solvent (g cm ) _3 d T density of test dispersion at temperature, T (g cm ) -3 d ,fcc.1 density of test s o l u t i o n at temperature, T (g cm ) I s o l d„„ density of water at 20 C.(g cm ) 20,w J d . density of t e s t s o l u t i o n at 20°C (g cm £m\j y SOX d density of d i s t i l l e d water at temperature, T (g cm ) w f frequency of o s c i l l a t i o n (Hz) h height (cm) h* e f f e c t i v e length or height (cm) h Q p h y s i c a l length of c y l i n d r i c a l portion of the spindle (cm) k Mooney shear stress c a l i b r a t i o n constant m power-law consistency index (dyne cm ^ s n ) n power-law flow behaviour index n percent (w/v) of solute n' number of moles of solute n number of moles of solvent o x i x r radius (cm) t time t retention time (min) 3 - 1 Vapp apparent p a r t i a l s p e c i f i c volume (cm g ) 3 -1 v apparent molar volume (cm mole ) app A area A a regression constant A Rotovisko shear stress c a l i b r a t i o n constant A ' Brookfield shear stress c a l i b r a t i o n constant A Q amount of HC i n the octanol layer (ug)ml) A^, t o t a l amount of HC i n the system (ygi)ml) A amount of HC i n the aqueous layer (yg)ml) w B Rotovisko shear rate c a l i b r a t i o n constant B an equation parameter C concentration (mole 1 "*") C concentration d i f f e r e n c e of a solute across a membrane s - 2 - 2 (yg cm ) or (moles cm ) . 2 -1 ' °obs experimentally observed d i f f u s i o n constant (cm s ) 2 - 1 D d i f f u s i o n constant (cm s ) 2 -1 D o n d i f f u s i o n constant corrected to standard conditions (cm s ) 2U j W . 3 - 1 . temperature corrected flow rate (cm min ) -2 G' storage modulus (dyne cm ) -2 G" loss modulus (dyne cm ) Im movement of the worm-shaft measured by the o s c i l l a t i o n input transducer (ym) -2 -1 -2 -1 J steady state f l u x of solute (pg cm h ) or (moles cm h ) XX K osmometer c a l i b r a t i o n constant Km the membrane-vehicle p a r t i t i o n c o e f f i c i e n t t o r s i o n bar constant (dyne cm pm K^, ... K^Q regression constants , ... L^Q regression c o e f f i c i e n t s M moment of a force or a torque (dyne cm) Mw weight-average molecular weight Mn number-average molecular weight P' pressure R gas constant (8.314 x 10^ ergs deg mole \ bob radius (cm) R c cup radius (cm) R l , 2 g a s . l i q u i d chromatograph peak r e s o l u t i o n S scale reading Sm 111. maximum movement of the to r s i o n head transducer (ym) obs experimentally observed Svedberg constant (s) S20,w Svedberg constant corrected to standard conditions (s) T temperature T i i n i t i a l temperature (°C) T f f i n a l temperature (°C) U Rotovisko instrumental gear s e t t i n g V 3 - 1 p a r t i a l molar volume (cm mole )_ V average bridge output (mV) V r 3 retention volume (cm ) W b gas l i q u i d chromatograph peak width at h height w T weight of test dispersion at temperature, T (g) w w weight of d i s t i l l e d water at temperature, T (g) x x i a cone angle (deg) y shear rate (s ^) 6 . membrane thickness (cm) n Newtonian v i s c o s i t y (poise) n' dynamic v i s c o s i t y (poise) n apparent or non-Newtonian v i s c o s i t y (poise) Si ' ri l i m i t i n g v i s c o s i t y at low shear rates (poise) r i s o ^ ' v i s c o s i t y of test s o l u t i o n at known temperature, T (poise) n,j, v i s c o s i t y of "water at temperature of centrifuge run (poise) ^20 v i s c o s i t y of water at 20°C (poise) n v i s c o s i t y of water at temperature, T (poise) w n ^ apparent v i s c o s i t y of the B r i j 30-HEC-water system (poise) ^a2 apparent v i s c o s i t y of the HEC-water system (poise) 1 ri „ apparent v i s c o s i t y of the B r i j 30-water system (poise) n ^ increased apparent v i s c o s i t y due to the B r i j 30-HEC-water system (poise) X thermal conductivity (Cal (g) h cm ^ °K ^) -2 a shear stress (dyne cm ) _2 shear stress at the bob surface (dyne cm ) _2 a c shear stress at the cup surface (dyne cm ) x lag time (h) tit radian frequency, 2irf (s ^) Ah increase i n bob length due to end e f f e c t s (cm) movement of the t o r s i o n head transducer (ym) 6 cone angle (rad) $ displacement of the s i n u s o i d a l stress and s t r a i n waves (deg) x x i i ti angular v e l o c i t y (rad s tiQ a low angular v e l o c i t y (rad s ^) fiM maximum angular v e l o c i t y (rad s ^) ACKNOWLEDGEMENTS To Dr. J.O. Runikis, thesis supervisor. To Drs. F.S. Abbott, M.A. Tung, A.G. M i t c h e l l , B. Roufb.galis, Prof. J . Lielmezs, committee members. To E l l e n Ng, Peggy Tom, Gary Sui and Linda Lee, summer students. To Dr. F.S. Abbott, f o r advice and use of the gas chromatograph-mass spectrometer. To Dr. S. Nakai, Department of Food Science, f o r advice and use of the ul t r a e e n t r i f u g e . To Dr. R.J. Bose, F i s h e r i e s Research, for the nuclear magnetic resonance spectrometry work. To B i l l Howald f or advice on mass spectrometry. To the Medical Research Council of Canada, for the i r generous f i n a n c i a l support through the award of a Studentship. zziv to ken 1 INTRODUCTION Rheology, the study of the deformation of materials, including flow (Reiner and Scott B l a i r , 1967) has intrigued such early philosophers and poets as Heracleitus (500 BC), A r i s t o t l e (384 - 322 BC) and Lucretius (96 - 55 BC) but i t was not u n t i l the 16th Century that the potter P a l i s s y (1510 - 1589) began to write s p e c i f i c a l l y on the science of the flow of matter (Durant, 1939; Durant and Durant, 1961; Scott B l a i r , 1938). Major advancements were made i n the 17th Century by Hooke (1635 4 1703) and Newton (1647 - 1727). While applying s p i r a l springs to the balance wheel of watches,jHooke observed the action of springs, 'ut tensio s i c v i s ' , now known as Hooke's law (Durant and Durant, 1963). Newton, i n 1676, defined v i s c o s i t y for simple or Newtonian l i q u i d s , s t a t i n g that the r a t i o of stress to rate of shear i s constant (Scott B l a i r , 1969). Rheological equations, based upon experimentation, to describe the rate of flow i n r e l a t i o n to f l u i d v i s c o s i t y appeared f i r s t i n the 19th Century, beginning with the Hagen-Poiseuille c a p i l l a r y work (Scott B l a i r , 1972). The desire for v a r i a b l e shear rates led to the design of the S Couette r o t a t i o n a l viscometer i n 1890 (van Wazer et a l . , 1963). The discovery of non-Newtonian flow properties soon followed and Wo. Ostwald proposed thatfflow processes consisted of a number of stages as shown i n Figure 1 (Scott B l a i r , 1969; Reiner, I960). Rheology as a formal branch of science was established with the foundation of the Society of Rheology at the Washington Conference i n 1929 (Scott B l a i r , 1969; 1972). Today, rheology has wide and varied a p p l i c a t i o n s , ranging from studies of metal creep and concrete flow to food texture, blood vessel e l a s t i c i t y , the 2 consistency of pharmaceuticals and the flow of the earth's mantle (Scott B l a i r , 1972; Barry, 1970; Post and Griggs, 1973). As a r e s u l t of the myriad applications of rheology, many devices have been constructed and numerous mathematical models have been derived for the determination and expression of r h e o l o g i c a l behaviour (Skelland, 1967; van Wazer et a l . , 1963; Oka, 1960; Sherman, 1970). In steady shear rheometry, the conversion of instrumental readings for non-Newtonian systems into absolute units of mass, length and time i s s t i l l a major problem for the oldest and most commonly used Couette geometry (Krieger, 1968).. In non-theoretical l i t e r a t u r e , a reluctance and an uncertainty p e r s i s t s to the expression of non-Newtonian' flow behaviour i n terms of r h e o l o g i c a l model parameters. ! Over a period of t h i r t y years, dynamic measuring techniques have been developed to examine f l u i d s at shear rates which do not s i g n i f i c a n t l y a l t e r f l u i d structure. 'Much work i s currently being done i n the area of polymer molecular modeling based on measurements of v i s c o -e l a s t i c behaviour but experimental r e s u l t s are s t i l l somewhat sparse (Ferry, 1970). Recently, pharmaceutical investigators have attempted to c o r r e l a t e v e h i c l e rheology with drug b i o a v a i l a b i l i t y (Ashley and Levy, 1973; Braun and Parrott,. 1972; Khristov, 1969; Khristov et a l . , 1969 and 1970; Davis, 1973). Davis (1973) has noted a tendency to use complex systems where r h e o l o g i c a l factors cannot be separated from drug-vehicle i n t e r a c t i o n s . 4 STATEMENT OF PROBLEM A model shear-thinning system with a wide range of pharmaceutically-interesting consistencies has been characterized 9 both physicochemically and r h e o l o g i c a l l y and then used to examine: a) the l i m i t a t i o n s of two Couette rheometers and shear rate equations to y i e l d rheometer-independent r e s u l t s , b) the equivalence of the modified Shangraw, the S t e i g e r - T r i p p i -Ory and the power-law models to represent non-Newtonian flow properties, c) the molecular d i s p o s i t i o n of the polymer and f l u i d structure based on dynamic and lowwshear rate measurements, and d) the influence of l i m i t i n g v i s c o s i t y ait low shear rates on v e h i c l e d i f f u s i o n of hydrocortisone. S p e c i f i c a l l y , the problem and thesis has been divided into three sections. SECTION I. A MODEL SHEAR-THINNING SYSTEM WITH RHEOLOGICAL FLEXIBILITY: MATERIAL SELECTION AND CHARACTERIZATION Because of the v a r i a b i l i t y i n materials due to commercial synthetic processes, the selected c e l l u l o s e polymer and nonionic surfactant have been characterized. Weight-average molecular weight and moisture content of the powder as w e l l as de n s i t i e s and apparent molar volumes of aqueous dispersions have been measured f or hydroxy-e t h y l c e l l u l o s e (HEC, Natrosol 250G). For polyoxyethylene (4) dodecyl ether ( B r i j 30), number-average molecular weight, c r i t i c a l m i c e l l e concentration, i n f r a r e d spectrum and the i d e n t i t y of the major gas 5 chromatographically v i s i b l e components using mass spectrometry have been determined. SECTION I I . RHEOMETRIC STUDIES OF A MODEL SHEAR-THINNING SYSTEM The rheometric studies are divided into two: studies of p r a c t i c a l , importance, and studies of a fundamental nature. A. Steady Shear Studies of P r a c t i c a l Importance answering the following questions: 1. What i s the r h e o l o g i c a l r e p r o d u c i b i l i t y and s t a b i l i t y of aqueous hydroxyethylcellulose dispersions as compared with the standard 2% w/w methylcellulose dispersion? 2. What are the l i m i t a t i o n s of two popular Couette rheometers, the Haake Rotovisko and Brookfield Synchro-lectric, to represent shear-thinning data? The r e s u l t s from the two Couette viscometers are compared with cone-plate r e s u l t s i n which the shear r a t e . i s more accurately known. 3. Can shear-thinning behaviour be represented adequately by the parameters of flow models thereby, f a c i l i t a t i n g t o t a l rheogram comparisons and formulation with predicted consistency? B. Rheometric Studies of a Fundamental Nature; Low Shear and Dynamic  Measurements answering the following questions: 1. Is there a l i m i t i n g v i s c o s i t y region at low shear rates f o r the hydroxyethylcellulose and hydroxyethylcellulose-polyoxyethylene (4) dodecyl ether systems? 2. What i s the polymer d i s p o s i t i o n of hydroxyethylcellulose i n solution? 6 3. What i s the nature of the shear-sensitive viscous i n t e r a c t i o n observed for the hydroxyethylcellulose-polyoxyethylene (A) dodecyl ether-water systems? SECTION I I I . LIMITING VISCOSITY AT LOW SHEAR RATES AND HYDROCORTISONE DIFFUSION This section endeavours to apply the r e s u l t s of the low shear rate determinations i n Section II to study the e f f e c t of v i s c o s i t y on d i f f u s i o n i n the presence of a r t i f i c i a l and b i o l o g i c a l membranes. The following questions were posed: 1. What i s the l i p o p h i l i c - h y d r o p h i l i c character of hydrocortisone? 2. Does hydrocortisone (HC) bind with HEC i n aqueous solution? 3. To what extent does the l i m i t i n g v i s c o s i t y at low shear rates of •&I a non-Newtonian v e h i c l e influence the rate of d i f f u s i o n of HC i n the presence of a r t i f i c i a l and b i o l o g i c a l membranes? 7 SECTION I. A MODEL SHEAR-THINNING SYSTEM WITH RHEOLOGICAL FLEXIBILITY: MATERIAL SELECTION AND CHARACTERIZATION A. HYDROXYETHYLCELLULOSE INTRODUCTION AND SELECTION Hydroxyethylcellulose (HEC) i s a nonionic water-soluble c e l l u l o s e ether derived from the reaction of the three hydroxyl groups (2-, 3- and 6-positions) of the anhydroglucose unit of the c e l l u l o s e molecule (Figure 2). The e t h e r i f i c a t i o n of c e l l u l o s e usually consists of the preparation of a l k a l i c e l l u l o s e . b y the i n t e r a c t i o n of c e l l u l o s e with d i l u t e sodium hydroxide tsolution followed by the rea c t i o n of the a l k a l i c e l l u l o s e with the e t h e r i f y i n g reagent at an elevated temperature (1). C e l l . (OH) 0 + RCH - CH_ \> C e l l . (OH)„ 0 CH_ CHR OH (1)' 0 The e t h e r i f y i n g agent, ethylene oxide, reacts i n i t i a l l y at the hydroxyls i n the c e l l u l o s e chain and secondly, at previously substituted hydroxyls forming a polymerized side chain (Brown, 1961). The water s o l u b i l i t y of the c r y s t a l l i n e regions of c e l l u l o s e i s increased through the addition of hydro p h i l i c substitutents which act as spacers reducing the con f i g u r a t i o n a l r e g u l a r i t y of the parent c e l l u l o s e molecule. Hydroxyethyl substitutents impart a higher degree of w a t e r - s o l u b i l i t y than i s the case with methyl substitutents (Desmaris and Esser, 1966). . HEC has an optimum molar s u b s t i t u t i o n of 2.5 which renders the aqueous dispersions more stable to addition of s a l t s , changes i n pH (Hercules Inc., 1969) and enzymic degradation (Desmaris and Esser, 1966). FIGURE 2. Idealized two-dimensional structure of HEC (Natrosol 250G) Of the three, carboxymethyl-, methyl- and hydroxyethyl-cellulose, Brownell and Purves (1957) have shown that HEC i s l i k e l y to be the most uniformly substituted c e l l u l o s e . Uniform s u b s t i t u t i o n aids i n producing clear dispersions (Desmaris and Esser, 1966). Because of the industriallimportance of HEC, extensive studies have been done on the physical-chemical properties of fractionated samples. Studies done on very d i l u t e solutions to estimate the unperturbed dimensions of HEC have found the molecule to behave as an extended chain i n water (Brown, 1961; Brown et a l . , 1963; Brown and Henley, 1964'and 1967). Increased chain f l e x i b i l i t y i n water was noticed with increased temperature (Brown et_ al., 1963). The s t r i k i n g dependence of i n t r i n s i c v i s c o s i t y on the nature of the solvent and the display of large negative temperature c o e f f i c i e n t s unique to c e l l u l o s e d e r i v a t i v e s (Flory et a l . , 1958) has been noted also for HEC by Brown (1961). Recently, Klug et a l . -(1973) have estimated 6 mole % of unsubstituted anhydroglucose units i n HEC (Natrosol 250G) using enzyme hy d r o l y s i s . D i l u t e solutions of high v i s c o s i t y HEC (Natrosol 250H) have been used i n rh e o l o g i c a l studies of engineering i n t e r e s t involving the following flow of high polymer solutions past spheres (Turian, 1967) and i n tubes (Meter and B i r d , 1964), v i s c o e l a s t i c modeling (Spriggs, 1965) , normal stress measurements (Denh and Roisman, 1969; Meister and Biggs, 1969) and drag reduction (Hoyt, 1971 and 1972) but few r h e o l o g i c a l studies have been done with Natrosol 250G. Cramer (1968) has used d i l u t e solutions of t h i s polymer i n modeling studies with engineering a p p l i c a t i o n s . The e f f e c t s of thermal exposure on the v i s c o s i t y - s t a b i l i t y of Natrosol 250G and 250H 10 solutions at concentrations of pharmaceutical i n t e r e s t were studied by Powell et a l . (1966). Although HEC i s used i n the manufacture of cosmetics and pharmaceuticals, only meagre information concerning the r h e o l o g i c a l properties of Natrosol 250G i s a v a i l a b l e i n the l i t e r a t u r e . For t h i s reason, plus the apparent s t a b i l i t y and a b i l i t y to form elegant dispersions, HEC was the polymer selected for study. EXPERIMENTAL 1. Molecular Weight and Moisture. Content Brown (1961) has demonstrated the polydisperse nature of HEC, therefore, the polymer used i n the present study was characterized through, the determination of molecular weight and moisture content to f a c i l i t a t e further studies. The determination of the weight-average molecular weight (Mw) of HEC was the most d i r e c t method of obtaining polymer s i z e information. The presence of a sing l e approximately symmetrical peak for more than an hour on a preliminary u l t r a c e n t r i f u g a t i o n run indicated that the HEC solute i n a 1% w/w aqueous dispersion was homogeneous i n the ul t r a e e n t r i f u g e (Figure 3). As a r e s u l t , the determination of Mw f o r the c e l l u l o s e polymer was pursued using an u l t r a c e n t r i f u g a t i o n technique (Chervenka, 1969) i n v o l v i n g sedimentation v e l o c i t y and synthetic boundary runs. The preliminary sedimentation v e l o c i t y run with HEC indicated that the standard 1.0% w/w concentration normally employed i n u l t r a c e n t r i -fugation studies was unsatisfactory due to the slow movement of the FIGURE 3. Photographs of the HEC peak taken at 1.5 and 2.5 hours during the sedimentation velocity run meniscus, therefore, a 0.25% w/w dispersion was analyzed. The general run procedure .for preparative u l t r a c e n t r i f u g e s (Beckman, 1968) was used. The sample loading and operation of ,the s c h l i e r e n o p t i c a l accessory was car r i e d out i n the prescribed manner (Beckman, 1969). During the se d i -mentation v e l o c i t y run (59,000 rpm, 25°C), photographs were taken at 90, 150, 180, 211 and 270 min. A photographic enlarger was used to obtain peak height and magnification factor information. The resultant data from the sedimentation v e l o c i t y determination (Table I) were analyzed using the common l i n e a r l e a s t squares f i t t i n g routine i n a programmable c a l c u l a t o r to obtain the Svedberg constant, s , ( s ) , ° ' obs 1 dr s obs n2 dt ' Q r (2) v where r_ i s the radiia-l! distance (cm) from the centre of r o t a t i o n to the meniscus, Q_, the angular v e l o c i t y (rad s ^) and _t i s time (s) (Chervenka, 1969). The d i f f u s i o n c o e f f i c i e n t was obtained from the synthetic boundary run. I n i t i a l l y , a sharp boundary was formed i n the c e l l and then the d i f f u s i o n c o e f f i c i e n t was determined from the spreading of the boundary with respect to time at a lower v e l o c i t y (4000 rpm). A second c a l c u l a t o r program analyzed the peak height and area data (Table II) to 2 -1 compute the d i f f u s i o n c o e f f i c i e n t , n D ^ g (cm s ), \ 'max • -2 where A£\is the area under the sch l i e r e n peak (cm ), jt, time (s) and dc/dr i s the concentration gradient represented by the maximum height of the 13 s c h l i e r e n peak (cm) A temperature-controlled, tared s p e c i f i c g ravity b o t t l e (25 ± 0.5°C, Appendix II) was used to obtain the s o l u t i o n density, _3 d_ (g cm ), required for the c a l c u l a t i o n of the apparent p a r t i a l — 3 - 1 s p e c i f i c volume, v (cm g ), r app 100 _ (100 - n) d d v = =-—2: , (4) app n where d Q was the density of the solvent and n was the percent (w/v) of solute (Dayhoff et a l . , 1952). The Svedberg constant and the d i f f u s i o n c o e f f i c i e n t were corrected to standard conditions through temperature-controlled v i s c o s i t y and density determinations^*or 0.25% w/w HEC (25.0 ± 0.5°C, Appendix I I ) . Following ASTM procedures for transparent l i q u i d s (ASTM, 1968), temperature-co n t r o l l e d , c a l i b r a t e d c a p i l l a r y viscometers (25.0 ± 0,5°C) were used to obtain the s o l u t i o n v i s c o s i t y to correct s , and D , . The corrected obs obs Svedberg constant ( s o r . , s) was calculated from Equation (5) (Chervenka, zu,w 1969), / S20,w "obs \ n 2 Q 1 - v ' d o r. app s 20,w ^ Vapp ^ T , s o l / (5) where n T was the v i s c o s i t y of water at the temperature of the centrifuge run (poise), T ^ Q J the v i s c o s i t y of water at 20°C (poise) (Weast, 1973). n ^ . t h e v i s c o s i t y of the sample s o l u t i o n at known temperature, T, (poise), s o l — n , the v i s c o s i t y of water at T (poise) (Weast, ,1973), ,d o n , the density 14 -3 of water at 20 C (g cm" , Weast,' 1973) and d T g Q l was the density of the -3, solu t i o n at the temperature of the centrifuge run (g'cm, ), The corrected 20,w 2 —1 d i f f u s i o n c o e f f i c i e n t , D O A „ (cm s ), was calculated from Equation (6), D20,w °obs 293.2 T 1\ 20, 'sol s V \ / (6) where T_ was the temperature of the centrifuge run (K ) . The weight-average molecular weight was calculated from Equation (7), RT s, Mw = 20,w D„« 1'XTV d o n 20,w\ app 20 ,sol)) (7) where R was the gas constant (8.314 x 10^ ergs deg ''"mole , and d_rt .. was the density of the 0.25% w/w.HEC dispersion at 20°C. 20,sol Using the general procedure for the Cenco Moisture Balance (Central S c i e n t i f i c Co., 1963), the moisture content of the HEC powder was determined at several time i n t e r v a l s . 2. Density and Apparent Molar Volume of Aqueous Dispersions Density-temperature r e l a t i o n s h i p s were determined and apparent volumes were calculated f o r the HEC dispersions as supplementary i n f o r -mation for polymer c h a r a c t e r i z a t i o n and a n c i l l a r y information required for Section I I I . The density of aqueous dispersions of HEC (1.0, 2.0 and 3.0% w/w), prepared according to the general procedure (Appendix I) excluding the preservatives, was determined at 15, 20, 30, 35 and 40°C. Two s p e c i f i c gravity b o t t l e s (50 ml) containing thermometers plus s i x standard . 15 s p e c i f i c gravity b o t t l e s (50 ml) were cleaned with chromic acid, rinsed with d i s t i l l e d water and acetone and then dried to constant weight (0.2 mg), The b o t t l e s were c a l i b r a t e d at' each temperature using b o i l e d d i s t i l l e d water. Three determinations were made and then averaged. Following c a l i b r a t i o n , the s p e c i f i c gravity b o t t l e s were f i l l e d with the test l i q u i d using a syringe, immersed i n a water bath (Blue M f i t t e d with appropriate trays) and eq u i l i b r a t e d f o r 2-3 h. The experimental temperature was averaged from the two b o t t l e s containing thermometers. P r i o r to weighing, the c a p i l l a r y heights were adjusted with-the test l i q u i d e q u i l i b r a t e d to the same temperature, wiped c a r e f u l l y and quickly weighed on an a n a l y t i c a l balance (0.1 mg). Before changing the te s t ; l i q u i d , the b o t t l e s were cleaned and dried to the o r i g i n a l constant weight. The density of the test dispersion at temperature T_, d^, was calculated from d T = (W Id ) . ( 8 ) w w where Wm was the weight (g) of the test l i q u i d at temperature, T, W , the i — w -3 weight.of d i s t i l l e d water at temperature, T and d was the density (g cm ) — w of water at the same temperature ( K e l l , 1967). The apparent molar volume 3 - 1 (v , cm mole ) of the polymer was calculated from a P P M | / d T _ d M v = --— - 1000 H ^ ) (9) app d Cd ' _ _ ^ w \ U w /T,P where M was the weight-average molecular weight i n t h i s instance, d^, the density of the aqueous polymer s o l u t i o n (g/ml) and C_ was the concentration of solute (moles/1) (Bauer and Lewin, 1959). 16 RESULTS AND DISCUSSION 1. Characterization Data f o r Hydroxyethylcellulose Using the common l i n e a r l e a s t squares f i t t i n g routine, the -13 Svedberg constant, s , = 1.81 x 10 s, was obtained from the sedimen-6 ' obs ta t i o n v e l o c i t y data f o r the 0.25% w/w HEC dispersion (Table I ) . The -7 2-1 d i f f u s i o n c o e f f i c i e n t , D „ = 1.88 x 10 cm s , was obtained from the obs ; synthetic boundary determination (Table I I ) . A f t e r applying the v i s c o s i t y c o r r e c t i o n obtained from c a p i l l a r y measurements, the corrected -13 Svedberg constant, s„„ , was 11.4 x 10 s and the corrected d i f f u s i o n & ' 20,w -7 2 -1 c o e f f i c i e n t , D 0 / % , was 11.6 x 10 cm s . The apparent p a r t i a l ' 2 0 ^ ' 3 - 1 s p e c i f i c volume f o r 0.25% w/w HEC was 0.721 cm g , the average density . at 25.0 ± 0.5°C was 0.9978 g cm - 3 and the average v i s c o s i t y at 25.0 ± 0.5°C 4 was 0.0632 poise. Using (7), a weight-average molecular weight of 8.6 x 10 was calcu l a t e d . This molecular weight indicated the presence of 314 repeating units with monomeric molecular weight, 272, of the i d e a l i z e d structure of HEC with molar s u b s t i t u t i o n 2.5 (Figure 2). Using membrane osmometry, Powell et al.((1966) determined the 4 o number-average molecular weight of HEC to be 4.73 x 10 (25 C, Natrosol 250G). Although these authors maintained a good c o r r e l a t i o n existed between the molecular weight averages derived from v i s c o s i t y and osmotic pressure techniques, they neglected to present a corresponding viscosity-molecular weight value. According to the manufacturer (Hercules Inc.), the approximate 4 molecular weight i s 8.0 x 10 (Powell et a l . , 1966) which i s i n agreement with the Mw r e s u l t obtained i n the present study. The lower than expected,.-Mn of Powell e_t a l . (1966) i s probably a r e s u l t of the permeation of low Table I Sedimentation v e l o c i t y data f or a 0.25% w/w HEC dispersion Time (min.) Peak Height (cm) Magnification Factor Measurement (cm) 90 5.65 17.20 150 7.35 17.15 180 8.30 17.21 211 9.13 17.25 270 10.85 17.15 Svedberg Constant, s , = 1.81 x 10 s 18 Table II Synthetic boundary data f o r a 0.25% w/w HEC dispersion Time (min.) Peak Area (cm ) Peak Height (cm) Magnification Factor Measurement (cm) 10 8.65 6.75 22.6 20 8.75 6.30 22.6 30 8.69 5.75 . 22.3 40. 8.28 5.55 22.5 50 8.56 5.20 22.2 60 8.51 4.90 22.5 89 8.52 4.40 22.3 120 8.94 4.06 22.2 150 8.35 1 3.65 22.6 180 9.33 3T65 22.5 D , = 1.88 x 10~ 7 cm2/s obs 19 molecular weight materials through the osmometer membrane because the HEC polymer was used as received from the manufacturer. Mn cannot be determined accurately using unpurified polymers containing reaction products because p r e c i s i o n measurements of osmotic pressure are only possible with samples from which a l l substances which show membrane permeability have been removed (Vink, 1971). The moisture content was found to be 6 ± 1% w/w when checked p e r i o d i c a l l y over a 3 year period using a moisture balance. This r e s u l t for moisture content i s i n agreement with the 6% by weight estimate of the manufacturer for the equilibrium moisture content i f the powder was kept at 50% r e l a t i v e humidity, 73°F (Hercules Inc., 1969). 2. Density- and Apparent Molar Volume-Temperature Relationships f o r  Aqueous Dispersions The values for density with respect to changing temperature are presented i n Table III for the HEC dispersions. A r e l a t i v e l y constant _3 increase i n density of 0.0027 g cm (± 0.0001 CL__a.) was noticeable f or each 1.0% w/w increase i n HEC concentration over the 15-40°C temperature range. The addition of the f i r s t 1.0% w/w HEC to water resulted i n an _3 i n i t i a l density change of 0.0032 g cm (± 0.0002 CL Q_„) at each test temperature.