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Compaction of pharmaceutical powders on a high-speed rotary press Zhao, Jinying 2003

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COMPACTION OF PHARMACEUTICAL POWDERS ON A HIGH-SPEED ROTARY PRESS by JINYING ZHAO B.Sc, TIANJIN UNIVERSITY, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Faculty of Pharmaceutical Sciences) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 2003 © Jinying Zhao, 2003 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 or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) 1 1 ABSTRACT BACKGROUND The compression behavior of pharmaceutical powders has been previously shown to significantly influence the quality and commercial viability of a tablet formulation. The compression conditions have also been reported to affect the behavior of a tablet formulation. Formulations developed on small-scale analytical tableting machines may not work on high-speed rotary presses that are the most commonly used commercial presses. OBJECTIVE The overall objective of this research was to model the in-process compression behavior of pharmaceutical powders during high-speed compression based on viscoelastic theory and porosity-pressure relationships, which might provide an effective tool in characterization and prediction of the compression behavior of pharmaceutical powders. METHODS Five pharmaceutical materials with well-established compression properties were compressed using an instrumented Manesty Betapress under representative manufacturing conditions. Two methods were used to model the compression data. Firstly, the time dependent behavior of the materials was investigated based on viscoelastic models describing a continuous body. Secondly, the compression data were evaluated based on two mathematical equations describing powder densification process, namely the Heckel equation (a well-known equation in the field) and the Gurnham equation (a new model proposed for pharmaceutical powder compaction in this work). RESULTS AND DISCUSSION Modeling of the compression process using viscoelastic theory was not very successful. The measured stress-strain responses suggested that powder densification behavior instead of viscoelastic behavior dominates most of the Ill compression phase. Nonetheless, the behavior of two ductile materials under relatively low pressures displayed viscoelastic characteristics during their peak offset phase. However, the modeling results using powder densification equations seemed promising. Using results at peak pressure, linear relationships between pressure and porosity following the Gurnham equation were observed and the slopes of these linear plots were related to the compressibility of materials. Compared to the well-known Heckel equation, the Gurnham equation provided reasonable predictions for pure brittle materials and processed compounds, which has always been a limitation of the Heckel equation. CONCLUSIONS The results of this work seem to suggest that the powder densification approach is more appropriate in describing the compression process under current experimental setting than the viscoelastic approach. Moreover, the powder densification equation proposed in this work, the Gurnham equation, shows potential in modeling the behavior of pharmaceutical powders during high-speed compression. iv TABLE OF CONTENTS A B S T R A C T ii T A B L E OF CONTENTS iv LIST OF T A B L E S viii LIST OF FIGURES x LIST OF ABBREVIATIONS xiii A C K N O W L E D G E M E N T S xiv 1 INTRODUCTION. 1 2 B A C K G R O U N D 5 2.1 Tablet compression 5 2.1.1 Tableting equipment 6 2.1.1.1 High-speed rotary press 7 2.1.2 Tableting materials : 9 2.1.2.1 Materials used for direct compression formulation 10 2.1.3 Factors influencing compression properties of materials 14 2.1.4 Materials selected 16 2.2 Powder compaction behavior during tableting 17 2.2.1 Porosity-pressure functions 17 2.2.1.1 Heckel equation 19 2.2.1.2 Gurnham equation 22 2.2.2 Viscoelasticity during compression 24 2.2.2.1 Viscoelastic theory 25 2.2.2.1.1 Combination of elastic and viscous elements 25 2.2.2.1.1.1 Elastic elements 25 2.2.2.1.1.2 Viscous elements .27 V 2.2.2.1.1.3 Viscoelasticity 28 2.2.2.1.2 Time-dependent strain and stress relationship 29 2.2.2.1.2.1 Creep - stress control test 29 2.2.2.1.2.2 Stress relaxation-strain control test 32 2.2 2.1.3 Linear viscoelastic models 35 2.2 2.1.3.1 Maxwell model 36 2.2 2.1.3.2Voigt/Kelvin model 38 2.2.2.1.3.3 Standard linear model (SLM) 39 2.2 2.1.3.4 More complex models 40 2.2.2.2 Studies of viscoelastic behavior during compression 42 2.2.2.2.1 Creep study 42 2.2.2.2.2 Stress relaxation study 43 2.2.2.2.3 Viscoelastic behavior on a high-speed rotary press 44 2.2.2.2.3.1 Peak offset time as a viscoelastic indication 45 2.3 Significance of proposed study 49 2.4 Objectives 50 3 E X P E R I M E N T A L 51 3.1 Materials 51 3.1.1 Drug 51 3.1.2 Excipients 51 3.2 Equipment 52 3.2.1 Compression equipment 52 3.2.2 Balance 52 3.2.3 Rotronic Hygroscope BT 52 3.2.4 Digimatic Outside Micrometer 53 vi 3.2.5 Multipycnometer 53 3.3 Methods 54 3.3.1 Compression protocol 54 3.3.1.1 Preparation of the tooling for compression 54 3.3.1.2 Experimental setting 54 3.3.1.3 Compression procedure 54 3.3.2 Data collection 56 3.3.3 Data analysis 56 3.3.3.1 Determination of punch displacement 57 3.3.3.2 Determination of strain and strain rate 57 3.3.3.3 Viscoelastic modeling 58 3.3.3.4 Determination of the compact porosity 61 3.4 Statistical treatment of data 62 4 RESULTS 63 4.1 Viscoelastic modeling 63 4.1.1 Stress-strain relationship during compression 63 4.1.2 Best-fit models 66 4.1.3 Viscoelastic coefficients 72 4.1.4 Stress-strain rate relationships during compression 77 4.2 Porosity and pressure functions 79 4.2.1 Heckel analysis - pressure-porosity relationship during the compression phase 79 4.2.2 Gurnham analysis - pressure-porosity relationship at peak pressure 84 5 DISCUSSION 93 5.1 Characterization of viscoelastic behavior during high-speed compression 93 vii 5.2 Use of the Heckel equation in describing powder densification during high-speed compression 96 5.3.Use of the Gurnham equation in describing powder densification during high-speed compression 98 5.4 Comparing the Heckel equation and the Gurnham equation 105 5.5 Limitations of the study 107 5.6 Future studies 108 5.7 Conclusions 109 6 REFERENCES 110 V l l l Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 LIST OF TABLES Steps in different methods of tablet manufacture (Unit operations) 10 Directly compressible filler-binders 13 Relationship between material properties and compaction behavior 15 A summary of powder compaction equations based on applied pressure and compact volume relationship 18 Mass of each material required to achieve a given peak pressure. Each material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm 55 Viscoelastic models and their mathematic expressions (a) Fluid models; (b) Solid models 59-60 True densities of the materials used in the experiments 61 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 50 MPa 69 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 100 MPa 70 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 150 MPa 71 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 200 MPa 72 Calculated coefficients of the 4-parameter viscoelastic models for each material. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 50MPa 73 Calculated coefficients of the 4-parameter viscoelastic models for each material. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of lOOMPa 74 i x Table 14 Calculated coefficients of the 4-parameter viscoelastic models for each material. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 150MPa 75 Table 15 Calculated coefficients of the 4-parameter viscoelastic models for each material. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 200MPa 76 Table 16 Calculated and literature mean yield pressure values for each material. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm 83 Table 17 Two-sample t-test to compare the two means: (1) the mean of the Gurnham slope value for brittle materials - dicalcium phosphate (EM), lactose (LA) and acetaminophen (AC) and (2) the mean of the Gurnham slope value for ductile materials - microcrystalline cellulose (AV) and corn starch (CS) in this work 92 Table 18 Gurnham slope values of single component systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures 101 Table 19 Gurnham slope values of acetaminophen (AC) formulations compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures 102 Table 20 Gurnham slope values of calcium carbonate systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures 103 Table 21 Gurnham slope values of calcium carbonate systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures 104 Table 22 Comparing the mathematical descriptions and the information derived from the Heckel and Gumham equations 105 X LIST OF FIGURES Figure 1 A schematic representation of the compression process of pharmaceutical powders 2 Figure 2 A simplified illustration of a compression cycle on a rotary press 8 Figure 3 Schematic representation of Heckel equation describing compaction behavior 20 Figure 4 A Hookean spring 27 Figure 5 A Newtonian dashpot 28 Figure 6 Relationship between stress (a) and time (t) illustrating the stress history of a solid material, ao is the instantaneous stress at t=0. When t=ti, ao is instantaneously removed 30 Figure 7 The strain (s) response of an elastic material with a stress history as shown in Figure 6. eo is the instantaneous strain at t=0. When t=ti, the strain instantaneously returned to zero 30 Figure 8 The strain (• e) and strain rate (. s) response of a viscous material with a stress history as shown in Figure 6. e starts from 0 at t=ti> and increases to eo at t=U; £•= so from t=0 to t= ti, and drops to 0 after t=ti. 31 Figure 9 The strain (e) response of a viscoelastic material with a stress history as shown in Figure 6. eo is the instantaneous elastic strain at t=0. When t=ti, the strain has an instantaneously recovery corresponding to eo 32 Figure 10 Relationship between strain (e) and time (t) illustrating the strain history of a solid material, eo is the instantaneous strain at t=0 33 Figure 11 The stress (a) response of an elastic material with a strain history as shown in Figure 9. c?o is the instantaneous stress at t=0 33 Figure 12 The stress (a) response of a viscous material with a strain history as shown in Figure 9. An instantaneous stress response a=oo at t=0 34 Figure 13 The stress (a) response of a viscoelastic material with a strain history as shown in Figure 9. Go is the instantaneous stress at t=0 34 Figure 14 Maxwell model Maxwell model (subscripts s - spring, d - dashpot) 36 Figure 15 Voigt/Kelvin model (subscripts s - spring, d - dashpot) 38 Figure 16 Standard linear model (SLM) 40 xi Figure 17 Complex viscoelastic models (a). N Maxwell elements in parallel; (b). N Maxwell elements in series 41 Figure 18 Pressure-time curves for: 1-microcrystalline cellulose (Avicel PH102); 2-spray-dried lactose; 3-dicalcium phosphate (Emcompress). The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm 46 Figure 19 Pressure and punch displacement-time curves showing stress relaxation at constant strain and peak offset time for microcrystalline cellulose (Avicel PHI02). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm 47 Figure 20 Geometric illustration of the T S M punch head profile 48 Figure 21 A representative time-force curve for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 50MPa. This profile is based on one compression 64 Figure 22 Representative stress-strain plots for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each profile of a given peak pressure represents the averaged profile of ten replicate compressions 65 Figure 23 Representative viscoelastic modeling results of microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 150 MPa. The stress-strain data for the material were obtained using the averaged profile of ten replicate compressions. The data were then fitted to fluid models listed in Table 6 (a) using a non-linear regression method 67 Figure 24 Representative viscoelastic modeling results of microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 150 MPa. The stress-strain data for the material were obtained using the averaged profile of ten replicate compressions. The data were then fitted to solid models listed in Table 6 (a) using a non-linear regression method.. 68 Figure 25 Representative stress-strain rate plots for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each profile of a given peak pressure represents the averaged profile of ten replicate compressions. The time interval between each data point is 0.4ms 78 Figure 26 Representative Heckel plots for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each profile of a given peak pressure represents the averaged profile often replicate compressions 80 X l l Figure 27 An illustration of the linear portion of a Heckel plot for microcrystalline cellulose (Avicel PH 102-AV). This Heckel plot is of the material compressed at a peak pressure of 150MPa. The pressure range of the linear portion was required to satisfy the following conditions: (a) a linear regression analysis of the data points within the pressure range had an R 2 > 0.97, and (b) a further narrowing of the pressure range resulted in a slope change < 5% 81 Figure 28 Relationship between peak pressure and porosity at peak pressure for five materials. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each profile for a given material shows 20 data points corresponding to a single compression of 20 tablets of different weights 85 Figure 29 The Gurnham plot for acetaminophen (AC). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each data point is the averaged peak pressure result of ten replicate compressions at a given peak pressure. The error bar represents the standard deviation 87 Figure 30 The Gurnham plot for dicalcium phosphate (EM). