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Diffusion and sedimentation of poly-α-methylstyrene in cyclohexane
0032-3950181[092113-09807.50[9
Pol)3mer Science U.S.S.R. ¥oi. 23, ~o. 9, pp. 2113-2121, 1 9 8 1 Printed in Poland
© 1982 Pergamon Press Ltd.
DIFFUSION AND SEDIMENTATION OF POLY-~-METHYLSTYRENE IN CYCLOHEXANE* D. ~ .
LAVRENKO, A . A . :BOIKOV, L . N . ANDREYEVA, Y E . V. B E L Y A Y E V A
and A. F. 1)ODOL'SKII t I i g h P o l y m e r s I n s t i t u t e , U . S . S . R . A c a d e m y of Sciences
{Received 8 April 1980) T r a n s l a t i o n a l diffusion, s e d i m e n t a t i o n v e l o c i t y and viscosity of l l fraetiol~s of different p o l y d i s p e r s e d p o l y - ~ - m e t h y l s t y r e n e s were studied u n d e r 0 couditions. The d e p e n d e n c e of diffusion coefficients on c o n c e n t r a t i o n was found a n d t h e coefficients D o = l . 3 6 x 1 0 - S . M w °'5°, S 0 = l . 6 7 x 1 0 - ' ~ . M ~ 5° a n d [ t l ] = 7 . 2 X 1 0 - ' ~ . M w °'5°. satisfying t h e M a r k - K u h n - I - ~ o u w i n k e q u a t i o n , were d e t e r m i n e d . The e x p e r i m e n t a l v a l u e o f t h e T s v e t k o v - K l e n i n p a r a m e t e r was A 0 = 3 - 1 5 x 10 -1~ J . d e g - ' . m o ] e -}. F r o m the h y d r o d y n a m i c data, using t h e v a l u e s of Z i m m , ¢ = 2.51 x 102a and t ' ~ 5-9!} for t h e F l o r y coefficients, t h e l e n g t h of a K u h n segment, A=(20.3=}=0.5) x l0 - ' ° m. t h e chain d i a m e t e r , d = ( 6 ± l ) x 10 - ' ° m, and t h e f a c t o r of r o t a t i o n a l r e t a r d a t i o n in t h e chain, were o b t a i n e d .
T}{E development of a synthesis of practically monodispersed samples of poly~-methylstyrene (PMS) makes these polymers prospective model compounds for the experimental basis of various theoretical ideas. In this investigation, we studied translational diffusion, sedimentation velocity and viscosity of both nearly monodispersed and moderately polymolecular samples of PMS in cyclohexane at 0-temperature. A set of hydrodynamic data was used for qua~titativ(determination of the conformational characteristics of PMS macromo|ecules in solution. c~~deg
2
q
6 9,fO~sec -1
F~(;. 1. Dependence of orientation angle ~ on velocity gradient'for PMS solutions (fracti(~ ! l) m tetra,bromoethane; 1 -- solutions before centrifuging, c o n c e n t r a t i o n range 25.4-16.:} kg/m3; 2 -- solutions a f t e r c e n t r i f u g i n g for 1 h r ~t 200 s e e - ' , c o n c e n t r a t i o n range 18-8-13-4 k g / m L S t r a i g h t line t h r o u g h p o i n t ~ = 4 5 ° - - n o r m a l line for ratio ~(g) for m o l e c u l a r l y (]i~persed solutions. * V y s o k o m o l . soyed. A23: No. 9, 1937-1944, 1981. 2113
2114
P. i~. L A V R E N X O ~ UZ.
PMS samples were obtained b y anionic polymerization of the monomer in T H F at 195°K. The monomer in T H F had been purified over a liquid alloy of K + N a . Before charging the reaction ampoule, the T]~:F was additionally dried with triphenylmethylpotassium. Sodium naphthalene and the disodium tetramer of ~-methylstyrene ("living polymer") were used as catalysts. Sodium naphthalene was obtained b y reaction of sublimed naphthalene with a sodium mirror in TI-IF in a vacuum. The preparation of "living" polymer and the polymerization method were described in [1]. The determination of the stereoisomerism of samples is given in [2].
7 8
I 1
,,
2 Time t , fO-5, sec
~ G . 2. Dependence of curves of dispersion-diffusion for PMS in cyclohexane on time; 1 - 3 - - fraction 4 with M ~ = 9 5 0 × 108 (c=0.27 (•); 5.13 (2) a n d 10.79 kg/m 3 (3)); 4 - - 1 0 - - fraction 1 with Mw=2940X 103 (~=0-62 (4); 0.4 (5); 1.72 (6); 2.52 (7); 3.10 (8); 4.80 (9) and 6.20 kg/m 3 ( 1 0 ) ) . High molecular PMS samples were fractionated at 294°K b y fractional precipitation from benzene solution with acetone. For preparation of "narrow" fractions of low molecular PMS, "mild" precipitants such as 1 : 2 benzene-methanol mixtures were used. I n order to get rid of insoluble fractions of polymer before fractionation of the benzene/PMS solution, it was purified b y centrifuging at 200 sec -z for one hour. The molecular dispersivity of the solution was monitored b y the change of the angle of orientation of birefringence (Fig. 1) [3]. Cyelohexane, grade Kh.Teh., was used as the solvent for study of the hydrodynamic properties of PMS. Its viscosity at 305°K was ~0=0.80X10 -s kg/ms and its density, po= 767 kg/m s. We determined the 8 temperature, according to Flory, as the temperature of polymer precipitation at infinitely largo MM. The value obtained (8= 305°K) did n o t
Diffusion a n d s e d i m e n t a t i o n of p o l y - a - m e t h y l s t y r e n e in c y c l o h e x a n e
21 15
c o n t r a d i c t t h e p u b l i s h e d d a t a , a c c o r d i n g to w h i c h for P M S w i t h similar iso-, syndio- a n d h e t e r o - t r i a d c o n t e n t in cyclohexane, t h e t e m p e r a t u r e lies b e t w e e n 304 and 310°K [2, 4, 5]. W e p r e p a r e d t h e solutions, placing t h e b a t c h e s o f l y o p h i l i c a l l y d r i e d fractions in cycloh e x a n e a n d m a i n t a i n i n g t h e m at 318°K for 2-3 hr. T h e specific p a r t i a l v o l u m e ~ was det e r m i n e d in a p y k n o m e t e r in t h e case of two PMS samples. The m e a n v a l u e was v ~ 8 9 × 10 -5 ma/kg. T h e i n c r e m e n t of t h e r e f r a c t i v e i n d e x was m e a s u r e d on I T R - 2 i n t e r f e r o m e t e r at 2 ~ 546-1 n m (An/Ac) = 19 × 10 -5 m3/kg, as in reference [6]. TABLE 1.
PMS
I-IYDRODYNAMIC AND MOLECULAR MASS P R O P E R T I E S OF
[7] x 10 ~, mS/kg
Fraction 1~o.
X
1"
1 "20
2* 3*
1"15
,S O×
× 1013, see
Do × .d__nn× 10 2, MaD × ! Mw X × 1 0 -a [ × 1 0 -'~ x 10~L de m~/see m3/kg kgfl~mole
5* 6* 7* 8t
0"85 0"65 0"62 0"63 0"63 0"49
29.9 28"8 21-6 16"6 15"3 14.6 14"2 11.6
9t
0"66
9.5
>/1.40
0"15
10" 11"
0"28 0"24
5.4
3.40 3.70
0.18 0"18
4*
* (MdM~)
0"82 I 0.83 1"08 1"45 1"52 1.62 1-62 1-92
? 1.1 < ( M d M w ) < l ' 2 .
SAMPLES AND FRAC-
305°K
TXOI~S I1~ CYCLOHEXANE AT
0"20 0.16 0.17 0.19 0"19 0.16 0"13 0"20
2910 2770 1600 930 800 720 700 480 ~<600
AoS ×
t Ao° ×
×10x7
I ×10~7
J . deg-1 m o l e - l l a
2940 3280 1840 950 880 760 790 540
3.2 3.1 3.1 3.1 3.1 3.2 3.2 3.0
3'2 3.3 3.2 3.1 3.2 3-3 3.3 3.2
150 110
3-1 3-0
3.1 3.0
150 120 !
