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Some studies on the dynamic mechanical properties of synthetic egg albumin and acetate rayon fibers McIntyre, Alan David 1952

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SOME STUDIES ON THE DYNAMIC OF  MECHANICAL PROPERTIES  SYNTHETIC EGG ALBUMIN AND ACETATE RAYON  FIBERS  by ALAN DAVID McINTYRE  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in  t h e Department of CHEMISTRY  We a c c e p t t h i s t h e s i s to t h e standard  as  required  conforming from  candidates  f o r t h e d e g r e e o f MASTER OF ARTS,  Members o f t h e D e p a r t m e n t o f Chemistry  THE  UNIVERSITY OF BRITISH COLUMBIA April,  1952  - i\ -  ABSTRACT  The d y n a m i c m e c h a n i c a l and  p r o p e r t i e s o f egg  albumin  a c e t a t e r a y o n f i b e r s have b e e n d i s c u s s e d i n t e r m s o f t h e  t h e o r i e s o f T o b o l s k y , D u n e l l and Andrews and  Preissman  (I**) and Kuhn,  (17).  The d e p e n d e n c e o f t h e s e p r o p e r t i e s has been d e t e r m i n e d 27 t o 82% RH. with  relative  Kunzle  f o r a series  The v a r i a t i o n  on r e l a t i v e  of r e l a t i v e  o f t h e energy  humidity  h u m i d i t i e s from  loss factor,  o u  h u m i d i t y i s i n agreement w i t h t h e p r e s e n t  *f(^)  t  theories  o f dynamic p r o p e r t i e s ; an i n c r e a s e i n t h i s f a c t o r w i t h i n c r e a s e d relative tion It  Less  o f t h e dependence  h a s been f o u n d  tive but  humidity.  that  s u c c e s s h a s been a t t a i n e d  o f t h e dynamic m o d u l u s  i n the  on r e l a t i v e  of acetate i s independent  Ejyn  correla-  of  humidity. rela-  h u m i d i t y a t low h u m i d i t i e s , i n agreement w i t h the t h e o r y i s abnormally h i g h at higher r e l a t i v e h u m i d i t i e s .  albumin crease cable  fibers,  i t has been f o u n d  i n r e l a t i v e humidity. i n terms o f the p r e s e n t The e f f e c t s  has been f o u n d j creased  effects are  inexpli-  theories. on vdij{<-s) o f a l b u m i n  i n the energy  The d e c r e a s e  t a t i o n disagrees with the result present  decreases with i n -  These l a t t e r  of orientation  a decrease  orientation.  that  For the  loss  factor with i n -  i n dynamic modulus w i t h  expected  t h e o r i e s o f polymer systems.  fibers  orien-  on t h e b a s i s o f t h e  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 and  s i n c e r e t h a n k s t o D r . B.A. D u n e l l f o r h i s i n v a l u a b l e and  encouragement throughout The  the course o f t h i s  author i s a l s o g r a t e f u l  Council f o r the g i f t  assistance  work.  to the National  Research  o f a B u r s a r y and a Summer R e s e a r c h  w h i c h h a s made most o f t h i s work p o s s i b l e .  Grant  TABLE OF CONTENTS  Page. ACKNOWLEDGEMENTS . . ABSTRACT I.  .  B.  Mechanical Properties  of High  PoXyrncrs •  •  Synthetic  V/.  •  •  *  •  •  •  «  o  «  «  a  o  *  >  Protein Fibers  2 6  RESULTS  A.  Preparation  B.  Mechanical Properties  Results  IV.  •  EXPERIMENTAL METHODS AND  1. 2.  III.  ' . . . ±\  INTRODUCTION A.  II.  i i  o f Albumin F i b e r s  . . . . .  11  .  Vibrator . . . . • • • * . . . « C a l i b r a t i o n of the Solenoids  12  and  17  Mass D e t e r m i n a t i o n  o f V i b r a t i o n a l Experiments  DISCUSSION OF RESULTS  . . . . . 22 24  APPENDIX  . 30  BIBLIOGRAPHY  . 39  INTRODUCTION  Although the new,  the  technical  very rapid  field  development of  work i n t h i s f i e l d .  and  the  plained 5,  6,  the  7,  8,  9).  and  object  mechanical properties  of varying correlate  synthetic  frequency.  t h e i r m a n u f a c t u r e and under which the tions will ture  and  In  p e r m i t an  unique  have b e e n  e l a s t i c nature  some p o l y m e r s  of  of t h i s i n v e s t i g a t i o n  (dynamic m o d u l u s , E ,  p a r t i c u l a r , an egg  w i t h the  has  attempt w i l l  be  of molecules) imparted  ^»  vis-  made  to  degree  during  arid t e m p e r a t u r e these  r e l a t i o n between  of f i b r o u s  ex-  vibration  albumin f i b e r s with the  of the  rela-  study  dynamic  harmonic  I t i s hoped t h a t  elucidation  i s to  and  relative.humidity  made.  mechanical properties  doing  properties,  elasticity  (orientation  t e s t s are  them,  k i n e t i c theory of  of  a  d i s c u s s e s q u a l i t a t i v e l y the  f i b e r s subjected to  these properties  steam s t r e t c h i n g  to t h e i r  arrangement t o m e c h a n i c a l  of the  The  2)  ^>  q u a n t i t a t i v e l y the  c o s i t y , ^ ) of  of  Mark  led to  knowledge c o n c e r n i n g  a g r e a t many i n v e s t i g a t o r s  chain structure application  empirical  i m p o r t a n c e i s l a r g e l y due  mechanical properties,  of  comparatively  i m p o r t a n c e o f t h e s e compounds h a s  Since t h i s technical  tion  of h i g h polymers i s  materials.  correlastruc-  A.  MECHANICAL PROPERTIES OF  2  -  POLYMERS  I n o r d e r t o d e s c r i b e c o n v e n i e n t l y and mechanical  behaviour  c o n d i t i o n s , the use pots has  of  o f systems under a v a r i e t y of mechanical  i n more, o r l e s s  concepts  and  some m e c h a n i c a l  analogies  complicated p a r a l l e l  been w i d e l y adopted  basic  (10*  12,  analogies i s given has  described  An is  modulus.  fluid  deformation  one  another  and  which i s completely  variation  g the  s t r a i n and  of s t r a i n w i t h time  by t h e f l o w c u r v e f o r an  be  shape, t h e p r o c e s s i s occur,  the  process  i s given i n Figure 1(b).  whose l a m i n a r f l o w c a n be  E i s Young*s  i s illustrated  ideally  r e p r e s e n t e d by a d a s h p o t  t-at  reversible  a Hookean s p r i n g :  stress-strain plot  p r o c e s s may  units  another.  whereas, i f permanent d e f o r m a t i o n s  i s the a p p l i e d s t r e s s ,  F i g u r e 1(a) a  elastic  The  structural  flow.  r e p r e s e n t e d by  where s  the  below.  returns to i t s original  as e l a s t i c ,  d e s c r i b e d as  dash-  arrays)  introduce  0  r e s p e c t t o one  t h e u n i t s have moved p e r m a n e n t l y p a s t is  T  series  occurred, the  w i t h i n t h e m a t e r i a l h a v e moved w i t h substance  stress-strain  ( s p r i n g s and  and  13).  of  the  necessary nomenclature a short d i s c u s s i o n  When a d e f o r m a t i o n  I f the  predict  elastic An  and  irreversible  containing a  d e s c r i b e d by t h e  body  in  Newtonian  equation:  c o  Tt  fc-  I  *if)  6 = s/E j  I  Ju T  o  Figure la.  :  Time  f |  A constant stress is applied at t  Strain Figure lb.  i  S t r e s s - S t r a i n Diagram.  0  and removed at t.  -  6  d?/dt  where 6 i s t h e s h e a r the  viscosity.  tinually of  stress  stant non  s t r a i n j the s t r a i n i s therefore  relaxation  of Voigt  and M a x w e l l u n i t s  describes  these e f f e c t s .  and  the rate  a  function  2.  s t r e s s decays with time at constant  s t r e s s the s t r a i n increases  and  on a d a s h p o t p r o d u c e s a c o n -  i s f o u n d w i t h most p o l y m e r s t h a t  being designated  3(a),  acting  and t i m e a s shown i n F i g u r e It  applied  - V  s t r e s s , ii£ t h e v e l o c i t y g r a d i e n t ,  Any s t r e s s  increasing  3 ~  an  instantaneously  s t r a i n , and a t c o n -  w i t h t i m e , t h e f o r m e r phenome-  and t h e l a t t e r  creep.  as mechanical a n a l o g i e s F o r the Maxwell u n i t ,  The u s e  partially  shown i n F i g u r e  of straini s :  f o r the Voigt  unit,  shown i n F i g u r e  3(b), the rate  of strain  is:  1 At  constant  s t r a i n the f i r s t  where 5 i s t h e i n i t i a l 0  1 equation reduces t o :  s t r e s s and T i s t h e r e l a x a t i o n  time,  Slope = l/^>  Shear  Stress  Figure 2a. Modified S t r e s s - S t r a i n diagram f o r  = creep  'o f i g u r e 2b.  '  "velocity  Time  A c o n s t a n t Shear S t r e s s is o p p l i e d  removed at t .  Shear.  Permanent  deformation.  att and 0  the  time r e q u i r e d  value.  f o r t h e s t r e s s t o decay t o l / e o f i t s  The p a r a l l e l  unit  (b) w i l l  not exhibit  such  relaxation  e f f e c t s because t h e s t r e s s a p p l i e d t o a t t a i n a d e s i r e d will  depend on t h e r a t e  p a r a l l e l unit the piston  to the spring. the  initially  b e g i n s t o move a t a r a t e  as t h e s t r e s s i s gradually  Thus a r e i n f o r c e m e n t applied  change o f s t r a i n  strain  o f d e f o r m a t i o n and, once t h i s s t r a i n i s  achieved, t h e s t r e s s remains constant a t t h e value  creases asymptotically  initial  occurs during  5.  For the  which detransferred flow.  When  s t r e s s I s s u d d e n l y removed, t h e r a t e o f  i s given by:  de dt w h i c h on i n t e g r a t i o n  _  2L. f E  gives:  In p r a c t i c e , t o d e s c r i b e  c r e e p and r e l a x a t i o n  phe-  nomena, i t i s n e c e s s a r y t o assume a d i s t r i b u t i o n o f r e l a x a t i o n times  15)  #  The s i m p l e  expression:  i.  JIS r e p l a c e d  Z e~'T-  by: t  T o b o l s k y and E y r i n g  (16) h a v e s u g g e s t e d t h a t  amorphous m a t e r i a l u n d e r f o r c e d v i b r a t i o n s b y an i n f i n i t e parameters  array  of Maxwell  o r Voig.t  which a r e f r e q u e n c y dependent.  Preissman  (17)  predicted  from creep experiments u s i n g  tion  h a v e shown how  of relaxation times.  to their  t h e dynamic  c o u l d be r e p r e s e n t e d units with  t h e dynamic  parameters  an e x t e n d e d M a x w e l l i a n r e l a x a t i o n t h e o r y . m o d u l u s and dynamic  J  and be  distribu-  The m a t h e m a t i c a l a n a l y s i s  parameters from s t r e s s . r e l a x a t i o n  f  can  a logarithmic  (I**) h a v e d e s c r i b e d a method o f  f o r t h e dynamic  dynamic  Kuhn, K u n z l e  c o n c l u s i o n s i s p r e s e n t e d i n the Appendix.  D u n e l l and Andrews  rived  the behaviour of  leading Tobolsky,  predicting  curves based  The  relations  viscosity  on  de-  are:  I + urT  j i 4- ufr 2  £(T) i s a d i s t r i b u t i o n  f u n c t i o n d e s c r i b i n g the spectrum  r e l a x a t i o n t i m e s . ET(T)dT total  s p e c i f i e s the c o n t r i b u t i o n t o the  i n s t a n t a n e o u s t e n s i l e modulus, £  Maxwell  of  , of the system from  u n i t s h a v i n g r e l a x a t i o n t i m e s between T  Using a d i s t r i b u t i o n function  of the  form:  and T  +dT  E  Figure  F i g u r e 4.  3a.  Maxwell Unit.  Stress  F i g u r e 3b. V o i g t  Unit.  re t a x a t i o n and distributi on function for a p o l y m e r .  - 6 t h e s e w o r k e r s h a v e f o u n d a good and  observed values  t o the curve  of the  straight line (Figure  relaxation  4)  of a logarithmic T  1^, and  t i m e s f o u n d by  E  dynamic p a r a m e t e r s .  portion  and  c o r r e l a t i o n between  denote the  L  predicted i s related  0  stress-relaxation  maximum and  extrapolation of this  minimum  straight  line  portion.  B.  SYNTHETIC PROTEIN FIBERS. The  reasons that  m e r c i a l l y u s e f u l are  synthetic  twofold:  the  p r o t e i n f i b e r s have d e s i r a b l e and  resilience  raw  materials  and are  an  of residues a  great  and  like  of the  many and  mechanical  listed  the  common  natural  c h a r a c t e r i s t i c s , warmth, d u r a b i l i t y  a f f i n i t y f o r dyes;  being  and  chain molecules,  formation  the  fact  that  the  high  are s t r u c t u r a l l y  of f i b e r s (Figure  arrangement o f p o l a r  other  5).  The d i v e r s i t y  side groups give Proteins  polymer systems ( F i g u r e  6)  rise  The  to  are not  but,  only  because  v a r i e d c r o s s l i n k i n g mechanisms, e x h i b i t  strength.  bumin i s g i v e n  a n a l y s i s f o r p o l a r groups of  high egg a l -  i n T a b l e I , w h i l e some s t r u c t u r a l p r o p e r t i e s  i n Table  n  (19,  Ultracentrifugal cosity  that  many d i f f e r e n t p r o t e i n m a t e r i a l s .  chains  are  fact  com-  abundant.  Proteins, s u i t a b l e f o r the  p r o t e i n f i b e r s are  20,  albumin i n i t s n a t u r a l  22)  (Table  axial  I I ) and  for fiber  ratio  leads  state i s coiled  s t r u c t u r e which i s unsuited  #  s e d i m e n t a t i o n , d i f f u s i o n and  studies i n d i c a t e that the  bumin i s a b o u t 4 t o 1  21,  of native  one  visegg a l -  t o assume  into a folded formation.  that  corpuscular  s  HOOC - C H - C H  Aspartic Acid  c-o  N  cH-M  MH N  Histidine  CH-CH,-C'  / Glycine  Arinine  II  OrC  Phenyl alanine  v  CH=Ctf MH  Glutamic  Acid  O-C  Lysine  / Alanine  Serine  AW Tyrosine  CU-CH ~CH ' X  ^  yt*  CH  3  Leucine,  Y  Cz,o  CH,  /4t  Cysteine  CH-CH  Valine Figure  ^COOH  CHS  5.  Chain  structure  of  a  protein.  .CH-CN  c~o* \H-CH v  c  C Rubber  chain  c  C  \:  C  c-.c  x  C s  Q Nylon  u  NH  c  chain  NH  o  X Protein  chain  ^  ©  c  C  o  (I  NH  O X= s i d e c h a i n w i t h p o l a r g r o u p s .  o CH •K  7? ,  and  //  f  I  o  C o m p a r i s o n of a P r o t e i n  Rubber  j  t  1? \  " \  (coo']  5 i O  Nylon,  .  H  ;  Cross-linkages  (  "  s  Protein  F i g u r e 6.  NH  skeleton  with t h o s e  of  showing some p o s s i b l e cross-linKages.  All very  truly  corpuscular  r e a d i l y , the process being  molecules  (23). Such u n f o l d i n g  concentrated, for a period  and h o l d  tion  rate  vious,  proteins  undergo  denaturation  accompanied by u n f o l d i n g  of time.  I t would  appear that  molecules a r e s u f f i c i e n t  indicates a return to a folded that  stand  electrostatic  to uncurl  them e x t e n d e d b e c a u s e , o n d i l u t i o n ,  therefore,  of the  may o c c u r m e r e l y b y l e t t i n g a  electrolyte-free solution of the protein  between a d j a c e n t cles  7 -  forces  t h e corpus-  t h e sedimenta-  structure.  I t i s ob-  t h e problem o f p r o d u c i n g p r o t e i n f i b e r s  r e d u c e s t o t h e p r o c e s s o f u n c o i l i n g t h e m o l e c u l e s and f i x a t i o n in  that  state u n t i l  suitable cross  linkages  h a v e b e e n s e t up  (Figure 7 ) . When a n a n i o n i c fonate, the  i s added t o a p r o t e i n  isoelectric  directly. the  detergent,  point,  s o l u t i o n on t h e a c i d  chain  sul-  side o f  p r e c i p i t a t i o n o f t h e p r o t e i n may o c c u r  When t h e d e t e r g e n t  isoelectric  such as a l o n g  i s added on t h e b a s i c  side of  p o i n t , p r e c i p i t a t i o n o f t h e p r o t e i n does n o t  occur but solutions e x h i b i t i n g high protein-detergent  mixtures y i e l d  viscosities  result.  These  on p r e c i p i t a t i o n b y s a l t c o -  agulating  b a t h s f i b e r s w h i c h c a n be o r i e n t e d  ditions.  T h i s b e h a v i o u r i s c h a r a c t e r i s t i c o f b o t h a n i o n i c and  cationic that  detergents but not of non-ionic  t h e lower molecular weight  characteristic  detergents.  sulfonates  i n d i c a t e s , however, t h a t  under proper  The f a c t  do n o t e x h i b i t  electrostatic  are  not alone s u f f i c i e n t  and  d e t e r g e n t s w h i c h c a n be drawn i n t o f i b e r s .  of t h e p r e c i p i t a t e varies with the proportion  this  forces  t o p r o d u c e a c o m p l e x between The  con-  proteins  character  of protein to  (a)  Figure  7...  (a)  Corpuscular'  (Native)  (b)  Unfolded  chains.  (c)  Denatured  Protein  (d)  Orientation  (e)  Fiber s h o w i n g  and  Protein.  (randomly  folded).  crosSnlinking.  a m o r p h o u s and  crystaline  re-gions.  - 8 TABLE I .  