The light scattering and viscometry of polyvinyltriorganosilane solutions

THE LIGHT SCATTERING AND VISCOMETRY OF POLYVINYLTRIORGANOSH, ANE SOLUTIONS* F. F. KHODZH~EVAlqOV,N. S. NAMETKIN,S. G. DURGARYAI¢ and I. YE. 0HERNYAKOV A. V. Topchiev Institute of Petrochemical Synthesis, U.S.S.R. A c a d e m y of Sciences

(Received 10 ~qeptember1970) TH~ parameters of the M a r k - K u h n - H o u w i n k equation, 1.e. the relatiousinp between the intrinsic viscosity a n d molecular weight of polymers

[¢]=K.M a,

(1)

and the relative thermodynamic flexlblhty of the macromolecules are factors with a major bearing upon problems of determination of the physicochemical properties of high-molecular compounds. There is much to be gained b y determining K and a in several different solvents as it is thereby possible to measure -Mw of the fractions na the same solvent under optimum conditions, and then to determine the viscosity of the same fractious in each of the solvents used in the investigation. The thermodynamic flexibility of macromoleeules is usually determined from the dlmeusions of polymer coils in the unperturbed state [1, 2]. This is generally done b y measuring t h e root-mean-square inertia radius of the coils (R~)~ under ideal conditions in respect to the t e m p e r a t u r e or solvent, using the hght scattering m e t h o d with subsequent calculation of the root-mean-square distance between chain ends (h~)~. However, a t t e m p t s to select an ideal solvent sometimes meet with no success, or else an ideal solvent m a y perhaps be unsuitable for the light-scattering measurements, as, for instance, m the case of polyvlnyltriorganosilanes [3]. I n such cases (h~)~ or (hSo/21~)~=Km a y be determined b y using certain well-known methods of extrapolating the results o f the hydrodynamic and optical measurements carried out in good solvents. Methods of extrapolation have been proposed b y F l o r y [4] (method A), Stockmayer and F i x m a n [5] (method B) K u r a t a and Stockmayer [6] (method C) and several other authors [4].

EXPERIMENTAL I n an earlier investigation we determined K and a and the unperturbed coil dlmeuslons for the macromolecules of polyvinyltrimethylsflane (PVTS), winch is the first member of the polyvinyltriorganosilane series [3, 7]. The results given here are for polyvmyldlmethylphenylsilane (PPS), polyvmyldJmethylamylmlane (PAS) and polyvinyldimethylheptylsilane (PHS) investigated m a series of five solvents. The samples were all prepared b y anionic * Vysokomol. soyed. A14: No. 4, 920--927, 1972. 1022

Light scattering and viseometry of polyvinyltriorganosilane solutions

1023

polymerization, and the structural formulae of the polymers are as follows [8-11]:

