- Email: [email protected]
Study of the compositional inhomogeneity of graft copolymers by the diffusion method
1382
A . N . CHE~SOV et al.
(2) I t WaS f o u n d t h a t in the region o f low c o n c e n t r a t i o n s of t h e resin solution (both of t h e original resin a n d its fractions) the a d s o r p t i o n is m o n o m o l e c u l a r , w i t h p l a n a r o r i e n t a t i o n of t h e p o l y e s t e r molecules. I n t h e h i g h c o n c e n t r a t i o n region a d s o r p t i o n increases u p to fivefold (for t h e higher fractions), a n d this is e x p l a i n e d b y the presence of a g ~ e g a t e s or b y a t t a c h m e n t of o n l y certain p a r t s of t h e molecules to t h e surface, t h e r e m a i n d e r being o r i e n t a t e d into t h e solution. Translated by E. O. P~r~IPS
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
13.
J. P. HELME, G. BOSSHARD and J. ROUZIER, J. Appl. Chem. 15: 103, 1965 R. WILSON and A. H. ROBSON, Official Digest 27: 111, 1955 A. R. H. TA~VN, J. Oil and Colour Chem. Assoc. 39: 223, 1956 R. A. BRETT, J. Oil and Colour Chem. Assoc. 41: 428, 1958 A. I. SEAVELL, J. Oil and Colour Chem. Assoc. 42: 319, 1959 Ye. P. SHCHIPANOVA, A. A. TRAPEZNIKOV and V. A. OGAREV, Kolloid. zh. 29: 872, 1967 Ye. P. BOGOMOLOVA, Dissertation, 1969 V. T. CROWL and M. A. MALATI, Disc. Faraday Soc. 42: 301, 1966 H. SCH~TTE, Plaste und Kautschuk 11: 248, 1964 J. E. LUCE and A. A. ROBERTSON, J. Polymer Sci. 51: 317, 1961 ~V. HELLER and T. L. PUGH, J. Polymer Sci. 47: 203, 1960 E. G. B O B A L E K , C. C. LEE and E. R. MOORE, Official Digest 447: 416, 1962 A. A. TRAPEZNIKOV and G. G. PETRZHIK, Kolloid. zh. 27: 453, 1965
STUDY OF THE CO~IPOSITIONAL INHOMOGENEITY OF GRAFT COPOLYMERS BY THE DIFFUSION METHOD* A. N. CHERK~SOV, S. I. K L E N n ~ and G. A. ANDREYEV-% Institute of Macromolecular Compounds, U.S.S.R. Academy of Sciences (Received 27 January 1969) WE ~r~VE p r e v i o u s l y p r o p o s e d a m e t h o d for d e t e r m i n i n g t h e compositional i n h o m o g e n e i t y of copolsuners b y m e a n s o f diffusion [1]. T h e m e t h o d p e r m i t s d e t e c t i o n of c o m p o s i t i o n a l h o m o g e n e i t y o f a c o p o l y m e r if it also involves i n h o m o g e n e i t y in .molecular weight. I n t h e general case t h e r e l a t i o n s h i p can be e x p r e s s e d by the equation
M=l11~lCl--x) * Vysokomol. soyed. AI2: No. 6, 1223-1232, 1970.
(1)
Study of compositional inhomogeneity of graft copolymers
1383
where M~ is the weight of the original homopolymer in the copols-mer molecule, x the weight fraction of the ~ a f t e d homopolymer and M the molecular weight of the copolymer of composition x. It was shown in references [1] and [2] that when the compositional inhomogeneity of a copolymer can be described by a bimodal x (M) distribution function it is possible by the proposed method to calculate the distribution function of the copolymer with respect to composition. In this paper we present a similar study of gTaft copolymers (polymethylmethacrylate (PMMA)-polystyrene (PS)), characterized by a unimodal M (x) distribution function. METHOD The study of diffusion and determination of the refractive index increment of the graft copol)~ner samples were carried out in a Tsvetkov diffusiometer [3]. The difference between the refractive index of the solution and solvent, z/n, was fotmd from the area, Q, under the (r) diffusion cu~-e. ~+~5 (r)=~-
dr,
(2)
2 where h is the length of the diffusion cell i n t h e direction of the light beam, )~the wavelength of the light, a the separation produced by the polarizer and d n / d r the refractive index gradient along the height of the cell, r. The value of 4 n was found from the formula ,dn = ).Q / h a .
(3)
The refractive index increment, v, was found from the initial slope of the dependence of z~n on the concentration of the solution, c. The composition of the copolymer was found from the refractive index increment of the copolymer, vc, and of its component homopolymers (vA and VB), assuming additi~dty of the increments VC - -
x
=
-
VA
-
(4)
YB--YA
The sedimentation constants were determined in a UTSA-5 analytical ultracentrifuge at concentrations of 0"02-0"050/o . THEORY
For analysis of the compositional inhomogeneity of the copolymers we made use of the separation of the molecules in the course of diffusion, with respect to molecular weight, and consequently also with respect to composition (taking equation (1) into account). Thus if the copolymer contains molecules differing sufficiently in their values of x (refractive index n) it is possible to choose a solvent with a suitable value of n such that the copolymer would as it were be divided into two parts; namely a high molecular weight part with a positive refractive index increment, h >0, and a low molecular weight part with a negative refrac-
1384
A.N.
CHE~KASOV et al.
