The Science of Macromolecules: Evolution and ... - ACS Publications

4 The Science of Macromolecules: Evolution and Early Elaborations ROBERT SIMHA

Downloaded by CORNELL UNIV on July 20, 2016 | http://pubs.acs.org Publication Date: December 10, 1981 | doi: 10.1021/bk-1981-0175.ch004

Case Western Reserve University, Department of Macromolecular Science, Cleveland, OH 44106

The occurence of the Symposium and its publication are most welcome occasions on at least two grounds. One, of course, to honor the man and his manifold contributions. Secondly, they induce us to think of our science in a retrospective and perspective manner, more so than we are wont to ordinarily do in the course of our particular research activities. What we want to do then is to discuss some crucial developments of the past, keeping in mind however that neither the recollections of an eyewitness, an essay of the historian of science, or finally a complete survey are to be expected. Instead, we merely ask: how did the two corner stones, namely the recognition of the macro or chainmolecule and the notion of chain flexibility evolve? What were some of the first applications, based on these concepts? An even sketchy consideration of these matters allows us to gage the flavor of the scientific methodology and at the same time, the impact of Hermann Mark's thoughts and work during that period. The student o f the e a r l y l i t e r a t u r e (jL) informs us that notions o f l a r g e p a r t i c l e weights, exceeding the molecular weights f a m i l i a r to the c l a s s i c a l organic chemist by orders o f magnitude, were extant already i n the nineteenth century. But we have known i n other instances that there can be a sometimes extensive s t r e t c h i n time between the hypothesis and i t s e l e v a t i o n to the rank of a w e l l founded theory. R e c a l l the c l a s s i c a l examples o f the atomic theory, o r i n more recent times the quantum, designated by Max Planck o r i g i n a l l y as a hypothesis r a t h e r than a theory. And so i t has been i n the present i n s t a n c e . We can then begin w i t h the mid twenties o f our century, when two opposing views had c r y s t a l l i z e d . Both accepted the e x i s t e n c e of l a r g e p a r t i c l e masses, although concrete numerical values were h a r d l y a c c e s s i b l e at that time. The p o i n t o f dispute was: aggregate vs. g i a n t molecule. The i s s u e i s i l l u s t r a t e d by the case o f n a t u r a l rubber (see Table I ) . Isoprene had been recognized long before as the b a s i c c o n s t i t u e n t . Does i t form some low molecular weight s t r u c t u r e , p o s s i b l y a r i n g ? Do a

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TABLE I


N a t u r a l Rubber:

Two

S t r u c t u r a l Views

1.

Isoprene + " B a s i c U n i t " (?) "Basic Unit" + C o l l o i d a l P a r t i c l e Secondary Forces (?) Solvent E f f e c t s

2.

Isoprene •> Long Chain Chain (Macro) Molecule Chemical Bonding No Solvent E f f e c t s