POLAR GROUPS OF EGG ALBUMIN Number p e r Molecule of  Group  45,000  M.W.  Basic Imidazole  4  =NH -NH2  -amino Guanidine  H  24 15  NH n  t  N - C - ,NH  2  Acidic Free c a r b o x y l i c  -C00H  acid  51  0  Phosphoric acid  -  1  ifi  0 - P - OH t  OH Phenolic  - OH  9  Sulfhydryl  - SH  6  Disulfide  - S - S -  3  Amide  = c - NH  36  2  0 TABLE I I .  S P E C I A L PROPERTIES OF EGG ALBUMIN 45,000  M o l e c u l a r weight A v e r a g e amino a c i d r e s i d u e Number o f r e s i d u e s  111.4  weight 451000  (DP)  •  404  111.4 Total  length,  Cross section  calculated  a s one c h a i n  calculated  as four  of single chain  chains  (X~ray)  1,414 Si 354 & 9.5  ^  - 9 detergent,  ranging from  p o s i t i o n to dried,  highly floculent  with high protein  slimy residues with high detergent  t h e u n o r i e n t e d f i b e r s become b r i t t l e ,  com-  composition.  indicating  When  that  water i s e s s e n t i a l f o r flow. Electrophoretic  studies of these mixtures  a c o m p l e x i s f o r m e d between p r o t e i n of detergent  t h a t can  be bound t o t h e  c o n s i d e r a b l y i n excess combination  and  detergent.  parts detergent,  p r o t e i n i s found  of t h a t corresponding t o a  one  With a r a t i o f i n d s no  o f 90  peaks i n d i c a t e s t h a t the  composition  t h r e e p a r t s p r o t e i n t o one  t h i s p r o p o r t i o n corresponds  electrostatic  combination.  finds  are found.  On  o f one  indicating  a  with  no f r e e p r o t e i n  In t h i s  stoichiometric  and  o f 10-90  free detergent  an i o n i c  detergent  about a or  peaks, the  the order o f nine detergent T h e s e r e s u l t s a r e summarized  case  the  i o n to  50-50  detergent propor-  analysis  t o one  of  of  protein  power o f  combination  i s of  i o n s f o r each b a s i c p r o t e i n i n Figure  basis,  stoichiometric  complex, r e p r e s e n t i n g t h e maximum c o m b i n i n g For t h i s  an  protein-detergent  of three parts detergent  protein f o r detergent.  10  detergent  case the s t o i c h i o m e t r i c  With a r a t i o  complex and  w h i c h shows a r a t i o i n the  be  complex i s a p p r o x i -  detergent.  For mixtures  of protein to detergent  t i o n s are exceeded. one  to  b o u n d a r y and  protein  o f the  to a r a t i o  each b a s i c group o f the p r o t e i n ,  boundaries  amount  parts protein to  free detergent  a n a l y s i s o f the r e l a t i v e h e i g h t s of the  ratio  The  of the l o n g c h a i n s a l t s with the b a s i c groups of  the p r o t e i n molecule.  mately  reveal that  group.  8.  V a r i a t i o n i n c o n c e n t r a t i o n of s o l i d s i n the t h r e e - t o -  Composition of Complex  Figure 8.  V a r i a t i o n of protein in complex with proportion by weight of  albumin and n a c c o n o l used in mixtures. proportion one  (3-1 by weight)  The region of c o n s t a n t  at upper left c o r r e s p o n d s to a ratio of  detergent ion for each basic group of the albumin. The region of  constant c o m p o s i t i o n at lower right (1-3) c o r r e s p o n d s to about nine detergent ions for each b a s i c group, complexes have flow p r o p e r t i e s  IOO  in between  (at  Ml)  the  d e s i r a b l e for making fibers.  Composition of Fibers. 6 0 %  Acetone e x t r a c t e d  Time Figures.  Recovery of detergent from 5 0 5 0 albumitr detergent :  Using washed fibers portion is removed. extracted  complex.  and &0°/o> acetone, all detergent except the With electrolyte  by the acetone.  present,  all detergent  is  3-1  - 10 one  combining r a t i o has  except t o  increase  dicates a strong non-ionic  the  no  e f f e c t on  height  by  d e t e r g e n t s w i l l not  acetone e x t r a c t i o n s .  move o n l y t h e for  electrophoresis  complex p e a k .  This i n -  The  fact  i n nature.  This i s further  Aqueous a c e t o n e  remove a l l t h e  f o r this portion  coagulating  bath.  Since  i n d i c a t i n g weak, n o n - p o l a r  precipitation  but  the  reactions  involved  The  structure  of the  Figure  10.  detergent  a f t e r 24 must be  i s not  of  an  binding  indicating polar salt  removed d u r i n g  equilibrium nature  complex p r o p o s e d by  flow  re-  the  hours e x t r a c t i o n i n acetone,  Lundgren  I t i s e a s i l y seen from Figure  e s s e n t i a l f o r the complex.  only  bound d e t e r g e n t ,  the  containing  somewhat w e a k e r t h a n t h a t o f t h e the  that  borne  (60-70%) w i l l  t h i s p o r t i o n ; w h i l e e x t r a c t i o n w i t h 60-70% a c e t o n e  binding  data  f o r m complexes i n d i c a t e s t h a t  excess detergent  electrolyte will  in  df the  the  a s s o c i a t i o n complex i s f o r m e d .  complexing i s e l e c t r o s t a t i c out  -  properties  of the  11  ^9)  that  (Figure i s shown  water i s  albumin-detergent  9).  /_._,  F i g u r e 10.  Diagramatic detergent  representation  complex  of  albumin-  formation.  H,0  +O  S  5  F i g u r e II.  R  RSO: s - '  j  \  P r o p o s e d structure of c o m p l e x ( L u n d g r e n ) .  The extra bound de-fergen-t gives rise to a d i s t r i b u t i o n similarly charged groups along the which f a v o r s  fiow.  protein  chain  -  11  -  EXPERIMENTAL METHODS AND  A.  PREPARATION OF The  egg  albumin  and  purified  made up  FIBERS  technique  and. e q u i p m e n t f o r t h e p r o d u c t i o n o f  f i b e r s are very nacconol  i n 0.1%  simple.  c o n t a i n i n g 25%  mereaptoethanol  it).  S o l u t i o n s of d r i e d by w e i g h t  (to prevent  s o l u t i o n s a r e mixed w i t h r a p i d mixture  stirring  The  c o a g u l a t i n g bath used acidified The  hypodermic  t o pH  2 with formic  solution.  with  infrared  weight. and with  rinsed  lamps u n t i l  superficially i t no  the f i b e r  i s then  coagulating  lowered  through  a  brass  rubber coagulating  f i b e r i s removed i n w a t e r and  then  from dried  l o n g e r s t r e t c h e s u n d e r i t s own  i n t o 70%  end  of the  aqueous acetone  e x t r a c t i o n with acetone  f o r 24  fiber saturated  then elongated  step t h a t the d e s i r e d degrees  hours the  i n steam.  o c c u r s when d e t e r g e n t  i s present.  The  fibers  It i s  of molecular  i s a t t a i n e d s i n c e , a c c o r d i n g t o Lundgren  orientation  sulfate  salt.  a r e d r i e d u n d e r t e n s i o n and during t h i s  viscous  deareate  containing the  A small weight i s attached t o the  After  tion  the r e s u l t a n t  by means o f a  being thrust  A f t e r about f i v e minutes the solution,  These  acid.  s p i n n i n g "dope" i s e x t r u d e d  syringe, i t s needle  are  i s a s a t u r a t e d magnesium  s t o p p e r a t the bottom o f a g l a s s tube  salt  gelation).  and  the  albumin  of solids  i s aged o v e r n i g h t i n a vacuum d e s s i c a t o r ( t o  solution  the  RESULTS  orienta-  flow  without  fiber  i s then  •» 12 — dried  u n d e r t e n s i o n and I t h a s been  a precipitated equipment  fiber  used.  a f i b e r which  i s ready f o r t e s t i n g .  found that of a size  Precipitation  a No.  20 h y p o d e r m i c  needle  gives  most r e a d i l y managed w i t h t h e of l e s s than f i v e minutes  i s too slimy t o handle i n that  yields  i t tends to elongate  and b r e a k d u r i n g t h e d r y i n g p r o c e d u r e , w h i l e more t h a n t e n m i n u t e s appears t o reduce t h e tendency t o f l o w almost t o z e r o even i n the acetone bath. elongate only  s l i g h t l y during drying  t h e most s u i t a b l e One  must be  tower  F i b e r s p r e c i p i t a t e d f o r about f i v e  (10-20$) and a p p e a r t o have  c h a r a c t e r i s t i c s f o r t h e subsequent  c a r e f u l t o h a v e t h e steam w e l l  or else  t h e whole f i b e r  quite useless.  on d r y i n g  steps.  