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Visco-elastic properties of aluminum soap-hydrocarbon gels Flynn, James Thomas 1951

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VISCO-ILASTIC PROPERTIES OF ALUMINUM SOAP - HYDROCARBON GELS by JAMES • THOMAS FLYNN  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF  Applied Science  i n the Department  1  of Physics  We accept t h i s thesis as conforming to standard required from candidates for degree of MASTER OF Applied Science  Members of the Department of Physio3 THE UNIVERSITY OF BRITISH COLUMBIA September,  1951  the the  ABSTRACT  Measurements o f v e l o c i t y o f p r o p a g a t i o n and damping of t r a n s v e r s e s o n i c w a v e s h a v e b e e n made f o r a l u m i n u m hydrocarbon g e l s . 1000  soap-  The f r e q u e n c y r a n g e c o v e r e d i s 100  c y c l e s p e r second.  to  The e x p e r i m e n t a l r e s u l t s h a v e b e e n  f i t t e d t o t h e o r e t i c a l mechanical models.  The  mechanical  * b e h a v i o r o f t h e g e l s i n v e s t i g a t e d c a n be a p p r o x i m a t e d  by a  Retarded Maxwell Element w i t h a r a t i o of p a r a l l e l t o s e r i e s v i s c o s i t y o f about o r d e r o f 10  0.01.  The r i g i d i t y o f t h e m o d e l i s o f t h e  dynes p e r square c e n t i m e t e r and t h e s e r i e s  v i s c o u s component o f t h e o r d e r o f 1 t o 10 r e l a x a t i o n t i m e o f t h e o r d e r o f 10  poise, giving a  seconds.  Ill  ACKNOWLEDGEMENTS  The a u t h o r w i s h e s t o e x p r e s s h i s a p p r e c i a t i o n : To t h e D e f e n c e R e s e a r c h B o a r d f o r g r a n t i n g l e a v e o f absense and f i n a n c i a l To D r . E . J . was  assistance.  W i g g i n s , u n d e r whose d i r e c t i o n t h i s  work  started at the Suffield Experimental station, f o r h i s  continued a d v i c e and  encouragement.  To D r . A.M. C r o o k e r , o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , f o r t h e l o a n o f o p t i c a l c o m p o n e n t s a n d f o r much helpful  advice.  To D r . F.A. K a e m p f f e r , o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , who a c t e d a s s u p e r v i s o r f o r t h i s w o r k a t t h e University.  I  TABLE OF CONTENTS I  INTRODUCTION  Page  a)  General  1  b)  Material  1  c)  Mechanical Properties of High Polymers The Use of Mechanical Models  II  PURPOSE AND THEORY OF THE EXPERIMENT  III APPARATUS AND PROCEDURE a) General b) Apparatus  IV  c)  Methods of Measurement  d)  Material  3 10 16 18  Method A Method B  24 26 28  EXPERIMENTAL RESULTS a)  Digel and Octoic Acid i n Gasoline  30  b)  Octal and Octoic Acid i n Benzene  33  c)  Octal and Octoic Acid i n Gasoline  35  V  DISCUSSIORZ  40  VI  BIBLIOGRAPHY  44  II  LIST OF ILLUSTRATIONS Figures  Page  1.  Maxwell Element  4  2.  Vo&gt Element  5  3.  Strain-Time Relations for simple models  4.  Four Parameter Model with Response Curve  5.  Theoretical Curves, G/G and ^ / x 0  6.  Theoretical Curves, G/^G and y'/y  7.  Photographs of s t r a i n patterns  8.  Schematic for Optical Components  9  Strobotron Trigger c i r c u i t  " 23  10  G/G vs Log f  " 31  11  Log G vs Log concentration for Digel i n Gasoline Log G vs 1/T " 32  12.  Log^  13  Log ^ vs Log f f o r Octal i n Benzene, v a r i a t i o n with the temperature  vs  n  8  vs Log  " 15  Log  " 15  v  s  for Digel i n Gasoline  Log f  follows 6  f o r Octal i n Benzene  " 18 n  18  " 33 " 34  Plate I  Apparatus f o r Studying Propagation of Transverse Sonic Waves  follows43  1  I.  IHTRODUCTIOH  a)  General Dispersions of aluminum soaps i n hydrocarbons such as  benzene, gasoline,  e t c . can exist i n a number of  different  forms ranging from mixtures of discrete swollen lumps of soap i n the solvent through v i s c o - e l a s t i c t o completely mobile solutions.  gels( or j e l l i e s )  The g e l state i s of p a r t i c u l a r  i n t e r e s t because of the rather s p e c i a l v i s c o - e l a s t i c The p h y s i c a l properties  properties.  of these gels d i f f e r markedly from  those of ordinary l i q u i d s and render them useful f o r a number of a p p l i c a t i o n s , preparations,  eg. l u b r i c a t i n g greases, pharmaceutical  etc..  During the l a s t war aluminum soap-  gasoline gels were used f o r incendiary bomb charging and flame thrower fuels  A flame thrower f u e l should have a  high v i s c o s i t y during f l i g h t t o prevent shattering and a low v i s c o s i t y during handling and operation of the flame thrower to prevent f r i c t i o n a l losses, permit low f i r i n g pressures  etc..  E l a s t i c i t y i s also believed to be important i n preventing shattering during f l i g h t . properties  However, the precise effeot of the  on the f i r i n g performance of a f u e l i s not  completely understood at the present time and w i l l not be discussed here. b)  Material The physical and chemical properties of aluminum soap 2.  hydrocarbon gels have been discussed by Rideal and others  •  They are quite stable and are characterized by a r e l a t i v e l y high v i s c o s i t y and r i g i d i t y .  The actual p h y s i c a l properties  2  obtained depend on the chain length of the soap, the solvent, the presence of peptizing agents, temperature, structure i e thought to be two phase.  etc..  The  One phase consists ©f  a network of solvated material, the second i s a solution of the soap i n the solvent and f i l l s the I n t e r s t i c e s of the network. crystals  The network may consistjfeither of r e l a t i v e l y r i g i d or of e l a s t i c long chain molecules.  Junctions i n  the network are formed by mechanical i n t e r l o c k i n g , by hydrogen bonding, true chemical l i n k s ,  etc..  a  Sheffer  has carried out v i s c o s i t y and osmotic pressure  measurements on d i l u t e benzene solutions of aluminum dicaprylate, d i l a u r a t e , and monostearate.  dimyristate, dipalmitate,  distearate,  He concludes that the soaps are polymers  of high molecular weight ( 60,000 to 900,000 ) whioh are formed by weak intermolecular l i n k s , probably hydrogen bonds. When preparing a g e l i t i s usual to add a peptizing agent to promote swelling and to increase the s o l u b i l i t y of the soap.  Peptizers are compounds with strong co-ordinating  properties eg. amines, alcohols, phenols, f a t t y acids  etc.,  and t h e i r a c t i o n i s a breaking of l i n k s i n the soap chains by a p r e f e r e n t i a l l i n k i n g with the peptizer.  After s o l u t i o n  i s complete the addition of more peptizer w i l l of course lower the v i s c o s i t y by reducing the chain l e n g t h . It i s very d i f f i c u l t to exactly duplicate conditions tt manufacture of the soap, so the molecular weight of the soap varies considerably from batch to batch.  Water i s a strong  p e p t i z e r so that i t and other impurities have a very marked  3  effect  on t h e g e l l i n g p r o p e r t i e s o f t h e s o a p and  of the r e s u l t i n g difficult  gel.  m a t e r i a l s and  The  Use  and  The  behavior  ( o r e l e c t r i c a l ) models t o  , Burgers  of p e r f e c t l y  t h e number o f c o n s t a n t s  others.  I f the material i s  r e q u i r e d r e d u c e s t o two,  isotropic  Lame's  the B u l k modulus, e t c . .  1  the i d e a l case the energy of deformation  is  A l l t h e w o r k done i n p r o d u c i n g  r e c o v e r e d when t h e s t r e s s e s a r e  In  completely a strain is  removed.  response of a Newtonian l i q u i d t o shearing s t r e s s  i s pure f l o w , the v e l o c i t y  g r a d i e n t d e p e n d i n g on t h e  and t h e a p p l i e d s h e a r i n g s t r e s s . i s not  and  e l a s t i c materials i s described  c o n s t a n t s , Y o u n g s m o d u l u s and  The  been  S  by a s e t o f e l a s t i c c o n s t a n t s .  recoverable.  of  represent  o f v i s c o - e l a s t i c m a t e r i a l s has  i n d e t a i l by A l f r e y  behavior  e v e n when  storage.  ^ considered  results  Models.  of mechanical  the mechanical  extremely  P r o p e r t i e s of H i g h Polymers  of Mechanical  use  aging  w i t h the greatest care i n the choice  i n mixing  Mechanical  The  reasons i t i s  t o get c o n s i s t e n t experimental  gels are prepared  c ) The  For these  on t h e  r e c o v e r a b l e and  I n t h i s case the  Where t h e r a t e o f f l o w i s n o t  a l i n e a r f u n c t i o n of the applied stress,  the f l u i d  i s said  to  A l s o i n some c a s e s t h e m e c h a n i o a l  p r o p e r t i e s depend upon t h e p r e v i o u s m e c h a n i c a l  treatment  t h e sample; i f f l o w i s accompanied by s t r u c t u r a l takes a f i n i t e  deformation  a l l t h e w o r k done b y t h e a p p l i e d f o r c e s  i s d i s s i p a t e d as J o u l e h e a t .  be n o n / N e w t o n i a n .  viscosity  of  changes i t  time f o r the m a t e r i a l to r e t u r n t o i t s rested  4  V//,.  state a f t e r mechanical working.  T h i s phenomenon i s c a l l e d  thixotropy. Many m a t e r i a l s , i n c l u d i n g h y d r o c a r b o n g e l s , e x h i b i t n e i t h e r pure e l a s t i c o r Newtonian  behavior.  -  Their mechanical  b e h a v i o r c a n o n l y be d e s c r i b e d b y c o n s i d e r i n g e l a s t i c a n d 6 v i s c o u s e f f e c t s a t t h e same t i m e .  A l f r e y and Doty  d i s c u s s e d t h e common m e t h o d s o f d e s c r i b i n g behavior,  have  visco-elastic  we w i s h t o c o n s i d e r b r i e f l y t h e u s e o f m e e h a n i c a l  (or e l e o t r i c a l )  models. 7  A Maxwell  element  c o n s i s t i n g o f a Hookean s p r i n g i f  s e r i e s w i t h a "Newtonian"  dashpot  describes the behavior of a material w h i c h undergoes an i n s t a n t a n e o u s elastic n  d e f o r m a t i o n a n d a t t h e same  t i m e f l o w s upon t h e a p p l i c a t i o n o f a stress,  such a n element  in figure Maxwell Element Figure  1  (1).  