I~S

PPS

1 CHs---~I--CHsI ~H3 J~ PAS

"--CHj--CH--

PHS ---CH2---CH--

CE.--S!--CE.] CHrSl,--CHs] C,H,~

The characteristics of the investigated samples were as follows: PPS ~/w=590 × l0 s, [~]--=0.68 dl/g in toluene at 25°; PAS ~ w = 4 2 0 × l0 s, [~1]=0.62 dl/g in cyclohexane at 25°; P H S 2~w=330× l0 s, [t/]=0.61 dl/g m cyclohexane at 25 °. The molecular weights ;of the samples and their fractions were measured b y the light-scattering method with a "Sofica" photogoniodiffusometer (made m France) at 25 °, using the green line of the mercury spectrum in cyclohexane. The refractive index increments were 0.087 (PTS), 0.142 (PPS), 0.070 (PAS) and 0.085 cmS/g (PHS). Benzene rendered free of dust by vacuum.distillation was used as the standard. The polymer solutions were purified b y filtration through Schott No. 5 glass filters (O5, pyrex, U.K.). The molecular weights were calculated b y Zmn,n doubleextrapolation with seattermg angles ranging from 150 to 30 ° for 5-7 concentratmns i~ every case. The viscosities of t~he samples and the frsctions were measured in the investigated solverLts using Ubbelohde viscometers (capillary diameter 0.1 ram); the lengths of the latter were varied so that outflow times of not less than 80-90 sec were obtainable. The preparative fractionation was carried out on a column with glass packing (globules 0.1 rnm in diameter) in gradients of solvent concentration (exponential gradient) and temperature. The temperature gradient was 1.5 deg/cm, and the rate of elution was varmd according to the stage of fractmnation witlnn the range 2-5 ml/min. The PTS fractionatmn cor~dltions were as described m [12]. The PPS fractionation was performed in a benzene-acetoee (solvent-precipitant) system, the volume fraction of acetone in the initial m lx~ure being the PAS and P H S were fractionated in a cyclohexane-absolute ethyl alcohol syste m (38% of alcohol in the initial mi~rture). Some detailed information regarding selection of the fractionation conditions and the process itself are given in [13]. The selection of the solvents for which the parameters of equation (1)and the unperturbed dimensions of the macromolecules were determined was based on the results of an investigation of the viscosity-temperature characteristics of PTS solutions [7, 14].

133.4%;

DISCUSSION OF RESULTS

T h e r e s u l t s o f t h e e x p e r i m e n t s a p p e a r in Figs. 1 - 4 a n d T a b l e s 1-3. T h e ~ a n d a v a l u e s f o r t h e P T S - s o l v e n t s y s t e m s w e r e t a k e n f r o m [3]. The value of a depends on the nature of the polymer and on the splvent q u a l i t y , b u t t h e s e p a r a t e c o n t r i b u t i o n s o f t h e o n e a n d t h e o t h e r c o u l d n o t be d e t e r m i n e d in [15, 16]. U n d e r n e a r - i d e a l c o n d i t i o n s e q u a t i o n (1) is w r i t t e n as [17, 18] I

(2)

I024

F.F.

KHODZHEVA~OV e¢ a/.

where

0=4.29 x 10, x (p is the effective length of a chain segment; M o is the molecular weight of the segment; ~ is the ratio of the radius of an equivalent solid sphere to the rotation radius of a polymer coil in solution).

a

/ogle.7

b

0

0.2

-0.2

0

o

-0.~

-0.6

-0.2

i

i

5

6

-O~ll

i

5

6

-0.81

1

x2 A3 ,z/ o5

-~6

'=

5

I

6

togM,,,

FzG. 1. Determination of the parameters of the Mark-Kuhn-Houwink equation in benzene (1), chlorobenzene (2), heptane (3), decahn (4) and cyclohexane (5) at 25° for PAS in the region of 90x 10a
Light scattering and viscometry of polyvinyltriorganosilane solutions

1025

Noteworthy are the relatively high a-values in the systems PTS-chlorobenzene PTS-decalin. I n these solvents the weight-average molecular weight Of the PTS samples m a y be determined directly, particularly as the molecular-Weight distribution for this polyvinyltriorganosilane has been ascertained [12]. i n the and

['rt] '/,'/M '~ ,,10~

I0

×_× I

I

5

I

0

8

I

I

z/

I

i

f2

gc%~M'/qr@~.~w'

M/[~],1o "5

[,1J/M",Io'

I

8

e

,.,|

....

g

ZOO

600

i~ll/Z

lOOO

FIO. 2. Extrapolation of the results of hydrodynarmc measurements for PAS using the~FloryFox-Shephgen method (a), the Kurata--Stockmayer method (b) and the Stockm~yer-Fixman method (e). Here and in Figs. 3, 4 the notation is the same as in Fig. 1. case of linear synthetic polymers there is no need at all to regard a-va~es of > 0 . 8 as indicative of the structural rigidity of the macromolecules. For instance, it is reported in [20] t h a t a = 0 . 9 2 was obtained for polyvinylchloride i n t e t r a hydrofuran. The K u r a t a - S t o c k m a y e r theory [6] fixes the upper limit for a-values TABLE 1. PA~.METFmS O~ T~E M A m ~ - K U K N - H o u w n ~ SILANES IN DIFFERENT