-Equation (10) describes the r e l a t i o n s h i p between temperature (°K) and the density of the HEC dispersions and water over the temperature range examined (Figure 4). d = A e " B T (10) Table I I I Density and apparent molar volume of aqueous HEC dispersions' at 15, 20, 30, 35 and 40°C Temperature HEC Density (± C L 9 5 % ) n v (104) app (°C ± 0.2) • (%w/w) (g/ml) (cm mole ) 15.0 0.0 0.99913 1.0 1.0023 0.0001 6 6.08 2.0 1.0052 0.0002, 8 5.98 3.0 1.0079 0.0000 -7 5.85 20.0 0.0 0.99823 1.0 1.0014 0.. 0003 6 6.09 2.0 1.0042 0.0001 8 6.03 3.0 1.0070 0.0001 7 5.86 30.0 0.0 0.99573 1.0 0.9990 0.0002 6 6.15 2.0 1.0016 0.0002 7 6.09 3.0 1.0044 0.0001 6 5.79 35.0 0.0 0.9941a 1.0 0.9975 0.0004 6 6.16 2.0 0.9999 0.0001 8 6.12 3.0 1.0027 0.0001 7 5.67 40.0 0.0 0,9922a 1.0 0.9953 0.0001 4 6.16 2.0 0.9981 0.0001 6 6.12 3.0 ' 1.0009 0.0001 6 5.98 a ( K e l l , 1967) 21 315 320 325 330 335 TEMPERATURE ( ° K ) FIGURE 4. Density-temperature relationship for aqueous HEC dispersions 22 -3 In this relationship, .A was required to have units of g cm and J3, units of deg \ An excellent f i t of the equation to the data was found (Table IV). The tabular values for 3i were numerically similar to the -4 -1 coefficient of expansion for water at room temperature (3 x 10 deg , Bauer and Lewin, 1959). Why the thermal expansion coefficient, which is a function of temperature i t s e l f , can be described by a simple exponential equation Is not clear at this time. The apparent correspond-ence between jB and the thermal expansion coefficient for water may have been the result of the narrow temperature range (15-40°C) and the low polymer concentration used in this experiment. The apparent molar volume of the HEC dispersions was calculated from (9) (Table III). At each temperature, the apparent molar volume decreased as the HEC concentration increased over the 15-40°C range. The v appeared to increase with increased temperature for only the 1 and aPP 2% w/w HEC dispersions. The fluctuations in v with respect to increasing aPP temperature noticed for the 3% HEC dispersion may have occurred because the density difference, (d^-d^), in Equation (9) could not be determined with sufficient accuracy using the experimental method. Using the method outlined by Yalkowsky and Zografii (1972), which was based on the early work of Traube published in 1899 and the later work of Mukerjee (1961), the partial molal volume of HEC was calculated to 4 3 - 1 be 10.3 x 10 cm mole . The partial molal volume (V) and the apparent molar volume (v ) were of the same order of magnitude. The partial molal app Table IV —BT Density-temperature r e l a t i o n s h i p , d = A e , f o r aqueous HEC d i s p e r s i o n s HEC Concentration A B , r (% w/w) (g cm" 3) (deg',' 10>4) 0.0 1.09 2.7 0.986 1.0 1.09 2.7 • 0.978 2.0 1-.10 2.8 0.990 3.0 1.10 2.8 0.988 24 volume was numerically larger as predicted by V = (ID where n*_ and n Q represent the number of moles of solute and solvent r e s p e c t i v e l y . According to theory, v should converge with V at i n f i n i t e d i l u t i o n (Bauer and Lewin, 1959), B. POLYOXYETHYLENE CA) DODECYL ETHER, 25 INTRODUCTION Polyoxyethylene (4) dodecyl ether ( B r i j 30) may be represented by the chemical formula, C H 3 ( C H 2 ) U 0 (CH 2 C H 2 0 ) 4 H, wi th formula molecular weight , 362.55. The a c t u a l surfac tant may conta in a mixture of repeat ing ether l inkages and unreacted a l c o h o l . Polyoxyethylene a l c o h o l s are prepared commercially by the base-ca ta lyzed a d d i t i o n of ethylene oxide to a l c o h o l (Satkowski e_t a l . , 1967; Equation 12 ) . ROH + n H-C CGH. * RO (CH. CH. 0) H (12) 0 For commercial purposes, the primary a l c o h o l s are prepared from n a t u r a l sources by the reduct ion of f a t t y esters with an a l c o h o l and an a l k a l i metal or from synthet ic sources by the Oxo and Z i e g l e r processes (Satkowski e_t a l . , 1967). A mixture of a l c o h o l s r e s u l t s from e i t h e r source. Although nonionic surfac tants are recognized to be heterogeneous systems (Schick, 1967), s e v e r a l workers have used estimates of molecular weight to i n d i c a t e surfac tant p o l y d i s p e r s i t y (Rhodes, 1967; Bloor et a l . , 1970). K a l i s h e_t a l . (1972) have used gas chromatography to demonstrate the complexity of a quaternary ammonium polyoxypropylene a l c o h o l surfac tant and nuclear magnetic resonance to i d e n t i f y 3 of the 24 peaks of the aminopolyether acetate d e r i v a t i v e . Gas chromatographic a n a l y s i s of nonionic 26 surfactants following acid cleavage of ether linkages has been done by T s u j i and Konishi (1974). These authors i n i t i a l l y removed the numerous ethylene oxide component peaks of several polyoxyethylene a l k y l ethers, polyoxyethylene a l k y l phenol ethers, polyoxyethylene a l k y l amines and polyoxyethylene a l k y l thioethers p r i o r to gas chromatography. The chromatography conditions chosen d i d not give good r e s o l u t i o n of the higher b o i l i n g components. Faveretto et al. (1972) have proposed t h i n -layer chromatography followed by spot densitometry for the determination of nonionic polyoxyethylene surfactants i n polluted water. A r i s i n g i n t e r e s t has been taken i n s t r a i g h t chain polyoxyethy-lene alcohol surfactants because of t h e i r favourable biodegradable properties (Satkowski e_t a l . , 1967) but problems s t i l l e x i s t .in the methods for component an a l y s i s . A gas chromatograph - mass spectrometer has been used i n the present study to separate and i d e n t i f y the major components of B r i j 30. The conventional number-average molecular weight and c r i t i c a l m i c e l l e concentration were determined also for comparative purposes. EXPERIMENTAL 1. Surfactant Selection To devise a system with increased r h e o l o g i c a l f l e x i b i l i t y , a number of nonionic surfactants were screened f o r t h e i r a b i l i t y to thicken HEC dispersions. Surfactants were added to a 2% w/w HEC dispersion i n volume r a t i o s of 1:4, 1:3, 1:2 or 1:1 and combined. The nonionic surfactants 27 which were i n s o l i d form were melted p r i o r to addition. The r e s u l t s of the combinations were evaluated su b j e c t i v e l y , immediately and a f t e r 2 and 7 days (Table V). 2. Molecular Weight, C r i t i c a l M i c e l l e Concentration and Infrared  Spectrum The number-average molecular weight was determined using non-aqueous vapour pressure osmometry (Hewlett Packard, 1968). The osmometer was c a l i b r a t e d at 37.00 ±. 0.01°C using a seri e s of b e n z i l solutions (2.112, 4.223, 8.445 and 16.890 g/1 i n benzene). The c a l i b r a t i o n f a c t o r , K, was obtained as the least squares intercept of b e n z i l at zero concen-t r a t i o n from the r e l a t i o n s h i p % = aC + K (13) where V_ i s the average bridge output measured i n m i l l i v o l t s , C_, the concentration (g/1) and a i s the slope. The l e a s t squares f i t of the average bridge output per concentration of the B r i j 30 solutions (4.857, 9.713, 19.425 and 38.850 g/1 i n benzene) was extrapolated to zero concentration and the molecular weight, MW, was calculated from (14) A molecular weight was estimated also from the integrated nuclear magnetic resonance spectrum of Brij,30 i n CD C l ^ (Figure 8). Dir e c t probe mass spectrometry at two probe temperatures (68 and 120°C) was used to examine B r i j 30 for the presence of components 28 with a higher degree of ether s u b s t i t u t i o n than represented by the manufacturer 's formula. The i n f r a r e d spectrum of B r i j 30 was obtained using a t h i n l i q u i d f i l m technique (Figure 9) (Coutts , 1969). i The c r i t i c a l m i c e l l e concentrat ion (cmc) of B r i j 30 was d e t e r -mined using surface tension measurements. A s e r i e s of aqueous B r i j 30 s o l u t i o n s were made (0.4, 0.2, 0.04, 0.02, : 0.004, ,.0v002 and 0.001% w/w) and the surface tension measured using the Wilhelmy p l a t e method at "22 ± 1°C (Federal P a c i f i c E l e c t r i c Co.. , 1968). F i v e determinations were made. The cmc was c a l c u l a t e d from the i n t e r s e c t i o n of the two p o r t i o n s of the surface tension versus B r i j 30 concentrat ion (% w/w) graph (Figure 10). 3. Component A n a l y s i s B r i j 30 (10 y g / p l i n absolute methanol) was gas chromatographed i n the temperature programming mode ( T i = 1 1 0 ° C , Tf = 2 5 0 ° C , d T / d t = 6 ° C / m i n , Separator Temperature = 2 7 5 ° C , I n l e t Temperature = 2 6 0 ° C ) and mass spectra were recorded (Scan = 500 mass u n i t s at 50 mass u n i t s / s , chart speed = 4.8 i n / s ) f o r the p r i n c i p a l components. Since temperature program-ming was used and a d e f i n i t e drop i n gas flow rate was d i s c e r n e d , the gas flow was measured at convenient i n t e r v a l s during each sample r u n . A p l o t of gas flow rate versus temperature revealed a l i n e a r r e l a t i o n s h i p over the temperature i n t e r v a l used (Figure 5) , By not ing the temperatures at which the major peaks were e l u t e d , the correc t flow rate f o r that temperature . could be obtained g r a p h i c a l l y . These values were then used to c a l c u l a t e the r e t e n t i o n volume (V^) f o r the major peaks from' 29 18 100 120 1 4 0 1 6 0 180 T E M P E R A T U R E ( ° C ) 2 0 0 2 2 0 2 4 0 FIGURE 5. T y p i c a l change i n c a r r i e r gas flow rate for B r i j 30 chromatographed i n the temperature programming mode 30 = F t (15) r c r where F c i s the temperature-corrected flow rate (ml/min) and t ^ i s the r e t e n t i o n time (min) determined from the leading edge of the solvent peak (Table V I I ) . Peak,: r e s o l u t i o n , R. „, was determined from 2 ( t r 2 - ^ R, , = r-.l . „ (16) '1,2 1.669 \ l \ J Wb2\ 2 i h l / \ h where t ^ and t ^ a r e t n e r e t e n t i o n times f o r peaks 1 and 2 r e s p e c t i v e l y , and W, . and W, _ are the widths of the respective peaks at h a l f - h e i g h t s b l bz h± and h 2 (Schupp, 1968). To remove the p o s s i b i l i t y that the numerous peaks present i n the spectrum were due to impurities or thermal degradation products, a s o l u t i o n of B r i j 30 SP (10 u/ul i n absolute methanol) and a sample of b o i l e d (200°C) t e c h n i c a l B r i j 30 (10 yg/yl i n absolute methanol) were chromatographed under i d e n t i c a l conditions and examined for d i f f e r e n c e s i n the number of peaks. In order to i d e n t i f y the dodecanol contaminant proposed previously (Nakagawa et a l . , 1961), a s o l u t i o n of a homologous s e r i e s of alcohols (octanol, decanol, dodecanol, tetradecanol, hexadecanol and octadecanol, each present at approximately 1.0 yg/yl i n absolute methanol Appendix I) was gas chromatographed i n the temperature programming mode under conditions i d e n t i c a l to those used f o r "Brij 30. The gas flow rates were measured at appropriate i n t e r v a l s while each sample was run. The temperatures at which the alcohol peaks eluted were used to obtain the respective flow rates (Figure 6) for retention volume c a l c u l a t i o n s . The s o l u t i o n of homologous alcohols and the B r i j 30 s o l u t i o n i n 3 separate volume r a t i o s (1:2, 1:3, 1:4 alcohol s o l u t i o n : B r i j 30 solution) were combined, chromatographed and examined for a s i n g l e symmetrical peak at the predicted dodecanol retention time. The retention times and volumes were calculated for the major peaks of the combined surfactant - alcohol series sample (Table V I I I ) . The percent of dodecanol contamination of the surfactant was also estimated. Dodecanol (1.0 yg/yl i n absolute methanol) was chromatographed i n the temperature programming mode under the conditions used for B r i j 30, the mass spectrum traced and compared to the mass spectrum of the predicted C-12 alcohol contaminant of B r i j 30. A mass spectrum was recorded for each of the major gas chromatograph peaks of B r i j 30. Molecular formulas were proposed and fragment maps developed f o r each of the major components. RESULTS AND DISCUSSION 1. Surfactant Selection B r i j 30 was selected from among ten nonionic surfactants found to s y n e r g i s t i c a l l y increase the apparent v i s c o s i t y of a 2.0% w/w HEC dispersion and which therefore were r e l a t i v e l y stable (Table V). This surfactant was chosen because i t had the lowest degree of ethylene oxide polymerization thereby f a c i l i t a t i n g component i d e n t i f i c a t i o n with gas l i q u i d chromatography - mass spectrometry. Atlas Chemical Industries Inc. (1965) has indicated several of t h e i r nonionic surfactants exhibit a t y p i c a l thickening behaviour on 32 FIGURE 6. Ty p i c a l change i n c a r r i e r gas flow rate for the s o l u t i o n of homologous alcohols chromatographed i n the temperature programming mode Table V The subjective v i s c o s i t y and s t a b i l i t y of nonionic surfactants i n combination with a 2% w/w HEC dispersion 3. b C ' Surfactant Composition HLB State Volume V i s c o s i t y S t a b i l i t y Ratio Arlatone T e Polyoxyethylene p o l y o l f a t t y acid ester 9.0 L 1:2 I Y B r i j 30f polyoxyethylene (4), dodecyl ether 9.7 L 1:4 I Y B r i j 76f POE (10) s t e a r y l ether 12.4 S 1:4 I Y B r i j 58f POE (20) c e t y l ether 15.7 S 1:3 I Gel B r i j 96f POE (10) o l e y l ether 12.4 L 1:3 I Y Atlas G-1086f POE s o r b i t o l hexaoleate 10 i 2 L 1:3 I Y Myrj 458 POE (8) monostearate l l j l U 1:3 I Gel. Renex 36^  POE (6) t r i d e c y l ether T l : 4 L 1:3 I Y Tween 65^ ; POE sorbitan t r i s t e a r a t e 10:5 S 1:3 I . ..Solid Tween 858 POE (20) sorbitan t r i -oleate m o L 1:3 I Y A r l a c e l 60^  sorbitan monostearate 4.7 S 1:3 s N S C Y A r l a c e l 83f sorbitan sesquioleate 3.7 L • .1:3 NSC Y Continued Table V contd. A r l a c e l sorbitan sesquioleate 3.7 L 1:3 NSC Y Brij. 72 f POE (2) s t e a r y l ether 4.9 S 1:3 NSC Y B r i j 92 f POE (2) o l e y l ether 4.9 L 1:3 NSC . N Atlas G-1425f POE s o r b i t o l l a n o l i n d e r i v a t i v e 8.0 U 1:3 NSC Y Atlas G-17348 POE s o r b i t o l beeswax d e r i v a t i v e 9.0 S 1:2 NSC Y Renex 20 f POE esters of mixed f a t t y and r e s i n acids 13.8 L 1:3 NSC N Renex 30 f POE (12) t r i d e c y l ether 14.5 L 1:3 NSC N Span 80 f sorbitan monooleate 4.3 L 1:3 NSC N Tween 60 e POE sorbitan monostearate 14.9 U 1:3 NSC N Tween 80 e POE sorbitan monooleate 15.0 L 1:4 NSC N A r l a c e l 20 f sorbitan monolaurate 8.6 L 1:2 D N A r l a c e l 85 f sorbitan t r i o l e a t e 1.8 L 1:3 D N Atmos 300 f mono- & d i g l y c e r i d e s of fat-forming f a t t y acids 2.8 L 1:2 D N Atmul 84 f mono- & di g l y c e r i d e s from the g l y c e r o l y s i s of edible f a t s 2.8 S 1:3 D N B r i j 35 e POE (23) dodecyl ether 16.9 S 1:3 D N Continued Table V ccmtd. B r i j 52 f POE (2) c e t y l ether 5.3 S 1:3 D N. B r i j 56 f POE (10) c e t y l ether 12.9 S 1:4 D N -B r i j 92 f POE (2) o l e y l ether 4.9 L 1:3 D N At l a s G-1441 6 POE (40) s o r b i t o l l a n o l i n d e r i v a t i v e 14.0 U 1:2 D N At l a s G-14716 POE (75) s o r b i t o l l a n o l i n d e r i v a t i v e 16.0 U 1:3 D Y Atla s G-21626 POE oxypropylene monostearate 16.0 s 1:3 D Y Atla s G-2859f POE s o r b i t o l -4, 5-oleate 3.7 L 1:3 D N Myrj 52S 6 POE (40) stearate 16.9 S 1:3 D N Myrj 53 e POE (50) stearate 17.9 S 1:3 D N Span 85 f, sorbitan t r i o l e a t e l i s L 1:3 D N Tween 20 S POE sorbitan monolaurate 16.7 L 1:3 D Y Tween 40 e POE (20) sorbitan mono-palmitate 15.6 L 1:5 D N Tween 61 e POE (4) sorbitan monostearate 9.6 S 1:3 D Y Continued Table V contd. i \ L = l i q u i d , S = s o l i d , U = unctuous k volume of surfactant :volume of 2% w/w HEC c I = i n c r e a s e , NSC = no s i g n i f i c a n t change, D = decrease ^ a f t e r 7 days, Y = yes , N = no A t l a s Chemical I n d u s t r i e s , 1967b f G r i f f i n , 1965 8 Schick , 1967 OJ ON . 37 d i l u t i o n wi th aqueous media. Only one of the agents contained i n Table V, B r i j 58, i s inc luded i n the A t l a s l i s t . The remainder of the surface a c t i v e agents l i s t e d by A t l a s d i d not show appreciable t h i c k e n i n g p r o p e r t i e s i n the present study, probably because a 30-50% lower concen-t r a t i o n of the agent was used. The a d d i t i o n o fHEC, and p o s s i b l y other c e l l u l o s e polymers, to the aqueous v e h i c l e s used f o r d i l u t i o n has the p o t e n t i a l f o r a s y n e r g i s t i c increase i n v i s c o s i t y wi th lower surfac tant concentra t ion . HEC a d d i t i o n to d i l u t i n g s o l u t i o n s has a p o t e n t i a l t h r e e - f o l d advantage: a) • expansion of the number of n o n - i r r i t a t i n g surfac tants (Atlas . Chemical Indust r ies I n c . , 1967a) which may be used f o r t w i n - b o t t l e f o r m u l a t i o n s , v i z . , h a i r dyes , b) , reduced incidence of s k i n i r r i t a t i o n because a s i g n i f i c a n t l y lower concentrat ion of the surfac tant i s necessary, and c) reduced manufacturing c o s t s . 2. C h a r a c t e r i z a t i o n Data f o r Polyoxyethylene (4) Dodecyl Ether Using common l i n e a r r e g r e s s i o n methods, a number-average molecular weight , Mn = 380, was obtained f o r the surfac tant d i s s o l v e d i n benzene using non-aqueous vapour pressure osmometry and a b e n z i l standard (Table VI and Figure 7 ) . Considering the f l a t n e s s of the l i n e and the magnitude of the c o e f f i c i e n t s on the y - a x i s a c o e f f i c i e n t of determination of 0.8533 represented a good f i t . Because vapour pressure osmometry i s a measurement of c o l l i g a t i v e p r o p e r t i e s and deviates from the t h e o r e t i c a l to the same extent as the s o l u t i o n behaviour departs from the i d e a l , a molecular weight was estimated a lso with nuclear magnetic 38* Table VI Vapour pressure osmometer data for B r i j 30 and b e n z i l standard dissolved i n benzene Benzil B r i j 30 Concentration Average Bridge* 5 Concentration c • • Average Bridge Output Output (g/D. . (mV) (g/D (mV) 2.112 179.5C 4,857 . 229.5 4.223 345.0 9.713 430.0 8.445 6 7 4 . 5 ° 19.425 831.5 16.890 ; i30i .o 38.850 1586.0 Linear regression r e s u l t s : B e n z i l , slope = -0.483, intercept = 84.72, r 2 = 0.8964; B r i j 30, slope = -0.166, intercept = 46.82, r 2 = 0.8533. number of r e p l i c a t e s = 4 number of r e p l i c a t e s = 3 5 2 o ^ UJ "j= Q Q£ CQ 30 10 1 5 20 25 30 C O N C E N T R A T I O N ( g - I " 1 ) 35 4 0 FIGURE 7. Extrapolation of the vapour pressure osmometer data to zero concentration for the number-average molecular weight determination of B r i j 30 AO 40 resonance. The integrated nuclear magnetic resonance spectrum yi e l d e d 383 for the molecular weight (Figure 8) which was i n excellent agreement with the c o l l i g a t i v e properties r e s u l t . Because the molecular weight estimate for the surfactant was greater than the formula molecular weight, the presence of polyethers with a higher degree of s u b s t i t u t i o n than indicated by the manufacturer's formula was suspected. Di r e c t probe mass spectrometry was used to explore t h i s p o s s i b i l i t y and consequent examination of the spectra revealed the presence of a strong peak at 407 which was.the P + 1 peak fo r polyoxyethylene (5) dodecyl ether, CH 3 ( C H 2 ) 1 Q CH 2 0(CH 2 CH 2 0> 5 H, and a smaller P + 1 peak at 451, CH 3 ( C H 2 ) 1 Q CH 2 0(CH 2 CH 2 0) g H, polyoxyethylene (6) dodecyl ether. This p a i r of peaks represented a degree of ether s u b s t i t u t i o n of +1 and +2 higher than the manufacturer's formula f o r B r i j 30, CH 3 (CH 2) 1 ( J CH 2 0(CH 2 CH 2 0 ) 4 H. The i n f r a r e d spectrum of B r i j 30 (Figure 9) revealed represent-ati v e bands f o r a l c o h o l i c stretching at 3450 cm ^ (Shriner et a l . , 1956), asymmetrical stretching (v CH„) of methylene groups of saturated hydro-carbons at 2925 cm - 1, symmetrical stretching (v CH.) of methylene groups of saturated hydrocarbons at 2850 cm \ and asymmetrical C-0-C stretching of ethers at 1120 cm A smaller peak for a methylene s c i s s o r i n g band (6 CH_) occurred at the c h a r a c t e r i s t i c 1465 cm p o s i t i o n . Methylene 41 1 L_ 300 200 100 F R E Q U E N C Y ( Hz ) FIGURE 8. Nuclear magnetic resonance spectrum of B r i j 30 i n CD C l at 31°C. Sweep width, 1000 Hz; sweep time, 250 sec; frequency response, 20 Hz. wagging and twisting v i b r a t i o n peaks at 1300 and 1250 cm were t y p i c a l l y smaller than the s c i s s o r i n g band at 1465 cm \ The methylene rocking v i b r a t i o n (p CH.^) band i n which a l l of the methylene groups rock i n phase appeared at 725 cm \ The p o s i t i o n of t h i s i n phase rocking v i b r a t i o n i s c h a r a c t e r i s t i c f or s t r a i g h t chain hydrocarbons of seven or more carbon atoms ( S i l v e r s t e i n and Bassler, 1967). The i n f r a r e d bands of Brij'30 were i d e n t i c a l to those for polyoxyethylene (5) dodecyl ether synthesized and examined by Hummel (1962). This s i m i l a r i t y arose because the only d i f f e r e n c e between the compounds,was the degree of polymerization. -4 A c r i t i c a l m i c e l l e concentration of 1.42 x 10 moles/1 (22 ± 1°C) (Mn¥= 380) was calculated f o r B r i j 30 (Figure 10). The cmc has been determined on the unpurified surfactant i n t h i s study merely as an i d e n t i f i c a t i o n parameter for future work. The r e s u l t i s predictably _4 higher than the commonly reported l i t e r a t u r e value, 0.40 x 10 moles/1 (25°C) (Mukerjee and Mysels,'1971)' which was obtained using molecularly-d i s t i l l e d ethylene oxide condensates (Schick, 1962), , 3. Polymerization Products I d e n t i f i e d A complex pattern of peaks t y p i c a l of polyether surfactants (Kalish et a l . , 1972) was obtained from the gas chromatogram of B r i j 30 but a d e f i n i t e r e p e t i t i v e nature i n the peak patterns was noticeable (Figure 11). With increasing retention time, each set of peaks may r e f l e c t ari increment i n the number of ethylene oxide u n i t s . The retention times and volumes for the major peaks of B r i j 30 are given i n Table VII. FIGURE 10. Relationship of surface tension to concentration of B r i j 30 i n d i s t i l l e d water at 22 ± 1°C -p-46 Table VII Retention time, retention volume and degree of r e s o l u t i o n f o r the major components of B r i j 30 Peak Program Temperature ; (°c) t . r (min.) V r (cm ) R l , 2 A 146 5.5 130.2 -B 165 8.9 199.3 24. C 169 9.6 211.8 D 191 13.0 271,5 18/ E 196 14.1 289.1 F 215 17.1 333,1 6. G 220 17.9 344.4 H 237 20.6 379.5 3. I 243 21.5 388.6 47 The degree of r e s o l u t i o n , (16), i s presented also f o r successive peaks. Resolution of the successive major peaks was good using temperature programming with a 3% SE 30 on Varaport 80/100 mesh 6 f t . x 2 mm i . d . s t a i n l e s s s t e e l column (Table VII). A commercially a v a i l a b l e better grade of B r i j 30 y i e l d e d the same number of major peaks when gas chromatographed under i d e n t i c a l conditions (10 yg/yl i n absolute methanol, T = 110°C, T f = 250°C, dT/dt = 6°C/min.). The only d i f f e r e n c e between the spectra was the absence of three small peaks indicated by the ' ^ ' i n Figure 11. The presence or absence of the second and t h i r d peaks was inconclusive with respect to the better grade of B r i j 30 because of the t a i l i n g and poor r e s o l u t i o n of these small peaks i n both spectra. There was no d i f f e r e n c e i n the number of peaks or the r e l a t i v e peak sizes when the spectra f o r the heated and non-heated samples of t e c h n i c a l B r i j 30 (10 yg/yl i n absolute methanol) were compared. The retention times and volumes f o r the s o l u t i o n of a homologous series of s t r a i g h t chain alcohols which was gas chromatographed under conditions i d e n t i c a l to those used for B r i j 30 are given i n Table VIII (Figure 12). This s o l u t i o n when combined with the t e c h n i c a l B r i j 30 s o l u t i o n i n three separate volume r a t i o s (1:2, 1:3, 1:4, alcohol s o l u t i o n : B r i j 30 solution) and chromatographed yielded a s i n g l e intense symmetrical peak for the dodecanol portion of the s o l u t i o n of alcohols and peak A of B r i j 30 (Figure 13). For comparison, the r e t e n t i o n times and volumes f o r the t e c h n i c a l B r i j 30 s o l u t i o n , the s o l u t i o n of the s e r i e s of homologous alcohols and the B r i j 30 - alcohol series combination are shown i n Table VIII Retention times and volumes f o r B r i j 30, the homologous series of alcohols and the B r i j 30 -alcohol series combination Peak PrP'Sdgram Temperature. (°C) a b B r i j 30 (I) Homologous Alcohols (II) t V r r (min.) C 3N (mm.) (cm ) r (min.) V r (cm3) Combination (I) + (II) r (min.) V r (cm ) Octanol 117 - - 1.0 26.8 ' 1.1 28.0 Decanol 122 - - 2.7 68.3 2.8 68.3 Dodecanol + 146 • 5.5 130.2 5.5 129.9 5.6 128.8 A - B r i j 30 165' Tetradecanol + 165 8.9 199.3 9.0 197.4 9.0 193.7 B - B r i j 30 159 C - B r i j 30 ,169 9.6 211.8 - - 204.9 Hexadecanol 186 s- - 12.4 254.6 12.5 . 250.0 D - B r i j 30. 191 13.0 271.5 - - - _d E - B r i j 30 196 14.1 289.1 - - . 14.2 275.3 Octadecanol 207 - - 15.5 298.3 15.6" 294.3 a Figure 11 b Figure 12 Figure 13 ^ poor peak r e s o l u t i o n prevents accurate ; retention time determination (Figure 12) 49 O c t a n o l D e c a n o l D o d e c a n o l T e t r a d e c a n o l . H e x a d e c a n o l O c t a d e c a n o l TIME FIGURE 12. Temperature programmed gas chromatogram of the homologous s e r i e s of a l c o h o l s . T = 1 1 0 ° C , T f = 2 2 0 ° C , d T / d t = 6°C/min 1X1 t o Z o Q_ CO uu O c ta n o I D o d e c a n o l + B r i j 3 0 P e a k A De c a n oI T e t r a d e c a n o l + B r i j 3 0 P e a k B H e x a d e c a n o l T I M E FIGURE 13. Temperature programmed gas chromatogram of a 1:3 volume r a t i o of the homologous alcohols solution and B r i j 30. T = 110°C, T^ = 250°C, dT/dt = 6°C/min U l o Table VIII. The retention times and volumes for the dodecanol f r a c t i o n of the homologous alcohol se r i e s and peak A of B r i j 30 s o l u t i o n were i n good agreement and r e l i a b l y indicated that peak A of B r i j 30 was dodecanol. Peak A of the surfactant was estimated to represent,a 6% w/w dodecanol contamination. When gas l i q u i d chromatography was a r e l a t i v e l y new technique, Nakagawa e_t a l . (1961) found an 8.9% concentration of dodecanol contaminant i n B r i j 30. The isothermal conditions and column chosen by these authors resulted i n a poorly resolved peak, therefore, the 6% w/w value obtained i n the present study i s probably a better estimate of the dodecanol content. The mass spectrum of component peak A of B r i j 30 (Figure 11) was i d e n t i c a l i n fragment pattern and peak r a t i o s to the spectrum for dodecanol, the suspected contaminant (Figure 14). Because dodecanol was a long chain alcohol (C > 6), the parent peak, P = 186, was.character-i s t i c a l l y absent from the spectrum and the cleavage pattern resembled that of thec'corresponding o l e f i n having c l u s t e r s of peaks at i n t e r v a l s of 14 mass u n i t s . In these c l u s t e r s , the C n (97, 83, 69, 55) and the C n H 2 n (140, 126, 112, 98, 84, 70, 56) peaks were more intense than the C n H 2 n + 1 peaks (141, 127, 113, 99, 85, 71, 57). A s i m p l i f i e d mass sp e c t r a l fragment pattern f or peak A of B r i j 30 and dodecanol i s shown i n Fragment Map 1. The mass spectrum of B r i j 30 peak C (Figures 11 and 15) was dominated by the r e p e t i t i v e l o s s of methylene groups. The ^ n + l P e a^ s were intense at m/e, 141 and 169, which revealed the presence of the 52 100-. 