i s illustrated  Since the flow  deforma-  t i o n d e p e n d s o n b o t h t h e m a g n i t u d e ax& duration of the stress i ti s necessary t o c o n s i d e r t h e r a t e o f change o f deformation o f t h e whole  If  element.  shearing stress  =? S  (dynes/cm. )  modulus o f r i g i d i t y  = G  (dynes/em  e l a s t i c d i s p l a c e m e n t =Yt  2  -  $/Q  flow displacement  ~ Y3.  t o t a l displacement  — y~= ^/ + ^2.  2  )  5  dr  s  i s +±<Ui  F o r t h e case where t h e sample i s f o r c e d t o s u d d e n l y undergo a g i v e n d e f o r m a t i o n and i s t h e n h e l d a t t h i s c o n s t a n t  The is  s t r e s s decays called  strain  VIQ.  e x p o n e n t i a l l y w i t h t i m e and t h e r a t i o  the r e l a x a t i o n time of the m a t e r i a l .  The v o i g t o r r e t a r d e d e l a s t i c  element,  f i g u r e 2.,  is  used t o represent the b e h a v i o r of t h o s e  I  m a t e r i a l s which undergo an  elastic  d e f o r m a t i o n upon t h e a p p l i c a t i o n o f but r e q u i r e s a c e r t a i n time i n which  I  t a k e up t h e new  equilibrium  response  i s l i k e t h a t of a s p r i n g surrounded by a  Element  v i s c o u s medium.  3  Figure  to  position.  S u c h a damped o r r e t a r d e d e l a s t i c Voigt  stress  two  The  displacement of the  c o m p o n e n t s must be t h e same a n d  the  d i f f e r e n t i a l equation describing the displacement i s  For a given stress,S, the deformation time r e l a t i o n  i s given  by t h e e q u a t i o n  & The  quantity  element. to  V/Q  i s called  the r e t a r d a t i o n time of the  Upon t h e r e m o v a l o f s t r e s s t h e sample w i l l  i t s original  shape a c c o r d i n g t o t h e e q u a t i o n  return  6  The  response to a constant  i n t e r v a l t±  to t  2  stress applied for a  i s i l l u s t r a t e d i n f i g u r e 3.  types of m a t e r i a l d i s c u s s e d  f o r the  time four  above.  Y  Elastic  Newtonian Figure  The so f a r .  Voigt  5.  e f f e c t o f t h e mass o f t h e m a t e r i a l h a s T h i s may  r e s p o n s e , and flow.  Maxwell  o n l y be s o f o r t h e  Where f o r c e s v a r y w i t h r e s p e c t  considering  to time the  considered.  mass o f t h e e l e m e n t s o f a b o d y d e l a y s  the response of  To  p r o d u c e d by t h e a p p l i c a t i o n o f f o r c e s a t  c o n s t r u c t a model t o represent the point  i n t h e s y s t e m o f s p r i n g s and The  present serves  use  points  behavior  appropriate  dashpots.  of mechanical ( o r e l e c t r i c a l ) models t o r e -  the mechanical p r o p e r t i e s of v i s c o - e l a s t i c two  parts  elastic  dynamic  of a m a t e r i a l i t i s necessary t o include/masses at places  the  stresses.  of t h e body are p r o p a g a t e d t h r o u g h o u t t h e body by waves.  inertial  Essentially  remote f r o m t h e p o i n t s o f a p p l i c a t i o n o f t h e Disturbances  neglected  s t a t i c case, f o r e l a s t i c  f o r steady state conditions i n  f o r c e s o f / i h e m a t e r i a l must be  been  main purposes.  i s that they provide  The  first,  a c o n v e n i e n t and  means o f r e c o r d i n g and  using data  and  most  relatively  obtained  systems  obvious, simple  experimentally,  7  e s p e s c i a l l y i n t h o s e c a s e s w h e r e t h e r e i s no theoretical basis f o r reference,  adequate  s e c o n d l y , i t i s sometimes  p o s s i b l e t o a s s o c i a t e t h e v a r i o u s components o f t h e model w i t h more o r l e s s e l e m e n t a r y p r o c e s s e s o f t h e m a t e r i a l T h e r e i s o b i r i L o u s l y no r e a s o n t o e x p e c t o n l y one element  itself. Maxwell  o r V o i g t model t o r e p r e s e n t t h e e n t i r e m e c h a n i c a l  behavior of a material.  Many d i f f e r e n t i n t e r n a l m e c h a n i s m s  d e t e r m i n e t h e m e c h a n i c a l r e s p o n s e , e a c h w i t h i t s own d i s t r i b u t i o n of parameters. to  However, i t i s u s u a l l y  possible  u s e a d i s c r e t e number o f p a r a m e t e r s , M a x w e l l e l e m e n t s i n  parallel,  o r V o i g t elements  i n series.  The t i m e s c a l e o f a n e x p e r i m e n t i s i m p o r t a n t i n determining a s u i t a b l e model.  B y t i m e s c a l e i s meant t h e  e f f e c t i v e l e n g t h o f t i m e t a k e n t o make a measurement o f to  stress.  response  C o n s i d e r a s y s t e m made up o f M a x w e l l e l e m e n t s i n  p a r a l l e l , w i t h the corresponding r e l a x a t i o n times decreasing i n g o i n g f r o m element the  1 t o element  2 ete.,^« i., ^ z / ^ ^ .  a p p l i c a t i o n of a s t r e s s a l l elements w i l l  undergo  e x t e n s i o n f r o m b o t h e l a s t i c d e f o r m a t i o n and f l o w . d u r a t i o n of the s t r e s s i s l o n g i n comparison w i t h short i n comparison w i t h  2^  Upon  2  I f the %  but  , the e f f e c t of tha a p p l i e d  s t r e s s w i l l be e s s e n t i a l l y d i f f e r e n t on t h e c o r r e s p o n d i n g e l e m e n t s t h o u g h t h e i r t o t a l d i s p l a c e m e n t s a r e t h e same. response o f element of  element  3 will  1  w i l l be m o s t l y due t o f l o w w h i l e t h a t  be m o s t l y e l a s t i c d e f o r m a t i o n .  In other  w o r d s , i f t h i s w e r e t h e o n l y o b s e r v a t i o n made, t h e p a r t o f element  The  1 and t h e v i s c o u s p a r t o f e l e m e n t 3  elastic would  8  p r a c t i c a l l y n o t be of  observed.  a l l s i x parameters  In order t o separate the  i n t h i s m o d e l i t w o u l d be n e c e s s a r y  perform at l e a s t three experiments  In  to  w i t h time scales corresp-  onding t o the t h r e e r e l a x a t i o n t i m e s , number o f e l e m e n t s  effects  The  extension to  any  i s obvious.  d e a l i n g w i t h m o l e c u l a r mechanisms t h e r e w i l l n o t  be  a d i s c r e t e d i s t r i b u t i o n of r e l a x a t i o n times f o r each i n d i v i d u a l meohanism but a c o n t i n u o u s some v a l u e .  distribution  about  However, i t i s u s u a l l y p o s s i b l e t o lump them  i n t o a s i n g l e element,  at l e a s t as a f i r s t  approximation.  t a k e s t h e f o u r p a r a m e t e r m o d e l shown i n f i g u r e 4  Alfrey  as  the simplest r e p r e s e n t a t i o n of the behavior of a polymer i n shear. G  2  The  provides the instantaneous e l a s t i c  and^  2  the retarded e l a s t i c  a n d 17  response  response, 3  true flow.  s t r a i n t i m e r e l a t i o n s h i p f o r such a system i s i l l u s t r a t e d 4.  in figure The  instantaneous e l a s t i c  corresponds  response  represented by  G^  t o the instantaneous deformation of the whole  s t r u c t u r e upon t h e a p p l i c a t i o n o f s t r e s s .  Suchk. d e f o r m a t i o n  would i n v o l v e changes o f d i s t a n c e between n e i g h b o r i n g molecules, The  s m a l l shape changes of m o l e c u l e s , e t c . . m o d u l u s Gg  i s taken t o represent the  configurational elasticity.  In the unstressed state  macromolecules are c o n s t a n t l y changing d e f i n i t e d i s t r i b u t i o n law. t h e i r shapes,  The  the  i n shape but  obey a  Upon t h e a p p l i c a t i o n o f  stress  on t h e a v e r a g e ,  equilibrium position.  so-called  w i l l be  changed from  effect i s completely  the  reversible  t o f o l l o w page 8  9  sinoe the molecules w i l l revert to t h e i r o r i g i n a l equilibrium p o s i t i o n upon the removal of s t r e s s , i t may be considered as an e l a s t i c  sinoe i t i s  reversible  effect.  The true flow represented b y ^ 3  and the viscous  component connected with the oonf igurational e l a s t i c i t y , rj 2 are governed by the same mechanisms. The biased thermal d i f f u s i o n of molecular segments .  ,  10  II  Purpose and Theory of the Experiment The i n v e s t i g a t i o n d^esoribed here i s part of a broader  program of experiments planned by the Defence Research Board S u f f i e l d Experimental S t a t i o n .  As explained i n Part I, i t  is  not expected that the measurements over the r e l a t i v e l y narrow frequenoy range used here w i l l describe the behavior of the material adequately.  Other investigators are working of the  measurement of properties over time intervals of the order of several seconds down to i n t e r v a l s of the order of 1/50 th of a second.  The measuremants to be described here extend  the time i n t e r v a l down to about 0.001  seconds.  Except f o r the work of Van Wazer, Goldberg and Sandvik measurements of the physical properties of hydrocarbon gels has been confined to r e l a t i v e l y long time i n t e r v a l s .  The  Q  resonance elastometer developed by Van Wazer et a l permits measuremants t o about l/50th of a seoond.  A few investigations  have been made; by suitable techniques on other materials, but so f a r as i s known t h i s i s a new region of investigation f o r flame f u e l s .  It i s of interest not only beoause i t w i l l  extend the data available f o r consideration of moleoular effects but also the time periods involved here are of the those involved i n f i r i n g . Thus the measurements are possibly of d i r e c t emperical use i n assessing  fuels.  The behavior of viseo-elastio  systems over short time  intervals i s much easier to study by means of p e r i o d i c a l l y varying stresses rather than attempting to study very rapid  11  transient phenomena.  Ferry  has described a method of  measuring the physical properties  of concentrated polymer  solutions by means of transverse sonic waves.  This method  depends upon the material being o p t i c a l l y c l e a r and s t r a i n birefringent.  