distributed  opaque u n o r i e n t e d p a t c h e s w i l l  p a t c h e s become e x t r e m e l y b r i t t l e  minutes  i n the  be o b t a i n e d .  and, o f c o u r s e , make  Variations i n cross  sectional  area along the length o f the f i b e r s are remarkably s l i g h t , average  d i a m e t e r b e i n g a b o u t 0.10  B.  M E C H A N I C A L PROPERTIES  1.  Vibrator The  apparatus used i n t h i s  ( 5). 2  i t i s a forced  investigation ^4)  apparatus.  solenoid  of f i n e  cemented  t o a d i s k and  The  and by  A detailed  i s g i v e n i n F i g u r e 12, a c c o m p a n i e d  the f i n i s h e d  i s very Dunell  vibrator f o r oscillating  h i g h polymer f i l a m e n t s l o n g i t u d i n a l l y . oscillator  the  mm.  s i m i l a r t o t h a t u s e d by L y o n s and P r e t t y m a n and D i l l o n  These  plan  single  of the  by p h o t o g r a p h s  of  d r i v i n g mechanism c o n s i s t s o f a  ,  Formex magnet w i r e wound on a p a p e r c o r e w h i c h i s s p i n d l e machined  f r o m a p i e c e o f magnesium.  r  WORKING PLAN OF VIBRATOR  i —  I  1 Ci*>>» tx>.••»•<*  C*d Clt<«tion  Figure 1 2 .  »»» 4, i*5l  13  The  solenoid l i e s  i n a r a d i a l magnetic f i e l d ,  s u p p o r t e d a t e a c h end justed there gap  so a s i s -no  Q  by  center  contact  f i n e nylon  the  between t h e  grams and  Dope" t o  coil  i s coated  reduce the  i s supplied with  to allow  forms the  spindle  field  and  and  the  ensure  an  with  a t h i n l a y e r of  a l t e r n a t i n g current  o f the  into small h e l i c a l  vibrator unit.  The  a n o t h e r on  ference. the  The  the  steel  ment i s f a s t e n e d  spindle.  The  other  t o a movable r o d  filament  passes over the p u l l i e s  weight.  The  length  by  f i l a m e n t s may  means o f t h e The  a  be  movable  t o be end  and and  inner are  of the  right-hand  the  other  c l a m p e d a t any  cessed  solenoid i s recorded  apparatus.  spindle. by  The  a Weston  current  coil  of the  fila-  o f the  left  tensioning  point  along  their  first  the  length  means  apparent  of the  supplied  of  to  rethe  Thermomiliammeter.  c o i l s were made d u r i n g  The  to  clamps.  during v i b r a t i o n of the  p o r t i o n o f the  Two  cemented  end  supports the  the  circum-  a m p l i t u d e o f v i b r a t i o n i s d e t e r m i n e d by  i n length  of  tested  c a t h e t o m e t e r w h i c h r e a d s t o w i t h i n 0.0002 cm.  increase  field  similar  circumference  c y l i n d e r forming the  f i l a m e n t s which are  ends o f t h e  outer  same  springs  magnetic  p o l e s , N,  the  The  from a v a r i a b l e  p o w e r f u l p e r m a n e n t m a g n e t s , two  and  annular  polystyrene  o s c i l l a t o r through leads  f r e e motion of the  gap  ad-  that  s i d e s of the  i s m a i n t a i n e d by two  radial  be  whole v i b r a t o r u n i t weighs  winding, c o i l e d  f a c i n g one  being  o x i d a t i o n o f t h e magnesium s p i n d l e .  frequency Hewlett-Packard wire that  coil  The  the  f i l a m e n t s w h i c h can  u n i t i n the  i n which i t i s l o c a t e d .  a b o u t 2.5 n  to  -  had  the  construction of  e f f e c t i v e l y three  the windings  - 14 w i t h about 250, winding  15 and 2 t u r n s per winding.  i s a s i n g l e c o i l w i t h two  A c t u a l l y the  e x t r a t a p s to i t , so t h a t  t h e r e are o n l y f o u r l e a d s i n a l l t o the c o i l .  Since the  tudes o b t a i n a b l e w i t h t h i s c o i l were too s m a l l , a second made w i t h 600,  50 and 5 t u r n s per  ampliwas  winding.  Since the v i b r a t o r u n i t of t h i s o s c i l l a t o r i s v e r y l i g h t , the machine can be used f o r v e r y f i n e s i n g l e f i l a m e n t s up t o f a i r l y high.resonant The apparatus  frequencies.  i s covered w i t h a c a b i n e t h a v i n g a  double t h i c k n e s s o f g l a s s separated by a 1/8 space t o permit temperature c o n t r o l .  i n c h dead a i r  Holes i n each end  of  the c a b i n e t permit the clamp d r i v e - s h a f t t o be t u r n e d t o a l l o w the clamps t o be a d j u s t e d from the o u t s i d e . to  P u l l e y s are f i x e d  the b o l t s o f the clamps (See photograph) over which s t r o n g  cords are looped and passed  out through  o t h e r h o l e s i n the  c a b i n e t ends to enable one t o l o o s e n and t i g h t e n the clamps from the o u t s i d e a l s o .  Thus, one i s able t o change the l e n g t h  of f i b e r b e i n g t e s t e d w i t h o u t . d i s t u r b i n g the humidity c o n d i t i o n s i n s i d e the c a b i n e t . The h u m i d i f y i n g apparatus figure.  i s shown i n the accompanying  I t c o n s i s t s of a d r y i n g tower c o n t a i n i n g s i l i c a g e l .  From t h i s tower, the d r y a i r i s s p l i t  i n t o two  streams,  one  going t o a packed tower submerged i n a t h e r m o s t a t i c a l l y cont r o l l e d bath where the a i r i s s a t u r a t e d w i t h water vapor and thence to a mixing chamber t o which the o t h e r stream goes d i r e c t l y . By means of flowmeters the r a t i o of d r y to s a t u r a t e d a i r i s cont r o l l e d t o g i v e the d e s i r e d humidity t o the a i r l e a v i n g the m i x i n g chamber.  From there the a i r i s taken to the c a b i n e t where  Figure  13.  Humidif ication  Apparatus.  -0-  1 Mixing  Chamber  X  ConsfaAt  Pressure  S ) t u r ato r  ] Air  Supply  T h e r m o s tat  Bath  Heads  15  -  -  a wet-dry b u l b hygrometer measures the  r e l a t i v e humidity.  a p p a r a t u s i s d e s i g n e d t o handle about 4 c u b i c  f e e t per  an  cabinet  amount s u f f i c i e n t  to  change t h e  a i r i n the  The  minute, once  every  minute. The forced  behaviour of a material  v i b r a t i o n s may  parameters E t i o n u n d e r an  M  if  no  rj  and  harmonic a p p l i e d  i  f f ^ f  +  frictional  and  s u p p o r t s and  action  , and of the  equation  E  =  resistance  mechanical parts  ^5.  described  or  of the  since the  R:  It  is difficult  resistance The  ^  >j  •  rewritten  R,  force  ***  (3)  x  ;  t o v e r i f y the  frequency  single Voigt  unit  of motion f o r f o r c e d F =  elastic  in with  vibra-  cos u>t  is:  <l)  C O S w t  reaction i s offered S i n c e the  by  leads  r e s u l t i n some d i s s i p a t i v e r e s i s t a n c e ,  spring part  oscillator unit be  a  one  vibrator itself.  Mx + Rx + p  where  f  air friction  ( 1 ) may  by  , whose e q u a t i o n  the  f(  be  a t any  of t h e  p r o v i d e an  leads  elastic  and  the  reaction,  pendulum P,x  as:  = F^  x  P*  cos  wt  (2)  +  *(4)  assumption t h a t  the  dissipative  i s proportional  to the  v e l o c i t y o f the  moving u n i t .  f a c t o r 2 takes account  of the  fact that  are  of f i b e r  i n the  have the  same a c c e l e r a t i o n , M  of the  apparatus.  s y s t e m and  i s not  ,  Since the  there  moving p a r t s  here r e f e r s t o the  equal t o the  sum  of the  do  two  lengths  not a l l  e f f e c t i v e mass masses o f  the  - 16 v a r i o u s components o f t h e If Equation a range  unit.  (2) i s t o be v a l i d  of frequencies, £  and ^  which are frequency dependent. are x  and  f , a steady s t a t e  ^  must be  c o n s i d e r e d as  solution i s given  ft'sih  +  f»«,  s  f o r any m a t e r i a l  over  parameters  Since the v a r i a b l e s o f equation  * a «C' cos aft where  -  by:  wt  (S)  P)  and  Differentiation of  (6)  (7)  and  of  (5)  w i t h r e s p e c t t o time  shows t h a t t h e d i s p l a c e m e n t  X N « ' F  « [ | M « )  h  4  The  (*m«* / f « ) m  x  analytically  :b y  ft on f r e q u e n c y . one that  assumes  ijttj  be  R**> be p u t  indicates  that £  a constant. condition  With  J-  found  force ratio  The  one  (fi)  of mechanical  at  differentiating(8)with  an o p e r a t i o n r e q u i r e s t h a t  amplitude i s  l  i s a maximum, was  amplitude t o impressed  resonance, i . e .  