75J 501 tO Z 25J i i D O D E C A N O L I i 100_ 30 50 70 90 110 130 150 170 75J — 50_ to Z LU 2 5 J BR IJ 3 0 — PEAK A 30 50 70 90 110 MASS UNITS 130 150 170 FIGURE 14. Mass spectra of dodecariol and Brij 30 ~ peak A Mass Spectral Fragment Map 1 Principal fragments of Brij 30 - peak A and dodecanol CH3 ( C H 2 ) n OH M = 186 parent not discernible -H20 CH3 (CH 2) 1 0 C H 2| + CH3 (CH2)g CH2] + CH3 (CH 2) 7 CH2"j + CH3 (CH 2) 6 CH^ + CH3 (CH 2) 4 GH = CH2 :1 CH3 (CH 2) 3 CH = CH2 + + m/e - 169 m/e = 140 m/e = 126 m/e = 112 m/e = 97 m/e = 83 fragments showing successive losses of CH2 100 75L CO UJ 50[ 25 L 80 100 120 M A S S UNITS "III, '(II —' r 180 ~n r 200 20 40 T — 60 140 160 FIGURE 15. Mass.spectrum of Brij 30 - peak C Cn 55 complete CH 3 ( C H 2 ) 1 Q C H 2 ] + fragment i n t h i s component. Evidence for the presence of oxygen containing fragments was obtained from the peak, m/e = 199, which represented CH 3 ( C H 2 ) n 0 C H 2 1 " + and the peak at m/e = 75, ••• [CH 2 0 CH 2 CH 2 OH, The combined B r i j 30 - alcohol se r i e s chromatogram (Figure 13) indicated that the molecular weight of t h i s component should be between 214 (tetradecanol) and 242 (hexadecanol) therefore, the p l a u s i b l e parent for B r i j 30 - C was CH 3 ( C H 2 ) 1 1 .0 (CH 2 CH 2 ,0) 1 H, polyoxyethylene (1) dodecyl ether with molecular weight, 230. The mass sp e c t r a l fragment pattern for t h i s component i s presented i n Map 2. The mass spectrum of B r i j 30 - peak E (Figures 11 and 16) showed the same r e p e t i t i v e loss of methylene groups as appeared with peak - C. Because the spectrum for component E i s very complex, the methylene cleavage pattern has been omitted from Figure 16 so as to c l a r i f y the more i n t e r e s t i n g oxygen-containing fragments. Similar peaks for oxygen-containing fragments were present at m/e 199 and 75 as were present f o r component C. New oxygen-containing peaks were also present at m/e = 243, Mass Spectral Fragment Map 2 P r i n c i p a l fragments of B r i j 30 - peak C, polyoxyethylene (1) dodecyl ether CH 3 ( C H 2 ) 1 0 CH 2 0 CH 2 CH 2 OH M = 230 parent not d i s c e r n i b l e m/e = 199 CH 3 i ^ ^ ' l l 0 CE2}. + m/e = 169 CH 3 ( C H 2 ) 1 ( ) CH 2 1 + see Map 1 + [ C H 2 ° CH 2 CH 2 OH m/e = 75 CH 2 CH 2 OH CH 2 OH m/e = 45 m/e = 31 100 1 80 CO Z L U 60 Z 40 20 i 20 40 60 80 100 120 140 160 180 MASS UN ITS zoo 220 240 FIGURE 16. Mass spectrum of B r i j 30 - peak E 58 CH 3 (CH 2) 1 1 0 CH 2 CH2 0 CH2~| +, m/e =89, + > j~CH2 CH 2 0 CH 2 CH 2 OH, and m/e - = 119, + °'pCH2 0 CH2 CH 2 0 CH 2 CH2 OH. Peaks at m/e 45, 59, 73, 87, and 101 were i n d i c a t i v e of successive methylene cleavages from a C n H 2 n 0 fragment (Figure 16). The combined B r i j 30 - homologous alcohol se r i e s chromatogram (Figure 13) indicated that the molecular weight of t h i s component should be approximately 242 -270. Polyoxyethylene (2) dodecyl ether, CH 3 ( C H 2 ) n 0 ((GH2 CH 2 0 ) 2 H, with a molecular weight of 274 appeared to f i t the mass s p e c t r a l fragment and gas chromatographic c r i t e r i a . The mass spe c t r a l fragment pattern i s shown i n Map 3. The intense methylene cleavage pattern (G H„ . , C H„ and n 2n-l n 2n **2n+P " c h a r a c t e r i s t i c f o r fragments l i g h t e r i n mass than m/e 169, CH 3 ( C H 2 ) 1 ( ) C H 2 ] + . has been omitted from Figure 17 i n order to c l a r i f y the numerous oxygen-containing fragments of B r i j 30 - peak G (Figure 11). As noted for peak E, oxygen-containing fragments representing successive methylene fragmentations from a C H n 0 backbone were v i s i b l e also at m/e = 45, 59, 73, 87 and 101 n 2n » > » f o r t h i s component. Only one new oxygen-containing peak was apparent at m/e = 133 (Figure 17), to which the following molecular formula may be assigned, Mass Spectral Fragment Map 3 Principal fragments of Brij 30 - peak E, polyoxyethylene (2) dodecyl ether 243 m/e m/e m/e m/e = 185 m/e =169 229 199 CH3 (CH 2) n 0 CH2 CH2 0 CH^ + CH3 (CH 2) n 0 CH2 CH2 o"| + CH3 (CH 2) 1 ; L 0 (CH2 CH2 0 ) 2 H M = 274 parent not discernible — + |"cH2 (0 CH2 CH 2) 2 OH m/e - 119 - + |~CH2 CH2 0 CH2 CH2 OH m/e = 89 — + [cH2 0 CH2 CH2 OH m/e = 75 — + |*CH2 CH2 OH m/e = 45 — + |"cH2 OH m/e = 31 CH$ (CH 2) n 0 CH2"j + -CH3 (CH 2) n 0 ] + -C H 3 ( C V l O C H2 see Map 1 100 75. > co so-ul H 25-1 ~1 r 200 T r 240 20 —r— 40 1 80 80 I 1 r 100 120 i r T 1 140 160 i r 180 220 M A S S UNITS FIGURE 17. Mass spectrum of B r i j 30 - peak G. CH 3(CH 2 ) l 0 j + fragment pattern omitted ON o 61 + j"cH2 CH 2 (0 CH 2 C H 2 ) 2 OH. No new peaks with masses greater than 243 were present therefore, combining the fragment, m/e = 133, with the compatible m/e = 185 fragment revealed, polyoxyethylene (3) dodecyl ether, CH 3 ( C H 2 ) 1 1 0 (CH 2 CH 2 0 ) 3 H, with formula molecular weight, 318. The mass s p e c t r a l fragment pattern for t h i s component i s shown i n Map 4. B r i j 30 peak - I showed an increased amount of t a i l i n g (Figure 11) t h e r e f o r e / the mass spectrum may be contaminated but i f the pattern emerging i s one of increasing ether s u b s t i t u t i o n then t h i s component should have molecular formula, CH 3 ( C H 2 ) 1 1 0 (CH 2 CH 2 0 ) 4 H, M = 362. Again, because of the complexity of the spectrum, the r e p e t i t i v e methylene cleavage pattern of fragments l i g h t e r i n mass than m/e 169, CH 3 ( C H 2 ) 1 ( ) CH 2] + , has been omitted from Figure 18 for c l a r i t y . A ser i e s of new oxygen containing peaks were present at m/e =163, 177, 193, 257 and 273 (Figure 18). . The mass s p e c t r a l fragment pattern i s shown i n Map 5. Because of poor peak r e s o l u t i o n due to the upper temperature l i m i t a t i o n s of the column, the mass spectra for the gas chromatograph \ peaks which indicated the possible presence of polyoxyethylene (n) dodecyl ether s u b s t i t u t i o n s , n = 5 and 6, were not pursued further. Mass Spectral Fragment Map 4 Principal fragments of Brij 30 - peak G, polyoxyethylene (3) dodecyl ether CH3 (CH 2) 1 1 0 (CH2 CH2 0 ) 3 H • M = 318 parent not discernible m/e = 243 CH3 ( C H 2 ) n 0 CH2 CH2 0 CH 2] + -m/e = 229 CH3 ( C H 2 ) n 0 CH2 CH2 0 | + m/e = 213 CH3 (CH 2) 1 1 0 CH2 CH^ + m/e - 199 CH3 ( C H 2 ) U 0 CH2"| + m/e - 185 CH3 ( C H 2 ) n 0 ] + m/e = 169 CH3 (CH 2) 1 0 CH?"| + see Map 1 + |CH2 CH2 (0 CH2 CH 2) 2 OH m/e - 133 + .["CH2 (0 CH2 CH 2) 2 OH m/e = 119 see Map 3 100 80 _ 60 o0 Z m 40 , 20 T "' ' I 230 250 270 30 50 70 i r 1 "r 90 HO 130 M A S S 150 170 U N I T S 190 210 FIGURE 18. Mass spectrum of B r i j 30 - peak I. C H ^ C H ^ Q C H ^ + fragment pattern omitted ON OJ Mass Spectral Fragment Map 5 P r i n c i p a l fragments of B r i j 30 - peak I, polyoxyethylene (4) dodecyl ether CH 3 ^ C H2^11 ° ^ C H2 C H2 H M = 3 6 2 Parent not discernible m/e - 273 CH 3 ( C H 2 ) n (0 CH 2 CH 2) 2 o] + — see Map 4 + |"(0 CH2 CH 2) 4 OH CH 2 CH2 (0 CH2 CH 2) 3 OH + CH2 (0 CH2 CH 2) 2 OH see Map 3 m/e = 193 m/e = 177 + j"cH2 (0 CH2 CH 2) 3 OH m/e = 163 + |"CH2 CH2 (0 CH2 CH 2) 2 OH m/e = 133 m/e = 119 65 B r i j 30 peak B (Figure 11) had the same retention time and a s i m i l a r retention volume as tetradecanol (Table V I I I ) . When the combined alcohol - B r i j 30 mixture was chromatographed f o r i d e n t i f i c a t i o n of the dodecanol peak, a single symmetrical peak was obtained also for t e t r a -decanol and B r i j 30 peak B (Figure 13). Examination of the mass spectra for peak B and for tetradecanol revealed s i m i l a r i t i e s i n fragmentation of the two components (Figure 19 and Fragment Map 6). From the simi-l a r i t i e s i n retention time and volume, as w e l l as mass s p e c t r a l fragment pattern, plus a si n g l e symmetrical gas chromatographic peak being obtained for both tetradecanol and the B r i j 30 peak B, i t was concluded that the B r i j peak was composed of tetradecanol. The tetradecanol content of B r i j 30 was estimated to be 1.0% w/w. T s u j i and Konishi (1974) analyzed the hydrophobic portions of commercial samples of polyoxyethylene dodecyl ether and demonstrated the presence of C ^ Q , a n d Oxo and Z i e g l e r alcohols, They found 0 .5, 97.0 and 2.5% of the respective alcohols i n polyoxyethylene dodecyl ether a f t e r a c i d i c cleavage of the ether linkages, The numbers they quote do not separate the free alcohol contaminants from the polymerization products of these alcohols. The 1.0% w/w contamination of B r i j 30 by free tetradecanol found i n the present study i s probably therefore a good estimate.,. The mass spectrum of B r i j 30 peak D (Figure 11) c l o s e l y resembled the spectrum for peak C (Figure 15) except for the presence of' two extra peaks at m/e = 197, C H 3 1 OCH 66 Tet radecano l >_ 75 tO Z • 11 7L 50 25 A 30 50 -4 70 90 110 130 150 170 190 l O O i 7 5 H to Z 50 2 5 B r i j 3 0 Peak B J L 30 50 70 90 M A S S 110 U N I TS 130 150 170 190 FIGURE 19. Mass spectra of tetradecanol and B r i j 30 - peak B Mass S p e c t r a l Fragment Map 6 P r i n c i p a l fragments of B r i j 30 - peak B and t e t r a d e c a n o l C H 3 ( C H 2 ) 1 3 OH M = 214 parent not d i s c e r n i b l e - H 2 0 C H 3 ( C H 2 ) 1 2 C H 2 ] + m/e = 197 C H 3 ( C H 2 ) 1 Q CH 2 "| + m/e = 169 see Map 1 68 and at m/e = 227, CH 3 ( C H 2 ) 1 3 0 CH 2] + . . Another oxygen-containing fragment was present at m/e 75 and had previously been noted- f o r peak C (Figure 15). The combined B r i j 30 -homologous alcohol series chromatogram (Figure 13) indicated that the molecular weight of t h i s component should be between 242 (hexadecanol) and 270 (octadecanol) therefore, the p l a u s i b l e parent for B r i j 30 - D was CH 3 ( C H 2 ) 1 3 0 (CH 2 CH2".0)1 H, polyoxyethylene (1) tetradecyl ether with-a molecular weight of 258. The mass s p e c t r a l fragment pattern for t h i s component i s presented i n Map 7. Tetradecanol, a second alcohol contaminant, appeared to have polymerized with ethylene oxide i n a manner analagous to dodecanol because the mass spectra of B r i j 30 peaks F and H (Figure 11) through the combination of compatible fragments revealed the following p l a u s i b l e parents, CH 3 ( C H 2 ) 1 3 0 (CH 2 CH 2 0 ) 2 H, . (M = 302) polyoxyethylene (2) tetradecyl ether and, CH 3 ( C H 2 ) 1 3 0 (CH 2 CH 2 0 ) 3 H, (M = 346) polyoxyethylene (3) tetradecyl ether, r e s p e c t i v e l y . The mass sp e c t r a l fragment patterns.for these two components are shown i n Maps 8 and 9, re s p e c t i v e l y . Mass Spectral Fragment Map 7 Principal fragments of Brij 30 - peak D, polyoxyethylene (1) tetradecyl ether CH3 (CH 2) 1 2 CH2 0 CH2 CH2 OH M « 258 parent not discernible /e = 227 CH3 (CH 2> 1 3 0 CH2"| + /e = 197 CH3 (CH 2) 1 2 CH 2] + -see Map 6 + [CH2 0 CH2 CH2 OH - + \ CH2 CH2 OH CH2 OH m/e = 75 m/e = 45 m/e = 31 Mass Spectral Fragment Map 8 Principal.fragments of Brij 30 - peak F, polyoxyethylene ( 2 ) tetradecyl ether C H 3 ( C H 2 ) 1 3 0 ( C H 2 C H 2 0 ) 2 H M = 3 0 2 parent not discernible m/e - 2 7 1 C H 3 ( C H 2 > 1 3 ( 0 C H 2 C H 2 > 0 C H 2 ] + — m/e = 2 4 1 C H 3 ( C H 2 > 1 3 0 C H , , C H 2 + m/e = 2 2 7 C H 3 ( C H 2 > 1 3 0 C H J + m/e = 1 9 7 C H 3 ( C H 2 ) N C H 2 ] + see Map 6 — + | ~ C H 2 ( 0 C H 2 C H 2 ) 2 O H m/e = 1 1 9 —•- see Map 3 •^ 4 o Mass Spectral Fragment Map 9 Principal fragments of Brij,30 - peak H, polyoxyethylene (3) tetradecyl ether CH 3 ^ra2^13 ^° C H2 C H2^3 0 H M = 3 4 6 Parent not discernible m/e - 271 CH3 (CH 2> 1 3 0 CH2 CH2 0 CU^\ + -m/e « 241 CH3 (CH 2> 1 3 0 CH2 CH2"| + see Map 8 (0 CH2 CH 2) 3 OH m/e = 149 + [cH 2 CH2 (0 CH2 CH 2) 2 OH m/e = 133 — + |"CH2 (0 CH2 CH 2) 2 OH see Map 3 m/e = 119 72 In summary, B r i j 30 i s a mixture of polyoxyethylene (n) dodecyl ethers, CH 3 ( C H 2 ) n 0 (CH 2 CH 2 0 ) n H, where n = 1, 2, 3 and 4 plus dodecanol 6% w/w. I t i s predicted that the ether substitutions of n = 5 and 6 are also present. B r i j 30 also contains 1% tetradecanol and polyoxyethylene (n) t e t r a d e c y l ethers, GH 3 ( C H 2 ) 1 3 0 (CH 2 CH 2 0 ) n H, where n = 1, 2 and 3. I t i s predicted that an ether s u b s t i t u t i o n of n = 4 is. also present i n the t e t r a d e c y l s e r i e s . The polyoxyethylene- a l k y l ether surfactants are b a s i c a l l y unstable under mass spectrometric conditions, breaking immediately into 2 or more segments. Depending upon the chain length, the point of i n i t i a l cleavage may occur at one or more posit i o n s (Table IX). The cleavage of the C - C bond next to the oxygen atom with a stable P - 31 fragment, t y p i c a l of primary alcohols, occurred with polyoxyethylene (n) a l k y l ethers where n = 1 and 2. With higher degrees of ether s u b s t i t u t i o n , the P - 31 fragment was not v i s i b l e and the cleavages became character-i s t i c of monomeric a l i p h a t i c ethers, C - C bond next to an oxygen atom and C - 0 bond cleavage (Table IX; S i l v e r s t e i n and Bassler, 1967). The parent peaks were c h a r a c t e r i s t i c a l l y absent from the mass spectra of dodecanol and tetradecanol. The highest molecular weight fragment observed, corresponded to the dehydration of a P + 1 molecule. Fragments corresponding to successive CH 2 or CH 2 = CH 2 fragmentations dominated the spectra of both these alcohols (Figures 14 and 19). Table IX Some positions of i n i t i a l fragmentation of polyoxyethylene (n) dodecyl and tetradecyl ethers POEa (1) alkyl ether CH3 (CH2>x CH2 0 CH2 CH2 OH x = 10 or 12 T T t T POE (2) alkyl ether CH- (CH,) CH- 0 CH, CH- 0 CH- CH- OH T T f T T t t x - 10 or 12 . I I I I I I I POE (3) alkyl ether CH, (CH_) CH. 0 CH- CH- 0 CH- CH, 0 CH, CH OH x = 10 or 12 1 POE (4) alkyl ether CH3 (CH 2) x CH2 0 CH2 CH2 0 CH2 CH2 0 CH2 CH2 0 CH2 CH2 x = 1 0 x T t t T T T polyoxyethylene 74 In conclusion, the r e s u l t s of the present study have revealed that average molecular weight determinations f o r surfactants are of l i m i t e d value because an experimentally determined (380) which i s r e l a t i v e l y close to the t h e o r e t i c a l molecular weight (362) i s not i n d i c a t i v e of a monodisperse system. Because the commercial synthetic process, e t h e r i f i c a t i o n by reaction of alcohol and ethylene oxide (Equation (11); Satkowski et a l . , 1967), may give r i s e to many polymerization products, there i s no reason to suppose that the polyoxy-ethylene a l k y l ether surfactant i n t h i s study i s unique. The hydrophobic intermediates, obtained from- natural or synthetic sources and used commercially, are also not monodisperse (Satkowski et a l . , 1967). Therefore, i t i s suggested that m i c e l l a r thermodynamic studies involving these surfactants should be done with a m o l e c u l a r l y - d i s t i l l e d f r a c t i o n where the p u r i t y and i d e n t i t y of the component i s assured or with mixtures of known composition. Without e s t a b l i s h i n g c a l i b r a t i o n curves for the i n d i v i d u a l components, K a l i s h et a l . (1972) have proposed integrated gas chromato-graph peak areas to describe the molecular weight d i s t r i b u t i o n of the surfactant derivatives they studied. This procedure i s i n error because the response of the detector i s not a constant f o r a l l gas chromatographically v i s i b l e components but i t i s a function of the composition of each component. For t h i s reason plus the d i f f i c u l t y of i s o l a t i n g pure components, the actual molecular weight d i s t r i b u t i o n for B r i j 30 has not been pursued further. With the advent of gas l i q u i d chromatographic - mass spectro-metric methods,, i t i s t h e o r e t i c a l l y possible to i d e n t i f y the components of commercial surfactants but t h i s approach, at present, i s l i m i t e d to surfactants with a low degree of s u b s t i t u t i o n . In the present study of a polyoxyethylene (n) a l k y l ether surfactant, the upper temperature l i m i t s of SE 30 columns and the degree of r e s o l u t i o n of the large number of polymerization products of two or more alcohols presented r e s t r i c t i o n s to a complete analysis of B r i j 30. 76 SECTION I I . RHEQMETRIC STUDIES OF A MODEL SHEAR-THINNING SYSTEM Pharmaceutical l o t i o n s , t h i n creams and suspensions commonly exhibit shear-thinning flow properties therefore, a model system with a wide range of consistencies has been used to represent these f l u i d s for the rheometric studies. The three rheometers employed i n the present study were: the Haake Rotovisko (Gebruder Haake, 1969a), reputedly the most v e r s a t i l e concentric-cylinder viscometer (van Wazer et a l . , 1963); the Brookfield Synchro-lectric (Brookfield Engineering Laboratories, Inc., 1971), the most economical and widely used rheometer and the Weissenberg rheogonio-meter (Sangamo Controls Ltd., 1970), a cone-plate instrument capable of steady and dynamic shear measurements. Instrument descriptions are given by van Wazer et a l , (1963). ' A. STEADY SHEAR'STUDIES OF PRACTICAL IMPORTANCE . Many r o t a t i o n a l viscometers have been designed (van Wazer et a l . , 1963) but few of these are used widely for pharmaceutical measurements. Of these, the commonly used Qouette rheometers have not been evaluated s t a t i s t i c a l l y to show t h e i r l i m i t a t i o n s to accurately represent flow curves of shear-thinning systems over a pharmaceutically important range of consistencies. Inherent i n t h i s evaluation i s the examination of shear rate c a l c u l a t i o n methods and instrument c a l i b r a t i o n techniques. The expression of shear-thinning properties i n terms of flow model parameters and the usefulness of these parameters as .an, a i d to consistency formulation also requires attention. This section of the present study therefore attempts to examine the above aspects for a model shear-thihning system with a wide range of consistencies. For economic reasons, the r h e o l o g i c a l r e p r o d u c i b i l i t y and s t a b i l i t y of HEC dispersions have also been determined and then compared with the commonly used 2% MC dispersion. LITERATURE SURVEY 1. Shear Stress/Shear Rate Determination i n Rotational Viscometry a) Coaxial Cylinder Geometry The c o a x i a l cylinder or Couette rheometer consists of a c y l i n d r i c a l cup of radius R c and a shorter c y l i n d r i c a l spindle of. radius R^. Either the cup or the spindle may rotate (Figure 20, van Wazer et a l . , 1963; Scott B l a i r , 1969). The material to be measured i s sheared between two c y l i n d e r s , one of which i s rotated at a constant speed while the other i s attached to a t o r s i o n wire or other device for determining the torque (Scott B l a i r , 1969). When laminar flow e x i s t s or EM = 0, the shear stress (a, -2 dyne cm ) may be represented by M n 7 a = x— (1/ 2^r h where M i s the moment of the forces acting on the c y l i n d r i c a l surface with area, 2irrh, at point _r (Figure 20). If r_ i s taken at the r o t a t i n g surface Equation (17) i s v a l i d for non-Newtonian as w e l l as Newtonian f l u i d s (Krieger and Maron, 1951). B A - 0 FIGURE 20;. Laminar flow of an i n e l a s t i c f l u i d i n the gap between two concentric c y l i n d e r s . A. the outer c y l i n d e r rotates with angular v e l o c i t y ft and the inner one i s stationary. B. the inner cylinder rotates with angular velocity-yn and the outer one i s stationary (adapted from Lielmezs and Runikis, 1967) oo 79 For t h i s geometry, the d e r i v a t i o n of fundamental equations r e l a t i n g shear rate to v i s c o s i t y f o r Newtonian f l u i d s i s based on the following,seven assumptions (van Wazer e t . a l . , 1963). i . The l i q u i d i s incompressible, i i . The l i q u i d motion i s laminar. -i i i . No motion ex i s t s between the f l u i d and the c y l i n d r i c a l surfaces, i v . The l i q u i d motion i s two dimensional, v. The l i q u i d motion i s steady, v i . The system i s isothermal, v i i . , The f l u i d v e l o c i t y i s only a function of radius. Since the design of the o r i g i n a l Couette viscometer i n 1890, Newtonian flow assumptions have been used for the derivation- of shear rate equations by some manufacturers (Gebruder Haake, 1969b; Fr y k l o f , . 1961). The equations are predominantly derived from the w e l l known Margules .equation, (18) which arose from the basic r e l a t i o n between shear stress and rate of shear i n Newtonian f l u i d s , ( ^\ n V r cIr -/ ' (19) where dft/dr i s the rate of r o t a t i o n at point x_ (Reiner, 1960). In the Margules equation, _n i s the Newtonian v i s c o s i t y (poise), M, the moment of force (dyne cm), h, the cylinder length (cm), f2, the angular v e l o c i t y at the r o t a t i n g surface (rad s '"'"). Equation (18) may be separated into shear stress (17) (where r = a n ( ^ sbear rate (y, s "*"), Y = 2Q . 2 ° . (20) R c ~ \ . ; Together (17) and (20) form the f a m i l i a r Newtonian shear stress-shear rate c a l i b r a t i o n equations for c o a x i a l cylinder rheometers. The problem of developing an exact shear rate s o l u t i o n for non-Newtonian f l u i d s sheared within the .coaxial gap stems from the absence of a set r e l a t i o n s h i p between shear stress and shear rate for these f l u i d s (van Wazer et a l . , 1963). Krieger.and co-workers (Krieger and Maron, 1951, 1952 and 1954; Krieger and Elrod, 1953; Maron and 'Krieger, 1960; Krieger, 1968 and 1969) have worked repeatedly on the shear rate problem for non-Newtonian f l u i d s sheared within the gap of a c o a x i a l rheotneter. The a p p l i c a b i l i t y of t h e i r equations to inner cylinder, r o t a t i n g instruments has been shown by Lielmezs and Runikis (1967). From Mooney, i t was known that the general expression for angular v e l o c i t y , (21), could be d i f f e r e n t i a t e d to give (22) (Krieger, 1968) ffb f(a) ^2. . (21) 2 ob{ir) - fK> - ^  <2> N b The Euler-Maclaurin formula was used to expand t h i s d i f f e r e n c e equation (Krieger and Elrod, 1953). The dominant term of the f i n a l form of the resultant shear rate equation, : 81 20 R 2 / n f 2/n f l R \") . . ( 2 3 ) was i d e n t i c a l to the power-law approximation f o r shear ra te (Krieger , 1968) where n was the power-law flow behaviour index. The c o r r e c t i o n term i n (23) i s almost always w i t h i n 1% of the t r u e ' r a t e of shear (Krieger , 1969) t h e r e f o r e , shear ra te may be. calculated, us ing 2 R 2 / n Y - ~ o/° TT n (24) n R c 2 / n - R b 2 / n . according to Krieger (1968). Shear rate approximation using the f i r s t term of (23) i s v a l i d even f o r extreme cases of non-power-law f l u i d s and large radius r a t i o s (Kr ieger , 1969). In (24), the l i q u i d v e l o c i t y as a f u n c t i o n of radius i s modif ied by the flow behaviour index to account f o r the non-Newtonian character of the f l u i d . A f i n i t e bob r o t a t i n g i n a cup of i n f i n i t e radius o f t e n approximates the measuring condi t ions i n the B r o o k f i e l d S y n c h r o - l e e t r i c viscometer . Kr ieger and Maron (1952) proposed a general s o l u t i o n i n v o l v i n g g r a p h i c a l d i f f e r e n t i a t i o n and the r e l a t i o n , * " - 2 3 & - ( 2 i ' L a t e r , Kr ieger (1968) i n d i c a t e d that thef.shear ra te f o r non-Newtonian f l u i d s sheared w i t h i n an i n f i n i t e gap may be represented ; by Y = -n , (26) n . which i s the l i m i t i n g case of (24). From geometric c o n s i d e r a t i o n s , Mooney and Ewart (1934) derived shear stress and v i s c o s i t y r e l a t i o n s h i p s for t h e i r c o n i - c y l i n d r i c a l viscometer which may be applicable to the Brookfield SC-4 spindles. Shear stress and shear rate may be computed from g = kS (27) 2 2 R c " \ i - —2—V0 ( 2 8 ) R c + V where k i s a shear stress c a l i b r a t i o n constant obtained from Newtonian oils*fand _S i s the meter reading. b) Cone-Plate Geometry Unlike the coax i a l - c y l i n d e r viscometer, an exact r e l a t i o n s h i p between shear rate and shear stress e x i s t s for the cone-plate rheometer i f two important assumptions.are made (Walters, 1968): r . i . the e f f e c t of f l u i d i n e r t i a i s n e g l i g i b l e i i . the angle.between the cone and plate i s less than 4 ° . This r e l a t i o n i s expressed as-n = - ^ | - (29) 2iTr a ' where 0_ i s the cone angle i n radians and r_ i s the cone radius. Fredrickson (1964) has evaluated the percent diffe r e n c e i n shear stress between the cone and plate for several cone angles. These differences were 0.49, 0.12, 0.03 and 0.008% for cone angles, 4, 2, 1 and H°, r e s p e c t i v e l y . For small cone angles, the assumption that shear s t r e s s , 83 and hence shear rate, are uniform throughout the f l u i d sample independent of r a d i a l p o s i t i o n , i s v a l i d (Fredrickson, 1964; Walters, 1968). Shear rate i s calculated from Y = f . ' (30) The r e l a t i o n s h i p between the measured torque and shear stress i s given by a = . (31) 2ur 2. Errors i n Rotational Viscometry End-effects, s l i p and Weissenberg e f f e c t s comprise the major sources of error i n viscometrie measurements performed with a Couette rheometer but they may be either mathematically corrected or minimized by design. End-effects are r e a d i l y corrected by s u b s t i t u t i n g an e f f e c t i v e spindle length for the actual p h y s i c a l length i n (17) (Lindsley and Fischer, 1947). These e f f e c t s may assume greater*• importance with non-Newtonian f l u i d s and require an end correction f o r each sample at each shear rate (Sherman, 1970). End-effects are minimized by designing c o n i - c y l i n d r i c a l spindles (Brookfield SC-4 spindles) and open-ended spindles ( F e r r a n t i Portable and Haake Rotovisko MV spindles) (van Wazer et a l . , 1963; Highgate and Whorlow, 1969). S l i p may be mathematically corrected (Skelland, 1967). Through the design of ribbed or rbughened cyl i n d e r surfaces s l i p may be minimized i n dispersed systems (Sherman, 1970). Weissenberg e f f e c t s are minimized either by repacking the gap or by the presence of a f l u i d cover but neither i s s a t i s f a c t o r y (van Wazer et a l . , 1963) . i Secondary flows due to f l u i d i n e r t i a , non-uniform shear rate within the gap and sample evaporation comprise the major sources of error i n cone-plate determinations. Secondary flows are minimal at shear rates le s s than 2800 s _ 1 (Skelland, 1967; Williams, 1965), the presence of non-uniform shear i s minimized by small cone angles (Fredrickson, 1964; Walters, 1968) and sample evaporation i s reduced by a thin coating of low v i s c o s i t y o i l on the exposed f l u i d surface (Boger, and. Murthy, 1969). Viscous heating i s another source of error i n r o t a t i o n a l viscometry. The maximum temperature r i s e f o r c o a x i a l instruments was estimated from A T " ^ ^ o - V 2 <32> where i s a low angular v e l o c i t y , fi^ i s the maximum angular v e l o c i t y and X_ i s the thermal conductivity of the f l u i d (Fredrickson, 1964). For the cone-plate, an estimate of maximum temperature r i s e as a r e s u l t of viscous heating may be calculated from A T = Tr^~ (33) 16iTXr as derived by Bird and Turian (1962). Using the thermal conductivity value f o r water (Weast, 1973), the maximum change i n temperature due to viscous heating, i n the present study, was 0 . 2 ° and 0.6°C f o r the Couette and cone-plate rheometers, r e s p e c t i v e l y . 