Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A study of stress relaxation phenomena in linear polymers at low temperatures Rye, Robin Tilley Brooke 1956

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1956_A6_7 R9 S8.pdf [ 2.07MB ]
Metadata
JSON: 831-1.0062428.json
JSON-LD: 831-1.0062428-ld.json
RDF/XML (Pretty): 831-1.0062428-rdf.xml
RDF/JSON: 831-1.0062428-rdf.json
Turtle: 831-1.0062428-turtle.txt
N-Triples: 831-1.0062428-rdf-ntriples.txt
Original Record: 831-1.0062428-source.json
Full Text
831-1.0062428-fulltext.txt
Citation
831-1.0062428.ris

Full Text

A STUDY. OP STRESS RELAXATION PHENOMENA IN LINEAR POLYMERS AT LOW TEMPERATURES  by  ROBIN TILLEY BROOKE RYE  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e Department of CHEMISTRY  We a c c e p t t h i s t h e s i s as conforming t o t h e standard r e q u i r e d from candidates f o r the degree o f MASTER OF SCIENCE.  Members o f t h e Department o f Chemistry'  THE UNIVERSITY OF BRITISH COLUMBIA October 1956  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  the r e q u i r e m e n t s f o r an advanced degree a t t h e  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t freely  a v a i l a b l e f o r r e f e r e n c e and  agree t h a t p e r m i s s i o n f o r e x t e n s i v e t h e s i s f o r s c h o l a r l y purposes may of my  study.  I further  copying of  this  be g r a n t e d by the Head  Department o r by h i s r e p r e s e n t a t i v e .  I t i s under-  stood t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my permission.  Department of  crhemi a t r y  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver Canada. Date October 1. 1956  written  - iii  -  ABSTRACT S t r e s s r e l a x a t i o n experiments have been c a r r i e d out on s i n g l e f i l a m e n t s o f n y l o n , v i s c o s e r a y o n and a c e t a t e rayon o v e r t h e temperature range 0°C. t o -80°C. S i m i l a r experiments were a l s o performed on v i s c o s e r a y o n y a r n s immersed i n w a t e r a t 35°C.  I n these l a t t e r  e x p e r i m e n t s , a marked change i n t h e shape o f t h e s t r e s s r e l a x a t i o n c u r v e was noted as t h e s t r a i n was d e c r e a s e d . At s t r a i n s o f t h e o r d e r o f 0.05$ the r e l a x a t i o n c u r v e had t h e shape c h a r a c t e r i s t i c o f a s i n g l e  Newtonian  Maxwell element, w h i l e t h e curve o b t a i n e d a t h i g h e r e l o n g a t i o n s c o u l d n o t be e x p l a i n e d i n terms o f a s i n g l e such element.  I t was c o n c l u d e d t h a t t h e f l o w p r o c e s s  i n v o l v e d was non-Newtonian i n c h a r a c t e r .  The low  temperature r e s u l t s , as w e l l as those o b t a i n e d p r e v i o u s l y by P r i c e (20) a r e d i s c u s s e d I n terms o f E y r i n g ' s h y p e r b o l i c tangent e q u a t i o n f o r d e s c r i b i n g s t r e s s relaxation.  - II ACKNOWLEDGEMENTS The a u t h o r wishes t o e x p r e s s h i s s i n c e r e t o Dr. B. A. D u n e l l f o r h i s I n v a l u a b l e  thanks  encouragement  and a d v i c e t h r o u g h o u t t h e c o u r s e o f t h i s work. The a u t h o r i s a l s o g r a t e f u l t o t h e Defense Board o f Canada f o r c i n a n c i a l and m a t e r i a l  Research  assistance,  and t o C o u r t a u l d s (Canada) L i m i t e d f o r samples o f fibres.  -  1  -  TABLE OP CONTENTS Page ACKNOWLEDGEMENTS  i i  ABSTRACT  . I i i  TABLE OP NOMENCLATURE  . iv  INTRODUCTION  1  I.  G e n e r a l I n t r o d u c t o r y Remarks  1  Mechanical  2  II.  Analogues  A.  L i n e a r Models  2  B.  N o n - l i n e a r Models  5  APPARATUS AND EXPERIMENTAL METHOD I. II.  8  Apparatus Experimental  8 10  Method  12  EXPERIMENTS AND RESULTS I. II.  12  R e s u l t s a t Low Temperatures R e s u l t s a t E l e v a t e d Temperature and  13  Low E l o n g a t i o n  15  DISCUSSION I.  General D i s c u s s i o n o f the I n t e r p r e t a t i o n of Stress R e l a x a t i o n Results  II. III. IV.  I n t e r p r e t a t i o n o f Present R e s u l t s Determination  o f Parameters  Discussion of Results  BIBLIOGRAPHY  . . . .  15  . . . .  19 21 23 30  - Iv TABLE OP NOMENCLATURE °C volume o f f l o w h o l e / a J k T £ s t r a i n on an assembly £ s t r a i n a t zero time a  ^ d i s t a n c e jumped by moving  segment  X d i s t a n c e between s u c c e s s i v e jumping segments #  "XJ\^'cross-sectional" 0~~ s t r e s s stress  d i m e n s i o n s o f jumping segment  on an assembly a t zero time  E modulus o f a s p r i n g F  characteristic  c o n s t a n t o f the "box" d i s t r i b u t i o n  0  of K  relaxation  coefficient  times  o f JaJvsVx oi e~  , a l s o d e f i n e d by  e q u a t i o n 20 \. Boltzmann's Constant T a b s o l u t e temperature "t time i n seconds activation ^  energy o f v i s c o u s f l o w  v i s c o s i t y o f a Newtonian relaxation  dashpot  time o f a Maxwell  1^ minimum v a l u e o f r e l a x a t i o n  unit time i n a box  distribution 'T"' maximum v a l u e o f r e l a x a t i o n distribution  t i m e I n a box  - 1 INTRODUCTION I.  General Introductory  Remarks:  In the p r a c t i c a l a p p l i c a t i o n s of h i g h polymers, their physical properties importance.  are obviously  of the greatest  N a t u r a l and s y n t h e t i c polymers a r e w i d e l y  used to-day as l u b r i c a n t s , waxes, s u r f a c e textiles.  c o a t i n g s and  I n a l l t h e s e a p p l i c a t i o n s some p h y s i c a l  c h a r a c t e r i s t i c such as v i s c o s i t y o r e l a s t i c i t y i s i n v o l v e d , and a knowledge o f t h e s e p h y s i c a l and  properties  t h e i r r e l a t i o n s h i p t o the molecular structure of  the polymer i s e s s e n t i a l . The filaments groups:  commonly used methods f o r i n v e s t i g a t i n g s i n g l e o f t e x t i l e f i b r e s may be d i v i d e d i n t o f o u r experiments a t c o n s t a n t s t r e s s o r l o a d ,  constant deformation, constant rate of deformation, and  s i n u s o i d a l v a r i a t i o n of stress o r s t r a i n with time.  The  r e s u l t s reported  here a r e f o r experiments o f t h e  second t y p e , i n w h i c h t h e r a t e o f decay o f s t r e s s i s measured i n a f i l a m e n t constant elongation. measuring t h i s decay:  or yarn o f m a t e r i a l held a t S e v e r a l methods a r e a v a i l a b l e f o r T o b o l s k y and co-workers used  a u t o m a t i c - r e c o r d i n g s t r e s s b a l a n c e s ( 1 , 2) and d i f f e r e n t i a l t r a n s f o r m e r d e v i c e s ( 3 , U» 5 ) »  Electro-  m e c h a n i c a l t r a n s d u c e r s such as s t r a i n gauges ( 6 ) and  - 2 -  e l e c t r o n i c tubes ( 7 ) have been used Using o s c i l l o s c o p e s  successfully.  ( 7 , 20) o r o s c i l l o g r a p h recorders  (8) i t has been p o s s i b l e t o measure t h e s t r e s s a t t i m e s as s h o r t as two one-hundredths o f a second a f t e r s t r e t c h i n g t h e sample. The r e s e a r c h r e p o r t e d  i n t h i s t h e s i s was under-  taken t o obtain f u r t h e r information mechanical properties  on c e r t a i n o f t h e  o f polymers a t low t e m p e r a t u r e s ,  and t o i n v e s t i g a t e t h e p o s s i b i l i t y o f c o r r e l a t i n g t h e r e s u l t s o f s t a t i c experiments w i t h t h e d i s p e r s i o n o f mechanical properties  found i n t h e dynamic experiments  o f N o l l e ( 9 ) and o t h e r s ( 1 0 , 1 1 ) . II.  M e c h a n i c a l Analogues: I t i s often convenient t o describe  the properties  and b e h a v i o r o f t e x t i l e f i b r e s i n terms o f m e c h a n i c a l analogues.  Some o f t h e more common analogues a r e t h e  Maxwell u n i t f o r s t r e s s r e l a x a t i o n , t h e V o i g t u n i t f o r creep and t h e t h r e e element model f o r s t r e s s s t r a i n studies  (Figure  we w i l l c o n s i d e r  1).  F o r purposes o f t h i s d i s c u s s i o n ,  l i n e a r and n o n - l i n e a r  Maxwell u n i t s  and t h e i r a p p l i c a b i l i t y t o s t r e s s - r e l a x a t i o n s t u d i e s . A.  L i n e a r models  The fundamental law o f v i s c o e l a s t i c b e h a v i o r was postulated  by Maxwell ( 1 2 ) as  where £  I s the t e n s i l e s t r a i n ,  E  0  i s the t e n s i l e  s t r e s s , 6" t h e e l a s t i c modulus and T"='>^E I s the a t i o n t i m e o f t h e system.  relax-  I f a system o b e y i n g t h i s l a w ,  such as t h e Maxwell u n i t , i s extended r a p i d l y t o a f i x e d strain  6  0  , and h e l d  there,  the decay o f s t r e s s  with  time w i l l f o l l o w t h e e q u a t i o n  <r-€.E-,-  M  V , k  T h i s p r e d i c t s t h a t the major p o r t i o n o f the s t r e s s decay o v e r two c y c l e s o f l o g t i m e .  will  W h i l e t h e r e a r e some  m a t e r i a l s whioh show t h i s b e h a v i o r , t h e s l o w e r r a t e o f decay commonly found l e d t o a g e n e r a l i z a t i o n o f t h e Maxwell t h e o r y , and t h e i n t r o d u c t i o n o f the c o n c e p t o f a d i s t r i b u t i o n of r e l a x a t i o n times. I f we now c o n s i d e r a p a r a l l e l a r r a y o f M a x w e l l u n i t s , the s t r a i n time r e l a t i o n s h i p i s g i v e n (12) by  4$ - ( E M ) ( ^ r ) ( * « « )  M  +  and where ECr)  6- _ JfV« -V(V) T )cKJi s t h e c o n t r i b u t i o n t o t h e t o t a l modulus  made by the Maxwell elements w i t h r e l a x a t i o n t i m e AT* , and c O )  between  and  i s thepartial  associated  w i t h the r e l a x a t i o n t i m e T*.  i s g i v e n a f i x e d and c o n s t a n t s t r a i n , e , o  s t r e s s a t any t i m e i s g i v e n by OO  /  ^Xf"  stress  I f t h i s system then the  - k Because CH3 a r i s e s f r o m a c o n t i n u o u s s e t o f d i f f e r e n t i a l e q u a t i o n s , the s o l u t i o n depends on a knowledge of t h e d i s t r i b u t i o n f u n c t i o n , w h i c h i s c a l l e d t h 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. have been proposed t o g e n e r a l i z e  Several d i s t r i b u t i o n s the Maxwell t h e o r y ;  a  " s t e p f u n c t i o n " w h i c h has been used i s  O r i g i n a l l y p o s t u l a t e d by B e c k e r (13)  to describe  h y s t e r s e i s i n f e r r o - m a g n e t i c b e h a v i o r , and l a t e r by Kuhn ( l l i ) ' t o v i b r a t i o n a l  applied  studies of polymers, t h i s  d i s t r i b u t i o n has been s u c c e s s f u l l y used t o d e s c r i b e stress relaxation i n polyisobutylene I t has a l s o been shown (15)  and o t h e r m a t e r i a l s .  t h a t i n the r e g i o n where t h e  s t r e s s versus l o g a r i t h m i c time curve i s l i n e a r , E ^ i s e q u a l t o t h e n e g a t i v e s l o p e o f the l i n e d i v i d e d by 2.303:  While i t i s t h e o r e t i c a l l y  p o s s i b l e t o describe the  r e l a x a t i o n b e h a v i o r of any m a t e r i a l i n terms o f a Maxwell a r r a y , the l a r g e number o f u n i t s and the comp l e x i t y o f t h e d i s t r i b u t i o n f u n c t i o n r e q u i r e d tends t o make such a model cumbersome and d i f f i c u l t t o u s e .  - 5  B.  N o n - l i n e a r models:  -  the E y r i n g approaoh:  Rather than d e a l w i t h the complex a r r a y s mentioned above, E y r i n g l e t the i n d i v i d u a l elements become more complex as r e q u i r e d t o e x p l a i n e x p e r i m e n t a l  results.  In p a r t i c u l a r , he no l o n g e r assumed t h a t the dashpot obeys Newton's Law  of v i s c o s i t y .  The b a s i c a s s u m p t i o n o f E y r i n g ' s  theory  (l6) i s  t h a t t h e r e are d i s c r e t e " f l o w u n i t s " I n the f i b r e which a r e always exchanging o l d n e i g h b o u r s f o r new  ones;  and  t h a t t h e s e exchanges o c c u r even when no e x t e r n a l f o r c e s are a c t i n g on t h e f i b r e .  Producation  of a s i t e f o r a  f l o w u n i t to more i n t o r e q u i r e s a c e r t a i n amount o f energy, and  the jump of a f l o w u n i t f r o m one  p o s i t i o n to a n o t h e r i s e q u i v a l e n t p o t e n t i a l energy b a r r i e r .  equilibrium  t o passage o v e r a  I f s t r e s s i s a p p l i e d t o the  f i b r e t h i s p r o c e s s i s a c c e l e r a t e d i n the d i r e c t i o n of a p p l i c a t i o n of t h e s t r e s s . Let  A  be t h e d i s t a n c e jumped between e q u i l i b r i u m  p o s i t i o n s , and  the c r o s s - s e c t i o n a l a r e a o f the  segment be A * X . t  3  jumping  Then i n jumping the d i s t a n c e ^  under an a p p l i e d s t r e s s 6" , the work done i s  ,  C\"X ~X^ i  •  I f we assume a s y m m e t r i c a l energy b a r r i e r , t h e work c o n t r i b u t e d by the a p p l i e d s t r e s s i s  where  'X i s the d i s t a n c e t o the peak of the energy b a r r i e r  - 6  i n the d i r e c t i o n o f f l o w .  -  The same amount o f work i s  done a g a i n s t the a p p l i e d s t r e s s i f t h e f l o w u n i t moves i n the opposite If K  direction.  i s t h e frequency  w i t h w h i c h an  unstrained  segment jumps m u l t i p l i e d by t h e r a t i o ^/"A, » where  ^  (  i s the d i s t a n c e between s u c c e s s i v e jumping segments, t h e n t h e frequency i s g i v e n by  o f jumping i n t h e f o r w a r d  direction  -v K  A  A  » "A  -0.  S i m i l a r l y , f o r t h e r e v e r s e d i r e c t i o n , the f r e q u e n c y  Va-iVr  jumping i s  of  C7I  a IT The net f o r w a r d v e l o c i t y f o r a f l o w u n i t i s , t h e r e f o r e , g i v e n by  /  -.WJ-VT  -^W/tMl  I  The r e s u l t i n g r a t e of s t r a i n i s g i v e n by d i v i d i n g v e l o c i t y by the d i s t a n c e between s u c c e s s i v e segments ( A,  ).  I f we  the  jumping  l e t d( be the volume of the  h o l e d i v i d e d by,3L-^T, Q 8^ s i m p l i f i e s to g i v e us  flow  the  h y p e r b o l i c s i n e law f o r rate of s t r a i n , namely  where  c< - ^ ^ 3 L e t us now  *  1  c o n s i d e r a a Maxwell element i n which t h e  dashpot i s non-Newtonian i n c h a r a c t e r .  If €  (  i s the  s t r a i n on t h e s p r i n g and C  t  i s t h e s t r a i n on t h e  dashpot, t h e n J -t  E  N  d  t  where 6~ i s t h e s t r e s s on t h e element. stress relaxation  d_§ = O  and  I~*o~\  I n the c a s e o f  reduces t o  which i n t u r n leads t o the equation where  6-  = e  o  £  Both t y p e s o f m e c h a n i c a l analogue have been u t i l i z e d i n the i n t e r p r e t a t i o n o f e x p e r i m e n t a l r e s u l t s . The concept o f an i n f i n i t e a r r a y and spectrum o f r e l a x a t i o n t i m e s has been used e x t e n s i v e l y by T o b o l s k y and co-workers i n t h e i r i n v e s t i g a t i o n o f p o l y i s o b u t y l e n e w i t h c o n s i d e r a b l e s u c c e s s (17)•  E y r i n g and h i s  a s s o c i a t e s have c o n s i d e r e d the b e h a v i o r o f many t y p e s of m a t e r i a l f r o m t h e p o i n t o f view o f non-Newtonian v i s c o s i t y , a l s o w i t h c o n s i d e r a b l e s u c c e s s (18,  19) •  APPARATUS AND EXPERIMENTAL METHODS I.  Apparatus: The a p p a r a t u s used i n t h e i n v e s t i g a t i o n o f s t r e s s  r e l a x a t i o n o f polymer f i b r e s a t low t e m p e r a t u r e s c a n be divided into three parts:  c o o l i n g chamber and temper-  a t u r e c o n t r o l ; measuring equipment and m e c h a n i c a l release details. Two c o o l i n g chambers were used, b o t h c o n s t r u c t e d from l / l 6 i n c h p l e x i g l a s . w i t h a p p r o x i m a t e l y 3M  Double c o n s t r u c t i o n was used,  o f * i i n c h o f r o c k wool a  insulation.  One box was b u i l t t o e n o l o s e t h e e n t i r e system, but a s t h e m a n u f a c t u r e r s p e c i f i e s t h a t t h e s t r a i n gauge s h o u l d n o t be used a t temperatures below -i+0 C., t h e equipment o  in its  f i n a l f o r m c o n s i s t e d o f a s m a l l e r c o o l e d space, t o c o n t a i n the f i b r e s o n l y , t o g e t h e r w i t h t h e s t r a i n gauges mounted o u t s i d e and above t h e c o l d b o x , and t h e s t r e t c h i n g s p r i n g s o u t s i d e and below t h e box. The d e s i r e d t e m p e r a t u r e s were o b t a i n e d by c i r c u l a t i n g vapour from l i q u i d t h r o u g h t h e t e s t chamber.  nitrogen  The "pump" used was e s s e n t i a l l y  a h e a t e r immersed i n t h e l i q u i d n i t r o g e n ; by c o n t r o l l i n g the current passing through t h i s heater temperatures i n t h e r a t e 0°C. t o -80°C. were e a s i l y a c h i e v e d and c o n t r o l l e d t o w i t h i n 0.1°C.  Temperature measurements were made u s i n g  i r o n c o n s t a n t a n thermocouples and a s t a n d a r d p o t e n t i o m e t e r circuit.  - 9 The o v e r a l l measuring and c a l i b r a t i o n c i r c u i t i s shown i n b l o c k f o r m i n F i g u r e 2.  Two Statham  strain  gauges, Model G 1, were used t o c o n v e r t t h e a p p l i e d s t r e s s t o an e l e c t r i c a l v o l t a g e .  For readings at short  times (0.002 t o 1.0 second) the o u t p u t o f t h e s t r a i n gauges was a p p l i e d , t h r o u g h a d i r e c t - c u r r e n t  amplifier,  t o a cathode r a y o s c i l l o s c o p e , and t h e t r a c e r e c o r d e d photographically.  F o r l o n g e r t i m e i n t e r v a l s (1.0 second  t o 10,000 seconds) r e a d i n g s were t a k e n on a Rhodes p o t e n t i o m e t e r which was a u t o m a t i c a l l y s w i t c h e d i n t o t h e circuit. The use o f seven r e s i s t o r s , R , i n t h e c a l i b r a t i o n c  circuit  ( F i g u r e 3) made i t p o s s i b l e t o o b t a i n a complete  c a l i b r a t i o n c u r v e i n o n l y a few m i n u t e s .  The r e s p o n s e  o f each gauge was checked a f t e r every r u n , and compared f r o m time t o t i m e w i t h t h e response t o s t a n d a r d w e i g h t s a p p l i e d t o t h e s t r a i n gauge.  E x c e l l e n t agreement between  t h e two methods o f c a l i b r a t i o n was f o u n d . F o r t h e t o t a l l y e n c l o s e d system, t h e c l a m p i n g and r e l e a s e mechanism was t h e same as t h a t used by P r i c e (20).  When t h e s m a l l e r c o o l e d box was used i t was  n e c e s s a r y t o mount t h e f i b r e between two s h o r t l e n g t h s o f nichrome w i r e t o ensure t h a t t h e whole sample was brought t o t h e r e q u i r e d t e m p e r a t u r e , and a c l a m p i n g d e v i c e was d e s i r e d w h i c h would g r i p t h e w i r e f i r m l y .  - 10 A f u r t h e r e o n s l d e r a t i o n a f f e c t i n g the design o f the clamping system was  the n e c e s s i t y f o r c o n t r o l l i n g t h e  mounting t e n s i o n a p p l i e d t o t h e sample.  S e v e r a l types  o f elamp were t r i e d ; the f i n a l arrangement made from a s m a l l p i n v i s e ( S t a r r e t 21+0-A) proved v e r y s a t i s f a c t o r y . The e l e c t r o m a g n e t i c r e l e a s e , used i n the e n c l o s e d system was  r e p l a c e d by a manually o p e r a t e d one, w h i c h proved t o  be somewhat more r e l i a b l e . II.  