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Temperature dependence of the intrinsic viscosity of solutions of polystyrene and polyalkylstyrenes
772
19. 20. 21. 22.
S. YA. MAGAR1K et aL kikh soyedinenii metodonl atomno-absorbtsionnoi spektroskopii (Study of Metal-Containing Organic Compounds by Atomic-Absorption Spectroscopy). p. 27, Moscow, 1982 E. FREY and R. D. PRESTON, Nature 196: 130, 1962 E. D. T. ATKINS, W. MACKIE, K. D. PARKER and E. E. SMOLKO, 1bid. 225: 626, 1970 L.L. RAZUMOVA, A. A. VERETENN1KOVA, G. Ye. ZAIKOV and L. A. VOL'F, Vysokomol. soyed. A25: 2085, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 10, 2418, 1983 Yu. A. FURMANOV, I. M. SAV1TSKAYA, V. P. SIL'CHENKO, L . P . BEZUGLAKYA, Ye. B. DOL'BERG, Ye. L. ILLARIONOVA, T. N. KALININA and L. A. MUKOVSKII, Tez. dokl. VI Vsesoyuz. nauch, simpoz. "Snteticheskiye polimery meditsinskogo naznacheniya" (Summaries of Reports to Sixth All-Union Scientific Symposium "Synthetic Medical Polymers"). p. 167, Alma Ata, 1983
PolymerScienceU.S.S.R, Vul.29, No. 4, pp. 772-778, 1987 Printed in Poland
0032-3950/87 $10.00+.00 © 1988PergamonPress pie
TEMPERATURE DEPENDENCE OF THE INTRINSIC VISCOSITY OF SOLUTIONS OF POLYSTYRENE AND POLYALKYLSTYRENES * S. YA. MAGARIK, A, p. FILIPI'OV a n d N. V. D'YAKONOVA Institutc of High Molccular Weight Compounds, U.S.S.R. Academy of Sciences (Received 12 August 1985)
The experimental findings on the temperature dependence of the intrinsic viscosity of solutions of PS and polyalkylstyrenes treated by the modified Flory equation gave values of the entropic parameter ~ concurring with the magnitudes ~ obtained from the molecular-mass dependence of the critical temperature of mixing. The excluded volume of the macromolecules of the polyalkystyrenes insignificantly exceeds that for PS pointing to the closeness of their transverse dimensions, i.e. the low rigidity of the side chains of the polyalkylstyrenes. STUDY o f the t e m p e r a t u r e d e p e n d e n c e of the intrinsic viscosity [q] o f p o l y m e r solutions gives an idea o f the value o f the e n t r o p i c p a r a m e t e r VI [1] a n d the thickness o f the w o r m like chain m o d e l l i n g the m a c r o m o l e c u l e [2, 3]. T h e first a t t e m p t to d e t e r m i n e by this m e t h o d the m a g n i t u d e VI was m a d e in references [4, 5J. It was b a s e d on the k n o w n F l o r y e q u a t i o n
(1 * Vysokomol. soy'ed. A29: No. 4, 698-702, 1987.
Intrinsic viscosity of solutions of PS and polyalkylstyrenes
773
where ez is the dimensional coefficient of swelling; h2o is the mean square distance between the ends of the unperturbed macromolecule; M is the molecular mass; T is temperature, K; O is the temperature at which the solution becomes ideal; F is the specific partial volume of the polymer; V~ is the molar volume of the solvent molecules; N is Avogadro's number. The ~q values obtained proved to be several times smaller than the gq magnitudes determined from the molecular-mass dependence of the critical mixing temperature Toy [6, 71.
F
T,~' = O - ' L 1 + gt~-' \\~-M,]
2~7J
(2)
In the present work to determine ~1 from the temperature dependence of [r/] we used the equation in reference [2] based on the strict theory of minor volumetric effects and their link with the intrinsic viscosity. This equation was also modified for application to comb-like polymers, as are the polyalkylstyrenes studied by us. Another possible model of the latter is the worm-like chain the diameter of which d is also evaluated here from the temperature dependence of It/]. In the work we investigated fractions of poly-p-hexylstyrene (PHS) and poly-p-decylstyrene (PDS) the preparation and characteristics of which were described earlier 18, 9]. The intrinsic viscosities were measured in an Ostwald viscometer with solvent flow time not less than 40 sec. The mixing temperature T.,~, was determined with an accuracy to 0.1 deg from the clouding of the solution on its slow cooling. Earlier the tbllowing 0-solvents were found by the light scatter method from the temperature dependence of the second virial coefficient: for P H S - M E K at 303.2 K [8] and for PDS a mixture of MEK-butylethylketone (BEK) in the ratio 1 : 1.24 by volume at the temperature 294.2 K [9]. The components of the mixed solvent are ketones of similar structure and, therefore, it may be assumed that the energy of their interaction with the PDS macromolecules is much the same. This justifies [1] the application to the three-component system of the procedure described by equation (2) strictly speaking applicable only to a two-component system. The molar volumes of these solvents V1 = 89.6 x 10- 6 m 3 and V1 = 112.6 x x 10 -6 m 3. The specific partial volume 0=0.93 x 10 -3 m3/kg for PHS and F = 0 . 9 2 x x 10 -a m3/kg for PDS. Figure 1 presents the concentration dependences of Tmi~ for the PHS and PDS fractions the molecular masses M of which are given in the Table. For the smallest PHS fraction M = 1 3 6 x 103. The critical temperatures of mixing Tcr are equal to Tmi, with the condition OTmlx/Oc=0. The construction of the dependence of Tcr on (VI/vM) ~ + Vt/2gM (Fig. 2), according to equation (2), helped in determining the values of O and ~tt. O =302.6 for PHS and 291.3 K for PDS. The values of the entropic parameter gq are 1.15 for PHS and 2.75 for PDS; published data for PS: ~'1 = 1.06 [6] and ~tI =0"7 [10].