by f r e q u e n c y t u n i n g .  resonance  i s found  respect to  w,  work o f D i l l o n  et a l  equal to a  constant.  i s largely  independent  these assumptions E2£  \  c  O  Such  c o n s i d e r the dependence o f P suggests  e q u a l t o a c o n s t a n t , and h e n c e f o r R  (4 -  use  . p ) f f i V j  I n most o f t h i s work t h e c o n d i t i o n when  and  one  Also, o f uj  that negligible,  since Dillon's , P  i f  work  i s set equal to  finds that  i s satisfied  t  and  rW-  the  P  resonance and  this  in  turn,  g i v e s , from  17  -  (8)  max  Thus, t h e parameters  -  _  £ and ^ a r e g i v e n b y  j^E  +• P,  rW  (9)  andi (10)  subject  t o t h e assumption  Determination  o f these parameters  D u n e l l and D i l l o n  f  Efi  t h a t )|a)"- c o n s t a n t and f o r a l lfibers  using these  equations,  s t u d i e s by y ^ -  showed  c o n s t a n t a n d E = c o n s t a n t and s u p p o r t e d  the v a l i d i t y  t a i n i n g t h e parameters  The method o f mass  tuning,  a s shown b y t h e s e w o r k e r s ,  parameters  2.  by t h i s m e t h o d .  The  o f t h e S o l e n o i d s and Mass  s o t h a t t h e f o r c e t h e y e x e r t c a n be  from the current that whole a p p a r a t u s  was  in  field  t h e magnetic  i s put through  The  them.  s e t up v e r t i c a l l y from  a linear  determined  To do t h i s ,  and t h e s o l e n o i d  spring  the suspended  o f a c c u r a t e l y known  The v i b r a t o r and s p r i n g were t h e n l o a d e d w i t h a  cession of a n a l y t i c a l weights, approximately  direct  Determination  two s o l e n o i d s , o r v i b r a t o r u n i t s , c o n s t r u c t e d  were c a l i b r a t e d  to  g i v e s t h e same v a l u e s t o t h e  but i s very t e d i o u s .  Calibration  modulus.  o f ob-  the vibrator  i t s o r i g i n a l unloaded  current through the c o i l  being brought  sucback  p o s i t i o n by p a s s i n g a  i n the appropriate d i r e c t i o n .  c u r r e n t and t h e d i s t a n c e b e t w e e n t h e l o a d e d a n d  unloaded  p o s i t i o n s were r e c o r d e d .  18 -  The f o r c e w h i c h t h e  current  exerts i s  given by  where F\ t h e  l o a d i n g mass, g t h e g r a v i t a t i o n a l  modulus o f t h e  s p r i n g a n d <a* t h e d i s t a n c e between t h e  unloaded p o s i t i o n s . line  The p l o t  o f s l o p e ^ dynes/ma.  mean-square v a l u e , mum f o r c e o f \Ii  against  I gives  a straight  An a l t e r n a t i n g c u r r e n t whose  root-  .  The c a l i b r a t i o n  f o r u n i t s 1 and  curves  16,  17,  2 0 , 21  22. The  e f f e c t i v e mass o f t h e  from V i b r a t i o n a l data In E q u a t i o n  s y s t e m may b e d e t e r m i n e d  when t h e s o l e n o i d s h a v e been c a l i b r a t e d .  ( 8 ) , Ru) i s n e g l i g i b l e compared t o  o f uJ w h i c h a r e n o t t o o c l o s e t o vo^, . against  o%  f o r any m a t e r i a l t e s t e d  d e v i a t e s from a s t r a i g h t l i n e being  i n the  should  a series o f frequencies  18,  23  la,  2a a n d 2b.  and  24 g i v e  values  of t ~  a curve  m  a  X  which  of F + m  X  N y l o n f i l a m e n t s were a n d *W*>r  obtained  on e i t h e r s i d e o f r e s o n a n c e .  p l o t s o f (F^^  The f a c t  yield  for  only near resonance, t h e slope  v i b r a t o r and v a l u e s  for  tfui-P  Hence a p l o t  PI, t h e e f f e c t i v e mass o f t h e s y s t e m .  placed  2a  l o a d e d and  on t h e A.C. ammeter, i s i " e x e r t s a m a x i -  read I  off  2, w i n d i n g s a , b and c , a r e shown i n F i g u r e s 15, and  K the  constant,  /Xm>tx)  against  of"  t h a t t h e e f f e c t i v e mass o b t a i n e d  Figures  f o r windings from  ;  a n d 2b d i d n o t a g r e e l e d t o t h e f o l l o w i n g method o f r e - e v a l u a t i n g  both t h e c o i l  calibration  a n d t h e e f f e c t i v e mass o f u n i t No. 2. — i  Assuming the be  coil  theforce corresponding  c a l i b r a t i o n t o be i n e r r o r , l e t  f ^ ^ x  t o a c u r r e n t J < a c c o r d i n g t o t h e D.C.  Current  (ma)  Current  (ma)  Current  (ma)  8  F i g u r e 19.  2  4  Calibration  6  8  of  Spring  10  Elongation  No. 2.  12 (cm)  14  16  18  400h  10  20  30  40  Current (mo)  5C  60  - 19 calibration, the  and l e t  c u r r e n t I,  n  Let  basis  Fmax  Now:  be t h e a p p a r e n t of  brational  F'  be t h e t r u e f o r c e c o r r e s p o n d i n g t o  mass o f t h e s y s t e m d e t e r m i n e d  v a l u e s , and l e t M be t h e t r u e mass.  data  o b t a i n e d we  on t h e  Using the v i -  have:  and:  sufficiently  f a r from  From t h e s e two  resonance  that  ^ui  may be n e g l e c t e d .  1  equations:  Now:  N e x t a known mass repeated.  M  +  M, :  Then we  M,  i s added t o t h e u n i t  experiment  have;  I"*"*' I  P  and t h e  9  H't '  (Hid  M ?  '  ; f- (»?»•)'-"' M  4  \  i  and  J  f l a n d .(M+M,)  experimental plots  20 -  are,  of course,  o f (F^^  the slopes  t*> ' .  against  /*»*«•*)  o f t h e two 2  This  c a l i b r a t i o n p r o c e d u r e was c a r r i e d o u t f o r b o t h w i n d i n g s No. 2 .  The r e s u l t s  a r e summarized i n t h e f o l l o w i n g  re-  of unit  table.  TABLE I I I  (M  Winding a  Winding b  M'  3.103  2.285 ± 0.085  M  5.237  5.237.  8.550 1 0 . 2 0 1  7.614  ± 0.266  p  1.038  1.018  i 0.067  M  2.990 ± 0 . 2 1 8  x  + M)»  x  F r o m t h e two v a l u e s was  i 0.072  i 0.052  2.245 i  of M i n thetable  0103(2.990)^0218(2  M  Using t h i s value  1  of M  _  2.5IG  0 218+ 0209  o f M, a v e r a g e  shown i n T a b l e  2^)  :  values  e a c h w i n d i n g and c o r r e c t e d v a l u e s  la  value  obtained:  —/y| - „  are  an average  0.209  IV, together  o f p were  obtained f o r  o f Jf d e t e r m i n e d .  with the ^ values  These for  results  winding  and 2 c . Unit  y Original  £  JT.Corrected  la  1.03.7  -  -  2a  568.0  1.233  460.6  2b  7.700  0.9082  8.478  ac  1.970  - 21 Evaluation  f> and  of The  gible  R,  elastic  compared t o t h e If h  unit.  placement of the  of  i s the the  u n i t and  direction  reaction  of the  ('$)  filaments  equation o f motion f o r f r e e  Very l i t t l e that  any  i s , variations ,  be  i s attainable  i n the  dis-  same  vibrator unit  Thus  t e s t s i s comparable t o  the  is :  obtained  from the  decrease  oscillations:  i n the  determination of  encountered  6 dyne-sec/cm, the  calculations.  to the  vibrations  the  i n the  vibrator  (10)).  f(  filament  negli-  height,  sample f i l a m e n t s .  magnitude o f  f  in  small  of the  attached  are  a rise  the  acting  >j s u c c e s s i v e  o f ± 20%  of  M$x/n  and  damping f a c t o r can  precision  pendulum a c t i o n  suspension, then a  reaction  Equations  amplitude during  c o i l e d leads i s quite  i s a c c o m p a n i e d by  elastic  W i t h no  in  the  a restoring force  (See  from which the  of  e f f e c t of the  height  unit  as t h e  P, a Mg/h  -  %  error  those  but,  because of  contribution  from the  other  f?,; the  to variables  = 22  -  RESULTS OF VIBRATIONAL EXPERIMENTS  Dunell  and  m o d u l u s w i t h t i m e and a filament  Dillon  found  a dead  r i g o r o u s l y t h e dynamic p a r a m e t e r s a n o t h e r , t h e dynamic p r o p e r t i e s  load.  o f one  In o r d e r t o  s h o u l d be m e a s u r e d a t a  of t e n s i o n t o the filament  Since p o i n t s f o r comparison  p e r i m e n t a l p r o c e d u r e was in  were n o t  the time  s m a l l a s t o be  The  temperature  c m  .2  and r e l a t i v e  f i b e r s were a l l o w e d a t l e a s t  all  strain  ex-  parameters  on t h e  during  fiber.  