*Samples with blmodal MMD.
C h a r a c t e r i s t i c viscosities were m e a s u r e d in an O s t w a l d v i s c o m e t e r w i t h c a p i l l a r y of d i a m e t e r 3 × 10 -4 m and w i t h a m e a n g r a d i e n t of v e l o c i t y o f flow for c y e l o h e x a n e a t 305°K of 355 sec -1. T h e g r a d i e n t d e p e n d e n c e of v i s c o s i t y was n e g l i g i b l y small u n d e r t h e s e conditions [7]. T h e results were c a l c u l a t e d f r o m t h e e q u a t i o n esp/e=[e]+k'[e]2c, t h e m e a n v a l u e o f H u g g i n s ' c o n s t a n t b e i n g k'-~ 7.6 k g / m 3. TABLE
2. S E D I M E N T A T I O I ~ P R O P E R T I E S OF MONODISPERSED P M S II~ CYCLOHEXANE A T
Fraction, No. 1 4
10 11
C~.
S e × 10 zs,
kg/m 3
sec
1 "38 1.39 1'32 2'08
26.1 15.2 5.9 5.1
kS~
V - - 0 - 2 2 4 - 0"02
--0.17±0.02 --0'25i0.07 --0.18~0.04
SAbYPLES A_~D F R A C T I O N S
305°K
ma/kg 0.097 0.052 0.018 0.017"
m
0"33 0"29 0"48 0"33
a × 108, m.sec2/kg
1.8 1.2 1.9 1-6
tO, sec~
360i6 3724-6 420 :t: 30 678:~ 30
* Calculated from the expression k,--3-1 × 10a°.S..
W e s t u d i e d t r a n s l a t i o n a l diffusion in a p o l a r i z i n g d i f f u s o m e t e r [8], w i t h a glass t u b e , o f l e n g t h h = 0.030 m a l o n g t h e l i g h t p a t h a n d in a m e t a l t u b e w i t h a Teflon insert, of w i d t h h ~ 0 . 0 1 0 m . Q u a n t i t a t i v e results were n o t d e p e n d e n t on t h e t u b e t y p e used. T e m p e r a t u r e was m a i n t a i n e d w i t h i n 0-01°K. The l a y e r i n g c o n d i t i o n in t h e glass t u b e was such t h a t t h e h a l f w i d t h of t h e diffimional b o u n d a r y at t i m e t = 0 was, on a v e r a g e , 0.0012 ra. T h ~
P. N. LAVRENKO et aL
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d i f f u s i o n c u r v e s w e r e c a l c u l a t e d b y t h e m e t h o d o f a r e a s a n d m a x i m u m o r d i n a t e s [3]. T h e r e l a t i o n o f d i s p e r s i o n (A s) t o t i m e t is g i v e n i n Fig. 2. F r o m t h e a r e a s Q u n d e r t h e d i f f u s i o n c u r v e s i n c r e a s e d Kuv t i m e s , w e c a l c u l a t e d t h e i n c r e m e n t o f r e f r a c t i v e i n d e x f r o m t h e e q u a t i o n (Ah/Ac)D=Quv)./ho(bKuv)(aspKustKuv) ( T a b l e 1). H e r e t h e d o u b l i n g o f s p a r s is asp = 0 . 0 0 1 1 m , t h e d i s t a n c e b e t w e e n t h e b a n d s of t h e c o m p e n s a t o r b----0.00188 m , ~ = 5 4 6 . 1 n m , a n d t h e coefficient o f e n h a n c e m e n t o f t h e d i f f u s i o m e t e r gust---~ 1.01. T h e a v e r a g e v a l u e ( A n / A 0 ) D = 1 7 × 10 -5 m 3 / k g f r o m t h e f r a c t i o n s is l o w e r t h a n o b t a i n e d o n t h e I T R - 2 . T h i s f a c t ( n o t i c e d also i n [10]) m a y b e e x p l a i n e d b y p a r t i a l p r e c i p i t a t i o n o f p o l y m e r i n e x p e r i m e n t a l p r e p a r a t i o n a n d losses o f a r e a i n t h e " t a i l s " of t h e diffusion c u r v e . T h e r e f o r e i n s e d i m e n t a t i o n - d i f f u s i o n s t u d i e s , t h e s o l u t i o n c o n c e n t r a t i o n was c o n t r o l l e d a c c o r d i n g t o t h e h e i g h t of t h e i n t e g r a l c u r v e s , u s i n g An/ztc= 19 x 10 -5 ma/kg. Sedimentation velocity was studied using the "MOM-3170" analytical ultra centrifuge ( V e n g r y a ) a t a r o t a t i o n f r e q u e n c y o f n----666.7 sec -z (for f r a c t i o n 1, n = 5 8 3 . 3 ) i n a u n i - s e c t o r t u b e w i t h a 0.012 m t h i c k a l u m i n i u m t u b e a t 3 0 5 ± 0 " 2 ° K . I n t h e a r r a n g e m e n t o f t h e p o l a r i z i n g - i n t e r f e r o m e t r y a t t a c h m e n t , we u s e d p a i r s o f s p a r s w i t h a d i v i s i o n o f 54 X 10 -5 a n d 2 1 × 10 -5 m [11].
002 10
!n (:c/xo) 10 e, secZ
i/o° o~~
-
o
o
S : I0 la 8ec 28
E
2G
~2
]
3Q 2q0
2
q G Time, z~.I0-~ sec FIG, 3
04
0.3 (x/%)~z FIG. 4
FIG. 3. D e p e n d e n c e o f d i s p l a c e m e n t o f s e d i m e n t a t i o n b o u n d a r y x o n t i m e : 1 -- f r a c t i o n 1, c = 1 . 2 8 kg/m3; 2 -- f r a c t i o n 4, c = 3 - 1 2 kg/ma; 3 - - f r a c t i o n 10, c = 1.32 k g / m a. FIG. 4. E x t r a p o l a t i o n o f a p p a r e n t v a h m of s e d i m e n t a t i o n coefficient S ff t o t h e m e n i s c u s , a c c o r d i n g t o (12) for f r a c t i o n 1 ( c = 1 . 2 8 kg/ma), w i t h t0-----420 (1), 360 (2) a n d 324 sec (3). S e d i m e n t a t i o n coefficients S¢P w e r e c a l c u l a t e d a c c o r d i n g t o t h e slope o f t h e r a t i o of l o g x t o t (Fig. 3); for x t h e a b s c i s s a o f t h e m a x i m u m o f t h e c u r v e or (for a s y m m e t r i c distri-, b u t i o n s ) t h e a b s c i s s a o f t h e c e n t r e of g r a v i t y w a s u s e d : t is t h e t i m e r e c k o n e d f r o m t h e s t a r t o f r o t a t i o n . A c l e a r d i s t o r t i o n i n t h e s e r a t i o s t o t h e side o f t h e a b s c i s s a i n d i c a t e s t h e i n f l u e n c e of h y d r o s t a t i c p r e s s u r e p o n t h e v a l u e o f S, so t h a t t h e a p p a r e n t v a l u e of SP=S~ X
Diffusion and sedimentation of poly-a-methylstyrene in eyclohexane
2117
× (1--/~p). E x t r a p o l a t i o n of the slope of the ratio of log x to t to the meniscus x0, was eam'ied out by a known method [12]. The dependence of S ~ - - l n (x/xo)/co2(t--to), where t--to is the true sedimentation time, on (X/Xo)~--l, the linearity of which is attained by variation of to (Fig. 4), intercepts the ordinate S c, but its slope equals V=[lcs.c--m(1-}-ks'c)J/2(1-i-ks.c). F r o m the; latter equation, we calculated the constant parameter for the above PMS-cyclohexane system, /1----2m/o~pox~o where ~o= 2nn rad/sec and P0 is the density of cyclohexa~le at 100 k])a. On account of the dependence on concentration of S(c), the average valu( • ]k)r syrrmletrical and " n a r r o w " samples (Table 2), /~--~(1.6_+ 0.2) × 10 -8 msec2/kg agrees with literature data [13]. The concentration dependence of S(c) was studied for the first, fourth and t en t h fractions (Fig. 5). TJsing the equation 1/Sc----(1/So)(l~]c,c ) we calculated the values of the p a r a m e t e r k s (Table 2) from t h e slopes of the straight-line dependence of l/So on c. These appear to be linearly connected with [S] : k s ~ 12× 10 TM [S]----51 × 10-e'M~. ttere k, is in m*/kg; IS] -=Sotlo/1---vpo is in kg/m. This experimental relationship, which agTees with published d a t a [13314], was used to calculate S Ofor the remaining fractions and samples, correcting t h e value of So obtained at the final concentration. The mean experimental value ks/ /[~/]=0.87 indicates, within the framework of the theory [15], the m u t u a l permeability of t h e molecules and agrees q u a n t i t a t i v e l y with the sphere-cylindrical approximatiolJ of this theory. S -I'~10"I~,~eC'l
77; IG ---o---'----°''-'''-'°'-''''3
15 2
I
2
3 C, k q/m 2
Fro. 5. Dependence of magzdtude of S -1 on concentration for fractions 1 (1), 4 (2) and 10 (3~ of ])MS in cyclohexane at 30ii°K. We also studied the dependence of the diffusion coefficients D (c) on concentration, for the :first and fourth fractions. I f the concentration dependence of the coefficient of translational friction f(c) is the same in sedimentation and diffusion, then according to references [16, 17], the dependence of D(c) must be governed by the equation D ( c ) ~ D o × × (1--~c)(1-}-2A~Mc~- ...... )/(l~-ksc ) i.e. for ])MS in cyclohexane at 0 temperature, t h e relationship D(c)=Do(1--~.c)/(1-~ksc)~_Do/(1-~-ksc) m i g h t be expected (see theoretical curves 1-6 in Fig. 6). The experimental points of Fig. 6, within the limits of error, satisfactorily agree with the theoretical curves~ plotted for values of the p ar am et er k s obtained from the sedimentation measurements i.e. a decrease in the value of D with an increase in e in O conditions, observed for ])MC in cyclohexmle, is in agreement with pr~sevation of the dependence of S(c) for ])MS in this solvent, but the magnitude of the change of D
2118
P . N . LAv~xsxo e~ a/.