It was known that hydrocarbon gels are  strain  ftf  birefringent  and since i t was thought that s l i p at polymer-  instrument interfaces was a possible source of error i n d i r e c t measurements of stress and s t r a i n t h i s method was chosen to begin the investigation of physical properties the higher frequency range.  in  It i s hoped that i t w i l l be poss-  i b l e to make measurements i n the same frequency range by other methods and investigate the effect of s l i p at some l a t e r date.  It i s known that very pronounced s l i p can be obtained  i n rotating c y l i n d e r viscometers with rapidly increasing rate of shear.  However, i t i s not known whether t h i s  effect  can be produced or observed at higher frequencies. When the mass of the material can be neglected the response to a shearing stress can be completely described e i t h e r by a complex v i s c o s i t y  ?*  to  ,  v/~ <• 7"  or a complex r i g i d i t y " g:= Qt  i &"  (l) (S)  With high polymers P o i s s o n « s Ratio i s usually very nearly one h a l f and so  E  =  3Q- , where E i s Youngs Modulus and  Gr i s the shear modulus as before.  Since behavior i n shear  i s generally easier to study experimentally we consider only behavior i n shear.  The r e a l part of the complex r i g i d i t y G*  i s equal to the componant of the stress i n phase with the  IE  s t r a i n divided by the s t r a i n . viscosity  The r e a l part of the complex  JJM i s the component of stress i n phase with the  rate of s t r a i n divided by the rate of s t r a i n .  If  i s 2ir  times the frequency then G^coy7  ,  etc.  -y"^  The values of G* and G w obtained experimentally generally vary with frequency and mechanical models are made up by combining springs and dashpots to duplicate the experimental results. For a Mastwell element with a spring of r i g i d i t y G and dashpot of viscosity37 and relaxation time t ~ y J G-  (3a)  G <# **~ x  W= 7  For a Voigt element  !  yj  (  (5b)  J + u^ ? 1  2  G  (4a)  V- *  (tt)  the values being independent of frequency i n t h i s case. For a retarded Maxwell element, that i s a spring with r i g i d i t y G i n s e r i e s with a dashpot of v i s c o s i t y yj s  and i n  p a r a l l e l with a dashpot of v i s c o s i t y ?7 : / p  «S -  ( s a )  13  », D+^Crs+tfi]  (5d)  In our case we wish to determine the mechanical behavior by studying the propagation of transverse sound waves,  we assume that the e l a s t i c wave may be described by  the following:  . (U)  U r U . t  _.  ,  7 7 r  _ j (- =^-~ i  t €  ^  *°  |A (6)  J  where u i s the displacement. By analogy with the theory f o r a p e r f e c t l y e l a s t i c s o l i d one can define a new r i g i d i t y £T f o r a v i s c o - e l a s t i c material such that the d i f f e r e n t i a l equation describing the motion i s / , A  and  = &y<*  (7)  „  ^  (8)  x  where v i s the measured T e l o c i t y of propagation of the wave. The two quantities  a  and A / x  c  may then be used t o  describe the physical properties of the material at the frequency at which they were measured. The r e l a t i o n between  G  and A / x # , and G« and 77» ,  may be found by substituting from equation  2  /O d u, ^  ^ fQ+  c  M*then putting  (8) into the d i f f e r e n t i a l  ooy'j  d_a,  ax^  14  from equation (8),  giving  Equating r e a l and imaginary parts  tS^Q  )£<- fro**/'  and  £' , g » f i ^ - f l f e ) ' J  ( a) 9  W  7  (9b)  ~ ~ [*wU  The measured values may then be compared with those f o r t h e o r e t i c a l models by substituting from relations sueh as (3)  , (4) or (5) into equations  (9a)  and (b).  For the three models considered t h i s gives: Maxwell Element Q = Q ^  -  ^"ill* f  „  (10a) (10b)  Yoigt Element  G-G X/ -  + 27Ta.y  (lla) (lib)  15  Retarded Maxwell Element  The above r e l a t i o n s are shown g r a p h i c a l l y i n figure  5.  It i s perhaps easier to v i s u a l i z e the quantities and  G*  *j* a l s o ^ i t i s necessary t o convert to these to make  comparisons with other types of measurements. retarded Maxwell element we define ?^ * VJ®  a  For the n  d  ^  =  9p/*  and the relations are:  These are i l l u s t r a t e d g r a p h i c a l l y i n figure 6 . . For the Maxwell element the value of G approaches a l i m i t i n g value at high frequencies and the damping i s severe at low frequencies and f a l l s t o zero as the frequency i s increased.  For the voigt element both G and the damping  increase i n d e f i n i t e l y with frequency.  For the retarded  Maxwell element the behavior i s l i k e that of a Maxwell element at low frequencies and of a Voigt element at high frequencies.  to follow page 15  EH  •  2  SL  voia^T^LgyE^  G  / / /  1 s 1 r  1  I r  RETARDED MAXWELL ELEMENT8 /  J £ = o.o/  1  \j  y  \  0  2  L O G «•>*"  \ \  VOIOT CLEMCMT  \  %=0- 005  MAXWELL ELEMENT  «H  1  2  / /  /  RETARDED MAXWELL ELEMENT  O  9  /  /  «  % I  i i  sy  OO1  >  * I  /  /  /  MAXWELL  ELEMENT  0  ^  L O G Wfr  FIGURE 5 •  \  * /  \>^~  1  2  t o f o l l o w page 15  16  APPARATUS AND EXPERIMENTAL PROCEDURE  III  a)  General To  o b t a i n t h e v a l u e s o f G a n d A./x  Q  f o r a given ,  sample i t i s n e c e s s a r y t o measure t h e v e l o c i t y o f p r o p a g a t i o n of  a p l a n e s h e a r wave a n d a l s o , t o m e a s u r e t h e d a m p i n g o f t h e  wave.  I f t h i s c a n b e done o v e r a w i d e e n o u g h f r e q u e n c y  range t h e n i t i s p o s s i b l e t o f i t t h e e x p e r i m e n t a l d a t a t o t h e o r e t i c a l curves and so f i n d a model t o represent t h e mechanical behavior o f the m a t e r i a l under the conditions o f the  experiment. The  e x p e r i m e n t a l method u s e d was e s s e n t i a l l y a s  described by Ferry •  T r a n s v e r s e sound waves were  produced  i n a sample o f g e l b y a t h i n vane v i b r a t i n g s i n u s o i d a l l y i n i t s own p l a n e .  T h e d i r e c t i o n o f p r o p a g a t i o n was h o r i z o n t a l  and a t r i g h t a n g l e s t o t h e d i r e c t i o n o f o b s e r v a t i o n . the a c t i o n o f the s t r e s s e s produced gel  Under  b y t h e s h e a r waves t h e  becomes b i r e f r i n g e n t w i t h a x e s a t f o r t y f i v e d e g r e e s t o  t h e d i r e c t i o n o f p r o p a g a t i o n o f t h e sound wave.  I f the g e l  i s o b s e r v e d between c r o s s e d p o l a r o i d s ' , w i t h t h e a x i s o f t h e p o l a r i z e r v e r t i c a l and that o f the a n a l y z e r h o r i z o n t a l , t h e f i e l d w i l l be dark i n t h e absense  o f s i g n a l and w i l l be  c r o s s e d b y a l t e r n a t e l i g h t a n d dark bands i n t h e presence o f a s h e a r wave.  I n o r d e r t o observe these l i g h t and dark  bands i t i s n a c e s s a r y t o , e i t h e r produce  s t a n d i n g waves i n  t h e g e l , o r , t o u s e t r a v e l l i n g waves a n d s y n c h r o n i z e t h e source o f l i g h t w i t h t h e s o u r c e o f t h e sound waves.  The  l a t t e r i s much s i m p l e r a n d i s t h e method u s e d h e r e .  The  17  s p a c i n g between adjaeent one  h a l f w a v e l e n g t h and  l i g h t and  dark bands corresponds  thus measuring tmis  g i v e t h e w a v e l e n g h t o f sound i n t h e g e l .  spacing  to  will  However, s i n c e the  i n t e n s i t y of l i g h t v a r i e s according t o sin §  where  2  S  is  the r e l a t i v e o p t i c a l r e t a r d a t i o n i n the g e l , i t i s d i f f i c u l t to  l o c a t e t h e mid  p o i n t o f t h e bands a c c u r a t e l y .  An  a l t e r n a t e method of o b s e r v i n g t h e b i r e f r i n g e n c e i s t o a c o m p e n s a t o r between t h e g e l and Babinet  the analyzer.  c o m p e n s a t o r i s u s e d i n t h e u s u a l way  insett  If a  with i t s optic  a x i s a t f o r t y f i v e degrees t o t h e axes of the p o l a r i z e r analyzer, the f i e l d  i s c r o s s e d b y l i g h t and  perpendicular to i t s optic axis.  and  darft bands  I n t h i s case/the r e t a r d a t i o n  p r o d u c e d b y t h e c o m p e n s a t o r i s e q u a l t o t h e amount o f d o u b l e r e f r a c t i o n introduced before i t .  However, i f t h e  i s u s e d w i t h i t s o p t i c a x i s a t a s m a l l a n g l e , «< , v e r t i c a l then the f i e l d  from  the  i s f a i n t l y i l l u m i n a t e d a l l over  and  a l t e r n a t e l y c r o s s e d by l i g h t and the  displacement  d a r k bands as b e f o r e .  p r o d u c e d b y a s m a l l amount o f  r e f r a c t i o n introduced before i t i s magnified the  relation tan  where the  $  ~  tan  A  Sin  2o<  But  double  according  to  i s t h e amount o f s t r a i n d o u b l e r e f r a c t i o n a n d  e q u i v a l e n t r e l a t i v e r e t a r d a t i o n i n t r o d u c e d by  compensator . the  compensator  The  A  the  e f f e c t of s t r o b o s c o p i c a l l y i l l u m i n a t i n g  s h e a r wave i s t h e n t o p r o d u c e w a v y l i n e s c r o s s i n g t h e  field  of view.  The  d i s t a n c e between s u c c e s s i v e  peaks  p.  corresponds method has  t o t h e w a v e l e n g t h o f around i n t h e g e l . t h e f u r t h e r a d v a n t a g e t h a t i f i t c a n be  This assumed  is  18  that the t o the  amount o f s t r a i n d o u b l e r e f r a c t i o n i s p r o p o r t i o n a l  amount o f s t r a i n , t h e n m e a s u r i n g t h e d e c a y  displacement of the the  l i n e s crossing the  g e l a t i n e g e l a t 500  c o m p e n s a t o r and  a t 1000  cycles per  b)  second w i t h the  shown i n f i g u r e  support stand  r o d s w e r e two  3/8  clamped a t any  consisted of three  7..  d e s i r e d p o i n t on t h e  1 inch diameter brass  g l a s s c e l l w h i c h i n t u r n was  rods.  d r i v e r and  p l a t e c a r r i e d t h e m a t e r i a l t o be  bath.  c h a n n e l on w h i c h t h e  vane.  tested i n a  a 631-P  The  be  plate bottom  rectangular  a piece  of s t e e l  mounted.  