f o r albumin  of the moduli 16  hours to  and  amplitude  was  gm.  experi-  viscosities.  come t o  at resonance  0.5  0.25  h u m i d i t y c o n d i t i o n s o f each  with the humidity conditions before the a d d i t i o n The  are  u s e d f o r a c e t a t e r a y o n was  c r o s s - s e c t i o n a l a r e a and  ment a r e g i v e n on t h e p l o t s  weights.  compa-  obtained, the  insignificant  the experiment  The t e n s i o n i n g w e i g h t p e r 10-6  such t h a t  b e f o r e d y n a m i c m e a s u r e m e n t s were  r e q u i r e d t o complete  gm.  time  concerned  A f t e r t h i s t i m e t h e c h a n g e i n t h e dynamic  w i t h time i s s u f f i c i e n t l y  of  t o allow the f i b e r to creep i n p o s i t i o n  t h e v i b r a t o r f o r 18 h o u r s  made.  compare  f i b e r with those  r a b l e p o i n t s on t h e c r e e p c u r v e s f o r t h e f i b e r s reached.  i n dynamic  a decrease i n the energy l o s s f a c t o r f o r  as i t creeps under  a f t e r the a p p l i c a t i o n  a marked i n c r e a s e  The  equilibrium of the about  tensioning  0.002 i n  experiments. I t was  thought  advisable  m e a s u r e t h e dynamic p a r a m e t e r s  that, before attempting to  o f the albumin  fibers,  tests  should  23  be  made on  obtained  acetate fibers  by D u n e l l and  and  differing 28 a n d  the  Dillon.  a r e g i v e n i n F i g u r e s 27 cosity  and  31.  E a c h f i b e r was  allowed  variation  o f two  and  of t h i s  120%)  egg  comparison  o f dynamic  are g i v e n  v i b r a t e d at the lower  r e l a x without  those  the  a d d i t i o n of the t e n s i o n i n g weights f o r the  humidity  before  second t e s t  variation  f i b e r to f i b e r  same r e g u l a r i t y o f v a r i a t i o n  was  decided  Here a l s o ,  test.  and  not  since the  found  to test  one  The  acetate f i b e r  at t h r e e  v i b r a t e d at the  t o r e l a x 16 h o u r s w i t h o u t  before the  of these  previously with acetate  t h e f i b e r was  allowed  humidity  at  o f t h e dynamic p a r a m e t e r s o f  albumin f i b e r s i s w i t h i n the  and  first  humidity. Since the v a r i a t i o n  was  of  i n Figures  t e n s i o n f o r 24 h o u r s  then  humidity  vis-  albumin f i b e r s  and  the higher  to  (54%  compared w i t h  results  The  modulus w i t h f r e q u e n c y steam e l o n g a t i o n  results  The  30.  and  -  lower  parameters  from with  ( F i g u r e 27),  i t  relative  humidities.  humidity  first  t e n s i o n at the  higher  t e n s i o n i n g w e i g h t s were added f o r t h e  r e s u l t s of these  egg  next  experiments are given i n F i g u r e s  29  and) 32. R e s u l t s of s t r e s s r e l a x a t i o n on  acetate with  varying humidity  in  F i g u r e s 33' and  34.  and  on  e x p e r i m e n t s by albumin  (54)  J. Pattison are  given  300  200  100  Figure 2 7 .  Comparison of V i s c o s i t y  for A c e t a t e ©O  with that of  Dunell a Dillon  • O  Different  10 10  " " 1 1  Durtell and Dillon  6 5 % R.H.  this i n v e s t i g o t i O n Q  Data  5 3 % R.H. 6 7 % R.H. 4 6 % RH.  ' Fibers  4 3 % R.H. Used  For  Each  -i—i  Run.  ' i 10'  Viscosity  J  I  1 L  8  10'  -H- Albumin  (54)  6 0 % RH,  72°F.  500  * *  (54)  7 8 % RH,  73°F.  400  OO  (|20)  6 0 % RH, 7I°F.  (|20)  77%RH,72°F.  XX 300  200  -  100 -  Figure  28.  Dynamic  Dependence Viscosity  F i b e r s on R e l a t i v e  30  of  of Albumin  Humidity.  J  id  6  I  )  l  .o  I. 7  Viscosity  J  I  I  i  I  10'  V iscosity  Figure 30-  Dynamic  Modulus of  Acetate.  Modulus given by Dunell about 2 0 % higher.  J uu  r  1  GO  74°F,  82%  RH.  + +  70°F,  46%  RH.  x X  7I°F,  53%  RH  L  ibo"  200  o  o  +  o +•  Figure  0 0 + + x  x  » 4  31.  Dynamic  Albumin  M o d u l u s of Albumin  (54)  7I°F,  6 0 %  (54)  72°F,  7  (|20K72°F, (120)  73°F,  Fibers.  RH.  7%RH.  60%RH.  x  *  *  77%RH.  •  J  10  *  I  L  100  •  -  *  •  200  300  400  X  6-  ©  °  o  *  +  ul  x o  5K  O  m  a• u  4h  Figure  32.  Dynamic  • • • •  4-J «  ©  '• +  +"  o  M o d u l u s of A c e t a t e .  3  0 0  71°F,  27%RH.  F i b e r I. + 4  7I°F , 48%RH.  XX  7 2 ° F , 7 7 % R H .  FlbarZ. J 10  +  +  Q  -  I ^  • • 7S°F, 39% RH. 0 3 76°F, 58% RH. d9 75°F, 82% PH. I  I  L_J  100  2-  I 200  t 300  l 400  H  y  Figure  34-.  .Stress Relaxation  7 5 ^ ,  >'0I  !  1  I  O)  ho  io Titrte  for  6 S % K H -  L ie>o (sec]  C i t ^ v e a  ! \Ooo  \o ooo t  - 24 -  DISCUSSION OF  The  fact  that  RESULTS  the p l o t s of l o g  are l i n e a r  with a  s l o p e o f about  hyperbolic  r e l a t i o n between t h e  -1  rj(uj a g a i n s t l o g  v e r i f i e s the  the  slopes from  caused  t h e v a l u e o f -1  by a p p r o x i m a t i o n s  of r e l a x a t i o n  i s not understood,  made i n d e t e r m i n i n g t h e  has  also  been f o u n d  but  may  be  distribution  f o r the p r e d i c t e d  o f d y n a m i c m o d u l u s on f r e q u e n c y .  i n d e t e r m i n i n g a c c u r a t e l y the  vibrator  fre-  Deviations of  The  c r e a s e i n modulus a t h i g h e r f r e q u e n c i e s i s c a u s e d culty  and  times.  Verification independency  approximate  internal viscosity  q u e n c y a s d e s c r i b e d by Kuhn e t a l ( A p p e n d i x ) .  aV  effective  slight by t h e  mass o f  dediffi-  the  unit. From t h e  where  equation:  mass added t o u n i t m  mass o f v i b r a t o r  3/n A  gravitational  UJ  y  the resonance  frequency  unit  constant/height of  cross-sectional  t  to lower  area of  l e n g t h of  fiber  resonance  frequency  fiber  suspension  - 25 it  i s easily  s e e n t h a t , when M  frequencies),  any d i s c r e p a n c y f r o m  have a n i n s i g n i f i c a n t to  effect  t h e t r u e value  to zero.  h i g h t o low resonance In  vibrational  decreases  strain  humidity  energy  loss  in  b u t , a s shown i n F i g u r e 2 9 ,  amplitude,  fibers  decreased.  t h e resonance  the v a r i a t i o n  area.  a b s e n c e o f t h e same r e g u l a r i t y  As shown i n T a b l e at  i s within  o f the humidity  effect  because  , appearing  o r the slope o f t h e creep  IV, i t h a s been f o u n d  h i g h e r h u m i d i t i e s , and h e n c e  caused  different  T h i s i n c r e a s e i s expected  22 o f t h e a p p e n d i x ,  relative  This explains the  ^(<^) d e p e n d s on t h e m a g n i t u d e o f t h e q u a n t i t y in Equation  This  frequency.  t h e d a t a f o r w h i c h were o b t a i n e d u s i n g  f o r each experiment.  about  the actual  which i n t u r n i s probably  i r r e g u l a r i t y of cross-sectional  F i g u r e 27,  obtained vary  f a c t o r , uotyfcd) , i n c r e a s e s w i t h  the f i b e r t o f i b e r v a r i a t i o n  apparent  of determining  a t h i g h e r f r e q u e n c i e s because  increases the % e r r o r i n determining  by  on E(<^) w i l l i n -  The a c c u r a c y  length of f i b e r being vibrated i s being  The  will  frequencies.  a d d i t i o n , a t constant amplitude  ofm  on El**) b u t , when M i s s m a l l (0  i s 7% and, i n g e n e r a l , t h e v a l u e s o f B(ui)  10% f r o m  the  (20 t o 100 gm. a t l o w  10 gm. a t h i g h e r f r e q u e n c i e s ) , t h e e f f e c t  c r e a s e a s f"l i s d e c r e a s e d ro  i s large  uuy(&)  that fibers should  creep  curve. faster  increase with  humidity. TABLE I V Elongation  o f A c e t a t e u n d e r 10 gm. T e n s i o n i n g W e i g h t f o r 18 H o u r s  38% RH. 58f 82%  0  RH. RH.  1.543 3.512 9.850  mm. mm. mm.  - 26 An i n c r e a s e i n t h e e n e r g y found  by H o n o l d  hysteresis  and Wakeham ( 7)  The p r e d i c t e d  77% RH.5 .0  1()9  x  ;  from  2  c u r v e s o f wet  l o s s f a c t o r h a s a l s o been comparison  value of  dynes/cm  3.0  dicted,  x 109  ( F i g u r e 34),  uoyj(o>)  (Figure  2  33)  f o r "albumin  x 109  .  