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each data point is the averaged peak pressure result of ten replicate compressions at a given peak pressure. The error bar represents the standard deviation 88 Figure 31 The Gurnham plot for lactose (LA). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each data point is the averaged peak pressure result of ten replicate compressions at a given peak pressure. The error bar represents the standard deviation 89 Figure 32 The Gurnham plot for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each data point is the averaged peak pressure result of ten replicate compressions at a given peak pressure. The error bar represents the standard deviation 90 Figure 33 The Gumham plot for com starch (CS). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Each data point is the averaged peak pressure result of ten replicate compressions at a given peak pressure. The error bar represents the standard deviation 91 Figure 34 Representative time vs. stress, strain and strain rate relationships for microcrystalline cellulose (Avicel PH 102-AV). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 50MPa. This profile is based on ten replicate compressions. Pressure is used as the primary Y axis. Strain in this plot ranges from 0 to 0.205, strain rate ranges from 0 to 20.47 s"1 95 Figure 35 Gurnham slope values of various pharmaceutical materials compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures 100 x i i i LIST OF ABBREVIATIONS A C Acetaminophen powder AIC Aka ike ' s information criterion AV A v i c e l P H 102 (Microcrystalline cellulose N F ) CS Corn Starch L A Lactose E M Emcompress (Dicalcium Phosphate Dihydrate N F ) SLM Standard Linear M o d e l SRS Strain Rate Sensitivity TSM Tableting Specifications Manual PTFE Polytetrafluoroethylene a Stress e Strain s Second SD Standard deviation MPa Mega Pascal K N K i l o Newton xiv ACKNOWLEDGMENTS I would like to thank my supervisors, Dr. Bob Miller, for his understanding and guidance, for providing me this opportunity as well as the support that helped me finish this work; and Dr. Helen Burt, for her precious help on my thesis and my final seminar, I am very grateful to have her guide me through the final stage of my work. I would also like to thank the members of my research committee: Dr. Keith MacErlane (Chair), Dr. Kishor Wasan, Dr. Wayne Riggs (Faculty examiner), Dr. Anoush Poursartip for their support and feedbacks into this project. A special thanks is given to Dr. Poursartip, for all the discussions we had. Thank you for being such a great help and inspiration to this work. My thanks to my co-workers in the lab: Mr. Randy Oates, who developed the programs involved in this work, Ms. Akaash Singh, for her mental support always, and Mr. Alain Musende, for all the information we shared, and for being a such a nice person to work with. 1 INTRODUCTION Systematic studies of the compression properties of tableting materials began in the mid 1950s with the introduction of the instrumented tablet press (Armstrong, 1989), which was equipped for the measurement of punch forces and punch displacements. Various techniques have been developed to instrument tablet presses and achieve in-process measurements for the study of material behavior during the compression process. A successful tableting process starts with a powder blend and ends with a coherent compact. It involves the transformation of a discrete powder bed to a continuous solid body (for a schematic representation of this process, see Figure 1). To study this complex process, there have been two approaches widely reported in the pharmaceutical literature, namely, powder densification and viscoelastic determinations. In the powder densification approach, mathematical models are used to describe the change of porosity in a powder column as a function of the applied pressure. These models have been derived from other fields of industry for the study of pharmaceutical compression processes (Paronen and Ilkka, 1996). The Heckel equation is widely used to model powder densification and shows that the change of porosity within a powder column follows a first-order relationship with the applied pressure. However, there are inherent limitations to the use of this equation. It is an empirical equation and great variability in Heckel constants has been reported between studies using different presses or compression conditions (Sonnergaard, 1999). l o a B i—* I" CJQ !=» u a fa ps £*• o 3 3 & oo o D 0 ° n C D * SB l-t Cn C D -g CD 3 o C D 05 cn cn 3* o 3 3 B co > cn o cr C D 3 5 o' O i-t cn a> o H s§ C D s — • r-t-3 5-C D 3 6 O S 2? C D cn fa cr •§ C D 3 cn 3" C D O o C D cn cn 5' 3 O o C D X J cr o C D 3 o o < SB ET p •a X J 5" CTQ C D fa O 3" 3 Cu C D 3* C D 63 3 era 3 " C D C D X J P v; 3 O cr X J X J C D 3 Viscoelastic theory is also used to describe compression processes. Viscoelastic theory assumes that the powder column is a continuous solid body possessing both elasticity and viscosity. This theory has been widely used to describe the time dependent behavior observed in tableting (Lum and Duncan, 1999; Lum et al., 1998). However, characterization of the viscoelastic behavior of pharmaceutical powders during compression has been limited due to the complexity of events during the compression cycle and the difficulty in measuring punch displacement during the high-speed commercial compression process (Alderborn et al., 1996; Lum and Duncan, 1999; Paronen and Muller, 1987; Rippie and Danielson, 1981). Numerous theories and equations have been proposed to describe the material behavior during tableting processes (Alderbom et al., 1996). However, no single theory or mathematical description has provided a comprehensive analysis of the compaction process. Discrepancies in material parameters also exist in the literature (Jain, 1999; Krumme et al., 2000) due to different presses and compression conditions used by different research groups. Our research group has instrumented a commercial tablet press (Manesty Betapress) to enable the measurement of punch forces and punch displacements during high-speed compression. In this work, representative conditions of commercial tablet compression were used. Five single component pharmaceutical powders with well-established 3 mechanical properties and compression abilities were compressed. The goal of this project was to evaluate the compression behavior of these five materials and establish a model that would characterize and predict the compression behavior/mechanical properties of materials during high-speed compression. The approaches employed in this work were two-fold. Firstly, the stress strain relationships during compression were fitted to various viscoelastic models and secondly, the Gumham equation, which describes the expression of liquids from fibrous materials, was evaluated for its application in pharmaceutical powder densification. 4 2 BACKGROUND 2.1 Tablet compression Tablets are manufactured by powder compaction. Powdered ingredients are compressed into shaped solid masses through the use of pressure (Helena, 2000). At the beginning of the process, under relatively low pressure, particles move within the die cavity to occupy void spaces, resulting in a closely packed structure. When the pressure increases, particles undergo deformation (elastic-reversible or plastic-irreversible changes) and/or fragmentation (division into a number of smaller discrete fragments) to further reduce the volume of the powder bed within the die cavity (Nystrom et al., 1993; Train, 1956). A coherent compact may then be formed when the particles are brought into close proximity with each other and interparticulate bonds are formed (Wray, 1992). In practice, these phenomena, i.e. particle rearrangement, elastic/plastic deformation and fragmentation usually overlap each other during compression, e.g. the stages of packing and deformation/fragmentation may occur concurrently (Leuenberger and Rohera, 1986). The overlapping of these phenomena causes the complexity of the compression process, which is one of the reasons why empirical solutions are often found in tableting problems (Masteau and Thomas, 1999). 5 2.1.1 Tableting equipment Pharmaceutical tablets are usually produced by two types of tablet presses: single-punch eccentric presses and rotary presses. A single-punch machine produces tablets by single-sided compaction. In this type of machine, the upper punch moves up and down above the stationary die. The die, and the lower punch, remain in fixed positions during the compression of a tablet. After the tablet has been compressed the lower punch is raised to eject the tablet through the upper opening of the die (Watt, 1989). Rotary presses produce tablets by double-sided compaction. For this type of machine, many punch and die sets are fitted around the periphery of a turret. The lower punch tip remains in the die at all times while the upper punch tip is removed from the die during tablet ejection and die fill. As the turret rotates, the punch heads are brought in turn between a pair of stationary metal rollers. Passing between the rollers, the upper and lower punch tips are moving toward each other and exert a compressive force on the powder bed between them (Watt, 1989). Compared to single-punch presses, rotary presses are capable of being operated at very high speeds (some of them can compress as many as 14,000 tablets per minute), so almost all commercial tablet production is carried out on rotary machines. Single-punch presses are mostly used for development and formulation studies, where only a small amount of drug is available. However, due to the intrinsic differences between the two types of machines, 6 they have different punch speeds, force-versus-time and displacement-versus-time characteristics (Charlton and Newton, 1983; Watt, 1989). Materials do not necessarily perform equally well in the two types of machines. Problems may occur during scale-up operations, when a formulation developed on a single-punch press is transferred to a rotary press. Quality problems such as capping and lamination, as well as low tablet strength are encountered more frequently under high-speed conditions. Therefore a further understanding of the high-speed compaction process would be necessary to predict the compression behavior of pharmaceutical materials and prevent costly batch rejections. 2.1.1.1 High-speed rotary press Almost all commercial tablet production is carried out on rotary machines, on which a complete compression cycle usually occurs in less than 50ms. A compression cycle (Figure 2) on a rotary press can be divided into two phases: (i) the compression phase, when an appropriate volume of pharmaceutical materials in a die cavity is compressed between an upper and lower punch to consolidate the material into a single solid matrix; and (ii) the subsequent decompression phase, when the punches move apart and the compact is ejected from the die cavity as an intact tablet (Watt, 1989). 7 2.1.2 Tableting materials A tablet formulation is usually composed of active ingredients and excipients. Broadly speaking, there are two classes of drugs administered orally in tablet form. These are (1) drugs intended to exert a local effect in the gastrointestinal tract and (2) drugs intended to exert a systemic drug effect following their dissolution in the gut and subsequent absorption (Peck et al., 1989). In order to produce a satisfactory tablet dosage form having the desired drug release, acceptable physical and mechanical properties, and with a low production cost, therapeutically inactive components or excipients are required in almost all tablet formulations. Compressed tablets usually contain a number of excipients including: (a) diluents or fillers, (b) binders or adhesives, (c) lubricants and glidants, (d) disintegrants, and (e) miscellaneous adjuncts such as colorants and flavors (Ansel et al., 1999). Some excipients may have several functions, for example starch may be used as a diluent, a binder or as a disintegrant in the tablet formulation (Peck et al., 1989). Numerous studies have reported the tableting behavior of diluents since these materials frequently comprise the largest proportion of a tablet. Examples of such materials are: Lactose NF (hydrous, anhydrous or spray-dried) (Hwang and Peck, 2001b; Perales et al., 1994), Pregelatinized starch NF (directly compressible starch-Starch 1500) (Maarschalk et al., 1997; Mitrevej et al., 1996), Mannitol USP (Debord, 1987; Schmidt, 1983), Microcrystalline cellulose N.F.(Avicel) (Hwang and Peck, 2001a; Johansson et al., 1995; Roberts and Rowe, 1987) and Dibasic calcium 9 phosphate USP (Hwang and Peck, 2001b). 2.1.2.1 Materials used for direct compression formulation There are three methods of preparing pharmaceutical tablets, (a) wet granulation, (b) dry granulation, and (c) direct compression (Bandelin, 1989). These are outlined in Table 1. Wet granulation is the oldest and the traditional method of making tablets. However, compared to the wet granulation method, tablet production by direct compression offers economic advantages (Table 1) and its use has increased steadily over the years. 10 H p a* o o CD cn O 3 P Cu CU f t CTQ P 3 3 era cn O "I CD CD 3 CD cu era pi CD* CO 3 o* o ' p 3 o i-t CD CD 3 3' era cu era CO 3 3 ON a 3 era 3 o era CO 3 3 O 3 o o CO cn o I-I CD CD 3 5' era CD CO cn cn ON U> CD P -o « Q $ 3 a* i-t_ o ' CO 3 rt-CO 3 Cu Cu cn' 5' CD era •-I CO 3 > Cu Cu rt' 5' 3 3 Cu CD cn O O 3 XJ O Cu CD CZ3 O |-I CD CD 3 5' era 3 era cn 3* CD CD O EL CD* Cu cn 5" era 3 *-+ O cn 3* CD CD CD XJ CO i-i P rt o ' 3 3 Cu CD i-t cn O o 3 n o I l-t CD cn cn 5" 3 I era CD rt I: CD* cn H P a* o o XJ I-I CD O 3 3 era o " 5 CD Cu XJ o CU CD | - i CD Cu XJ O Cu CD 3 era 3 era i—i CD CU CD' 3 3 era o era cn P 3 Cu CD X a to 5 ' 3' era era o o era cn P 3 Cu CD X O CD' 3 K> i — £ *. £ 3 era o I era cn P 3 CU CD X o era P 3 3 era i-t P 3 3 H P a* CD XJ 3 Cu CD 3 3" O Cu p 3 3 |-^ P 1 o c 3 . O X) CD i-l P rt 5' 3 cn The simplicity of the direct compression process is obvious. However, before the sixties few materials possessed both the flow properties and the compressibility required by the process. The development of direct compression was only made possible when spray-dried lactose and some other directly compressible excipients were introduced into the pharmaceutical market in the sixties (Table 2). The introduction of the very effective filler-binder microcrystalline cellulose (Avicel PH) in 1964 raised the interest in the production of tablets by direct compression. It may be assumed that by the early nineties about 50% of all tablets were manufactured by direct compression in the United States (Bolhuis and Chowhan, 1996). In addition, special directly compressible forms of the active ingredients have been developed in cases when the drugs are moisture and/or heat sensitive (e.g., ascorbic acid) or when compression by wet granulation leads to weak tablets (e.g., acetaminophen). 