E x p e r i m e n t a l Method: A sample of the f i b r e to be t e s t e d , a p p r o x i m a t e l y  e l e v e n c e n t i m e t r e s i n l e n g t h , was mounted between two p i e c e s o f nichrome w i r e u s i n g a p o l y s t y r e n e cmenet.  In  b e i n g mounted, t h e f i b r e was wrapped s e v e r a l t i m e s around a s m a l l l o o p at the end o f the w i r e and cemented I n p l a c e .  The assembly was  then  then t h r e a d e d  t h r o u g h the c o l d box w i t h t h e ends o f t h e w i r e s o u t s i d e t h e box.  The t o p end o f the w i r e was wrapped around  s t r a i n gauge probe and cemented i n p l a c e .  The  the  bottom  w i r e was t h r e a d e d t h r o u g h t h e chuck o f the p i n v i s e  and  t h e h o l l o w body of the clamp, and l o a d e d w i t h t h e d e s i r e d tensioning weight.  A w e i g h t o f two o r t h r e e grams was  found t o be s u f f i c i e n t t o keep t h e f i b r e sample t a u t . C o o l i n g was  then commenced, and when t h e d e s i r e d  temperature had been reached t h e p i n v i s e was t i g h t e n e d and the e l o n g a t i o n a d j u s t e d by means o f two nuts on t h e  - 11 t h r e a d e d clamp body.  The sample was m a i n t a i n e d a t t h e  d e s i r e d t e m p e r a t u r e f o r a p p r o x i m a t e l y h a l f an hour b e f o r e t h e e x p e r i m e n t a l s t r e s s was a p p l i e d .  I t was  c o n s i d e r e d t h a t i n t h i s time e q u i l i b r i u m between the f i b r e and i t s s u r r o u n d i n g s was a c h i e v e d , and t h a t the I n i t i a l mounting t e n s i o n had reached the s t e a d y v a l u e c h a r a c t e r i s t i c o f t h e temperature run.  of that  experimental  - 12  -  EXPERIMENTS AND RESULTS S t r e s s r e l a x a t i o n e x p e r i m e n t s have been c a r r i e d out on s i n g l e f i l a m e n t s o f t e x t i l e f i b r e s .  The f i b r e s  chosen f o r i n v e s t i g a t i o n were n y l o n , v i s c o s e r a y o n and acetate rayon.  The samples were s i n g l e c o n t i n u o u s  f i l a m e n t m a t e r i a l s or continuous f i l a m e n t yarns supplied by t h e m a n u f a c t u r e r .  The t e m p e r a t u r e range oovered was  0°G. t o -80°G., u s u a l l y i n twenty degree s t e p s b u t o c a s i o n a l l y Increments o f t e n degrees were u s e d .  At  the s t a r t o f t h e work, an e l o n g a t i o n o f 2 . 7 $ , c a l c u l a t e d on t h e b a s i s o f t h e u n s t r e t c h e d l e n g t h , was d e c i d e d upon. I t was f o u n d , however, t h a t i n t h e c a s e o f t h e r a y o n s , t h i s e l o n g a t i o n gave an i n i t i a l s t r e s s o f t h e maximum p e r m i s s i b l e f o r t h e s t r a i n gauges i f t h e temperature was below -kO°C.  F o r t h i s r e a s o n , samples o f v i s c o s e  and a c e t a t e rayon were i n v e s t i g a t e d a t an e l o n g a t i o n o f 1.5%;  t h i s was found t o be s a t i s f a c t o r y a t a l l t h e  experimental temperatures. I.  R e s u l t s a t Low Temperatures: The r e s u l t s o b t a i n e d f r o m s t r e s s  relaxation  experiments c a r r i e d out o v e r t h e t e m p e r a t u r e range Q°G. t o 80°G. on samples o f n y l o n a t 2.7%  elongation,  a c e t a t e r a y o n and v i s c o s e a t 1.$% and v i s c o s e and a c e t a t e r a y o n at 2 . 7 $ e l o n g a t i o n are p r e s e n t e d  -  13  -  g r a p h i c a l l y i n F i g u r e s 1+., 5 ,  6,  respectively.  7(a) and  7(b),  Certain general s i m i l a r i t i e s w i l l  be  n o t i c e d ; t h e r e i s a f a i r l y r e g u l a r i n c r e a s e i n modulus w i t h decreasing  t e m p e r a t u r e , the e x c e p t i o n b e i n g  case of v i s c o s e r a y o n a t 1 . 5 $  elongation, f o r which a  pronounced drop i n the modulus i s n o t i c e d a t The  the  ij.0 C. O  r  e f f e c t of temperature on the s l o p e o f t h e s t r e s s  r e l a x a t i o n c u r v e i s not v e r y n o t i c e a b l e ; the  general  tendency seems to be f o r a s l i g h t i n c r e a s e i n s l o p e as t h e temperature i s l o w e r e d . The  r e s u l t s o b t a i n e d f o r v i s c o s e r a y o n at an  e l o n g a t i o n o f 1.5%  show none o f the r e g u l a r i t y f o u n d  i n the c a s e o f n y l o n o r a c e t a t e r a y o n .  While i t i s  i n t e r e s t i n g t o s p e c u l a t e on a p o s s i b l e c o r r e l a t i o n between the e f f e c t s n o t i c e d h e r e and the d i s p e r s i o n o f m e c h a n i c a l p r o p e r t i e s r e p o r t e d elsewhere ( 2 0 ,  21),  It  is f e l t that f u r t h e r Investigation i s required. II.  R e s u l t s at E l e v a t e d Temperature and  Low  I n o r d e r t o d e t e r m i n e whether the f l o w  Elongation: process  i n v o l v e d i n s t r e s s r e l a x a t i o n i s Newtonian o r  non-  Newtonian I n c h a r a c t e r , a s e r i e s of e x p e r i m e n t s were done w i t h v i s c o s e r a y o n y a r n s immersed i n w a t e r a t 35°C» w o r k i n g a t s t r a i n s o f the o r d e r of 0 . 0 5 $ , one  When  requires  a sample o f l a r g e c r o s s - s e c t i o n a l a r e a t o o b t a i n a f o r c e l a r g e enough to g i v e a good r e s p o n s e on the  strain  - Ik gauge t h a t was  used.  M u l t i f i l a m e n t y a r n s were t h e r e f o r e  used to g i v e the n e c e s s a r y  cross-section, i n six foot  l e n g t h s so t h a t an e l o n g a t i o n o f 1 mm. s t r a i n o f the o r d e r o f 0 . 0 5 $ . Figure 8,  a decrease i n p e r c e n t  c o r r e s p o n d s to a  As w i l l be seen f r o m s t r a i n was  accompanied  by a marked change I n t h e shape o f the r e l a x a t i o n curve.  The  discussed  s i g n i f i c a n c e o f t h i s change w i l l  be  later.  D u p l i c a t e samples o f f i b r e were t e s t e d o u s l y a t each o f the e x p e r i m e n t a l  simultane-  temperatures i n v o l v e d .  I n cases where t h e d i s p a r i t y between samples e x c e s s i v e , a f u r t h e r p a i r o f f i b r e s was t e s t e d a t t h e same e x p e r i m e n t a l  was  mounted and  conditions.  For  the  r e s u l t s r e p o r t e d h e r e , t h e d e v i a t i o n f r o m the mean I s o f the o r d e r of S% t o 1 0 $ .  R e s u l t s at s h o r t  times  o c a s i o n a l l y show g r e a t e r d e v i a t i o n due t o the  inherent  i n s t a b i l i t y o f the d i r e c t - c u r r e n t a m p l i f i e r . I t s h o u l d a l s o be borne i n mind t h a t s y n t h e t i c spun f i b r e s show the same v a r i a t i o n s i n f i l a m e n t s i z e and shape t h a t a r e found i n n a t u r a l f i l a m e n t s , to  a l e s s e r degree.  