correlates with the change in solution viscosity, with increasing concentration. In the experimental values of D for the other fractions, corrections (not exceeding 7%) were m~de in D(c), according to the equation Do=D(l~-kae ) for corresponding values of the parameter /¢e" MM (molar) was calculated from Svedberg's equation MsD~(RT/1--'~po)(So]Do) and the mean weight value Mw from MMD of fractions, obtained from the sedimentation diagrams. The poly-dispersion of saznples and fractions is shown in Table 1. The hydrodynamic Tsvetkov-Klenin parameter [3] calculated from the equations
(A~D~o[~o]Mw/lO0)~/T and
A~=R[S] ([~/100M~) ¢
has mean values for samples and fractions of A----~3.1 × 10 -1~ and A ~ 3.2 × 10 -1T J . d e g -1. mole- t. •
8o~ 10 '3
Do'lo'~,,~/sec cvj.1o~, ,.~/kj
1"0
3
qo ~ 20 fO 5
1 3
I
5
10c,kq//mz FiG. 6
I
I
[ IIIlil
5 I0
J
I
Ilflll
50 IVw ~ lO-S
FiG. 7
Fro. 6. Dependence of diffusion coefficient D of PMS in cyclohexane at 305°K on solution concentration for fraction 1 (lower series of points) and 4 (upper points): light and dark points are data obtained in glass and metal tubes respectively: continuous curves -- theoretical ratios D(c)=Do/(1-.Fkzc ) constructed with ks=0.2 (1), 0.4 (2), 0.6 (3), 1-0 (4), 1.5 (3) and 2.0 × 10 -1 mS]kg (6) respectively. :FIG. 7. Logarithmic dependence of So (1), Do (2) and [~/] (3) on Mw for fractions and samples of PMS in eyclohexane at 305°K. F i g u r e 7 shows t h e d e p e n d e n c e o f [~/], So a n d Do on Mw on l o g a r i t h m i c scales. W i t h i n t h e limits o f error, t h e e x p e r i m e n t a l p o i n t s b o t h for p r a c t i c a l l y m o n o d i s p e r s e d a n d u n i f o r m l y p o l y d i s p e r s e d s a m p l e s ( a p a r t f r o m b i m o d a l ones) lie on t h e g e n e r a l curves described b y t h e M a r k - K u h n - H o u w i n k equations. [~/]-~ 7.2 × 10 .5 × M ~ 5° So~_ 1.67 × 10-z5 × M ~ s° D O----1"36 × 10 -s × M ~ °'s° T h e indices a=b~0.50 in t h e v i s c o s i t y a n d diffusion e q u a t i o n s confirms t h e r e a l i z a t i o n o f 8 conditions for P M S in c y c l o h e x a n e a t 305°K. T h e a b s e n c e
Diffusion and sedimentation of poly-a-methylstyrene in cyclolaexane
2119
of volume effects allow calculation of the length of a statistical K u h n segment of the equivalent chain, from the hydrodynamic data using the equations:
As=ML[(1--Vpo)/NArlo-PK°s]2=740 X 10-1°//) ~ AD = ML(kT/~IoPK~) 2= 710 × 10-l°/P 2 A,=ML(K°,/4)t=8.18 × 10s/4 j Here ML is the molecular mass of a unit length of PMS chain, equal to 47.25 × 1010/ /m, b is the Boltzmann constant, NA is Avogadro's number, _P and 4 are Flory constants, / ~ , -~D and /ffs are the coefficients for the M a r k - K u h n - H o u w i n k equations. The condition A I = A ~ is fulfilled with (4/100)*/P=2.29 × 106 which is different from the value (2.87× lO~a/lOO)~r/5× 1 1 = 2 " 7 8 × 1 0 e predicted from theory [18, 19] :in the case of the absence of volume effects and strong hydrodynamic interaction (non-flowing Gaussian balls) b u t is confirmed b y other work [13, 14, 20, 21]. In accordance with the latter, the mean value (4/100)*/P for PMS in cyclohexane at 0 temperature equals (2-29=]=0.10)× l0 s and for PS in the same solvent at 0 temperature (35°)--(2.234-0.11)×10 ~ i.e. likewise appreciably less than 2.78 × 10 e. The difference between experimental and theoretical values of ¢ and P is often ascribed to heterogeneity of samples. However, the small poly-dispersivity of PMS fractions, from which K~,/~D and K°~ were determined in our s t u d y (Mz/Mw <<.1-04) excludes the necessity of introducing a correction for heterogeneity i.e. even in the case of homogeneous polymers and in the absence of volume effects, the cited theories of viscosity and translational friction [18, 19] inadequately describe the properties of macromolecular solutions. The selection of absolute values of each of the 4 and P coefficients, necessary for calculation of A, cannot be accomplished from hydrodynamic data only. Direct (truly few) measurements of molecular sizes, as in polydispersed PMS in cyclohexane, b y the light diffusion method [6, 27] from which is obtained A v = 2 4 X 10 -1° m, give values of 4 = 2 × 10 ~a mole -1 and P ~ 5 . 5 [14, 22]. For PS in cyclohexane at 0 temperature, the mean (of 8 studies) value of 4 = (2.2=}=0.4)× x 10 *a mole -1 [23] agrees with theoretical values, obtained from the theory of viscosity of worm-like chains [24] for the limiting case of a non-flowing Gaussian coil and much smaller than 2.87 × 10 ~3, predicted from theory [18, 19]. For PS with Mw----6.5 × l0 s and Mz[Mw <~1"03 the value 4 = ( 2 . 5 5 4 - 0 . 1 ) × 1023 mole -1 was obtained [23] and for PS with Mw=(208--1010) × 10a and Mw/Mn=l.02-1"14 with a P value of 5-3 [10]. The experimentally determined values, 4 < 2 . 8 7 × 10 ea and / ) > 5 . 1 1 confirm the conclusions of reference [25] in which as a result of changes in a series of preneutralized hydrodynamic interactions between chain segments (as the number of segments N-~ ¢o) the limiting theoretical values 4 ~ = 2 - 5 1 X 102a and P ~ = 5 - 9 9 were obtained. Their ratio k(4~/lOO)~/P,~=3.16× 10 -17 agrees with the mean experimental value A0=(3.154-0.10)×10 -17 obtained in the present study.