12 Table 2 Directly compressible filler-binders (Bolhuis and Cho whan, 1996; Maarschalk and Bolhuis, 1998) Year Introduced Material Trade Name 1963 Spray-dried lactose 1964 Microcrystalline cellulose Avicel PH Anhydrous lactose Dicalcium phosphate dihydrate Emcompress Pregelatinized starch NF STA-Rx 1500 1967 Spray-crystallized dextrose/maltose Emdex 1982 Calcium sulphate dihydrate Compactrol 1983 y-Sorbitol Neosorb 1984 Tricalcium phosphate Tri-Tab 1988 a-lactose monohydrate with poly (vinylpyrrolidone) and crospovidone Ludipress 1990 a-lactose monohydrate and powdered cellulose Cellactose 1991 Modified rice starch Eratab 1992 Anhydrous 6-lactose and lactitol Pharmatose DCL 40 13 2.1.3 Factors influencing compression properties of materials The compression properties of the tableting materials are affected by both the properties of the constituent materials and the manufacturing process (Mattsson, 2000). Material properties such as particle size, particle shape, surface area, surface geometry, crystalline and/or hydrate forms, and moisture content have been studied and their effects on interparticulate bonding mechanisms and mechanical properties (Table 3) of tablets have been determined (Alderborn et al., 1996; Debord, 1987; Nystrom et al., 1993; Roberts and Rowe, 1987; Sebhatu et al., 1997). Process effects such as the compression speed, the type of press, the applied pressure and the dwell time (the time when the powder was under minimum vertical compression on a rotary press) have also been investigated for their influences on the tablet properties (Armstrong, 1989; Konkel and Mielck, 1997; Roberts and Rowe, 1985). These process factors mainly affect the time-force profile during the compression cycle (Armstrong, 1989). Hence, the bonding mechanisms and the mechanical properties of the powder particles as well as the compression conditions are critical factors for a successful compression formulation. This work is focused on the latter two factors. 14 Table 3 Relationship between material properties and compaction behavior (Roberts and Rowe, 1987) Description Consolidation Material behavior examples Brittle 1—I Fragmentation 1 — | Inorganics^ Moderately hard — | Brittle Ragrnentation some flow at contact points — | Paracetamol Brittle/ duetto — | Lactose | — | Ductile Less fracture more plastic flow — | Sucrose Soft ; — Ductile — Plastic flow | Ductile/ elastic - Elastic and plastic deformation Microcrystalline cetfulose — | Starch Very soft Highly visco-elastic Total plastic flow PTFE 15 2.1.4 Materials selected Five single component materials that have been extensively reported in the literature (Hwang and Peck, 2001a; Hwang and Peck, 2001b; Jain, 1999; Lin and Duncan, 1994) were selected in this work. 1. Acetaminophen (AC) is a poorly compressible drug and produces tablets that frequently cap or laminate (Lin and Duncan, 1994). Tablets can be successfully compressed when the drug is mixed with microcrystalline cellulose. 2. Microcrystalline cellulose (AV) is a good direct compression excipient. It has been reported to deform plastically (Hwang and Peck, 2001a; Kothari et al., 2002). 3. Corn starch (CS) by itself forms weak tablets. It has been reported to deform plastically and have a significant elastic recovery (Maarschalk and Bolhuis, 1998). 4. Lactose (LA) itself also forms weak tablets. It has been reported to fragment under pressure (Hwang and Peck, 2001b). 5. Dicalcium phosphate dihydate (EM) forms strong tablets and has been reported as a brittle material (Hwang and Peck, 2001b), i.e. a material which does not deform but rather fragments under pressure. The ability of the five excipients to deform in a plastic manner has been ranked as follows: CS > AV > AC > LA > EM (Rowe and Roberts, 1996). 16 2.2. Powder compaction behavior during tableting 2.2.1 Porosity-Pressure Functions Numerous mathematical models (Table 4) describing the change of porosity (e) in a powder column as a function of the applied pressure (P) have been derived and adopted from other fields of industry for use in pharmaceutical compression processes (Celik, 1992; Paronen and Ilkka, 1996; Stanley-Wood, 1983). A general sub categorization of the listed models could be achieved, if density p were to be replaced by porosity e in these equations. Equations 1-6 illustrate the exponential relationships between pressure, P and porosity, e expressed as P and In e; equations 7-13 and 18 illustrate the polynomial relationships between P and porosity e expressed as Pn and e; while equations 14-17, 19 also illustrate the exponential relationships between P and porosity e expressed as e and In P. Among these equations, equation 1 and 15 are the two simple equations describing linear relationships between P and In e (equation 1) and e and In P (equation 15). Equation 1 is the Heckel equation, which is the most widely used powder densification equation in pharmaceutical research. While equation 15, the Gurnham equation, was chosen as a novel approach for analysis of tablet compaction in this work. 17 Table 4 A summary of powder compaction equations based on applied pressure and compact volume relationship (Paronen and Ilkka, 1996) No. Equation Authors j l n Pi~ Pi = K p Athy, Shapiro, Heckel, Pc A Konopicky, Scelig 2 In ^ I * 2 — J = KPA Batlhauscn Pi \Pt ~ Pj 3 In ^ (Px ~ P \ = KPK Spencer 4 In — = KP\ Nishihara, Nutting Pi 5 In + K f—^—Y'1 = a P A Murray Pi \Pi - Pc/ 6 In — r c ~ P t 1 = In K a - (6 + c)P A Cooper and Eaton P« \P i ~ Pi / 7 ^ = 1 - K P ^ Umeya 8 P« = K P 1 Jaky 9 p c = K ( l - PfX Jcnike 10 P. - Pi = KP\!* Smith 11 P « - P i = ^ i s h a l c r 12 ^ i = ^ Kawakita P, 13 " L . Akcta P « \ P I - P I / 1 + K P A 1 „ . D Walker, BaTshin, pc Williams, Higuchi, Terzaghi 15 p c = K + a ln P A Gurnham 16 — = K — a ln P A Jones P. 17 — = K - a ln ( P A - b) Mogami Pc 18 P c - P i = KPApt + al „ P a . ) Tanimoto Pc \ P A + 19 P , ~ P i = ln ( K P A + b) Rieschel *p„ net density of powder; pH initial apparent density of powder, pt, density of powder under applied pressure PA; K, a, b and c are constants. 18 2.2.1.1 Heckel equation Heckel (Heckel, 1961a; Heckel, 1961b) introduced a first order equation for the densification phenomenon. The equation is ln(—-—) = kP + A (equation 1) 1 - D Where k and A are constants obtained from the slope and intercept of the plot ln(l/(l-D)) versus P, respectively, D is the relative density of a powder column at the pressure P (Figure 3). Since porosity e equals (1-D), the Heckel equation can also be written as ln(-) = kP + A. . „ (equation 2) e In his original work Heckel studied the densification of metal powders. A relationship between the slope, k and the yield strength of the material (Y) was proposed as k = Y / 3 (equation 3) The reciprocal of k was later defined (Hersey and Rees, 1971) to be the mean yield pressure (PY). Hence, the slope k is inversely related to the ability of material to deform plastically under pressure. Greater slopes indicated a greater degree of plasticity of materials. The constant A is a function of the initial compact volume and can be related to the densification during die filling and particle rearrangement prior to bonding. The initial curvature of Heckel plots (Figure 3) may be due to particle fragmentation, or particle rearrangement at low pressures. 19 Figure 3 Schematic representation of Heckel equation describing compaction behavior (Heckel, 1961b) CO O p r e s s u r e J 20 The effects of experimental conditions on the constants derived from the Heckel equation have been investigated (Celik and Marshall, 1989; Roberts and Rowe, 1985; Rue and Rees, 1978). Roberts and Rowe observed that ductile materials (which undergo considerable plastic deformation before reaching the break point) exhibited an increase in the yield pressure with increasing punch velocity, while brittle materials (tend to break easily without much deformation) did not exhibit any significant change. To reflect this time-dependent factor, a strain rate sensitivity (SRS) index was introduced SRS = ? Y 2 ~ ? Y 1 * 100% (equation 4) PY 2 where Py2 and Pyi are the main yield pressures at the velocities of 300 mm/s and 0.033mm/s respectively. Hence, materials that have high SRS index tend to deform by plastic flow. The Heckel equation has been used to relate the compression behavior of a powder column to the mechanical properties (ductile or brittle) of the compressed material (Paronen and Ilkka, 1996). The determined mean yield pressure value gives a general perception of the deformation tendency of a powder, which has been accepted in pharmaceutical practice. However, there have been several reports on the limitations of the Heckel equation (Ilkka and Paronen, 1993; Krumme et al., 2002; Rue and Rees, 1978; Sonnergaard, 1999; Sun and Grant, 2001). Sonnergaard has pointed out that the mean yield pressure determined by the Heckel equation, cannot be taken as the actual yield point of a compressed material. 21 Significant variation of the determined constants have been reported, e.g. the following values have been reported for the mean yield pressure of Avicel PH 101: 47.6 MPa (Roberts and Rowe, 1987), 84.4 MPa (Yu et al., 1989) and 104 MPa (Paronen, 1986). Moreover, reports have suggested that the Heckel equation should be used with caution for studies of multi-component powder systems (Ilkka and Paronen, 1993). 2.2.1.2 Gurnham equation Gurnham (Gurnham and Masson, 1946) introduced an equation for the expression of liquids from fibrous materials. Although it was included in Table 3, it has not been applied in the pharmaceutical field like some of the other equations. The reason to include it here will be clear in the later discussion. Gurnham proposed in his study that any increase in pressure, expressed as a fractional increase over the existing pressure, results in a proportional increase in the bulk density of the mass. where P is the applied pressure, AP is the increase in pressure, AD is the increase in apparent density based on solid weight and total volume and A is the constant. The equation in this form is suitable only for small changes and is better written in differential form ( A P ) =A(AD) (equation 5) P (equation 6) 22 If D is replaced by porosity e, the equation is dP -^-=-Ade (equation 7) The equation can be integrated to give the following arrangements: e =-a In P + b (equation 8) where a, b are constants. Gurnham reported a good fit for this equation for experimental data for cotton, wool, paper pulp, felt, sawdust, asbestos, sugar cane, and bagasse (both dry and soaked with water or oil). However, some deviations from the model were noticed for soaked materials, which might due to the interaction between the material and the liquid (Gurnham and Masson, 1946). 23 2.2.2 Viscoelasticity during compression It has been well established in the pharmaceutical literature that time dependent processes are involved in mechanisms of tablet formation (Morehead, 1992). Increased rates of tablet production may cause mechanical failures such as capping and lamination and may necessitate modifications to the tablet formulation. One of the reasons for the discrepancies in material parameters reported in the literature is also related to this time dependency. Changing the rate of production, or changing from one type of press to another (which usually changes the time over which the pressure is applied to the powder bed) can affect the quality of the resultant tablets (Little and Mitchell, 1963) and the parameters determined during their compression. Viscoelastic theory is the theory that has been widely used to describe this time dependent behavior observed in tableting (Lum and Duncan, 1999; Lum et al., 1998). Principles of viscoelasticity have been applied in investigations of the time-dependent behavior under controlled conditions (creep and stress relaxation) (Hiestand, 1977; Staniforth, 1987; Travers et al., 1983) or under the high-speed compression conditions (Dwivedi, 1991; Lum and Duncan, 1999; Paronen and Muller, 1987; Rippie and Danielson, 1981). 24 2.2.2.1 Viscoelastic theory Viscoelastic theory arose from the study of polymers. Polymers are described as viscoelastic because they can display the properties of both elastic solids and viscous fluids depending on the temperature or time scale of the experiment. More specifically, at temperatures below Tg, the glass transition temperature, the behaviour is predominantly elastic while above T g it is predominantly viscous or rubber-like; in the transition region both types of responses make significant contributions (Ward, 1971). All materials exhibit some viscoelastic response to the application of force. Wood, human tissue as well as metals at high temperature all display significant viscoelastic effects (Lakes, 1999). More recently, studies of viscoelasticity have been not only seen in pharmaceutical tableting (Celik and Aulton, 1996; Danielson and Morehead, 1983; Lum and Duncan, 1999; Lum et al., 1998; Malamataris, 1992; Malamataris and Rees, 1993a; Malamataris and Rees, 1993b; Paronen and Muller, 1987; Rippie and Danielson, 1981) but in pharmaceutical gels (Jones et al, 1997), blood (Vilastic Scientific, 2001) and bone (King et al., 2001) as well as foods and cosmetics (Gallegos C and Franco J.M., 1999; Martin R.Okos, 1994). 