Microscopic examination  of  although the  f i b r e s under i n v e s t i g a t i o n r e v e a l e d a good d e a l of  non-  u n i f o r m i t y , even w i t h i n a s h o r t l e n g t h of sample, and t h i s non-uniformity  undoubtedly i n f l u e n c e d the  r e p r o d u c i b i l i t y o f t h e r e s u l t s to a c e r t a i n e x t e n t .  -  15  -  DISCUSSION I.  G e n e r a l D i s c u s s i o n o f the I n t e r p r e t a t i o n o f Stress Relaxation Results: I n the measurement of r e l a x a t i o n o f s t r e s s i n a  polymer, the m a t e r i a l i s s u b j e c t e d t o an e f f e c t i v e l y i n s t a n t a n e o u s d e f o r m a t i o n , w i t h the development o f an associated stress.  The decay o f t h i s s t r e s s , w i t h the  sample h e l d a t c o n s t a n t d e f o r m a t i o n , i s a r e s u l t o f the f l o w o f the m o l e c u l a r u n i t s from the s t r a i n e d c o n f i g u r a t i o n to the o r i g i n a l e q u i l i b r i u m c o n f i g u r a t i o n . I n t e r p r e t a t i o n o f t h i s f l o w p r o c e s s has l e d t o the development o f two p r i n c i p a l t h e o r i e s ; one based on a Newtonian type f l o w , the o t h e r on a non-Newtonian flow process. 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 based on an a r r a y o f Newtonian Maxwell elements has been used e x t e n s i v e l y by Kuhn (  9  Tobolsky  the treatment o f the m e c h a n i c a l  (17) and o t h e r s i n  p r o p e r t i e s of  polymers.  V a r i o u s d i s t r i b u t i o n f u n c t i o n s have been u s e d ; f o r example the s t e p f u n c t i o n o f B e c k e r , mentioned e a r l i e r , w h i c h imposes the c o n d i t i o n s  E T C H « E„/<r  has been used a g r e a t d e a l .  f], <; 1- <  The  ^  shape o f the r e l a x a t i o n  curve i n t h i s case depends o n l y on the r e l a t i v e v a l u e s  - 16 chosen f o r ^ i n which f-1  7^  and and IV  .  A  d i s t r i b u t i o n of t h i s form  d i f f e r by a number of powers o f  t e n w i l l g i v e a r e l a x a t i o n curve w h i c h i s a s t r a i g h t l i n e over a l a r g e i n t e r v a l of l o g a r i t h m i c t i m e . a curve f r e q u e n t l y describes experimental T h i s i n t e r p r e t a t i o n , which i s convenient  Such  results. mathematically  i n c o r r e l a t i n g s t r e s s r e l a x a t i o n data with r e s u l t s o t h e r types o f e l a s t o v i s c o u s e x p e r i m e n t s , on a t h e o r e t i c a l b a s i s by T o b o l s k y ( 2 2 ) , Kirkwood (2LL)  and o t h e r s .  of  has been put (23),  Frenkel  Tobolsky assumes t h a t the  m o l e c u l a r c o n f i g u r a t i o n i n the u n s t r a i n e d s t a t e may d e s c r i b e d by a s p h e r i c a l l y s y m m e t r i c a l vectorial distances. c o n s i d e r a t i o n may  be  d i s t r i b u t i o n of  The v e c t o r i a l d i s t a n c e s t a k e n f o r  be between temporary c r o s s  links,  c h a i n ends, c h a i n segments o r o t h e r s t r u c t u r a l u n i t s . The  i n i t i a l s t r a i n w i l l then cause a d i s t o r t i o n i n t h i s  d i s t r i b u t i o n f u n c t i o n , and the' r e s u l t i n g r e l a x a t i o n process  can be c o n s i d e r e d as the decay o f t h e s t r a i n e d  d i s t r i b u t i o n o f v e c t o r i a l d i s t a n c e s back t o t h e s p h e r i c a l l y symmetrical  distribution.  original  A treatment  of  t h i s d i f f u s i o n of a c h a i n m o l e c u l e f r o m a d i s t o r t e d d i s t r i b u t i o n to the e q u i l i b r i u m d i s t r i b u t i o n has g i v e n by F r e n k e l ( 2 3 ) .  been  By assuming t h a t the s t r e s s i s  p r o p o r t i o n a l to the d e v i a t i o n o f the a c t u a l d i s t a n c e between c h a i n ends f r o m the most p r o b a b l e F r e n k e l concludes  distance,  t h a t the d i s t a n c e between c h a i n ends  - 17  -  i n the d i s t o r t e d c o n f i g u r a t i o n w i l l r e t u r n t o the most p r o b a b l e d i s t a n c e , e q u i v a l e n t t o t h e e q u i l i b r i u m conf i g u r a t i o n , a t an e x p o n e n t i a l r a t e , A  , w i t h the  r e l a x a t i o n time, f " , being p r o p o r t i o n a l to the molecular /  weight.  I n t h i s c a s e , t h e r e l a x a t i o n c u r v e of a whole  polymer might be g i v e n a s i m p l e i n t e r p r e t a t i o n i n terms of  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 c o r r e s p o n d i n g  d i r e c t l y t o the d i s t r i b u t i o n of m o l e c u l a r w e i g h t s i n the sample.  I f such an i n t e r p r e t a t i o n i s u s e d , t h e  " s t e p f u n c t i o n " t y p e of d i s t r i b u t i o n w i l l n o t be for  valid  the whole polymer, but r a t h e r a d i s t r i b u t i o n more  r e s e m b l i n g t h e G a u s s i a n d i s t r i b u t i o n s h o u l d be D i s t r i b u t i o n f u n c t i o n s more r e f i n e d than t h e  expected. "box"  f u n c t i o n have been developed by T o b o l s k y and o t h e r s  (17)  and t h e s e tend I n the d i r e c t i o n o f t h e m o l e c u l a r weight d i s t r i b u t i o n f o r the whole polymer, a l t h o u g h t h e y s c a r c e l y approximate  it.  A l f r e y ' s treatment  (25),  i n v o l v i n g c o n s i d e r a t i o n o f the m o t i o n o f a l l component s e c t i o n s o f the c h a i n molecule, a r r i v e s a t a d i s t r i b u t i o n of  r e l a x a t i o n t i m e s f o r a l i n e a r amorphous polymer,  even  where the m o l e c u l a r weight i s c o m p l e t e l y homogenous. This t h e o r y i s s u p p o r t e d by e x p e r i m e n t a l d a t a f o r p o l y i s o b u t y l e n e o b t a i n e d by Tobolsky and co-workers A similar p r e d i c t i o n o f a d i s t r i b u t i o n of r e l a x a t i o n times i n a c o m p l e t e l y homogenous polymer has been advanced by Kirkwood  (2k).  (17).  - 18 The  -  second p o s s i b i l i t y f o r i n t e r p r e t i n g s t r e s s  r e l a x a t i o n c u r v e s whioh extend over a number of c y c l e s o f l o g a r i t h m i c t i m e i s t h a t of a non-Newtonian Flow process.  