o f foam r u b b e r  extraneous v i b r a t i o n s .  are  o p t i c a l system are  s k e t c h e d i n f i g u r e 8.  strobotron  vane.  top  o p t i c a l c o m p o n e n t s c o u l d be  p r i n c i p l e p a r t s of the  P l a t e I and  the  i n s i d e a temperature c o n t r o l  w h o l e a s s e m b l y r e s t e d on a t h i c k p i e c e  The  M o u n t e d on  The  A l s o m o u n t e d on t h e b o t t o m p l a t e was  t o damp o u t  compensator.  i n c h t h i c k aluminum p l a t e s w h i c h c o u l d  c a r r i e d the electromagnetic  N e x t was  synchronized a three  The  The  l i g h t source  w i t h the o s c i l l a t i o n s  gel.  The  p o l a r i z e d i n the v e r t i c a l d i r e c t i o n before b y t h e P o l a r o i d P.  shown i n  inch diameter condensing  t o d i r e c t the l i g h t through the  gel  compensator  a p p a r a t u s as used w i t h t h e  rods screwed i n t o a 1x12x12 i n c h b r a s s p l a t e .  the  no  Apparatus P l a t e I shows t h e  The  give  photographs  c y c l e s per second w i t h  a x i s a t 5° t o t h e v e r t i c a l a r e  The  compensator w i l l  damping f a c t o r f o r s h e a r waves i n t h e g e l .  o f a 10%  of  light  was of  lens  was  entering  p o r t i o n of the g e l i n the  the plane  L-l  L-2  B  FIGURE  8  O M> O H H  a  09  •  19  c o n t a i n i n g t h e g l a s s vane and a t r i g h t angles t o t h e d i r e c t i o n o f o b s e r v a t i o n was f o c / u s s e d o n t o t h e c o m p e n s a t o r b y a t w o i n c h ( f 1.5) camera l e n s .  Then t h e image o f t h e s t r a i n e d g e l  and B a b i n e t c o m p e n s a t o r was p r o j e c t e d t h r o u g h t h e P o l a r o i d a n a l y z e r A onto t h e f o c a l plane o f a f i l a r micrometer p i e c e b y a sma 1 1 t e l e s c o p e l e n s .  With t h i s  eye-  optical  a r r a n g e m e n t i t was p o s s i b l e t o make o b s e r v a t i o n s e i t h e r w i t h o r w i t h o u t t h e c o m p e n s a t o r a n d t o make w a v e l e n g t h  measurements  e i t h e r d i r e c t l y w i t h t h e c r o s s h a i r and micrometer  movement o r  w i t h a photograph.  The p o l a r i z e r , a n a l y z e r a n d c o m p e n s a t o r  c o u l d be r o t a t e d i n d e p e n d e n t l y . A l l t h e components e x c e p t t h e l i g h t  source,  condensing  l e n s a n d p o l a r i z e r w e r e m o u n t e d o n a 1 1/4 i n c h s t e e l T h i s c h a n n e l h a d a 1/4 i n c h s l o t m i l l e d  o u t f o r most o f i t s  l e n g t h a n d was f a s t e n e d t o t h e b o t t o m o f t h e l o w e r p l a t e b y means o f t w o 1/4 i n c h s c r e w s . and s e c o n d channel.  l e n s were mounted permenantly  channel.  aluminum  The e y e p i e c e , a n a l y z e r onto t h e end o f the  A brass c a r r i a g e which s l i d along t h e t o p o f t h e  channel c a r r i e d t h e compensator mounting and t h e o b j e c t i v e l e n s . T h u s i t was p o s s i b l e t o f o c u s o n t h e p l a n e o f t h e Babinet by s l i d i n g the c a r r i a g e along t h e channel. of t h e plane i n t h e g e l onto  t h e c o m p e n s a t o r was  Focussing accomplished  b y m o v i n g t h e o b j e c t i v e l e n s i n i t s m o u n t , e i t h e r b y means fif a course s l i d i n g adjustment  o r , b y means o f t h e r e g u l a r  screw f o c u s s i n g adjustment.  Adjustment o f t h e w v e r - a l l  m a g n i f i c a t i o n was made b y m o v i n g t h e c h a n n e l o n i t s supporting  screws.  20  The  g e l s a m p l e was  held i n a rectangular glass  Two  s i z e s w e r e u s e d , t h e f i r s t was  2x3  centimeters  s e c o n d was h i g h amd  a small absorption  i n c r o s s . s e c t i o n and  2x10  centimeters  5 centimeters  i n c r o s s s e c t i o n and  the d i r e c t i o n of propagation  d i r e c t i o n i n both cases.  The  use  was  cell  high.  5  i n the  cell.  The  centimeters  lengthwise  of c e l l s of f i n i t e s i z e  has  13  been i n v e s t i g a t e d  and  i t has  b e e n shown t h a t w i t h  reasonable  c a r e t h e e r r o r i n t r o d u c e d b y a s s u m i n g p l a n e w a v e s i n a medium o f i n f i n i t e e x p e n t i s s m a l l compared w i t h t h e  experimental  errors.  T h i s i s p a r t i c u l a r l y so w i t h measurements o f wave-  length.  M e a s u r e m e n t s o f d a m p i n g w e r e n o t made w i t h t h e  oells.  The  l a r g e c e l l s were c o n s t r u c t e d o f o r d i n a r y window  g l a s s , c u t and  g r o u n d t o s i z e and  D e K o h t i n s k y Cement. these double  short  cells,  No  cemented t o g e t h e r  d i f f i c u l t y has  with  been encountered w i t h  e i t h e r from mechanical f a i l u r e or from  spurious  refraction. The  t e m p e r a t u r e o f t h e s a m p l e was  the glass c e l l  i n s i d e a L u c i t e box  c o n t r o l l e d by  8x15x5  holding  centimeters,insfl.de  dimensions, through which water of the d e s i r e d temperature was  circulated.  The  aluminum p l a t e and t h e b o t t o m and  L u c i t e b o x was  held securely t o the  s i n c e t h e g l a s s c e l l was  lower  clamped between  t o p c o v e r o f t h e box t h e s a m p l e was  held  securely i n place. V i b r a t i o n s w e r e s e p up v a n e w h i c h was  o s c i l l a t e d v e r t i c a l l y i n i t s own  horn loudspeaker approximately  i n t h e s a m p l e b y means o f a  d r i v e r ( A t l a s Sound C o r p . ) .  glass  plane by  The  vane  a was  0.1x0.6x8 c e n t i m e t e r s : t made b y c u t t i n g a  microscope s l i d e lenghtwise  and  p o l i s h i n g down t h e  edges.  21  It  i n t u r n was c e m e n t e d i n t o a s l o t i n a d u r a l u m i n a d a p t e r  w h i c h was t h r e a d e d on i t s o p p o s i t e e n d .  The a d a p t e r s c r e w e d  i n t o a s m a l l L u c i t e c y l i n d e r w h i c h was c e m e n t e d d i r e c t l y t o the  t h i n b a k e l i g h t diaphram o f t h e d r i v e r .  The L u c i t e  c y l i n d e r was c e m e n t e d c e n t r a l l y a n d p a r a l l e l t o t h e a x i s o f the  d r i v e r by f i r s t mounting  the  mounting  on a c a p w h i c h t h r e a d e d  thread of the driver.  onto  I t was made t o m a t c h t h e  s p h e r i c a l c o n t o u r o f t h e d i a p h r a m b y s o f t e n i n g t h e end w i t h g l a c i a l a c e t i c a c i d and t h e n a p p l y i n g s u f f i c i e n t f o r c e d u r i n g the  c e m e n t i n g t o make t h e m a t e r i a l  flow.  The t e m p e r a t u r e was m a i n t a i n e d b y a c i r c u l a t i n g system. degrees  water  T h e t e m p e r a t u r e o f a b a t h o f w a t e r was h e l d t o ± 0 . 5 c e n t i g r a d e b y means o f a b i m e t a l l i c t h e r m o - r e g u l a t o r  ( A m e r i c a n I n s t r u m e n t Go.) a n d a 2 5 0 w a t t k n i f e h e a t e r ( C e n c o ) . Temperatures  b e l o w room t e m p e r a t u r e w e r e o b t a i n e d b y  c i r c u l a t i n g cold t a p water o r by surrounding t h e bath w i t h i c e . W a t e r f r o m t h e b a t h was pumped t h r o u g h t h e L u c i t e b a t h p a s t the  cell  b y a s m a l l c e n t r i f u g a l pump ( E a s t e r n I n d u s t r i e s  Model B - l ) a t a bout 5 l i t e r s  p»r m i n u t e .  A l i g n m e n t o f t h e a p p a r a t u s was c h e c k e d b y f i r s t  lining  up t h e v e r t i c a l c r o s s h a i r o f t h e m i c r o m e t e r e y e p i e c e w i t h a h a n g i n g plumb l i n e .  The v e r t i c a l c r o s s h a i r was t h e n u s e d  as a r e f e r e n c e f o r t h e r e s t o f t h e components.  The p o l a r i z e r  was s e t w i t h i t s a x i s p a r a l l e l t o t h i s c r o s s h a i r . B a b i n e t compensator at  The  h a s a l i n e o n t h e s t a t i o n a r y wedge a n d  r i g h t angles t o the optiB axis thus the angular scale  and v e r n i e r c o u l d be u s e d t o measure a n g l e s f r o m t h e v e r t i c i l .  I  The  a n a l y z i n g P o l a r o i d was  22  set w i t h i t s a x i s h o r i z o n t a l by  f i n d i n g t h e p o s i t i o n f o r minimum t r a n s m i s s i o n w i t h b o t h p o l a r i z e r and  compensator axes v e r t i c a l .  S t a t i c a l i g n m e n t o f t h e g l a s s v a n e was with the v e r t i c a l truly  i n i t s own  be done b y  cross h a i r . p l a n e was  of the  a l s o checked v i s u a l l y .  light  s o u r c e was  about f o r t y times  adjusted  The  The  ohms.  The  d r i v i n g s i g n a l was  conditions  s i g n a l was  s p e a k e r by a t h r e e tube audio of conventional design. capacitance  coupled  the t r i g g e r i n g impulses The  watts,  ordinary  a g a i n s t t h e 60  a m p l i f i e d and oscillator.  phase i n v e r t e r and  1637,  vane  fed to the The  cycle  loud-  a m p l i f i e r was  I t c o n s i s t e d of a r e s i s t a n c e  6S3LJ7GT a n d two  a Hammond t y p e  no  observed.  s u p p l i e d by an  p u s h - p u l l output tubes transformer t u b e s w e r e one  Slowly  d r i v e r , r a t e d a t 25  o s c i l l a t o r c a l i b r a t e d f o r frequency The  6S1-B  fraction  transducer used t o d r i v e the  a commercial horn loudspeaker  house supply;  was  circuit  over-all magnification -  and u n d e r t h e s e  electro-magnetic  could  manually  s e e n t o move  a p p r e c i a b l e l a t e r a l m o t i o n o f t h e v a n e was  audio  driving  i t d i f f e r e d f r o m t h a t o f the v i b r a t i n g vane by a  throughout I t s complete c y c l e .  16  This  was  R a d i o c o . s t r o b o t a c Type  o f a c y c l e a s e c o n d t h e v a n e c o u l d be  was  compared  i t s motion  replacing the regular synchronized  I f the frequency  was  simply  Whether o r not  of the s t r o b o t r o n w i t h a General  until  the  The  d r i v e r and  coupled  6L6jGs.  