2.2.2.1.1 Combination of elastic and viscous elements 2.2.2.1.1.1 Elastic elements The elastic solid has a definite shape and is deformed by external forces into a new shape. On removal of these external forces it reverts exactly to its original form. The solid stores 25 all the energy that it obtains from the work done by external forces during deformation. This energy is then available to restore the body to its original shape when these forces are removed (Wineman and Rajagopal, 1999). In general, most engineering materials are described, for small strains, by Hooke's law of linear elasticity: stress a is proportional to strain e. In one dimension, Hooke's law is as follows: a = Ee (equation9) with E as Young's modulus (Elastic modulus). Hooke's law for elastic materials can also be written in terms of the elastic compliance J: s = Ja (equation 10) The elastic compliance is the inverse of the Young's modulus, E = — (equation 11) J The one-dimensional mechanical response of a linear elastic solid is often represented by a mechanical analog, a linear spring (Figure 4) 26 Figure 4 A Hookean spring 2.2.2.1.1.2 Viscous elements In contrast to the elastic solid, the viscous fluid has no definite shape and is forced to flow by external forces. There is dissipation of energy and irreversible shape changes, associated with the flow. The energy applied is used to overcome the energy barriers to flow and dissipates in the form of heat. Viscous flow is a time dependent process, where stress is associated with the rate of the strain (Flugge, 1967). Under low strain rates, Newton's law of viscosity is used to describe the mechanical behavior of viscous fluids: de a = ri ( ) (equation 1 2 ) dt where stress a is proportional to strain rate de/dt and n is the Newtonian viscosity. The one-dimensional mechanical response of a linear viscous fluid is often represented by a 27 mechanical analog, a linear dashpot (Figure 5). This dashpot is filled with fluid where the rate of movement of the piston is directly proportional to the viscosity of the fluid and the applied stress (Alyson, 2001). Figure 5 A Newtonian dashpot 2.2.2.1.1.3 Viscoelasticity A viscoelastic material is, as the name suggests, one that shows a combination of viscous and elastic effects. The viscous term leads to energy dissipation, while the elastic term leads to energy storage (Methven, 2001). Viscoelasticity therefore describes the case where a deformed specimen exhibits both viscous and elastic behavior through simultaneous dissipation and storage of mechanical energy. A viscoelastic material is characterized for its time dependent behavior. The stress strain 28 relationship of an elastic solid is time independent as shown in Hooke's law. However the stress strain relationship of viscous fluid is time dependent. A combination of elastic and viscous behavior thus results in a stress and strain relationship that depends on time. 2.2.2.1.2 Time-dependent strain and stress relationship The time dependent behaviors of viscoelastic materials are usually investigated under two conditions, constant stress and constant strain, which give rise to the two functions below (Methven, 2001): (a) Creep - The time dependent strain that accompanies a constant stress is called creep. (b) Stress relaxation - The time dependent stress that accompanies a constant strain is called stress relaxation. The result (strain/stress) of removing a stress or strain is called recovery. 2.2.2.1.2.1 Creep - stress control test Creep is a slow, progressive deformation of a material under constant stress (Lakes, 1999). Suppose a stress history as shown in Figure 6. The stress a is instantaneously increased to coat t=0 and held constant until it is instantaneously removed at ti. A comparison of the mechanical responses of elastic, viscous and viscoelastic material will be given in Figures 7, 8, 9 respectively (Wineman and Rajagopal, 1999). Figure 6 Relationship between stress (a) and time (t) illustrating the stress history of a solid material, oo is the instantaneous stress at t=0. When t=ti, Go is instantaneously removed. By definition, ideally, for an elastic material (Figure 7), strain, e, instantaneously rises to 80 and remains there until the stress is removed at time ti, s instantaneously returns to zero. This follows Hooke's law, a = E e. Figure 7 The strain (s) response of an elastic material with a stress history as shown in Figure 6. eo is the instantaneous strain at t=0. When t=ti, the strain instantaneously returned to zero. i S £0 0 1 I I 30 By definition, ideally, for a Newtonian fluid as shown in Figure 8 (The strain (• s) and strain rate (• «?) response of a viscous material) the material does not reach a fixed deformed state instantaneously. There is continued strain with a constant strain rate till the stress is removed at ti. At ti, the strain does not change, but the strain rate reduces instantaneously to zero. This follows Newton's law, a = n (ds/dt). Figure 8 The strain (• s) and strain rate (. s) response of a viscous material with a stress history as shown in Figure 6. e starts from 0 at t=ti, and increases to eo at t= ti; s= £o from t=0 to t= ti, and drops to 0 after t=ti. 8 0 31 By definition, ideally, for a viscoelastic material (Figure 9), strain,e, instantaneously rises to eo and continues to rise at a non-constant rate. This is a combination of elastic and viscous effects. At ti, there is some instantaneous strain recovery followed by non-linear recovery. Figure 9 The strain (e) response of a viscoelastic material with a stress history as shown in Figure 6. Eo is the instantaneous elastic strain at t=0. When t=ti, the strain has an instantaneously recovery corresponding to eo. 8 I s o 0 Creep is the continued strain or flow under constant stress. Elastic materials do not exhibit creep. Viscous materials have a constant rate of creep under constant stress. Viscoelastic materials exhibit time-dependent creep under constant stress. 2.2.2.1.2.2 Stress relaxation - strain control test Stress relaxation is the gradual decrease of stress when the material is held at constant strain (Lakes, 1999). Suppose a strain history as shown in Figure 10. The strain e is instantaneously increased to eo at t=0 and held constant. A comparison of the mechanical responses of elastic, viscous and viscoelastic materials will be given in Figures 11, 12, 13 respectively (Wineman and Rajagopal, 1999). 32 Figure 10 Relationship between strain (e) and time (t) illustrating the strain history of a solid material, eo is the instantaneous strain at t=0. J 0 0 t By definition, ideally, for a linear elastic solid (Figure 11), stress, a instantaneously increases to aoand remains constant. This follows Hooke's law a = E e. Figure 11 The stress (a) response of an elastic material with a strain history as shown in Figure 10. o"o is the instantaneous stress at t=0. 33 By definition, ideally, for a Newtonian fluid (Figure 12), a very large stress a is needed to produce the sudden shape change. If e is fixed at eo for t>0, a required to maintain eo reduces immediately to zero and remains zero at all times t>0. This follows Newton's law, a = n (de/dt). Figure 12 The stress (a) response of a viscous material with a strain history as shown in Figure 10. An instantaneous stress response G=CO at t=0. By definition, ideally, for a viscoelastic material (Figure 13), stress, a instantaneously jumps to some value oo. The stress required to maintain eo decreases gradually with time asymptotically to some value. Figure 13 The stress (a) response of a viscoelastic material with a strain history as shown in Figure 9. Go is the instantaneous stress at t=0. <70 0 t rj 0 t 34 Stress relaxation is the decrease of stress at constant strain. Elastic materials do not exhibit stress relaxation at constant strain. Viscous materials have an instantaneous relaxation. Viscoelastic materials exhibit time-dependent relaxation at constant strain. 2.2 2.1.3 Linear viscoelastic models Different combinations of elastic springs and viscous dashpots have been proposed to describe the viscoelastic behaviors observed in real life. Compared to the stress strain relationship of elastic solids and viscous fluids, a constitutive equation for viscoelastic materials should be more complicated than for either Hooke's law or Newton's viscoelasticity law. Thus a general differential representation that includes both viscous and elastic elements is given as (Ward, 1971) da d 2 a de d 2e Poa + P l — + P 2 7 T T - + . . . = q 0 B + q 1 — + q 2 7 T T - + ... (equation 1 3) The most general form of the above equation is Pa = Qe (equation 14) where P and Q are linear differential operators with respect to time. It is often adequate to represent the experimental data obtained over a limited time scale by including only one or two terms on each side of this equation. Model elements (elastic and viscous) are combined in various ways in an attempt to simulate real materials. The simplest models consist of a single spring and dashpot, which 35 are known as the Maxwell model and the Voigt/Kelvin model. 2.2 2.1.3.1 Maxwell model The Maxwell model has a spring and dashpot in series as shown in Figure 14 (Burcham, 1999) Figure 14 Maxwell model (subscripts s - spring, d - dashpot) = < Spring os = Ee < Dashpot a d = r|(de/dt) In the Maxwell model, each element carries an equal stress (a = a<j = as), while the total strain is the sum of each element (e = es+ ed). Hence, the total strain rate is the sum of the strain rate of the spring and the dashpot (de/dt = des/dt + dea/dt), according to Hooke's and Newton's law, de da a dt Edt -q (equation 1 5) if r|/E is defined as characteristic time t (it is called relaxation time in stress relaxation), then 36 _ de da a E = + — dt dt i (equation 16) where po =l/i, pi = 1 and qi=E. The Maxwell model reflects some aspects of stress relaxation in real solids but is unrealistic in creep. For stress relaxation, under constant strain, when de/dt = 0, equation 16 can be integrated to give the following form cf = c> (equation 17) But for creep, under constant stress, da/dt = 0, equation 15 is now = — (equation 18) d t T] which indicates that Newtonian flow is observed. This is not generally true for viscoelastic materials. 37 2.2 2.1.3.2 Voigt/Kelvin model The Voigt/Kelvin model has a spring and dashpot in parallel as shown in Figure 15. Figure 15 Voigt/Kelvin model (subscripts s - spring, d - dashpot) Spring a = Ee Dashpot a = r|(de/dt) In the Voigt/Kelvin model, both elements carry equal strain (s = 8 d = ss), the total stress is the sum of each element (a = as+ CM). Hence, according to Hooke's and Newton's law, d e a = E e + n (equation 19) d t if n/E is defined as the characteristic time i (it is called retardation time in creep), then —— = s + i (equation 20) E d t where po=l/E, qo=l, and qi = i . In contrast to the Maxwell model, the Voigt/Kelvin model predicts creep behavior well, but is inadequate for stress relaxation. For creep, under constant stress, when a = ao, equation 20 can be integrated into the following form 38 a o 1 - e (--) (equation 21) e = E Considering recovery, when a = 0, then s = o e (equation 22) For stress relaxation, under constant strain, when de/dt = 0, equation 20 is now (equation 23) E implying elastic behavior, which is inadequate to represent stress relaxation of a viscoelastic material. 2.2.2.1.3.3 Standard linear model (SLM) More realistic predictions of viscoelastic behavior can be achieved by extending these rather simple models to include more elements. In order to represent both creep and stress relaxation, at least two terms on each side of equation 13 must be retained, as the simplest equation will be of the form P o ^ + P i - 3 7 - = q 0e + Q. 4T (equation 24) dt dt The model that follows this equation is known as the standard linear model (Figure 16). The standard linear model provides an adequate representation of both creep and stress relaxation behavior of many materials. It has a Maxell model in parallel with a spring. 3 9 Figure 16 Standard linear model (SLM) l l l l l l l l l l l j l l l l l i l l l l l l E l E 2 The mathematical description of the above SLM is d a (equation 2 6) a + t dt where i = r\l E2, and po =1, pi = v, qo=/E, and qi = (Ei + E2)t. 2.2.2.1.3.4 More complex models To describe the behavior of real materials, more complicated models may be necessary. There are two ways of systematically building up more complicated models (Figure 17) (Ward, 1971). N Maxwell elements can be assembled in parallel (Figure 17 - a) or N in series (Figure 17 - b). 40 Figure 17 Complex viscoelastic models (a). N Maxwell elements in parallel; (b). N Maxwell elements in series The complex models can be mathematically described as a certain form of equation 13. Comparing equation 13 to equations 16, 20 and 24, when the models become more and more complex, more terms are added on either or both sides of the equation, which makes the solution more and more complicated. These models may be much more representative of real materials, but the Maxwell and Voigt/Kelvin models have simplicity as their advantage. 41 2.2.2.2 Studies of viscoelastic behavior during compression 2.2.2.2.1 Creep study Studies about the creep of pharmaceutical materials under constant stress have provided a demonstration of viscoelastic behavior. In 1975, Okada and Fukumori (Okada and Fukumori, 1975) examined the creep properties of several materials by maintaining a constant upper punch pressure on an isolated punch and die assembly for up to 10 hours. The thickness of the powder bed decreased and leveled off during this period of time, suggesting that the particles of these solids undergo some type of time-dependent deformation by flow under stress. Travers et al. (Travers et al., 1983) and Celik and Travers (Celik and Travers, 1985) used a hydraulic press and recorded creep as "strain movements", i.e. change in the height of the compact within the die, when the stress was maintained at a constant level for up to 60 s. Staniforth et al. (Staniforth, 1987) used a similar testing procedure to measure the creep behavior of microcrystalline cellulose in powders and granules with different moisture contents. In order to obtain constant stress during the tableting process, the creep compliance of pharmaceutical tablets has to be investigated on slow speed compaction equipment such as a hydraulic press or a rotary press under static conditions. Analysis achieved by the above methods is therefore based on conditions uncharacteristic in real tableting processes (Dwivedi, 1992). 