Two  r e l a t i o n s h i p s , i m p l y i n g non-Newtonian  b e h a v i o r , were examined by T o b o l s k y (26)  as p o s s i b l e  means f o r i n t e r p r e t i n g s t r e s s r e l a x a t i o n r e s u l t s i n p o l y i s o b u t y l e n e ; t h e s e a r e the h y p e r b o l i c  o( and  L  the e x p o n e n t i a l i n t e g r a l  where  ET  t  represents  Of t h e s e two  tangent  equation  the e x p o n e n t i a l I n t e g r a l f u n c t i o n .  r e l a t i o n s h i p s , the h y p e r b o l i c  e q u a t i o n , d e r i v e d on page 7 has  tangent  r e c e i v e d the more  a t t e n t i o n , e s p e c i a l l y i n the work o f E y r i n g and associates.  his  From the p o i n t of view of s t r e s s r e l a x -  a t i o n s t u d i e s , i t g i v e s , g e n e r a l l y , a more s a t i s f a c t o r y agreement w i t h e x p e r i m e n t . I n a r e c e n t paper ( 2 7 ) ,  Ree  and E y r i n g d i s c u s s  some of the o b j e c t i o n s t h a t have been made a g a i n s t h y p e r b o l i c tangent f u n c t i o n .  the  They p o i n t out t h a t most  of the c r i t i c i s m s can be c l e a r e d up by c o n s i d e r i n g  a  d i s t r i b u t i o n o f f l o w u n i t s i n t h e system, I.e. Newtonian and non-Newtonian f l o w u n i t s p r e s e n t  i n the same system.  Three t y p e s of f l o w u n i t s a r e p o s t u l a t e d :  Newtonian,  non-Newtonian but showing Newtonian b e h a v i o r  at  low  - 19 v a l u e s o f s t r a i n , and  -  completely  non-Newtonian u n i t s .  By d e s c r i b i n g a s u i t a b l e d i s t r i b u t i o n f u n c t i o n f o r t h e s e u n i t s , Ree  and E y r i n g o b t a i n e x c e l l e n t agreement w i t h  experiment f o r m a t e r i a l s such as n a t u r a l and r u b b e r , p o l y s t y r e n e and These a u t h o r s  synthetic  polyisobutylene.  also deal with other objections to  the h y p e r b o l i c tangent e q u a t i o n .  Several authors  have r e p o r t e d a d e c r e a s e I n the s i z e o f t h e f l o w meter A J X , ^ w i t h i n c r e a s i n g e l o n g a t i o n . has  been c o n s i d e r e d  E y r i n g (29), the  (28) para-  This decrease  as a d e f e c t i n the t h e o r y .  Ree  by a p p l y i n g the v i r i a l theorem, d e r i v e d  equation  where 6 ^  i s a l o c a l micro s t r e s s which, they c l a i m , i s  f r e q u e n t l y s i m p l y r e l a t e d t o the a p p l i e d s t r e s s , 6~ and  and  ^  i s a constant.  I f we  ,  r e w r i t e i n the f o r m  the d e c r e a s e o f t h e parameter ' V X i ' X ? w i t h i n c r e a s i n g s t r a i n i s e x p e c t e d , s i n c e €~  a  increases with  L i k e w i s e the volume of t h e f l o w h o l e ( V. by Ree and absolute II.  strain.  ) Is p r e d i c t e d  E y r i n g to be d i r e c t l y p r o p o r t i o n a l to the  temperature.  I n t e r p r e t a t i o n of Present An e x a m i n a t i o n  Results:  o f the r e s u l t s o b t a i n e d  using  v i s c o s e r a y o n y a r n s immersed i n w a t e r a t 3J?°C. shows an  - 20 i n t e r e s t i n g change i n the shape of the r e l a x a t i o n c u r v e a t an e l o n g a t i o n o f 0.0$%.  I t w i l l be n o t i c e d  t h a t , I n t h i s c a s e , a major p o r t i o n of the decay over two c y c l e s o f l o g a r i t h m i c t i m e .  occurs  Such b e h a v i o r i s  c h a r a c t e r i s t i c of a s i n g l e Maxwell element or even an a r r a y of such elements s h o u l d n o t show a change i n the shape of t h e r e l a x a t i o n c u r v e w i t h a change i n strain.  Prom F i g u r e 8 i t w i l l be seen t h a t , I n f a c t ,  a change i n t h e shape of t h e r e l a x a t i o n c u r v e does o c c u r as t h e s t r a i n i s d e c r e a s e d . are i n c o n s i s t e n t i f c o n s i d e r e d  The r e s u l t s , t h e r e f o r e ,  I n terms o f a Newtonian  Maxwell element. An a l t e r n a t i v e e x p l a n a t i o n f o r t h e shape of curve o b t a i n e d a t an e l o n g a t i o n o f 0.0$%  the  i s to consider  t h a t i t r e p r e s e n t s t h e b e h a v i o r of a non-Newtonian Maxwell element i n the l i m i t i n g c a s e .  One  of  the  r e s u l t s o f the h y p e r b o l i c s i n e e q u a t i o n of f l o w Is t h a t i n the r e g i o n where the a p p r o x i m a t i o n ^ k d g v a l i d the e q u a t i o n reduces t o the s i m p l e form.  _P e< 6"  exponential  An i n t e r p r e t a t i o n of t h e r e p o r t e d s t r e s s  r e l a x a t i o n r e s u l t s i n terms of a non-Newtonian element would t h e r e f o r e account f o r t h e shape of the c u r v e  at  low e l o n g a t i o n s and a l s o the dependence on s t r a i n o f the c u r v e shape.  I f we assume t h a t the f l o w  process  i s e s s e n t i a l l y the same under t h e s e c o n d i t i o n s as i t  is  - 21 Is a t low t e m p e r a t u r e s , i n t e r p r e t a t i o n o f t h e c u r r e n t r e s u l t s , as w e l l as t h o s e o b t a i n e d e a r l i e r i n t h i s l a b o r a t o r y by P r i c e , I n terms o f non-Newtonian f l o w seems t o be  justified.  While i t would be o f v a l u e I n t h i s r e s p e c t t o c a r r y out low e l o n g a t i o n experiments a t low t e m p e r a t u r e s , t h e r e a r e d i f f i c u l t i e s i n t h e way.  I t would be e x p e c t e d  t h a t a t low t e m p e r a t u r e s and s m a l l s t r a i n s t h e r e l a x a t i o n  6 time T "  would i n c r e a s e t o t h e o r d e r o f 10  8 t o 10 .  Experiments o f s u c h d u r a t i o n would be e x t r e m e l y d i f f i c u l t t o conduct at low t e m p e r a t u r e s i n t h i s laboratory. III.  D e t e r m i n a t i o n o f Parameters: Consider the equation  The s l o p e o f t h e l o g be w r i t t e n t" t o t , we o b t a i n  Por v a l u e s o f  .  e  x  -  t plot i s  - which can  I f we d i f f e r e n t i a t e £123 w i t h r e s p e c t *Efct  7  R  I  /  ^  such t h a t C r j ^ i s 10 o r g r e a t e r , as  i s t h e c a s e f o r the r e p o r t e d r e s u l t s , t a n h a p p r o x i m a t e l y e q u a l t o u n i t y , and IT'^becomes  / is  - 22 -  I f e f E k i i s muoh l e a s than u n i t y , t h e n we can make the  approximations =  \-<AEKt  •= |  es  C o n v e r t i n g t o l o g , , we o b t a i n n  o(_ As °(  / s l o p e o f r e l a x a t i o n c u r v e _j*v_  3 303  i s e q u a l t o ^ " X O ^ / ^ J s T by d e f i n i t i o n , t h e  volume o f t h e f l o w h o l e can be c a l c u l a t e d . Having determined  t h e v a l u e o f <* , i t i s p o s s i b l e  to c a l c u l a t e t h e a c t i v a t i o n energy o f v i s c o u s f l o w . F o r such a c a l c u l a t i o n i t i s n e c e s s a r y t o assume and f i n a l v a l u e s o f t h e modulus.  