2120
P . N . LAVRENKOetal.
S u b s t i t u t i n g these values of ~ a n d P ~ in t h e e q u a t i o n p r e s e n t e d above, we o b t a i n , for a s t r a i g h t K u h n s e g m e n t , t h e values A z = 2 0 . 6 X 1 0 -l°, AD~-19.SX X 10 -l° a n d A,----20.6X 10 -i° m. T h e m e a n v a l u e o f A is ( 2 0 . 3 + 0 . 5 ) X 10 -1° m. T h e possible d i v e r g e n c e of ~ a n d P values f r o m ¢b~ a n d P ~ owing to t h e finiteness of m a c r o m o l e c u l e l e n g t h s p r e d i c t e d b y t h e o r y [19] for h i g h m o l e c u l a r P M S fractions, a m o u n t s to several p e r c e n t a n d w a s t h e r e f o r e n o t considered. T h e n u m b e r of m o n o m e r u n i t s in a K u h n s e g m e n t is s=A/~=8.1: h e r e A----2-52 X 10 -l° m , t h e p r o j e c t i o n of l e n g t h o f a m o n o m e r u n i t on t h e m o l e c u l a r axis. T h e l e n g t h o f a K u h n s e g m e n t w i t h c o m p l e t e f r e e d o m of r o t a t i o n in t h e c h a i n a r o u n d t h e b o n d s of l e n g t h l = 1.54 X 10 -l° m joined t o g e t h e r a t a n angle 0 = 110 °, equals [26] A s v = ( 1 - - c o s 0). ( l ~ - c o s 0 ) . / / s i n ( 0 / 2 ) = 3 . 8 X 1 0 -1° m. Consequently, t h e f a c t o r a for r e t a r d a t i o n of r o t a t i o n a r o u n d t h e links o f t h e P M S chain, as o b t a i n e d f r o m h y d r o d y n a m i c d a t a , is a=(A/Asv)~=2.3, w h i c h is c h a r a c t e r i s t i c # f flexible c h a i n molecules in t h e v i n y l p o l y m e r series [3, 21]. W i t h t h e p r o p o r t i o n a l i t y So ~ M t a n d also t h e r a t i o In (A/d) = c o n s t . , t h e h y d r o d y n a m i c c h a i n d i a m e t e r for PMS, d = 7 . 1 X 10 -l° m for a const.-----1.056 [19] or d = 4 . 9 X 10 -i° m for a c o n s t . = 1.431 [18], m a y be e s t i m a t e d . T h e a u t h o r s t h a n k V. N. T s v e t k o v for v a l u a b l e c o m m e n t s .
Translated by C. W. CAPP REFERENCES 1. A. F. PODOLSKY, R. Ch. DASKIN and A. A. KOROTKOV, J. Polymer Sci. A - l , 9:
2259, 1971 2. V. Ye. ESKIN, T. N. NEKRASOVA, U. B. ZHURAYEV, A. F. PODOLSKII and A. A. TARAN, Vysokomol. soyed. A19: 525, 1977 (Translated in Polymer Sci. U.S.S.R. 19:
3, 602, 1977) 3. V. N. TSVETKOV, V. Ye. EKSIN and S. Ya. FRENKEL, Struktura makromolekul
v rastvorakh, p. 377, 418, 504, Nauka, 1964 4. J. M. G. COWIE and S. BYWATER, J. Polymer Sei. A-2; 6: 499, 1968
5. L. BISKUP and H. J. CANTOW, Prepr. IUPAC Intern. Symp. on Macromol., Helsinki 3: 47, 1972 6. P. F. MIJNLIEFF and D. J. COWMOU, J. Colloid Interf. Sci. 27: 553, 1968 7. I. NODA, K. MIZUTANI, T. KATO, T. FUJIMOTO and M. NAGASAWA, Macromolocubs 3: 787, 1970 8. V. N. TSVETKOV, Zh. eksp. teoret, fiziki 21: 701, 1951 9. P, N. LAVRENKO, O. V. OKATOVA and K. S. KHOKHLOV, Pribory i tekhnika eksperimenta 5: 208, 1977 10. J. M. G. COWIE and E. I. CUSSLER, J. Chem. Phys. 46: 4886, 1967 11. V. N. TSVETKOV, Vysokomol. soyed. 4: 1575, 1962 (Not translated in Polymer Sei. U.S.S.R.) 12. J. E. BLAIR and J. W. WITJT.IAMS, J. Phys. Chem. 68: 161, 1964 13. M. ABE, K. SAKATO, T. KAGEYAMA, M. FIrKATSU and M. KURATA, Bull. Chem~ Soe. Japan 41: 2330, 1968 14. J. NODA, K. MIZUTHANI and T. KATO, Macromolecules 19: 618, 1977 15. C. W. PYUN and M. FIXMAN, J. Chem. Phys. 41: 937, 1964 16. H. YAMA, Modern Theory of Polymer Solutions, p. 262, Harper and R o w Publ., :New York, San Francisco, London, 1971
Secondary structuring during polymerization of vinyl chloride
2121
17. It. SIMHA, In: High Polymer Physics (edited b y It. A. l~obinson) p. 398, Chem. l~lbl., N.Y., 1948 18. J. HEARST a n d W. STOCKMAYER, J. Chem. Phys. 37: 1425, 1962; J. HEARST, J. Chem. Phys. 37: 2547, 1962 19. H. Y A M A K A W A and M. FUJII, Macromolecules 6: 407, 1973; 7: 128, 1974 20. A. ]KOTERA, T. SATO and T. HAMADE, Polymer J. 3: 421, 1972 21. J. BRANDRUP and E. H. IMMERGUT, Polymer Handbook, 2nd edn., p a r t IV, pp. 16, 17, 41, Willey, 1975 22. T. I(ATO, K. MIYASO, L. NODA, T. FUJIMOTO and M. NAGASAWA, Macromolecules 3: 777, 1970 23. Y. MIYAKI, Y. EINAGA, M. F U J I T A and M. FUKUDA, Macromolecules 13: 588, 1980 24. J. E. HEARST, J. Chem. Phys. 40: 1506, 1964 25. B. H. ZIMM, Macromolecules 13: 592, 1980 26. H. BENOIT, J. chmi. phys et phys. chim. biol. 44: 18, 1947
:Polymer Science U.S.S.R. Vo]. 23, 1%. 9, pp. 2121-2127, 198]. Printed in Poland
0032-3950/81/092121-07507.50/~ © 1982 Perga~aon Press Ltd.
SECONDARY STRUCTURING DURING THE POLYMERIZATION OF VINYL CHLORIDE* A. V. NErMARK a n d L . I. KHErFETS V. A. Kargin Research I n s t i t u t e for tlle Chemistry and Technology of Polymers
(Received 9 April 1980) An analysis of the genesis of porous structures formed during the polymerization of vinyl chloride has been carried out, based on a model of randomly dispersed spheres, the radius of which is increased with time. Equations were derived for n~ean macropore radius, specific surface and porosity, in relation to the degree of monomer conversion. The results m a y be used for the descriptioll of other similar processes. IN t h e p r e s e n t r e p o r t , b u l k o r s u s p e n s i o n p r o c e s s e s f o r p o l y m e r i z a t i o n o f v i n y l chloride are examined. I n t h e l o w c o n v e r s i o n r a n g e s ( u p t o 10°//o) t h e p o l y m e r i z a t e r e s e m b l e d l i q u i d monomer, in which a finely dispersed polymer phase was beginning to develop. T h e p a r t i c l e g l o b u l e c o n c e n t r a t i o n in t h i s p h a s e d e p e n d s o n t h e o r i g i n a l r a t e o f i n i t i a t i o n a n d b e c o m e s s t a b i l i z e d a t ~ 1 % c o n v e r s i o n , r e a c h i n g a v a l u e o f 5 × 10 l ° - 5 × 1011 p a r t i c l e s / c m a o f p o l y m e r i z a t e . T h e i n n e r s t r u c t u r e o f t h e g l o b u l e ( t h e s o - c a l l e d p r i m a r y s t r u c t u r e ) is a l s o d e f i n i t e l y f o r m e d a t a c o n v e r s i o n o f a b o u t
1% [1] * Vysokomol. soyed. A23: No. 9, 1945-1950, 1981.