2.2.2.2.2 Stress relaxation study During tableting it is generally easier to measure the change in pressure as a function of time, which is the case in stress relaxation (time dependent stress reduction under constant strain). So the analysis of the stress relaxation phenomenon has been employed much more often than creep analysis. The phenomenon of stress relaxation in pharmaceutical powders was first reported by Shlanta et al. (Shlanta and Milosovich, 1964) in 1964. They observed a decrease in punch stress with time for a number of pharmaceutical solids on an instrumented hydraulic press. Using a hydraulic press similar to the one used by Shlanta et al., Hiestand et al. (Hiestand, 1977) found that tablets made of materials, which showed slow stress relaxation, had a greater chance of failing by capping or lamination. Ho and Jones (Ho and Jones, 1988) studied the stress relaxation of a number of pharmaceutical materials on a modem compaction simulator. Casahoursat et al. (Casahoursat, 1988) developed a new method for estimating capping risks during compression, which was based on a comparison of stress relaxation behavior of materials. David et al. (David and Augsburger, 1977) were the first group to model the stress relaxation using a simple viscoelastic model, the Maxwell model. They studied four direct compression excipients, compressible lactose, dicalcium phosphate, compressible starch and microcrystalline cellulose. They determined a value they called "viscoelastic slope" for 43 each material. This value is inversely proportional to the characterization time (as described in Equation 16) of the Maxwell model. It has been found that the values of these four materials have the following order: compressible starch > microcrystalline cellulose > compressible lactose > dicalcium phosphate. Since the plastic deformation ability of the four materials follows the same order, it seemed to indicate that this "viscoelastic slope" value might be used to reflect the ability of the materials to undergo plastic deformation. However, Rees and Rue (Rees and Rue, 1978) later pointed out that the compression speed of David's work is far slower than real manufacturing speed and that the Maxwell model is inadequate in characterizing the performance of sodium chloride. 2.2.2.2.3 Viscoelastic behavior on a high-speed rotary press Paronen et al. (Paronen and Muller, 1987) studied the compression behavior of the four materials in David's work using a high-speed rotary press. The compression data for the whole compression cycle were fitted with a series of viscoelastic models. The determined best - fit model was an 8-parameter solid (four Voigt/Kelvin models in series), which consisted of 8 coefficients, i.e. pi , p2, P3 and qo, qi, q2, q3, q4- The viscoelastic coefficients calculated from the complex models were not constants characterizing single elements in the models. They were different combinations of several element constants as shown later in Table 6. It was suggested that certain coefficients of complex models (Table 6) be too complicated to be used as basic physical data to interpret material behaviors during the process. It was also suggested that it was very likely that only part of the compression 44 profile was valid for linear viscoelastic modeling. Danielson et al. (Danielson and Morehead, 1983) and Rippie and Danielson (Rippie and Danielson, 1981) studied the decompression and post compression phases (the phase after compression when the tablet is kept for some minutes in the die) of several pharmaceutical solids on a rotary press. Using force versus time curves from radial and axial load measurements and with displacement versus time functions deduced mathematically from the rotary machine's geometry, the stress-strain relationships were resolved and fitted to equations derived from three - dimensional linear viscoelastic models. However, some parameters determined turned out to be negative, which eluded physical explanations. 2.2.2.2.3.1 Peak offset time as a viscoelastic indication In 1991, Dwivedi, Oates and Mitchell (Dwivedi, 1991) provided the definition for peak offset time and pointed out that peak offset time could be taken as an indication of stress relaxation during tableting on a rotary tablet press. On a rotary press, the punches travel between the upper and lower rollers (Figure 2). It was assumed that the peak punch pressures occur at maximum punch displacement, where the punches are vertically aligned with the centers of the upper and lower compression rollers (dead center) (Figures 2 and 18). However, as shown in Figure 18, the peak punch pressures occur before the dead center. The time by which the peak pressure was set off from such an 45 alignment was called the 'peak offset time' (toff) (Figure 19). Several reports (Morehead, 1992; Morehead and Rippie, 1990) have indicated the same phenomena and attributed this toff to time-dependent viscoelastic behavior in the compression. Figure 18 Pressure-time curves for: 1-microcrystalline cellulose (Avicel PHI02); 2-spray-dried lactose; 3-dicalcium phosphate (Emcompress). The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm. (Dwivedi, 1992) Pressure (MPa) Line of -40 -30 -20 -10 0 10 Time (ms) 46 Figure 19 Pressure and punch displacement-time curves showing stress relaxation at constant strain and peak offset time for microcrystalline cellulose (Avicel PHI02). The material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. (Dwivedi, 1992) Time(ms) . o d A D CfeNTRE 47 Dwivedi et al. (Dwivedi, 1991) also suggested that peak offset time may occur as part of stress relaxation using TSM punches (Figure 20) on the Manesty Betapress. The TSM punches conform to the Tableting Specifications Manual of the American Pharmaceutical Association (Washington, DC). Due to the flat punch head, there is a short period of time when the punches should move horizontally along its flat punch head (the distance 1.270 cm in Figure 21). Hence, during this period of time, the compact was assumed to be under constant strain and showed the stress relaxation characteristic of a viscoelastic material. Figure 20 Geometric illustration of the TSM punch head profile (All dimensions are in Based on the above observation, a further investigation of these viscoelastic behaviors during the compression phase (Figure 2: from the start of compression to the dead center position) may reveal valuable material information. Moreover, by fitting these data to various viscoelastic models, viscoelastic constants may be determined, which could be used to describe and/or predict materials behaviors. cm) 2.540 0.794 R 48 2.3 Significance of proposed study Further understanding of the compaction behavior of pharmaceutical materials during the high-speed process could help to develop new models (based on viscoelasticity and/or porosity-pressure relationship) that may fulfill the requirement for a informative and robust characterization/prediction of the compressibility of powders in development and formulation as well as in quality control. These findings may also be carried forward for characterization/prediction of the compression behavior of granulations and pellets as well as powder mixtures. 49 2.4 Objectives The overall objective of this research was to model the in-process compression behavior of pharmaceutical powders during high-speed compression based on viscoelastic theory and porosity-pressure relationships, which might provide an effective tool in characterization and prediction of the compression behavior of pharmaceutical powders. Specific aims The specific aims of the proposed research were to: 1. Determine the stress-strain and porosity-pressure relationships of various pharmaceutical powders on a high-speed rotary press 2. Fit the stress-strain relationships to a series of viscoelastic models and determine the best-fit viscoelastic models to compression data on a high-speed rotary press 3. Calculate the viscoelastic coefficients of the determined best-fit models and correlate these coefficients to compression properties of materials 4. Evaluate the porosity-pressure relationships using the Heckel equation and the Gurnham equation and determine the appropriate constants 5. Compare how the Heckel equation and the Gurnham equation characterize and predict material behaviors during high-speed compression 50 3 EXPERIMENTAL 3.1 Materials Four common excipients and one drug were used as received. Materials were stored in closed containers under ambient conditions. 3.1.1 Drug Acetaminophen USP (AC): 3.1.2 Excipients Microcrystalline cellulose NF (AV): Starch NF (CS) Lactose NF (LA) Dicalcium Phosphate Dihydrate NF (EM) Powder, crystalline, 60% particles larger than 38 um (Mallinckrodt, St. Louis, MO, USA) Avicel PH 102, average particle size 90 pm (FMC Corporation, Philadelphia, PA, USA) Corn starch, average particle size 5 pm (Stanly Pharmaceutical, North Vancouver, BC) Hydrous, average particle size 100 pm (Kraft Inc, Norwich, NY, USA) Emcompress, average particle size 100 pm (Edward Mendell, Patterson, NY, USA) 51 3.2 Equipment 3.2.1 Compression Equipment A Manesty Betapress (Manesty Machines Ltd. Liverpool, England) was used to compress all tablets. This is a sixteen-station rotary tablet press. One of the sixteen stations of the press was fitted with 1.270 cm round flat-faced TSM tooling (Thomas Engineering, Hoffman Estates, IL) and the remaining fifteen stations were blanked off. The hopper and feed frame were removed for easy access to the tooling. The TSM punches conform to the Tableting Specifications Manual of the American Pharmaceutical Association (Washington, DC). TSM punches were used because they have a relatively large flat portion on the head. Punch force measurements were made using strain gauges on the upper compression roll pin. Punch displacement can be determined analytically from measurements of punch forces, the procedure for which was developed by Oates and Mitchell (Oates and Mitchell, 1994). 3.2.2 Balance Sartorius balance, model B310P (Mississauga, Ontario) was used to weigh the powders and the tablets. 3.2.3 Rotronic Hygroscope BT The Rotronic Hygroscope BT instrument (Badenerstrasse, Zurich) was used to measure both relative humidity and temperature under ambient conditions. Materials were stored in 52 closed containers under ambient conditions. Compression was also carried out under ambient conditions. The recorded average values were: Temperature(±SD): 22.21 + 0.45°C; Relative Humidity(±SD): 27.46% + 3.53%. 3.2.4 Digimatic Outside Micrometer The Digimatic Outside Micrometer (Mitutoyo, Japan) was used to measure the thickness and diameter of a tablet. The values were recorded for each compact, with the exception of those whose structure was not maintained. 3.2.5 Multipycnometer The true densities of the five materials were determined by helium-displacement pycnometry using a Quantachrome Multipycnometer (Syosset, New York). A 149.59 cm sample cell was used for all the powders, which gave results consistent with those determined from a suspension density method (Dwivedi, 1988). 53 3.3 Methods 3.3.1 Compression protocol 3.3.1.1 Preparation of the tooling for compression All excipients were compressed after lubricating the die wall with a 5% solution of stearic acid in chloroform. The solution is applied in a smooth motion using an applicator and produces a layer of stearic acid in a few seconds when the chloroform evaporates. In addition, the punch faces were lubricated with the stearic acid solution before the compression of acetaminophen (due to its poor compressibility and stickiness). The punch faces and die wall are cleaned and the solution is reapplied for each tablet. 3.3.1.2 Experimental setting The tablets were compressed at a fixed thickness setting on the Betapress. The thickness setting was 1.839, which corresponds to a theoretical tablet thickness of 3.030 mm at zero pressure. Machine speed was 60 RPM and 251 equally spaced data points were collected over a 0.1 second period during the compression of each tablet. Different peak pressures were achieved by adjusting the amount of mass filled into the die cavity. Peak pressures ranging from 50 to 200 MPa (50, 100, 150, 200) were used to cover the normal range of compression pressures employed in pharmaceutical industry. 3.3.1.3 Compression procedure In order to achieve the target peak pressures, a series of 20 tablets was first made for each 54 material to determine their mass-pressure relationships. Peak force as a function of tablet mass was fitted to a polynomial equation and the masses corresponding to peak pressures of 50 MPa, 100 MPa, 150 MPa, and 200MPa were calculated. The determined mass and pressure relationships are shown in Table 5. The mass was then used for later experiments. Profiles consisting of single determinations are referred to as series data in this document. Table 5 Mass of each material required to achieve a given peak pressure. Each material was compressed using an instrumented Manesty Betapress at a speed of 60 rpm. Material Mass (mg) of materials at each peak pressure3 *• 50MPa lOOMPa 150MPa 200MPa AV 462 567 630 675 CS 458 557 626 663 LA 489 546 594 633 EM 685 775 839 894 AC 452 499 534 565 a The mass value for each material was obtained by curve fitting the mass and peak pressure relationship of 20 tablets of different weights. Based on the above mass-pressure relationships, each material was compressed at the four pressure levels. Ten replicates were compressed at each pressure level. The weight of the powder compressed is within the target mass ± 2mg. More precise control of tablet weight is not possible due to equipment constraints. The measurements of the ten replicates were averaged for the analysis. Compression force profiles of this type of data are referred to as 55 cluster data in this document. 