number of these r i n g s combine to form a c o l l o i d a l p a r t i c l e by the i n t e r v e n t i o n o f secondary f o r c e s , i n t h i s i n s t a n c e p o s s i b l y a r i s i n g from the presence of double bonds? I f so,the medium ought to p l a y a s i g n i f i c a n t r o l e i n determining the p a r t i c l e mass. A l t e r n a t i v e l y , could isoprene molecules c o n t r i v e to form long chain s t r u c t u r e s , and c o u l d these s t r u c t u r e s be r e s p o n s i b l e f o r the c o l l o i d a l c h a r a c t e r i s t i c s observed i n s o l u t i o n ? The e x i s t e n c e o f such a c h a i n o r macromolecule i m p l i e s chemical bonding of s m a l l u n i t s and hence no s o l v e n t e f f e c t s on the p a r t i c l e mass, p r o v i d e d of course we operate i n s u f f i c i e n t l y d i l u t e s o l u t i o n . What were then the approaches used to s e t t l e the i s s u e ? In view of the outcome which was decided more than f o r t y years ago, we need to d e a l here only with the methodologies s u p p o r t i n g the e x i s t e n c e of the macromolecule. One was from the o r g a n i c chemical d i r e c t i o n . Hermann Staudinger showed t h a t the e l i m i n a t i o n of double bonds by hydrogénation d i d n o t e l i m i n a t e the c h a r a c t e r i s t i c c o l l o i d a l f e a t u r e s (2). During the same p e r i o d , he a l s o i n v e s t i gated a s y n t h e t i c polymer, namely poly(oxymethylene) (3)· He was able to produce by c o n t r o l l e d chemical degradation a homologous s e r i e s of pure o l i g o m e r i c poly(oxymethylene d i a c e t a t e s ) w i t h η £ 17 and demonstrate the systematic v a r i a t i o n of t h e i r p h y s i c a l p r o p e r t i e s . He concluded that the repeat u n i t s of the o r i g i n a l p a r t i c l e s were l i n k e d to each other so as to form long c h a i n s . By analogy he reasoned, other polymers would be s i m i l a r l y constituted. The other approach o r i g i n a t e d from the physicochemical s i d e , s p e c i f i c a l l y X-ray spectroscopy of s e m i c r y s t a l l i n e systems, i n particular cellulose. Hermann Mark concluded t h a t the microb u i l d i n g b l o c k s contained but a s m a l l number of s t r u c t u r a l residues and t h a t these were h e l d together at d i s t a n c e s c o r r e sponding to valence bonds and with f o r c e s o f the i n t e n s i t y corresponding to valence forces ( 4 ) . From these c o n s i d e r a t i o n s there evolved the concept o f "primary valence c h a i n s " i n c e l l u l o s e , h e l d together i n bundles, o r m i c e l l e s ( c r y s t a l l i t e s ) by secondary f o r c e s , as propounded by Meyer and Mark (j>) · This view was then extended to encompass other high polymers as w e l l . I t should be noted however, t h a t Freudenberg had already proposed a chain s t r u c t u r e f o r c e l l u l o s e , based on degradation experiments (6). I f the m i c e l l e s were to