Pol)3mer Science U.S.S.R. ¥oi. 23, ~o. 9, pp. 2113-2121, 1 9 8 1 Printed in Poland
© 1982 Pergamon Press Ltd.
DIFFUSION AND SEDIMENTATION OF POLY-~-METHYLSTYRENE IN CYCLOHEXANE* D. ~ .
LAVRENKO, A . A . :BOIKOV, L . N . ANDREYEVA, Y E . V. B E L Y A Y E V A
and A. F. 1)ODOL'SKII t I i g h P o l y m e r s I n s t i t u t e , U . S . S . R . A c a d e m y of Sciences
{Received 8 April 1980) T r a n s l a t i o n a l diffusion, s e d i m e n t a t i o n v e l o c i t y and viscosity of l l fraetiol~s of different p o l y d i s p e r s e d p o l y - ~ - m e t h y l s t y r e n e s were studied u n d e r 0 couditions. The d e p e n d e n c e of diffusion coefficients on c o n c e n t r a t i o n was found a n d t h e coefficients D o = l . 3 6 x 1 0 - S . M w °'5°, S 0 = l . 6 7 x 1 0 - ' ~ . M ~ 5° a n d [ t l ] = 7 . 2 X 1 0 - ' ~ . M w °'5°. satisfying t h e M a r k - K u h n - I - ~ o u w i n k e q u a t i o n , were d e t e r m i n e d . The e x p e r i m e n t a l v a l u e o f t h e T s v e t k o v - K l e n i n p a r a m e t e r was A 0 = 3 - 1 5 x 10 -1~ J . d e g - ' . m o ] e -}. F r o m the h y d r o d y n a m i c data, using t h e v a l u e s of Z i m m , ¢ = 2.51 x 102a and t ' ~ 5-9!} for t h e F l o r y coefficients, t h e l e n g t h of a K u h n segment, A=(20.3=}=0.5) x l0 - ' ° m. t h e chain d i a m e t e r , d = ( 6 ± l ) x 10 - ' ° m, and t h e f a c t o r of r o t a t i o n a l r e t a r d a t i o n in t h e chain, were o b t a i n e d .
T}{E development of a synthesis of practically monodispersed samples of poly~-methylstyrene (PMS) makes these polymers prospective model compounds for the experimental basis of various theoretical ideas. In this investigation, we studied translational diffusion, sedimentation velocity and viscosity of both nearly monodispersed and moderately polymolecular samples of PMS in cyclohexane at 0-temperature. A set of hydrodynamic data was used for qua~titativ(determination of the conformational characteristics of PMS macromo|ecules in solution. c~~deg
2
q
6 9,fO~sec -1
F~(;. 1. Dependence of orientation angle ~ on velocity gradient'for PMS solutions (fracti(~ ! l) m tetra,bromoethane; 1 -- solutions before centrifuging, c o n c e n t r a t i o n range 25.4-16.:} kg/m3; 2 -- solutions a f t e r c e n t r i f u g i n g for 1 h r ~t 200 s e e - ' , c o n c e n t r a t i o n range 18-8-13-4 k g / m L S t r a i g h t line t h r o u g h p o i n t ~ = 4 5 ° - - n o r m a l line for ratio ~(g) for m o l e c u l a r l y (]i~persed solutions. * V y s o k o m o l . soyed. A23: No. 9, 1937-1944, 1981. 2113
2114
P. i~. L A V R E N X O ~ UZ.
PMS samples were obtained b y anionic polymerization of the monomer in T H F at 195°K. The monomer in T H F had been purified over a liquid alloy of K + N a . Before charging the reaction ampoule, the T]~:F was additionally dried with triphenylmethylpotassium. Sodium naphthalene and the disodium tetramer of ~-methylstyrene ("living polymer") were used as catalysts. Sodium naphthalene was obtained b y reaction of sublimed naphthalene with a sodium mirror in TI-IF in a vacuum. The preparation of "living" polymer and the polymerization method were described in [1]. The determination of the stereoisomerism of samples is given in [2].
7 8
I 1
,,
2 Time t , fO-5, sec
~ G . 2. Dependence of curves of dispersion-diffusion for PMS in cyclohexane on time; 1 - 3 - - fraction 4 with M ~ = 9 5 0 × 108 (c=0.27 (•); 5.13 (2) a n d 10.79 kg/m 3 (3)); 4 - - 1 0 - - fraction 1 with Mw=2940X 103 (~=0-62 (4); 0.4 (5); 1.72 (6); 2.52 (7); 3.10 (8); 4.80 (9) and 6.20 kg/m 3 ( 1 0 ) ) . High molecular PMS samples were fractionated at 294°K b y fractional precipitation from benzene solution with acetone. For preparation of "narrow" fractions of low molecular PMS, "mild" precipitants such as 1 : 2 benzene-methanol mixtures were used. I n order to get rid of insoluble fractions of polymer before fractionation of the benzene/PMS solution, it was purified b y centrifuging at 200 sec -z for one hour. The molecular dispersivity of the solution was monitored b y the change of the angle of orientation of birefringence (Fig. 1) [3]. Cyelohexane, grade Kh.Teh., was used as the solvent for study of the hydrodynamic properties of PMS. Its viscosity at 305°K was ~0=0.80X10 -s kg/ms and its density, po= 767 kg/m s. We determined the 8 temperature, according to Flory, as the temperature of polymer precipitation at infinitely largo MM. The value obtained (8= 305°K) did n o t
Diffusion a n d s e d i m e n t a t i o n of p o l y - a - m e t h y l s t y r e n e in c y c l o h e x a n e
21 15
c o n t r a d i c t t h e p u b l i s h e d d a t a , a c c o r d i n g to w h i c h for P M S w i t h similar iso-, syndio- a n d h e t e r o - t r i a d c o n t e n t in cyclohexane, t h e t e m p e r a t u r e lies b e t w e e n 304 and 310°K [2, 4, 5]. W e p r e p a r e d t h e solutions, placing t h e b a t c h e s o f l y o p h i l i c a l l y d r i e d fractions in cycloh e x a n e a n d m a i n t a i n i n g t h e m at 318°K for 2-3 hr. T h e specific p a r t i a l v o l u m e ~ was det e r m i n e d in a p y k n o m e t e r in t h e case of two PMS samples. The m e a n v a l u e was v ~ 8 9 × 10 -5 ma/kg. T h e i n c r e m e n t of t h e r e f r a c t i v e i n d e x was m e a s u r e d on I T R - 2 i n t e r f e r o m e t e r at 2 ~ 546-1 n m (An/Ac) = 19 × 10 -5 m3/kg, as in reference [6]. TABLE 1.
PMS
I-IYDRODYNAMIC AND MOLECULAR MASS P R O P E R T I E S OF
[7] x 10 ~, mS/kg
Fraction 1~o.
X
1"
1 "20
2* 3*
1"15
,S O×
× 1013, see
Do × .d__nn× 10 2, MaD × ! Mw X × 1 0 -a [ × 1 0 -'~ x 10~L de m~/see m3/kg kgfl~mole
5* 6* 7* 8t
0"85 0"65 0"62 0"63 0"63 0"49
29.9 28"8 21-6 16"6 15"3 14.6 14"2 11.6
9t
0"66
9.5
>/1.40
0"15
10" 11"
0"28 0"24
5.4
3.40 3.70
0.18 0"18
4*
* (MdM~)
0"82 I 0.83 1"08 1"45 1"52 1.62 1-62 1-92
? 1.1 < ( M d M w ) < l ' 2 .
SAMPLES AND FRAC-
305°K
TXOI~S I1~ CYCLOHEXANE AT
0"20 0.16 0.17 0.19 0"19 0.16 0"13 0"20
2910 2770 1600 930 800 720 700 480 ~<600
AoS ×
t Ao° ×
×10x7
I ×10~7
J . deg-1 m o l e - l l a
2940 3280 1840 950 880 760 790 540
3.2 3.1 3.1 3.1 3.1 3.2 3.2 3.0
3'2 3.3 3.2 3.1 3.2 3-3 3.3 3.2
150 110
3-1 3-0
3.1 3.0
150 120 !
*Samples with blmodal MMD.