3.3.2 Data collection The data collection begins when a reed switch is actuated by a small bar magnet affixed to the upper turret. The magnet is positioned on the turret such that the data collection is triggered a few milliseconds before the punches come in contact with the compression rolls. The signals from the strain gauges are collected for a period of 0.1s which is a sufficient interval to accommodate the compaction cycle of all materials tested. Methods used for data collection and storage were reported by Oates and Mitchell (Oates and Mitchell, 1994). The computer used for data analysis has been upgraded since the time of that report. The analogue signals from the strain gauges on the press are amplified, filtered and converted to digital form and then collected by computer at a rate of 2500 readings per second. Software has been written to analyze the raw data and calculate force and displacement as function of time. 3.3.3 Data analysis The time and force signals collected by the instrumented Betapress were converted to time and force data by the program MTest V2.3, which was written by Oates and Mitchell (Oates and Mitchell, 1988; Oates and Mitchell, 1994). The pressure (stress) was then calculated by dividing the force by the punch surface area. 3.3.3.1 Determination of punch displacement MTest V2.3 was also used to calculate the punch displacement based on the time and force data. Hence the tablet thickness (H) which was later used to calculate strain and porosity can be described as H = DQ(fr) + K ! + K ^Ts) p m *F(fr) (equation 26) where: fr is the turret position which corresponds to the time during the compression; Do is the distance between the punch faces when there is no force exerted on the tooling; T s is the thickness setting which in this experiment is set to 1.839; Kp"1 and Km-1are the deformation constants of the punches and the press respectively. 3.3.3.2 Determination of strain and strain rate The strain (e) was calculated from: g _ H H_o_ (equation 27) H o where: H is the tablet thickness Ho is the tablet thickness at 2KN. This value was chosen as the threshold pressure below which noise was excessive. Since the time interval between each detected point is the same t = 0.4ms, the strain rate ( 8) 57 was calculated as e = 8 n + 1 ~~ 8 " * 1 000 (equation 28) 0.4 3.3.3.3 Viscoelastic modeling The stress-strain relationships determined were fitted to various viscoelastic models (Table 6) using a commercially available technical graphics and data analysis program, Axum 5.0 (MathSoft, Massachusetts, USA). A non-linear regression method was used in the modeling program for data above the 2KN cutoff pressure and before the end of the compression phase. Akaike's information criterion (AIC) was used to determine the best-fit model in viscoelastic modeling (Paronen and Muller, 1987). AIC = N * ln Re+ 2 * P (equation 29) where: N is the number of experimental points; P is the number of parameters in the model; Re is the residual sum of squares. The lowest AIC value would indicate the best-fitting model. 58 3 3 I 8-+ + + B: «>5 <5 + Oo ^ t*| Oo ^ + tm Oo * + Oo + tm Oo * tm Oo tm No * tm Oo •S5 II II tm I tm tm I tm * + No t s j tm (NO tm 11 tm + tm m^ NO tm + tm No o 3.3.3.4 Determination of the compact porosity The porosity (e) of the compact was calculated as e = 1 -D a p p a r e n t 1 Mass U true true where: e is the porosity, Dapparent and D t r U e are the apparent and true density of the materials; H is the tablet thickness; A is the punch surface area; Mass is the recorded weight of each compact. The true densities of the five materials are listed in Table 7. (equation 3 0) Table 7 True densities of the materials used in the experiments. Material AC AV CS EM LA True density (g/cm3) 1.297 (± .004)" 1.549 (± .001)a 1.480 (± .008)" 2.353 (+ .002)a 1.538 (± .003)" a The value in parentheses indicates the standard deviation of the determined true density. 61 3.4 Statistical treatment of data The series data has been found to be statistically sound in determining the mass and pressure relationships by consulting the statistical department in UBC (Er, 2000). It has been reported that the series data is most suitable for a "relationship study". Spreading the data points out over the interested peak pressure range helps us capture the true relationship between mass and peak pressure throughout this peak pressure range (Er, 2000). The AIC value was chosen as the criteria to determine the best-fit model achieved by the modeling program. In selecting the linear portion for the Heckel analysis, a range of measurement points where the linear regression coefficient is higher than the threshold 0.97 (Paronen and Ilkka, 1996) was used. The constants of both the Heckel and Gurnham equations were determined by the linear regression analysis. T-tests were performed to compare the Gurnham constants between brittle and ductile materials. 62 4 RESULTS 4.1 Viscoelastic modeling 4.1.1 Stress-strain relationship during compression A representative time-force curve is shown in Figure 21. To avoid signal noise at the beginning of the compression cycle, a 2KN force was chosen as the threshold value for the start of the compression phase, while the dead center position represented the end of the compression phase. Stress-strain relationships of the five materials were calculated and a representative stress - strain curve is shown in Figure 22 for microcrystalline cellulose. 63 stress(MPa) o U l «-»• P O o to U l p L o M M o u i o o o o o g ^ ^ ^ h i h i hrj hd P p p p i—> U l  o o 3 5' **i % cfo* s CD 3 £2. 3 O 3 •1 rs a Cu 3 >i fD fD CO cn § W ET < 01 XJ fD rt-cn 3 co fD cn a; cn XJ CT S3 o o *-b co O C ? •3 a 3 3. 3^ cn XJ ET •-i j—; si' 3- CT « O O CT i-tj p OQ O* • co CT > < CT 3 XJ CT w CT "3 ^ CT ffi CO " cn C o CT ^ 3 > < CT ^ cn 3 H 3, 3-cn CT 3- 3 CT ffl CO CT < 3. S et OQ £ CT S Cu Sn XJ O o ® 2 i J? .—• XJ rt 3 _ CT O cn rt> co rt- CT CT Cu 3 C 3 «> Co ^ • X) 3 s : OQ to g CT 4.1.2 Best-fit models The stress-strain relationships were then fitted to various viscoelastic models using a non-linear regression method. The calculated and the observed stress-strain curves are plotted for each material under different peak pressures. Figure 23, 24 are representative model fitting curves. Overall it seems that the calculated solid model curves are closer to the experimental ones than the calculated fluid model curves. With an increase in the number of parameters (the complexity of the model), the calculated curves, both for the fluid and the solid models, are approaching the experimental curves. Tables 8-11 list the AIC values of the five materials compressed at different peak pressures. It supports the above observation that within a group of solid/fluid models, the AIC value is the lowest when a 4-parameter model is used. Combining all the modeling results, the 4-parameter fluid models give the lowest AIC values for all the materials under all compression conditions. The 4-parameter models (both solid and fluid models) showed a good description of the compression process. However, AIC values suggested that the 4-parameter fluid model gives the best fit. 66 o o o U l o p I—1 U l o o to U ) o I-p o o o o p o o o k) o o to U l o u> o Stress (MPa) o o o o o o o o o I — I — I I I I I I 1 • • • • • • • • u> I p P CD <-»> CD o o o U l p o o t—» U l o k> o o k> U l o o o o o o o o o o J I I L T3 P P CP a> o o o o U l o o o U l o k> o o k> U l o Stress (MPa) o o o o o o o o o o 3 ON to NJ ON O 4^  O O O O O O oo A 4^ - oo t o ON O O O O O O O • • p X \\ ol 3 £0 a o 3 o c cr c« £> 3 3 (n 5' re o-c CO 3' rt (I) era c co re f t 3* o a. era a. 3, « S i fD « O CD Q> s» ca § « a n 03 fD T3 fD s« 3 o rt 3 s era o o rt 3 ^ e. £ *T* n o co *3 2, 5' 3 3 I 3 SO o " co g Q Q. O sf ^ S* S-fii. ^ 32 fo 3 fB rt c >—• B . 3 £. rt O * o > o rt s. H a D . 3-i-t rt cn O to co <; co O co" cr s. O- 3 S3" D . 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Q o CD C O 3 X J ON 5- 3 3 p w 3 •. a . o o 5 3 Cu p p PC P X J 3 CD co CD 3 e (1 £ Ft CD Ul Q o. & $. — a 2 O CD P cu 3* — CD g « 0 cr 8* 3 CD co vT « > — C O CD 3. P 3 Cu P H P o t o I > H 3-CD P 3> O N 3* CD ^ 3 3 3\ J2. CD OQ P C O o o ^ 3 3 - X J P ^ •— CD <; co < CO CD CD - 1 cu CD ^ Table 8 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 50 MPa. Model3 AIC values for each material AC AV CS EM LA Solid 1-P 255 440 396 319 311 2-P 155 327 278 212 197 3-P 137 329 265 214 187 4-P 117 162 164 94 105 Fluid 1-P 346 645 519 450 399 2-P 347 646 496 451 378 3-P 349 528 469 412 322 4-P 61 145 146 76 86 31-P, 2-P, 3-P and 4-P indicate one parameter, two parameter, three parameter and four parameter models as described in Table 6 (a and b) bAIC values were calculated using: AIC = N * l n R e + 2 * P Table 9 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 100 MPa. Model3 AIC values for each materialb AC AV CS EM LA Solid 1-P 304 643 460 419 348 2-P 299 639 453 420 329 3-P 293 605 450 382 331 4-P 218 312 284 247 239 Fluid 1-P 528 904 781 639 575 2-P 524 889 781 626 576 3-P 498 809 772 625 568 4-P 152 293 213 187 182 31-P, 2-P, 3-P and 4-P indicate one parameter, two parameter, three parameter and four parameter models as described in Table 6 (a and b) bAIC values were calculated using: AIC = N * l n R e + 2 * P 70 Table 10 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 150 MPa. Model3 AIC values for each material13 AC AV CS EM LA Solid 1-P 461 847 659 598 493 2-P 457 829 649 590 490 3-P 424 788 608 538 466 4-P 342 476 267 350 369 Fluid 1-P 640 1061 922 770 709 2-P 622 1025 902 746 697 3-P 621 825 786 716 697 4-P 216 456 248 247 255 31-P, 2-P, 3-P and 4-P indicate one parameter, two parameter, three parameter and four parameter models as described in Table 6 (a and b) b AIC values were calculated using: AIC = N * l n R e + 2 * P Table 11 Akaike's information criterion (AIC) values calculated based on the viscoelastic modeling results. The materials were compressed using an instrumented Manesty Betapress at a speed of 60 rpm and a peak pressure of 200 MPa. Model3 AIC values for each materialb AC AV CS EM LA Solid 1-P 588 974 800 696 620 2-P 584 952 783 687 614 3-P 546 915 735 629 575 4-P 456 585 395 443 460 Fluid 1-P 732 1162 1017 849 802 2-P 705 1110 974 817 781 3-P 704 911 740 794 777 4-P 269 560 381 294 298 a 1-P, 2-P, 3-P and 4-P indicate one parameter, two parameter, three parameter and four parameter models as described in Table 6 (a and b) bAIC values were calculated using: AIC = N * l n R e + 2 * P 4.1.3 Viscoelastic coefficients The determined viscoelastic coefficients based on the 4-parameter models are listed in Tables 12 - 15 for all the materials at different peak pressures. The coefficients, as listed in Table 6, shall be combinations of Young's modulus and viscosity. So valid viscoelastic coefficients should be positive values. However, negative coefficients were observed in the results. 72 p o rt ^ _ rt Fr 0 3 rt g-p 3 3 P. 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W + o to ON W + O 4^ ON OJ W + o OJ NO W + o 4^  NO ffl + o to tt + O 4^  to tt + O OJ Ul w + o to ho — 4^  © W + o o tt a. tt + o to to Ui tt O tt • o to I—> NO >—' NO ON W W W + + + o o O u i OJ ON OJ to Ul U l ^— W W ffl + + + o o O OJ to O to ON ffl + O O 4^  © ffl • O to ffl + O OJ 4 > 4^ ffl + O ( O OJ ffl + o to OJ ffl + o o NO j> ffl + o o to ffl ± NO 1 -00 ffl + o OJ Ul W + o to o ffl + o to to © ffl I o U l ON ffl + O o o ffl I o to o W + o OJ ON ^ OJ W W + + o o to to W + o to to © tt • o OJ Ul tt + o o o W i o to K J 42 o 1? 4^  OJ bo Ul w w W tt + + + + o o o o 4^  4^  OJ o 0 0 O 2 o C u fD to 'oo Ul U l to tt tt w + + + o o o OJ to I — » " — ' s — ' " — ' 00 OJ ON OJ ON W tt tt 4- + + o o o Ul OJ to o tt , ^ , v to Ul J> Ul bo W tt tt + + + o o o OJ to o " — ' v — ' 1 — ' to _* 4^  NO bo tt W W + + + o o o Ul to to W + o OJ © W I O / s r ^  / ^ OJ to Of! to W W W + + + o o o OJ to o w w 4^  w + o to b W oo i—» OJ NO ON tt tt W ffl + + + + o O o o 4^  OJ o to 4*. 1—' ON NO to b w W ffl ffl i + + + o o o o OJ to -^^  " — ' NO K ) OJ *—t NO tt W w ffl + + + + o o o o 4^  OJ OJ o ^ to Ul to to OJ NO b W W ffl ffl l + + + o o o o OJ to v t t : > > < o oo ffl tt > fD Eft i fD C3 fD P >-t to 3 fD O o 2. 3 I' fD fD P S-i 3 P fD 5' H cn » fD Cu 2 p ^ 4.1.4 Stress-strain rate relationships during compression The stress-strain rate relationships of each material under different peak pressures were also calculated. Representative plots of the stress-strain rate relationships for microcrystalline cellulose are shown in Figure 25. It seems that during most of the compression phase, stress increases with a decrease in strain rate. Only a small part of the curve (from peak pressure to the end of the compression phase) indicates a trend where stress decreases with a decrease in strain rate, which may be a hint of viscoelastic behavior. At the same time, as shown in Figure 25, that period diminishes as the pressure increases. It can hardly be observed when the pressure reaches 150Mpa and higher. All the materials show similar stress-strain rate relationships, though the small periods mentioned above are shorter and less obvious for AC, LA and EM at all compression pressures. 77 stress(MPa) MM tO O o o o o o g ^ S ^ hfl ^ hj P p p p o o I 3 " T J rt 3 £ rt 5£ 3 O 3 co 1 rt C u H 3-t?" rt rt rt rt _ CO CO If* 3 (1 CO p i — . rt cr. 3 fBpj co rt a-cr fB CO rt co fO CO «-»• I to » >-! to rt CO 0> 5 co rt >rt 2 rt 3 o fB C u s a & T •a •s 3 o • ^ 3 ' w 3 « . « o « S* 3 P « q 3 «3 3 2, w K » S' rt czt 2, 5 ' fB «° o cro rt. < n 3 •o n R-<-l fB CO CO C 3 O CO fB > < o" 2. *0 •2 o rt co rt 3 > < 1 3 n co 8. s-3 5 0 2 o rt O o 3 •-»> T3 *-t rt fB 3 Co _ CO 3 8. O co O CTQ to 3 4.2 Porosity and pressure functions 4.2.1 Heckel analysis - pressure-porosity relationship during the compression phase Representative Heckel plots of AV compressed at different pressures are seen in Figure 26. Figure 27 illustrates the determination of the linear portion of the Heckel plot for AV at a peak pressure of 150Mpa. The Heckel plots at different peak pressures in Figure 26 are not parallel, suggesting that different mean yield pressures may be determined for compression at different peak pressures. 