3. Flow Model Selection The expression of shear-thinning flow properties i n terms of flow model parameters would f a c i l i t a t e t o t a l rheogram comparisons and thereby aid i n product development and q u a l i t y c o n t r o l . Hence, three models, the modified Shangraw structure equation, the Steiger-Trippi-Ory model and^.the power-law equation, were selected for evaluation, Yakatan and Araujo (1968) proposed that the Shangraw structure equation (Shangraw et a l . , 1961) can be modified to a three parameter model for the shear-thinning flow region, a = ay + b ( l - e " C Y ) . (34) a_, b_ and c_ are empirical parameters describing the system. They used an analogue.computer to simulate the rheograms of carboxymethylcellulose mucilages. The second model, Y = a'a 3 + c'a, (35) was.proposed by S t e i g e r - T r i p p i and Ory (1961) for shear-thinning pharma-c e u t i c a l systems. aj_ i s the l i q u e f a c t i o n factor and cj_ i s the r e c i p r o c a l of the l i m i t i n g v i s c o s i t y at low shear rates. O r i g i n a l l y , Eisenschitz (1933) had used t h i s equation to describe the rheology of concentration c e l l u l o s e dispersions. Kassam and Mattha (1970a, b, c, d; 1971a, b) have used (35) i n t h e i r work with guaran, methylhydroxyethylcellulose and polyvinylpyrrolidone dispersions. The well-known power-law or Ostwald-de Waele equation, 86 a = my1 1, (36) (Reiner, 1960; Scott B l a i r , 1970) has been widely used to descr ibe the s h e a r - t h i n n i n g behaviour of non-Newtonian systems ( B i r d , 1965; Cramer, 1968; Tung et a l . , 1971). m i s known as the consis tency index and n , as the flow behaviour index (Skel land , 1967). EXPERIMENTAL 1. Rheometers and Methods Haake Rotovisko, Model RV1 (van Wazer et a l . , 1963). An MVI s p i n d l e wi th a gap width of 0.91 mm was used over a range of shear rates from 8.5 - 1370 s ^ . The sample temperature was maintained by a thermo-stated water jacket surrounding the measuring head. Each sample was subjected to a stepwise shear rate increase and then a decrease wi th the shear s t ress s i g n a l e i t h e r being read d i r e c t l y from the meter or traced onto a s t r i p c h a r t . The manufacturer 's equations, used to obta in shear s t ress and shear ra te r e s p e c t i v e l y , were as fo l lows a = AS • (37) and y = B/U-. . (38) !S was the meter r e a d i n g , U , the gear s e t t i n g and A and 13 were c a l i b r a t i o n constants . A incorporated a c o r r e c t i o n f o r e n d - e f f e c t s . B r o o k f i e l d S y n c h r o - l e c t r i c (van Wazer et a l . , 1963). The SC-4 c o n i - c y l i n d r i c a l s p i n d l e s e r i e s was used over a shear ra te range of 0.37 - 20 s " 1 . The sample temperature (25.0 ± 0 . 5 ° C ) i n the SC-4 cup was c o n t r o l l e d by a c i r c u l a t i n g water b a t h . Each sample was subjected 87 to a stepwise shear rate increase and then a decrease with the shear stress s i g n a l being read d i r e c t l y from the meter. At each shear rate, one minute was allowed for speed e q u i l i b r a t i o n followed by three consecutive readings taken at 30 second i n t e r v a l s . C a l i b r a t i o n constants were obtained f o r the spindles using o i l v i s c o s i t y standards (Cannon Instrument Co., Appendix I) as suggested by the manufacturer (Brookfield Engineering Laboratories Inc., 1971). Shear stress and shear rate were calculated from (39) and (20), r e s p e c t i v e l y , where Aj_ i s a shear stress c a l i b r a t i o n constant. a = A'S (39) The geometrical shape of the spindles was accounted for through the shear stress c a l i b r a t i o n constant, A', obtained from Newtonian o i l s and the r e l a t i o n A' = f- , (40) where jn was the Newtonian v i s c o s i t y (poise) of an o i l at a constant temperature. The influence of ;the c o n i c a l ends of the c y l i n d r i c a l spindle was included i n the e f f e c t i v e length,(h*), h* = h Q + Ah, (41) where h^ was the length of the c y l i n d r i c a l portion (cm) and Ah, the extended length due to the submerged -surface area of the spindle ends. Weissenberg Rheogoniometer (van Wazer et a l . , 1963). Several platen diameters, 5.0, 7.-5 and 10.0 cm, with varying cone angles, 2.0, 1.0, 0.5, 0.25 deg, were used i n combination with selected t o r s i o n bars to accommodate several decades of shear rate. In each instance,, the 88 cone was mounted on the top and the plate on the bottom. The sample temperature was maintained by an a i r bath surrounding the measuring head and a thermocouplerombunted i n the upper platen recorded the sample temperature. Sample symmetry was checked p r i o r to subjection to a step-wise shear rate increase and then a decrease i n forward and reverse d i r e c t i o n s with the shearsstress s i g n a l recorded on a s t r i p chart. The manufacturer's equations (Sangamo Controls Ltd., 1971) were used to c a l c u l a t e shear rate, 1800 Y = , (42) and shear s t r e s s , 3A K a = —V" . ' (43) 2irr £2 was the angular r o t a t i o n of the platen (rad s "*"), _a, the corie angle, (deg), . A , the movement of the t o r s i o n head transducer (ym), r_, the platen radius (cm) and Kv^ , was the t o r s i o n bar constant (dyne cm ym "*") . 2. Rheological Properties, R e p r o d u c i b i l i t y and S t a b i l i t y of  Hydroxyethylcellulose and Methylcellulose Dispersions Ten r e p l i c a t e dispersions of HEC were prepared at concentrations of 1.5, 2.0, 2.5, 3.0 and 3.5% w/w following the general procedure outlined i n Appendix I. Af t e r aging 0.13, 1 and 5 years at room temperature, rheograms for each dispersion were obtained using the Haake Rotovisko viscometer (y = 8.5 - 1370 sec "*"). The shear stress s i g n a l was. read d i r e c t l y from the meter, A l l tests were made at a sample temperature of 30.0 ± 0.5°C. C a l i b r a t i o n constants were obtained f o r the spindle/ cup combination using o i l v i s c o s i t y standards (Cannon Instrument Co.) as 89 suggested by the manufacturer (Gebruder Haake, 1969a). A fresh sample was used for each viscometric measurement. Between rheometric deter-minations, a l l sample containers were sealed with p a r a f f i n and stored at room temperature i n the absence of l i g h t . For comparison, a set of ten r e p l i c a t e 2% w/w methylcellulose (MC, 1500 cP) dispersions wass treated i n a s i m i l a r manner. The data were put on punch cards to f a c i l i t a t e c a l c u l a t i o n s and s t a t i s t i c a l analyses using an IBM 360/67 computer. Shear stress and shear rate were calculated using (37) and (38) r e s p e c t i v e l y . The rheograms were compared for p r e p a r a t i o n " r e p r o d u c i b i l i t y using a logarithmic transform of the power-law model (36) i n a co-variance program (Appendix I I I , Program 1) to t e s t f or differences i n slope (flow behaviour index) and l e v e l (consistency index) (Snedecor, 1965). At each polymer concentration, confidence l i m i t s (95%) and c o e f f i c i e n t s of v a r i a t i o n , CV (44), were calculated for the power-law parameters at measuring times, 0.13, 1 and 5 years (Tables X and XI). CV = x 100% (44) X SD was the standard deviation' and X was the average power-law flow behaviour, index or consistency index. To acquire s t a b i l i t y information, the apparent v i s c o s i t y of the HEC and MC polymers was examined with respect to time (Figures 25 to -27). The-power-law consistency index was taken as a dependent v a r i a b l e to c a l c u l a t e l i n e a r , quadratic, logarithmic and hyperbolic functions with respect to time. These functions were then compared for accuracy of f i t 90 to the data ( 47 , F igure 24). • 3. R h e o l o g i c a l Proper t ies of H y d r o x y e t h y l c e l l u l o s e - Polyoxyethylene  (4) Dodecyl Ether Systems Four r e p l i c a t e d i s p e r s i o n s of HEC were prepared at concen-t r a t i o n s of 2 .0 , 2 .5 , 3.0 and 3.5% w/w f o l l o w i n g the general procedure o u t l i n e d i n Appendix I . A f t e r aging f o r 1 day, flow curves f o r each of the four r e p l i c a t e HEC d i s p e r s i o n s at each concentrat ion were measured w i t h the Haake Rotovisko viscometer . The three d i s p e r s i o n s wi th the c l o s e s t rheograms were se lec ted f o r f u r t h e r e v a l u a t i o n . At each of the HEC concentra t ions , t r i p l i c a t e sets of B r i j 30 - HEC d i s p e r s i o n s were made conta ining 0.0, 4 .0 , 8 .0 , 12.0 and 16.0% w/w of the surfac tant (Appendix I ) . R h e o l o g i c a l p r o p e r t i e s of the HEC - B r i j 30 systems were determined with a Rotovisko a f t e r I and 7 days s torage. A l l t e s t s were made at a sample temperature of 30.0 ± 0 . 5 ° C over a shear ra te range of 8.5 - 685 s Shear ra te and shear s t ress were c a l c u l a t e d from (38) and (37), r e s p e c t i v e l y . 4. Comparison of Rotovisko Shear Stress C a l i b r a t i o n Methods The manufacturer suggests that two shear s t ress c a l i b r a t i o n constants , A (37), are s u f f i c i e n t f o r the ten shear ra tes assoc ia ted with the two: dynamometer s e t t i n g s of the Rotovisko . Because t h i s procedure ignores the p o s s i b i l i t y of changed f l o w ^ e f f e c t s at h i g h shear r a t e s , an attempt has been made to examine whether a s i n g l e value f o r the shear s t ress f a c t o r i s adequate f o r a l l ten shear ra tes associa ted 91 w i t h each dynamometer s e t t i n g or whether there should be a shear s t ress constant f o r each shear r a t e . A s e r i e s of Newtonian o i l s '(Appendix I) was measured under constant temperature condi t ions and a shear s t ress constant was c a l c u l a t e d from A = | i (45) f o r each of the ten gear s e t t i n g associa ted wi th the two ranges of dynamometer s e n s i t i v i t y (Table XII). The manufacturer 's method was a lso used to evaluate the shear s t ress c a l i b r a t i o n constant (Gebruder Haake, 1969a); Table X I I ) . A s e l e c t i o n of s h e a r - t h i n n i n g f l u i d s wi th a power-law flow behaviour index range of 0.48 to 0.69 was then measured and the shear s t ress r e s u l t s c a l c u l a t e d using both the proposed method and the manufacturer 's method. To determine which c a l i b r a t i o n method y i e l d e d the best representa t ion of the shear s t ress -shear ra te parameters, the data c a l c u l a t e d w i t h both methods were separately compared with shear s t r e s s -shear rate data obtained f o r the same d i s p e r s i o n s using the Weissenberg rheogoniometer (Appendix I I I , Program 1; - Table X I I I ) . 5. E v a l u a t i o n of Non-Newtonian Rheograms Derived from Two D i f f e r e n t  Types of Rheometers The choice of viscometers f o r the r h e o l o g i c a l e v a l u a t i o n of pharmaceuticals poses an i n t e r e s t i n g problem because comparisons among instruments of d i f f e r e n t geometry are l a c k i n g f o r a range of non-Newtonian f l u i d s . Constant shear throughout the sample i s t h e o r e t i c a l l y p o s s i b l e with the cone-plate viscometer (Fredr ickson, 1964) however, the commonly used instruments have a Couette geometry i n which the sheer ra te v a r i e s across the sample gap. The Haake•Rotovisko i s a v e r s a t i l e Couette instrument wi th w e l l def ined geometry and minimal e n d - e f f e c t s t h e r e f o r e , a comparison of t h i s instrument wi th the cone-p l a t e Weissenberg rheogoniometer would be v a l u a b l e . A l s o a Couette attachment wi th temperature c o n t r o l i s c u r r e n t l y a v a i l a b l e f o r the B r o o k f i e l d S y n c h r o - l e c t r i c viscometer . The e v a l u a t i o n of t h i s instrument would have p r a c t i c a l s i g n i f i c a n c e because I t has the p o t e n t i a l of p r o v i d i n g the manufacturer wi th a Couette rheometer at nominal c o s t . Dispers ions of 2.0 and 2.5% w/w HEC were prepared f o l l o w i n g the general procedure o u t l i n e d i n Appendix I and aged f o r 1 day. Sets of B r i j 30 i n HEC d i s p e r s i o n s were made conta ining 0.0, 4 .0 , 8 .0 , 12.0 and 16.0% w/w of the surfac tant i n both of the HEC d i s p e r s i o n s c o n c e n -t r a t i o n s (Appendix I ) . Rheologica l p r o p e r t i e s of the HEC - B r i j 30 systems were determined a f t e r 1 day of storage using the Haake Rotovisko (y = 8.5 - 685 s \ a c a l c u l a t e d using the proposed c a l i b r a t i o n method Sect ion I I . 4 . ) , the B r o o k f i e l d (SC-4 - 27 and 29 s p i n d l e s ,vy = 0.4 -20 s and the Weissenberg rheogoniometer (platen diameter = 7.5 cm, angle = 0 . 9 8 4 2 ° , y = 0.11 - 690 s ^) instruments . The sample temperature was 25.0 ± 0 . 5 ° C . The Rotovisko and rheogoniometer shear s t ress s i g n a l s were recorded. An undisturbed sample was used f o r each v i s c o m e t r i c measurement and a l l tes ts were done i n t r i p l i c a t e . B r i e f l y , s e v e r a l methods f o r shear ra te c a l c u l a t i o n were se lec ted f o r the Rotovisko and B r o o k f i e l d rheometers. The rheograms 93 obtained using the selected c a l c u l a t i o n methods were compared separately with data generated with the Weissenberg rheogoniometer (Appendix I I I , Program 1). In d e t a i l , two separate shear rate equations were used with data from the Rotovisko and Brookfield rheometers. The f i r s t equation, designated as the c a l i b r a t i o n equation was (20). The second shear rate equation evaluated for both rheometers was a t h e o r e t i c a l equation proposed by Krieger and Maron (Krieger, 1968).((24). An a d d i t i o n a l p a i r of shear rate equations were examined with the Brookfield data. The f i r s t of these was the Mooney and .Ewart equation, (28), for coni-c y l i n d r i c a l spindles and the second was the Krieger i n f i n i t e gap equation, (26). In a l l instances, shear stress was calculated from (17) except for the Mooney and Ewart equation where (27) was used. The manufacturer's method was used for shear rate-shear stress determination with the data generated using the rheogoniometer i n steady - r shear (Equations 42 and 43 , respectively) P r i o r to pooling the data for the instrument comparisons, a preliminary screen of the t r i p l i c a t e data sets for each rheometer was performed to r e j e c t any members of the sets which d i f f e r e d at. P < 0.01. The pooled shear rate and shear stress values calculated by the methods being tested for the Rotovisko and Brookfield instruments were read d i r e c t l y into the co-variance program f o r comparison with the rheogonio-meter r e s u l t s (Appendix I I I , Program 1; Tables XVI and XIX). 94 6. Evaluation of Rheological Models f o r Shear-Thinning Systems B r i j 30 i n HEC dispersions were prepared and measured as described previously i n Section I I . 3. The data were put on punch cards to f a c i l i t a t e c a l c u l a t i o n s and s t a t i s t i c a l a n alysis by computer. Shear stress and shear rate were calculated from (37) and (38), res p e c t i v e l y . A non-linear l e a s t squares f i t t i n g routine was then applied to obtain the best f i t to the data by the modified Shangraw, the Steiger-Trippi-Ory and the power-law models, (34), (35) and (36), res p e c t i v e l y (Appendix I I I , Program 2). Calculations were made i n double p r e c i s i o n and the i t e r a t i v e procedures were continued u n t i l successive estimates of the parameters d i f f e r e d by less than 0.0001. The program printed the model parameters along with the root mean square t o t a l error of estimate f o r each. The parameters were also punched on cards to f a c i l i t a t e p l o t t i n g and further programming. A f i l e containing the actual and f i t t e d shear stress-shear rate values was created and used to ca l c u l a t e c o e f f i c i e n t s of determination for each r h e o l o g i c a l model. As a'test of dispersion s t a b i l i t y , flow curves obtained a f t e r 1 and 7 days storage were compared f o r each HEC - B r i j 30 combination (Appendix I I I , Program 1). When the pair s of flow curves d i f f e r e d s i g n i f i c a n t l y (P < 0.01), the 7 day values were discarded from the follow-ing analysis to determine the e f f e c t of varying HEC and B r i j 30 concen-t r a t i o n s on the flow model parameters. For each HEC concentration, the parameters a_, b_, c_, a', c', m and n. were taken as dependent v a r i a b l e s and 95 the Brij 30 concentration as the independent variable to calculate linear, quadratic, logarithmic and hyperbolic functions. The highest coefficient of determination denoted the best f i t (Figures 33 to 39 and Equations 52 to 58 ). Dispersions containing 16% w/w Brij 30 in d i s t i l l e d water were also prepared and measured under identical conditions to those used for the Brij 30 - HEC systems. At each shear rate, the increase in apparent viscosity, T\&^> due to the combination of Brij 30 - HEC -water was calculated from n na4 " n a l - ( \ 2 + na3 ) ( 4 6 ) where r\ .. was the viscosity of the Brij 30 - HEC - water system, na2» t n e viscosity of the HEC - water dispersion and n^, the viscosity of the Brij 30 - water system. RESULTS AND DISCUSSION 1. Rheological Properties, Reproducibility and Stability of  Hydroxyethylcellulose and Methylcellulose Dispersions a) Rheological Properties The HEC dispersions exhibited shear-thinning flow properties within the concentration range of 1.5 - 3.5% w/w when measured with the Rotovisko. Figure 21 presents a typical rheogram for each HEC concen-tration. At a constant shear rate, a distinct shift to higher shear stress i s noticeable for each 0.5% w/w increment in polymer concentration. 96 FIGURE 21. Rheograms f o r aqueous HEC d i s p e r s i o n s Cage = 0 . 1 3 yr) —1 measured w i t h the Rotovisko rheometer (y = 8 . 5 - 1370 s , T = 30,0 ± 0 , 5 ° C ) With each addition of HEC, a substantial increase i n the apparent v i s c o s i t y i s revealed by the increased slope of the rheograms at low shear rates. V a r i a t i o n i n shear stress with changing polymer concen-t r a t i o n (age = 0.13 years) i s shown i n Figure 22 f o r a selected range of shear rates. The shear-thinning flow properties of a t y p i c a l 2.0% w/w MC (1500 cps) dispersion are compared with those for HEC 3.0 and 3.5% w/w i n Figure 23. From t h e i r rheograms, 2.0% w/w MC and 3.0% w/w HEC exhibited i d e n t i c a l flow properties at shear rates l e s s than 100 sec 1 . Above 100.sec" 1, 2.0%^MC was more viscous than 3.0% HEC (250G) but l e s s viscous than 3.5% w/w HEC. The r h e o l o g i c a l properties exhibited by MC and HEC.were a function of both polymer grade and concentration. b) R e p r o d u c i b i l i t y The r e p r o d u c i b i l i t y of r h e o l o g i c a l properties from batch to batch i s an i n d u s t r i a l concern because of consumer requirements f o r a consistent product. A s t a t i s t i c a l estimation of preparation and storage e f f e c t s on r h e o l o g i c a l r e p r o d u c i b i l i t y through examination of flow" curves i s lacking i n the l i t e r a t u r e for HEC and MC. The v a r i a b i l i t y i n sample preparation was examined for the 1 .5 , 2 .0 , 2 .5 , 3.0 and 3.5% w/w HEC and 2.0% w/w MC dispersions and summarized i n Table X. A comparison of the r e p l i c a t e flow curves (Appendix I I I , Program 1) resulted i n l / l 0 of the 1.5%, 1/10 of the 2.0%, 0/10 of the 2.5%, 0/10 of the 3.0% and 0/10 of the 3.5% w/w HEC dispersions being s i g n i f i c a n t l y d i f f e r e n t (P < 0.05) i n power-law flow behaviour index or 98 3H C O N C E N T R A T I O N ( % w/w) •FIGURE. .22.- Shear stress - HEC concentration relationship for a selected range of shear rates 99 3 r 0 4 8 12 S H E A R R A T E ( s " 1 , 1 0 " 2 ) FIGURE 23. Rheograms f o r 2.0% w/w MC i n comparison with two HEC d i s p e r s i o n s measured with the Rotovisko rheometer (y = 8.5 - 1370 s - 1 , T = 30.0 ± 0 . 5 ° C , age = 0.13 yr) 100 consistency index (36). At the same p r o b a b i l i t y l e v e l , none of the ten 2.0% w/w MC d i s p e r s i o n s was s i g n i f i c a n t l y d i f f e r e n t . For the d i s p e r s i o n s that were not s i g n i f i c a n t l y d i f f e r e n t , the power-law parameters, m and nt were averaged and C L Q _ a / and CV were c a l c u l a t e d to i n d i c a t e the reproduc-i b i l i t y of r h e o l o g i c a l p r o p e r t i e s with r e p e t i t i v e sample prepara t ion (Table X ) . The small range i n the confidence l i m i t i n t e r v a l s , 2.0 - 5.2% f o r m and 0.6 - 1.6% f o r n , shows.that the reported sample avg avg ' preparat ion method and HEC polymer were s u f f i c i e n t l y r e l i a b l e r h e o l o g i c a l l y to be used as the b a s i s f o r a system to examine shear ra te equations , rheometers and flow models f o r s h e a r - t h i n n i n g systems. The e f f e c t of aging on the r h e o l o g i c a l r e p r o d u c i b i l i t y of HEC and MC d i s p e r s i o n s i s summarized i n Table X I . At HEC d i s p e r s i o n age of 1 year , the range i n the confidence l i m i t i n t e r v a l s about the mean c o n s i s -tency index was 2.4 - 5.1% and the corresponding range f o r the mean flow behaviour index was 0.8 - 177%. These ranges i n the confidence l i m i t , i n t e r v a l s were the same as found f o r the d i s p e r s i o n s at age, 0.13 y e a r s . A f t e r 5 years of storage, a 4.1 - 14.6% range i n the confidence l i m i t i n t e r v a l s about the mean consistency index and a corresponding range of 0.6 - 1.7% f o r the mean flow behaviour index was noted f o r the HEC d i s p e r s i o n s . The confidence l i m i t i n t e r v a l f o r the 2% w/w MC d i s p e r s i o n s remained at 5% of the mean consis tency index over the 5 year per iod whereas, the s i z e of the corresponding- confidence i n t e r v a l f o r the f low behaviour index appeared to decrease s l i g h t l y with i n c r e a s i n g storage time (Tables X and X I ) . Table X Rheological reproducibility data for HEC and MC dispersions after 0.13 yr. storage concentration (% w/w) m Average Power-C L95% •law Parameters^ m and CV n (%) n C L95% CV (%) 1.5 HECC 2.4606 0.0807 4.3 0.7631 0.0053 0.9 2.0 HECC 6.7507 0.3501 6.7 0.7051 0.0076 1.4 2.5 HECd 14.9798 0.3212 2.8 0.6474 0.0037 0.8 3.0 HECd 29.9016 0.6016 2.6 0.5980 0.0042 0.9 3.5 HECd • 52.6414 .2.5670 6.3 0.5478 0.0085 2.0 2.0 MCd 23.1781 1.1316 6.4 0.6520 0;0098 2.0 3. • O T = 30.0 ± 0.5 C, Rotovisko rheometer equipped with the MVI spindle/cup combination k a = rn^v (Equation 36 ) 9 replicates d 10 replicates 1 Table XI Rheological reproducibility data for HEC and MC dispersions after 1 and 5 years storage' Time Concentration Average Power-law Parameters, m and.n (years) a w/w) ••'Tn; m CLAc;ff/ > V /o C L95% n C L95% 1 1.5 HEC 2.3214 0.0947 0.7693 0.0090 2.0 HEC 5.6380 0*4575 0.7335 0.0127 2.5 HEC 13.1684 0.5663 0.6729 0.0052 3.0 HEC 28.3076 0.6878 0.6157 0.0095 3.5 HEC 50.0584 2.5667 0.5810 0.0083 2.0 MC '•21.8539 0.8399 0.6708 0.0066 5 1.5 HEC 2.2086 0.1346 0.7439 0.0130 2.0 HEC 4.3958 0.1791 0.7492 0.0047 2.5 HEC 8.8610 1.2982 0.7269 0.0148 . 3.0 HEC 19.0388 1.7432 0.6848 0.0099 3.5 HEC 33.8490 3.0685 0.6561 0.0071 2.0 MC 12.4315 0.7727 •0.7599 0.0054 3 T meas. = 30.0 ± 0.5°C, Rotovisko Rheometer e quipped with an MVI spindle/cup combination a = mfn (Equation 36 5) 103 c) S t a b i l i t y A polymer inc luded i n the formulat ion of a f l u i d product to enhance v e h i c l e v i s c o s i t y must be s t a b l e during i t s s h e l f l i f e . No s t a b i l i t y information at 25°C has been published f o r HEC t h e r e f o r e , the e f f e c t of storage time on the apparent v i s c o s i t y of aqueous d i s p e r s i o n s has been determined over a 8.5 - 1370 s 1 shear ra te range. Except f o r the 2.0% HEC d i s p e r s i o n s , the power-law consistency and flow behaviour i n d i c e s a l t e r e d minimally over the f i r s t year of storage (Tables X and X I ) . Within t h i s time p e r i o d , i t i s improbable that the measured decrease i n polymer v e h i c l e v i s c o s i t y would be detected s u b j e c t i v e l y . A d i s t i n c t decrease i n the consistency index was observed a f t e r 5 years of d i s p e r s i o n storage (Tables X and X I ; F igure 24). A mathematical examination of the change i n consis tency index wi th respect to time revealed that a l i n e a r f u n c t i o n , m = K i " L i ( t ) . (47) descr ibed the r e l a t i o n s h i p best f o r the 2.0, 2 .5 , 3.0 and 3.5% w/w HEC and 2.0% w/w MC d i s p e r s i o n s . and were e m p i r i c a l equation parameters. None of the funct ions tested descr ibed the r e l a t i o n s h i p w e l l f o r the 1.5% w/w HEC d i s p e r s i o n . which descr ibed the change i n consistency index with respect to time was a lso c l o s e l y r e l a t e d to HEC concentra t ion as f o l l o w s L± = 0.01 ( H E C ) 4 ' 9 4 , (48) o r = 0,9670. For the 2 . 0 - 3.5% w/w d i s p e r s i o n s , the consistency index was r e l a t e d to both time and HEC polymer concentrat ion as descr ibed by 10A 1 2 3 4 5 T I M E ( y r ) FIGURE 24. Relationship of the power-law consistency index to storage time for aqueous MC and HEC dispersions Cm ± CL..,.) 105 m = 1 ^ - 0 . 0 1 . ( 0 ( H E C ) 4 * 9 4 (49) where t_ i s time i n years. The apparent v i s c o s i t y of the HEC dispersions increased from day 1 to day 47 (Figures 25 and 26). Whether a further increase i n v i s c o s i t y occurred a f t e r day 47 i s not known. The increase i n apparent v i s c o s i t y was shear s e n s i t i v e and decreased i n magnitude as the shear rate increased. At shear rates greater than 152 s \ the increase was not noticeable. The magnitude of the increase appeared to be a function of polymer concentration. At shear rates over 25 s \ the apparent v i s c o s i t y of the 2.0% w/w MC (1500 cP) dispersions appeared to increase s l i g h t l y when remeasured a f t e r aging 1 year (Figure 27). Previously, a 10 to 15% increase i n the v i s c o s i t y of a medium grade of MC a f t e r a year of storage had been noted by Davies and Rowson (1958). Why the apparent v i s c o s i t y of the MC dispersions did not appear to increase at shear rates below 25 s i n the present study i s not known at t h i s time. Cel l u l o s e i s a l i n e a r , c r y s t a l l i n e high molecular-weight polymer insoluble i n water even though there are three hydrophilic hydroxyl groups per anhydroglucose u n i t . The high degree of c r y s t a l l i n i t y (60 - 70%) prevents s u f f i c i e n t c e l l u l o s e hydroxyl-water i n t e r a c t i o n necessary for hydration. Substitutents such as methyl and hydroxyethyl groups function as spacers, reducing the con f i g u r a t i o n a l r e g u l a r i t y and c r y s t a l l i n i t y . Therefore, the type, s i z e , amount and d i s t r i b u t i o n of the substitutent w i l l s i g n i f i c a n t l y a f f e c t the degree of s o l u b i l i t y i n water (Desmarais and, Esser, 1966). I t follows therefore, that bulky h y d r o p h i l i c hydroxyethyl 106 0 1 2 3 4 T I M E ( d a y s , 1 0 " 2 ) FIGURE 25. E f f e c t of storage time on the apparent v i s c o s i t y of 2.0% w/w HEC d i s p e r s i o n s measured with a Rotovisko over a shear ra te range of 8.5 - 685 s " 1 (T = 30.0 ± 0 . 5 ° C ; age = 1 day, ri ± range; age = 47 and 365 days, n ± CLac.v) a a y JA 107 15 CD t/» O CL > - i o CO O CO > Z M ^ a: J < < I a o t x _ 9 • X 1 1 • w ft. T 4 5 0.7 « 76.1 152 228 4 5 6 ^ 6 85 0 1 2 3 4 T I M E ( d a y s , 1 0 " 2 ) FIGURE 26. E f f e c t of storage time on the apparent v i s c o s i t y of 3.0% w/w HEC dispersions measured with a Rotovisko over a shear rate range of 8.5 - 685 s " 1 (T = 30.0 ± 0.5°C; age = 1 day, "n ± cl range; age = 47 and 365 days, n ± CL Q-„) 108 T I M E (year) FIGURE 27. E f f e c t of storage time on the apparent v i s c o s i t y of 2.0% w/>w MC (1500 cP) dispersions measured with a Rotovisko rheometer over a" shear rate range of 8.5 - 1370 s ^ (rf ± CL Q J. a /, n = 9) 109 substitutents would impart a greater degree of w a t e r - s o l u b i l i t y to the c e l l u l o s e molecule than methyl substitutents. The observed shorter time required for the increase i n the apparent v i s c o s i t y of HEC as compared with that for MC would appear to be re l a t e d to the degree of hydrophilic character and spacer e f f i c i e n c y of t h i s substitutent. The exact reason for the decrease i n v i s c o s i t y of the HEC and MC dispersions over the 5 year storage period i s not known at t h i s time. Marriott and John (1973) have rel a t e d the decrease i n v i s c o s i t y of MC dispersions on storage i n the absence of microbial contamination to polymer dehydration. This would explain a portion of the observed HEC v i s c o s i t y decrease i n t h i s study. 