C h a r a c t e r i s t i c viscosities were m e a s u r e d in an O s t w a l d v i s c o m e t e r w i t h c a p i l l a r y of d i a m e t e r 3 × 10 -4 m and w i t h a m e a n g r a d i e n t of v e l o c i t y o f flow for c y e l o h e x a n e a t 305°K of 355 sec -1. T h e g r a d i e n t d e p e n d e n c e of v i s c o s i t y was n e g l i g i b l y small u n d e r t h e s e conditions [7]. T h e results were c a l c u l a t e d f r o m t h e e q u a t i o n esp/e=[e]+k'[e]2c, t h e m e a n v a l u e o f H u g g i n s ' c o n s t a n t b e i n g k'-~ 7.6 k g / m 3. TABLE
2. S E D I M E N T A T I O I ~ P R O P E R T I E S OF MONODISPERSED P M S II~ CYCLOHEXANE A T
Fraction, No. 1 4
10 11
C~.
S e × 10 zs,
kg/m 3
sec
1 "38 1.39 1'32 2'08
26.1 15.2 5.9 5.1
kS~
V - - 0 - 2 2 4 - 0"02
--0.17±0.02 --0'25i0.07 --0.18~0.04
SAbYPLES A_~D F R A C T I O N S
305°K
ma/kg 0.097 0.052 0.018 0.017"
m
0"33 0"29 0"48 0"33
a × 108, m.sec2/kg
1.8 1.2 1.9 1-6
tO, sec~
360i6 3724-6 420 :t: 30 678:~ 30
* Calculated from the expression k,--3-1 × 10a°.S..
W e s t u d i e d t r a n s l a t i o n a l diffusion in a p o l a r i z i n g d i f f u s o m e t e r [8], w i t h a glass t u b e , o f l e n g t h h = 0.030 m a l o n g t h e l i g h t p a t h a n d in a m e t a l t u b e w i t h a Teflon insert, of w i d t h h ~ 0 . 0 1 0 m . Q u a n t i t a t i v e results were n o t d e p e n d e n t on t h e t u b e t y p e used. T e m p e r a t u r e was m a i n t a i n e d w i t h i n 0-01°K. The l a y e r i n g c o n d i t i o n in t h e glass t u b e was such t h a t t h e h a l f w i d t h of t h e diffimional b o u n d a r y at t i m e t = 0 was, on a v e r a g e , 0.0012 ra. T h ~
P. N. LAVRENKO et aL
2116
d i f f u s i o n c u r v e s w e r e c a l c u l a t e d b y t h e m e t h o d o f a r e a s a n d m a x i m u m o r d i n a t e s [3]. T h e r e l a t i o n o f d i s p e r s i o n (A s) t o t i m e t is g i v e n i n Fig. 2. F r o m t h e a r e a s Q u n d e r t h e d i f f u s i o n c u r v e s i n c r e a s e d Kuv t i m e s , w e c a l c u l a t e d t h e i n c r e m e n t o f r e f r a c t i v e i n d e x f r o m t h e e q u a t i o n (Ah/Ac)D=Quv)./ho(bKuv)(aspKustKuv) ( T a b l e 1). H e r e t h e d o u b l i n g o f s p a r s is asp = 0 . 0 0 1 1 m , t h e d i s t a n c e b e t w e e n t h e b a n d s of t h e c o m p e n s a t o r b----0.00188 m , ~ = 5 4 6 . 1 n m , a n d t h e coefficient o f e n h a n c e m e n t o f t h e d i f f u s i o m e t e r gust---~ 1.01. T h e a v e r a g e v a l u e ( A n / A 0 ) D = 1 7 × 10 -5 m 3 / k g f r o m t h e f r a c t i o n s is l o w e r t h a n o b t a i n e d o n t h e I T R - 2 . T h i s f a c t ( n o t i c e d also i n [10]) m a y b e e x p l a i n e d b y p a r t i a l p r e c i p i t a t i o n o f p o l y m e r i n e x p e r i m e n t a l p r e p a r a t i o n a n d losses o f a r e a i n t h e " t a i l s " of t h e diffusion c u r v e . T h e r e f o r e i n s e d i m e n t a t i o n - d i f f u s i o n s t u d i e s , t h e s o l u t i o n c o n c e n t r a t i o n was c o n t r o l l e d a c c o r d i n g t o t h e h e i g h t of t h e i n t e g r a l c u r v e s , u s i n g An/ztc= 19 x 10 -5 ma/kg. Sedimentation velocity was studied using the "MOM-3170" analytical ultra centrifuge ( V e n g r y a ) a t a r o t a t i o n f r e q u e n c y o f n----666.7 sec -z (for f r a c t i o n 1, n = 5 8 3 . 3 ) i n a u n i - s e c t o r t u b e w i t h a 0.012 m t h i c k a l u m i n i u m t u b e a t 3 0 5 ± 0 " 2 ° K . I n t h e a r r a n g e m e n t o f t h e p o l a r i z i n g - i n t e r f e r o m e t r y a t t a c h m e n t , we u s e d p a i r s o f s p a r s w i t h a d i v i s i o n o f 54 X 10 -5 a n d 2 1 × 10 -5 m [11].
002 10
!n (:c/xo) 10 e, secZ
i/o° o~~
-
o
o
S : I0 la 8ec 28
E
2G
~2
]
3Q 2q0
2
q G Time, z~.I0-~ sec FIG, 3
04
0.3 (x/%)~z FIG. 4
FIG. 3. D e p e n d e n c e o f d i s p l a c e m e n t o f s e d i m e n t a t i o n b o u n d a r y x o n t i m e : 1 -- f r a c t i o n 1, c = 1 . 2 8 kg/m3; 2 -- f r a c t i o n 4, c = 3 - 1 2 kg/ma; 3 - - f r a c t i o n 10, c = 1.32 k g / m a. FIG. 4. E x t r a p o l a t i o n o f a p p a r e n t v a h m of s e d i m e n t a t i o n coefficient S ff t o t h e m e n i s c u s , a c c o r d i n g t o (12) for f r a c t i o n 1 ( c = 1 . 2 8 kg/ma), w i t h t0-----420 (1), 360 (2) a n d 324 sec (3). S e d i m e n t a t i o n coefficients S¢P w e r e c a l c u l a t e d a c c o r d i n g t o t h e slope o f t h e r a t i o of l o g x t o t (Fig. 3); for x t h e a b s c i s s a o f t h e m a x i m u m o f t h e c u r v e or (for a s y m m e t r i c distri-, b u t i o n s ) t h e a b s c i s s a o f t h e c e n t r e of g r a v i t y w a s u s e d : t is t h e t i m e r e c k o n e d f r o m t h e s t a r t o f r o t a t i o n . A c l e a r d i s t o r t i o n i n t h e s e r a t i o s t o t h e side o f t h e a b s c i s s a i n d i c a t e s t h e i n f l u e n c e of h y d r o s t a t i c p r e s s u r e p o n t h e v a l u e o f S, so t h a t t h e a p p a r e n t v a l u e of SP=S~ X
Diffusion and sedimentation of poly-a-methylstyrene in eyclohexane
2117
× (1--/~p). E x t r a p o l a t i o n of the slope of the ratio of log x to t to the meniscus x0, was eam'ied out by a known method [12]. The dependence of S ~ - - l n (x/xo)/co2(t--to), where t--to is the true sedimentation time, on (X/Xo)~--l, the linearity of which is attained by variation of to (Fig. 4), intercepts the ordinate S c, but its slope equals V=[lcs.c--m(1-}-ks'c)J/2(1-i-ks.c). F r o m the; latter equation, we calculated the constant parameter for the above PMS-cyclohexane system, /1----2m/o~pox~o where ~o= 2nn rad/sec and P0 is the density of cyclohexa~le at 100 k])a. On account of the dependence on concentration of S(c), the average valu( • ]k)r syrrmletrical and " n a r r o w " samples (Table 2), /~--~(1.6_+ 0.2) × 10 -8 msec2/kg agrees with literature data [13]. The concentration dependence of S(c) was studied for the first, fourth and t en t h fractions (Fig. 5). TJsing the equation 1/Sc----(1/So)(l~]c,c ) we calculated the values of the p a r a m e t e r k s (Table 2) from t h e slopes of the straight-line dependence of l/So on c. These appear to be linearly connected with [S] : k s ~ 12× 10 TM [S]----51 × 10-e'M~. ttere k, is in m*/kg; IS] -=Sotlo/1---vpo is in kg/m. This experimental relationship, which agTees with published d a t a [13314], was used to calculate S Ofor the remaining fractions and samples, correcting t h e value of So obtained at the final concentration. The mean experimental value ks/ /[~/]=0.87 indicates, within the framework of the theory [15], the m u t u a l permeability of t h e molecules and agrees q u a n t i t a t i v e l y with the sphere-cylindrical approximatiolJ of this theory. S -I'~10"I~,~eC'l
77; IG ---o---'----°''-'''-'°'-''''3
15 2
I
2
3 C, k q/m 2
Fro. 5. Dependence of magzdtude of S -1 on concentration for fractions 1 (1), 4 (2) and 10 (3~ of ])MS in cyclohexane at 30ii°K. We also studied the dependence of the diffusion coefficients D (c) on concentration, for the :first and fourth fractions. I f the concentration dependence of the coefficient of translational friction f(c) is the same in sedimentation and diffusion, then according to references [16, 17], the dependence of D(c) must be governed by the equation D ( c ) ~ D o × × (1--~c)(1-}-2A~Mc~- ...... )/(l~-ksc ) i.e. for ])MS in cyclohexane at 0 temperature, t h e relationship D(c)=Do(1--~.c)/(1-~ksc)~_Do/(1-~-ksc) m i g h t be expected (see theoretical curves 1-6 in Fig. 6). The experimental points of Fig. 6, within the limits of error, satisfactorily agree with the theoretical curves~ plotted for values of the p ar am et er k s obtained from the sedimentation measurements i.e. a decrease in the value of D with an increase in e in O conditions, observed for ])MC in cyclohexmle, is in agreement with pr~sevation of the dependence of S(c) for ])MS in this solvent, but the magnitude of the change of D
2118
P . N . LAv~xsxo e~ a/.