tire index increment, v2<0. I f the coefficients of diffusion of these supposed parts differ sufficiently the screen of the diffusiometer will show a 6 (r) curve that is a combination of two curves with maxima on different sides (Fig. 1). Curve 1, which varies slowly with time, is due to the high molecular weight part of the copols-mer (maximum pointing upward), and curve 2, corresponding to the low n4
~
ni
fi
na
/
2
~,.,, FIG. 1
x
1
FIG. 2
FzG. 1. Diffusion curve (3) of a compositionally inhomogeneous copolymer, consisting of a curve of the high molecular weight fraction of the copolyraer (vl> 0) (1) and a curve of the low molecular weight fraction (v~<0) (2). FIG. 2. Weight-average compositional (refractive kndex) distribution function of a compositio~lally inhomogeneous copol~m~er(n.~and nB are the refractive indices of the component homopolymers). molecular weight part of the copolymel, varies more rapidly with time (maximum pointing downward). Splitting of the 5(r) curve of a copolymer in the course of diffusion thus indicates its compositional in_homogeneity. We shall characterize the compositional inhomogeneity of the copolymer by its weight-average compositional distribution function fw (x) (Fig. 2). Conventional normalization of such a function will take the form 1
j'fw(z)dx=l . 0
(5)
The composition of the copolymer determined by means of the diffusiometer is the weight-average composition 1
~w=y f~,(z)xdx. 0
(6)
I f we choose a solvent with a refractive index n~ lying between n A and n B (the refractive indices of the component homopolymers) the differences between
Study of compositional inhomogeneity of graft copolymers
1385
the mean refractive indices of the high molecular weight (zlnl) and low molecular weight (An.,.) parts of the copolymer and the solvent will be given by the expressions
c
g
A =' =,'fL (x) [xv~,+(1-z>.ddx
Ji
0
(7)
"
Here vi, and vB, are the refractive index increments of the component homopolymers in solvent i and x i is the composition of the copolvmaer with n = n i. Let us now define the conditions for selection of a solvent to obtain the maximal possible eplitting of the a (r) curve during diffusion of a copolymer with compositional inhomogeneity. I t is obvious that the maximal possible splitting is obtained when the areas Q~ and O~ (Fig. 1) are equal, and consequently when A n , i = - - A n u (see squation (3)). By equating expressions (7) and (Ta), using the normalizing condition (5) and determining the weight-average composition (6), we obtain vc = ~,~VB, + ( 1 --.~,~) L~, = O, (8) i.e. the greatest possible splitting of the 5 (T) curve in diffusion of a copolymer with compositional inhomogeneity will be obtained in a solvent in which the refractive index increment of the topoi)tuner will be zero (this condition can be formulated in the form xi=~¢). I f the solvent is chosen so that the 5(~) curve is split f~(x) can be calculated quantitatively b y finding An i and An=. For this we write an analytical form of the function fw (x) based on the assumption that the distribution of the number of molecules with respect to grafted chains (f.v (iV)) is Gaussian (.v-.Vo)' (9) f.v(k')dh"~-----Ae
~' tiN,
where A is a constant, N the number of grafted chains, No the number-average number of grafted chains and a the dispersion of the quantity (N--2i 0)\/z. By introducing the variable y = N M ~ / M . ~ - = x / ( 1 - - x ) , changing to the weightaverage distribution function with respect to y and determining the constant from the normalizing condition we finally obtain ( y + l ) e .--7-,
,
(10)
where ¢ (yox/2/a) is the probability integral of Gauss and y o = N o M B / . M a . Since diffusional analysis of compositional inhomogeneity is effective in the region where x->1 (y--,~) (see formula (1)), and the compositional inhomogeneity
1386
A. ~.
C~K,~sov
et al.
of graft copolymers is usually small (a----1-10), equation (10) can with an error of 1-2% (when Yo/a~l'7) be rewritten in the form
fw(y)=
(y+l)e
- ~
(11)
G x / - ( y o ~'1- )
Substituting function (11) in the expressions for we obtain
xw, (Anl/c)~ and (Anjc)~ (12)
~ y0 ~
1 --:~
x/ (yoq_1) {7
\ c /¢
2x/~(yoq_l ) ff
Equations (12) to (14) form two systems of equations, namely (12)-(13) and (12)-(14), the solution of each of which permits two unknown parameters of the distribution function to be determined. EXPERIMENTAL
For experimental verification of the proposed method of determination of the compositional inhomogeneity of copolymers we studied four samples of PMMA-PS graft copolymers, having a unimodal M(x) distribution function as indicated by sedimentation data. The graft copolymer samples 242, 243, 215 and 216 were synthesized by a previously described method. The main characteristics of the homopolymers are given in Table 1. For selection of a solvent with a suitable refractive index for this study we made use of the dependence of the refractive index increment on temperature [8]. Figure 3 shows 5 (r) curves obtained for the diffusion of sample 243 (~w----0.898) in bromoform at different temperatures. It is seen that splitting of the 5 (v) curve occurs, indicating compositional inhomogeneity of graft copol~-mer 243. We present below the values of (~nl/c)~ and (~n2/c)¢ found from Q1 and Q2 (by means of equation (3)) at various temperatures in bromoform T e m p e r a t u r e , °C (~nl/c)~× 10 -4, c m * / g (~n~/c) t × 10 -4, c m * / g v~× 10 -4, c m ~ / g
30-3 15
24.3 13'6 - - 10.3 3.3
* vz is t h e t o t a l r e f r a c t i v e i n d e x i n c r e m e n t .
17'9 7.7 - - 17 --9.6
13.5 6 --24 --18
9.7 2.7 --27 --24
1387
Study of compositional inhomogeneity of graf~ copolymers TABLE 1. 5[.~IN CI~u%_RACTERISTICSOV PSISL-k (StArt,- c m ~ , ' ) .~_','o PS (SIDE CIL~'N COPOT,YXE~S 215, 216, 243 ~t-';D 242 D o x l0 v, em'-/sec
Copolymer
SoS
Ms~ "< 10 -3
6-2 21 Acetone Acetone 28.6 Benzene 9-2 Benzene 2.3 8.2 B u t y l acetate Butyl acetate i7 Benzene 3 i Benzene
PMSLk-215, 216 PS-215 PS-216 PMSLk-242, 243 PS-242 PS-243
216
G RAFT
3f~ ;.: 10 -~ 2
214"
l.Tt
290 360: 5+ 160+
* Calculatedfrom [*1]in toluene,using data from ref. [5] ([,;]=0.62 x 10~ cma/g) + Calculatedfrom Do iu benzene, using data from rcf. [6]. Calculatedfrom Do in chloroform(Do=2'J. y.10-7 crab/see),using data from ref. [71.
S u b s t i t u t i n g in (12)-(14) t h e r e f r a c t i v e i n d e x i n c r e m e n t s o f P S (:,s,) a n d P S I S I A (r~,), d e t e r m i n e d in b r o m o f o r m a t T i , also t h e v t d u e s o f (dnt/c).~ and (_Jr,_jc)i, a n d u s i n g for Yi t h e s o l u t i o n o f t h e e q u a t i o n
1 +y#
\
TY#
we obtain a total of eight solutions of equations T A B L E 2. V . k L U E S OF T H E
PA/~ASfETEP,
(13) a n d (14) ( T a b l e 2).
0", O B T A I N E D B Y S O L U T I O N
OF EQUATIONS (13) A.~D (14) (yo= 8-8) Values of a at ternperat.ure, °C Equation
(13) (14)
9.7
i
13.5
17.9
24.3
5 4.1
i
6 4
5.5 4.3
4.2 4.2
I
~Ve a l s o s t u d i e d t h e c o m p o s i t i o n a l i n h o m o g e n e i t y o f g r a f t c o p o l y m e r 242 ( x = 0 . 8 9 ) . F i g u r e 4 r e p r e s e n t s 5 (r) c u r v e s o b t a i n e d in t h e d i f f u s i o n o f t h i s e o p o l y m e r i n b r o m o f o r m a t v a r i o u s t e m p e r a t u r e s . I t is s e e n t h a t i n c o n t r a s t t o c o p o l y m e r 243 i n v e r s i o n o f t h e sig-n o f t h e r e f r a c t i v e i n d e x i n c r e m e n t o c c u r s w i t h o u t s p l i t t i n g o f t h e d (r) cmn,-e, i n d i c a t i n g t h a t c o p o l y m e r 242 is h o m o g e n e o u s in c o m p o s i t i o n ( a ~ 0 ) . T o v e r i f y t h e s e r e s u l t s e o p o l y m e r s 243 a n d 242 w e r e f r a c t i o -
1388
A.N.