Solvent Benzene Chlorobenzene Cyclohexane Heptane Decahn

PAS

PTS K × 10 ~ I 4-60 0.007 0.16 0"26 0.024

EQUATION F O R P O L Y V I N I r L T R I O R G A N O

SOLVENTS

2"90 3"70 0-12 9"40

2"03

0"59 0"57 0"67 0"51 0"61

-

25°

PP$

PHS K × 10' I

K × lO s I 0-54 1"03 0.86 0.82 0"98

AT

4.84 4.60 2.93 2.52 2.84

K × 10' I 0.56 0.56 0.60 0.62 0.62

a

9.5 7.8 8.1

0.50 0.54 0.52

8.5

0-52

at around 1 in the case of coils t h a t are impermeable by the solvent. Similarly the theory of Debye and Bueche [21] predicts a value close to u n i t y for the upper limit o f a . I n view of this the a-values of > 0 . 8 obtained b y us for the P T S solvent systems m a y be attributed to the high thermodynamic quality iof the solvent (decalin). I n the case of chlorobenzene the magnitude of the polymer-

1026

F. F. K ~ o o z m ~ v ~ o v

s~ a/.

solvent interaction parameter is lower compared with decalin, and the viscosity is lower than in other good solvents [3, 7]. We may therefore assume that specific interactions take place between PTS and chlorobenzene and are capable of distorting the Gaussian type of distribution of the units in a maeromoleeular coil, e.g. by selective solvation of the PTS macromolecules by chlorobenzene [3]. This assumption was confirmed experimentally by means of the dynamic birefringence of PTS solutions in chlorobenzene [22]. The authors of [22] carried out measurements in different solvents and found a marked difference in the optical segmental anisotropy due to the existence of short-range orientational ordering in solution. Structuration of the solvent around the PTS macromolecules in chlorobenzene would therefore account for the relatively high a-value, and confirms the assumption made in [3] that specific interactions take place between PTS and chlorobenzene. [ ~] ~I3/M ~IJ,m 3

I0

~-x I

'

~

I

I

I

I

I

I

!

5 M/[~],m -5

S

[rl] IM'IZ'ms

3

5

g¢ez).M2/Vf~1,/s.m"J

c

~0 I

I

i

I

300

Io0

I

I

500 M I/z

FIG. 8. Extrapolation of the results of the hydrodynamic measurements for PES. The other polyvinyltriorganosilanes studied have a-values in the region of 0.5 to 0.7, which is characteristic of ordinary high-molecular carbochain compounds. Table 2 gives the results of extrapolation to the unperturbed dimensions, using the methods referred to above. The extrapolation curves for PTS were

9

.

J I

I

i

I

I

i

M/I,7] ~Io"~ o [~2]/,~z"o* o o e l

0

_

_

000

0

800

×_×----~-----×, 0

.

I

I

I

i

i

s

s

~

12

/5

~

x_×.-----x

0

"----'-"

~

g(~z)'M~/'/['7] 'h''°-3

X

1200 M lh

FXG. 4. Extrapolation of the results of the hydrodynamzc measurements for PPS.