initial  For the results  r e p o r t e d here, t h e i n i t i a l modulus was t a k e n t o be t h e same as t h e dynamic modulus measured a t s i m i l a r conditions.  I f such d a t a were n o t a v a i l a b l e , t h e I n i t i a l  modulus was approximated modulus.  f r o m the s t r e s s  relaxation  The c h o i c e o f a f i n a l modulus v a l u e was  c o n s i d e r a b l y more a r b i t r a r y , b u t c a l c u l a t i o n s that quite  show  t h e r e s u l t i n g v a l u e o f t h e a c t i v a t i o n energy i s i n s e n s i t i v e t o t h e f i n a l modulus v a l u e  Having a s s i g n e d v a l u e s t o cr  and 5 -  chosen.  , i t i s then  -  23 -  p o s s i b l e t o s o l v e equat i o n L7»2 3  which by  fo r  d e f i n i t i o n (30) i s equal t o ^ ^ - ^ ^  RAlthough  i t I s not p o s s i b l e f r o m t h e d a t a o b t a i n e d t o c a l c u l a t e the v a l u e o f t h e r a t i o ,  i t has been shown ( 3 0 ) t h a t  At  a v a l u e o f 0 . 5 f o r t h i s parameter i s a good approximation.  Making t h i s s u b s t i t u t i o n  and t h e a c t i v a t i o n energy o f v i s c o u s f l o w , , can t h e n be c a l c u l a t e d . Values of o(  »^CX^»  a  by means of e q u a t i o n s  n  d  ^  have been c a l c u l a t e d  3and L^o]]; t h e v a l u e s  o b t a i n e d f o r n y l o n , v i s c o s e r a y o n and a c e t a t e r a y o n a r e t a b u l a t e d i n Tables  I , I I and I I I , r e s p e c t i v e l y .  S i m i l a r c a l c u l a t i o n s were made u s i n g r e s u l t s  obtained  by P r i c e ( 2 0 ) . H i s r e s u l t s a r e i n c l u d e d f o r r e f e r e n c e i n F i g u r e s 9 , 10 and 1 1 . IV.  Discussion of Results: (a)  Temperature independence o f o(  Kauzmann ( 3 1 ) , Sherby ( 3 2 ) and E y r i n g have presented  experimental evidence  t o i n d i c a t e t h a t o(  i s e s s e n t i a l l y independent o f t e m p e r a t u r e . the s u b s t i t u t i o n ^ = ^ ^ T T ^ / ^ - k T 3  £<5^><j  i  n  LjsJ»  I f we make w  e  obtain  w h i c h I n d i c a t e s t h a t t h i s temperature  independence o f  can b e expected  from t h e o r e t i c a l  -  considerations.  2k  Examination  h e r e show t h a t  °<  -  of t h e r e s u l t s r e p o r t e d  i s e s s e n t i a l l y constant  temperature f o r the systems s t u d i e d .  t o v a r y w i t h h u m i d i t y ; and  the volume o f t h e f l o w h o l e may v a r i a t i o n o f o(  As w i l l  be  l a t e r , the value of A ^ ^ c a n  mentioned a l i t t l e expected  with  be  t h i s v a r i a t i o n of  account f o r some of the  for a particular material.  The  same  i s t r u e , o f c o u r s e , f o r any f a c t o r w h i c h i n f l u e n c e s the v a l u e o f 'XCb^ (b) Two  • The magnitude of A ^ X ~ X 3  d i r e c t r e s u l t s of Ree  theorem treatment  •  and E y r i n g ' s  virial  a r e the c o n c l u s i o n s t h a t t h e v a l u e o f  ^iTX,~^ s h o u l d be d i r e c t l y p r o p o r t i o n a l to t h e  absolute  temperature,  strain.  and  i n v e r s e l y p r o p o r t i o n a l t o the  R e f e r e n c e to the t a b l e s shows t h a t f o r a c o n s t a n t  strain  o f 0 . 0 2 7 , t h e r e i s a q u a l i t a t i v e agreement o f the e x p e r i m e n t a l r e s u l t s w i t h the p r e d i c t i o n t h a t the of the flow h o l e ,  "\  , i s d i r e c t l y proportion to  the temperature as the temperature i s i n c r e a s e d . r e s u l t s f o r a c e t a t e r a y o n , w h i c h was  for  1'he  i n v e s t i g a t e d at  s t r a i n s o f 0 . 0 2 7 and 0 . 0 1 5 , show a t l e a s t the expected  size  qualitatively  e f f e c t of s t r a i n on t h e f l o w parameter;  a p a r t i c u l a r temperature a d e c r e a s e i n t h e  strain  Is accompanied by an I n c r e a s e i n the v a l u e o f "XO^^X * These p r e d i c t i o n s are q u a l i t a t i v e l y s a t i s f i e d by  our  - 25  -  r e s u l t s a s . w i l l be seen f r o m t h e T a b l e s .  It will  also  be n o t i c e d t h a t , f o r a s p e c i f i e d t e m p e r a t u r e and s t r a i n , the values of humidity.  increase with increasing  T h i s e f f e c t i s p a r t i c u l a r l y marked i n t h e  case of v i s c o s e r a y o n , where an i n c r e a s e i n the r e l a t i v e h u m i d i t y o f 69$ I s accompanied by a t h r e e f o l d increase i n the s i z e of the flow hole. dependence o f  A similar  on h u m i d i t y has been r e p o r t e d by  B u r l e i g h and Wakeham (6 ) , who i n v e s t i g a t e d s t r e s s r e l a x a t i o n b e h a v i o r of r a y o n cords a t e l e v a t e d tempera t u r e s and v a r y i n g h u m i d i t y .  These authors  advance  the t h e o r y t h a t the w a t e r p r e s e n t weakens the i n t e r c h a i n hydrogen bonds.  Such a bond weakening would  r e s u l t i n an i n c r e a s e i n t h e s i z e o f t h e f l o w u n i t , perhaps even t o t h e p o i n t where t h e e n t i r e c h a i n moves as a s i n g l e u n i t . where  (19)  B e a r i n g i n mind t h a t  I s the volume o f the f l o w u n i t , an i n c r e a s e  i n t h e s i z e o f t h e f l o w u n i t w i l l be r e f l e c t e d i n an increase i n the s i z e of the flow h o l e .  This  theory  o f f e r s at l e a s t a q u a l i t a t i v e explanation f o r the dependence of " X ^ ^  on  humidity.  The agreement between o u r r e s u l t s and  those  p r e d i c t e d by theory seem t o j u s t i f y the I n t e r p r e t a t i o n of t h e f l o w process  i n terms o f a non-Newtonian f l o w  - 26 process.  The  -  exception i s v i s c o s e rayon at  e l o n g a t i o n o f 1.5$;  a t p r e s e n t no  an  satisfactory  e x p l a n a t i o n f o r t h e s e r e s u l t s can be o f f e r e d , f u r t h e r i n v e s t i g a t i o n of t h i s m a t e r i a l temperatures i s s t r o n g l y  Indicated.  at  low  a  TABLE I VALUES OF PARAMETERS FOR NYLON  e  T°C  E  y-fRH  o  x l O * " d y n e s / cm 10  -80 -70 -60 -40 -20 0 2 2 2 25 25 25 &  0.027 0.027 0.027 0.027 0.027 0.027 0.042 0.046 0.042 0.045 0.033 0.033  -— — — —  40 65 84 16 53 97  Indicates value of E  t(l) 2  xl0~ dynes/cm 1 0  8.61 7.90 6.65 6.11 5.25 4.75 £8.0 A7.8 A7.4 A9.0 2*6.8 A6.5  0  6.3 5.5 5.0 3.9 3.4 2.9 2.2 2.0 1.6 2.6 1.7 0.7  (1)  xlO^cm  2  10  2  2 io£ 1 0  10* 10 2  io| io 2  10 1 2 2  0  io  10 10  2  2 2  t a k e n from dynamic modulus d a t a .  