C~E~tK.~SOV et al.
]
.
FIo. 3. d (~) clu:ves for difl\isio~l of graft copolymer 243 in bromoform (concentration .~o~) Temperature, °C: 1--30-3; 2--24.2; 3--17.9; 4--13.5; 5--9.7; time, hr: 1--33; 2--43; 3--30; 4--32; 5--40. -
o
Study of compositional inhomogeneky of ~zraftcopolymers
1389
na.teci b y precipk
~g
FIG. 4. 6 (:) curves for diit'usioll of graft copolyrner 242 in bromoform (concentration 2°o) Temperature, °C: 1 - - 3 2 ; 2--24; 3--17; time, hr: 1 - - 2 4 ; 2--30; 3 - - 3 2 ; Vc, cra~/g: 1--1"7× ×lO-S; ' 2 - - 1 × 1 0 - h 3--1.7 x 1 0 - <
copolymer 243 is shown by the difference of 540o in the compositions of the extreme fractions. Figure 5 shows the curve of the distribution of copolymer 243 with respect to composition, constructed from tile fractionation results. The theoretical curve, obtained from the formula dy
1
f~.(x) dx=f~,(y) dy=fw(y (z)) ~'x dx=A(1--x) ~ e
-
~'
dx
with the parameters y0=8.8 and a = 5 , is included in the same d i a ~ a m .
(16)
1390
A . N . C~ERKASOV et al.
I t is seen from Fig. 5 t h a t the diffusion m e t h o d o f analysis o f compositional in_homogeneity enables a reliable assessment o f t h e b r e a d t h o f the compositional distribution f u n c t i o n to be obtained, t a k i n g into a c c o u n t the a p p r o x i m a t e natttre o f its theoretical basis. The difference in shape between the theoretical
TABLE 3. 5L~ix CHARACTERISTICSOF GRAFTCOPOLY~A[ER243, -°49_, 216 A-~ T H ~ FRACTIONS Butyl acetate Copolymer
x PS
-Do× 107,
SoS
MSD
57
28 × 10~
ern2/sec 243 (unfraetionated) 243/I 243/II 243/III 243/IV 243/~J 242 (unfract ioIlated) 242/I 242/II 242/III 216 (unfraction-
0-32 0.375 0.45 0.75 surplus
0-12 0.5 0.25 0-1 0-03
0-8984-0.005 0-98 '-- 0.01 0'94 4-0.01 @87 4-0.01 0-66 _ 0.03 0-44 4-0.05
2.2 2.54 3-1
0.2 0.5 0-3
0"89 0"89 0"89 0'89
_+_0-005 '-- 0.005 ± 0-005 ± 0'005
1'1 2"1 3-2
0'5 0.7 1-2
0.57 0.36 0.07
0'93 0-96 0"93 0'88
'-- 0-01 --0"01 --0"01 ±0"005
1.2 1.92 2-2
ated) 216/I
216/II 216/III
0-23
M
0'9
17
2.4 x 10~
1"7
10-6
1 x 106
3 X 10e* 1 X 10~* 0'6 "< l0 s*
23 12-3 9
2-2 0'8 0"6
Re'marks. 7 is tile volumefractionof thc precipitant and w the weightfraction of the fraction. * Calculated from Do, using data from reL [9].
a n d experimental/~o(x) curves is e v i d e n t l y due to the arbitrariness of the assumption o f Gaussian distribution of t h e molecules with respect to the n u m b e r of grafted chains. As was s t a t e d above, in a s t u d y of t h e compositional i n h o m o g e n e i t y of a c o p o l y m c r b y the diffusion m e t h o d t h e m o s t i m p o r t a n t f a c t o r is the choice of a solvent with a suitable refractive index, sufficiently close to n o f the copol)nner. E v e r y c o p o l y m e r t h a t is i n h o m o g e n e o u s in composition can be characterized b y some m a x i m a l refractive index increment, ~_Vmax, t h e a t t a i n m e n t of which (by the choice of solvent,) causes splitting of the 5 (v) diffusion curve. ~-aturally the n a r r o w e r the compositional distribution function the lowec is the value of ±Vmax neceasary for detection o f compositional i n h o m o g e n e i t y o f the copolymer. W e u n d e r t o o k to characterize the compositional i n h o m o g e n e i t y of copolymers 215 a n d 216 b y m e a n s of the p a r a m e t e r ±~'max" F o r this purpose t h e main a t t e n t i o n was paid to selection of a solvent to give the lowest possible refractive index i n c r e m e n t o f the copolymer. This s t u d y o f c o p o l y m e r 216 was carried out b y
Study of compositional inhomogeneity of graft copolFTners
1391
varying the composition of a mixture of bromoform (BF) and tetrabromoethane (TBE). When the value of Vc=8× 10-dcm~/g was reached (with a solvent composition of BF : TBE 0.91 : 0.09) the subsequent ~election was made by varying the temperatln'e. Figure 6 (curve 1) shows the temperature dependence of the refractive index increment of ~ a f t copolymer 216 in this mixture of BF and TBE. 12
~,, /O?cmalg zl #
8
I
l 8
0
i
l
o
2
-2
3-6 L ~
0-#
"~'~>~L
0.8 F~o. 5
~'/" I
O~
I
1.0
S
21
23 77,°O
F1o. 6
Fro. 5. Comparison of the f~(x) curve for copolymer 243, constructed from fraetionation data (continuous curve) with the f~(x) curve calculation by equation (16) wkh yo=S'8 and ¢=5 (broken curve). FIG. 6. Temperature dependence of the refractive hldex increment of graft copolx~ner 216 in a BF-TBE mixture (0-91 : 0-09) (1) and of gTaft copolymer 215 in bromoform (2). Splitting of the 5 (v) curve in diffusion of copolymer 216 began at rmax= (6 ~ 3) × 10 -~ cm a/g (Fig. 7, curve 1). Since copols-mer 243 had Vm~x ~ 1"5 × 10-a em 3/g it is evident t h a t copol~aer 216 is considerably more homogeneous in composition. Copol)maer 216 was fractionated by precipitation by methanol from benzene-chlorobenzene (Table 3). It is seen from Table 4 t h a t copolymer 216 is in fact inhomogeneous in composition, but the difference in composition between tlle extreme fractions is only 8%. The compositional inhomogeneity of copolymer 215 (2w=0.91) was studied in bromoform. In this instance the selection of a solvent, in which the refractive index increment of the copol~mer was only (3--1.5)× 10-Scma'g did not give rise to splitting of the curve in the course of diffusion (Fig, 7, curve 2), showing t h a t this copolymer is homogeneous in composition. Let us now consider the relationship between compositional inhomogeneity and the molecular weight of the ~'afted PS*.* * Translator's note: PS * represents polystyrenelithkun (see ref. [4]), the grafting mechanism involving reaction between the latter and the ester groups of PM)L~.