2  v a l u e o f 1.2  a t 65% RH. and 4.5  2.24  x K)9 d y n e s / c m  a t 77%  RH.  2  a t 67%  ( F i g u r e 29).  RH.  be e x p e c t e d  u n l e s s both  curves are obtained from  relaxation  experiments  of a viscous nature of deformation)  and n e g l e c t s a n y s o l i d  effects  of the energy  i n the vibrational  i n most f i b e r s lost  RH.  27)  and  e x a c t agreement and  vibrational fiber.  of f r i c t i o n a l  friction  forces  effects  studied  per c y c l e /  of the presence experiments  In a d d i t i o n ,  D u n e l l and of  solid  assumes  of the h y p e r b o l i c  by E y r i n g e t a l ( $ ) t o d i s c u s s t h e s t r e s s 2  and s t r e s s - s t r a i n  curves of acetate.  i n this  investigation.  relaxa-  I t seems r e a s o n a b l e ,  however, t o assume N e w t o n i a n b e h a v i o u r f o r t h e s m a l l amplitudes used  them  fraction  the theory  case  (dissi-  and f o u n d  or only a small  Newtonian v i s c o s i t y which i s t h e l i m i t i n g s i n e law used  (Figure  of rate o f deformation).  investigated the p o s s i b i l i t y  t o be a b s e n t  tion  a t 76%  ( d i s s i p a t i v e f a c t o r p r o p o r t i o n a l to v e l o c i t y  p a t i v e f a c t o r independent  friction  109  pre-  i ^ l j ( ^ )  x 109  on t h e same  The t h e o r y assumes t h e p r e s e n c e  Dillon  x  Because o f the f i b e r t o  f i b e r v a r i a t i o n o f t h e energy l o s s f a c t o r , cannot  at  n  d o e s n o t compare t o o  For acetate the values of  dynes/cm  (54)  compare more f a v o r a b l y w i t h t h o s e e x p e r i m e n t a l l y  determined, 2.15  28)  (Figure  2  stress-strain  and d r y f i b e r s .  f a v o r a b l y with the e x p e r i m e n t a l l y determined dynes/cm  of  strain  - 27 The fibers  i s as  effect  ideal  s l o p e and  on u)y(co) f o r t h e  of orientation  expected.  The  r e l a x a t i o n mechanisms and o f an  -  spring.  The  t h i s would  more h i g h l y  approaches relaxation  f i b e r has  more c l o s e l y t h e  fewer  behaviour  curve would have a s m a l l e r  the u » y M  cause  oriented  albumin  f a c t o r t o have a  smaller  value. It  has  been f o u n d  m o d u l u s on r e l a t i v e  that  the dependence of  h u m i d i t y i s not  present theory of the mechanical The  dynamic  e x p l a i n a b l e i n terms of  behaviour o f polymer  the  systems.  equation:  f o r t h e dynamic m o d u l u s d i s c u s s e d i n t h e  I n t r o d u c t i o n reduces  to:  E with the  E°  £ + E to r 1  w  S  +e*io u>  m  S  »I  and  \JJl\ « |  i s the slope of the  stress  relaxation  a r e t h e maximum and minimum t i m e s o f t h e  spectrum, event t h a t 4 but and  -  restrictions:  uj'fo  and  v  W  E,  takes i n t o account  any  the s t r e s s does not decay  approaches  asymptotically  residual to  7^  relaxation  stress  zero as  curve,  ( i n the  shown i n F i g u r e  some v a l u e g r e a t e r t h a n  zero)  i s t h e f r e q u e n c y a t w h i c h the modulus i s measured.  With the humidity of  correct, and  the  slope of the  elastic  acetate,  relaxation  calculated  n  cycle  t o decay to  curve,  f r o m the  in  is  slopes  t i m e s s h o u l d be  This,  of course,  esis in  a s s u m p t i o n o f Hookean b e h a v i o u r  t h i s c a l c u l a t i o n , the  of  l o g time at 29.  On 7*,^  z e r o , were n e x t  of the  stress  where  E,  relaxation  , as b e f o r e ,  i s the  basis  , the  of  of  of  stress  f o r the  Because of the  stress  geometry  diagram,  i s any  residual  stress greater  curve to  E,  instead  of t o  contributions  r e l a x a t i o n mechanisms and  any  residual  summarized  to  stress.  i n Table  V .  zero  of  zero s t r e s s .  the  c a l c u l a t i o n are  than  extrapolation  completely define  of t h i s  in  h u m i d i t y , were  time required  calculated.  for  decrease  these rates  r e l a x a t i o n t i m e o b t a i n e d by  stress relaxation £,°io<j7£ w i l l  t o the  each r e l a t i v e  the  utye**)  values of  directly proportional  decay, r e l a x a t i o n t i m e s ,  sults  £<jy  initial  obtained from Figure  of the  stress  same a t a l l h u m i d i t i e s .  which are  s t r e s s per  relative  mechanisms.  For  1^  v a r i a t i o n with  c o r r e s p o n d i n g maximum r e l a x a t i o n  agreement w i t h t h e  and  the  ,. w h i c h a c c o r d i n g t o t h e o r y i s e q u a l  i t i s found t h a t  s e n t i a l l y the  any  -  assumption t h a t  tu^(u>)  magnitude t o the  28  the Thus,  Edyn The  re-  - 29 TABLE V  E°OC  U)tf(Ui)  0.09 x 1 0  4.75  10  4.87 x I O  39% RH.  0.125 x 1 0  48% BH.  0.17  0.10  4.76  4.86  77$ RH.  0.23  0.16  4.60  4.76  The tate  1 (  variation  Hjy  of  n  1 0  x  with r e l a t i v e  a t t h e l o w e r h u m i d i t i e s i s s m a l l (5%)  1 0  humidity  of ace-  and, c o n s i d e r i n g t h e  many a p p r o x i m a t i o n s made, c o n f o r m s t o t h e t h e o r y b u t t h e l a r g e i n c r e a s e a t t h e h i g h e r h u m i d i t i e s f o r a c e t a t e and t h e s i g n i f i c a n t decrease  i n t h e modulus o f t h e a l b u m i n  midities  are inexplicable The  dependence o f  t o be n e g l i g i b l e The  expected from i n degree  a t t h e h i g h e r hu-  on t h e b a s i s o f t h e p r e s e n t t h e o r y .  Edy*»  on temperature,  w i t h t h e work o f o t h e r i n v e s t i g a t o r s found  fibers  (17,  2  9,  f o r s m a l l temperature  30)  f  i n agreement h  a  s  D e  variations.  i n c r e a s e i n dynamic m o d u l u s o f e g g a l b u m i n increased orientation  of c r y s t a l l i n i t y  en  fibers  and accompanying i n c r e a s e  has n o t been  found.  1 0  - 30 -  APPENDIX DETERMINATION OP DYNAMIC PARAMETERS FROM. CREEP EXPERIMENTS BY THE METHOD OP KOBE? KUNZLE AND  lor  this  a n a l y s i s the simple  E -  PREISMANN,..  expression:  O  -f-  i s r e p l a c e d by:  where  t h e e l a s t i c m o d u l u s i s now  the p a r t i a l the  infinite  that u n i t . by  elastic  an  time  modulus b e l o n g i n g  a r r a y and  dependent.  E{  0  i s called  t o t h e i t h component i n  7j I s t h e c o n s t a n t r e l a x a t i o n  I n t h e l i m i t , t h e summation  time o f  i n (2) c a n be. r e p l a c e d  integral:  £<+)--e"^  13)  o vrhere arising trum;  AT  i s t h e sum o f t h o s e  i n the i n t e r v a l  between T  i e . i t i s the d i s t r i b u t i o n  moduli.  Infinity.  and T + ^ o f  modulus  the e n t i r e  d e n s i t y o f the p a r t i a l  F o r the i d e a l  i n (3) must h a v e t h e l i m i t s  c a s e \^hen  t , the time between  spec-  elastic  S i n c e t h e v a l u e s o f 1r i n (2) assume a l l p o s s i b l e  c r e t e v a l u e s , the i n t e g r a l  of  components o f the e l a s t i c  dis-  z e r o and initia-  t h e e l o n g a t i o n arid measurement o f the t e n s i o n i s z e r o ,  then:  - 31 -  It  i s seen from  (2) and  e l a s t i c "behaviour o f a s u b s t a n c e spectrum, of  a s 'soon a s t h e r e l a x a t i o n  T ~ i n ( 3 ) , i s g i v e n as a f u n c t i o n dT  by:  '.. .  and  this  strain  increment  increment  of stress  decays  time  o f time.  i n a time e l e m e n t  i n a time p e r i o d t a t .  i s c o n s t a n t a t t , , b y an  dt , final  can p r e d i c t the  i e . . a l l v a l u e s o f £;„ a n d 7^ i n ( 2 ) o r t h e magnitude.  An  The  ( 3 ) t h a t we  4t  i s given  to t a t , ,  i f the  amount:  ld  s t r e s s a t the time t  {  i s found by e v a l u a t i n g  the i n t e -  a On t h e b a s i s  of a continuous d i s t r i b u t i o n of r e l a x a t i o n  substitution  o f (.3) i n (7) y i e l d s : Sf|  , fjL Jf^-WjTJt  Similarly, F. M  and —  i s the r a t e  i f a shearing force of shear,  times,  (8) a t any  instant  t, i s  then:  flf  19) where p. i s P q i s s o n ' s r a , t i o ,  - 32 -  i  Assuming  i s large  the  s p e c t r um um then, f o r ^  (9)  "becomes:  c Thus t h e f o r c e velocity  t,»T  t  constant  i l  !  