Light scattering and viscometry of polyvinyltriorganosilane solutions

1027

taken from [3]; Figs. 2-4 show the extrapolation for the samples of PASi P H S and PPS, and Table 3 gives the parameters of the K u r a t a - S t o c k m a y e r equation [6] at 25 ° for all four samples. TABLE

2. P ) , R A M ~ , T E R S OF TJ~LI~ P O L Y M ~ R - S O L V E ~

UNPEB,'A'u'.~BED P O L ~ T R I O R G A _ , N T O S V F ,

IN~I?ER.A.CTIOI~', A.N'D DIM]~NSION8 OF T]~I~

A~TE M A C R O M O I ~ C U L E S AT

IN

DIFFE~NT

SOI~V~lgTS

25° Method

Polymer

Solvent

B K×

PTS

PPS

PAS

PHS

Cyelohexane Heptane Benzene Chlorobenzene Decalm Cyclohexane Benzene Chlorobenzene Decahn Cyclohexane Heptane Benzene Chlorobenzene Decalm Cyclohexane Heptane Benzene Chlorobenzene Decalin

IO n

450 560 650 320 320 590 650 610 600 620 730 640 640 640 67O 67O 66O 660 67O

I

] B× 10 ~7 I

1-740 1.120 0.070 0-685 1.480 0.011 0.0 0.056 0.028 0.430 0-0 0.210 0.210 0.310 0.650 0.340 0.280 0.280 0.530

c I A 1011 ] B× 10 s7 I K×lOn 420 560 650 220 220 580 650 590 590 680 720 680 675 680 69O 67O 67O 670 67O

1.550 0.970 0.090 0.640 1.360 0.032 0.0 0.077 0.034 0.190 0.0 0.054 0.040 0.160 0.500 0.320 0.230 0.160 0.510

650 580 690 620 620 650 710 650 650 650 650 650 650 65O 650

The data in Tables 1 and 2 show t h a t the slope of the ex%rapolation lines (the parameter B for polymer-solvent interaction) is a function of a. This is particularly evident in the case of PTS for which the values of exponent a exceed 0.8. Extrapolation according to method A is consequently impossible for PTS in cyclohexane, heptane, chlorobenzenc and decalin [3] as the intercepts of the extrapolation line cutting the ordinate axis are negative in these solvents. The highest a-values are obtained for PTS in chlorobenzene and decalin; accordingly, it is precisely in these two solvents t h a t we have the smallest unperturbed dimensions calcula¢~l in accordance with methods B and G (see Table 2, and [3]). I n benzene, where a is close to 0.5, practically identical values of K are obtained for all three methods of extrapolation. The low value of parameter B in benzene points to near-ideal conditions (see also Table 3). The value of K=650~< 10 -11 cm.mole°'Sg-°'5 obtained in benzene shows the marked flexibility of th~ PTS macromolecules in the absence of any intermolecular interactions. I n v i e ~ o f the results of extrapolation obtained for the PTS we conclude t h a t in general the

1028 T,riLE

F.F. 3. P A R A ~ r ~ T E R S

OF

K~ODz-~.v~_~OV e~ a/.

','n~ K U R A T A - S T O C W ~ A Y E R

ORGANOSILANE8

Polymer PTS

Solvent Cyclo~x~e

Heptane

Benzene

Chlorobenzene

Decalin

KOXx 10'

1.6

[q]o

0.030 0.040 0.050 0.060 0.070 0.060 0.090 0.107 0.121 0.127 0.134 0.140 0.143 0-146 0.149 0.199 4.4 0-253 0.294 0"350 0.386 0.393 0-417 0.440 8.7 i 0.393 i 0.500 i i 0.580 0.690 0.764 0.777 0.820 0.869 14"7 0.066 0.085 0.098 0.117 0-129 0.131 0-139 0.147 14-7 0.066 0.085 0.098 0.117 0.129 0.131

IN D I F F E R E N T

an g(~,) 1.71 1.78 1.84 1-93 2.00 2.18 2.32 2.32 2-41 2.41 2.47 2.49 2.47 2-52 2.50 1.41 1"44 1.54 1.59 1.64 1"64 1.65 1.67 0.99 0.99 1.00 1.00 1.01 1.01 1.01 1.01 1.55 1.62 1.66 1.83 1-87 1.88 1-93 1.97 1-93 2.07 2.14 2.31 2-39 2.40