1392
A . N . CgE~:.,sov et at..
Table 4 shows w h e t h e r or not the copolymers discussed in the p a p e r a n d in references [10] a n d [11] are i n h c m o g e n e o u s in composition." I t is seen t h a t the compositional i n h o m o g e n e i t y of the graft eopolymers increases as the l e n ~ h o f the P S * side eh~ins increascs. This explained b y the fact t h a t grafting to the PM3L-k chaizx is controlled by diffusion of the PS * molecules into the coil of the main chain. T.~BLE
4. CO.'k~OSITIO-N'A-L I.N'IIO3IOGEN"EITY
OF
P.-%I3L%-PS
G~T
COPOLYMERS
Sample
2:~,
215 242 5 [10] 216 1 [10] 230 [i1] 243
0-9 0.89 0.91 0.93 0-83 0-6 0.9
* ,t.:
3 I B x 10-s
Compositional inhomogeneity
ax, ?g PS
No
1 '7 5
0--0-5 0--2
,,
ll i7 25 100 150
,, Yes ,, ,, ,,
8 8
38 54
is the difference Ill COUlpositioll between tile ex.trellle fractions,
I f the P S * is of low molecular weight this m e c h a n i s m leads to m a x i m a l conversion of the ester ~ o u p s
(>c=o )
<
. . . . . <~_4~_::=;~o~ f
p-~
i
--t-2
~~° ~
and thus ~ v e s
~ _ ~~m ~ _~.~.
compositionally
_~o~ ~i ( V~ ~ - ~7~
Fro. 7. Curves for diffusion of gTaft copol.vmer 216 hi BF-TBE (0.91 : 0.09) a~ 21.3°; time-37 hr, 2=765 rolL, c=3'47o (1), and of graft eopolymer 215 in bromoform a~ 23.7°; time-40hr; ).=765m/z, c=9°o (2).
Study of compositioaal inhomogeneity of graft copolymers
1393
homogeneous graft copolymers. When the molecular weight (molecular size) of the ~S* is increased its diffusion into the P)[.~IA coils will be hindered, which results in a reduction in the average conversion of the ester groups, and a distribution of copolymer molecules with resl~ect to the number of grafted chains (i.e. to compositional inhomogeneity). Let us now consider some advantages and disadvantages of the proposed method. It must be borne in mind that it is based on a relationship between the compositional inhomogeneity and polydispersity of the copolymers and therefore cannot be applied to random copol)-mers, for which there is no such relationship. In the case of graft and block copolymers the relationship between x and ,If is greater in the region where x-->l (see equation (1)), so that the possibilities of the method increases as the component increases. Hence the method is more efficient in the case of copolymers with a higher proportion of grafted chains, i.e. in the region where the study of compositional inhomogeneity by light scattering is difficult. Another advantage of the proposed method is its applicability to the study of copolymers of low moleular weight, and also the possibility of studying the compositional inhomogeneity of copolymers containing low molecular weight impurities (adsorbed solvent, unreacted components etc). It has been sho~,m previously that diffusion analysis of such polymers easily permits account to be taken of error introduced by impurities to the values of 2n and c of the copoIymer. CONCLUSIONS
(1) The compositional inhomogeneity of graft copolymers of polymethylmethacrylate and polystyrene, with a unimodal distribution with respect to composition, has been studied by the diffusion method. (2) It is shown that for samples with a high proportion of grafted chains diffusion analysis permits the detection of very slight compositional i,~aomogeneity, and also enables the breadth of the compositional distribution function to be determined. (3) The compositional inhomogeneity of the graft copolymers is reIated to the molecular weight of the grafted PS*, increasing with increase in the latter. This is explained by the particular mechanism of the grafting reaction. Translated by E. O. Pmz_~.~s REFERENCES
1. S. I. KLENIN et al., Vysokoraol. soyed. Ag: 1435, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 7, 1604, 1967) 2. G. P. ~HKtI_4J~OV, L. L. BURSHTEIN et al., Vysokomol. soyed. A10: 556, 1965 (Translated in Polymer Sei. U.S.S.R. 10: 3, 647, 1968) 3. Y. N. TSVETKOV, Zh. eksp. i teor. fiz. 21: 701, 1951 4. S. P. MITSF_~NGENDLERet al., Vysokomol. soyed. 4: 1366, 1962 (Translated in Polymer Sci. U.S.S.R. 4: 3, 436, 1963)
1394
A.I.
SIDNEV et at.
S. CHINAI, I. M A T L A K et al., J. Polymer Sci. 17: 391, 1955 C. ROSSI, Proprietei e strutttLradi basspolimer, I t a l y , 1963 V. N. TSVETKOV and S. I. KLENL-~, Zh. tekh. fiz. 28: 1019, 1958 I. O'MARA and D. MeLNTYRE, J. Phys. Chem. 63: 1435, 1959 A. N. CHERKASOV et al., Vysokomol. soyed. A10: 1348, 1968 (Translated in Polymer Sci. U.S.S.R. 10: 6, 1563, 1968) 10. T. KADYROV, A. N. CHERKASOV et al., Vysokomol. soyed. A9: 2094, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 10, 2364, 1967) 11. T. KADYROV, Dissertation, 1968 5. 6. 7. 8. 9.
QUANTITATIVE DETERMINATION OF ALKOXY GROUPS IN POLYARYLALKOXYSILOXANES BY INFRARED SPECTROSCOPY* A. I. StD~EV, Yu. V. KHVASHOHEVSKAYAand A. iN'. P~AVED.~'IXOV L. Ya. K a r p o v PhysicochemieM I n s t i t u t e Ministry of Chemical I n d u s t r y (Received 31 J a n u a r y 1969)
IT wAS shown in reference [1] that thermal-oxidative degradation of polyphenyl butoxysiloxanes (PPBS) begins with oxidation of the butoxy group. Consequently for determination of the rate of degradation of PPBS and other polymers with alkoxy groups it is necessary to follow the fall in the content of alkoxy groups during the course of degradation. For this purpose it is usual to make use of very laborious chemical analysis [2, 3], which when applied to study of the kinetics of degradation would increase the volume of experimental work considerably. At the same time in some instances it is possible in the study of the degradation of polymers to follow the variation in the content of certain functional groups, either quantitatively or semiquantitatively, by infrared spectroscopy [4, 8]. For example, to determine ester carbonyl in an acrylonitrile-methyl methacrylate copolymer the authors of reference [9] made a direct comparison of the intensities of the absorption bands of appropriate groups, which to a first approximation are proportional to the content of the groups in question. For the copolymer cm
A~=lT33
ca
A~=~..,_3~
where cm and ca are the molar concentrations of the methyl methacrylate and acrylonitrile units and A is the absorption at the given wavelength. * V,vsokomol. soyed. A12: No. 6, 1233-1239, 1970.