2,. Rheological Features of Hydroxyethylcellulose - Polyoxyethylene  (4) DodecyiL Ether Systems HEC exhibited shear-thinning flow properties within the concentration range of 2.0 — 3.5% w/w. With 0.5% w/w increments i n HEC concentration i n the absence of B r i j 30, the flow curves s h i f t e d to higher shear stresses at each shear rate (Figure 28). Each flow curve was f i t t e d to the pooled data (51 i n t o t a l ) from the tests of the dispersions prepared i n t r i p l i c a t e . With the addition of 4.0% w/w B r i j 30, a d i s t i n c t s h i f t of the rheograms to higher shear stresses occurred showing an increase i n n for a l l HEC concentrations (Figure 28). For 2; 5% w/w HEC plus increasing concentrations of B r i j 30, there was a pronounced s h i f t i n the flow curves to higher shear stress with successive additions of the 110 FIGURE 28. Flow behaviour of HEC d i s p e r s i o n s conta ining 0 and 4% B r i j 30 I l l surfactant (Figure 29). Also, the increase i n the non-Newtonian character with increasing B r i j 30 concentrations was d i s c e r n i b l e as an increase i n the slope of the flow curve at low shear rates. The addition of B r i j 30, a nonionic surfactant, to the HEC dispersions provided a r e l i a b l e means of obtaining a s e r i e s of systems showing predictable increments i n shear-thinning properties at each polymer concentration. Simply stated, the surfactant gave r h e o l o g i c a l f l e x i b i l i t y to the HEC dispersions without changing the type of flow properties exhibited i n steady shear. 3. An Improved Rotovisko Shear Stress C a l i b r a t i o n Method Although the shear stress constant (A) determined for each shear rate fluctuated with increasing shear rate, a trend was apparent with respect to the two dynamometer settings (Table XII). The A values appear to increase and then to decrease with increasing shear rates. Because the shear stress constant i s calculated from Equation (45) -where the v i s c o s i t y of the Newtonian o i l and the shear rate are both constant, the trend noticed must be the r e s u l t of greater or l e s s e r changes i n S_, the scale reading. A higher scale reading and, therefore, a lower shear stress constant r e f l e c t an increased resistance of the o i l to flow at that shear rate. This increased resistance may be due to increased end-effects. I t should be noted that the manufacturer recommends the determination of shear stress constants at the mid-shear rate region where the o i l s were found to e x h i b i t l e s s resistance to flow (Table X I I ) . 112 FIGURE 29. Flow behaviour of 2.5% HEC dispersions containing d i f f e r e n t l e v e l s of B r i j 30 Table XII Shear s t ress c a l i b r a t i o n data f o r the Rotovisko rheometer f i t t e d wi th an MV1 spindle Shear Rate 50 b c n A a 500 b n 8.46 3.09 7 29.00 2 16.91 3.12 5 29.52 5 25.37 3.06 5 30.08 7 50.74 3.12 9 30.61 7 76,11 3.14 10 30.30 8 152.22 3.18 10 30.51 6 228.33 3.16 7 29.19 3 456.67 3.16 2 29.77 10 685.00 3.14 2 29.89 • 9 1370.00 3 .13 d - 29.52 6 Manufacturer 's Method 3.08 30.78 a a = AS (Equation 37) k dynamometer s e t t i n g c number of r e p l i c a t e s d average of the above values 114 Shear stress was calculated using both calibration methods and.the results compared to corresponding sets of data generated with the Weissenberg rheogoniometer over a similar range of shear rates. The results from the proposed method were not significantly different (P > 0.05) in power-law flow behaviour index (n) and consistency index (m), (36), for thesshearOthinning fluids with n > 0.55 (Table XIII). A further increase in non-Newtonian character (n < 0.55) resulted i n the Rotovisko data calculated using the proposed method deviating from those of the cone-plate Weissenberg rheogoniometer. Using the manufacturer's method for calculation, a l l the fluids tested were significantly different (P < 0.05) in ii or m. From the noted improvement in the Rotovisko shear stress-shear rate data correspondence to similar data from the Weissenberg rheogoniometer, a shear stress calibration constant should be determined for each Rotovisko shear rate for non-Newtonian shear-thinning fluids with power-law parameters, m < 41.5 and n >, 0.55. Shear stress calibration using Newtonian oils may be inadequate or Weissenberg effects, may be significant for the fluids with a higher degree of non-Newtonian shear-thinning 1 character (n < 0.55). 4. Limitations of the Couette Rheometers in Shear Stress/Shear Rate  Determination of Non-Newtonian Shear-Thinning Systems A uniform shear rate within the sample was obtained using the cone-plate, Weissenberg rheogoniometer, because of the following imposed conditions: i ) the highest shear rate (1095 s ^) employed was considerably less Table XIII Comparison of the two Rotovisko shear stress c a l i b r a t i o n methods to data generated using the Weissenberg rheogoniometer Rheogoniometer Rotovisko (Calibr a t i o n Methods) - Rheogoniometer Comparison Consistency index a m Flow Behaviour index a n Proposed Method m n Manufacturer's m Method n m D f n 12.0 0.69 NC N N sd 1/138 1/139 • 22.0 0.62 N N S s 1/127 1/128 41.5 0.55 N N S s 1/165 1/166 56.9 0.52 S S s s 1/170 1/171 84.6 0.48 S s s s 1/172 1/173 a >n a = my (Equation 36 ; shear rate range, 10.9 - 690. s" 1) degrees of freedom N = not s i g n i f i c a n t l y d i f f e r e n t at P > 0.05 d S = s i g n i f i c a n t l y d i f f e r e n t at P< 0.05 116 than the shear rate region (2800 s 1 ) requiring i n e r t i a l corrections (Skelland, 1967; Williams, 1965), i i ) cone angles ^ 2° were used, and i i i ) the maximum sample temperature r i s e due to viscous heating was 0.6°, (33). Therefore, the shear stress/shear rate data obtained with t h i s instrument were considered accurate and were used to evaluate the accuracy and l i m i t a t i o n s of the two Couette rheometers and several shear rate equations for a ser i e s of shear-thinning systems. a) Haake Rotovisko - Weissenberg rheogoniometer comparison Measured with the Rotovisko over a 8.5 - 685 s 1 shear rate range, the HEC - B r i j 30 systems spanned a 0.76 - 0.48 range i n flow behaviour index, n, (Table XV) andsshowed shear-thinning flow properties (Figure 28). As an i n d i c a t i o n of dispersion v a r i a b i l i t y , a range has been presented for each of the power-law parameters (Table XIV). The power-law model parameters for data generated with the rheogoniometer which overlap the shear rate range of the Rotovisko are given i n Table XV. The power-law flow behaviour indices for both the Rotovisko c a l i b r a t i o n and Krieger-Maron shear rate c a l c u l a t i o n methods (Equations 220anand4)24 ) corresponded well with those for the rheogonio-meter f o r n > 0.55 (Tables XIV and XVI). The consistency index, m, was more s e n s i t i v e to r h e o l o g i c a l changes and revealed a s l i g h t d i f f e r e n c e between the two shear rate c a l c u l a t i o n methods when they were separately compared with data from the rheogoniometer (Table XVI). ^ Table XIV a o Power-law parameters for HEC - B r i j 30 systems measured with the Haake Rotovisko at 25 C Dispersion Composition C a l i b r a t i o n Equation Krieger-Maron Equation (% w/w) HEC B r i j 30 n ± R d m ± R n i . R m ~- R 2.0 0.0 0.757 0.002 4.85 0'.088 > 0.757 0.002 4.80 0.08 2.0 4.0 0.678 0.006 10.35 0.39?9 0.678 0.006 10.21 01:42 2.0 8,0 0.584 0.020 21.31 2.17:170.598 0.004 20.92 1.05 2.0 12.0 0.515 0.004 42.42 1.53 0.515 0.004 41.48 1.49 2.0 16.0 0.453 0.010 73.26 7.50 0.453 0.010 71.48 7.24 2.5 0.0 0.703 0.002 11.07 0.15 0.703 0.002 10.93 0.14 2.5 4.0 0.616 0.001 22.51 0.41 0.616 0.001 22.15 0.41 2.5 8.0 0.544 .0.008 41.61 1.47 0.544 0.008 40.85 1.43 2.5 12.0 0.470 0.007 76.07 2.92 0.470 0.007 74.34 3.42 2.5 16.0 0.409 0.008 125.79 5.80 0.409 0.008 122.45 5.60 a a = my1 (Equation 36) ^ Equation 20 ° Equation 24, Rc/Rb =1.04 d Range, 3 r e p l i c a t e s Table XV Power-law parameters f or the HEC - B r i j 30 systems measured with the Weissenberg rheogonio-o„ meter at 25 C Dispersion Composition Shear Rate Range Overlap (% w/w) Rotovisko^ Brookfield HEC B r i j 30 c n m n m Shear Rate Range (s 2.0 0.0 0.758 4.85 d d 0 7 -••10:95 ' 2.0 4.0 0.678 9.89 0.872 5.90 0.7 - 10.95 2.0 8.0 0.599 20.09 0.715 14.45 0.4 - 17.3 2.0 12.0 0.544 33.19 0.620 27.61 0.7 ' - 27.5 2.0 16.0 0.490 55.59 2.5 0.0 0.691 11.97 .0.922 6.44 0.7 - 10.95 2.5 4.0 0.622 21.98 0.807 13.30 0.3 - 17.3 2.5 8.0 0.546 41.50 0.689 28.64 . 0.4 - 1 7 . 3 2.5 12.0 0.521 56.88 0.563 53.33 0.6 - 10.95 2.5 16.0 0.477 84.53 a = my (Equation 36) b Y = 10.95 - 690 s - 1 from pooled Weissenberg rheogoniometer data d system v i s c o s i t y too low to be measured accurately at these shear rates with the chosen instrumental conditions Table XVI Comparison of two shear rate c a l c u l a t i o n equations for the Rotovisko with r e s u l t s from the Weissenberg rheogoniometer for shear-thinning systems Dispersion Composition Significance (% w/w) C a l i b r a t i o n Method Krieger-Maron Method HEC B r i j 30 a n m n m 2.0 0,0 N C N N N 1/116 2.0 4.0 N S N N 1/136 2.0 8.0 N S N N 1/151 2.0 12.0 S S S S 1/182 2.0 16.0 S s S S 1/180 2.5 0.0 N N . N N". 1/139 2.5 4.0 N N N • N 1/128 2.5 8.0 N N N N 1/166 2.5 12.0 S S S S 1/135 2.5 16.0 s S S S 1/173 a a = my11 (Equation 36) k degrees of freedom for m, D^ for n i s one l e s s , i . e . 1/115 instead of 1/116' ° N = not s i g n i f i c a n t l y d i f f e r e n t (P > 0.05); S = s i g n i f i c a n t l y d i f f e r e n t (P < 0.05) 120 The Krieger-Maron method for shear rate c a l c u l a t i o n , (24), for the Rotovisko was more r e l i a b l e and gave a better i n d i c a t i o n of the true shear rate for shear-thinning f l u i d s with a flow behaviour index, n > 0.55, than the c a l i b r a t i o n method, (20) (Table XVI). Both methods f a i l e d to represent Couette shear rate adequately f o r f l u i d s with n < 0.55 measured with the Rotovisko rheometer (Rc/Rb = 1.04). Re-examination of Tables XIV and XV showed that the Rotovisko values for m and n were markedly higher and lower, r e s p e c t i v e l y , than those for the. rheogoniometer for HEC dispersions containing 12 and 16% B r i j 30. The changed power-law parameters for these concentrations of B r i j indicated that the Rotovisko was sensing a higher degree of non-Newtonian character than was a c t u a l l y present. This phenomenon could be due to two reasons: i l ) the use of Newtonian o i l s to obtain c a l i b r a t i o n constants for each shear rate i s no longer adequate or i i ) true laminar flow no longer e x i s t s within the sample gap because of Weissenberg e f f e c t s . b) Brookfield Synchro-lectric - Weissenberg rheogoniometer . comparison Measured with the Brookfield rheometer over a shear rate range of 0.4 to 20.0 s" 1, the HEC - B r i j 30 systems spanned a 0.95 - 0.52 . range i n flow behaviour index, n (Tables XVII and XVIII). A range has been given for the power-law parameters describing the data from the four shear rate c a l c u l a t i o n methods, Equations (20), (24), (26) and (28). The power-law parameters for the rheogoniometer for the shear rate range corresponding to that of the Brookfield are given i n Table XV. Table XVII Power-law a parameters for the HEC - B r i j 30 systems measured with the Brookfield rheometer at 25 C. C a l i b r a t ion and Krieger-Maron shear rate equations. Dispersion Composition Radius C a l i b r a t i o n Equation* 3 c Krieger-Maron Equation (% w/w) Ratio n •fi R d m m £ R n • R m .> -' R HEC B r i j 30 Rc/Rb 2.0 0.0 1.64 0.954 0.001 2.68 UO.Q05 0.951 0.002 2.68 0.05 2.0 4.0 1.64 0.827 o:o4o 6.80 0.07 0.822 0.001 6.40 0.07 2.0 8.0 2.50 0.682 0.020 17.17 0.81 0.682 0.020 14.19 0.55 2.0 12.0 2.50 0.553 0.040 43.17 5.25 0.553 0.040 33.55 2.91 2.5 0.0 1.64 0.932 0.001 . 6.40 0.21 0.926 0.001 6.22 0.20 2.5 4.0 2.50 0.804 0.005 14.54 0.50 0.801 0.003 12.86 0.44 2.5 8.0 2.50 0.672 0.010 32.16 1.51 0.672 0.010 26.46 1.15 2.5 12.0e 2.50 0.523 0.005 72.61 0.34 0.523 0.005 55.72 0.16 a a = my11 (Equation 36) k Equation 20 Equation 24 d Range, 3 r e p l i c a t e s 6 2 r e p l i c a t e s Table XVIII Power-law a parameters f or the HEC - B r i j 30 systems measured with the Brookfield rheometer at 25°C. Krieger and Mooney shear rate equations. Dispersion Composition Radius Krieger Equation c Mooney Equation . (% w/w) Ratio n ± R d m ±> R R m : R HEC B r i j 30 Rc/Rb 2.0 .0.0 1.64 0.951 0.002 2.68 0.01 0.951 0.002 4.12 0.14 2.0 4.0 1.64 0.822 0.002 6.43 0.13 0.822 0.002 8.68 •.0.16 2.0 8.0 2.50 0.682 0.016 14.43 2.11 0.682 0.016 14.89 1.04 2.0 12.0 . 2.50 0.553 0.039 33.80 5.49 0.554 0.039 34.27 5.53 2.5 0.0 1.64 0.926 0.002 6.22 0.40. 0.926 0.002 9.30 0.56 2.5 4.0 2.50 0.801 0.004 13.05 0.89 0.801 0.004 14.01 0.97 2.5 8.0 2.50 0.672 0.011 26.91 2.33 0.672 0.011 27.70 2.31 2.5 12.0e 2.50 0.523 0.005 55.86 0.22 0.523 0.005 56.63 0.24 a acr^  = my11 (Equation 36) Equation 26 C Equation 28 3 r e p l i c a t e s e 2 r e p l i c a t e s 123 Examination of Tables XVIII and XIX showed that the Brookfield r e s u l t s calculated using the Mooney shear rate equation, (28), were not s i g n i f i c a n t l y d i f f e r e n t (P > 0.01) from those generated with the rheo-goniometer for a power-law flow behaviour index greater than or equal to 0.81. For the Krieger-Maron and the c a l i b r a t i o n equations (1.24 and 20 , r e s p e c t i v e l y ) , flow behaviour indices greater than or equal to 0.87 and 0.92, re s p e c t i v e l y , are required f or data correspondence with the rheo-goniometer (Tables XVII and XIX). The shear rate r e s u l t s calculated using the Krieger equation f o r an i n f i n i t e gap, (26), were not s i g n i f i c a n t -l y d i f f e r e n t (P > 0.01) from those of the rheogoniometer for only the most non-Newtonian dispersion measured (Table XIX). This r e s u l t was expected because the coaxial, geometry, Rc/Rb = 2.50, may behave as an i n f i n i t e gap with high v i s c o s i t y shear-thinning f l u i d s at the low shear rate range of the Brookfield. I t i s d i s t i n c t l y p ossible that the degree of Brookfield -rheogoniometer data correspondence could have been improved by generating a shear stress c a l i b r a t i o n constant for each shear rate as was done with the Rotovisko (Tables XII and X I I I ) . At t h i s point, the accuracy of the rheogoniometer shear s t r e s s / shear.rate data may be emphasized. A semilogarithmic equation described the r e l a t i o n s h i p between the'power-law consistency and flow behaviour indices f or the HEC - B r i j 30 dispersions measured with the rheogoniometer over a 10,95 — 690 s ^ range i n shear rate (Figure 30, Equation 50 ). log m = K, + L, n (50) Table XIX Comparison of several shear rate equations for the Brookfield Synchro-lectric with r e s u l t s from the Weissenberg rheogoniometer for shear-thinning systems Dispersion Composition Significance (% w/w) C a l i b r a t i o n Krieger-Maron Mooney Krieger D HEC B r i j 30 a n m n m n m n m 2.0 4.0 NC S N N N N, m S 1/73 2.0 8.0 S S S S S ' S s S 1/126 • 2.0 12.0 S S S S S S s S 1/130 2.5 0.0 N N N N NN N N s 1/80 2.5 4.0 N S N S N N N s 1/95 2.5 8.0 N S N S N S N s 1/129 2.5 12.0 N s N S S N N N 1/49 a r.n a = my k degrees of (Equation 36) freedom f o r m • D f for n i s one le s s , i . e . 1/72 instead of 1/73 ° N = not s i g n i f i c a n t l y d i f f e r e n t (P > 0.01); S = s i g n i f i c a n t l y d i f f e r e n t (P < 0.01) 125 K 2 and were equation parameters. The m .and 11 values obtained from the Rotovisko rheometer deviated from the l i n e a r r e l a t i o n s h i p noted for the rheogoniometer at n < 0.55 and showed a greater degree of non-Newtonian character than was ascertained with the cone-plate instrument (Tables XIV and XV). Figure 31 shows a s i m i l a r r e l a t i o n s h i p between m and n for the HEC - B r i j 30 systems measured with the rheogoniometer over a low shear rate range (y = 0.3 - L17,3 s "*") . The m and n values generated with the Brookfield showed minimal correspondence to those obtained with the rheogoniometer i n t h i s region (Tables XV, XVII and XVIII). In a l i n e a r power-law region described by log a = log m + n log y, (51) a l i n e a r r e l a t i o n s h i p between m and n as shown by (50) and Figures 30 and 31 provided a d d i t i o n a l evidence that the rheogoniometer measurements are correct for the range of shear-thinning f l u i d s measured. With an increase i n the concentration of HEC, the consistency index changed by a constant amount for each system but the slope, I^, (50) which may r e f l e c t or describe the i n t e r a c t i o n between the B r i j 30 -HEC components did not change. If the i n t e r a c t i o n between the HEC -B r i j 30 - water components had changed with an increase i n HEC concen-t r a t i o n i n the l i n e a r log a - log y region then the slope of (50) would also have changed. 5. Rheological Models for Shear-Thinning Systems The modified Shangraw, S t e i g e r - T r i p p i Ory and power-law models accurately f i t t e d the flow data for the HEC - B r i j 30 dispersions as 127 ~ r i i 1 i 0.5 0.7 0.9 n FIGURE 31. Consistency index - flow behaviour index r e l a t i o n s h i p f or the HEC - B r i j 30 systems measured with the rheogoniometer at 25°C over a 0.3 - 17. s 1 range i n shear rate 128 indicated by respective average c o e f f i c i e n t s of determination of 0.989, 0.990 and 0.993 (Equations 34 , 35 and 36 ). A t - t e s t of the three 2 sets of r values showed no s i g n i f i c a n t difference among the means (P > 0.05). Thus, a l l three models f i t t e d the data equally well for the dispersions studied. At most concentrations of HEC, the power-law f i t t e d the data best at low shear rates whereas the Steiger-Trippi-Ory model f i t t e d the data more accurately at higher shear rates (Figure 32). The modified -Shangraw equation appeared to o s c i l l a t e around the experimental data. Functions that s u i t a b l y described the v a r i a t i o n of flow parameters with B r i j 30 concentration (B) were: Modified Shangraw model a = K3• + L 3 B (52) b = K 4 + L 4 B 2 (53) c = K 5 + L 5 log B (54) Steiger-Trippi-Ory model a' = Kg + L f i log B (55) c' = K ? + L ? log B (56) Power-law model m = Kg + Lg log B (57) n = Kg + L g log B (58) where K and.L are regression constants and c o e f f i c i e n t s , r e s p e c t i v e l y . The fu n c t i o n a l r e l a t i o n s h i p chosen i n each instance had c o e f f i c i e n t s of 129 FIGURE 32. Flow behaviour of 2.5% HEC dispersions containing 16% B r i j 30. The modified Shangraw, Steiger-Trippi-Ory and power-law models are shown f i t t e d to the data 130 determination with the highest magnitude and frequency. The modified Shangraw structure equation parameters, a, b_ and c_, were dependent upon both HEC and B r i j 30 concentration (Figures 33, 34 and 35). With 2.0% w/w HEC and increasing B r i j 30 l e v e l s , the values for the parameter _a increased i n a l i n e a r fashion. Increasing HEC concentrations resulted i n an upward s h i f t of the curve while the slopes remained approximately constant. There was an exception to the above generalization with 3.5% w/w HEC and B r i j 30 concentrations over 8.0% w/w for which the parameter appeared to plateau and then decrease. Values of b_ increased i n a c u r v i l i n e a r manner with increasing B r i j 30 and showed upward.shifts of the curves for increasing HEC concentrations. Parameter c^varied as the logarithm of dispersion composition (Figure 35). These values were not as s e n s i t i v e to changes i n HEC concentration as were those for a and b_. On the other hand, c_ was 'more s e n s i t i v e to increasing surfactant concentrations. Deviations of b_ and c_ from the selected fu n c t i o n a l r e l a t i o n s h i p s ('"(Equations 52 , 53 and 54 ) were noted for 3.5% w/w HEC containing over 8.0% B r i j 30. Curves i n Figures 33, 34 and 35 for 3.5% HEC are truncated at 8.0% B r i j 30 because the function does not apply at higher surfactant concentrations. The Steiger-Trippi-Ory parameters, a' and c', decreased i n a" logarithmic manner with increased B r i j 30 and HEC concentrations (Figures 36 and 37). The s e n s i t i v i t y to a l t e r a t i o n s i n HEC concentration decreased, exponentially with Increasing c e l l u l o s e polymer concentration. At 2.0% w/w HEC, a large decrease i n the values of the two parameters was n o t i c e -able with increasing surfactant concentration, whereas at 3.5% HEC l i t t l e change was d i s c e r n i b l e . Deviations of these parameters from the f i t t e d 131 Br i j 30 ( % ) 'FIGURE 33. Variation of the modified Shangraw parameter, a., with HEC and Brij 30 concentration 132 FIGURE 34. V a r i a t i o n of the modified Shangraw parameter, b_, with HEC and B r i j 30 concentration 133 B i i j 30 ( o / c ) FIGURE 35. V a r i a t i o n of the modified Shangraw parameter, c_, with HEC and B r i j 30 concentration 134 B r i j 3 0 ( % ) FIGURE 36. Variation of the Steiger-Trippi-Ory model parameter, a', with HEC and Brij 30 concentration 135 0.6 L B r i j 30 ( o / Q ) FIGURE 37. V a r i a t i o n of the Steiger-Trippi-Ory model parameter, c', with HEC and B r i j 30 concentration 136 functions at higher polymer and surfactant concentrations are r e l a t i v e l y small i n comparison with those of the other two r h e o l o g i c a l models. The power-law parameters were s e n s i t i v e to both surfactant and c e l l u l o s e polymer concentrations (Figures 38 and 39). The consistency index, m, increased as a c u r v i l i n e a r function of polymer and surfactant concentrations. Curves for the flow behaviour index, n, showed a decrease with increasing HEC and B r i j 30, i . e . , the dispersions became more shear-thinning as the two solute species increased i n concentration (Figure 39). Deviations of parameter values from the selected functions (Equations 57 and 58 ) were evident f o r 3.5% HEC dispersions containing over 8.0% B r i j 30. These discrepancies may a r i s e from concentration-dependent i n t e r a c t i o n s among the dispersion components or from s i g n i f i c a n t Weissenberg e f f e c t s occurring during rheometric measurement i n a c o - a x i a l viscometer. Although the equations evaluated were empirical models, use of flow model parameters to describe rheograms i n the shear-thinning flow region and determination of parameter-viscosity inducing agent(s) concentration r e l a t i o n s h i p s can aid i n formulating with desired consistency and flow properties. Construction of f i g u r e s , such as 38 and 39 for the power-law model i n the shear-thinning flow region, would enable rapid determination of the e f f e c t of alterations- i n processing conditions or formulation components. The areas of acceptable consistency and flow c h a r a c t e r i s t i c s as obtained from rheometric measurements of panel-selected formulations may also be blocked i n and used as an adjuvant to 137 Brij 30 ( o / o ) FIGURE 38. V a r i a t i o n of the power-law model parameter, m, with HEC and B r i j 30 concentration 138 FIGURE 39. V a r i a t i o n of the power-law model parameter, n , wi th HEC and B r i j 30 concentrat ion 139 q u a l i t y control and storage information. The magnitude of apparent v i s c o s i t y r e f l e c t e d an i n t e r -a c t i o n between the components of the HEC - B r i j - water system at low shear rates (Figure 40). A possible explanation f o r t h i s increase i n apparent v i s c o s i t y was an i n t e r a c t i o n of HEC molecules with B r i j 30 m i c e l l e s (cmc = 0.0055% w/w, Figure 10) to form large bulky aggregates. The postulated aggregate was thought to be shear-sensitive as indicated by a very large decrease i n apparent v i s c o s i t y with i n i t i a l increments of shear rate (Table XX). This form of shear-sensitive, v i s c o s i t y -increasing i n t e r a c t i o n with B r i j 30 additions at low shear rates was noted for a l l HEC concentrations tested. This i n t e r a c t i o n w i l l be discussed further i n Section I I . B. 3. 140 0 I I I I 1 L _ O 1 2 0 2 4 0 3 6 0 4 8 0 6 0 0 SHEAR RATE ( s"1) FIGURE 40. Apparent v i s c o s i t y of 2.5% HEC d i s p e r s i o n s containing 0, 4, 8, 12 and 16% B r i j 30. The power-law model i s shown Table XX Viscous i n t e r a c t i o n at low shear rates i n a 2.5% HEC dispersion containing 16% B r i j 30 Apparent v i s c o s i t y (Poise) Shear 2.5% HEC rate I (sec i 16.0% B r i j 30 \l 2.5% HEC na2 ' 16.0% B r i j 30 \ 3 b •\4 8.5 32.79 6.10 4.69 22.00 16.9 21.65 4.98 3.52 13.15 25.4 16.97 4.43 2.97 9.57 50.7 11.20 3.62 2.23 5.35 76.1 8.78 3.21 1.88 3.69 152.2 5.79 2.62 1.41 1.06 228.3 4.54 2.33 1.19 1.02 456.7 3.00 1.90 0.89 0.21 685.0 . 2.35 1.69 0.76 -0.10 3. ' Calculated from the power-law f i t t e d to the data fa \4 " \ l " ( na2 + Equation 46 142 B. RHEOMETRIC STUDIES OF A FUNDAMENTAL NATURE: LOW SHEAR AND DYNAMIC MEASUREMENTS Cellu l o s e d e r i v a t i v e s have been noted to have unique properties i n water e x h i b i t i n g higher i n t r i n s i c v i s c o s i t i e s and lower sedimentation c o e f f i c i e n t s than other polymers with the same molecular weight (Flory et a l . , 1958) . The i n t r i n s i c v i s c o s i t y i n water shows a strong solvent dependence and i n v a r i a b l y displays large negative temperature c o e f f i c i e n t s (Flory et a l , , 1958; Brown and Henley, 1964 and 1967). Brown and Henley (1967), i n studying the unperturbed dimensions of c e l l u l o s e d e r i v a t i v e s , have stated that HEC i s considerably more extended i n a good solvent such as water. The determination of l v i s c o e l a s t i c properties i n conjunction with low shear rate measurements should confirm these findings concerning the deposition of HEC i n aqueous media. The nature of a shear-sensitive HEC - B r i j 30 - water i n t e r a c t i o n noted previously (Section I I . A. 5), may be c l a r i f i e d also through low shear rate and dynamic measurements. INTRODUCTION 1. Li m i t i n g V i s c o s i t y at Low Shear Rates Shear-thinning f l u i d s t h e o r e t i c a l l y have two Newtonian regions, one at very low shear rates and the second at very high shear rates (van Wazer et a l . , 1963; Scott B l a i r , 1969). Between these two regions, the f l u i d shear-thins or the v i s c o s i t y i s no longer constant but rather i s a function of shear rate (Figure 1). The l i m i t i n g v i s c o s i t y at low shear rates i s an extremely 143 important parameter i n characterizing the properties of systems with a structure which i s unaffected by external influences (Dreval et al_. , 1973). The Newtonian v i s c o s i t y i n t h i s shear rate region i s s e n s i t i v e to changes i n polymer molecular weight d i s t r i b u t i o n and molecular structure, polymer concentration and ^goodness" of the solvent. Mendelson et al_. (1970) examined the melt r h e o l o g i c a l properties of l i n e a r and branched polyethylenes at low shear rates. The degree of polymer branching was found to lower the c h a r a c t e r i s t i c shear rate required for the onset of the lower Newtonian region (Figure 1). The magnitude of the Newtonian v i s c o s i t y of a branched polyethylene i n t h i s low shear region was observed to be greater than that for a l i n e a r molecule of the same molecular volume. The zero-shear v i s c o s i t y - concentration dependence f o r a s e r i e s of polymers of d i f f e r e n t chain f l e x i b i l i t i e s i n various solvents was examined by Dreval et a l . (1973). Their r e s u l t s showed that the parameters ch a r a c t e r i z i n g the i n d i v i d u a l macromolecular chain, v i z . , the dimensions of the polymer c o i l and the r h e o l o g i c a l effectiveness of solvent-polymer i n t e r a c t i o n s , were s i g n i f i c a n t i n determining the v i s c o s i t y of polymer solutions from very d i l u t e to highly concentrated. The nature of the solvent was observed to a f f e c t the magnitude of the l i m i t i n g v i s c o s i t y at low shear rates of concentrated polymer solutions i n a manner dependent upon the f l e x i b i l i t y of the polymer chains (Tager and Dreval, 1970). I t was shown that the nature of the solvent had a greater e f f e c t on the v i s c o s i t y of polar polymer solutions with very strong s p e c i f i c i n t e r a c t i o n s than on the v i s c o s i t y of nofepolar'solutions. 