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s u r v i v e as e n t i t i e s i n s o l u t i o n , then a p a r t i c l e mass determina t i o n by whatever method would y i e l d a lower l i m i t f o r the mean chainlength o f the c o n s t i t u e n t chains. The f a c t that one was i n any case d e a l i n g with a d i s t r i b u t i o n of masses, was recognized by a l l concerned. However the q u a n t i t a t i v e consequences of t h i s feature f o r the i n t e r p r e t a t i o n and comparison o f data d e r i v e d by means of d i f f e r e n t experimental methods remained to be a p p r e c i ated, u n t i l r e l i a b l e s o l u t i o n methods f o r l a r g e (molecular) weights became a v a i l a b l e . We recognize at t h i s p o i n t the common ground between the i n v e s t i g a t o r s at the u n i v e r s i t y of F r e i b u r g on the one hand and the Ludwigshafen l a b o r a t o r y of the I. G. Farben on the other. That i s , both supported, w i t h the a i d of d i f f e r e n t methodologies, the second view i l l u s t r a t e d i n Table I ; t h i s a t a time when the opposing view was s t i l l defended by a r e s p e c t a b l e group of i n v e s t i g a t o r s , organic as w e l l as p h y s i c a l chemists. This i s not the p l a c e to i n j e c t p e r s o n a l matters i n t o the d i s c u s s i o n and consider reasons why the expected cooperation d i d not m a t e r i a l i z e . The reader i n t e r e s t e d i n the h i s t o r y of the ensuing c o n t r o v e r s i e s should consult the o r i g i n a l l i t e r a t u r e of the l a t e twenties and t h i r t i e s and Réf. 1. Let i t o n l y be s a i d that Mark attempted to mediate and to emphasize s c i e n t i f i c aspects and the b a s i c common ground. One might s p e c u l a t e that cooperation would have a c c e l e r a t e d the s t a r t of the second stage, i . e . , a p p l i c a t i o n s (see below). To r e v e r t to the main trend of our d i s c u s s i o n , the i s s u e to be considered at that stage, was c h a r a c t e r i z a t i o n i n s o l u t i o n . The unequivocal t h e o r e t i c a l b a s i s f o r c o l l i g a t i v e p r o p e r t i e s had been provided by the c l a s s i c a l thermodynamics of s o l u t i o n s . Svedberg's sedimentation e q u i l i b r i u m i n the u l t r a c e n t r i f u g e had only r e c e n t l y begun to make i t s impact, p r i m a r i l y w i t h p r o t e i n s o l u t i o n s . The theory o f Rayleigh s c a t t e r i n g i n s o l u t i o n was a l l there by 1930, but i t s r e a l i z a t i o n as a t o o l f o r determinations of l a r g e masses had to await another decade. These l a r g e masses rendered the use of c o l l i g a t i v e p r o p e r t i e s , i n c l u d i n g osmotic pressure, a d i f f i c u l t experimental task. An experimentally comparatively easy procedure however was and i s the determination o f the v i s c o s i t y increment i n s o l u t i o n . Indeed these increments had been shown e a r l i e r to be much h i g h e r i n suspensions of s t a r c h or rubber than f o r , say, a sugar s o l u t i o n . In 1929 Staudinger (7) reported a s e r i e s of v i s c o s i t y s t u d i e s on n a t u r a l and guttapercha s o l u t i o n s . No ( s i g n i f i c a n t ) v a r i a t i o n s i n the r e l a t i v e v i s c o s i t i e s with changing s o l v e n t medium were observable. This i n c o n t r a s t to the r e d u c t i o n brought about by h i g h temperature treatments. Staudinger concluded that degradation o f i n d i v i d u a l macromolecules was i n v o l v e d . Moreover, the r e s u l t s f o r the degradation products suggested a p r o p o r t i o n a l i t y between v i s c o s i t y increments and osmatic molecular weights i n a range below M - 10^. From these

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and f u r t h e r v i s c o s i t y s t u d i e s there evolved Staudinger's famed v i s c o s i t y r e l a t i o n (8): (η-η )/(η c) = η /c = K x M o o sp s

(1)

f i r s t enunciated f o r p o l y s t y r e n e s o l u t i o n s . The s u b s c r i p t ο r e f e r s to the s o l v e n t and the parameter K v a r i e s with the s o l v e n t and s o l u t e , but, the important p o i n t , i s to be independent of molecular determinations o f M i n the low, s o - c a l l e d "hemic o l l o i d a l " range. The s i g n i f i c a n c e o f t h i s r e l a t i o n f o r f u r t h e r developments can not be overemphasized. We s h a l l r e v e r t to t h i s matter but have f i r s t to r e c a l l the s t a t u s o f v i s c o s i t y theory (9). E i n s t e i n ' s methodology was to be the g u i d i n g s p i r i t o f a l l subsequent work on s o l u t i o n v i s c o s i t y o f c o l l o i d a l suspensions and polymer s o l u t i o n s up to the present time. He considered a suspension o f Ν compact spheres each o f volume ν i n a volume V and obtained the r e s u l t : ^


g

Um(n-n c-X)

0

)/n 0

= [ n ] c = fxNv c = f(c/M)N v Ρ A

A

(2)

p

where c stands f o r the c o n c e n t r a t i o n i n weight p e r u n i t volume, and f i s a geometric f a c t o r depending on p a r t i c l e shape and hence on molecular o r p a r t i c l e mass M. F o r the E i n s t e i n spheres f i s a pure numeric, v i z . 2.5, when the i n t r i n s i c [η] i s expressed as cm /g. I t i s worth r e c a l l i n g the immediate a t t e n t i o n eq. (2) r e c e i v e d by c o l l o i d chemists, which u l t i m a t e l y l e d to the detec t i o n o f a numerical e r r o r i n the o r i g i n a l d e r i v a t i o n . The above r e s u l t was invoked by Mark and Fikentscher (10) . To make the necessary extension o f eq. (2) to h i g h e r c o n c e n t r a t i o n s , they w r i t e : 3