A . N . CHE~SOV et al.
(2) I t WaS f o u n d t h a t in the region o f low c o n c e n t r a t i o n s of t h e resin solution (both of t h e original resin a n d its fractions) the a d s o r p t i o n is m o n o m o l e c u l a r , w i t h p l a n a r o r i e n t a t i o n of t h e p o l y e s t e r molecules. I n t h e h i g h c o n c e n t r a t i o n region a d s o r p t i o n increases u p to fivefold (for t h e higher fractions), a n d this is e x p l a i n e d b y the presence of a g ~ e g a t e s or b y a t t a c h m e n t of o n l y certain p a r t s of t h e molecules to t h e surface, t h e r e m a i n d e r being o r i e n t a t e d into t h e solution. Translated by E. O. P~r~IPS
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
13.
J. P. HELME, G. BOSSHARD and J. ROUZIER, J. Appl. Chem. 15: 103, 1965 R. WILSON and A. H. ROBSON, Official Digest 27: 111, 1955 A. R. H. TA~VN, J. Oil and Colour Chem. Assoc. 39: 223, 1956 R. A. BRETT, J. Oil and Colour Chem. Assoc. 41: 428, 1958 A. I. SEAVELL, J. Oil and Colour Chem. Assoc. 42: 319, 1959 Ye. P. SHCHIPANOVA, A. A. TRAPEZNIKOV and V. A. OGAREV, Kolloid. zh. 29: 872, 1967 Ye. P. BOGOMOLOVA, Dissertation, 1969 V. T. CROWL and M. A. MALATI, Disc. Faraday Soc. 42: 301, 1966 H. SCH~TTE, Plaste und Kautschuk 11: 248, 1964 J. E. LUCE and A. A. ROBERTSON, J. Polymer Sci. 51: 317, 1961 ~V. HELLER and T. L. PUGH, J. Polymer Sci. 47: 203, 1960 E. G. B O B A L E K , C. C. LEE and E. R. MOORE, Official Digest 447: 416, 1962 A. A. TRAPEZNIKOV and G. G. PETRZHIK, Kolloid. zh. 27: 453, 1965
STUDY OF THE CO~IPOSITIONAL INHOMOGENEITY OF GRAFT COPOLYMERS BY THE DIFFUSION METHOD* A. N. CHERK~SOV, S. I. K L E N n ~ and G. A. ANDREYEV-% Institute of Macromolecular Compounds, U.S.S.R. Academy of Sciences (Received 27 January 1969) WE ~r~VE p r e v i o u s l y p r o p o s e d a m e t h o d for d e t e r m i n i n g t h e compositional i n h o m o g e n e i t y of copolsuners b y m e a n s o f diffusion [1]. T h e m e t h o d p e r m i t s d e t e c t i o n of c o m p o s i t i o n a l h o m o g e n e i t y o f a c o p o l y m e r if it also involves i n h o m o g e n e i t y in .molecular weight. I n t h e general case t h e r e l a t i o n s h i p can be e x p r e s s e d by the equation
M=l11~lCl--x) * Vysokomol. soyed. AI2: No. 6, 1223-1232, 1970.
(1)
Study of compositional inhomogeneity of graft copolymers
1383
where M~ is the weight of the original homopolymer in the copols-mer molecule, x the weight fraction of the ~ a f t e d homopolymer and M the molecular weight of the copolymer of composition x. It was shown in references [1] and [2] that when the compositional inhomogeneity of a copolymer can be described by a bimodal x (M) distribution function it is possible by the proposed method to calculate the distribution function of the copolymer with respect to composition. In this paper we present a similar study of gTaft copolymers (polymethylmethacrylate (PMMA)-polystyrene (PS)), characterized by a unimodal M (x) distribution function. METHOD The study of diffusion and determination of the refractive index increment of the graft copol)~ner samples were carried out in a Tsvetkov diffusiometer [3]. The difference between the refractive index of the solution and solvent, z/n, was fotmd from the area, Q, under the (r) diffusion cu~-e. ~+~5 (r)=~-
dr,
(2)
2 where h is the length of the diffusion cell i n t h e direction of the light beam, )~the wavelength of the light, a the separation produced by the polarizer and d n / d r the refractive index gradient along the height of the cell, r. The value of 4 n was found from the formula ,dn = ).Q / h a .
(3)
The refractive index increment, v, was found from the initial slope of the dependence of z~n on the concentration of the solution, c. The composition of the copolymer was found from the refractive index increment of the copolymer, vc, and of its component homopolymers (vA and VB), assuming additi~dty of the increments VC - -
x
=
-
VA
-
(4)
YB--YA
The sedimentation constants were determined in a UTSA-5 analytical ultracentrifuge at concentrations of 0"02-0"050/o . THEORY
For analysis of the compositional inhomogeneity of the copolymers we made use of the separation of the molecules in the course of diffusion, with respect to molecular weight, and consequently also with respect to composition (taking equation (1) into account). Thus if the copolymer contains molecules differing sufficiently in their values of x (refractive index n) it is possible to choose a solvent with a suitable value of n such that the copolymer would as it were be divided into two parts; namely a high molecular weight part with a positive refractive index increment, h >0, and a low molecular weight part with a negative refrac-
1384
A.N.
CHE~KASOV et al.