144 2. V i s c o e l a s t i c Moduli Although i t i s well recognized that the addition of small amounts of polymer to a solvent may increase the v i s c o s i t y , i t i s l e s s w e l l known that d i l u t e polymer solutions may also possess e l a s t i c properties (Ferry, 1973). The determination of the e l a s t i c and viscous components of such a polymer s o l u t i o n comprises an estimate of the energy stored and l o s t as the r e s u l t of short range deformations. The c h a r a c t e r i s t i c shapes of the v i s c o e l a s t i c functions can be associated q u a l i t a t i v e l y with d i f f e r e n t types of molecular responses (Ferry, 1970). The Storage Modulus This modulus i s a measure of the energy stored and recovered per cycle i n simple l i n e a r s i n u s o i d a l shear deformation. The _2 storage modulus (G"(C J), dyne cm )- i s defined as the stress i n phase with the s t r a i n divided by the s t r a i n (Ferry, 1970) therefore, as the phase angle approaches 90°, only n e g l i g i b l e energy i s recovered and the f l u i d i s predominantly viscous. -2 The Loss Modulus The loss.modulus (G"(a)), dyne cm ) i s a measure of the energy dis s i p a t e d as heat per cycle and i s defined as the stress out of phase with the s t r a i n divided by the s t r a i n i n s i n u s o i d a l shear deformation (Ferry, 1970). As the phase angle approaches 0° only n e g l i g i b l e energy i s l o s t as heat and the material i s predominantly e l a s t i c i n nature. The Loss Tangent This v i s c o e l a s t i c function i s a dimensionless r a t i o and i s a measure of the energy l o s t to the energy stored i n a c y c l i c deformation, 145 tan <f> = G"/G'. (59) The loss tangent i s of considerable p r a c t i c a l i n t e r e s t (Ferry, 1970). Davis (1971a) has referred to the loss tangent as a consistency spectrum and has indicated i t s p o t e n t i a l usefulness to follow rheo-l o g i c a l changes i n formulation, q u a l i t y control and storage s t a b i l i t y . Dynamic V i s c o s i t y Dynamic v i s c o s i t y (n', poise) i s the r e a l part of complex v i s c o s i t y and describes the d i s s i p a t i v e e f f e c t s of a l t e r n a t i n g s t r e s s , n' = ^ . (60) (A) This parameter i s useful i n discussing uncross - r l inked polymers because at low frequencies, _n*_ approaches the steady shear v i s c o s i t y . The value the dynamic shear - steady shear correspondence assumes, for uncross-linked polymers at low frequencies and shear rates i s a function of temperature, molecular weight .and polymer concentration (Ferry, 1970). 3. Dynamic Testing The complex r h e o l o g i c a l properties of pharmaceutical semisolids may be elucidated by dynamic te s t i n g where the method of test does not s i g n i f i c a n t l y a l t e r the f l u i d structure (Barry, 1971). Davis (1969a, 1969b, 1971a and 1971b) used creep response and o s c i l l a t o r y t e s t i n g (destructive and non-destructive) for ointment bases and creams and has interpreted the observed r h e o l o g i c a l behaviour with mechanical models. In the 1969 papers, Davis c l e a r l y showed the l i m i t a t i o n s of steady shear viscometry to detect the l i m i t i n g v i s c o s i t y at low shear rates of pharmaceutical semisolids. A comparison of long time creep and short ; 146 time non-destructive o s c i l l a t o r y t e s t i n g was made for pharmaceutical semisolids i n the 1971 papers. Davis proposed a log G"/G' (loss tangent) versus log to p l o t or consistency spectrum f o r the character-i z a t i o n of these materials. Destructive o s c i l l a t o r y t e s t i n g was proposed as a means of assessing consumer acceptance of t o p i c a l preparations. Although not a new idea, the problem of c o r r e l a t i n g sensory assessment with r h e o l o g i c a l measurement (reviewed by Scott B l a i r , 1969), has remained unsolved. Barry and co-workers (Barry and Grace, 197;1 and 1972; Barry and Meyer, 1973) have studied the r h e o l o g i c a l assessment of texture p r o f i l e and of sensory t e s t i n g of sp r e a d a b i l i t y . They, l i k e others, have used ranking methods to evaluate subjective sensory assess-ment, a procedure which does not separate v i s c o s i t y , e l a s t i c i t y and d u c t i l i t y . In addition, they have combined continuous shear and v i s c o -e l a s t i c measurements to construct master curves of the r h e o l o g i c a l conditions operative during spreading. The master curves showing the acceptable ranges of v i s c o s i t y f o r t o p i c a l a p p l i c a t i o n were d i f f e r e n t f o r l i p o p h i l i c and hydrophilic gels as w e l l as for the 0/W emulsion studied (Barry and Meyer, 1973). The master.curve concept, when l a t e r used.to evaluate the consumer a c c e p t a b i l i t y of a t o p i c a l v e h i c l e , appeared to correlate, with subjective-assessment conclusions (Barry, 1973). Barry and Eccleston (Barry and Eccleston, 1973a and 1973b; Eccleston e_t a l . , 1973) have studied the l i n e a r v i s c o e l a s t i c behaviour of 0/W emulsions s t a b i l i z e d with mixed emulsifiers of the self-bodying type. They have correlated increased v i s c o e l a s t i c functions (G' and w') with the formation of emulsion networks r e s u l t i n g from increased concentration and chain length of the mixed e m u l s i f i e r . These authors have used 147 o s c i l l a t o r y and creep t e s t i n g over a"wide frequency range as the basis f o r the conclusion of network formation. EXPERIMENTAL 1. Low Shear Rate Studies of Hydroxyethylcellulose and Hydroxyethyl- c e l l u l o s e - Polyoxyethylene (4) Dodecyl Ether Systems Low shear rate measurements were performed because polymer information about the d i s p o s i t i o n and i n t e r a c t i o n of macromolecules can be acquired from these measurements i n conjunction with dynamic determinations. Hydroxyethylcellulose dispersions were prepared at concentra-tions of 1, 2, 3 and 4% w/w following the general procedure outlined i n Appendix I. Flow curves were measured at 23.0 ± 0.5°C using the o Weissenberg rheogoniometer i n the steady shear mode. Several decades of -shear rate were covered with s p e c i a l attention given to the low shear rate region (y < 1.0 s ^ ) . The shear stress s i g n a l was recorded. The equilibrium shear stress s i g n a l at each shear rate wase.taken as the true reading,. Calculations were done using Equations (42) and (43) . The procedure was repeated with B r i j 30 (8, 12 and 16% w/w) i n HEC dispersions (2, 3 and 4% w/w) to obtain information about a shear s e n s i t i v e i n t e r a c t i o n noted with these dispersions i n Section I I . A. 5. 2. V i s c o e l a s t i c Studies: Rheometer and Methods V i s c o e l a s t i c behaviour was studied using the Weissenberg rheogoniometer i n small amplitude o s c i l l a t o r y shear (van Wazer e_t a l . , 148 1963). The sample was subjected to a s i n u s o i d a l s t r a i n with both the input s t r a i n and the resultant stress signals recorded simultaneously. The dynamic response was measured i n terms of an amplitude r a t i o (Sm/Im) and the,displacement.of the two curve traces (<(>). Using two d i f f e r e n t platen combinations (both the radius and angle were changed), the l i n e a r v i s c o e l a s t i c region was determined i n i t i a l l y at a f i x e d frequency through v a r i a t i o n of the .strain wave amplitude. An amplitude was selected i n the l i n e a r v i s c o e l a s t i c region and then dynamic measurements were made progressing from low to high o s c i l l a t o r y frequencies. The s t r a i n and stress sine waves were traced by a potentiometric s t r i p chart recorder at lowffrequencies and an o s c i l l o g r a p h at high frequencies. The wave amplitudes and displacements were measured as suggested by the manufacturer (Sangamo Controls Ltd., 1971). -2 -2 Dynamic shear storage (G', dyne cm ) and los s (G"; dyne cm ) moduli were computed using the manufacturer's equations (Equations 60 and 61 , r e s p e c t i v e l y , Sangamo Controls Ltd., 1971). 2160 a L , Sm G' = • . • — — cos <f) (61) d Im 2160 a L, Sm 3 G" = z — s i n <|> ' (62) d Im Sm was the maximum movement of the t o r s i o n head transducer (ym), Im, the maximum movement of the worm-shaft measured by the o s c i l l a t i o n input transducer (ym), d_, the platen diameter (cm) and j>_ was the phase differe n c e between the recorded s t r a i n and stress waves (deg). Dynamic 149 v i s c o s i t y (poise) was determined from the loss modulus, r " " K F . < 6 3 ) where f_ was the frequency of o s c i l l a t i o n (Hz) and 2nf was the radian frequency (u), s "*"). 3. V i s c o e l a s t i c Features of Hydroxyethylcellulose and Hydroxyethyl- c e l l u l o s e - Bdlyoxyethylerie (4) Dodecyl, Ether . Systems Aqueous dispersions of HEC were prepared at concentrations of 1.0, 2.0, 3.0 and 4.0% w/w following the general procedure (Appendix I ) . A second set of 2.0, 3.0 and 4.0% w/w HEC dispersions were prepared and allowed to age one day. After aging, B r i j 30 (8.0, 12.0 and 16.0% w/w) was added to each of the three HEC dispersions (Appendix I ) . A l l dispersions were measured using the o s c i l l a t o r y mode of the rheogoniometer. For the HEC dispersions, the l i n e a r v i s c o e l a s t i c region was determined at a constant frequency using the following conditions: 1 and 2% w/w HEC platen diameters, 7.5 and 10.0 cm; cone angles, 0.9842 and .0.2522 deg; t o r s i o n bar constant 94 dyne -1 cm ym 3 and 4% w/w HEC platen diameters, 5.0 and 7.5 cm; cone angles, 2.0242 and 0.9842 deg; t o r s i o n bar constants 94 and 875 dyne cm ym The l i n e a r v i s c o e l a s t i c region was determined for only the most.non-Newtonian of the B r i j 30 i n HEC dispersions (4.0% HEC + 16.0% B r i j 30). 150 S i g n i f i c a n t conditions i n the frequency curve generation for each of the dispersions using the rheogoniometer are given i n Table XXI. The storage and loss moduli, dynamic v i s c o s i t y and loss tangent were calculated and examined over the frequency i n t e r v a l for both sets of dispersions (Equations 61, 62, 63 and 59). RESULTS AND DISCUSSION 1. Flow C h a r a c t e r i s t i c s of Hydroxyethylcellulose and Hydroxyethyl- c e l l u l o s e - Polyoxyethylene^(4) Dodecyl Ether Systems at Low  Shear Rates A t h e o r e t i c a l Newtonian flow region at low shear rates (Figure 1) was detected for each,of the 1, 2, 3 and 4% w/w HEC dispersions (Figure.41). The shear rates at which Newtonian flow i n i t i a l l y occurred appeared to decrease with increasing polymer concentration. For example, t h i s region i n i t i a l l y began at 75 s ^ for the 1% dispersion and at 0.18 s 1 for the 4% HEC dispersion (Figure 41). The l i m i t i n g v i s c o s i t y at low shear rates (ri Q) was found-to be a logarithmic function of HEC concentration (% w/w), log n Q = l o g K 1 Q + L 1 Q iogC:(HEC) (64) where K^^ and L^Q are regression constants and c o e f f i c i e n t s , r e s p e c t i v e l y (Figure 42). The discussion of the d i s p o s i t i o n of HEC polymers i n aqueous so l u t i o n w i l l follow the v i s c o e l a s t i c studies (Section I I . B. 2.). The detection of a Newtonian region for the HEC dispersions y i e l d s systems Table XXI S i g n i f i c a n t instrumental condi t ions i n : HEC - B r i j 30 d i s p e r s i o n frequency curve generation D i s p e r s i o n Composition P l a t e n T o r s i o n Bar Constant Maximum Frequency Range (/ I w/w) d a S t r a i n HEC B r i j 30 (cm) (deg) (dyne cm^m ) (ym) (Hz). 1.0 . 0.0 10.0 0.2522 94 2.6 0.38 - 7.54 2.0 . 0.0 10.0 0.2522 94 1.9 0.06 - 3.77 2.0 0.0 7.5 0.9842 94 0.5 0.06 - 3.77 2.0 8.0 7.5 029842 94 0.3 0.06 - 3.77 2.0 12.0 7.5 0.9842 94 0.3 0.04 - 2.99 2.0 16.0 7.5 0.9842 875 0.3 0.06 - 3.77 3.0 0.0 7.5 0.9842 94 0.4 0.04 - 4.75 3.0 8.0 7.5 0.9842 875 0.3 0.05 - 3.77 3.0 12.0 7.5 0.9842 875 0.3 0.075 - .3.77 3.0 • 16.0 7.5 0.9842 875 0.3 00.04 - 2.99 4.0 0.0 7.5 0.9842 94 0.4 0.04 - 5.96 4.0 8.0 7.5 0.9842 875 0.3 0.05 - 3.77 4.0 12.0 7.5 0.9842 875 0.3 0.04 - 3 - 7 7 4.0 16.0 7.5 0.9842 985 0.3 0.04 - 2.99 0.01 0.1 1 10 100 1 0 0 0 S H E A R RATE (s" 1 ) FIGURE 41. Viscosity-shear rate r e l a t i o n s h i p for the HEC dispersions showing the l i m i t i n g v i s c o s i t y region at low shear rates. Measured with the rheogoniometer at 23,0 ± 0.5°C 153 FIGURE 42. Low shear rate l i m i t i n g v i s c o s i t y - HEC concentration r e l a t i o n s h i p : 154 with predictable viscosity at zero shear rates for the investigation of viscosity effects on the diffusion of hydrocortisone (Section I I I ) . Steady shear measurement of the 2, 3 and 4% HEC dispersions containing Brij 30 (8, 12 and 16%) did not reveal a Newtonian region at low shear rates (Figure 43). These dispersions exhibited shear-thinning flow properties over 4 to 5 decades in shear rate. At Tow shear rates, the flow properties showed a marked dependence on surfactant concentration whereas, at high shear rates the HEC - Brij 30 rheograms appeared to converge with the HEC flow curve reflecting minimal surfactant contribution (Figure 43). It was not conclusively determined whether or not a Newtonian region existed at low shear rates because these fluids s t i l l showed shear-thinning flow properties at the shear stress signal sensitivity-limits of the rheogoniometer. These measurements w i l l be discussed.further under Section I I . B. 3. 2. Viscoelastic Properties of Hydroxyethylcellulose Dispersions The storage moduli for the HEC dispersions formed a slightly curvilinear relationship with radian frequency (Figure 44). With an increase in UJ_ there was a pronounced increase in the storage modulus at each of the cellulose polymer concentrations. A substantial increase in the storage modulus at each radian frequency was evident also with an increase in cellulose concentration. The HEC dispersion loss moduli were typical of a viscoelastic liquid at low frequencies (Figure 45). was directly proportional to < 1 I I I I I 0.01 0;1 1 10 100 S H E A R R A T E ( s " 1 ) FIGURE 43. V i s c o s i t y - shear rate r e l a t i o n s h i p for the 3% HEC plus 0, 8, 12 and 16% B r i j 30 dispersions showing the absence of a l i m i t i n g v i s c o s i t y region at low shear rates. Measured with the rheogoniometer at 23.0 ± 0.5°C 156 3 2 1 0.01 0.1 1.0 10. R A D I A N F R E Q U E N C Y ( s _ 1 ) FIGURE 44. Storage modulus as a function of o s c i l l a t o r y frequency for 1, 2, 3 and 4% w/w HEC dispersions'(T =23.0 + 0.5°C) 0.1 0.01 RAD IAN F R E Q U E N C Y ( s _ 1 ) 1.0 FIGURE 45. Loss modulus as a function of o s c i l l a t o r y frequency f or 1, 2, 3 and 4% w/w HEC dispersions (T = 23.0 ± 0.5°C) 158 the radian frequency as described by Equation (65) f o r a simple Newtonian l i q u i d . G" = (65) The calculated values of n_' i n t h i s flow frequency region were 0.31, 3.5, 18 and 57 poise for the 1, 2, 3 and 4% w/w HEC dispersions, r e s p e c t i v e l y . These values agreed well with the corresponding n values (0.4, 3.5, 17 and 60 poise) obtained from steady shear measure-ments at low shear rates (Section I I . B. 1., Figure 41). The shape of the storage and l o s s moduli (Figures 44 and 45)were c h a r a c t e r i s t i c of a d i l u t e polymer s o l u t i o n i n which the v i s c o e l a s t i c i t y was a r e l a t i v e l y minor perturbation of the Newtonian behaviour of the solvent (Ferry, 1970). The r e l a t i o n s h i p of the storage moduli to the l o s s moduli (Figure 46) resembled the springy wormlike model of Harris and Hearst (Hearst et a l . , 1966). This molecular model represented a degree of s t i f f n e s s between the p e r f e c t l y f l e x i b l e bead-spring model and the r i g i d rod model of Kirkwool and Auer (Ferry, 1970). This r e s u l t was i n agreement with Brown's conclusions from i n t r i n s i c v i s c o s i t y studies that the HEC molecule was considerably more extended or l e s s f l e x i b l e i n a good solvent such as water (Brown, 1961; Brown and Henley, 1967). These workers c i t e d s p e c i f i c e f f e c t s of the solvent on the chain rather than conventional short range polymer-solvent i n t e r -actions to be the cause of decreased f l e x i b i l i t y . F l o r y et a l . (1958) reached a s i m i l a r conclusion i n t h e i r i n t r i n s i c v i s c o s i t y studies on c e l l u l o s e d e r i v a t i v e s . Solvents, p a r t i c u l a r l y water, were v i s u a l i z e d to i n t e r a c t with c e l l u l o s e chains so as to r e s t r i c t r o t a t i o n about the ether linkages thereby decreasing molecular f l e x i b i l i t y . 159 0.01 0,1 1 10 R A D I A N F R E Q U E N C Y ( s " 1 ) FIGURE 46. Storage - loss moduli relationship for the 3 and 4% HEC dispersions 160 Dynamic v i s c o s i t y or the r e a l component of complex v i s c o s i t y was another means of describing the d i s s i p a t i v e e f f e c t s of a l t e r n a t i n g s t r e s s . From Figure 47, i t was evident that dynamic v i s c o s i t y approached the steady shear apparent v i s c o s i t y of the HEC d i s p e r s i o n at low shear rates. The agreement between the n' and n Q values at low frequencies and shear rates was i n d i c a t i v e of an uncross—linked polymer (Figure 47). The s i m i l a r i t y i n the two types of v i s c o s i t y i n t h i s region implied that the dynamic v i s c o s i t y values were also r e l a t e d l o g a r i t h m i c a l l y to the HEC polymer concentrations as depicted by Figure 42. The small differences (0.11 poise) observed between n_|_ and n for the 1% HEC dispersion, were considered n e g l i g i b l e . The v i s c o e l a s t i c properties of the aqueous HEC dispersions Xl, 2, 3 and 4% w/w) were a r e l a t i v e l y minor perturbation of the Newtonian f l u i d properties of the solvent. The HEC molecules were found to be uncross-1inked and to have intermediate s t i f f n e s s as described by the Harris and Hearst springy wormlike model. 3. V i s c o e l a s t i c Features of Hydroxyethylcellulose - Polyoxyethylene (4) Dodecyl Ether Systems The storage moduli for the most non-Newtonian HEC - B r i j 30 systems are shown i n Figure 48. With the a d d i t i o n of 8% B r i j 30 to the c e l l u l o s e polymer dispersion,tfche storage moduli increased dramatically to higher values at corresponding radian frequencies. The pronounced s h i f t plus a f l a t t e n i n g of the curves at radian frequencies l e s s than 0.5 s 1 indicated the presence of an increased e l a s t i c component. This e l a s t i c component disappeared at higher frequencies 1 0 0 oo o u < UJ X £ '2 OO o a •o v y c o i < z > 10 1.0 o . i 4 7<^HEC_ 3 % ^ H E ^ 2 % HEC l 7 Q H E C 0,01 0.01 FIGURE 47. o . i 1.0 RAD IAN F R E Q U E N C Y 1000 10 1 0 0 and SHEAR R A T E ( s"1 ) Dynamic and steady shear viscosity relationship for 1, 2, 3 and 4% HEC dispersions (T = 23.0 ± 0.5°C) 162 0.01 0.1 1.0 RAD IAN F R E Q U E N C Y ( s - 1) FIGURE 48. Storage modulus as a function of o s c i l l a t o r y frequency f or 4% HEC plus 0, 8, 12 and 16% B r i j 30 (T = 23.0 ± 0.5°C) 163 because the HEC and HEC - B r i j 30 storage moduli assumed s i m i l a r shapes and appeared to approach each other. Similar changes i n v i s c o -e l a s t i c properties were noted when B r i j 30 (8, 12 and 16%) was added to the 2.0 and 3.0% w/w HEC dispersions. At low radian frequencies, the l o s s moduli of the 4% HEC -B r i j 30 dispersions were not longer d i r e c t l y proportional to the radian frequency as described by Equation (65) (Figure 49). This proportion-a l i t y region, c h a r a c t e r i s t i c of v i s c o e l a s t i c l i q u i d s and evident f o r the HEC dispersions without B r i j 30 (Figure 45), now t h e o r e t i c a l l y would occur at lower frequencies than were measured. The f l a t t e n i n g of the HEC - B r i j 30 loss moduli curves showed the presence of an increased e l a s t i c component due to the addition of B r i j 30. At the low frequencies and shear rates measured, the dynamic and steady shear v i s c o s i t i e s s t i l l coincided f o r 4% HEC + 8% B r i j 30 and 3% HEC + 12% B r i j 30. This correspondence indicated that the systems were not cross-linked. There was a progressive divergence i n the dynamic and steady shear r e s u l t s f o r 3% HEC + 16% B r i j 30, 4% HEC + 12 and 16% B r i j 30 over the same frequency and shear rate range (Figure 50). The large divergence noted for 4% HEC + 16% B r i j 30 may be due i n part to experimental errors. I t i s expected that the two v i s c o s i t y parameters of the 3% HEC + 16% B r i j 30 and the 4% HEC + 12% B r i j 30 systems would also converge at lower frequencies and shear rates than were measured. This p r e d i c t i o n was made because the general shape of the storage and l o s s moduli parameters was s i m i l a r to uncross-linked v i s c o e l a s t i c polymers (Ferry, 1970). 164 FIGURE 49. Loss modulus as a f u n c t i o n of o s c i l l a t o r y frequency f o r 4% HEC plus 0, 8, 12 and 16% B r i j 30 (T = 23.0 ± 0 . 5 ° C ) FIGURE 50. Dynamic and steady shear v i s c o s i t y r e l a t i o n s h i p for selected HEC and B r i j 30 systems 166 The loss tangent or consistency spectrum (Davis, 1971a) was. also examined for the HEC and HEC - B r i j 30 systems (Figure 51). The logarithmic tan $ - radian frequency r e l a t i o n s h i p for the 4% HEC -B r i j 30 dispersions coincided f o r a l l three B r i j 30 concentrations therefore, the energy l o s t and stored for each cycle of deformation can be assumed to be independent of the surfactant concentration a f t e r the f i r s t a ddition. Comparison of the loss tangent curves for 4% HEC and 4% HEC + B r i j 30 revealed pronounced e l a s t i c behaviour i n the presence of B r i j at radian frequencies l e s s than 0.-3 s \ Increasing the HEC concentration from 3 to 4% w/w i n the presence of the surfactant caused a radian«frequency-sensitive increase i n the loss tangent (Figure 51). ; Examination of the loss tangent over a range of frequencies i s of i n t e r e s t because i t has the p o t e n t i a l of providing information on the destructive, non-destructive or v i s c o s i t y - i n d u c i n g e f f e c t s of various formulation additives upon macroscopic r h e o l o g i c a l properties. The introduction of a pronounced e l a s t i c component, evident at low radian frequencies, into the HEC dispersions when B r i j 30 was added indicated that the hydrated HEC molecules were i n t e r a c t i n g with B r i j 30 or i t s micelles (cmc = 0.0055% w/w) to form a loose three-dimensional network. The presence of a l o o s e l y bonded network rather than c r o s s - l i n k i n g would explain the shear-sensitive viscous i n t e r a c t i o n observed i n Section I I . A. 5. 0.05 0.1 05 1. 5. R A D I A N F R E Q U E N C Y ( s " 1 ) FIGURE 51. Consistency spectrum or los s tangent of selected HEC and HEC - B r i j 30 systems 168 SECTION I I I . LIMITING VISCOSITY AT LOW SHEAR RATES AND HYDROCORTISONE DIFFUSION INTRODUCTION Davis (1971) noted a s c a r c i t y of data r e l a t i n g r h e o l o g i c a l properties to drug b i o a v a i l a b i l i t y . Khristov (1969) observed a strong c o r r e l a t i o n between the r h e o l o g i c a l parameters of a complex ointment base and the r a t e of l i b e r a t i o n of incorporated drugs. Relationships between decreasing v i s c o s i t y and an increase i n drug release rate were also described for complex calcium soap-liquid paraffin-hydroxypropyl-methylcellu-lfbse-water and polyethylene glycol-hydroxypropylmethylcellulose-water systems (Khristov et a l . , 1969 and 1970) Linear r e l a t i o n s h i p s , log n = 0.22 (%PPE) + 0.23, (66) a were observed between the release of s a l i c y l i c a c i d and the r e c i p r o c a l of apparent v i s c o s i t y f or a Plastibase system containing varying amounts of polyethylene (PPE) (Davis and Khanderia, 1972). The p l a s t i b a s e system did not e x h i b i t a l i m i t i n g Newtonian v i s c o s i t y region at low shear rates therefore, the v i s c o s i t y at the shear rates of d i f f u s i o n i s not known. Generally, experimental d i f f u s i o n studies involving membranes ignore the r o l e of v e h i c l e v i s c o s i t y at very low shear rates even though the study may be examining the e f f e c t of surfactants on drug d i f f u s i o n (Short and Rhodes, 1972). Therefore, a portion of the present work has attempted to i d e n t i f y the e f f e c t of a change i n l i m i t i n g v e h i c l e v i s c o s i t y at low shear rates on the d i f f u s i o n of hydrocortisone (HC) through a r t i f i c i a l and b i o l o g i c a l membranes. 169 EXPERIMENTAL 1. Determination of Solubility and Partition Coefficient for  Hydrocortisone The solubility of hydrocortisone at 25.0 ± 0.5°C was determined using an equilibrium solubility technique. An excess of hydrocortisone was tumbled mechanically with 100 ml of d i s t i l l e d water (pH = 6.5) in a water bath. Samples were withdrawn at 1, 3 and 4 days, f i l t e r e d through a 0.22 ym Millipore f i l t e r and diluted appropriately for analysis at 249 nm. FFrom the absorbance, the concentration of steroid in solution was calculated using Beer's law (Pernarowski, 1969). The absorptivity valueswas obtained,from the regression slope of the standard curve for HC in d i s t i l l e d water (Figure 52) . Triplicate samples were done. Preliminary experiments had shown that HC reached distribution equilibrium in the two phase octanol/water system within five days. Therefore, duplicate HC samples of 10 ml (20.4 mg/50 ml in water saturated octanol) were tumbled with 20 ml of d i s t i l l e d water (pH'= 6.5) for 5 days in amberbglassabpt't'les. After five days, the octanol and aqueous phases were allowed to separate, samples were withdrawn from both layers and centrifuged (1 h) to remove.any suspended droplets of the alternate phase (Leo et a l . , 1971). Absorbance of the aqueous samples at 249 nm was read directly. Octanol samples were diluted (1:50) for analysis at 245 nm,-(The standard curve is shown in Figure 53).). Partitionicoefficients were calculated from the ratio of octanol to aqueous concentration of HC. A second series of partition samples was done to explore the accuracy of analyzing the aqueous layer only thereby determining the 170 l .O U C O N C E N T R A T I O N ( lO~ 3 g I " 1 ) FIGURE 52. UV spectrophotometric standard curve f o r hydro-cortisone 171 FIGURE 53. UV spectrophotometric standard curve for hydrocortisone in octanol 172 amount of drug i n the octanol layer i n d i r e c t l y . T r i p l i c a t e samples of two separate volume r a t i o s (10 and 15 ml) of HC i n water saturated octanol (44 mg/100 ml) were tumbled with 50 ml of d e i o n i z e d - d i s t i l l e d water (pH = 6.5) for f i v e days i n amber glass b o t t l e s . The aqueous layer was separated, removed, centrifuged and analyzed d i r e c t l y at 249 nm. Ther amount iineitfre_;beit5mo:l^ , A = A - A \ (67) o AT W where A q was the amount of s t e r o i d i n the octanol layer (ugYyiiA^, the t o t a l amount of HC i n the system and A was the amount of HC i n the _w aqueous layer. The p a r t i t i o n c o e f f i c i e n t s obtained from the d i r e c t and i n d i r e c t methods were compared. 