7 9 -ln(porosity) o T3 i-t CD t/3 C/l >-t CD h j P O o o K J o o to Ul o T + T t to H-> Ui o Ui o o OM OM OM MP •a P P P P o o 3 T3 3' ''i a- w rt 3 •3 O 3 ON rt P-rt S X J 3 |-i rt rt CO CO <? 3 rt ZT. ET < x> » rt ffi w rt co o ?i ST «" xT CO s l TJ O 8 GT o 3» O >-i •^*> ON 3 O o' •a § W ET to 3j O S t 3- 3 Xi n 3 n 2, n o ° • i . co OQ > <' s. rt K 3 rt rt *0 SL ffi *S 5 n t o CO I CO s> "= S rt O •8 H fS rt S 3 F> 3. « BL 2. S <K § rt s, a . 3 x i ^ 2. to t i l CO cs ci. 2. 3 rt 3 3 OQ rt 1 3 P 3 o p -ln(porosity) 05 05 N J O 4 ^ O ON O C50 O O O N J O o ON O 3 ta CD CO 3! £L 3 C ? cn cn (a Cu - i -t a CD 3 era fa ~t 52. co X) 3 T l Si CTQ CD e 2. "i ca rt ~ K> P. o CD rt fa 3* 3 ta ja 3 «8 1. A o U l H , rt C u fa «-»-fa X3 o 5" 3* rt TJ i CD CD C u fa f - » -ta Xi CD ta TT Xi | - i CD co > 3 u> o 1 s o 3 O !-+> B-CD 5" CD fa >-i X3 O g 5' 3 O 3* ffi n CD xt 0. rt rt P. C CD CD rt-5" l - l ta 3 OQ rt & 5' &*• IV o fa 3 era CD cr t» Cu § Cu f ? CD l - l 3 fa rt O 3 era 3 CD to l - l Xi O g 5' 3 3 CD O cp_ ET o* ta rt > CD 3" CD CD i CD " Cu 13 s a ta O cr. N> CO > si 3* V CD 2- tr s era CD CD O CD 3 era o C u o" 3-* rt-The determined mean yield pressures for all the materials at different peak pressures are listed in Table 16. The values in parentheses are the pressure ranges used to determine the slopes of the linear part of the Heckel plot. The values in the shaded area are those that are comparable to the reference values (Rowe and Roberts, 1996). The determined mean yield pressures of the five materials in increasing order are: CS < AV < AC < LA < EM. This corresponds to their reported material properties. CS and AV have low mean yield pressures and are reported to be ductile materials, while AC, LA and EM, which have higher mean yield pressures, are reported to be brittle materials (Rowe and Roberts, 1996). At the same time, the influence of compression pressure on the determined mean yield pressures can hardly be ignored. For the ductile materials, i.e. AV and CS, the mean yield pressures varied from 93MPa to 151MPa and 62MPa to 116MPa, while for the brittle materials, i.e. AC, LA and EM, the mean yield pressures varied from 114MPa to 1053MPa, 159MPa to 625MPa and 164MPa to 1370MPa. Significant variation exist between the values. Unless the proper compression pressures are used, the determined mean yield pressure may cause confusion due to the broad range of values it covers, especially for the brittle materials. 82 H cr „ m ft H cr 8 s C 3 CD fa g fa 3 fD 3 fD CO fD T J <* 5 > a £ 3 fD OQ O o 3 rt fD " | E L ? n ~ S rt- NO O NO ^ fD i-i £ 3 a fD Ct O 3 O - i TJ H cr < £L s fD TJ | a 3 £f rt cn rt CO H cr o o p_ o 3 O 3 P CO cr CO CO rt CL ES fD fD 5. <» CO 3" ft to < fD -1 CO OQ ft a o 3 ft CO cn cn 3 - i fD CO n 3 OQ © ft 3" rt co o l | rt ft o (» tt 5 rt cr o cr o 3 CL ro ^ TJ U 3 3 CD ft] CL TJ rt rt CO CO 3 3 3 3 -< w i s P IT co 5 p TJ S fD P ffi ™ ft O O O 3 fD CL fD rt < Ct 3- OQ g rt 3 ft 2L g 3 3 fD rt cr o CL rt TJ O 3 rt CL rt P o pr T J rt r > > > < o c/o rtN t—» NJ OO L/l ON rt* N) NO OJ 1 -rt NO ON h-N O Ul NO -k OJ • Ol o a- o- cr cr OTl _ 2 ON CXI OJ NJ oi KJ j g ON OJ -rt N) O J > o Ni O rt-NO ON N> Ul Ui Ui ON Jrt O N N> i LO 1 LO ON ON • rt* N> i—» 00 o rt* L/l Ui OJ Ui LO LO J> ON o OJ Ui 00 NO of cr a* OO ON rt* ' OJ N) ° - J i ON rt* KJ Ul N> 00 H © L/l 1 / 1 KJ W O J r t rt* - * NO N) Oh - * ON >-* 00 ON KJ V OJ o o 00 o o 00 © © l oo © j> © • oo © 2 CO ft Ul o § TJ P o o TJ P LO O § TJ P KJ O O TJ P rt p 3 a . TJ rt ro co CO C 3 < c a TJ P 3 P fD rt SL CO ft p o cr TJ rt & TJ rt rt CO rt rt - v P i if 5 3 P p_ 3 fD 2 H P » fD S" co r B ^ ON CO fD rt is 3 P M FT 3_ p" P CD co CL T J fD ft CL P Er P 3 CL o §1 fD 3 - i | rD P 3 ro p 3 L< £ CL T J rt fD CO CO 3 rt fD < £L 3 rt CO s» rt n P o cr p f? rt cL H cr fD 3 P rt CD rt SL CO s-ro rt ro o o 3 TJ rt ro CO CO CD CL 3 co 3' co i 3 rt 3 a CL 4.2.2 Gurnham analysis - pressure-porosity relationship at peak pressure To date, the Gurnham equation has not been used to describe the compression behavior of pharmaceutical powders. However, it was found in this work that using data at peak pressure, the Gurnham equation does describe the pressure-porosity relationships of the five experimental materials. The Gurnham equation describes an exponential relationship between porosity and pressure. Figure 28, using series data, shows the pressure-porosity relationships of the five materials. Five exponential curves were observed, and the shape of the curves seemed to fall into two categories. The shape of the curves of the two ductile materials are flatter than curves for the brittle materials, which indicates that a bigger porosity change can be achieved for the ductile materials within the applied pressure range than for the brittle materials. 84 pressure (MPa) xi o o 9 IO O to U l o r w o > > > £ c « < o o o 3 xi CO CO 5' 3 5" i f 3 » 2 »o 3 00 Ol Cu 8. S g? g g S. t l . ^ CO ft W c t CO fD O S» r fD - 1 C/5 CD G> rw <•» rt R 3 3 03 X J rt co <» 3 "S SL fD X J Cu i-t O co as 6o 3 OQ CO •3 Sj 3 £l X J tt 2 I I. X J ^ ? §, ~ 3J X J fD fD & * * i X J OQ co co 3 3 CJ 6 ' pi I-I a Hi ffl CD CO 3 cr tfl 3 2. CO (fl t O to* o • Cu X) o 5' H cr fD 3 to o o fD CO XI O 3 Cu 3' OQ SB fD co C u 5' 3 OQ J2. » rg OQ ffl 3 To further quantify the observed relationships, the average of the cluster data was used for the linear regression analysis, as shown in Figures 29-33. When expressed in the form of porosity vs. natural log of pressure, five linear plots with regression coefficients > 0.98 were observed. The slopes of the five linear plots are 6.41 (AC), 8.16 (EM), 9.04 (LA), 16.78 (AV) and 17.62 (CS). The order of the slopes seems to reflect the compressibility (ability to reduce in volume) of the materials, as suggested by Gurnham (Gurnham and Masson, 1946), the higher the slope, the better the compressibility. 86 Porosity (%) L/l l_ to LO L/l NJ NJ VO 13 bo O NJ 4^  4^  4^ p VO vo ON o I 00 I—I in * " CD {-O w CD CO CO 3 co Ov o H 3* CD «4? co 3 P • el Fd O P P 3 rt o n cu cr 3 °- cu gf CO ca o 3 P 3 13 U O O co Ef CD 9i o' 3 3 XI P OQ X) co CD XJ - a-P XI CD CO rty CD • CD H 3* CD 4^ bo L/l o L / i to L/l 4^ fl" CD § 3. 3 (a xi i " cr B P o o 3 CD CO tJ-£2. 3 O co 3 3' OT OQ B § P 3 OQ 5' !3.* co g 2 CD CD p 3 pr CD xi cu co ^ g § a CD CD co cr1 W CD 2. f ^ 3 ^  O CD rt CO cr w ta P rt P oo Porosity (%) to J > O N oo to o to to 3 u> bo 4 ^ O to 4^  ON 4^  bo o to p NO NO 0 0 ON 0 0 I NO © * £ • W 1) *5 to JS* < O (TO o to ™ ? P 52 13 o 3' H — a-o o ' rt & 9 rt c: to 3 rt (O 3 3 Cu o 13 to rt O %  00 CO C rt •-t ,—s 2 I - 1 3 > CO ^ — ' 3 • O S »-»> o> « 3 3 to 3 « 13 3. K to rt T to £ rt rt K o o .3 o o rt T3 rt 3 co rt co co rt Cu t= to CTQ <' rt 3 13 rt » 13 rt rt CO CO C 3 09 to 3 3 rt 3 rt-rt Cu to 3 rt 4 ^ CD rt o CO CD cr 13 to rt rt . CD rt co 3 « 13 to t  CD co CD CO 3 13 CD CD Cu CO C T 1 CD CO B ON o Cu J Cu P Porosity (%) o i_ i _ o U l _ J _ to o to U l o o o 4 ^ o -rt> to 4 ^ 4^  O S 4 ^ b o U l o U l to U l 4 ^ o • V© 00 - 4 4 t 00 3 2 23 £ n n CD fD c r w to 1 3 •-i fD cn cn 8-to fD 13 rt fD H ar fD o c 3 c r to 3 cn TJ fD °" ~-fD O O at »-•> ~ " g o 1 « *3 3 S. 3 rt" c l W rt cu cr rt. C u C u . rt to C : I S rt rt 3 . to 5- 1 3 fD rt _ rt cn' O rt 1X1 £ r rt rt > co rt era ~ fD C u TJ fD to > T J rt fD cn rt 3 n 1 3 H cr fD 3 to rt fD 3. JO. i* to cn rt O 3 TJ TJ rt fD rt cn cn fD C u 3 era to 3 to r - 3 to cn <2. $ " 3 < fD 3 TJ fD to fD 3 fD Cu Porosity (%) MD bo 4^ O 4> ro 4 ^ 4 ^ 4^ bo o MD l_ KJ 4> 50 II O MS 00 00 L*> M5 ON K J * < P H cr CD CO °- ' S g rn ce o. g. w CD ' CL P rt-P 2 x» •° 2. o 3. s - . 3 CO g . rt, (B CD 3 P XI >-i p rt, og <? CD O. O XI 0 1 3 rt-XI P CD £L co cr 5 O CD 00 rt V CD 6 cr o rt »-•> 3 rt- fV) CD rt-Cl CD rt 3 . CD P XI P co CD O 0 2 11 « 3 CD X I 3 CO CO 5" S co Si . co a. P 3 TO TO » 00 3 5' CD co L/l KJ L / i 4 ^ 2 3 *• g X) £• rt CD CD a-CO CO p CD 3 CD _ CO 3 " ^ CD 00 CD CD 3 P O XI <-t rt y CO P CO CD ~ XI P CO XI CD fD rt CD rt D-cr •-•> CD ON A comparison of the means of the slopes for brittle materials and ductile materials is listed in Table 17. The means of the Gurnham slopes are 7.87 for brittle materials and 17.2 for ductile materials. A two-sample t test was conducted to compare the two means. The result suggests that the mean of the Gumham slopes for brittle materials and ductile materials are significantly different in this work. Table 17 Two-sample t-test to compare the two means: (1) the mean of the Gurnham slope value for brittle materials - dicalcium phosphate (EM), lactose (LA) and acetaminophen (AC) and (2) the mean of the Gumham slope value for ductile materials -microcrystalline cellulose (AV) and corn starch (CS) in this work. Materials Gurnham slope value of brittle materials Gurnham slope value of ductile materials AC 6.41 N/A EM 8.16 N/A LA 9.06 N/A AV N/A 16.78 CS N/A 17.62 Mean of the Gurnham slope values 7.87 17.2 Two sample t test: 8.93a > 3.18 (t0.05(2), 3)b a 8.93 is the calculated t value based on the sample means. b 3.18 is the critical value oft with 3 degrees of freedom and a given probability of 0.05 for a two-tailed test. 9 2 5 DISCUSSION 5.1 Characterization of viscoelastic behavior during high-speed compression The viscoelastic modeling results suggest that 4-parameter fluid models give the best description of the compression behavior of the five materials compressed at different peak pressures. Negative viscoelastic coefficients were determined according to the current compression profile. However, these results do not provide valid physical explanations for the compression process. First the negative viscoelastic coefficients can not be explained by viscoelastic theory. Secondly, these results are not consistent with established material properties. Diverse time-dependent behavior of the brittle materials AC, LA and EM and the ductile materials AV and CS has been well reported (Armstrong, 1989; Rees and Rue, 1978). Therefore the modeling results suggest that linear viscoelastic theory may not be applicable for the compression phase on a high-speed rotary press. Or at least, the viscoelastic behavior cannot be investigated using the current experimental settings. This suggestion was further verified by the analysis of stress-strain rate relationship. For a viscoelastic material, an increase in strain rate will produce an increase in stress. However, the opposite was observed for the five materials during most of their compression phases, indicating that powder densification predominates during high-speed compression. The viscoelastic behavior, if present, may very well be obscured by the dominating powder densification effect. Hence, powder densification equations may be a better choice to describe the overall 93 compression phase during the high-speed process. At the same time, as shown in Figure 34, there was a short period of time from peak pressure to the dead center, when the stress and strain rate are changing in the same direction. This period of time was defined by Dwivedi as the peak offset time (Dwivedi, 1991). He suggested that this peak offset time is an indication of viscoelastic behavior. In Figure 34, it was found that the compression behavior during this peak offset time does show viscoelastic characteristics. He also reported longer peak offset time for ductile materials than for brittle materials, and a decrease of peak offset time with increases in peak pressure, which were also observed in this study. An attempt to further quantify the compression behavior during this peak offset period using the current experimental settings was considered. However, due to the short period of time involved (less than 7ms), limited information could be obtained, the small number of data points which could be collected was insufficient to permit accurate mathematical analysis. 94 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • f a ci> P c/o • OO <rt-ta • • • . • • • • • • - > — • • • • • • • CD o VI CD CD IF o o o o o o o U J o o o 4^ O O O U l o o o ON o © o >-t CD OO oo l-t CD CD 3 *n o' o M Q 3 TJ CD cn CD UJ CD JO Cu CD rt 1 , 3 C rt oo CD cn CD 3 P p CD 3 cn cn cn rt - I CD 3 55' g £ ft 55 ta &> CD =^ cn CD < CD rt-3" CD < cn cn cr CD cn cn cn a- w 3 2 ta fa fa Cu 3 ? cn p P 3 rt P rt cn rt CO TJ 2 CT CD 2L §. a g. 3 o o — rt, 3 ON g . ' T J ' T3 cn 3 S» P ^ cu 3. cr rt. cn TJ_ O* rt rt p. 3CTQ „ CD T J P cn CD G i l l O cn _T cn rt rt O H 3' CD rt rt O rt u i u i o O cn rt ^ a 3. J ? > 3 • <. S -? rt P T J X 3 rt CTQ O C-l N) 2. > s- < p • CD H u Cu 3" N> O a O 3 CD cn O 3 o 3 cn 3 P rt CD a. P 5.2 Use of the Heckel equation in describing powder densification during high-speed compression The Heckel equation has been the most accepted powder densification equation in describing the pharmaceutical powder compression process. It provides information about the mean yield pressure of materials as illustrated in Table 16. The value reflects the brittleness or ductility of the materials. It defines the main volume reduction mechanism of the materials during compression, i.e., plastic deformation (AV and CS), or fragmentation (AC, LA and EM). This information is also useful when considering the bonding of the materials, e.g., fragmentation produces clean new surfaces that may form stronger bonds and contribute to the strength of the compacts (Hiestand, 1997). However, limitations of the Heckel equation were observed. First, as illustrated in Table 16, at different peak pressures, significant variations existed between the mean yield pressures. Sonnergaard (Sonnergaard,, 1999) reported the same observation. With such variability, the mean yield pressure has been used qualitatively instead of quantitatively in the pharmaceutical field (Paronen and Ilkka, 1996). Useful information can be obtained from the Heckel analysis, but the mean yield pressure is not an absolute value that can be used to describe and calculate certain properties of the materials in formulation design. Secondly, it was also found that the compression pressure has a greater influence on the determined mean yield pressure of brittle materials than that of ductile materials. The mean yield pressures of AV and CS varies from 93 - 151MPa, and 62 - 116MPa respectively, 96 while the mean yield pressure of AC, LA and EM varies from 114 - 1053MPa, 159 -625MPa and 164 - 1370MPa respectively. It seems that greater variation existed for brittle materials. This is not surprising, since Heckel developed the equation based on the compression of metal powders which mainly deform plastically (Heckel, 1961a; Heckel, 1961b). When applied to pharmaceutical powders, limitations of the Heckel equation have been well reported (Paronen and Ilkka, 1996). In fact, pharmaceutical powders involve different materials, ductile materials, brittle materials, as well as materials that behave in both ductile and brittle manners. For a tablet formulation that involves granulations or mixtures, its mechanical behavior during compression may be even more complicated. It is understandable that, as reported by Ilkka and Paronen, care should be taken when using the Heckel equation to predict the behavior of a multi-component system (Ilkka and Paronen, 1993). 