tire index increment, v2<0. I f the coefficients of diffusion of these supposed parts differ sufficiently the screen of the diffusiometer will show a 6 (r) curve that is a combination of two curves with maxima on different sides (Fig. 1). Curve 1, which varies slowly with time, is due to the high molecular weight part of the copols-mer (maximum pointing upward), and curve 2, corresponding to the low n4
~
ni
fi
na
/
2
~,.,, FIG. 1
x
1
FIG. 2
FzG. 1. Diffusion curve (3) of a compositionally inhomogeneous copolymer, consisting of a curve of the high molecular weight fraction of the copolyraer (vl> 0) (1) and a curve of the low molecular weight fraction (v~<0) (2). FIG. 2. Weight-average compositional (refractive kndex) distribution function of a compositio~lally inhomogeneous copol~m~er(n.~and nB are the refractive indices of the component homopolymers). molecular weight part of the copolymel, varies more rapidly with time (maximum pointing downward). Splitting of the 5(r) curve of a copolymer in the course of diffusion thus indicates its compositional in_homogeneity. We shall characterize the compositional inhomogeneity of the copolymer by its weight-average compositional distribution function fw (x) (Fig. 2). Conventional normalization of such a function will take the form 1
j'fw(z)dx=l . 0
(5)
The composition of the copolymer determined by means of the diffusiometer is the weight-average composition 1
~w=y f~,(z)xdx. 0
(6)
I f we choose a solvent with a refractive index n~ lying between n A and n B (the refractive indices of the component homopolymers) the differences between
Study of compositional inhomogeneity of graft copolymers
1385
the mean refractive indices of the high molecular weight (zlnl) and low molecular weight (An.,.) parts of the copolymer and the solvent will be given by the expressions
c
g
A =' =,'fL (x) [xv~,+(1-z>.ddx
Ji
0
(7)
"
Here vi, and vB, are the refractive index increments of the component homopolymers in solvent i and x i is the composition of the copolvmaer with n = n i. Let us now define the conditions for selection of a solvent to obtain the maximal possible eplitting of the a (r) curve during diffusion of a copolymer with compositional inhomogeneity. I t is obvious that the maximal possible splitting is obtained when the areas Q~ and O~ (Fig. 1) are equal, and consequently when A n , i = - - A n u (see squation (3)). By equating expressions (7) and (Ta), using the normalizing condition (5) and determining the weight-average composition (6), we obtain vc = ~,~VB, + ( 1 --.~,~) L~, = O, (8) i.e. the greatest possible splitting of the 5 (T) curve in diffusion of a copolymer with compositional inhomogeneity will be obtained in a solvent in which the refractive index increment of the topoi)tuner will be zero (this condition can be formulated in the form xi=~¢). I f the solvent is chosen so that the 5(~) curve is split f~(x) can be calculated quantitatively b y finding An i and An=. For this we write an analytical form of the function fw (x) based on the assumption that the distribution of the number of molecules with respect to grafted chains (f.v (iV)) is Gaussian (.v-.Vo)' (9) f.v(k')dh"~-----Ae
~' tiN,
where A is a constant, N the number of grafted chains, No the number-average number of grafted chains and a the dispersion of the quantity (N--2i 0)\/z. By introducing the variable y = N M ~ / M . ~ - = x / ( 1 - - x ) , changing to the weightaverage distribution function with respect to y and determining the constant from the normalizing condition we finally obtain ( y + l ) e .--7-,
,
(10)
where ¢ (yox/2/a) is the probability integral of Gauss and y o = N o M B / . M a . Since diffusional analysis of compositional inhomogeneity is effective in the region where x->1 (y--,~) (see formula (1)), and the compositional inhomogeneity
1386
A. ~.
C~K,~sov
et al.
of graft copolymers is usually small (a----1-10), equation (10) can with an error of 1-2% (when Yo/a~l'7) be rewritten in the form
fw(y)=
(y+l)e
- ~
(11)
G x / - ( y o ~'1- )
Substituting function (11) in the expressions for we obtain
xw, (Anl/c)~ and (Anjc)~ (12)
~ y0 ~
1 --:~
x/ (yoq_1) {7
\ c /¢
2x/~(yoq_l ) ff
Equations (12) to (14) form two systems of equations, namely (12)-(13) and (12)-(14), the solution of each of which permits two unknown parameters of the distribution function to be determined. EXPERIMENTAL
For experimental verification of the proposed method of determination of the compositional inhomogeneity of copolymers we studied four samples of PMMA-PS graft copolymers, having a unimodal M(x) distribution function as indicated by sedimentation data. The graft copolymer samples 242, 243, 215 and 216 were synthesized by a previously described method. The main characteristics of the homopolymers are given in Table 1. For selection of a solvent with a suitable refractive index for this study we made use of the dependence of the refractive index increment on temperature [8]. Figure 3 shows 5 (r) curves obtained for the diffusion of sample 243 (~w----0.898) in bromoform at different temperatures. It is seen that splitting of the 5 (v) curve occurs, indicating compositional inhomogeneity of graft copol~-mer 243. We present below the values of (~nl/c)~ and (~n2/c)¢ found from Q1 and Q2 (by means of equation (3)) at various temperatures in bromoform T e m p e r a t u r e , °C (~nl/c)~× 10 -4, c m * / g (~n~/c) t × 10 -4, c m * / g v~× 10 -4, c m ~ / g
30-3 15
24.3 13'6 - - 10.3 3.3
* vz is t h e t o t a l r e f r a c t i v e i n d e x i n c r e m e n t .
17'9 7.7 - - 17 --9.6
13.5 6 --24 --18
9.7 2.7 --27 --24
1387
Study of compositional inhomogeneity of graf~ copolymers TABLE 1. 5[.~IN CI~u%_RACTERISTICSOV PSISL-k (StArt,- c m ~ , ' ) .~_','o PS (SIDE CIL~'N COPOT,YXE~S 215, 216, 243 ~t-';D 242 D o x l0 v, em'-/sec
Copolymer
SoS
Ms~ "< 10 -3
6-2 21 Acetone Acetone 28.6 Benzene 9-2 Benzene 2.3 8.2 B u t y l acetate Butyl acetate i7 Benzene 3 i Benzene
PMSLk-215, 216 PS-215 PS-216 PMSLk-242, 243 PS-242 PS-243
216
G RAFT
3f~ ;.: 10 -~ 2
214"
l.Tt
290 360: 5+ 160+
* Calculatedfrom [*1]in toluene,using data from ref. [5] ([,;]=0.62 x 10~ cma/g) + Calculatedfrom Do iu benzene, using data from rcf. [6]. Calculatedfrom Do in chloroform(Do=2'J. y.10-7 crab/see),using data from ref. [71.
S u b s t i t u t i n g in (12)-(14) t h e r e f r a c t i v e i n d e x i n c r e m e n t s o f P S (:,s,) a n d P S I S I A (r~,), d e t e r m i n e d in b r o m o f o r m a t T i , also t h e v t d u e s o f (dnt/c).~ and (_Jr,_jc)i, a n d u s i n g for Yi t h e s o l u t i o n o f t h e e q u a t i o n
1 +y#
\
TY#
we obtain a total of eight solutions of equations T A B L E 2. V . k L U E S OF T H E
PA/~ASfETEP,
(13) a n d (14) ( T a b l e 2).
0", O B T A I N E D B Y S O L U T I O N
OF EQUATIONS (13) A.~D (14) (yo= 8-8) Values of a at ternperat.ure, °C Equation
(13) (14)
9.7
i
13.5
17.9
24.3
5 4.1
i
6 4
5.5 4.3
4.2 4.2
I
~Ve a l s o s t u d i e d t h e c o m p o s i t i o n a l i n h o m o g e n e i t y o f g r a f t c o p o l y m e r 242 ( x = 0 . 8 9 ) . F i g u r e 4 r e p r e s e n t s 5 (r) c u r v e s o b t a i n e d in t h e d i f f u s i o n o f t h i s e o p o l y m e r i n b r o m o f o r m a t v a r i o u s t e m p e r a t u r e s . I t is s e e n t h a t i n c o n t r a s t t o c o p o l y m e r 243 i n v e r s i o n o f t h e sig-n o f t h e r e f r a c t i v e i n d e x i n c r e m e n t o c c u r s w i t h o u t s p l i t t i n g o f t h e d (r) cmn,-e, i n d i c a t i n g t h a t c o p o l y m e r 242 is h o m o g e n e o u s in c o m p o s i t i o n ( a ~ 0 ) . T o v e r i f y t h e s e r e s u l t s e o p o l y m e r s 243 a n d 242 w e r e f r a c t i o -
1388
A.N.