The  o u t p u t was  a p a i r of  to the,load. output  transformer  a l s o used t o  f o r the synchronized  light  c i r c u i t f o r the strobotron l i g h t source  The  supply  source. i s shown  £3  in figure  9,.  I t h a s t w o m a i n s e c t i o n s , t h e s t r o b o t r o n and  i t s associated discharge c i r c u i t , triggering circuit.  a n d , t h e p u l s e s h a p i n g and  The l e n g t h o f t h e d i s c h a r g e i s d e t e r m i n e d  by t h e 1 m i c r o f a r a d condenser and t h e t u b e i n t e r n a l and l e a d resistance.  W i t h a s i m i l a r c i r c u i t and a 4 m i c r o f a r a d  condenser a d u r a t i o n of l e s s than 5 microseconds i s claimed for the light flash  •  The d i s c h a r g e i s i n i t i a t e d b y c a u s i n g  a glow d i s c h a r g e between t h e two g r i d s .  T h i s i s done b y a  v o l t a g e p u l s e t o e i t h e r one o f t h e g r i d s ; t h e m a g n i t u d e aled s i g n being determined  b y t h e s t a t i c p o t e n t i a l s o f b o t h g r i d s r.  To o b t a i n g o o d s y n c h r o n i z a t i o n t h e t r i g g e r i n g p u l s e s  should  h a v e a s h a r p f r o n t a n d s h o u l d be o f s h o r t d u r a t i o n c o m p a r e d t o t h e i n t e r v a l between p u l s e s . w i t h a pulse shaping c i r c u i t .  Sharp p i p s were A 6N7 d o u b l e  obtained  t r i o d e was u s e d  as a s q u a r e wave g e n e r a t o r b y a p p l y i n g a v e r y l a r g e i n p u t s i g n a l and thus o v e r - d r i v i n g i n both g r i d and p l a t e The  r e s u l t i n g approximately  circuits.  s q u a r e wave was t h e n c h a n g e d t o  a s e r i e s o f s h a r p p i p s b y a n RC d i f f e r e n t i a t i n g c i r c u i t .  The  t r i g g e r i n g p i p s were a p p l i e d ; t o t h e i n n e r g r i d and,since t h e s e c o n d g r i d was n o r m a l l y 1 0 0 v o l t s p o s i t i v e , , o n l y  negative  p u l s e s p r o d u c e d a g l o w d i s c h a r g e . T h u s t h e t u b e was t r i g g e r e d once e v e r y c y c l e , p r o v i d e d p l a t e and second g r i d were near normal.  voltages  The 6 3 1 - P i s r a t e d a t a maximum o f 250  f l a s h e s p e r second so t h e c i r c u i t  constants a r e such t h a t at  a r o u n d 300 c y e l e s p e r second t h e r e c h a r g e t i m e  of the  d i s c h a r g e c o n d e n s e r i s o f t h e same o r d e r a s one p e r i o d o f t h e signal.  F r o m t h i s p o i n t a d i s c h a r g e o c c u r s o n l y when t h e  t o f o l l o w page 23  24  s e c o n d g r i d r e a c h e s some l i m i t i n g v a l u e ; s y n c h r o n i z a t i o n i s m a i n t a i n e d hut t h e f l a s h i n g r a t e does n o t exceed t h e r a t e d maximum.  T h i s m e t h o d o f s y n c h r o n i z i n g was f o u n d t o he  superior t o that of applying a synchronizing s i g n a l t o the multivibrator circuit by F e r r y et a l e)  i n the General Padio Strobotae  as used  .  M e t h o d s o f M e a s u r i n g W a v e l e n g t h a n d Damping Two methods o f m a k i n g m e a s u r e m e n t s w e r e u s e d , one  p e r m i t t e d measurement o f w a v e l e n g t h o n l y , t h e s e c o n d measurement o f w a v e l e n g t h and damping,  we w i l l  permitted  r e f e r t o them  as Method A and Method B r e s p e c t i v e l y ; Method  A  A c o m p e n s a t o r was n o t a v a i l a b l e when t h e s e e x p e r i m e n t s w e r e s t a r t e d s o i t was n e c e s s a r y t o f i n d some o t h e r m e t h o d o f m e a s u r i n g t h e w a v e l e n g t h o f sound i n t h e g e l .  As  mentioned  b e f o r e , t h e i n t e n s i t y of l i g h t t r a n s m i t t e d by a doubly r e f r a c t i n g medium ( i n t h i s c a s e a s t r a i n e d g e l ) b e t w e e n crossed  P o l a r o i d s , o p t i c a x e s o f medium a t f o r t y f i v e  to those of the Polaroids, i s proportional t o s i n  S  i s the relative retardation.  2  6  degrees , where  I t h a s b e e n shown t h a t i f  a s e c o n d d o u b l y r e f r a c t i n g medium, w i t h r e l a t i v e r e t a r d a t i o n A, i s placed  before t h e a n a l y z e r w i t h i t s o p t i c a x i s a t an  a n g l e <•< t o t h a t o f t h e p o l a r i z e r , t h e i n t e n s i t y i s g o v e r n e d by t h e f o l l o w i n g : jo< Suppose A  =-A/4  sivf z£- + i - stoAsm2*csi*£ and t h a t  +  5-in_4 sml* cosS  «< i s a s m a l l a n g l e .  i s always s m a l l i n t h e p r e s e n t case ( « i r ) , cosS  Then s i n c e 8 will  always  25  b e p o s i t i v e a n d i t s e f f e c t w i l l be t o i n c r e a s e t h e o v e r a l l illumination.  However,  s i n S w i l l be p o s i t i v e f o r p o s i t i v e S  and n e g a t i v e f o r n e g a t i v e §  .  Thus i t s s i g n w i l l r e v e r s e  every h a l f wavelength i n the g e l .  The t r a n s m i t t e d  w i l l be i n c r e a s e d f o r p o s i t i v e r e t a r d a t i o n $ for  negative S  and  light decreased  .  A m i c a p l a t e was  used t o produce t h e d e s i r e d A  was  o b t a i n e d by s p l i t t i n g m i c a s h e e t and s e l e c t i n g by  for  t h e d e s i r e d e f f e c t , t h e t h i c k n e s s was  •  It trial  a b o u t 0.027  mm..  By a d j u s t i n g t h e a n g l e o f t h e p l a t e f o r o p t i m u m e f f e c t i t was at the  p o s s i b l e t o p r a c t i c a l l y eliminate every other l i n e  and  t h e same t i m e g r e a t l y i n c r e a s e t h e a p p a r e n t s h a r p n e s s o f remaining l i n e s . M e a s u r e m n e t s o f w a v e l e n g t h w e r e made w i t h t h e m i c r o m e t e r  eyepiece.  The  p o s i t i o n o f p o i n t s o f e q u a l i n t e n s i t y on  either  s i d e o f a l i n e o f minimum o r i m x i m u m i n t e n s i t y w e r e m e a s u r e d and t h e average t a k e n as t h e p o s i t i o n o f t h e m i d - p o i n t r e f e r r e d to  some a r b i t r a r y d a t u m l i n e .  T h i s was  done f o r a l l t h e  lines  v i s i b l e on e a c h s i d e o f t h e vane, u s u a l l y about t h r e e o r f o u r . D i f f e r e n c e s between a d j a c e n t l i n e s gave t h e w a v e l e n g t h . M e a s u r e m e n t s w e r e n o t made c l o s e r t h a n a h a l f w a v e l e n g t h the  v a n e i n o r d e r t o a v o i d p o s s i b l e e r r o r s due t o  changes  e t c . a t t h e vane s u r f a c e .  w a v e l e n g t h was  systematic v a r i a t i o n i n  f r e q u e n c y was  vane.  d e t e r m i n e d by the  o f s e t t i n g t h e c r o s s h a i r a c c u r a t e l y on t h e  r e l a t i v e l y broad l i n e s . was  structural  observed at v a r y i n g d i s t a n c e s from the  The l o w e s t m e a s u r e a b l e difficulty  No  from  The  u p p e r end o f t h e f r e q u e n o y  d e t e r m i n e d by t h e d i s a p p e a r a n c e o f d o u b l e  range  refraction.  26  Method  B  This method used the Babinet compensator set up as described above,  A few measurements, only, were taken with  the micrometer eyepiece.  Measurements of wavelength could be  made r e l a t i v e l y e a s i l y but i t was not possible to measure the decay of l i n e displacement by t h i s method.  The l a t t e r  measurement was attempted by rotating the eyepiece 90 degrees so that the motion of the cross h a i r was v e r t i c a l .  The  v a r i a t i o n of i n t e n s i t y i s s i n u s o i d a l , f o r monochromatic l i g h t , and with the compensator at a small angle ( 5 ° ) small so that i t i s impossible t o hake accurate settings of the cross h a i r . This d i f f i c u l t y was overcome by photographing the image i n the eyepiece and p r i n t i n g on high contrast paper.  High speed  panchromatic f i l m was used (Kodak Super XX r o l l film) •  By  suitable exposure and development on high contrast enlarging paper i t was possible to get quite sharp v a r i a t i o n between the l i g h t and dark l i n e s and i t was then possible to make measurements of decay of amplitude.  Measurements of wave-  length were also made on the photographs, the image of the vane being used as a c a l i b r a t i o n .  As i n Method A , readings  were not taken c l o s e r than a h a l f wavelength from the vane. Measurements of wavelength could be made over the same frequency range as with Method A , but measurements of decay of l i n e displacement could only be made over a much smaller range due to the rapid decay of birefringence with increasing frequenoy.  27  The loudspeaker d r i v e r was driven at maximum rated input f o r a l l measurements.  Measurements were made on a  6% Digel-3%0otoie Acid i n Gasoline g e l to determine the v a r i a t i o n i n amplitude of m § t i o n of the vane with frequency and the effect  of input power on measured wavelength.  The  results are shown i n Table 1. f o r amplitude frequency measurements. Table  1.  Amplitude of vane, speaker input 20 watts Frequency cycles/sec.  Amplitude millimeters  100 200 300 400 500  0.5 0.8 0.4 0.15 0.05  The maximum around 200 cycles/second was caused by a mechanical resonance i n the system. wavelength was less than  2.5% f o r driving powers between  10$ and 140% of the rated power cycles/second, 5 0 ° C .  The v a r i a t i o n i n  f o r the same g e l at 340  Because of these r e s u l t s no attempt  has been made to l i m i t the vane amplitude to any p a r t i c u l a r value, t o attempt to have a constant s t r a i n e t c . .  strains  and rates of s t r a i n are apparently small enough to avoid thixotropic effects, e t c . .  No systematic v a r i a t i o n of  wavelength with distance from the vane was ever noted. The measurement of damping i s d i f f i c u l t to do accurately, p a r t i c u l a r l y i n the case of the experiments reported here.  