exerted  compared t o t h e 1^'s  5-  derived  i n the i n t e r v a l , zero  (JO)  p e r cm.2 "becomes s i m p l y  i n d e p e n d e n t o f a n y c h o s e n f, p r o v i d e d  a constant  i s observed. viscosity  defined as:  in)  r-jiit C o m p a r i s o n o f (10) and  Therefore  ( l l ) gives:  i t i s seen t h a t  the v i s c o u s  nature  of a material  "be d e t e r m i n e d f r o m t h e r e l a x a t i o n time d i s t r i b u t i o n . continuous d i s t r i b u t i o n  1 • ifc) where ft'  flow  the r e s t r i c t i o n  S u c h a r e l a t i o n h o l d s f o r H e w t o n i a n f l u i d s whose is  to t , ,  y  p  from  i t i s assumed t h a t  , and t h a t  held  P& ™ r  s  (12) becomes:  (9)  i s still  connecting  limit,  7j'.  n o t f u l f i l l e d b u t 4r  v a l i d b u t the s h e a r i n g  d e p e n d e n t on b o t h t and v i s c o s i t y . (  (l3)  I n i t i a t i o n and measurement  i s large-', compared t o  t h e c o n d i t i o n t,»%Is  constant,  For a  t h e d i s t r i b u t i o n h a s an u p p e r  t h e time b e t w e e n f l o w  of the shear f o r c e If  of  can  force  The c o n t r i b u t i o n  mechanism f o r w h i c h T r j f r t i s :  is still i s now  t o rj  of a  -  w h i c h , on elastic  comparison  to  33  (5),  -  i s merely a c o n t r i b u t i o n  to  an  mechanism.  If,  for  (8)  s h e a r T e l o c i t y , £~ dT to t, b u t  are  , are  replaced  parameters are  Y  :  ample,  and  (9), not  by  the  constant  periodic  o b t a i n e d which are  fco * s  0 ) s  ****  h  f r o m  rate  of e l o n g a t i o n ,  i n the  functions  time of  ~t- »  interval  time,  time d e p e n d e n t .  ^-  an<  zero  "dynamic"  If, for  ex-  which:  dr The  contribution  g i v e n by  (cf  of  the  kth unit  to the  shear f o r c e w i l l  9):  -  C  &w *o  |  £  s h e a r and the  after  the.time between  the  measurement o f  the  of  shear, T = j ^ »  i e . the  several  ligible  cos tut + ui s i n tut  If  period  and  be  cycles,  E  the  the  He©  initiation tension  on  *  oscillatory  compared  measurements are  the  of  first  (16)  ./T  *  the  i s large  second f r a c t i o n  t h e n depends o n l y  of  f  made  to only  becomes n e g -  fraction.  ** The due hy:  to  the  mechanical energy l o s t per  kth u n i t during  a period  cm^  to.  JT  of  the  ^T+Xij w i  material 1 1  he.  given  - 34 The  accompanying work p e r cm  plication  By  o f (17) b y  3  .  p e r second  i s o b t a i n e d by., m u l t i -  w  summing o v e r a l l k, t h e w o r k t r a n s f o r m e d  per  second  For  a material  i s found  i n t o h e a t , p e r cm3  due t o s h e a r i s :  h a v i n g v i s c o s i t y >^ , t h e w o r k d i s s i p a t e d  as heat  ( f r o m 11 a n d 15) t o b e :  ft- S 7 ^ - i F  a  w ,  *?7  ( i 0 )  C o m p a r i s o n o f (19) a n d (20) y i e l d s :  or,  assuming a g a i n a continuous  The  relations  since, latter. damping cy  spectrum  (21) and (22) a r e g e n e r a l i z a t i o n s  i f TV<JL,  in periodic  If  o f (12) a n d (13)  shear  time  to the  the v i s c o s i t y m e a s u r e d b y t h e  i s i n g e n e r a l d e p e n d e n t on t h e f r e q u e n -  t h i s f r e q u e n c y dependence  the r e l a x a t i o n  times:  t h e n uiTv<l and t h e f o r m e r p a i r r e d u c e s  These e q u a t i o n s show t h a t  and t h a t  of r e l a x a t i o n  is totally  determined  by  spectrum.  t h e sample  i s stretched  p e r i o d i c a l l y rather  than  - 35 -  s u b j e c t e d to shear,  analogous  mechanical energy, transformed  to the above d e r i v a t i o n , the i n t o heat by a p e r i o d i c e x t e n s i o n  w i l l be:  44 - 1 U J V I  £  '»  (2+)  7 1  and f o r a continuous d i s t r i b u t i o n of r e l a x a t i o n  4*. -  -L  ulV  .oo  (* ° E  ^  tes)  At-  B r e n s c h e d e ^ ) found t h a t between 1 0 " 32  times:  2  and 1 0  4  sec.  the creep curve f o r rubber was adequately r e p r e s e n t e d by the empirical  relation: 1  E'  =  q + b ih t b  (26)  where £ i s the creep modulus and Q and b are e m p i r i c a l c o n s t a n t s . Since t h i s equation i s u n d e f i n e d f o r t = 0 ,  i t is arbitrarily  transformed t o :  or: 6  f o r which  .i,  I h C ='d-Vflj:and £  exponential  inr.E^-ct)  (Z7cl  i s E u l e r ' s constant and E; -is the  integral: oo  E x p r e s s i o n (27a) remains f i n i t e f o r t r O and f o r s m a l l v a l u e s of time becomes  i d e n t i c a l with.(27).  36 -  ITow, on the b a s i s of  iL  ,  8  (27a):  ft - e  -ct .  )  (29)  which i n d i c a t e s t h a t the r a t e of s t r a i n remains f i n i t e f o r  t-O,  and f o r l a r g e v a l u e s of time can be r e p l a c e d by:  R e f e r r i n g back to (8) and u s i n g (29), the shear  stress  a f t e r time 1j w i l l be g i v e n by:  O  O  By means of the Laplace T r a n s f o r m a t i o n , Kuhn e t a l obtained a continuous f u n c t i o n s a t i s f y i n g t h i s l a s t  equation:  E<t) = Comparison of t h i s equation w i t h  (3) shows t h a t f o r ?">^«:  f3 3 )  and f o r o < T < J - :  C  3f These two  equations agree w i t h that e m p i r i c a l l y determined •'-cv  the flow diagram. by  ± c  (33«)  - O  r  •  from  - • •  According to (33a)  the continuum i s bounded  f o r which the d i s t r i b u t i o n d e n s i t y ,  dt  T h i s l i m i t i s caused by the a r b i t r a r y replacement  vanishes. of (26) by  (27)  - 37 and h a s no t h e o r e t i c a l  significance.  The c o n s t a n t s a and  b  c a n he d e t e r m i n e d e x p e r i m e n t a l l y f r o m c r e e p c u r v e s a t c o n s t a n t stress using  the e m p i r i c a l r e l a t i o n  Substitution  1  Zd-f)  of Brenschede.  o f (33) and (33a) i n t o  J  T inlet" -1)  •t-'iM  (22) g i v e s :  tu'r'+i  J. C  Letting ration  T  $  ? 4?"»  the v i s c o s i t y ,  i n terms o f t h e p e r i o d  of v i b -  becomes:  S u b s t i t u t i o n o f (34) i n t o  (20) g i v e s f o r s h e a r :  and:  as t h e . e n e r g y l o s t p e r s e c . i n compression the v i s c o s i t y energy  i s a hyperbolic  function  i s directly proportional  or e x t e n s i o n .  Thus,  o f the f r e q u e n c y and the  t o the f r e q u e n c y and to. t h e  square o f the amplitude o f d e f o r m a t i o n . M a k i n g - t h e f o l l o w i n g a s s u m p t i o n s , Kuhn e t a l show Eft)  i n e q u a t i o n (32) i s i d e n t i c a l  schede.  o~ * ' ~ ( V7e =0 //  ih  Therefore,  C  T  that  t o the c r e e p .modulus o f B r e n -  >l)  i a.  the m o d u l u s f r o m r e l a x a t i o n a t c o n s t a n t s t r a i n  i s the  -38 Bame as  -  that from creep a t constant s t r e s s . The . e l a s t i c modulus i n e q u a t i o n (32)  t i m e b u t , a s was is  independent  stresses.,  shown p r e v i o u s l y , we  is. a function  c a n o b t a i n a modulus, w h i c h  o f the l e n g t h o f the e x p e r i m e n t b y u s i n g  Then  Of)depends  of  i n g e n e r a l on the f r e q u e n c y .  periodic In  this  case:  £(U>) In If  the p e r i o d  of v i b r a t i o n  ^ c -  in  ( /„  C  " lh UJ » l )  cu  i s such that  Lnc»/nuV  then:  Hence, t h e dynamic m o d u l u s , i n the r e g i o n o f • a p p l i c a b i l i t y (33a)  i s independent  o f the f r e q u e n c y .  of  39 -  BIBLIOGRAPHY • '• 1) Mark, Am.  J . Phys.,  1  13, 207 ( 1 9 4 5 ) .  2) ' M a r k , I n d . E n g . Chem., 34, 449 ( 1 9 4 2 ) . 3)  Simha, Ann. M.Y. A c a d .  S c i . , 44, 263, 297 ( L 9 4 3 ) .  4) . P l o r y a n d Rehman, Ann. F.Y. A c a d . 5) Gehman, J o n e s  and Woodford,  6) Mooney, J . App. P h y s . ,  8) P l o r y ,  J . Chem. 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