C~E~tK.~SOV et al.
]
.
FIo. 3. d (~) clu:ves for difl\isio~l of graft copolymer 243 in bromoform (concentration .~o~) Temperature, °C: 1--30-3; 2--24.2; 3--17.9; 4--13.5; 5--9.7; time, hr: 1--33; 2--43; 3--30; 4--32; 5--40. -
o
Study of compositional inhomogeneky of ~zraftcopolymers
1389
na.teci b y precipk
~g
FIG. 4. 6 (:) curves for diit'usioll of graft copolyrner 242 in bromoform (concentration 2°o) Temperature, °C: 1 - - 3 2 ; 2--24; 3--17; time, hr: 1 - - 2 4 ; 2--30; 3 - - 3 2 ; Vc, cra~/g: 1--1"7× ×lO-S; ' 2 - - 1 × 1 0 - h 3--1.7 x 1 0 - <
copolymer 243 is shown by the difference of 540o in the compositions of the extreme fractions. Figure 5 shows the curve of the distribution of copolymer 243 with respect to composition, constructed from tile fractionation results. The theoretical curve, obtained from the formula dy
1
f~.(x) dx=f~,(y) dy=fw(y (z)) ~'x dx=A(1--x) ~ e
-
~'
dx
with the parameters y0=8.8 and a = 5 , is included in the same d i a ~ a m .
(16)
1390
A . N . C~ERKASOV et al.
I t is seen from Fig. 5 t h a t the diffusion m e t h o d o f analysis o f compositional in_homogeneity enables a reliable assessment o f t h e b r e a d t h o f the compositional distribution f u n c t i o n to be obtained, t a k i n g into a c c o u n t the a p p r o x i m a t e natttre o f its theoretical basis. The difference in shape between the theoretical
TABLE 3. 5L~ix CHARACTERISTICSOF GRAFTCOPOLY~A[ER243, -°49_, 216 A-~ T H ~ FRACTIONS Butyl acetate Copolymer
x PS
-Do× 107,
SoS
MSD
57
28 × 10~
ern2/sec 243 (unfraetionated) 243/I 243/II 243/III 243/IV 243/~J 242 (unfract ioIlated) 242/I 242/II 242/III 216 (unfraction-
0-32 0.375 0.45 0.75 surplus
0-12 0.5 0.25 0-1 0-03
0-8984-0.005 0-98 '-- 0.01 0'94 4-0.01 @87 4-0.01 0-66 _ 0.03 0-44 4-0.05
2.2 2.54 3-1
0.2 0.5 0-3
0"89 0"89 0"89 0'89
_+_0-005 '-- 0.005 ± 0-005 ± 0'005
1'1 2"1 3-2
0'5 0.7 1-2
0.57 0.36 0.07
0'93 0-96 0"93 0'88
'-- 0-01 --0"01 --0"01 ±0"005
1.2 1.92 2-2
ated) 216/I
216/II 216/III
0-23
M
0'9
17
2.4 x 10~
1"7
10-6
1 x 106
3 X 10e* 1 X 10~* 0'6 "< l0 s*
23 12-3 9
2-2 0'8 0"6
Re'marks. 7 is tile volumefractionof thc precipitant and w the weightfraction of the fraction. * Calculated from Do, using data from reL [9].
a n d experimental/~o(x) curves is e v i d e n t l y due to the arbitrariness of the assumption o f Gaussian distribution of t h e molecules with respect to the n u m b e r of grafted chains. As was s t a t e d above, in a s t u d y of t h e compositional i n h o m o g e n e i t y of a c o p o l y m c r b y the diffusion m e t h o d t h e m o s t i m p o r t a n t f a c t o r is the choice of a solvent with a suitable refractive index, sufficiently close to n o f the copol)nner. E v e r y c o p o l y m e r t h a t is i n h o m o g e n e o u s in composition can be characterized b y some m a x i m a l refractive index increment, ~_Vmax, t h e a t t a i n m e n t of which (by the choice of solvent,) causes splitting of the 5 (v) diffusion curve. ~-aturally the n a r r o w e r the compositional distribution function the lowec is the value of ±Vmax neceasary for detection o f compositional i n h o m o g e n e i t y o f the copolymer. W e u n d e r t o o k to characterize the compositional i n h o m o g e n e i t y of copolymers 215 a n d 216 b y m e a n s of the p a r a m e t e r ±~'max" F o r this purpose t h e main a t t e n t i o n was paid to selection of a solvent to give the lowest possible refractive index i n c r e m e n t o f the copolymer. This s t u d y o f c o p o l y m e r 216 was carried out b y
Study of compositional inhomogeneity of graft copolFTners
1391
varying the composition of a mixture of bromoform (BF) and tetrabromoethane (TBE). When the value of Vc=8× 10-dcm~/g was reached (with a solvent composition of BF : TBE 0.91 : 0.09) the subsequent ~election was made by varying the temperatln'e. Figure 6 (curve 1) shows the temperature dependence of the refractive index increment of ~ a f t copolymer 216 in this mixture of BF and TBE. 12
~,, /O?cmalg zl #
8
I
l 8
0
i
l
o
2
-2
3-6 L ~
0-#
"~'~>~L
0.8 F~o. 5
~'/" I
O~
I
1.0
S
21
23 77,°O
F1o. 6
Fro. 5. Comparison of the f~(x) curve for copolymer 243, constructed from fraetionation data (continuous curve) with the f~(x) curve calculation by equation (16) wkh yo=S'8 and ¢=5 (broken curve). FIG. 6. Temperature dependence of the refractive hldex increment of graft copolx~ner 216 in a BF-TBE mixture (0-91 : 0-09) (1) and of gTaft copolymer 215 in bromoform (2). Splitting of the 5 (v) curve in diffusion of copolymer 216 began at rmax= (6 ~ 3) × 10 -~ cm a/g (Fig. 7, curve 1). Since copols-mer 243 had Vm~x ~ 1"5 × 10-a em 3/g it is evident t h a t copol~aer 216 is considerably more homogeneous in composition. Copol)maer 216 was fractionated by precipitation by methanol from benzene-chlorobenzene (Table 3). It is seen from Table 4 t h a t copolymer 216 is in fact inhomogeneous in composition, but the difference in composition between tlle extreme fractions is only 8%. The compositional inhomogeneity of copolymer 215 (2w=0.91) was studied in bromoform. In this instance the selection of a solvent, in which the refractive index increment of the copol~mer was only (3--1.5)× 10-Scma'g did not give rise to splitting of the curve in the course of diffusion (Fig, 7, curve 2), showing t h a t this copolymer is homogeneous in composition. Let us now consider the relationship between compositional inhomogeneity and the molecular weight of the ~'afted PS*.* * Translator's note: PS * represents polystyrenelithkun (see ref. [4]), the grafting mechanism involving reaction between the latter and the ester groups of PM)L~.