correlates with the change in solution viscosity, with increasing concentration. In the experimental values of D for the other fractions, corrections (not exceeding 7%) were m~de in D(c), according to the equation Do=D(l~-kae ) for corresponding values of the parameter /¢e" MM (molar) was calculated from Svedberg's equation MsD~(RT/1--'~po)(So]Do) and the mean weight value Mw from MMD of fractions, obtained from the sedimentation diagrams. The poly-dispersion of saznples and fractions is shown in Table 1. The hydrodynamic Tsvetkov-Klenin parameter [3] calculated from the equations
(A~D~o[~o]Mw/lO0)~/T and
A~=R[S] ([~/100M~) ¢
has mean values for samples and fractions of A----~3.1 × 10 -1~ and A ~ 3.2 × 10 -1T J . d e g -1. mole- t. •
8o~ 10 '3
Do'lo'~,,~/sec cvj.1o~, ,.~/kj
1"0
3
qo ~ 20 fO 5
1 3
I
5
10c,kq//mz FiG. 6
I
I
[ IIIlil
5 I0
J
I
Ilflll
50 IVw ~ lO-S
FiG. 7
Fro. 6. Dependence of diffusion coefficient D of PMS in cyclohexane at 305°K on solution concentration for fraction 1 (lower series of points) and 4 (upper points): light and dark points are data obtained in glass and metal tubes respectively: continuous curves -- theoretical ratios D(c)=Do/(1-.Fkzc ) constructed with ks=0.2 (1), 0.4 (2), 0.6 (3), 1-0 (4), 1.5 (3) and 2.0 × 10 -1 mS]kg (6) respectively. :FIG. 7. Logarithmic dependence of So (1), Do (2) and [~/] (3) on Mw for fractions and samples of PMS in eyclohexane at 305°K. F i g u r e 7 shows t h e d e p e n d e n c e o f [~/], So a n d Do on Mw on l o g a r i t h m i c scales. W i t h i n t h e limits o f error, t h e e x p e r i m e n t a l p o i n t s b o t h for p r a c t i c a l l y m o n o d i s p e r s e d a n d u n i f o r m l y p o l y d i s p e r s e d s a m p l e s ( a p a r t f r o m b i m o d a l ones) lie on t h e g e n e r a l curves described b y t h e M a r k - K u h n - H o u w i n k equations. [~/]-~ 7.2 × 10 .5 × M ~ 5° So~_ 1.67 × 10-z5 × M ~ s° D O----1"36 × 10 -s × M ~ °'s° T h e indices a=b~0.50 in t h e v i s c o s i t y a n d diffusion e q u a t i o n s confirms t h e r e a l i z a t i o n o f 8 conditions for P M S in c y c l o h e x a n e a t 305°K. T h e a b s e n c e
Diffusion and sedimentation of poly-a-methylstyrene in cyclolaexane
2119
of volume effects allow calculation of the length of a statistical K u h n segment of the equivalent chain, from the hydrodynamic data using the equations:
As=ML[(1--Vpo)/NArlo-PK°s]2=740 X 10-1°//) ~ AD = ML(kT/~IoPK~) 2= 710 × 10-l°/P 2 A,=ML(K°,/4)t=8.18 × 10s/4 j Here ML is the molecular mass of a unit length of PMS chain, equal to 47.25 × 1010/ /m, b is the Boltzmann constant, NA is Avogadro's number, _P and 4 are Flory constants, / ~ , -~D and /ffs are the coefficients for the M a r k - K u h n - H o u w i n k equations. The condition A I = A ~ is fulfilled with (4/100)*/P=2.29 × 106 which is different from the value (2.87× lO~a/lOO)~r/5× 1 1 = 2 " 7 8 × 1 0 e predicted from theory [18, 19] :in the case of the absence of volume effects and strong hydrodynamic interaction (non-flowing Gaussian balls) b u t is confirmed b y other work [13, 14, 20, 21]. In accordance with the latter, the mean value (4/100)*/P for PMS in cyclohexane at 0 temperature equals (2-29=]=0.10)× l0 s and for PS in the same solvent at 0 temperature (35°)--(2.234-0.11)×10 ~ i.e. likewise appreciably less than 2.78 × 10 e. The difference between experimental and theoretical values of ¢ and P is often ascribed to heterogeneity of samples. However, the small poly-dispersivity of PMS fractions, from which K~,/~D and K°~ were determined in our s t u d y (Mz/Mw <<.1-04) excludes the necessity of introducing a correction for heterogeneity i.e. even in the case of homogeneous polymers and in the absence of volume effects, the cited theories of viscosity and translational friction [18, 19] inadequately describe the properties of macromolecular solutions. The selection of absolute values of each of the 4 and P coefficients, necessary for calculation of A, cannot be accomplished from hydrodynamic data only. Direct (truly few) measurements of molecular sizes, as in polydispersed PMS in cyclohexane, b y the light diffusion method [6, 27] from which is obtained A v = 2 4 X 10 -1° m, give values of 4 = 2 × 10 ~a mole -1 and P ~ 5 . 5 [14, 22]. For PS in cyclohexane at 0 temperature, the mean (of 8 studies) value of 4 = (2.2=}=0.4)× x 10 *a mole -1 [23] agrees with theoretical values, obtained from the theory of viscosity of worm-like chains [24] for the limiting case of a non-flowing Gaussian coil and much smaller than 2.87 × 10 ~3, predicted from theory [18, 19]. For PS with Mw----6.5 × l0 s and Mz[Mw <~1"03 the value 4 = ( 2 . 5 5 4 - 0 . 1 ) × 1023 mole -1 was obtained [23] and for PS with Mw=(208--1010) × 10a and Mw/Mn=l.02-1"14 with a P value of 5-3 [10]. The experimentally determined values, 4 < 2 . 8 7 × 10 ea and / ) > 5 . 1 1 confirm the conclusions of reference [25] in which as a result of changes in a series of preneutralized hydrodynamic interactions between chain segments (as the number of segments N-~ ¢o) the limiting theoretical values 4 ~ = 2 - 5 1 X 102a and P ~ = 5 - 9 9 were obtained. Their ratio k(4~/lOO)~/P,~=3.16× 10 -17 agrees with the mean experimental value A0=(3.154-0.10)×10 -17 obtained in the present study.