Other v a l u e s a r e from s t r e s s r e l a x a t i o n c u r v e s . Value o f t used i n s o l v i n g  •  <*  1,96 2.12 2.87 2.55 2.58 2.54 1.27 1.22 1.63 1.11 1.23 1.34  AF xlO  cm  10.40 11.80 16.80 16.30 17.90 19.05 9.6 9.23 12.3 9.09 10.01 10.99  *  Kcal/mole 16.5 17.40 18.15 20.7 22.1 23.6 22.79 22.80 22.80 22.79 22.50 22.9  TABLE I I VALUES OF PARAMETERS FOR VISCOSE RAYON  T°C  E  xl0~ dynes/cm 1 0  -40 -20 0 2 2 2 25 25 25 A  0.027 0.027 0.027 0.020 0.0204 0.0238 0.0222 0.0296 0.0244 Indicates  — —  50 58 82 15 ' 70 84  2  x 10" ^ d y n e a/cm  23.8 21.2 20.0 A15.5 414.5 *12.2 £17.0 £10.3 A 9.2  v a l u e of £ „  7.76 5.95 4.50 1.7 1.5 0.7 2.5 1.0 0.7  Value of t u s e d i n s o l v i n g £l<a^ •  AF xl0 cm 8  2  10 10$ 2  1 0  2  10*  10J  10^ 10%  io  2  10^  t a k e n from dynamic modulus d a t a .  Other v a l u e s a r e from s t r e s s r e l a x a t i o n c u r v e s . (1)  *  t(l)  n  1.06 1.11 1.06 2.02 2.09 2.33 1.77 2.64 5.32  xl0 cm 2 2  6.79 7.71 7.95 15.2 15.8 17.6 14.5 21.6 43.5  .  Kcal/mole 22.3 24.2 25.7 25.9 25.4 24.6 28.8 27.1 26.0  TABLE  T°C  t(l)  E„  xl0~ dynes/cm 1 0  -80 -60 -40 -20 0 -40 -20 0 2 2 2 25 25 25 4  III  0.015 0.015 0.015 0.015 0.015 0.027 0.027 0.027 0.0197 0.0204 0.0197 0.0276 0.0204 Indicates  — —  -  — — —  30 50 97 20 46 97 value of  2  xlO  xlO  4.0 3.0 2.0 1.0 1.0 3.80 2.7 2.1 —  mm mm  £6.5 45.2 45.9 46.1 45.6  0 0 0 0 0  io| io io io  10^  log iof  10°  io  3  10, 10 3  3  3 3  10*  t a k e n f r o m dynamic modulus d a t a .  Other v a l u e s a r e from s t r e s s r e l a x a t i o n c u r v e s . (1)  3  — 10 2 dynes/cm  12.80 9.15 8.40 7.1 5.4 5.95 4.9 4.05 —  Value o f t used i n s o l v i n g  L7l<^ •  or  xlO cm 2 2  cm  2.56 3.75 3.07 2.77 2.74 2.30 2.35 2.62 2.84 3.65 3.43 1.95 2.95 3.33  13.6 21.9 19.6 19.2 20.6 14.7 16.3 19.6 21.4 27.6 25.9 16.0 24.2 27.3  Kcal/mole 24.2 27.4 29.3 28.4 26.4 20.4 22.2 24.0 mm tm.  31.6 27.7 30.5 31.5 29.6  - 30 BIBLIOGRAPHY 1. 2. 3.  T o b o l s k y , A. V., Prettyman, J . B., and D i l l o n , J . W.,  J . A p p l . Phys., l£: 380 (19UU) Andrews, R. D., Hofman-B ng, N., and T o b o l s k y , A. V., J . Polymer S c i . , y. 669 (1948) S t e i n , R. S., and S c h a e r i t z , H., Rev. S c i . I n s t r . , a  19: 835 (191+8) 4.  B i s c h o f f , J . , C a t s i f f , E., and T o b o l s k y , A. V., J . Am. Chem. S o c , j j . : 835 (1948)  5.  M c L o u g h l i n , J . R., Rev. S c i . I n s t r . ,  6.  B u r l e i g h , E. G., and Wakeham, H., T e x t i l e Research  23: 459 (1952)  J . , 17: 2k5 (1947) 7.  P r i c e , S. J . W., B. A. T h e s i s , 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 , 1953  8.  Watson, M. T., Kennedy, W. D., and Armstrong, G. M., a b s t r a c t e d i n Phys. Rev., 82:  9. 10.  301 (1951)  M o l l e , A. W., J . Polymer S c i . , $: 1  (1950)  Sauer, J . A., and K l i n e , D. E., J . Polymer S c i . ,  18: 491 (1955) 11. 12.  Thomas, D. A., and Robinson, D. W., B r i t . J . A p p l . Phys., 6: k l (1955) A l f r e y , T., I n " P h y s i c a l C h e m i s t r y o f H i g h P o l y m e r i c Systems", ed. by Mark, H., and T o b o l s k y , A. V., I n t e r s c i e n c e , New Y o r k , 1950  13.  B e c k e r , R., "Probleme d e r t e c h n i s c h e n M a g n e t i s i e r u n g s kurve", Springer, B e r l i n ,  1938  14.  Kuhn, W., H e l v . Chem. A c t a . ,  15.  D u n e l l , B. A., T o b o l s k y , A. V., and Andrews, R. D.,  16.  3£: 307, 464, 839 (1947)  T e x t i l e R e s e a r c h J . , 21: 40k (195D G l a s s t o n e , S., L a i d l e r , K. S., and E y r i n g , H., "Theory o f Rate P r o c e s s e s " , McGraw H i l l , New York 1st e d . 194l  - 31 17.  T o b o l s k y , A. V., and C a t s l f f , 12?  18.  E., J . Polymer S c i . ,  I l l (1956)  E y r i n g , H., and H a l s e y , B., T e x t i l e Research J . , 16: 382, 378, 335, 329, 201, 12k, 53, 13 TT9U6), 15: k 5 i , 295, (191+5)  19.  B u r t e , H., H a l s e y , G., and D i l l o n , Research J . , 1 8 1 1+1+9 (19k8)  S. H., T e x t i l e  20.  P r i c e , S. J . W., M. Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1955  21.  P r i c e , S. J . W., M c l n t y r e , A. D., P a t t i s o n , J . P., and D u n e l l , B. A., T e x t i l e R e s e a r c h J . , 26: 276 (1956)  ~~  .22.  Andrews, R. D., Rofman-Bang, N., and T o b o l s k y , A. V., op. c i t .  23.  F r e n k e l , J . , " K i n e t i c Theory o f L i q u i d s " , Oxford U n i v e r s i t y P r e s s , L o n d o n 19I1.6  2ij..  K i r k w o o d , S. G., J . Chem. Phys., lij.: 51 (19M>)  25.  A l f r e y , T., J . Chem. Phys., 12: 37U (191+1+)  26.  T o b o l s k y , A. V., and E y r i n g , H., J . Chem. Phys.,  27.  Ree, T., and E y r i n g , H., J . A p p l . Phys., 26: 793  11: 125 (I9k3) (1955)  "~  28.  (a) K i s t l e r , S. S., J . A p p l . Phys., 11: 769 U9U0) (b) T o b o l s k y , A. V., and Andrews, R. D., J . Chem. Phys., 13: 3 (19U5) (c) Ree, T., and E y r i n g , H., U n i v e r s i t y o f Utah T e c h n i c a l Report 38, Dec. 1, 1952  29.  E y r i n g , H., and Ree, T., P r o c . N a t l . Acad. S c i . U. S., tjJ.: 1+.8 (1955)  30.  H a l s e y , G., White, H. J . , and E y r i n g , H., T e x t i l e Research J . , 15: 295 U9k5)  31.  Kauzmann, W., Am. I n s t . M i n . Met. Eng. T r a n s . , Ik3? 57 (191+1)  32.  Sherby, 0. D., and Dorn, J . E., J . M e t a l s , ii: 959 (1952); J . M e t a l s , 5: 321+ (1953)  Figure |.  Models used in describing the  Properties of high polymers  Parallel  array  of Maxwell units  mechanical  Control a Calibrote  Timer a relay  3 To transducer  Potentiometer  Figure 2. Block circuit diagram  Transducer  To measuring  Figure 3. Calibration  device  circuit  10  i  Figure 4- S l r e s s filaments  1  i  r  relaxation in single  of nylon  £=0.027  9  8  $  7  a? o  3  ro  Time J 10'  10"  1.0  in s e c o n d s  I 10  10  10"  10'  1 Figure 10.  1  r  1  Stress relaxation  filaments  of  acetate  in single  rayon  2 C.,307,R.H. 2 ° C. 5 0 \ R.H. 25°C.  25  2°C.  Time in seconds o| 10  _  2 5 C.  L 10  10  10  10  10  20%&H.  C. 4 6 % R H . 9  7 % R H .  H Figure II. filaments  1  I —  1  S t r e s s relaxation of  viscose  in  single  rayon  25° c. is \  2 e  C.  %  R.H.  S O X R.H.  R.H.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062428/manifest

Comment

Related Items