1392
A . N . CgE~:.,sov et at..
Table 4 shows w h e t h e r or not the copolymers discussed in the p a p e r a n d in references [10] a n d [11] are i n h c m o g e n e o u s in composition." I t is seen t h a t the compositional i n h o m o g e n e i t y of the graft eopolymers increases as the l e n ~ h o f the P S * side eh~ins increascs. This explained b y the fact t h a t grafting to the PM3L-k chaizx is controlled by diffusion of the PS * molecules into the coil of the main chain. T.~BLE
4. CO.'k~OSITIO-N'A-L I.N'IIO3IOGEN"EITY
OF
P.-%I3L%-PS
G~T
COPOLYMERS
Sample
2:~,
215 242 5 [10] 216 1 [10] 230 [i1] 243
0-9 0.89 0.91 0.93 0-83 0-6 0.9
* ,t.:
3 I B x 10-s
Compositional inhomogeneity
ax, ?g PS
No
1 '7 5
0--0-5 0--2
,,
ll i7 25 100 150
,, Yes ,, ,, ,,
8 8
38 54
is the difference Ill COUlpositioll between tile ex.trellle fractions,
I f the P S * is of low molecular weight this m e c h a n i s m leads to m a x i m a l conversion of the ester ~ o u p s
(>c=o )
<
. . . . . <~_4~_::=;~o~ f
p-~
i
--t-2
~~° ~
and thus ~ v e s
~ _ ~~m ~ _~.~.
compositionally
_~o~ ~i ( V~ ~ - ~7~
Fro. 7. Curves for diffusion of gTaft copol.vmer 216 hi BF-TBE (0.91 : 0.09) a~ 21.3°; time-37 hr, 2=765 rolL, c=3'47o (1), and of graft eopolymer 215 in bromoform a~ 23.7°; time-40hr; ).=765m/z, c=9°o (2).
Study of compositioaal inhomogeneity of graft copolymers
1393
homogeneous graft copolymers. When the molecular weight (molecular size) of the ~S* is increased its diffusion into the P)[.~IA coils will be hindered, which results in a reduction in the average conversion of the ester groups, and a distribution of copolymer molecules with resl~ect to the number of grafted chains (i.e. to compositional inhomogeneity). Let us now consider some advantages and disadvantages of the proposed method. It must be borne in mind that it is based on a relationship between the compositional inhomogeneity and polydispersity of the copolymers and therefore cannot be applied to random copol)-mers, for which there is no such relationship. In the case of graft and block copolymers the relationship between x and ,If is greater in the region where x-->l (see equation (1)), so that the possibilities of the method increases as the component increases. Hence the method is more efficient in the case of copolymers with a higher proportion of grafted chains, i.e. in the region where the study of compositional inhomogeneity by light scattering is difficult. Another advantage of the proposed method is its applicability to the study of copolymers of low moleular weight, and also the possibility of studying the compositional inhomogeneity of copolymers containing low molecular weight impurities (adsorbed solvent, unreacted components etc). It has been sho~,m previously that diffusion analysis of such polymers easily permits account to be taken of error introduced by impurities to the values of 2n and c of the copoIymer. CONCLUSIONS
(1) The compositional inhomogeneity of graft copolymers of polymethylmethacrylate and polystyrene, with a unimodal distribution with respect to composition, has been studied by the diffusion method. (2) It is shown that for samples with a high proportion of grafted chains diffusion analysis permits the detection of very slight compositional i,~aomogeneity, and also enables the breadth of the compositional distribution function to be determined. (3) The compositional inhomogeneity of the graft copolymers is reIated to the molecular weight of the grafted PS*, increasing with increase in the latter. This is explained by the particular mechanism of the grafting reaction. Translated by E. O. Pmz_~.~s REFERENCES
1. S. I. KLENIN et al., Vysokoraol. soyed. Ag: 1435, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 7, 1604, 1967) 2. G. P. ~HKtI_4J~OV, L. L. BURSHTEIN et al., Vysokomol. soyed. A10: 556, 1965 (Translated in Polymer Sei. U.S.S.R. 10: 3, 647, 1968) 3. Y. N. TSVETKOV, Zh. eksp. i teor. fiz. 21: 701, 1951 4. S. P. MITSF_~NGENDLERet al., Vysokomol. soyed. 4: 1366, 1962 (Translated in Polymer Sci. U.S.S.R. 4: 3, 436, 1963)
1394
A.I.
SIDNEV et at.
S. CHINAI, I. M A T L A K et al., J. Polymer Sci. 17: 391, 1955 C. ROSSI, Proprietei e strutttLradi basspolimer, I t a l y , 1963 V. N. TSVETKOV and S. I. KLENL-~, Zh. tekh. fiz. 28: 1019, 1958 I. O'MARA and D. MeLNTYRE, J. Phys. Chem. 63: 1435, 1959 A. N. CHERKASOV et al., Vysokomol. soyed. A10: 1348, 1968 (Translated in Polymer Sci. U.S.S.R. 10: 6, 1563, 1968) 10. T. KADYROV, A. N. CHERKASOV et al., Vysokomol. soyed. A9: 2094, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 10, 2364, 1967) 11. T. KADYROV, Dissertation, 1968 5. 6. 7. 8. 9.
QUANTITATIVE DETERMINATION OF ALKOXY GROUPS IN POLYARYLALKOXYSILOXANES BY INFRARED SPECTROSCOPY* A. I. StD~EV, Yu. V. KHVASHOHEVSKAYAand A. iN'. P~AVED.~'IXOV L. Ya. K a r p o v PhysicochemieM I n s t i t u t e Ministry of Chemical I n d u s t r y (Received 31 J a n u a r y 1969)
IT wAS shown in reference [1] that thermal-oxidative degradation of polyphenyl butoxysiloxanes (PPBS) begins with oxidation of the butoxy group. Consequently for determination of the rate of degradation of PPBS and other polymers with alkoxy groups it is necessary to follow the fall in the content of alkoxy groups during the course of degradation. For this purpose it is usual to make use of very laborious chemical analysis [2, 3], which when applied to study of the kinetics of degradation would increase the volume of experimental work considerably. At the same time in some instances it is possible in the study of the degradation of polymers to follow the variation in the content of certain functional groups, either quantitatively or semiquantitatively, by infrared spectroscopy [4, 8]. For example, to determine ester carbonyl in an acrylonitrile-methyl methacrylate copolymer the authors of reference [9] made a direct comparison of the intensities of the absorption bands of appropriate groups, which to a first approximation are proportional to the content of the groups in question. For the copolymer cm
A~=lT33
ca
A~=~..,_3~
where cm and ca are the molar concentrations of the methyl methacrylate and acrylonitrile units and A is the absorption at the given wavelength. * V,vsokomol. soyed. A12: No. 6, 1233-1239, 1970.