1.32 1.32 1.32 1.34 1.36 1.37 1.38 1.3~ 1.41 1-41 1.42 1.43 1.42 1.44 1.43 1.22 1-2.~ 1.2e 1.28 1.28 1-28 1-30 1.30 0.98 0-98 1.00 1.0O 0.99 0.99 0.99 0.99 1-46 1.48 1.48 1.49 1.49 1.49 1.50 1.51 1.50 1-51 1.51 1.52 1.52 1.52

PolY-mer

PPS

PHS

EQUATION F O R

POLYVINYLTRI-

SOLV]~NT8 A T 25 °

Solvent

X 10'

Chlorobenzene

3.8

0.22 0.31 0-34 0-37

1.32 1.35 1.36 1.36

1.20 1.21 1.22 1.22

I)eealm

7.8

Cyclohexane

5.3

Benzene

7.8

0.44 0.63 0.71 0.76 0.16 0.21 0.34 0.39 0.50 0-68 0.24 0"31 0.51 0.57 0.74 0"97

1.081 1.11! 1.12 1.13 1.00 1-03 1.03 1.03 1.04 1.04 1.00 1"01 1.00 1-01 1.01 1.00

1.05 1.08 1.08 1.08 1.00 1.02 1.02 1.02 1.03 1.03 1.00 1.01 1.00 1.01 1.01 1.00

Chlorobenzene

6.1

Decalin

6.1

Cyclohexane

8.7

Heptane

8.7

0"18 0"24 0"40 0 "44 0"58 0"75 0"18 0"24 0"40 0"44 1,0"58 '0"75 :0.25 0-35 0.39 0.44 0.45 0.53 0.29 O.35 0 41 0-51 0.54

1.02 1.01 1.01 1.03 1.03 1.03 1.02 1.01 1.01 1.03 1.03 1.03 1.10 1.12 1.14 1.14 1.161 1-16 1.0~ 1.07

1"01 1"01 1"01 1 "02 1"02 1 "02 1"01 1"01 1"01 1"02 1"02 1 "02 1"06 1"07 1"09 1"09 1"09 1"09 1"03 1.04 1-05 1.06 1.05

1.Og 1.10 1.0g

Light scattering and viscometry of polyvinyltriorganosilane solutions

1029

TAB~ 3 (cont.) Polymer

PAS

Solvent

Cyclohexane

Heptane

Benzene

K0 X × 10'

[q]e

~w g C~,) Polymer

2.44 0-139 I 0.147 2.50 0.22 1.40 3.8 10.25 1.45 0.31 1.46 i0"32 1.47 0.34 1.48 10"37 1-49