2120
P . N . LAVRENKOetal.
S u b s t i t u t i n g these values of ~ a n d P ~ in t h e e q u a t i o n p r e s e n t e d above, we o b t a i n , for a s t r a i g h t K u h n s e g m e n t , t h e values A z = 2 0 . 6 X 1 0 -l°, AD~-19.SX X 10 -l° a n d A,----20.6X 10 -i° m. T h e m e a n v a l u e o f A is ( 2 0 . 3 + 0 . 5 ) X 10 -1° m. T h e possible d i v e r g e n c e of ~ a n d P values f r o m ¢b~ a n d P ~ owing to t h e finiteness of m a c r o m o l e c u l e l e n g t h s p r e d i c t e d b y t h e o r y [19] for h i g h m o l e c u l a r P M S fractions, a m o u n t s to several p e r c e n t a n d w a s t h e r e f o r e n o t considered. T h e n u m b e r of m o n o m e r u n i t s in a K u h n s e g m e n t is s=A/~=8.1: h e r e A----2-52 X 10 -l° m , t h e p r o j e c t i o n of l e n g t h o f a m o n o m e r u n i t on t h e m o l e c u l a r axis. T h e l e n g t h o f a K u h n s e g m e n t w i t h c o m p l e t e f r e e d o m of r o t a t i o n in t h e c h a i n a r o u n d t h e b o n d s of l e n g t h l = 1.54 X 10 -l° m joined t o g e t h e r a t a n angle 0 = 110 °, equals [26] A s v = ( 1 - - c o s 0). ( l ~ - c o s 0 ) . / / s i n ( 0 / 2 ) = 3 . 8 X 1 0 -1° m. Consequently, t h e f a c t o r a for r e t a r d a t i o n of r o t a t i o n a r o u n d t h e links o f t h e P M S chain, as o b t a i n e d f r o m h y d r o d y n a m i c d a t a , is a=(A/Asv)~=2.3, w h i c h is c h a r a c t e r i s t i c # f flexible c h a i n molecules in t h e v i n y l p o l y m e r series [3, 21]. W i t h t h e p r o p o r t i o n a l i t y So ~ M t a n d also t h e r a t i o In (A/d) = c o n s t . , t h e h y d r o d y n a m i c c h a i n d i a m e t e r for PMS, d = 7 . 1 X 10 -l° m for a const.-----1.056 [19] or d = 4 . 9 X 10 -i° m for a c o n s t . = 1.431 [18], m a y be e s t i m a t e d . T h e a u t h o r s t h a n k V. N. T s v e t k o v for v a l u a b l e c o m m e n t s .
Translated by C. W. CAPP REFERENCES 1. A. F. PODOLSKY, R. Ch. DASKIN and A. A. KOROTKOV, J. Polymer Sci. A - l , 9:
2259, 1971 2. V. Ye. ESKIN, T. N. NEKRASOVA, U. B. ZHURAYEV, A. F. PODOLSKII and A. A. TARAN, Vysokomol. soyed. A19: 525, 1977 (Translated in Polymer Sci. U.S.S.R. 19:
3, 602, 1977) 3. V. N. TSVETKOV, V. Ye. EKSIN and S. Ya. FRENKEL, Struktura makromolekul
v rastvorakh, p. 377, 418, 504, Nauka, 1964 4. J. M. G. COWIE and S. BYWATER, J. Polymer Sei. A-2; 6: 499, 1968
5. L. BISKUP and H. J. CANTOW, Prepr. IUPAC Intern. Symp. on Macromol., Helsinki 3: 47, 1972 6. P. F. MIJNLIEFF and D. J. COWMOU, J. Colloid Interf. Sci. 27: 553, 1968 7. I. NODA, K. MIZUTANI, T. KATO, T. FUJIMOTO and M. NAGASAWA, Macromolocubs 3: 787, 1970 8. V. N. TSVETKOV, Zh. eksp. teoret, fiziki 21: 701, 1951 9. P, N. LAVRENKO, O. V. OKATOVA and K. S. KHOKHLOV, Pribory i tekhnika eksperimenta 5: 208, 1977 10. J. M. G. COWIE and E. I. CUSSLER, J. Chem. Phys. 46: 4886, 1967 11. V. N. TSVETKOV, Vysokomol. soyed. 4: 1575, 1962 (Not translated in Polymer Sei. U.S.S.R.) 12. J. E. BLAIR and J. W. WITJT.IAMS, J. Phys. Chem. 68: 161, 1964 13. M. ABE, K. SAKATO, T. KAGEYAMA, M. FIrKATSU and M. KURATA, Bull. Chem~ Soe. Japan 41: 2330, 1968 14. J. NODA, K. MIZUTHANI and T. KATO, Macromolecules 19: 618, 1977 15. C. W. PYUN and M. FIXMAN, J. Chem. Phys. 41: 937, 1964 16. H. YAMA, Modern Theory of Polymer Solutions, p. 262, Harper and R o w Publ., :New York, San Francisco, London, 1971
Secondary structuring during polymerization of vinyl chloride
2121
17. It. SIMHA, In: High Polymer Physics (edited b y It. A. l~obinson) p. 398, Chem. l~lbl., N.Y., 1948 18. J. HEARST a n d W. STOCKMAYER, J. Chem. Phys. 37: 1425, 1962; J. HEARST, J. Chem. Phys. 37: 2547, 1962 19. H. Y A M A K A W A and M. FUJII, Macromolecules 6: 407, 1973; 7: 128, 1974 20. A. ]KOTERA, T. SATO and T. HAMADE, Polymer J. 3: 421, 1972 21. J. BRANDRUP and E. H. IMMERGUT, Polymer Handbook, 2nd edn., p a r t IV, pp. 16, 17, 41, Willey, 1975 22. T. I(ATO, K. MIYASO, L. NODA, T. FUJIMOTO and M. NAGASAWA, Macromolecules 3: 777, 1970 23. Y. MIYAKI, Y. EINAGA, M. F U J I T A and M. FUKUDA, Macromolecules 13: 588, 1980 24. J. E. HEARST, J. Chem. Phys. 40: 1506, 1964 25. B. H. ZIMM, Macromolecules 13: 592, 1980 26. H. BENOIT, J. chmi. phys et phys. chim. biol. 44: 18, 1947
:Polymer Science U.S.S.R. Vo]. 23, 1%. 9, pp. 2121-2127, 198]. Printed in Poland
0032-3950/81/092121-07507.50/~ © 1982 Perga~aon Press Ltd.
SECONDARY STRUCTURING DURING THE POLYMERIZATION OF VINYL CHLORIDE* A. V. NErMARK a n d L . I. KHErFETS V. A. Kargin Research I n s t i t u t e for tlle Chemistry and Technology of Polymers
(Received 9 April 1980) An analysis of the genesis of porous structures formed during the polymerization of vinyl chloride has been carried out, based on a model of randomly dispersed spheres, the radius of which is increased with time. Equations were derived for n~ean macropore radius, specific surface and porosity, in relation to the degree of monomer conversion. The results m a y be used for the descriptioll of other similar processes. IN t h e p r e s e n t r e p o r t , b u l k o r s u s p e n s i o n p r o c e s s e s f o r p o l y m e r i z a t i o n o f v i n y l chloride are examined. I n t h e l o w c o n v e r s i o n r a n g e s ( u p t o 10°//o) t h e p o l y m e r i z a t e r e s e m b l e d l i q u i d monomer, in which a finely dispersed polymer phase was beginning to develop. T h e p a r t i c l e g l o b u l e c o n c e n t r a t i o n in t h i s p h a s e d e p e n d s o n t h e o r i g i n a l r a t e o f i n i t i a t i o n a n d b e c o m e s s t a b i l i z e d a t ~ 1 % c o n v e r s i o n , r e a c h i n g a v a l u e o f 5 × 10 l ° - 5 × 1011 p a r t i c l e s / c m a o f p o l y m e r i z a t e . T h e i n n e r s t r u c t u r e o f t h e g l o b u l e ( t h e s o - c a l l e d p r i m a r y s t r u c t u r e ) is a l s o d e f i n i t e l y f o r m e d a t a c o n v e r s i o n o f a b o u t
1% [1] * Vysokomol. soyed. A23: No. 9, 1945-1950, 1981.