The method of measurement was as  The positions of peaks and troughs of the  n e v y  follows. l i n e s were  28  measured r e l a t i v e t o an a r b i t r a r y base l i n e , t h e l i n e on t h e B a b i n e t .  D i f f e r e n c e s were t a k e n  s u c c e s s i v e measurements and differences.  in this  r a t i o s taken  I f t h e de£ay o f  of the  case  between successive  double r e f r a c t i o n  S  is -  exponential these  r a t i o s w i l l be c o n s t a n t  s i n c e r e a d i n g s were t a k e n quantityA/x  was  and  equal t o e  every h a l f wavelength.  °  The  t h e n f o u n d by t a k i n g t h e l o g _  of  the  average r a t i o . The and  1.5  r a t i o s found i n these and  e x p e r i m e n t s were between  were g e n e r a l l y measured w i t h a v a r i a t i o n  F r o m t h i s i t was r e f r a c t i o n and  1.1  of ~£o.l,  assumed t h a t t h e d e c a y o f s t r a i n d o u b l e  t h e r e f o r e t h e d e c a y o f s t r a i n was  exponential.  U n f o r t u n a t e l y w i t h r a t i o s of t h i s magnitude the v a r i a t i o n the c a l c u l a t e d A / x o f 0.1  i n t h e argument, so t h e v a l u e s  to considerable d)  i s o f t h e o r d e r o f 100%  Q  0  are  variation subject  error.  Material The  a l u m i n u m s o a p s u s e d i n t h e two  ments r e p o r t e d h e r e a r e since the behavior c a s e s , we  supposedly of the  s e r i e s of measuresame t y p e .  a p p e a r s t o be q u i t e d i f f e r e n t  l a b e l the f i r s t  C a n a d i a n name D i g e l a n d The  of A/x  for a  in  soap used by t h e  However  i# the  original  t h e s e c o n d b y t h e l a t e r name O c t a l .  o r i g i n o f t h e D i g e l p o w d e r i s n o t known a t p r e s e n t  a n a t t e m p t i s b e i n g made t o t r a c e i t . The particulars  two  origin  o f m a n u f a c t u r e e t c . a r e known f o r t h e  and  and Octal  powder u s e d . The  g a s o l i n e used i s o r d i n a r y commercial grade  but  29  requires some comment.  An attempt was made to make gels i n  Vancouver with l o o a l l y ohtaine^gasoline and considerable d i f f i c u l t y was encountered i n making observations due to the small amount of s t r a i n double r e f r a c t i o n .  This could possibly  have been due to a d i f f e r e n t miTing procedure or to different soaps.  However, i t was learned that other d i f f i c u l t i e s  have been experienced with gels during the past year and that much of the d i f f i c u l t y was caused by the q u a l i t y of the gasolines used.  Samples of gasoline have heen checked by  Defence Research chemical Laboratories, Ottawa^and the only acceptable gasoline at the present time appears t o be straight run from Alberta crude..  For t h i s reason a l l the gels used  were obtained from the Defence Research Board S u f f i e l d Experimental Station and were prepared with  "acceptable"  gasoline• The benzene used was reagent  grade.  Mixing was done at 2 5 ° C ± 1 ° C , i n a large " f i e l d mixer" f o r the f i r s t series and i n a small scale laboratory mixer f o r the Octal s e r i e s .  The small mixer i s designed to give  r e s u l t s s i m i l a r to those obtained with operational mixers but t h i s i s not necessarily so with the properties investigated here.  30  IV"  EXPERIMENTAL RESULTS M e a s u r e m e n t s h a v e b e e n made o n t w o g r o u p s  s e r i e s o f mixes o f D i g e l  and  i n benzene.  Maxwell  The r e s u l t s o f t h e s e t w o g r o u p s o f  mixes i n e i t h e r a)  I t was p o s s i b l e t o  the behavior of the f i r s t  element  Method B has been  (soap) w i t h o c t o i c a c i d i n g a s o l i n e  measurements a r e q u i t e d i f f e r e n t . approximate  A  (soap) w i t h o c t o i c a o i d i n g a s o l i n e  have been i n v e s t i g a t e d u s i n g Method A. used on a s e r i e s o f O c t a l  of gels.  group w i t h a s i m p l e  b u t t h i s c o u l d n o t be done f o r t h e O c t a l solvent,  D i g e l and O c t o i c A c i d i n G a s o l i n e Method A I t was f o u n d p o s s i b l e t o f i t  measurements t o M a x w e l l models.  the results of these  T h e p r o c e d u r e was a s f o l l o w s .  V a l u e s o f G were c a l c u l a t e d f r o m t h e measured according t o the equation t a k e n t o b e 0.75 gm/cm assuming  G-  f «Vy<? • 2  wavelengths  The d e n s i t y / * ? was  i n a l l oases; errors introduced by  3  c o n s t a n t a r e n e g l i g i b l e compared t o e x p e r i m e n t a l  errors.  T h e l i m i t i n g v a l u e o f G was f o u n d b y p l o t t i n g  G / f , t h e i n t e r c e p t on G / f 2  2 s  with t h i s r e s u l t v a l u e s of  G/G w e r e c a l c u l a t e d a n d p l o t t e d a g a i n s t l o g f .  element  f o r best f i t .  from t h i s  vs  0 b e i n g t a k e n a s G, t h e r i g i d i t y  of t h e e q u i v a l e n t Maxwell Model,  p o i n t s were superimposed  G  The p l o t t e d  on a s t a n d a r d p l o t f o r a  The v a l u e o f f f o r  Maxwell  = 1 was t a k e n  curve g i v i n g t h e r e l a x a t i o n time o f t h e model.  T a b l e 2.summarizes t h e r e s u l t s o f t h e s e measurements. Typical"* curves a r e i l l u s t r a t e d  in„figure ' i b .  31  Tafcle 2 Constants f^j? Maxwell Model Digel and Octoi© Acid i n Gasoline Concentration Temperature R i g i d i t y Relaxation Time v i s c o s i t y ^DigeHOotoic 3  3/4  1 1/4  1 1/2  2 1/2  6  °c  dynes/cm 2  2.5 11.2 20.5 31.2  1200 750 650 700  0.6 0.7 >1.6 >1.6  0.7 0.4 >1. >1.1  1.5 11.2 21.5 30.7 41.2 50.5  1600 1600 1500 1300 1270 1160  0.5 0.5 0.7 0.8 1.0 >2.0  0.8 0.8 1. 1. 1.5. >2.  0.7 12.3 21.7 32.2 42.0 51.3  3900 3400 2800 2200 1900 1700  0.2 0.3 0.4 >1.1  0.8 1. 1.1 >2.  1.2 7.0 14.5 25.3 36.7 49.0  780 640 600 520 500 470  0.5 0.8 0.9 1.3 1.1 1.8  0.4 0.5 0.5 0.7 0.6 0.8  0.5 11.7 21.0 31.3 41.3 51.3  1220 1120 1020 940 940 900  0.6 0.6 0.8 0.9 0.9 1.2  0.7 0.7 0.8 0.8 0.8 1.1  1.0 11.7 20.0 31.3 41.7 51.3  4600 4100 3400 3100 2900 2600  0.3 0.3 0.5 0.6 0.6 0.9  1.4 1.2 1.7 1.9 1.7 2.3  1.1 10.5 20.5 30.6 40.7 50.7  3900 4900 4100 3500 2800 2800  0.4 0.3 0.4 0.5 >1 ^1  1.6 1.5 1.6 1.8 >2.8  10"" 3 sec.  poise  ———  t o f o l l o w p a g e 31  32  The  r i g i d i t y , G,  increases with concentration.  Results f o r  b o t h s o a p t o p e p t i z e r r a t i o s a r e shown i n d f i g u r e 1<I>, log. The  G i s p l o t t e d a g a i n s t l o g . (soap c o n c e n t r a t i o n , r e l a t i o n i s approximately  three i n both cases. p r o p o r t i o n a l to the  where weight^).  l i n e a r w i t h a s l o p e of about  Thus t h e r i g i d i t y i s cube of t h e  soap  approximately  concentration.  R i g i d i t y decreases w i t h i n c r e a s i n g temperature. v s 1/T, line  where T i s t h e a b s o l u t e t e m p e r a t u r e , g i v e s a s t r a i g h t  f o r any  one  mix  b u t t h e s l o p e v a r i e s somewhat w i t h s o a p  c o n c e n t r a t i o n and w i t h s o a p t o p e p t i z e r r a t i o . for  the  and  those  8:1  f o r t h e 4:1 I f we  d e p e n d e n c e c a n be  s e r i e s were s i m i l a r but w i t h  d e s c r i b e d by an e q u a t i o n  - Oc  slightly  Q,  such  f o r the r i g i d i t y  as  i s between  2 K e a l . per mole. Since the values  f o r the r e l a x a t i o n times  by a r a t h e r i n d i r e c t p r o c e d u r e here, considered  as v e r y a p p r o x i m a t e .  they can  are  The  {yj - G>^),  to increase  magnitude of the  component o f t h e M a x w e l l m o d e l was o f G and t  and  t  However, i n a l l c a s e s i t  w i t h i n c r e a s i n g s o a p c o n c e n t r a t i o n and increasing temperature.  found  o n l y be  been found t h a t t h e r e l a x a t i o n t i m e tended t o  values  curves  assume t h a t t h e r i g i d i t y - t e m p e r a t u a r e  then the a c t i v a t i o n energy  has  These  s o a p t o p e p t i z e r s e r i e s a r e shown i n f i g u r e 1 1 .  higher slope.  1 and  Log.G  decrease with  viscous  c a l c u l a t e d from  found t o i n c r e a s e  1  the with  i n c r e a s i n g s o a p c o n c e n t r a t i o n and w i t h i n c r e a s i n g t e m p e r a t u r e and  t o dearease w i t h i n c r e a s i n g p e p t i z e r .  Viscosities  w e r e o f t h e o r d e r o f 1 p o i s e and t h e v a r i a t i o n was  about  33  100 <f i n t h e t e m p e r a t u r e 0  b)  i n t e r v a l 0 ° t o 50°G.  O e t a l - O c t o i c A c i d i n Benzene Two m i x e s w e r e i n v e s t i g a t e d , 5 % O c t a l 1 . 2 5 % O c t o i c A c i d  and 5 % O c t a l 1.7% O c t o i c A c i d . B o t h w e r e m e a s u r e d a t 25°C, t h e r e s u l t i n g v a l u e s f o r to G a r e shown i n T a b l e 3 . b e l o w . Table  5.  R i g i d i t y , G*, f o r O c t a l - O c t o i c A c i d i n B e n z e n e a t 25°C 5ft 4:1 Frequency,  c/s  6T, B y n e s / c m  126 2350  2  I§1§ 2320  199  251  2 1 7 0 2240  316 2460  397 2400  500 2320  5% 5:1  Frequency,  c/s  dynes/cm  2340  2  T26"  100  2620  158 2520  224 2280  The 4:1 g e l g a v e v a l u e s o f r i g i d i t y independent  355 2500  500 2730  630 792 2900 3 0 1 0  approximately  o f f r e q u e n c y , t h e v a l u e s f o r t h e 3:1 g e l show  a s l i g h t i n c r e a s e a t t h e h i g h f r e q u e n c y end o f t h e m e a s u r e ments.  F i g u r e 1 2 . shows l o g . A  plotted against log. freq.,  t h e c u r v e s a r e s t r a i g h t l i n e s drawn a t f o r t y f i v e i n d i c a t i n g t h a t i n b o t h cases approximated  degrees  l o g . X - f - l o g . f may b e  b y a constant o v e r t h e f r e q u e n c y range  coverdd.  The v a l u e s o f f A c a l c u l a t e d f r o m t h e i n t e r c e p t s o f t h e s e l i n e s w i t h e i t h e r a x i s are taken a s the average v e l o c i t y o f p r o p a g a t i o n and used t o c a l c u l a t e t h e average rigidity,  G  & y  value of the  .  