2. The Interaction of Hydrocortisone with Hydroxyethylcellulose To i s o l a t e the e f f e c t s of v i s c o s i t y on d i f f u s i o n from possible retardation of molecular movement due to extensive HC - HEC binding, i n t e r a c t i o n studies were done using an equilibrium d i a l y s i s technique (Kazmi, 1971). a) Membrane Preparation and Selection Three a r t i f i c i a l membranes commonly used i n equilibrium d i a l y s i s studies were prepared i n the following manner. Cellophane d i a l y z e r tubing was soaked i n d i s t i l l e d water, cut f l a t and then washed with several changes of d i s t i l l e d water. Nylon membrane was soaked (24 h) and washed with several changes of d i s t i l l e d water. Dimethylpolysiloxane membrane was washed thoroughly with a soap s o l u t i o n , 173 washed with several changes of d i s t i l l e d water and soaked i n d i s t i l l e d water (24 h). A l l membranes were pressed between absorbent paper to remove excess moisture. The prepared cellophane membrane was placed between the compartments of a two chambered d i a l y s i s c e l l (Appendix I I ) . Ten ml of a 0.25% w/w HEC so l u t i o n (no preservatives) was pipetted into one compartment of two c e l l s and 10 ml of d i s t i l l e d water was pipetted into the other compartment. The c e l l s were tumbled i n a water bath (23.0 ± • 0.5°C) and a f t e r 24 h, equal volumes of the solutions were pipetted from both sides of each c e l l . qThe samples were d i l u t e d (1:4) f o r analysis at 206 nm (blank = d i s t i l l e d water). The a b s o r p t i v i t y value was obtained from the regression slope of the standard curve for HEC i n d i s t i l l e d water (Figure 54). The prepared nylon membrane was placed between the compartments of a p a i r of d i a l y s i s c e l l s . Ten ml of d i s t i l l e d water was added to one compartment of each c e l l . Ten ml of a 82.2 mcg/ml HC" s o l u t i o n was added to the second compartment of one c e l l and 10 ml of a 25.4 mcg/ml HC i n 0.25% w/w HEC so l u t i o n (no preservatives) was added to the second c e l l . The c e l l s were tumbled i n a water bath (25.0 ± 0.5°C) and at i n t e r v a l s (44, 68, 135, 183h)y equal volumes of the solutions were pipetted from both sides of each c e l l . The absorbance was noted at 249 nm for the HC species (blank = d i s t i l l e d water and 0.25% w/w HEC i n d i s t i l l e d - w a t e r r e s p e c t i v e l y ) . This procedure was repeated with dimethylpolysiloxane membrane. 174 C O N C E N T R A T I O N ( l O _ 1 g I"1) FIGURE 54. UV spectrophotometric standard curve for hydroxyethylcellulose 175 b) Binding of Hydrocortisone with Nylon Membrane Hydrocortisone solutions of varying concentration were made i n d i s t i l l e d water. Twenty ml of HC sol u t i o n was pipetted into one compart-ment of the d i a l y s i s c e l l and 20 ml of d i s t i l l e d water was pipetted into the other compartment. Three glass beads were added to each compartment to ensure continuous s t i r r i n g during d i a l y s i s . The c e l l s were tumbled inaa water bath (23.0 ± 0.5°C) f or 4 days. Aliquots were taken from both compartments and, aft e r p r o p e r - d i l u t i o n , the HC concentrations were determined using UV\spectrophotometry. The percentage recovery was calculated to estimate membrane binding. c) Interaction of Hydrocortisone with Hydroxyethylcellulose Hydrocortisone solutions of various concentrations were prepared a s e p t i c a l l y inQs.25% w/w HEC (Stock solutions: 200.6 vig/ml HG i n 0.25% w/w HEC and 0.25% w/w HEC). The HEC dispersions were not preserved. Twenty ml of the HC i n HEC sol u t i o n was pipetted into one compartment of a two-chambered d i a l y s i s c e l l (rinsed with 70% EtOH and s t e r i l e d i s t i l l e d water) and 20 ml of s t e r i l e d i s t i l l e d water was placed in'the second chamber. The c e l l s were tumbled i n a water bath (23.0 ± 0.5°C) u n t i l the concentration of HC i n the receptor chamber was the same on two consecutive days (35 days) . Aliquots. were withdrawn from the receptor compartment, d i l u t e d appropriately with d i s t i l l e d water f o r analysis at 249 nm. Nylon membrane was used i n t h i s study and was prepared as p r e v i o u s l y described previously described. 176 3. Hydrocortisone - Hydroxyethylcellulose D i f f u s i o n Studies i n the  Presence of a Membrane Two membranes were used i n t h i s study, nylon membrane (pre-pared as previously described, Section I I I . 2.) and human autopsy epidermis (prepared as described by Scheuplein, 1965). The int e g r i t y , of the skin samples was determined by measuring the e l e c t r i c a l resistance a f t e r i t was mounted i n the d i f f u s i o n c e l l (Table XXII). The prepared membranes were sandwiched between the Teflon discs of the d i f f u s i o n c e l l (Appendix II) and clamped t i g h t l y i n place atop the ground glass surface of the receptor chamber, 8 ml of 0.9% w/v sodium chloride s o l u t i o n was pipetted into the lower chamber. The c e l l s were c a r e f u l l y inverted to d i s p e l any a i r bubbles below the skin surface. 0.3 g of the test dispersion (, lis yg/ml HC i n 1% w/w HEC or 11 / yg/ml HC i n 4% w/w HEC or10;8 yg/ml HC i n d i s t i l l e d water) was added to the donor 8 chamber and 0.1 ml of t r i t i a t e d HC s o l u t i o n (2.17 x 10 dmp/ml) was layered on to the surface of the upper r e s e r v o i r . Samples were occluded with a grease-edged cover s l i p and the side arm stoppered to prevent evaporation (T = 23 ± 1°C). 0.5 ml samples were withdrawn at convenient time i n t e r v a l s and added to 14 ml of Bray's s c i n t i l l a t i o n c o c k t a i l and counted i n the Nuclear Chicago Isocap 300 using the t r i t i u m program f or low quench samples as supplied by the manufacturer. The amount of HC. present i n the sample was calculated using a channels r a t i o technique i n conjunction with a quench correction curve (Figure 55). The receptor volume was renewed by the addition of 0.5 ml of normal s a l i n e . D i f f u s i o n curves were constructed -2 -1 for a l l samples and the rate of penetration (Js, yg cm h ) was 48 5 2 5 6 CHANNELS RATIO FIGURE 55. Quench cor r e c t i o n curve f o r (1, 2 H) C o r t i s o l , • 4% HEC and o d i s t i l l e d water 178 c a l c u l a t e d from the steady slope of the cumulative d i f f u s i o n - time 2 -1 p l o t (Figure 56). D i f f u s i o n constants (D, cm h ) were computed from J s = ^ L D _ C s ( 6 8 ) o where Km was the membrane-vehicle p a r t i t i o n c o e f f i c i e n t , C_s, concentrat ion d i f f e r e n c e of solute across the membrane, &_ was the membrane thickness (cm). Km was assumed to be 5 (Scheuplien and Blank, 1971). To check the i d e n t i t y of the r a d i o a c t i v e l y l a b e l l e d d i f f u s i n g s p e c i e s , samples of receptor f l u i d were subjected to t h i n layer chromatography i n two solvent systems (chloroform/absolute ethanol (90:10) and chloroform/acetone/acet ic a c i d (10 :8 :1) . At l e a s t 80% of the r a d i o a c t i v i t y was recovered from an area corresponding to the ' • value f o r ' c o l d ' HC : 0.63 - 0.72 f o r chloroform/absolute ethanol and 0. 75 - 0.79 f o r chloroform/acetone/ace t ic a c i d . Although some t r i t i u m exchange may occur during the per iod of the d i f f u s i o n process , the r a d i o a c t i v e compound penetra t ing the membranes was p r i m a r i l y HC. RESULTS AND DISCUSSION 1. Hydrocortisone S o l u b i l i t y and P a r t i t i o n C o e f f i c i e n t In the present work, 301 ug/ml (± 5 SD) was obtained f o r the aqueous s o l u b i l i t y of HC at 25.0 ± 0 . 5 ° C . This r e s u l t was i n e x c e l l e n t agreement wi th the 302 ug/ml r e s u l t of Short et a l . (1972); and a lso f a l l s w i t h i n the l i m i t s of 285 yg/ml (± 10% CV) found by Kabasakalian (1966). Macek ejt a l . (1952) obtained a s o l u b i l i t y value of 280 yg/ml f o r HC from shaking an excess of HC one hour p r i o r to a n a l y s i s . This i s the commonly quoted value but i t i s improbable that HC can achieve e q u i l i b r i u m 179 s o l u b i l i t y within one hour. An average p a r t i t i o n c o e f f i c i e n t of 33.65 was determined from measurement of the HC concentration i n both.the aqueous and octanol layers and 33.28 - 0.60 CL o c t r / from the i n d i r e c t method (Equation 67). These values agreed w e l l with each other therefore, i t was s u f f i c i e n t to determined, the octanol concentration i n d i r e c t l y . The experimental r e s u l t s were also i n excellent agreement with Flynn's p a r t i t i o n c o e f f i c i e n t i n d i e t h y l ether (Flynn, 1971) which had been converted by Leo et al_. (1971) to a corresponding octanol value of 33.88. 2. Hydrocortisone - Hydroxyethylcellulose Interactions Cellophane membrane was rejected as a su i t a b l e d i a l y s i s membrane for studying the i n t e r a c t i o n of HC with HEC because the 0.25% w/w HEC disp e r s i o n showed 90% e q u i l i b r a t i o n on both sides of the d i a l y s i s c e l l within 24hh. Although dimethylpolysiloxane membrane (DMPS) did not permit the transfer of HEG, i t was rejected also because of the extremely slow passage rate of HC. The passage rate of HC through nylon membrane was better than through DMPS and also nylon membrane did not allow the transfer of HEC. HC did not bind with nylon membrane. Within the errors of the experimental technique and a n a l y t i c a l emthod, HC d i d not i n t e r a c t with HEC therefore, t h i s was a good system to study the e f f e c t s of v i s c o s i t y upon the d i f f u s i o n of HC. 180 3. Influence of Lim i t i n g V i s c o s i t y at Low Shear Rates on the D i f f u s i o n  of Hydrocortisone i n Hydroxyethylcellulose Dispersions The following factors permit the i d e n t i f i c a t i o n of v e h i c l e v i s c o s i t y e f f e c t s on the release or d i f f u s i o n r a t e of HC: a) HC and HEC are both nonionic solutes b) HC does not bind with nylon membrane (Section I I I . 2) c) HC and HEC do not i n t e r a c t (Section I I I . 2) d) the HGcconcentration gradient i s constant e) two d i f f e r e n t types of membranes are used f) the veh i c l e s are aqueous solutions of uncross-linked polymers (Section I I . B. 2) and have a known v i s c o s i t y at the shear rates of d i f f u s i o n (Section I I . B. 1). An increase i n the l i m i t i n g v i s c o s i t y at low shear rates from 0.4 to 60 poise (Section I I . B. 1) resulted i n a 22% decrease i n the steady state penetration rate of HC ( J g ) through a r t i f i c i a l nylon membrane and a corresponding 19% decrease i n the passage rate through human autopsy epidermis at 23 ± 1°C (Table XXII). The s i m i l a r i t y i n the r e s u l t s using two membranes indicated that the decrease i n J was due to the increase s i n v e h i c l e v i s c o s i t y . •, . The e f f e c t of increasing v e h i c l e v i s c o s i t y on the d i f f u s i o n of HC through an a r t i f i c i a l nylon membrane i s shown i n Figure 56. The decrease i n slope with an increase i n v e h i c l e v i s c o s i t y indicated that the fl u x or the amount of drug transferred per unit time at steady state had! decreased. With human autopsy epidermis f o r a membrane, the cumulative Table XXII Comparison of ve h i c l e v i s c o s i t y e f f e c t s on the d i f f u s i o n of HC through nylon membrane and human autopsy epidermis Vehicle V i s c o s i t y (P) J g ± Range (yg cm 2 h 1 ) Vx) (b) 2 r E l e c t r i c a l Resistance (ohms) D , 2 -1. (cm sec ) nylon water 0.01 0.320 0.020a 7.7 0.984 - -1% HEC 0.40 0.258 0.001 6.3 0.998 - - • 4% HEC 60. 0.200 0.020 7.0 0.994 - -human autopsy water epidermis 1% HEC 0.01 0.40 0.059 0.037 26. 30. 0.995 0.997 90,000 110,000 1.4 x 10" 1 1 1.0 x 10" 1 1 4% HEC 60. 0.030 28., 0.994 90,000 0.8 x 10" 1 1 2 r e p l i c a t e s 182 1 % H E C 2 0 4 0 6 0 8 0 1 0 0 1 2 0 T I M E ( h ) FIGURE 56. Cumulative d i f f u s i o n of HC through nylon membrane from i a 11 yg/ml s o l u t i o n i n 1.0 and 4.0% w/w HEC dispersions and d i s t i l l e d water 183 d i f f u s i o n curves were i n the same order as noted f o r the nylon membrane (Figure 57). The lag times remained unaffected by the increase i n v i s c o s i t y but were influenced by the nature of the membrane. The lag time f o r the d i f f u s i o n of HC through the epidermis was four times longer than that f o r the nylon membrane. Also, the HC f l u x , J g , through nylon membrane was approximately s i x times f a s t e r than through epidermis (Table XXII). Since the thickness of both membranes was comparable, these two r e s u l t s may be due to diff e r e n c e s i n the p o l a r i t y of the membranes. The octanol/water p a r t i t i o n c o e f f i c i e n t (Section I I I . 1) and the Km (Equation 68) showed that the r e l a t i v e l y polar HC molecule was not s u f f i c i e n t l y l i p i d soluble to penetrate the epidermis r a p i d l y (Scheupleingand Blank, 1971) but should show an increased penetration through the more hydrophilic nylon membrane. The d i f f u s i o n c o e f f i c i e n t f o r HC dissolved i n water and pene-t r a t i n g hyman epidermis as calculated from Equation (68) was 100 times -13 greater (Table XXII) than the corresponding l i t e r a t u r e values, 3 x 10 2 -1 -13 2 -1 cm s noted by Scheuplein and Blank (1971), 0.68.x 10 cm s calculated -13 2 -1 from p a r t i t i o n data by L i e n and Tong (1973) and 4.8 x 10 cm s determined by Yotsuyangi and Higuchi (1972). The experimental temperatures for the above were not stated. The higher value determined i n t h i s study was explained by one, or a combination of, the following: i . a higher concentration gradient (Scheuplein and Ross, 1974), or, i i . i n s u f f i c i e n t l y i n t a c t epidermal sheets, or, i i i . aahhigher experimental temperature. 4 184 H 2 0 2 0 T IME ( h ) FIGURE 57. Cumulative d i f f u s i o n of HC through human autopsy epidermis from a 11 ug/ml s o l u t i o n i n 1.0 and 4.0% w/w HEC dispersions and d i s t i l l e d water 185 Although the calculated d i f f u s i o n c o e f f i c i e n t was s i g n i f i c a n t l y higher, t h i s does not i n v a l i d a t e the r e s u l t s because r e l a t i v e changes rather than absolute changes were examined. A portion of the noted decrease i n steady state f l u x with increasing v e h i c l e v i s c o s i t y may be explained by an estimated 1.8% decrease i n apparent molar volume with an increase i n HEC concentration from 1.0 to 4.0% w/w (Section I, A. 2). This decrease i n apparent molar volume i s i n d i c a t i v e of a corresponding decrease i n free volume or the number of av a i l a b l e positions for the d i f f u s i n g molecule i n the f l u i d . The amount of free volume i s a factor i n the d i f f u s i o n process whether the mechanism of d i f f u s i o n involves a p o t e n t i a l energy b a r r i e r (Eyring, 1936) or thermal motion (Alder and Hildebrand, 1973). It i s expected that the magnitude of the v i s c o s i t y e f f e c t s on HC d i f f u s i o n noted i n the presence of a membrane which i s rate l i m i t i n g to the transport process would be larger i n the absence of such a membrane. Theo r e t i c a l studies involving determination of the influence of v e h i c l e components on drug d i f f u s i o n should separate drug^-component absorption or adsorption e f f e c t s from any increase i n v e h i c l e v i s c o s i t y due to the addition of the component, i . e . a surfactant. 186 SECTION IV. SUMMARY AND CONCLUSIONS A. RHEOMETRIC STUDIES OF A MODEL SHEAR-THINNING SYSTEM 1. Material Characterization Because of the v a r i a b i l i t y i n materials due to commercial synthetic processes, HEC and B r i j 30 were characterized physico-chemically. The Mw of the HEC sample. (Natrosol 250G) was 86,000. Between 15 - 40°C, the density-temperature r e l a t i o n s h i p for 1.-3% HEC dispersions was described adequately by Equation (10), , » -BT d = A e , where 13 was numerically s i m i l a r to the thermal expansion c o e f f i c i e n t of water. The apparent molar volumes of these dispersions decreased with increasing c e l l u l o s e concentration. The Mn of B r i j 30 was determined to be 380 from vapour pressure measurements and 383 from nuclear magnetic resonance determinations. The -4 c r i t i c a l m i c e l l e concentration was 1.42 x 10 moles/l (Mn = 380, 23 ± 1°C). The surfactant was well resolved using gas l i q u i d chromato-graphy and the major polymerization products i d e n t i f i e d were i . dodecanol 6% i i . polyoxyethylene (n) dodecyl ether, where n = 1, 2, 3 and 4 i i i . tetradecanol 1% i v . polyoxyethylene (n) tetradecyl ether, where n = 1, 2 and 3. 2. Steady Shear Studies of P r a c t i c a l Importance 187 These studies were concerned with the r h e o l o g i c a l properties of HEC and HEC - B r i j 30 systems, the determination of rheometer-independent shear rate-shear stress parameters and the equivalence of r h e o l o g i c a l models. a) Repro d u c i b i l i t y and S t a b i l i t y of HEC and MC Dispersions For s i m i l a r consistencies, the preparation of HEC and MC dispersions was equally reproducible r h e o l o g i c a l l y . The decrease i n apparent v i s c o s i t y on prolonged storage was comparable. Both HEC and MC dispersions exhibited increases i n apparent v i s c o s i t y during the i n i t i a l storage period. The time required for the maximum increase was ascribed to the spacer e f f i c i e n c y of the substitutent or the degree of hydrophilic character of the substitutent. The power-law consistency index was re l a t e d to both storage time and HEC concentration (Equation 49). 4 94 m = K± - 0.01 t (HEC) . b) HEC - B r i j 30, A System with Rheological F l e x i b i l i t y The addition of Brij.30, a nonionic surfactant, to the HEC dispersions provided a r e l i a b l e means of obtaining a s e r i e s of systems showing predictable increments i n shear-thinning behaviour at each polymer concentration. Simply stated, the surfactant gave r h e o l o g i c a l f l e x i b i l i t y to the HEC dispersions without changing the type of steady shear flow properties. (y = 8,5 - 685 s."*"). 188 c) An Improved Rotovisko Shear St ress C a l i b r a t i o n Method The manufacturer's method and a method i n v o l v i n g the determination of shear stress c a l i b r a t i o n constants for each shear rate were compared for a series of shear-thinning f l u i d s . The l a t t e r method allowed determination of rheometer-independent shear stress and shear rate parameters to a s i g n i f i c a n t degree of non-Newtonian character. d) Limitations of Couette Rheometers i n Shear Stress/Shear Rate Determination of non-Newtonian Shear-Thinning Systems The determination of a shear stress c a l i b r a t i o n constant for each Rotovisko shear rate y i e l d e d shear rate-shear stress parameters which were rheometer-independent for shear-thinning f l u i d s with power-law parameters n >, 0.55 and m < 41.5. The Krieger-Maron shear rate equation (24) was more r e l i a b l e than the c a l i b r a t i o n equation (20) f o r t h i s rheometer. The r e s u l t s were rheometer independent for the Br o o k f i e l d f i t t e d with the SC-4 spindles when n ~& 0.81 and m^ 14.0. The Mooney shear stress and shear rate equations (Equations 27 and 28) were the most r e l i a b l e . The non-Newtonian region for shear rate-shear stress rheometer-independent r e s u l t s may be extended by the determination of shear stress c a l i b r a t i o n constants f o r each shear rate. e) Flow Models for Shear-Thinning Systems The modified Shangraw, Steiger-Trippi-Ory and power-law models were not s i g n i f i c a n t l y d i f f e r e n t and a l l accurately f i t the shear-thinning systems measured:(y = 8.5 - 685 s 1 ) . For a constant concentration, parameters of the flow models varied with the surfactant concentration. The 189 modified Shangraw parameters a_ and b_ followed l i n e a r and squared functions of B r i j 30 concentration r e s p e c t i v e l y , whereas the Shangraw parameter c_, the Steiger-Trippi-Ory parameters a_"_ and c_*_ and the power-law parameters m and n varied as the logarithm of B r i j 30 content. These curves may be used to obtain the flow parameters f o r HEC - B r i j 30 dispersions of composition within the range used i n t h i s experiment. 3. Rheometric Studies of a Fundamental Nature: Low Shear and Dynamic  Measurements a) Low Shear Rate Studies The 1 - 4 % w/w HEC dispersions exhibited a t h e o r e t i c a l l i m i t i n g v i s c o s i t y at low shear rates. This v i s c o s i t y was a function of polymer concentration (Equation 64), log n Q = log K 1 Q + L 1 Q log (HEC). The B r i j 30 i n HEC dispersions did not show a l i m i t i n g v i s c o s i t y region over the shear rate range measured. b) Molecular D i s p o s i t i o n of HEC The storage and loss moduli, dynamic v i s c o s i t y and loss tangent were computed from dynamic measurements f o r the 1 - 4 % w/w HEC dispersions. The loss moduli, were d i r e c t l y p roportional to radian frequency as described by Equation (65). The shape of the storage and loss moduli p l o t s were c h a r a c t e r i s t i c of a d i l u t e polymer s o l u t i o n i n which the v i s c o e l a s t i c i t y was a r e l a t i v e l y minor perturbation of the Newtonian behaviour of the solvent. The convergence of the dynamic and steady shear v i s c o s i t i e s at low radian frequencies and shear rates showed the absence of c r o s s - l i n k i n g . 190 In aqueous so l u t i o n , HEC resembles the springy-wormlike model of Harris and Hearst. This model represents a degree of s t i f f n e s s between the p e r f e c t l y f l e x i b l e bead-spring model and the r i g i d - r o d model of Kirkwood and Auer. c) V i s c o e l a s t i c Features of HEC - B r i j 30 Dispersions The storage and l o s s moduli, dynamic v i s c o s i t y and loss tangent were computed f or the 0 - 16% B r i j 30 i n 2 - 4% w/w HEC dispersion. At low frequencies, the storage and l o s s moduli f o r the HEC - B r i j 30 systems were not as s e n s i t i v e to changes i n radian frequency as were the HEC dispersions. This decrease i n s e n s i t i v i t y revealed the presence of a pronounced e l a s t i c component with the add i t i o n of B r i j 30 to the HEC dispersions. The general shape of the storage and loss moduli curves were s i m i l a r to uncross-linked polymers. The dynamic and steady shear v i s c o s i t i e s showed increased divergence with the three most non-Newtonian dispersions but i t was expected that these parameters would converge at lower frequencies and shear rates than were measured i n t h i s study. B. EFFECT OF LIMITING VISCOSITY AT LOW SHEAR RATES ON HC DIFFUSION The aqueous s o l u b i l i t y and octanol/water p a r t i t i o n c o e f f i c i e n t of hydrocortisone were determined to be 301 yg/ml (25.0 - 0.5°C) and 33.65, r e s p e c t i v e l y . HC d i d not bind with HEC within the l i m i t a t i o n s of the equilibrium d i a l y s i s technique and UV a n a l y t i c a l method. In the absence of drug-vehicle i n t e r a c t i o n s , and increase i n the l i m i t i n g v i s c o s i t y at low shear rates of an uncross-linked nonionic polymer from 014 to 60 poise resulted i n a 22% decrease i n the steady state f l u x of HC through a r t i f i c i a l nylon membrane and a corresponding 19% decrease i n the passage rate through human autopsy epidermis at 23 - 1°C. The s i m i l a r i t y i n the r e s u l t s using the two membranes indicated that the observed decrease i n J was due to the a l t e r a t i o n s of v e h i c l e v i s c o s i t y . 192 CONCLUSIONS The region of rheometer-independent shear rate-shear stress r e s u l t s f o r a range of shear-thinning f l u i d s was l e s s f o r the Brookfield Synchro-lectric (SC-4 spindles) than for the Haake Rotovisko (MV1 spin d l e ) . This r e s u l t f o r the Brookfield may be improved through the determination of a shear stress constant at each shear rate. The use of flow model parameters to describe a non-Newtonian flow curve and the construction of parameter - v i s c o s i t y inducing agent(s) concentrations graphs was advocated to f a c i l i t a t e product development, l i t e r a t u r e comparisons, q u a l i t y c o n t r o l measurements and consumer a c c e p t a b i l i t y assessments through objective measurements. Dynamic and low shear rate parameters provided a method of determining molecular d i s p o s i t i o n and f l u i d structure. HEC was observed to be a molecule with intermediate f l e x i b i l i t y i n aqueous s o l u t i o n and HEC -B r i j 30 systems has a pronounced e l a s t i c component at low frequencies which was i n d i c a t i v e of a loose three-dimensional shear-sensitive structure. In the absence of drug-vehicle i n t e r a c t i o n s , increased l i m i t i n g v e h i c l e v i s c o s i t y at low shear rates of an uncross-linked nonionic polymer decreased the steady state f l u x of hydrocortisone by s i m i l a r amounts through nylon membrane an human autopsy epidermis. 193 APPENDIX I MATERIALS 1. NATROSOL 250G, hydroxyethylcellulose ( l o t # 22201, Hercules Incorporated t Wilimington, Delaware). 2. METHYLCELLULOSE, 1500 cps ( l o t # 17316, B r i t i s h Drug Houses, Toronto, Ontario). 3. BRIJ 30, polyoxyethylene (4) dodecyl ether, t e c h n i c a l grade ( l o t # 5165B, I.C.I. America Inc., Wilimington, Delaware). 4. BRIJ 30 SP, polyoxyethylene (4) dodecyl ether, pharmaceutical grade ( l o t # 7078B, I.C.I. America Inc., Wilimington, Delaware). 5. METHYL p-HYDROXYBENZOATE, reagent grade ( l o t #38809, B r i t i s h Drug Houses, Laboratory Chemicals D i v i s i o n , Poole, England). 6. n-PROPYL p-HYDROXYBENZOATE, reagent grade ( l o t # 26922", B r i t i s h Drug Houses). 7. HYDROCORTISONE, l i e , 17a, 21-trihydroxy-4-pregnene-3, 20-dione, micronized free alcohol ( l o t # 45909, B r i t i s h Drug Houses, Toronto, Ontario). 8. CORTISOL (1, 2 - 3H) 5.5 mCi/mg, 98 + % pure radiochemically, supplied i n benzene/ethanol (9:1 v/v) sealed under vacuum (The Radiochemical Centre, Amersham, Bucks, England). A portion of the newly opened, t r i t i u m l a b e l l e d C o r t i s o l was chromatographed em activated s i l i c a g e l using two solvent systems: chloroform/absolute ethanol (90:10 v/v) and chloroform/acetone/acetic acid (12:8:1 v/v) to check for r a d i o a c t i v e degradation or reaction products. Two of the developed s t r i p s from each solvent system were 194 sectioned and counted (Dioxane s c i n t i l l a t i o n solvent, Cornish and and J u h l i n , 1969). Also a s t r i p from each solvent system was auto-radiographed. Although some t a i l i n g was apparent i n both solvent systems "(Figures 58 and 59)» the Rf values f o r the l a b e l l e d HC were comparable to those f o r 'cold' HC: 0 .63 - 0.72 for chloroform/absolute ethanol and 0.75 - 0.79 for chloroform/acetone/ a c e t i c a c i d . 9. POPOP, 1,4-bis J2-(5-phenyloxazolyl )J -benzene (Sigma Chemical Company, 3500 de Kalb Street, St, Louis, M i s s o u r i ) . 10. PP0, 2,5-diphenyloxazole (Sigma Chemical Company). 11. NAPHTHALENE, s c i n t i l l a t i o n grade (Kent Laboratories, 1292 F r a n k l i n Street, Vancouver, B r i t i s h Columbia). 12. GAS CHROMATOGRAPHY STANDARDS a) Octan-l-ol, s p e c i a l l y pure ( l o t # 1345810, B r i t i s h Drug Houses Chemicals Ltd.'} Poole, England). b) Decan-l-ol, s p e c i a l l y pure ( l o t # 1218340, B r i t i s h Drug Houses Chemicals L t d . ) . c) . Dodecan-l-ol, s p e c i a l l y pure ( l o t # 1197800, B r i t i s h Drug Houses-Chemicals L t d . ) . d) Tetradecan-l-ol, Baker grade ( l o t # 1 -8238, J.T. Baker Chemical Co,, P h i l l i p s b u r g , New Jersey). e) Hexadecan-l-ol, reagent grade ( l o t B2A, Eastman Kodak Co., Rochester, New York). f) Octadecan-l-ol, s p e c i a l l y pure ( l o t # 1062770, B r i t i s h Drug Houses Chemicals L t d . ) , 195 O r i g i n S o l v e n t F r o n J 3 FIGURE 58. Thin layer chromatogram of (1, 2 H) Cortisol. Solvent system, chloroform/absolute ethanol (90:10 v/v) 196 O r i g i n S o l v e n t F r o n t FIGURE 59. Thin layer chromatogram of (1, 2" H) C o r t i s o l . Solvent system, chloroform/acetone/acetic acid (12:8:1 v/v) 197 13. MEMBRANES FOR EQUILIBRIUM DIALYSIS STUDIES a) Fisher cellophane membrane (1 47/64 i n . f l a t width, Dialyzer tubing, Fisher S c i e n t i f i c Co., F a i r Lawn, New Jersey)1-b) Nylon membrane (0.0005 In. thick, Capran 77, A l l i e d Chemical Corp., Morristown, New Jersey). c) Dimethylpolysiloxane membrane (0.005 i n . thick, S i l a s t i c Sheeting, non-reinforced, 500-1, Dow Corning Corp., Medical Products D i v i s i o n , Midland, Michigan). 