(η-η )/(η c) = A. + A c 0

0

1

(3)

2

where the E i n s t e i n term A has been augmented by an i n t e r a c t i o n term. The A depend on p a r t i c l e shape i n a manner which could not be e x p l i c i t l y formulated a t the time. Equation (3) i s patterned a f t e r the v i r i a l expansion o f the equation o f s t a t e i n a gas o r o f the osmotic pressure equation o f a s o l u t i o n . This i n t u i t i v e e m p i r i c a l r e l a t i o n was one o f the motivations i n R. Simha's d o c t o r a l d i s s e r t a t i o n to d e r i v e the f i r s t extension o f E i n s t e i n ' s theory by the i n t r o d u c t i o n o f hydrodynamic i n t e r a c t i o n s (11). Mark and F i k e n t s c h e r d e r i v e d from eq. (3) a r e l a t i o n between molecular weight and c o n c e n t r a t i o n o f a s e r i e s o f e q u i v i s c o u s suspensions. Staudinger a l s o made use o f E i n s t e i n ' s r e s u l t . To account f o r higher c o n c e n t r a t i o n s , he proposed an e x p o n e n t i a l r e l a t i o n which however i s not obeyed by polymer s o l u t i o n s . Reverting to d i l u t e s o l u t i o n s , he recommended f o r the c o n c e n t r a t i o n below which 1

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eq. (1) would become v a l i d , the s o - c a l l e d base molar s o l u t i o n (8), i . e . c of the order of f i f t y to hundred g/£, h a r d l y a d i l u t e s o l u tion. The e x t r a p o l a t i o n o f η /c to zero c o n c e n t r a t i o n was adopted only subsequently, s l l u d i n g e r then o f f e r e d a d e r i v a t i o n based on E i n s t e i n s b a s i c i d e a s . To o b t a i n the parameter f i n eq. (2), be represented the s o l u t e as a rod, r o t a t i n g i n the plane o f shear. Now i n a homologous s e r i e s o f such rods o f l e n g t h I and thickness d we have: 1

I

« M

d « M °

The c y l i n d r i c a l hydrodynamic volume swept out by the p a r t i c l e , £ d , i s a c c o r d i n g l y p r o p o r t i o n a l to M and thus the v i s c o s i t y increment p r o p o r t i o n a l to M, i . e . eq. (1) i s obtained. Staudin ger' s v i s c o s i t y r e l a t i o n has exerted a great invluence on both experimental and t h e o r e t i c a l research. As i s w e l l e s t a b l i s h e d , eq. (1) i s not v e r i f i e d by e i t h e r f o r the type of polymers under d i s c u s s i o n here. The i n v e s t i g a t i o n s r e s u l t i n g i n t h i s i n c l u s i o n tend to confirm the b a s i c concepts of macromolecular science mentioned a t the beginning and thus may a l s o be regarded as one o f the f i r s t a p p l i c a t i o n s o f these concepts. Returning to Staudinger's d e r i v a t i o n , i t must be r e v i s e d on two grounds. F i r s t the kinematics of motion i s three r a t h e r than two-dimensional and the hydrodynamic volume s p h e r i c a l r a t h e r than c y l i n d r i c a l , i . e . « i3. The d e t a i l e d c a l c u l a t i o n f o r t h i n e l l i p s o i d a l p a r t i c l e s (13) shows an approximate p r o p o r t i o n a l i t y o f the i n t r i n s i c v i s c o s i t y w i t h Μ · , a considerable d i f f e r e n c e from eq. (1) f o r l a r g e M. While the u n d e r l y i n g model i s appropriate f o r r i g i d macro molecules, i t i s not a p p l i c a b l e to the types of systems, such as c e l l u l o s e , c e l l u l o s e d e r i v a t i v e s , p o l y i s o p r e n e or v i n y l polymers, f o r which Staudinger had intended i t . The reason i s chain f l e x i b i l i t y which a r i s e s from an at l e a s t l i m i t e d freedom of r o t a t i o n of bonds, connecting the repeat u n i t s o f the c h a i n , a freedom p r e v a i l i n g f o r s i n g l e C-C and other linkages as w e l l . Quantita t i v e i n f o r m a t i o n f o r s m a l l organic s t r u c t u r e s had been generated by a v a r i e t y of s p e c t r o s c o p i c and thermochemical experimentation, and the measurement o f d i p o l e moments i n p o l a r molecules (14). The consequences of t h i s r e l a t i v e i n t e r n a l freedom o f thermal motion f o r the conformations of a chain c o n t a i n i n g a l a r g e number o f bonds are profound. I t was r e a l i z e d by s e v e r a l o f Staudinger's contemporaries (14) although not by him, that a s t a t i s t i c a l d i s t r i b u t i o n o f p o s s i b l e bond c o n f i g u r a t i o n s n e c e s s a r i l y r e s u l t s i n a s t a t i s t i c a l d i s t r i b u t i o n of o v e r a l l chain conformations. The average represents a loose c o i l r a t h e r than an extended s t r u c t u r e with dimensions i n c r e a s i n g as and ρ at most a s m a l l 2