The a v e r a g e v a l u e s f o u n d w e r e : 5%0ctal 1.25%0ctoic Acid  G  = 2700 d y n e s / e m  2  & v  5 % 0 o t a l 1.7 % 0 c t o i c A c i d  G  = 2400 d y n e s / c m  2  a v  t o f o l l o w page 3 3  34  The e f f e c t o f t e m p e r a t u r e was a l s o d e t e r m i n e d f o r t h e 3:1 m i x .  The r e s u l t s a r e shown i n f i g u r e 1 4 , b e l o w .  Rigidity, Log. f Temp. 4  °C  2.0  f o r 5 % 0 e t a l 1.7#0etoic Benzene.  2.1  2 i 2 2*3  2.4  Acid i n  2.45 2.6  2.7  2.75 2.8  2800 2 9 0 0 2850 2 8 5 0  2750 3050  17  2 7 5 0 2 9 0 0 2800 2750  2750 3 4 0 0 3 2 7 0  35  2 8 0 0 2 8 0 0 2 8 0 0 2650 2 6 0 0  3200 3500  47.3  2 6 0 0 2 6 5 0 2400 2400 2500  2550 2650 2600  3400  A s f o u n d i n t h e m e a s u r e m e n t s a t 25°C, t h e r i g i d i t y G i s independent  o f f r e q u e n c y a t l o w f r e q u e n c i e s a n d tj'ends t o  h i g h e r v a l u e s a t t h e h i g h f r e q u e n c y end o f t h e range measured. T h i s i s i l l u s t r a t e d g r a p h i c a l l y i n f i g u r e 14... l o g ^ + l o g . f 2* 2.78 U n l i k e t h e mixes  and  G  a  v  ^  2850 d y n e s / c m . 2  of Digel i n gasoline  investigated  by Method A t h e r i g i d i t y o f t h i s m i x appears t o be a l m o s t independent  o f temperature over t h e range  covered.  I n f a v o r a b l e c a s e s , i t i s p o s s i b l e t o make m e a s u r e m e n t s of t h e decay o f b i r e f r i n g e n c e . dependence o f ^ / x  0  The t e m p e r a t u r e and f r e q u e n c y  i s i l l u s t r a t e d i n U a b l e 5. b e l o w .  I t is  n o t p o s s i b l e t o make a c c u r a t e m e a s u r e m e n t s o f d a m p i n g w i t h t h i s m e t h o d a n d i n many c a s e s i t was n o t p o s s i b l e t o make any m e a s u r e m e n t a t a l l .  H o w e v e r , t h e v a l u e s shown i n T a b l e 5.  i n d i c a t e a minimum i n t h e v a l u e o f A / x  Q  as a f u n c t i o n o f  f r e q u e n c y a n d t h a t t h i s minimum t e n d s t o move t o h i g h e r frequencies as t h e temperature i s increased.  35  Table  <Vx  0  5.  f o r 5 % 0 c t a l 1 . 7 % 0 c t o i c A o i d i n Benzene 4  17  35  £.0  .5  .6  .8  2.1  .4  .4  .7  2  .3  .4  2.3  .3  .3  .5  2.45  .5  .4  .3  2.6  —  .5  —  2.7  —  .7  Log.  Temp.°C f  ,2i  Comparison  47.5  n.5  .4  .3 —  w i t h the t h e o r e t i c a l curves of f i g u r e  5.  shows t h a t t h e b e h a v i o r c a n n o t be a p p r o x i m a t e d b y a s i m p l e Maxwell element  i n t h i s case.  t h a t the r i g i d i t y remains  Not  o n l y because of the  independent  fact  o f f r e q u e n c y and  then  tends t o r i s e at h i g h f r e q u e n c i e s , but a l s o because of the minimum f o r ^ / x  Q  vs frequency.  r i g i d i t y a n d d a m p i n g may  The v a r i a t i o n o f b o t h Retarded  be a p p r o x i m a t e d  w i t h t h e r a t i o ^ j j ^ = 0.005.  by a / M a x w e l l  I t i s not p o s s i b l e t o  element  determine  t h e p o s i t i o n o f t h e minimum p r e c i s e l y s o a d e t e r m i n a t i o n o f r e l a x a t i o n t i m e has not been attempted. magnitude f o r r e l a x a t i o n t i m e i s about c)  The  order of  lOxlO"  8  seconds.  Octal-Octoic Acid i n Gasoline Method B The  r e s u l t s of t h i s series  e s s e n t i a l l y t h e same a s f o r t h e  o f measurements a r e Octal-Octoic-Benzene  36  m e a s u r e d b y t h e same m e t h o d a n d , t h e r e f o r e , c o n s i d e r a b l y from those  differ  o f t h e D i g e l mixes i n g a s o l i n e .  M e a s u r e m e n t s h a v e b e e n made n e a r room t e m p e r a t u r e o n gels ranging  i n s o a p c o n c e n t r a t i o n f r o m 3 % t o 6^ a n d w i t h  s o a p t o p e p t i z e r r a t i o s o f £:1, 3:1 a n d 4 : 1 . has  been o b t a i n e d  etc..  difficulty  i n obtaining consistent relationships  between g e l s o f d i f f e r i n g c o n c e n t r a t i o n s . due  Some  t o differences i n aging  This i s possibly  r a t e s , presence o f i m p u r i t i e s ,  I n c e r t a i n - o a s e s i t has been found t h a t t h e r i g i d i t y  o£ a p a r t i c u l a r g e l i s l e s s t h a n g e l s of^Lower s o a p concentration. A>  The  v a r i a t i o n o f r i g i d i t y , G, w i t h f r e q u e n c y i s  illustrated  i n T a b l e 6 f o r some o f t h e s a m p l e s t e s t e d . Table  6  R i g i d i t y G o f O e t a l - O c t o i c A c i d i n G a s o l i n e a t 25°G (age 2 w e e k s ) Concentration #Ootal ^Octoic  100  126  Frequency cycles/second 1 5 8 199 2 5 1  316  597  500  4 5  1 1.25  8 5 0 950 950 1 0 0 0 950 950 1150 1 5 0 0 1 5 5 0 1 5 0 0 1450 1600 1 6 5 0 1 6 6 0  3 4 5  1 1.33 1.7  1 0 5 0 1 0 0 0 1 0 0 0 1 2 5 0 1150 1 2 0 0 1250o 9 0 0 900 900 900 850 8 5 0 1200 1 3 0 0 700 700 750 800 8 0 0 950  4 5  2 2.5  400  500 4 5 0 450 550 6 5 0 750 1 4 0 0 1300 1 4 0 0 1 3 5 0 1 4 0 0 1 4 0 0 1 6 0 0  AS w i t h t h e b e n z e n e m i x e s , t h e r i g i d i t y t e n d s t o b e independent o f frequency  at low frequencies  and t o begin t o  increase r a t h e r sharply a t t h e high frequency spectrum i n v e s t i g a t e d .  end o f t h e  37  The to the  behavior of the quantity A / x  t h a t f o r t h e benzene m i x e s .  Q  i salso  similar  T h e minimum i n t h e e a s e o f  g a s o l i n e g e l s was n o t q u i t e a s l o w a s f o r t h e b e n z e n e g e l s ,  i n t h e m a j o r i t y o f c a s e s i t was a r o u n d  .5.  This together  w i t h thm f r e q u e n c y c h a r a c t e r i s t i c f o r t h e r i g i d i t y  suggests  t h a t t h e m e c h a n i c a l b e h a v i o r may be a p p r o x i m a t e d b y a r e t a r d e d M a x w e l l element w i t h a r a t i o o f p a r a l l e l t o s e r i e s v i s c o s i t y o f t h e o r d e r o f 0.01. The  d e p e n d e n c e o f r i g i d i t y o n t e m p e r a t u r e was  determined f o r t h e 5 $ 0 c t a l 1.7%0ctoie A c i d mix. w e r e made a t 2.5, 21.2 a n d 4 2 . 5  °G.  found t o be s u b s t a n t i a l l y independent  Measurements  T h e r i g i d i t y , G, w a s o f temperature  over  t h i s s m a l l range and a s b e f o r e was a p p r o x i m a t e l y i n d e p e n d e n t of  f r e q u e n c y f r o m 100 t o 5 0 0 c y c l e s p e r s e c o n d .  The average  v a l u e o f t h e r i g i d i t y was a p p r o x i m a t e l y 750 d y n e s / c m . 2  This  i s t h e same m i x a s i n T a b l e 6. a n d t h i s v a l u e c o m p a r e s w e l l w i t h t h e v a l u e s shown t h e r e f o r  25°C.  As a c h e e k o n t h e f a l l o f r i g i d i t y w i t h  increasing  c o n c e n t r a t i o n a s e c o n d measurement was made o n t h e 4% O c t a l m i x w i t h t h e same p e p t i z e r r a t i o . a p p r o x i m a t e l y 900 d y n e s / c m  2  An average r i g i d i t y o f  was f o u n d . T h i s c o n f i B m e d t h e  r e a d i n g s o f T a h l e 6. a n d a g a i n i n d i c a t e d a d e c r e a s e o f rigidity with  concentration.  The a b o v e t w o g r o u p s  o f t e s t s w e r e made a t a g e s o f  two and t h r e e weeks r e s p e c t i v e l y .  The two g e l s  appear t o be q u i t e s t a b l e and t h i s would  rechecked  seem t o e l i m i n a t e  d i f f e r i n g aging rates as a p o s s i b l e e x p l a n a t i o n o ft h e anomaly.  38  The  e f f e c t s of aging present  experiments o f t h i s type w i t h g e l s . to  a difficult I t i s very  problem i n difficult  determine t h e e f f e c t o f soap c o n c e n t r a t i o n , soap t o  peptizer ratio,  etc., unless the gels a r e . r e l a t i v e l y  o r a v e r y d e t a i l e d knowledge o f t h e i r a g i n g i s known.  stable  characteristics  T h e p r a c t i c e h a s b e e n t o make a l l m e a s u r e m e n t s  on a p a r t i c u l a r s e r i e s a t t h e same a g e , i f p o s s i b l e .  This  i s p o s s i b l y not t h e best procedure, s i n c e , i n general, d e t e r i o r a t i o n w i t h a g e i s l i k e l y t o b e more r a p i d f o r low  soap c o n c e n t r a t i o n s  o r f o r l o w soap t o p e p t i z e r r a t i o s .  V e r y m a r k e d d i f f e r e n c e s may b e c a u s e d b y i m p u r i t i e s , e g . m i n u t e t r a c e s o f a c i d on t h e w a l l s o f c o n t a i n e r s c a n c a u s e v e r y r a p i d b r e a k down o f t h e g e l . The  d i f f e r e n t a g i n g r a t e s o f t w o g e l s o f t h e same  soap c o n c e n t r a t i o n b u t d i f f e r e n t p e p t i z e r are  illustrated  concentration  i n Table 7 below.  T a b l e < 7. E f f e c t o f A g i n g on O c t a l - O c t o i c A c i d i n G a s o l i n e ( a t 21°C) Concentration ^Octal  ^Octoic Acid  5  2.5  5  1.25  Age Days  Average R i g i d i t y . G . dynes/cm'  13  1500  42  750  8  1850  48  1500  39  It  i s n o t p o s s i b l e t o make a n a c c u r a t e  o f t h e values o f A / x  determination  and so locate t h e p o s i t i o n o f t h e  Q  minimum a n d f i n d a v a l u e o f f  a  .  A l s o measurements do n o t  e x t e n d f a r enough i n t o t h e d i s p e r s i o n r e g i o n s t o f i x t h e v a l u e o f "2?  f r o m r i g i d i t y measurements a l o n e .  p o s s i b l e t o make a n e s t i m a t e o f o r d e r . always occurs  i n t h e frequency  u>lra z 1 0 i n t h i s f r e q u e n c y s  It i s  S i n c e t h e minimum  r a n g e 100 t o 500 c y c l e s / s e c o n d ,  range.  Therefore  'tf &  i s of  —3  the order of  10 x 1 0  seconds and t h e c o r r e s p o n d i n g  v a l u e o f *77 _ o f t h e o r d e r o f  10  poise.  40  Y  DISCUSSION Measurements have been c a r r i e d o u t on aluminum soap  hydrocarbon systems a t l o w s o n i c f r e q u e n c i e s .  The p r i m a r y  aim o f t h e present i n v e s t i g a t i o n has been t o determine t h e p r a c t i c a b i l i t y of u s i n g t h e transmission of transverse sonic waves a s a method o f d e t e r m i n i n g t h e m e c h a n i c a l  properties.  