97 5.3 Use of the Gurnham equation in describing powder densification during high-speed compression The Gumham equation has not been discussed before in the pharmaceutical field. However, it was found in this work that the Gurnham equation provides a good description of the porosity-pressure relationship at peak pressure for the five experimental materials. The constants determined from the Gurnham equation show a good correlation with the compressibility of the materials. The higher the Gurnham slope, the better the compressibility of the material. In this work, com starch had the highest slope value, which was anticipated due to its plasticity, while acetaminophen, which compressed very poorly, had the lowest slope value. The means of the Gurnham slopes for brittle materials and ductile materials determined in this work are 7.87 and 17.2 respectively. The two means for brittle materials and ductile materials are significantly different, which indicates that the material properties (brittleness or ductility) may have an effect on the material behavior during compression expressed by the Gurnham slope value. In fact, pharmaceutical materials may be ductile and brittle at the same time as illustrated in Table 3. In this work, lactose, a brittle material, which is known to possess plasticity had a slope value of 9.06, while microcrystalline cellulose, a ductile material that was reported to possess brittleness had a slope value of 16.78. It seems that the Gurnham slope values for materials possessing both brittleness and ductility may lie between about 8 and 17. Increased ductility (lactose) was reflected by an increase in the Gurnham slope, and an increased brittleness (microcrystalline cellulose) was reflected by a 98 decrease in the Gurnham slope. It thus suggested that the Gurnham slope value might be used as a scale to indicate the brittleness and ductility of pharmaceutical materials. A Gurnham slope value of about 8 or less may indicate brittleness of the material, a Gumham slope value of about 17 or higher may indicate ductility of the material, and a value between about 8 and 17 may indicate a combination of brittleness and ductility of the material. The above observations suggest that the Gurnham equation might have potential in providing quantitative information for use in tablet formulation design. However, so far only five materials have been analyzed using the Gurnham equation. In order to obtain more support for this suggestion, some previous compression data (series data) using the same experimental settings were analyzed and the results are listed in Tables 18-21 and Figure 35. 99 o c a <-+ FT a CO CO rt g ro 3 fa FD 2 . £L O O II o BL o o w rt cr O 3 ta rt ro r^j> A6 o/ °0 X 1 4, % Ox-"4 cn co cn C D CD ro o CD oo CO r o C D ro ro b co o bo CD -rt C D 00 CO C D b CD 00 bo ro oo CD 0 CD 3 o 0 o T3 Cu 3 Cu o £ — • • o SL 3 0) 0 SL 3'-a a ct 3 tro o rr ca a H cr rD 0 3 3 cr CD OJ on o TJ CD cn iS ro - i CD O SL o 3 o 3 3 3 " ca 3 o T J CD < £L 3 ro ro CL 5 3 cn 3 TJ CL fa ta a rt 3 Ca 3 CO W o T J ro ffl re CD ffl ° § fa 3 & ^  r r * O 1 1 § |. •2 era 5. B 3 3 a 3. 3 3 re re O-p- 5 O CD 3 cn re a o" HH >< CO > a rt; rtj H — rt re re rt CO re " f—r-£3 % % 2 re re 5' 3 CL a CL ro CL ON o Table 18 Gurnham slope values of single component systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures. Materials Gurnham slope value Calcium carbonate 6.289a Emcompress (dicalcium phosphate dihydrate) 8.95a, 8.16b Mannitol 8.817a Dipac (compressible sugar NF) 10.643 Sorbitol 12.03a Avicel PHI02 (microcrystalline cellulose) 17.02a, 16.78b a values were based on previous experiments done by Miller et al.. b values were based on this experimental work Predictions made about these materials based on their Gurnham slopes show a good correlation with their reported properties. Calcium carbonate is reported as a brittle material (Roberts and Rowe, 1987), the sugars are reported as possessing brittleness and ductility (Debord, 1987; Maarschalk and Bolhuis, 1998). At the same time, the Gurnham slopes of AV and EM obtained using previously compressed data indicate good agreement with these experimental results. 101 Table 19 Gurnham slope values of acetaminophen (AC) formulations compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures. Materials Gurnham slope value Acetaminophen USP (fine powder) 6.41a Acetaminophen USP and Corn starch NF 90:10 (dry granulation) 10.87a Corn starch 17.62b a values were based on previous experiments done by Miller et al.. b values were based on this experimental work The improved compressibility and plasticity of the formulation by mixing acetaminophen with the ductile material - corn starch (Bolhuis and Chowhan, 1996) has been reflected by the increase in the Gurnham slopes in Table 19. 102 Table 20 Gumham slope values of calcium carbonate systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures. Materials Gurnham slope value Calcium carbonate USP (fine powder) 6.29a Calcium carbonate granulation (wet granulation) 9.33a Calcium carbonate granulation and Avicel PHI02 (microcrystalline cellulose NF) 1:1, physical mixture 12.923 Avicel PHI02 (microcrystalline cellulose NF) 16.78b a values were based on previous experiments done by Miller et al.. b values were based on this experimental work The effect of granulation on the brittle material, calcium carbonate and the effect of mixing microcrystalline cellulose with the granulation are seen in Table 20. The granulation has a better compressibility (Bolhuis and Chowhan, 1996), compared to the pure material, while a mixture of the granulation with the ductile material, microcrystalline cellulose, further improves its compressibility as reflected by the increase in the Gurnham slopes. 103 Table 21 Gurnham slope values of calcium carbonate systems compressed using an instrumented Manesty Betapress at a speed of 60 rpm. The Gurnham slopes were calculated using data at peak pressures. Materials Gurnham slope value A - Calcium carbonate USP (fine powder) 6.29a Physical mixture of A and B 11.71a Co-processed powder (spray dried slurry) of A and B 14.73a B - Avicel PHI02 (microcrystalline cellulose NF) 16.78b a values were based on previous experiments done by Miller et al.. b values were based on this experimental work The co-processed (spray dried) mixture of microcrystalline cellulose and calcium carbonate has been reported to compress better than the physical mixture of the two materials (Bolhuis and Chowhan, 1996). This difference is reflected by the higher Gurnham slope of the co-processed mixture than for the physical mixture of both materials. The results from previously compressed systems support the observation about the Gurnham equation. The determined Gurnham slope seems to be consistent between studies (Table 18). The predictions made about the compressibility of the materials, involving brittle materials, ductile materials, brittle and ductile materials, formulations, granulations and mixtures are showing a good correlation with their reported behaviors. However, since only a limited number of materials were investigated and only a preliminary 104 evaluation was given in this work, further investigation on various tableting systems/experimenting conditions would be necessary to support the above observation. 5.4 Comparing the Heckel equation and the Gurnham equation The Heckel and Gurnham equations both provided useful information of material behavior during compression as discussed in previous sections. A comparison of the two equations is given in Table 22. Table 22 Comparing the mathematical descriptions and the information derived from the Heckel and Gurnham equations. The Heckel equation The Gurnham equation Originally proposed as ^ = -kAP e Ae = -a — P Generally used as ln(-) = kP + A' e e = -alnP + b Constant derived 1 Mean yield pressure: k Gurnham slope: a Information obtained Ability of materials to deform plastically Compressibility of materials As shown in Table 22, the mathematical description of the Heckel equation and the Gurnham equation seem alike. They both describe an exponential relationship between porosity and pressure during the powder densification process, although the position of 105 porosity and pressure is different in the two equations. The Heckel equation shows that given a certain pressure change, the change of porosity that can be achieved is dependent on existing porosity of the material and the higher the existing porosity, the bigger the porosity change. The Gurnham equation shows that given a certain pressure change, the change of porosity that can be achieved is dependent on existing pressure on the material and the lower the existing pressure, the bigger the porosity change. Both equations reflect the non-linearity nature of the porosity-pressure relationship during powder densification as illustrated in Figure 28. The mean yield pressure in the Heckel equation has been mainly used to represent the material property (the tendency of the material to deform) during compression. It is related to the compressibility of materials, e.g. materials having lower mean yield pressures may be easily compressed as compare to materials having higher mean yield pressures, such as AV and CS are easier to be compressed than LA and EM. However, no quantitative relationship between the mean yield pressure and the compressibility of materials has been established. Gurnham reported that the Gurnham slope value reflected the compressibility of materials during the expression of liquids from fibrous materials. In this work, the Gurnham slopes also gave a good representation of the compressibility of pharmaceutical powders. Compressibility of solid materials has been defined as the percentage volume reduction given a certain pressure change. For pharmaceutical powders, D M a s s / V V _ j _ apparent _ j apparent _ | v true D.rue M a s s / V t r u e V a p p a r e n t V V V V - V ^ _ v true Y true _ Y true I apparentp apparent, . V V V V apparent] apparentp apparent] apparentp where D is the relative density of materials, Vt m e is the solid volume without porosity (given a certain mass, V t r U e is a constant), V,„,„ .„ V. . V a p p a r e n t l y V t m e, T 7 ^ - < 1, if 7 7 - ^ - i s negligible, V V apparent | apparent j V -V A V then Ae ~ "PP a r e n '0 apparent] _ " V V V apparentp So if Ae can be taken as an approximation for the percentage change in volume, the constant "a" in Table 22, referred as the Gurnham slope, describes the relationship between the percentage volume reduction and the applied pressure. The calculated Gurnham slope value for this experimental data and the previous data seem to support that the Gurnham slope "a" as listed in Table 22 is a representation of the compressibility of pharmaceutical materials. 107 5.5 Limitations of the study The current experimental settings proved to be limiting in investigating viscoelastic behaviors during compression. Only one compression speed was used, since the press has a small range of operating speeds that are all relatively high. The compression speeds available may be too high to detect viscoelastic behavior. Presses that can be operated under a good range of compression speeds and have required instrumentation for the punch forces and punch displacements measurement would be desirable to further investigate the viscoelastic behavior of powders during compression. At the same time, it would be helpful if more materials involving granulations, formulations and even pure pharmaceutical materials had been included in the experiments. More evidence would be provided to evaluate the newly proposed Gurnham equation in predicting compression behavior of pharmaceutical materials. 5.6 Future studies This work has suggested that an instrumented press such as a compaction simulator may be necessary for the investigation of the viscoelastic behavior of pharmaceutical materials during high-speed compression. It would be interesting to evaluate the Heckel equation using the peak pressure data and evaluate the Gurnham equation using the compression phase data to gain a better understanding of the theoretical background of these powder densification equations. 108 5.7 Conclusions Powder densification is the dominating phenomenon during the compression phase of a high-speed compression process. Viscoelastic behavior was not detected during most of the compression phase using the current experimental settings. The viscoelastic behavior, if present, may very well be obscured by powder densification. The material behavior observed during the peak-offset period shows viscoelastic characteristics. This behavior can be well observed for ductile materials compressed at low peak pressures; however further characterization was limited due to the instrumental reasons. The Gurnham equation is proposed as a new method to describe the powder densification process during the compression phase. 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