;

2

1

7

number (15, 16, 17). This element o f chain f l e x i b i l i t y was soon recognized to pervade the p h y s i c a l p r o p e r t i e s i n s o l u t i o n as w e l l as i n the amorphous bulk s t a t e . Reverting to the v i s c o s i t y problem, eq. (1) must be r e p l a c e d by the two-parameter expression


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[η] = KM

a

OVERVIEW

(la)

where Κ i s a constant f o r a given s o l u t e - s o l v e n t p a i r and the exponent does not assume a u n i v e r s a l value f o r a l l systems but i s i n g e n e r a l l e s s than u n i t y . An equation of t h i s form with a = 2/3 was f i r s t d e r i v e d by W. H a l l e r (18). I t has s i n c e then entered the l i t e r a t u r e as the Houwink-Mark r e l a t i o n . I t should be noted i n t h i s connection that even i n Staudinger's l a b o r a t o r y d e v i a t i o n s from eq. (1) were observed f o r p o l y ( v i n y l acetate) and p o l y a c r y l a t e s (19). These were q u a l i t a t i v e l y c o n s i s t e n t with eq. ( l a ) , that i s , osmotic molecular weights were found to be c o n s i d e r a b l y l a r g e r than expected from eq. ( 1 ) . We have devoted the considerable amount of a t t e n t i o n to the v i s c o s i t y problem which i s i t s due i n the development of macromolecular s c i e n c e . Staud i n g e r ' s work has exerted a great i n f l u e n c e , i n a d i f f e r e n t manner than E i n s t e i n ' s of course, by i n i t i a t i n g and c a t a l y z i n g extensive experimental and t h e o r e t i c a l r e s e a r c h . This has aimed at o b t a i n i n g an acceptable p i c t u r e of macromolecular dimensions i n ( i n f i n i t e l y ) d i l u t e s o l u t i o n , at a c a l i b r a t i o n of eq. ( l a ) , and f i n a l l y at p r o v i d i n g a t h e o r e t i c a l b a s i s f o r t h i s equation, based on E i n s t e i n ' s o r g i n a l i d e a s . At the same time, s o l u t i o n v i s c o s i t y represents an e a r l y a p p l i c a t i o n of the n o t i o n of the f l e x i b l e macromolecule to a m a t e r i a l property. The importance of thermodynamic methods f o r the c h a r a c t e r i z a t i o n of the macromolecule was obvious, as was the p a r t i c u l a r r o l e among c o l l i g a t i v e p r o p e r t i e s p l a y e d by osmometry. Beyond t h i s and a c c e p t i n g the second view i l l u s t r a t e d i n Table I, one was l e d to i n q u i r e i n t o the consequences of t h i s view f o r the thermo dynamics of macromolecular s o l u t i o n s . By the mid nineteen t h i r t i e s a s e r i e s o f experimental s t u d i e s on s o l u t i o n s of o l i gomers and polymers were being undertaken, of which those c a r r i e d out i n Kurt H. Meyer's l a b o r a t o r y i n Geneva should be p a r t i c u l a r l y r e c a l l e d because of t h e i r d e t a i l e d and systematic c h a r a c t e r (20). The c r u c i a l r e c o g n i t i o n was the enhanced entropy of mixing a r i s i n g from the d i s p a r i t y i n s i z e between s o l u t e and s o l v e n t , c l e a r l y even i f only q u a l i t a t i v e l y d i s c u s s e d by Meyer (Ref. 20, p. 586). Q u a n t i t a t i v e r e s u l t s f o r i d e a l i z e d models were d e r i v e d f i r s t by the E n g l i s h s c h o o l of s t a t i s t i c a l mechanics (21, 22). F i n a l l y , we t u r n from s o l u t i o n s to the bulk s t a t e of amor phous polymers, s p e c i f i c a l l y the t h e r m o e l a s t i c p r o p e r t i e s of the rubbery s t a t e . The c o n t r a s t i n g behavior of rubber, as compared with other s o l i d s , such as the temperature decrease upon a d i a b a t i c e x t e n s i o n , the c o n t r a c t i o n upon h e a t i n g under l o a d , and the p o s i t i v e temperature c o e f f i c i e n t of s t r e s s under constant elonga t i o n , had been observed i n the n i n e t e e n t h century by Gough and J o u l e . The l a t t e r was able to i n t e r p r e t these experiments i n terms of the second law of thermodynamics, which r e v e a l e d the connection between the d i f f e r e n t phenomena observed. One could conclude the primary e f f e c t to be a r e d u c t i o n of entropy