1.53 1.54 1.23 1.24 1.24 1.24 1.2~ 1.2~

1.47 1.47 1.46 1.46

1-24 1.24 1.24 1.24

3.4

0.19 0.27 0.31 [0.33

3.8 i0.22

0.31 10.34 0.37

1.34 1.19 1-37 1.20 1"38 1.21 1"37 1.20

Solvent

Ko × [q]l ~w gi (~) × 104

Benzene

8.7

0-29 0.35 0-41 0"51 0"54

1-03 1.04 1-05 1"07 1.071

Chlorobenzene

8"7

0"29 0"35 0.41 0.51 0.54

1"03 1.01 1-03 1.01 1.04 11.03 1.05! 1.03 1.04 1.02

D~m

8"7 0"29 0-35 0~tl 0-51 0"54

1.10 1.10 1.14 1-1~ 1.19

1.02 11.02 i1.03 1.04 1.04

1.06 1.07 1.09 i1.10 1.11

dimensions of the unperturbed macromolecules diminish with increasing Values of a. There are corresponding changes in the intrinsic viscosity values under ~ conditions, and in the coefficient of the coil swelling according to the data in T~ble 3 where it is seen t h a t the swelling coefficient is close to u n i t y only in the case of benzene, while in the other solvents it varies from 1.4 to 2.5 according to the molecular weight of the fractions. Assuming t h a t the nature of the solvent is unable to influence the unpertUrbed dimensions of the macromolecule in the case of linear uncharged chains, an~ t h a t the differences in the K-values are due to the inadequacy of the extrapolation techniques in t h a t t h e y fail to take ~11 account of the effects of the excluded volume when a~0.8-0.9, we will take the average value of K according to the solvents. This gives a-values of (400~-40)× 10 -11 for PTS (method B), (~t20± 60) × 10 -11 (method C) and 650× 10 -11 cm.mole 0"5.g-0.5 (method A, in benzene) [3]. I f we then take the average for the three methods of extrapolation we obtain h(206/M)~=(510±80)× 10 -11 cm.mole 0.5.g-0.5. This value m a y be taken as the relative unperturbed dimensions of the PTS macromolecules. The value of a for the other polyvinyltriorganosflanes is not more t h a n 0.7. This is probably why the differences in K whether in respect to the extrapolation techniques or the solvents used in the experiments are a lot smaller t h a n in the case of PTS. The value of a for PPS varies within limits of 0.50-0.54 (benzene and c~lorobenzene); the maximum limits of variafion in K for this polyvinyltriorgan0silane

1030

F. F. KHODZ~mV~OV~ a/.

are 580 × 10-1i-690 × 10 - n cm.moleH.g -°'5 (method A, see Table 2). Parameter B for this sample is zero in benzene for all three extrapolation techniques, and K in the same solvent is close to (660±20) × 10 -11 cm.mole°'S.g-H. The average value of K according to the solvents is (610±10) x 10 - u (method B), (600±15) × 10 -il (method C) and (630-~20) x 10 -ll (method A) cm.mole°'~.g-°'~. The smaller average deviations compared with those for PTS are clearly due to the smaller differences between the values of exponent a and the relatively low levels of the a-values themselves. This is also borne out by the low values of the swelling coefficient a (see Table 3). The average value based on the extrapolation methods for PPS is (h~/M)*----(610±10)x 10 -11 cm.mole°'S.g-°'5. We will take this value as representing the relative unperturbed dimensions of the PPS macromolecules. Nearly-ideal conditions are obtained for PAS in heptane (B-----0)as is shown by the results of extrapolation to the unperturbed dimensions (Fig. 2, Table 2), and by the value of a = 0 . 5 (Table 1). The swelling coefficient a is close to unity in deealin, and varies within limits of 1.3-1.5 for the other solvents (Table 3). In benzene, chlorobenzene and decalin there is no difference between the unperturbed dimensions of the PAS macromolecules, which agrees with the inconsiderable variation in the value of a in these solvents (0.57-0.61). Averaging K for the solvents, and then taking the average for the different methods of extrapolation, we obtain the dimensions of the PAS macromolecules in the unperturbed state, i.e. (~/M)a= (670-{- 20) X 10 -ll cm'mole°'5"g-°'5. Finally small differences in the a-values appear for PHS also (0.56-0.62, Table 1). The use of the methods in question to determine the unperturbed dimensions of the PHS macromolecules results in only slight differences (Fig. 3, Table 2); the differences in the swelling coefficients are likewise only inconsiderable for the investigated solvents (see Table 3). The value of (h~/M)~ is (670± 10) × 10 -il cm.mole°'5.g -°'5. In view of the results of determining the unperturbed dimensions of the polyvinyltriorganosilane macromolecules we conclude that the relative thermodynamic flexibility in the series P T S - P P S - P A S - P H S in solution varies only inconsiderably for each sample with increase in the size of the side substituent at the Si atom. This likewise appears to be the case if we compare the unperturbed dimensions obtained by the three methods used in the experiments under ideal or nearly ideal conditions. CONCLUSIONS

(1) The parameters a and K of the relationship between intrinsic viscosity and molecular weight [t]]=KM a have been determined by the light scattering method and by viscometry for four samples of polyvinyltriorganosilanes (PVTOS) with differences in the chemical nature of the silicon atom, in a group of five solvents. (2) The unperturbed dimensions of the macromolecules of PVTOS have been

Light scattering and viseometry of polyvinyltriorganosilane solutions

1031

d e t e r m i n e d b y e x t r a p o l a t i o n of t h e results o f optical a n d h y d r o d y n a m i c m e a s urements. T h e relative t h e r m o d y n a m i c flexibility differs o n l y inconsiderably for P V T O S with different side substituents.