W i t h c e r t a i n l i m i t a t i o n s t h i s has been found t o be a u s e f u l m e t h o d , p a r t i c u l a r l y f o r t h e measurement  of r i g i d i t y .  The  f r e q u e n c y r a n g e o v e r w h i c h m e a s u r e m e n t s c a n b e made i s r a t h e r limited.  A l s o t h e measurement  is difficult  o f damping o r v i s c o u s f o r c e s  b e c a u s e m e a s u r e m e n t s must b e made i n a f r e q u e n c y  range where damping, i n s p a c e , i s s m a l l ; a t l e a s t f o r t h e cases  investigated. An a t t e m p t h a s b e e n made t o a p p r o x i m a t e t h e m e c h a n i c a l  behavior w i t h mechanical models. ing  T h i s i n one way o f comparO  r e s u l t s o f experiments u s i n g d i f f e r e n t techniques, i n  d i f f e r e n t f r e q u e n c y ranges e t c . . I t has been found t h a t may be done w i t h r e l a t i v e l y s i m p l e m o d e l s ,  m  certain  Maxwell elements a r e s u f f i c i e n t , i n o t h e r s , Retarded elments a r e necessary.  T h e d a t a a v a i l a b l e , i n most  this cases  Maxwelih  cases,  i s n o t s u f f i c i e n t t o make a r e a l l y a c c u r a t e f i t t o a m o d e l . When more d a t a f r o m o t h e r e x p e r i m e n t s a t d i f f e r e n t f r e q u e n c i e s are  a v a i l a b l e i t w i l l b e p o s s i b l e t o c h o o s e much more u s e f u l  models. ally  By u s i n g e l e c t r i c a l analogs,and a d j u s t i n g  experiment-  f o r t h e c o r r e c t impedance c h a r a c t e r i s t i c , i t i s p o s s i b l e  ( i n p r i n c i p l e ^ t o f i n d models t o match b e h a v i o r o f any complexity.  41  The  r e s u l t s f o r m i x e s made w i t h t w o s u p p o s e d l y  identical  soaps g i v e d i f f e r e n t r e s u l t s , though o n l y i n degree.  I n one  case a s i m p l e M a x w e l l element i s s u f f i c i e n t o f d e s c r i b e t h e behavior,  i n t h e s e c o n d a more c o m p l i c a t e d  Within the accuracy  model i s necessary.  o f t h e measurements and f r e q u e n c y  covered  a r e t a r d e d M a x w e l l element w i t h a v e r y s m a l l  viscous  component i s n e e d e d i n t h e s e c o n d c a s e .  G-, n e c e s s a r y  range parallel  The r i g i d i t i e s ,  f o r t h e r e s p e c t i v e m o d e l s a r e o f t h e same  order  but t h e s e r i e s v i s c o u s elements d i f f e r by a f a c t o r o f about ten,  being h i g h e r i n t h e case w i t h t h e r e t a r d e d element.  i s probable in the f i r s t  t h a t a r e t a r d e d Maxwell element would be  lb  necessary  c a s e a l s o i f m e a s u r e m e n t s c o u l d be made a t h i g h  enough f r e q u e n c i e s .  Because o f t h e l o w v i s c o s i t y and r e l a x a -  t i o n t i m e m e a s u r e m e n t s h a v e b e e n made i n t h e r e g i o n w h e r e a Maxwell element i s s u f f i c i e n t certainly i s i nthis  i f ^f/tr  s  i s small which i t  case.  A f u r t h e r d i f f e r e n c e has been o b s e r v e d . d i f f e r e n c e i n t h e range o f frequencies may b e made w i t h t h e t w o s o a p s .  This i s the  over which  observations  I n o n l y one c a s e w i t h t h e  D i g e l m i x e s was i t n o t p o s s i b l e t o make m e a s u r e m e n t s u p t o 1000  c y c l e s p e r second, i n t h e m a j o r i t y o f cases measurements  w e r e made a t f r e q u e n c i e s  o v e r 1000 c y c l e s p e r s e c o n d .  With  O c t a l mixes, b o t h i n g a s o l i n e and benzene t h e r a p i d decay of s t r a i n double r e f r a c t i o n w i t h i n c r e a s i n g frequency i m p o s s i b l e t o make m e a s u r e m e n t s p a s t most c a s e s .  made i t  500 c y c l e s p e r second i n  T h i s may b e due t o d i f f e r e n c e s i n s t r a i n  optical  c o e f f i c i e n t s o r t o d i f f e r e n c e s i n t h e d a m p i n g o f t h e ssonic  42  w a v e s . I n t h e D i g e l m i x e s m e a s u r e m e n t s h a v e b e e n made i n the  r e g i o n w h e r e <*r«l a n d ^/Xo  frequency.  decreases w i t h  increasing  A r e t a r d e d H a r w e l l element i s n e c e s s a r y f o r t h e  Octal miies,A/X6  h a s a m i n i m u m and t h e n i n c r e a s e s w i t h i n -  creasing frequency .  At t h e h i g h e r f r e q u e n c i e s t h e damping  i s more i n t h e s e c o n d c a s e a n d t h e r e f o r e l i m i t of  of o b s e r v a b i l i t y  the double r e f r a c t i o n i s lowered.  3 .  The  r i g i d i t i e s f o u n d a r e o f t h e o r d e r o f 10  square c e n t i m e t e r i n a l l eases.  dynes  per  T h e s e a r e o f t h e same o r d e r 1ST  as r i g i d i t i e s d e t e r m i n e d b y Gunn  f o r aluminum soaps i n . b  benzene a t f r e q u e n c i e s o f a few c y c l e s p e r second i n a concentric cylinder apparatus. this rigidity  I t must b e s t r e s s e d h e r e  i s neither of the r i g i d i t i e s  i n t h e model,  d i s e u s s e d i n t h e I n t r o d u c t i o n but the c u m u l a t i v e e f f e c t s e v e r a l mechanisms.  We  that  of  f i n d that the r i g i d i t y tends t o  deorease w i t h i n c r e a s i n g temperature but t h a t the e f f e c t i s small.  Now,  the retarded or configurational.  elasticity,  w h i c h a r i s e s f r o m t h e c h a n g e o f e n t r o p y due t o m o l e c u l e s u n c u r l i n g f r o m t h e i r most p r o b a b l e c o n f i g u r a t i o n s , i s p r o p -  yl o r t i o n a l t o the absolute temperature .  On t h e o t h e r h a n d ,  intermoiiecular forces give r i s e t o a r i g i d i t y which decreases with increasing temperature. to  A l s o i f we  consider the  system  be t w o p h a s e t h e r e i s t h e a d d i t i o n a l c o m p l i c a t i o n o f  i n t e r c h a n g e o f soap between t h e network and t h e s u r r o u n d i n g solution.  T h i s w o u l d p r o b a b l y temd t o r e d u c e t h e  rigidity  w i t h i n c r e a s i n g temperature by removing m a t e r i a l f r o m t h e network. the  above  The  o b s e r v e d t e m p e r a t u r e d e p e n d e n c e i s t h e sum  effects.  of  43  It  i s not  p o s s i b l e t o conclude anything  dependence of r i g i d i t y  about  the  One  would  on s o a p c o n c e n t r a t i o n .  e x p e c t t h a t t h e c o n c e n t r a t i o n w o u l d have a v e r y marked on t h e r i g i d i t y due  t o t h e r a p i d i n c r e a s e i n t h e number o f  mesh . p o i n t s w i t h i n c r e a s i n g c o n c e n t r a t i o n ? s o n t r a d i e t o r y here,  effect  The  results  i n some c a s e s t h e r i g i d i t y d o e s  r a p i d l y w i t h c o n c e n t r a t i o n and  vary  i n others i t appears  decrease w i t h i n c r e a s i n g concentration.  to  It is felt  the presence of i m p u r i t i e s i s t h e main cause of  are  that  these  differences. The  v i s c o s i t y o f t h e s e r i e s damping element i s o f  o r d e r o f 1 t o 10  poise.  T h i s i s 10  3  t o 10  5  times  the  smaller  t h a n t h e v i s c o s i t y as measured i n c o n v e n t i o n a l v i s c o m e t e r s T h i s i s t o be two  e x p e c t e d s i n o e t h e mechanisms i n v o l v e d i n t h e  cases are d i f f e r e n t .  consider the breaking In the present  .  and  I n t h e c a s e o f t r u e f l o w one reforming  o f bonds o f t h e  must  network.  case s t r a i n s are s m a l l , t h e network i s deformed  but bonds a r e a p p a r e n t l y not b r o l e n o r t h i x o t r o p i c e f f e c t s would have been o b s e r v e d . probably  e n t i r e l y due  molecules. at present  The  v i s c o s i t y observedshere i s  t o t h e movement o f s e g m e n t s o f m a c r o -  Measurements o f damping a r e not  extensive  t o d e t e r m i n e t h e d e p e n d e n c e on t e m p e r a t u r e  c o n c e n t r a t i o n e s p e c i a l l y siince i t i s a l s o c o m p l i c a t e d two  phase s t r u c t u r e of the  system.  From the  results  a v a i l a b l e t h e e f f e c t o f t e m p e r a t u r e seems t o be  small.  enough or by  the  To f o l l o w page  PLATE  I  43  VI 1.  BIBLIOGRAPHY F i e s e r , L . F . , H a m s , S.C., H s r s h b e r g , E.B., M o r g a n a , M., N o v e l l a , F.C.,and P u t m a n , S.T. Ind.  2  E n g . Chem.,38, 788 (1946)  R i d e a l , E.K., a n d o t h e r s P r o o . R o y . S o c , A 2 0 0 , 135  3  S h e f f e r , H. Can.  4  (1950)  J o u r . R e s . , B 2 6 , 4 8 1 (1948)  Alfrey,  T.  Mechanical Behavior o f High Polymers, I n t e r s c i e n c e P u h l i s h e r s I n c . , N.Y., 1 9 4 8 . 5  Burgers, F i r s t Report on V i s c o s i t y and P l a s t i c i t y R o y a l N e t h e r l a n d s Acamemy o f S c i e n c e s , N o o r d - H o l l a n d s c h e , Amsterdam, 1 9 3 5 .  6  A l f r e y , T. a n d D o t y ,  P.M.  J o u r . A p p . P h y s . , 1 6 , 700 7  (1945)  M a x w e l l , J.C. P h i l . T r a n s . Roy. S o c . London, 157, 49, 1867.  8  V a n W a z e r , J.R. a n d G o l d b e r , H. J o u r . A p p . P h y s . , 1 8 , 207  (1947)  G o l d b e r g , H. a#d S a n d v i k , 0. A n a l . Chem,, 1 9 , 1 2 3  (1947)  9  Ferry,  J.D.  R e v . S c i . I n s t . , I S , 79, ( 1 9 4 1 ) 10  Gemant, A. T r a n s . F a r a d a y S o c , 3 1 , 1 5 8 2 (1935)  11  W e g e l , R.L. a n d  W a l t h e r , H.  P h y s i c s , 6 , 1 4 1 (1935) 12  F e r r y , J.D., S a w y e r , W.M.,  and Ashworth,  J.W.  J o u r . P o l y m e r S c i . , 2, 593 ( 1 9 4 7 ) 13  A d l e r , F.T., S a w y e r , W.M.,  and F e r y y ,  J.D.  J o u r . A p p . S c i . , 2 0 , 1036 ( 1 9 4 9 ) 14  G r a y , V.R., A l e x a n d e r , A . E . J o u r . P h y s . a n d C o l l . Ohem., 5 3 , (1949)  15  Gunn, G<.B'. M o G i l l Ph.D. T h e s i s , A p r i l ,  16  1950  M a r k , H. J o u r . App. P h y s . , 12, 41 (1941)  17  Ferry,  J.D.  J o u r . Am. Chem. S o c , 6 4 , 1 3 2 3 (1942)  

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