14. VISCOSITY STANDARDS Newtonian o i l s used i n rheometer c a l i b r a t i o n are l i s t e d i n Table XXIII, (Cannon Instrument Co., Boalsburg, Pennsylvania). Table XXIII /' V i s c o s i t y Standards Used i n Rheometer C a l i b r a t i o n o i l ' temp v i s c o s i t y designation 0 ,o„ s /T.«-» \ ( C) (Poise) S - 20 20.0 0.410 S - 200 25.0 3.936 S - 200 37.78 1.747 S - 60 20.0 1.467 S - 60 25.0 1.059 S - 600 20.0 20.66 S - 600 25.0 13.50 198 GENERAL PROCEDURE FOR THE PREPARATION OF HYDROXYETHYLCELLULOSE AND METHYLCELLULOSE DISPERSIONS Four hundred and f i f t y ml of d i s t i l l e d water (65 - 70°C) preserved with methyl and propylparahydroxybenzoates (Hoover, 1970) were trans-ferred to a Waring blendor.' The weighed HEC was added slowly into the vortex with the blendor on low speed and agitated f o r a t o t a l time, that depended upon the concentration of HEC (Table XXIV). The dispersion was q u a n t i t a t i v e l y transferred to a 1000 ml tared beaker and brought to 500 g t o t a l weight with 70°C preserved water. I t was then placed i n an i c e bath and s t i r r e d u n t i l i t cooled to below 20°C. The cold dispersion was r e f r i g e r a t e d (3°C) for 2 - 4 h p r i o r to b o t t l i n g . This procedure yielded clear,, stable dispersions. Table XXIV Blending time for HEC and MC dispersions Concentration (% w/w) Time Blended (sec) 1.0 105 1.5 120 2.0 135 2.5 150 3.0 165 3.5 • 180 4.0 195 199 16. GENERAL PROCEDURE FOR THE PREPARATION OF BRIJ 30 IN HYDROXYETHYL-CELLULOSE DISPERSIONS HEC dispersions were prepared as described under item 15 and aged for 1 day. Using a balance with a s e n s i t i v i t y of 10 mg, the B r i j 30 and HEC dispersions were weighed, combined and mixed u n t i l homogeneous. The r e s u l t i n g 70 or, 120 g samples were bot t l e d i n amber glass ointment j a r s because the e f f e c t of l i g h t on the dispersions was unknown. 200 SOLVENTS AND REAGENTS 1. Octan-l-ol (Fisher S c i e n t i f i c Company, F a i r Lawn, New Jersey). 2. p-Dioxane, s c i n t i l l a t i o n q u a l i t y (Mallinckrodt Chemical Works, St. Louis, M i s s o u r i ) . 3. Dioxane s c i n t i l l a t i o n solvent (Bray's Solution, Bray, 1960): Naphthalene. .60.0 gm PPO ......4.0 gm POPOP. .0,2 gm Methanol (absolute)...................100,0 ml Ethylene Glyco l ..................20.0 ml p-Dioxane.... .qs 1000.0 ml 4. Dioxane s c i n t i l l a t i o n solvent (Cornish and J u h l i n , 1969): PPO , , 7.0 gm POPOP..................... ....0.3 gm Naphthalene 100.0 gm p-Dioxane ,. qs 1000.0 ml 3 solvent f o r the (1, 2 H) Cortisol t h i n layer chromatography studies. 5. Receptor s o l u t i o n f o r the d i f f u s i o n c e l l s : Methyl p-hydroxybenzoate ..,.,...0.18 % w/v n-Propyl p-hydroxybenzoate... 0.02 % w/v Sodium Chloride... , ....0.90 %• w/v D i s t i l l e d Water qs 100.0 % w/v 6. Thin Layer Chromatography solvents a) Chloroform ,. 90 201 Ethanol (absolute) 10 b) Chloroform 12 • Acetone 8 Acetic Acid .1 7. Saturated preserved water Aicarboy of d i s t i l l e d water was heated to 80°C and the weighed preservatives (methyl p-hydroxybenzoate (0.26% w/v) and n-propyl p-hydroxybenzoate (0.04 % w/v)) were added gradually while stir r i n g . The stirring and heating were continued u n t i l a l l the preservative had melted. The preserved water was then allowed to cool. The excess parabens formed a hard white cake on the bottom leaving the solution clear. As the water was withdrawn, i t was.filtered through eight layers of cotton gauze. A l l fitti n g s used on the carboy were glass to decrease the possibility of microbial growth. The preserved water was diluted 1 in 2 prior to use. 8. Water saturated octanol and octanol saturated water were prepared by gently shaking water and octanol in a 1 l i t r e separatory funnel. The two phases were separated after standing 24 h. 9. Ethylene Glycol, analytical reagent (Mallinckrodt Chemical Works). 10. Solution of a Homologous Series of Alcohols for Gas Chromatography 0ctan-l-6i ...0.0467 g Decan-l-ol. .0.0497 g Dodecan-l-ol 0.0495 g Tetradecan-l-ol 0.0531 g Hexadecan-l-ol. .0.0504 g Octadecan-l-ol........................0.0470 g Methanol (absolute) qs 50.0 ml 202 APPENDIX II APPARATUS A. A n a l y t i c a l Equipment 1. BECKMAN DB-GT SPECTROPHOTOMETER and 10 inch l i n e a r recorder equipped with 1P28A photomultiplier, deuterium and tungsten sources (Beckman Instruments, Inc., F u l l e r t o n , C a l i f o r n i a ) . 2. BECKMAN IR-10 SPECTROPHOTOMETER recording spectra l i n e a r i n wave number i n the 4000 - 300 cm ^ range (Beckman Instruments Inc., F u l l e r t o n , , C a l i f ornia). 3. BECKMAN PREPARATIVE ULTRACENTRIFUGE, Model L2-65B, equipped with the Schlieren optics attachment (Spinco D i v i s i o n , Beckman Instruments Inc., Palo A l t o , C a l i f o r n i a ) . 4. CENTRIFUGE, Model SVB, (International Equipment Co., Boston, Massa-chusetts) for separation of l i p i d droplets suspended i n the aqueous layer during the octanol/water p a r t i t i o n c o e f f i c i e n t determination. 5. NUCLEAR CHICAGO ISOCAP/300, ambient temperature, automatic programming 133 l i q u i d s c i n t i l l a t i o n counter with Ba external standard (Nuclear Chicago, Des Plaines, I l l i n o i s ) . 6. ROSANO SURFACE TENSIOMETER, R o l l e r Smith P r e c i s i o n Balances (Federal P a c i f i c E l e c t r i c Co., Newark, New Jersey). 7. SKIN DIFFUSION CELL designed by Coldman et a l . (1969) and used f o r the v i s c o s i t y - s t e r o i d d i f f u s i o n studies. 8. SPECIFIC GRAVITY BOTTLES, 50 ml adjusted at 20°C, # 10655-50 and with thermometer, # 10669-50 (CENCO, Central S c i e n t i f i c Co. of Canada Ltd., Mississauga, Ontario). 203 9. TWO CHAMBERED PLEXIGLASS DIALYSIS CELLS, as described by Pa t e l and Foss (1964), f o r tbe s t e r o i d - polymer binding determination. 10. THIN LAYER CHROMATOGRAPHY was done using the Eastman Chromagram Developing Apparatus with sheets # 6061 and # 6060 which were activated at 100°C f or 20 min. immediately p r i o r to spotting and developing (Eastman Kodak Co., Rochester, New York). 11. VAPOUR PRESSURE OSMOMETER, Model 302B equipped with v a r i a b l e temperature c o n t r o l l e r (18575A) (Hewlett Packard, Avondale, Pennsylvania). 12. VARIAN GAS CHROMATOGRAPH/MASS SPECTROMETER SYSTEM, MAT 111, 70 ev, equipped 3% SE 30 on Varaport 80/100 mesh 6 f t . x 2 mm i . d . s t a i n l e s s s t e e l column, electron i o n i z a t i o n detector and Kompensograph and • O s c i l l o f i l L recorders (Varian MAT, 28 Bremen 10, Postfach, Germany). 13. VARIAN NUCLEAR MAGNETIC RESONANCE SPECTROMETER, Model HA 100, high r e s o l u t i o n , 100 Megahertz instrument (Varian Associates', Palo A l t o , C a l i f o r n i a ) . B. Balances 1. CENCO MOISTURE BALANCE, # 26675, f o r the determination of the moisture content of hydroxyethylcellulose (Central S c i e n t i f i c Co., Chicago, I l l i n o i s ) . 2. METTLER TOP LOADING, Model P(K) 1200, i n the preparation of the c e l l u l o s e and hydroxyethylcellulose - surfactant dispersions (Mettler Instruments AG, Zurich, Switzerland). 3. SARTORIUS, Model 2743, a n a l y t i c a l balance (Sartorius Werke AG, Gottingen, Germany). 204 C. Constant Temperature Baths 1. CANNON, Model Ml, c i r c u l a t i n g water bath f o r the c a p i l l a r y v i s c o -meters (Cannon Instrument Co., Boalsburg, Pennsylvania). 2. HAAKE, Model FE, c i r c u l a t i n g water bath for the Brookfield rheometer small sample adaptor (Gebruder Haake K.G., B e r l i n , Germany). 3. HAAKE, Model E-51, c i r c u l a t i n g water pump for temperature c o n t r o l l e d s o l u b i l i t y and p a r t i t i o n c o e f f i c i e n t measurements (Gebruder Haake K.G., B e r l i n , Germany). 4. MAGNI-WHIRL constant temperature bath f o r density measurements (Blue M E l e c t r i c Co., Blue Island, I l l i n o i s ) . 5. ULTRA-KRYOMAT, Model TK-30D, c i r c u l a t i n g water bath f o r the Weissenberg rheogoniometer and the Haake Rotovisko rheometer (Lauda Instruments, Westbury, New Jersey). D. Mixing Equipment 1. POWER STIR, Model 58, s t i r r e r for the preparation of preserved water (Eberbach Corp., Ann Arbor, Michigan). 2. WARING BLEND0RR, Model PB-5, i n the preparation of the c e l l u l o s e dispersions (Waring Products Corp., New York, New York). E. Recorders 1. MOSELEY AUTOGRAF, Model 7100A, two channel, 10 inch s t r i p chart recorder f o r tracing the Haake Rotovisko shear stress s i g n a l (F.L. Moseley Co., Pasadena, C a l i f o r n i a ) . 2. RECORDING OSCILLOGRAPH, Model 5-127, for recording the Weissenberg rheogoniometer o s c i l l a t o r y output ( B e l l & Howell Ltd., Consolidated 205 Electrodynamics, Basingstoke, England), 3. RIKEN, Model SP-H3, 10 inch s t r i p . c h a r t recorder for the Weissenberg rheogoniometer steady shear traces (Riken Design Co, Ltd., Tokyo, Japan). F. Viscometers 1. BROOKFIELD SYNCHRO-LECTRIC, Model LVT, powered by a general e l e c t r i c synchronous induction type motor. The instrument was equipped with a water-jacketed small sample adaptor and the SC-4 spindle se r i e s (D.W. Brookfield Ltd., Cooksville, Mississauga, Ontario). 2. CANNON-FENSKE ROUTINE VISCOMETER FOR TRANSPARENT LIQUIDS, Size 50, c a p i l l a r y viscometers c a l i b r a t e d at four temperatures (ASTM, 1968a and 1968b) (Cannon Instrument Co., Boalsburg, Pennsylvania)..'. 3. HAAKE ROTOVISKO, Model Ml, powered by a synchronous e l e c t r i c motor operating at 3000 rpm (Gebruder Haake K.G., B e r l i n , Germany). 4. WEISSENBERG RHEOGONIOMETER, Model R-18, equipped with steady and dynamic shear f a c i l i t i e s and an a i r bath f o r sample temperature con t r o l (Sangamo Controls Ltd., North Bersted, Bognor Regis, Sussex, England). 206 APPENDIX I I I COMPUTER PROGRAMS 1. General Co-variance Program 2. Modified Shangraw, Steiger-Trippi-Ory and Power-law Model Program * * r FORTRAN IV ;i CCM°ItER MAIN 09-06-73 09: 26: 51 PAGE 0001 0001 0002 0003 000^ CALL PLOTS DOUBLE PRECIS ION SX, SY, SXY, S XX, SXXC OR , SYYCOP... S XYCOR , SYY , AI, BI ,C I 0OURLE PRECISION XBAR,YBAR,A,B,REDZ,BPO,RPOZ,REPZ,GOA,GOB,GOC,GOE DOUBLE PRECISION RE SZ , GDF , GOG , GOH ,GC I , GO J ,GOK , GOL , GOM, GGN > : — 0C05 00 0 5 01 MENS ICN X(200),Y(200),AI(2 ) ,81(2),C K 2),N(2),RESS(2),REDS(2) , 10FRS(21 ,NAME<10),T(200),YB(2),YE(2),XB(21,XE< 2),YS( 2),YT( 2) 0007 000 3 000<5 YS(2)=9.77 Y T U ) = 1C. YT(21=9.7 ono 001 1 C NL = 2 RNL = HI * * * INSERT FORMAT CARD AND NP=NUMBER OF PAIRS OF DATA TESTED «** 2 0013 001 4 1 3 F0RMAT(F5.2,F5.4) N? = 40 FORMAT(//IX.I 3,10A4) 001 5 0016 001 7 3 FORMAT ( 13 ,10A4) DO ?<? KK=1,NP WRITE!6.11) 001 3 0019 00'0 11 FORMAT I1H1) NA = 1 OJ 100 J=1,NL 0021 0022 002 3 READ(5,3,END=89) N(J),(NAME! I) ,1 = 1,10) PRI^ IT 2,IN(J) , (NAME! 11,1 = 1,10) ) RN=N(J) 00 24 . 00 2 5 0026 NT=NA+N(J)-1 NIO = J SX = 0.0 • 0027 0023 0029 SY = 0 . 0 SXY = 0.0 sxx = o.o 0030 00 31 003 2 SXXCOR = 0.0 SYYCOR = C O SYY = 0.0 0033 0034 0035 DO 20 I=NA,NT REAC(5,1) Y ( I ) , X ( I ) SX = SX + X(I) 00 3 6 0037 003 8 S Y = S Y + Y ( I ) SXY = SXY + XII) * Y(I) SXX = SXX + X(I) * XII) 0039 004 0 0041 2 0 SYY = SYY + YI I) * Y11) XBAR = SX / RN YPAR = SY / FN 004 2 004 3 0044 SXYCQR = SXY - (SX * SY) / RN DO 30 I=N A,NT SXXCOR = SXXCOR + 1X!Il-XBAR1**2 004 5 004 6 004 7 3 0 SYYCOR = SYYCOR + (Y(I)-YBAR)**2 8 = SXYCCR / SXXCOR A = YPAR - B * XBAR 0048 004 9 0050 R=SXYCOR/DS0RT(SXXC0R*SYYC0R) SEY=DSORT((SYYCOR-8*SXYC0R)/(RN-2.)) DF=RN-1. 00 51 0052 00 5 3 RE OS(J)=B*SXYCOR RESS(J)=SYYCOR-REDS(J) DFRSI J ) =FA'-2. 0 00 5 4 0055 42 PRPIT 42, (N!0,A,B,SEY,P. ,DF I FORMAT ( / IX, A4 , 4 X , ' A=',F12. 5, 10X, • B= ' , F12. 5, 10X", * SEY= • , F 10.4 ,1 OX , • R 1=' ,F8 . 4,1 OX,•DF = <,F6.0) 1 FORTRAN IV G COMPILER 0056 0057 005 3 0059 A l ( JI 3 I ( J I CI ( J ) NZ=MT MAIN - SXXCQR ' = SXYCOR = SYYCOR 09-06-73 09:26:51 PAGE 0002 00 6 0 0 061 00.6 2 006 3 0064 0065 ,NZ 103 DT 10B I = NA, T( !)=X( I) . NN.\ = NA+1 NNZ=NZ-1 • 0 109 I = NNA,NZ IF ( Tl NA ). I .F.T ( I ) ) GO TO 109 0066 006 7 006 < 006? 0070 0071 007? 0073 00 7 4_ 007 5 007 6 007-7 007 9 0079 00 j 1 . 0032 00 3 3 00 3* .00 3 \ 003 6 008 7 OOPS 0039 0090 0091 0J92 0093 . 009 4 0095 00 9 6 0097 03 c 3 0099 010 0 0101 010 2 010 4 0105 010 6 0107 010 3 Oi 0 J_ oi i o 01 ! 1 011 2 109 TEl1P = T ( NA I T( NAI = T ( I I ,n 11 - r r v p cr -J T INUE 00 110 I=fJNA,NNZ IF 1 Tl NZ I.GE.TU ) ) GO TO 110 1 10 T='-1P=T(NZ') T(NZ)=TU ) J( I ) = TEMP CGNTIN'JE XBIJ)=T!NA) XE1J)=T(MZ) Y3(JI = A + 3*XB! J) YE(J)-A+B*XE(J) _CALL_S_YKROL (. 5,,YS( J) . .J4_»- J »?-•.t—ll C4LL SYMBOL (1 • , YT( J ) , . 14, NAM F , 0. , 40 ) NA=NT+1 100 CONTINUE SI'«EG C0P POOLED DATA SX = 0. __ _SY = 0. ' SXX = 0. SYY = 0. SXY=0.  SXXCOR=0. SYYCOl = 0. _SXYCOi=0. WT = NT 00 120 1 = 1 ,NT SX=3X*X( I )' 120 SY=SY*Y1 I ) SXX=SXX+X(I>**2 _SYY = SYY + Y< I )**2 SYY=SXY+X( ri*Y("i) X3AP.= $X/RNT YBA?. = ?.Y/RNT 130 SXYCOR=SXY-(SX*SY)/RNT 00 130 1 = 1,NT ' _SXXCCH=SXXCOR«-< X!I )-X6AR)**2 SYYe6V=SYYC0R + ("Y( l')-YBAR)**2 3TAW = SXYCCR/SXXC0P. A=YHA?.-BT AW*XBAR S=9TAH R=SXYCnR/OS0RT(SXXCOR*SYYCOR) 5 E Y = ^ S 0 R T 11 S Y Y C 0 R - B T A w * S X Y C 0 P.) / ( R N T - 2 . ) ) "OF = P.NT-T. 3E0Z=3*SXYCOR Rt SZ = SYYCOR-REOZ I ho ' O. i 00 FORTRAN IV G COMPILER MAIN 09-06-73 09:26:51 PAGE 0003 O i l 3 Oil 4 0115 43 OFRZ=RNT-2.0 PRINT 4 3,(A,8,5EY,R,OF) FORMAT!///12X,' SIMREG FOR POOLED DAT A'//9 X , ' A = • , F20. 5,10X , • 8= • , F20 1.5//.10X,'SCY-',F20.4.10X,'R='.F8.4,10X,1DF=',F6.0) i 1 • < ? 0116 0117 500 WRITE(6,500) FORMAT!///,30X,'COVARIANCE ANALYSIS' ) i 01 18 RPQ= ( 3 I (1 ) +81 ( 2 ) )/( A K 1 )+A I ( 2 ) ) ... . I 0119 RPOZ=BPC*IGI(1>+BI(21) i 0120 RE?Z=CI (J ) + CI< ?. I-RPDZ i 01 ? 1 GOE-n"RS(1)+DFRS(2) 0122 OFPZ = ;OE+I.O 0123 G0A=!RESS!1)+RESS(2)l/GOE i 01 1 4 r,riR-RFP7-RFSS-< 1 l-RESS! 2 ) 0125 GOOOOB/OCA 1 0126 01 ~> 7 610 WRITE!6,610) F - TRM iT ( / / . ? 0 X , • TEST FOR HOMOGENEITY OF RESIDUAL VARIANCES') 01 23 30L=REfS(11/DFRSI1) O i 2 9 G 1 M = RESS!2I/DFRS(2> 01 3 0 GPM-Gr.l /GC.M • 01 3 1 WRITE! 6,590)DFRS(i) ,DFRS(2) , G O N 0132 WRITE(6,t50) 013 3 5 50 FORMAT(//,20X,'TEST FOR SLOPES') 0134 WRITE(6,560) GOE.GOC 013 5 5 50 * F O R M AT ( 30X, 1 F , 1 / •, F 5. 0, ' = '.F15.31 01 3 6 WRTTFI6.570) 0137 570 FORMAT (//,20X , • TEST FOR LEVELS') 013 3 GOF=RFPZ/0FPZ 01 39 - G0G = R5SZ-REPZ 0140 G O H = G O G / G G F ' 01 41 WRITE(6,560) DFPZ.GOH 0142 WRITE 1 6,530) 014 3 5 30 FORMAT ( / / ,20.X,'OVERALL TEST') 0144 DFOT=OFRZ-GOE 0145 GOI=RESZ-RESS(11-RESSI2) • • 0146 G0J=GOI/DFOT 0147 GOK=GCJ/GCA 0143 WRITE!6,530)DFOT,G0E,G0K 014Q 590 FORMAT(30X,'F,•,F5.0,'/',F5.0,• = ',F15.31 015 0 CALL SCALE(X,NT,10.,XMIN,DX,11 0151 CALL SCALE!Y,NT ,10. ,YMIN.DY,1) 015 2 0^ 12 1=1,2 0153 XK(I)=(X3(Il-XMIN)/DX 01 5 4 X F ( I )= ( XE ! I l-XMIN)/DX 0155 Y E ( I )= ( Y8( I )-YM IN)/DY 0156 Y E I!I = (YE !I l-YMIN)/DY 01 5 7 12 CONTINUE • • 01 5 3 CALL \XIS<0.,0.,7HY VALUE,7,10.,90.,YMIN,DY) 01 59 CALL AXIS ( 0 . , 0 . ,7HX VAL UE ,-7 ,1 0. , 0. , XM IN , DX ) 0160 N Z = N( 1 ) D i 51 DO 13 1=1 , N Z 0162 13 CALL SYM30L (X (I ) ,Y (I),.07 , 1 , 0 . , - 1 ) 016? NA=NZ+1 01 6 4 DO 14 I = N A , NT 0165 14 CALL SYMBOL(X!I),Y(I),.07,2,0.,-1) 016 6 CALL PLOT f X8I 1) , Y B ( 1 ) , + 3) 0167 CALL ^LOT(XE(1) >YE!1 ) , + 2) 0163 CALL PLCT(X8(2),Y3(2),+3) V 0169 CALL PLOT(XE(2),YE(2),+21 FORTRAN IV G COMPILER MAIN 09-06-73 017 0 0171 017 2 017 3 CALL P L 0 T ( 1 5 . , 0 . , - 3 ) £8 COMTIMUE 89 PRINT 11 r.AI I 3I.CTN0 :  01 74 017 5 STOP END TOTAL MEMORY R=OU IR EMENT S 001R6C BYTES *.9 SECONDS 09:26:51 PAGE 0004 N 3 1—• ... o 62SEPT/72 ROTOVISK KR I EG YA + 8? 4= 1.31005 P= 0.59809 SEY = 0 . 0 2 Z 8 40SEPT/72 RHEOGCN HEC 2.0 + BRIJ S% YA 1.30452 B= 0.59861 SEY= 0.0133 S I MR EG FOR POOLED DATA 1. 30327 B= 0.59811 0.0196 R = 0.9988 DFS 101. COVARIANCE ANALYSIS TEST FOR HOMOGENEITY OF RESIDUAL VARIANCES F , 60 . / 38. = 2.918 ! TEST FOR SLOPES j — FTT7 93. = 0.003 j • -1 TEST FOR LE V E T S : F , l / 99. = 1.252 OVERALL TEST F , Z.I 98. = 0.621 :3a FORTRAN IV G COMPILER MAIN 08-31-71 17:46:58 PAGE 0001 0001 DIMENSION X( 60) ,Y( 60) ,YF(60) ,W(60) ,E1(3) , E2I3) , P (3 ) , MOO ) ,NAME (9 ) 0002 DIMENSION YSH(60),YPL(60),YST(60),YT(6C) ,V(60) ,Z(60) 0003 EXTERNAL AUX > 0004 EXTERNAL AUXPL J 0005 EXTERNAL AUXST < 0006 DATA NI ,WZ,EP/20, 0 .0 , 0. 0001/ 0007 1 FORMAT(I3,9A4) OC08 2 F 0 R M A T U H l , l X , 9 A 4 / / > 0009 3 FORMAT! 32X, 2F7. 2) 0010 4 FORMAT(//7X,'SHEAR STRESS SHEAR RATE •/19X,•ACTUAL FITTED' / ) 0011 5 FORMAT!//IX,•ROOT MEAN SQUARE ERROR OF ESTIMATE IN PARAMETERS'/) 0012 6 FORMAT! IX, 3G 1 5. 5) 0013 7 FORMAT!/ /7X, 1 SHEAR RATE SHEAR STRESS•/19X,•ACTUAL FITTED' / ) 0014 8 FORMAT! 1X,I2,3X,3F10.2> 0015 9 FORMAT!1H1) 0016 11 FORMAT(/IX,* SHANGRAW MODEL PARAMETERS') 0017 12 FORMAT(/IX,'POWER LAW MODEL PARAMETERS') 0018 13 F0RMATI//9X, 'SHEAR RATE',13X,'SHEAR STRESS VALUE S * /6X , 'AC TUAL ST 1GR-TPPI ACTUAL SHANGRAW POWER LAW'/) 0019 14 FORMAT! IX,12,2F10.2 ,3F12.2) 0020 15 FORMAT(/IX,'STEIGER-TRIPPI PARAMETERS') 0021 22 F()RMAT(5F12.2 ) 0022 DO 200 N0K=1,10 C023 ICO READ(5,1) N,NAME 00 24 PRINT 2 , ( NAME) ! 0025 DO 10 1= 1,N . j 0026 RE AD(5 ,3 ) Y ( I ) , X ( I ) 0C27 10 CONTINUE 0028 PRINT 11 i C SHANGRAW MODEL SECTION 0029 M=3 i 0030 P(l)=.05 i 0031 P(2)=760. j 0032 P(3)=.01 0033 CALL DPLOFIX, Y, YF.W, E l , E2,P,WZ,N,M, NI,NO,EP, AUX) ~ 0034 SHA=P(1) C035 SHB=P(2) 0036 SHC=P(3 ) 0037 PRINT 5 • 0038 PRINT 6,(E2( I ),I = 1,M) ' } 0039 PRINT 7 0040 'DO 20 1=1 |N i l 0041 PR INT 8,( I,XI I ) , Y ( I ) , Y F I I ) ) % 0042 20 YSH(I)=YF(I) C POWER LAW MODEL SECTION 0043 M=2 0044 32 PRINT 2,(NAME) 0045 PRINT 12 0046 DO 70 1=1,N 0047 V! I ) =ALOG (X ( I)') 0048 70 Z(I )=ALOG(Y(I)) Is 0049 P! l ) = 5. 0050 P(2)=.5 0051 CALL DPLOF! V , Z , YF , W,E 1 ,C2 , P , WZ , N , M, NI ,NO, EP, AUXPL ) 00 52 IF(ND.EO.O) GO TO 31 J FORTRAN IV G COMPILER MAIN 08-31-71 17:46:58 PAGE 0002 0053 C054 0055 PLM=P(1 ) PLN=P(2 ) PRINT 5 r 0057 PRINT 7 ) 0053 DO 30 1 = 1,N 0059 0060 YFtI)=P(1)*X(I)**P(2) PRINT 8 , ( I , X ( I ) , Y ( I ) , Y F t I ) ) 0061 30 YPL(I)=YF(I) 0062 31 CONTINUE C STEIGER-TRIPPI MODEL SECTION 0063 00 50 1=1,N • 0064 TEMP = X(I) • • _ 0065 X( I ) = Y( I ) 0066 50 Y( I) = TEMP 0067 PRINT 2,(NAME)" 0068 PRINT 15 0069 P( l )=3.E-6 0070 P(2)=l . 0071 CALL DPLQFtX,Y,YF,W,E1,E2»P,WZ,N,M»NI,ND,EP,AUXST) C072 STA=P(1) 0073 STC = P(2) »• 0074 PRINT 5 0075 PRINT 6 , ( E2 ( I ) , 1 = 1, M) 0076 PRINT 4 0077 DO 60 1 = 1,N 0073 PRINT 8 , ( I , X ( I ) , Y ( I ) , Y F ( I ) ) 0079 YST( I ) = YF( I) 0080 60 CCNT INUE 0081 PRINT 2 , (NAME) 5 00 3 2 PRINT 13 0083 DO 40 1=1,N 0084 WRITE (8,221 Y d ) ,YST( I) ,X( I I ,YSH( I ) ,YPL (I ) C035 40 PRINT 14, ( I, Y( I ), YST( I ) , XI I ) ,YSH(I) , YPL (I) I 0086 • ENOFILE 8 0087 17 FORMAT!/IX, 'A =• ,G16.6 , •B =• ,G16.6 , •C =' ,G16.6/) 0088 18 F0RMAT(/1X,'M = ' , G 1 6 . 6 » ' N =',G16.6/> 0089 19 FORMAT(/IX, 'A = ' , G 1 6 . 6 , ' C =' ,G16.6 / ) 0090 PRINT 11 0091 PRINT 17,(SHA,SH3,SHC) 0092 PRINT 12 • <3 0093 PRINT 18,(PLM,PLN) 0094 PRINT 15 . . . 0095 PRINT 19, (STA.STC) 0096 PUNCH 21, (NAME, SHA,SHB,SHC,NAME,PLM,PLN, STA, STC) 0097 21 FORMAT ( 9A4.3E11.5/9A4 , 4 E U .5 ) 0098 PRINT 9 0099 200 CONTINUE 0100 111 STOP .. . . . . . . 0101 END TOTAL MEMORY REQUIREMENTS 001546 BYTES N5 h-• 4 > COMP ILE TIME = 4.3 SECONDS FORTRAN IV G COMPILER AUX 08-31-71 0001 FUNCTION AUX(P,0,X,L) 0002 DIMENSION P(3),D(3) 0003 ECX=EXP(-P(3)*X) 0004 D(1) = X  00C5 D(2)=1.-ECX 0006 D(3)=P(2)*X*ECX 0007 AUX = P( 1 )*X+P( 2)*D( 2) .. 0008 RETURN 0009 END TOTAL MEMORY REQUIREMENTS 0001CO BYTES COMPILE TIME = . C.4 SECONDS 17:47:20 PAGE 0001 i o i i FORTRAN IV G COMPILER AUXST 08-31-71 17:47:21 PAGE 0001 0001 FUNCTION AUXSTtP,0,X,L> 0002 OIMENSION P(2) .D(2) 0003 0(1)=X**3 0004 Dl 2)=X  0005 AUXST = P(1I*(X**3)+P(2)*X 0006 RETURN • 0007 END TOTAL MEMORY REQUIREMENTS 00018C 8YT ES COMPILE TIME = ' 673 SECONDS o JON i FORTRAN IV G COMPILER . AUXPL 08-31-71 17:47:20 PAGE 0001 0001 FUNCTION AUXPL ( P , D, V, L ) 0002 DIMENSION P (2 ) ,D (2 ) 0003 D(1) = 1./P<1> 0004 D(2 )=V  0005 AUXPL=ALOG(P(1))+P(2)*V 0006 RETURN 0007 END TOTAL MEMORY REQUIREMENTS C0019E BYTES COMPILE TIME = 0.3 SECONDS SERIES A 2.01 + BRIJ 30 4.0? SHANGRAW MODEL PARAMETERS INTERMEDIATE ESTIMATES OF PARAMETERS, SUM OF SQUARES 0.500COE-01 760.00 0. 10000E-01 .._ 0. 18424E 07. 0.70706 253.95 0.10169E-01 13227. 0.7CS43 253.20 0. 10559E-01 13009. 0.71170 251 .33 0. 10686E-01 13004. 0. 712S1 C.71318 0.71331 0.71335 0.71336 250.76 250.55 250 .48 250.46 250.45 FINAL ESTIMATES OF PARAMETERS 0.71337 250.45 0. 10729E-01 0. 10743E-01 0. 10748E-01 0.10749E-01 0. 10750E-01 13004. 13003. 13003. 13003. 13003. NO OF ITERATIONS= 0.10750E-01 SUM OF SQUARES 13003. ROOT MEAN SQUARE ERROR OF ESTIMATE IN PARAMETERS 0.36264E-01 18.794 0.11583E-02 SHEAR RATE SHEAR STRESS ACTUAL FITTED 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 27 8.46 16 .91 25.37 42.93 70.28 94.28 27. 81 53.69 77.88 50.74 76.11 152.22 228.33 456.67 685.00 149.36 191.97 298.89 424.45 617.50 747. 50 141. 49 194.23 310.27 391. 81 574.37 738.94 456.67 228 .33 152.22 76.11 50.74 25. 37 611.00 418.60 289. 98 186.30 142.56 89. 10 574.37 391.81 310.27 194.23 141.49 77.88 16.91 8.46 . 8. 46 16.91 25.37 50.74 66.03 42 .31 43. 74 70.66 9 4 . 7 7 149.36 53.69 27.81 27. 81 53.69 77.83 141.49 76.11 152.22 228.33 456 .67 635.00 456.67 190.35 295.65 388.C5 56F. .75 703.62 568. 75 194.23 310.27 391. 81 574.37 738.94 574. 37 o f-i r- ro o> co o 00 (\J (M -d - OD »c • • • * • • o ,-< cr -j" f - m O -4" co *o i-t CO f - «£> a* CO CO ^ O >t O LO sC r— co cc vj- co o n i CM ~ * r - — m f \ i - i h ro CO CM sO O LA fM IT, M H ^ CO P 1 f i CO CO O 00 -4" M U -O O C ' O 1 fM r— m co r\i 0 s r> ~« O co f -vf o ffi *t OJ *o *o —< r~ -< ^- m f*- ^ CO CO .£ lO c *o -n <\j in r--vf IA ^ r-* co O1 ro ro ro ro ro f*- •—i t~- -t r— *~< • rsj co rn 0> ro co O H CO ^' H ro ro m r - m ro r - m o> co o »-< C M fM - j - oo O co O ^ r - ro r— M cr s i n (NJ ro - * <-» . >o co r - rj* ro *o O" -o —1 ro | r ^ r O L O - r ^ T r - i C O v J ' O O i n O l o ~ c o r v j r - - c o c o c o > 3 - C G y D ^ ' | (Ni p« r>- o r- ro rvt ro %o O O ro N co o i n -o © tn r\i m co tn f\i (\J sj O *f f\l O H tM ro i n >r >t -4- -j-N H f - H vOl f \ ^ r - <^  O 1 I r - co CT* o >r c i n i n SERIES A 2.OS + BRIJ 30 4.OS POWER LAW MODEL PARAMETERS INTERMEDIATE ESTIMATES OF PARAMETERS, SUM OF SQUARES 5.0000 0.50000 106.64 8.7441 0.65928 1.9333 10.404 0.65929 0. 10759 10.571 0.65929 0.94502E-01 10.572 0.65929 0-94502E-01 10. 572 0.65929 0.94501E-01 FINAL ESTIMATES OF PARAMETERS NO OF I TERATI ONS = 6 10. 572 0.65929 SUM OF SOU ARES 0.94501E -01 ROOT MEAN SQUARE ERROR OF ESTIMATE IN PARAMETERS 0.21414 0.45190E-02 SHEAR RATE SHEAR STRESS ACTUAL FITTED ' 1 8 .46 42.93 43.21 2 16.91 70. 28 68.21 3 25 .37 94.28 89. 13 4 50.74 149.36 140.76 5 76. 11 191.97 183.89 6 152.22 298.89 290.42 7 228.33 424.45 379.43 8 456.67 617. 50 599. 24 9 685.00 747.50 782.87 10 456.67 611 .00 599 .24 11 228. 33 413. 60 379.43 12 152.22 289.98 290.42 • -13 76.11 186.30 183.89 14 50.74 142.56 140.76 15 25 .37 89. 10 89.13 16 16.91 66.03 68.21 17 8.46 42.31 4 3. 21 18 a .46 43.74 43.21 19 16. 91 70. 66 68.21 20 25.37 94. 77 89.13 21 50.74 149.36 140.76 •„ _ . 22 76. 11 190.35 183.89 23 152 .22 295.65 290.42 24 228.33 3e8.05 379.43 25 456.67 568. 75 599.24 26 685.00 703.62 782.87 27 456.67 56e.75 599.24 28 228.33 371. 80 379.43 29 152.22 286.74 290.42 V . 30 76.1 1 184.68 183.89 J DiU f 31 50.74 140.94 140.76 32 25 .37 8 5.86 89.13 33 16.91 66. 81 68.21 34 8.46 41. 73 43. 21 35 8 .46 40.56 43.21 36 16.91 64. 80 68.21 < > — 37 25.37 88.29 89.13 38 50.74 144.99 1 40 . 7 6 39 76. 11 18 7. 92 183.89 40 152 .22 293.22 290.42 41 228.33 393.90 379.43 42 456.67 585. 00 5 99. 2 4 43 685 .00 724.75 782.87 44 456.67 574.92 599.24 45 228.33 381.88 379.43 46 152 .22 288.36 290.42 47 76.11 184.68 183.89 48 50.74 140.94 140.76 • 49 25 .37 86.67 89. 13 50 16.91 65. 19 68.21 51 8.46 40. 31 43.21 o |N3 r SERIES A 2.0? + BRIJ 30 4.0? STEIGER-TRIPPI PARAMETERS INTERMEDIATE ESTIMATES OF PARAMETERS, SUM OF SQUARES 0.300CCE-05 1.0000 0. 88696E 07 0.10233E-05 0.40905 14876. 0.10232F-05 0.40907 14876. FINAL ESTIMATES OF PARAMETERS 0.10232E-.05 0.40907 NO OF ITERATlONS = SUM OF SQUARES 14876. ROOT MEAN SQUARE ERROR OF ESTIMATE IN PARAMETERS 0.43342E-07 0. 15636E-01 SHEAR STRESS SHEAR RATE ACTUAL FITTED 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 42.93 70.2 8 94.2 8 8.46 16.91 25.37 17.64 29. 10 39.42 149.36 191 .97 298.89 424.45 617.50 747.50 50. 74 76. 11 152.22 223.33 456.67 685.00 64.51 85.77 149.59 251. 87 493.53 733.15 611.00 418.63 289.98 186.30 142.56 89.10 456.67 228.33 152.22 76. 11 50.74 25.37 483. 34 246.29 143.57 82. 83 61.28 37.17 66.03 42.31 43. 74 70.66 94.77 149.36 16. 91 8.46 8. 46 16. 91 25.37 •50. 74 27. 31 17. 39 17.98 29. 27 39.64 64.51 190.35 295.65 3B8.05 568.75 7C3.62 '568. 75 76. 11 152 .22 228. 33 456.67 685.00 456. 67 84.92 147.38 218.53 . 420.91 644 .27 420. 91 28 29 30 31 32 33 371.80 286.74 184.68 140.94 85.86 66.81 228.33 152.22 76.11 50.74 25.37 16. 91 204.68 141.42 81.99 60.52 35.77 27. 64. 34 41.73 8.46 17.14 35 40.56 8.46 16.66 36 64.80 16.91 26.79 37 88.29 25.37 36.82 38 144.99 50.74 62.43 39 187.92 76.11 83.66 o ' 40 293.22 152.22 145.74 41 393.90 228.33 223. 67 42 585 .00 456.67 444.16 43 724.75 685. 00 686.00 44 574.92 456.67 429.63 45 381 .83 228.33 213.20 46 283.36 152.22 142.49 47 184.68 76. 11 81.99 48 140.94 50.74 60.52 • 49 86. 67 25.37 36.12 50 65-19 16.91 26.95' 51 40.31 8 .46 16.56 -iro-SERIES A 2.0? • BRIJ 30 4.0% . — — . SHEAR RATE SHEAR STRESS VALUES • > — ACTUAL STGR-TRPI ACTUAL SHANGRAW POWER LAW 1 8.46 17. 64 42.93 , 27.81 43.21 2 16.91 29. 10 70.28 53.69 68. 21 3 25.37 39.42 94.28 77.88 89.13 4 50.74 64.51 149. 36 141.49 140.76 5 76.11 85.77 191.97 194.23 183.89 i 6 152.22 149.59 298. 89 310.27 290.42 7 228.33 251.87 424. 45 391.81 379.43 8 • 456.67 493.53 617.50 574.37 599.24 9 685.00 733. 15 747.50 ' 738.94 782.87 10 456.67 483.34 611.00 ' 574.37 599. 74 11 22 8.33 246.29 418.60 391.81 379.43 12 152.22 143. 57 289.98 310.27 290.42 13 76.11 82.83 186.30 194. 23 183. 89 14 5C.74 61.28 • 142.56 141.49 140.76 15 25.37 37. 17 89. 10 77. 88 89.13 16 16.<H 27.3 1 66.03 53. 69 63.21 17 8.46 17.39 42.31 27.31 43.21 18 8.46 17.98 43. 74 27. 81 43.21 19 16.91 29.27 70.66 53.69 68.21 20 25. 37 39. 64 94. 77 77.88 89.13 21 50.74 64. 51 149.36 141.49 140. 76 22 76. 11 84.92 190.35 194.23 183.89 23 152.22 147. 33 295-65 310.27 290.42 24 228.33 218.53 383.05 391.81 •379. 43 25 456. 67 420.91 568.75 574.37 599.24 26 685.00 6 44.2 7 70-3. 62 738.94 782.87 27 456.67 420.91 568.75 574.37 599.24 28 228.33 2 04.6 3 371.80 391.81 379.43 29 152.22 141.42 286.74 310.27 290.42 30 76.11 81.99 184.68 194.23 183.89 31 50.74 60. 52 14C. 94 ) 141.49 140.76 32 25.37 35.77 85.86 77. 88 89. 13 33 16.91 27.64 66.81 53.69 68.21 34 8. 46 17. 14 41.73 27.81 43.21 35 8.46 16.66 40. 56 27. 81 43. 21 36 16.91 26.79 64.80 53.69 68.21 37 25.37 36.82 88. 29 77. 88 89.13 38 . 50.74 62.43 144.99 141.49 140.76 • 39 76. 11 83.66 187.92 194.23 183.89 40 152.22 145.74 293. 22 310.27 290.42 41 228.33 223.67 393.90 391.81 379.43 42 456.67 444. 16 585.00 574.37 599.24 43 685.00 686.00 724.75 738.94 782. 87 4 4 456.67 429.63 ' 574.92 574.37 599.24 45 228.33 213. 20 381. 88 391.81 379.43 46 152.22 142.49 288.36 310. 27 290. 42 47 76.1 1 81.99 184.68 194.23 133.89 48 50.74 60. 52 140.94 141.49 140.76 49 25.37 36. 12 86.67 77.88 89.13 50 16.91 26.95 65.19 53.69 68.21 51 8 .46 16.56 40.31 2 7. 81 43.21 SHANGRAW MODEL PARAMETERS i A = 0.713369 B = 250.445 C = 0.1C7499E-01 I O POWER LAW MODEL PARAMETERS  M = 10.5720 N = 0.659286 STEICER-TRIPPI PARAMETERS 0.102324E-05C = 0.409069 -ts> (in J 226 REFERENCES ASTM (1968). 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