Tra1~slc~ed by R. J. A. H~.m)R~ REFERENCES 1. V. N. TSVETKOV, V. Ye. ESITIN and S. Y&. FRENKEL', Struktura makromolekul v rastvorakh (Structure of Macromolecules in Solutions). Izd. "Nauka", 1964 2. B. KI, (Ed.), Latest Methods of Polymer Research, (in Russian). Izd. "Mir"~ 1966 3. F. F. lgHODZHEVANOV, S. G. DURGAR'YAN and O. B. SEMENOV, Izv. AN SSSR, chem. series, 1090, 1969 4. P. FLORY and T. G. FOX, J. Amer. Chem. See. 78: 1904, 1951 5. W. H. STOCKMAYER and M. FIXMAN, J. Polymer SoL C1: 137, 1963 6. M. KURATA and W. H. STOCKMAYER, Fortschr. Hochpol. Forsch. 2: 196J 1963 7. F. F. KHODZHEVANOV, N. S. NAMETKIN, S. G. DURGAR'YAN and O. B. SEM]~OV, Izv. AN SSSR, chem. series, 283, 1970 8. A. V. TOPiTH~V, N. S. NAMETKIN, TSYU SYO PEI, S. G. DURGAR'YAN andiN. A. KUZ'MINA, U.S.S.R. Pat. 162531, 1962; Byull. izob., No. 10, 1964 9. N. S. NAMETKIN, V. S. KHOTIMSKII and S. G. DURGAR'YAN, Dokl. ANiSSSR 185: 97, 1969 10. N. S. NAMETKIN, V. S. KHOTIMSKII and S. G. DURGAR'YAN, Dokl. ANISSSR 166: 1118, 1966 i 11. N. S. NAMETKIN, S. G. DURGAR'YAN, V. I. KOPKOV and V. S. KHOT[M~KT[;! Dokl. AI~ SSSR 185: 366, 1969 12. F. F. K'HODZHEVANOV, O. V. SEMENOV, N. S. NAMETITIN and S. G. DURGAI~'YAN, Dokl. AN SSSR 186: 1336, 1969 13. F. F. wHODZI~rRVANOV,Thesis, 1970 14. F. F. ]RHODZHEVANOV, S. G. DURGAR'YAN and N. S. NAMETITIN, IV All~tYnion Conf. on the Chem. and Applications of Organosilicon Compounds, Chem. Research Inst., (NIITE~hlm), p. 138, 1968 15. P. FLORY, Principles of Polymer Chemistry, Ithaca, 1953 16. C. TENFORD, The Physical Chemistry of Polymers, 1965 17. S. Y&. FRENKEL', Introduction to the Statistical Theory of Polymerization (in RuSsian). 1965 18. J. G. KIRKWOOD and I. RISEMAN, J. Chem. Phys. 16: 565, 1948 19. D. W. Van KREVELEN and P. J. HOFTYZER, J. Appl. Polymer Scl. 10: 1331, 1966 20. H. BATZER and A. NISCH, Makromolek. Chem. 22: 131, 1957 21. P. DEBYE and A. M. BUECHE, J. Chem. Phys. 16: 573, 1948 22. S. A. AGRANOVA, S. Ya. FRENKEL' and I. Ye. CITF.RNYAKOV, Vysokomol. isoyed. A15: 2460, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 11, 2763, 1971) /