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r a t h e r than an i n c r e a s e i n energy. This i s as f a r as phenomenolo g i c a l theory could go. I t became now p o s s i b l e to aim at a molecular theory, based on a s t a t i s t i c a l mechanics of bulk polymers, and thus to r e f e r to a rubbery s t a t e of matter, i n the same sense as, f o r example, to the l i q u i d s t a t e . I n i t i a l attempts to r e l a t e the deformation o f rubber to the thermal motion of r i g i d rods (23) and to a h e l i c a l conformation (24) were superseded by c o n s i d e r a t i o n s of a r e a l i s t i c chain s t r u c t u r e f i r s t advanced by Meyer, v. Susich, and Valko (25). The e s s e n t i a l i d e a i s an entropy r e d u c t i o n , r e s u l t i n g from a r e d u c t i o n of the number of conforma t i o n s of a c o i l i n g chain upon deformation. A q u a n t i t a t i v e e v a l u a t i o n of t h i s p i c t u r e by Guth and Mark followed soon t h e r e a f t e r (16). A model o f a c r o s s - l i n k e d rubbery network was f i r s t analyzed by W. Kuhn (26). The a p p l i c a t i o n s of the b a s i c tenets i n macromolecular science d i s c u s s e d here have been concerned with c e r t a i n p h y s i c a l p r o p e r t i e s . We d e s i s t from a d i s c u s s i o n of the k i n e t i c s and s t a t i s t i c s o f formation and decomposition o f high polymers by the various chemical r o u t e s , which evolved a t about the same time. The l i n e s o f research sketched i n t r o d u c e d a h e r o i c age of macromolecular science during the f o l l o w i n g two decades or so. In t h i s p e r i o d the primary emphasis i n p h y s i c a l research remained on the plane of general phenomena r a t h e r than s p e c i f i c polymers per se. That Hermann Mark w i t h h i s c o l l a b o r a t o r s o f backgrounds ranging from o r g a n i c chemistry to t h e o r e t i c a l p h y s i c s , exerted a strong and c h a r a c t e r i s t i c i n f l u e n c e i s evident from even a cursory examination o f the p e r i o d ' s l i t e r a t u r e . Mark's i n t e r e s t s nevertheless were not confined to the t o p i c s of t h i s a r t i c l e . In l a t e r y e a r s , h i s more urgent concerns turned to other d i r e c t i o n s i n the polymer arena. However throughout, he has continued as an a c t i v e witness of developments the o r i g i n s of which can be t r a c e d back to those e a r l y y e a r s . One needs to r e c a l l only t y p i c a l areas such as the chain dynamics of the s i n g l e chain, dynamics and rheology of moderately and h i g h l y concentrated s o l u t i o n s and the melt, the s t a t i s t i c a l thermodynamics o f b u l k polymers, the thermoe l a s t i c i t y of the rubbery melt and g e l , the v a s t s t r u c t u r a l e f f o r t s on s y n t h e t i c and biopolymers, and the e x t e n s i v e k i n e t i c s t u d i e s . In the course of h i s long s c i e n t i f i c career Hermann Mark has witnessed a l l t h i s and he w i l l , of course continue to do so.

Literature Cited 1.

2. 3. 4.

Useful references and documentary material are found in Priesner, Claus, "H. Staudinger, H. Mark and Κ. H. Meyer: Thesen zur Gröβe und Struktur d. Makromolekiile"; Verlag Chemie: Deerfield Beach, Fla., 1980. Staudinger, H. Ber. 1925, 57, 1203. Staudinger, H. Helv. Chim. Acta 1925, 8, 65. Mark, H. Ber. 1926, 59, 2982.



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POLYMER SCIENCE OVERVIEW

5. Meyer, Κ. H.; Mark, H. Ber. 1928, 61, 593. 6. Freudenberg, K.; Braun, E. Liebigs Ann. 1928, 460, 288. 7. Staudinger, H.; Bondy, H. F. Liebigs Ann. 1929, 468, 1. 8. Staudinger, H.; Heuer, W. Ber. 1930, 63, 222. 9. Einstein, A. Ann. Physik 1906, 19, 289; 1911, 34, 591. 10. Mark, H.; Fikentscher, H. Koll.-Z. 1929, 49, 135. 11. Guth, E . ; Simha, R. Koll.-Z. 1936, 79, 266. 12. Detailed discussions and references are found in Staudinger, H., "Die hochmolekularen organischen Verbindungen"; J. Springer Verlag: Berlin, 1932. 13. Simha, R. J. Phys. Chem. 1940, 44, 25; J. Chem. Phys. 1945, 13, 188. 14. A detailed survey of the literature of the period is given in Mark, H. "Physical Chemistry of High Polymeric Systems"; Interscience Publ. Inc.: New York, 1940. 15. Eyring, H. Phys. Rev. 1932, 39, 746. 16. Guth, E . ; Mark, H. Monatsh 1934, 65, 93. 17. Kuhn, W. Kolloid-Z. 1934, 68, 2. 18. Haller, W. Koll.-Z. 1931, 56, 257. 19. Staudinger H.; Warth, H. J. Prakt. Chemie 1940, 155, 261 20. See Meyer, Κ. H. "Natural and Synthetic High Polymers"; Interscience Publ. Inc.: New York, 1942. 21. Guggenheim, E. A. Trans. Faraday Soc. 1937, 33, 151. 22. Fowler, R. H.; Rushbrooke, G. S. Trans. Faraday Soc. 1937, 33, 1272. 23. Wohlisch E.; de Rochemont R. Z. Biol. 1927 85, 406. 24. Mark, H.; Valko, E. Kautschuk 1930, No. 10, 210. 25. Meyer, K. H.; v. Susich, G.; Valkó, E. Kolloid-Z. 1932, 59, 208. 26.

Kuhn, W. Kolloid-Z. 1936, 76, 258.

RECEIVED

August 19, 1981.


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