S. YA. MAGARIK et al.
774
CHARACTERISTICS OF POLYSTYRENE AND
POLYALKYLSTYRENE FRACTIONS~ THEIR PARAMETERS OF
ENTROPY AND EXCLUDED VOLUME
Polymer
M x 10 -a
[t/]0, ma/kg
H
K
qzx
1270 360 92 4400 1560 1050 620 765 900 715 600 570 360 213
0.089 0.047 0'023 0"171 0.100 0.083 0.062 0.080 0.045 0.038 0"034 0"030 0.023 0.018
8'2 2'8 0"7 40"0 9"09 6'06 4"59 6'67 2"00 1 "40 1'36 1 "09 0"726 0"342
1 '27 1 "22 1"10 1 "30 1"28 1"26 1 '25 1 "25 1"26 1"25 1"24 1"21 1'18 1'14
0'62 0'78 0"89 1"08 0"78 0'77 I "03 0"71 1-33 1 "24 1"41 2'70 3"04 2'45
--~
X IU-
,
m
PS
[51
[131
[141 PHS
PDS
1 "40 1'80 1 '90 1 "86 1 "23 1"22 1'62 1 "62 1 '56 1"52 1"68 2'20 2'47 2"00
1 i .I?
~
°
~
299 -
to3/r~,~ 3.5~.
297 g
1..
4
2954
Z93
8 34
,2 I L
q
i I
4
I
4
L
I
8
(4)
l I
8
I
tz (6)
c, lo -~, kgtm3 FIG. 1
(5)
ff I
I
1 2 3 (1/x '/z + l & z ) , 102 Fro. 2
FIG. 1. Temperature of mixing of solutions T,,,, for PHS (1-3) and PDS (4-6) as a function of their concentrations c. FIG. 2. Reciprocal of the critical temperature of mixing 1/Tc ~for PDS (1) and PHS (2) as a function of the parameter 1Ix ~ + ½x) where x = v M / V ~ .
Intrinsic viscosityof solutions of PS and polyalkylstyrenes
775
Comparison of the ~tI values for the polymers and low molecular weight analogues in reference [7] convincingly showed that this method gives for polymers theoretically substantiated values which must be regarded as standard in determining g/1 by other methods. Therefore, Flory proposed [l ] that the ~'1 values obtained from the temperature dependence of [~/]are well understated because of the incorrect numerical coefficient in the formula (1). In reference [2] on the basis of the exact theory of volumetric effects [11 ] an equation was proposed linking the viscosity coefficient of swelling ~ = [r/]/[r/]o with temperature T, the contour length of the macromolecule L, its rigidity A (length of the Kuhn segment) and the parameter ~q a~-l---0.8K
°'~t, 1
T]A ~
(3)
where K is a tabulated function L/A [12]; floz is the parameter of the excluded volume of a portion of the chain of length I. It must be emphasized that in the theory of far-action for flexible chain polymers the breakdown into portions is arbitrary since the value of the ratio flol/l 2 is invariant [11]. Also valid from this point of view, in particular, is the breakdown into portions in the Flory lattice model [1]: the macromolecule breaks down into x parts such that each of them has the volume -vM/Nx equal to the volume of one molecule of the solvent V,/N, i.e.
x=-vM/Vl
(4)
Accordingly, the contour length may be broken down into x portions of length lx
tx-
LVl
(5)
b-M Equation (1) may be represented in the form \2n]
NR.
\
T]~'
(6)
if it is borne in mind that h2/M=-h2/LML=A/ML, where Mz=Mo/2 is the molecular mass of unit length; Mo is the molecular mass of the monomer unit; 2 is its length in the conformation stretched to the limit. Comparison of expressions (3), (5) and (6) shows 2 2 that the invariant flol/l 2 =flox/l~, = -v- 2 M~,/NVI and the parameter of the excluded volume flox on breakdown of the macromolecule, according to the Flory model, is numerically equal to the volume of the solvent molecule V1/N, which is natural. In the light of all this we propose for the determination of the entropic parameter ~tl the use of the equation H A~N Va ~" -- [q]o (~n)~O"SKL~-62M~ ' (7) which follows from relation (3) differing from the Flory equation in the numerical
S. YA. MAGARn( et al.
776
coefficient 3s/2/0"8 K ~ 5, and also the form of the functional dependence of the swelling coefficient in the left-hand part. Here, the viscosity swelling coefficient eqa is used and not the dimensional e2 =R2/R g, where/~2 and/~g are the mean square radius of the swollen and unperturbed macromolecule determined from the asymmetry of light scatter. t) /[r/] In equation (7) instead of ~a _ 1 is substituted the value H = ( ~ 1- - O T o ,equalto the initial slope of the experimental dependence of [r/] on the parameter 1 - O/T.
[ql,"s/l~9 0.035
a
~
o o o
0 o
1 1 2 / 1
t)
l
0025
[
[ .
o.os
o oq
.
.
.
.
.
. o.o5
,
1_
z-o/r
olo
F~a. 3. Instrinsic viscosity [~/]as a function of the parameter I - O/Tfor PDS solutions in the mixture M E K : BEK = 1 : 1.24 (a) and PHS in MEK (b). The Table indicates the treatment of the published data from formula (7) taking into account the fact that for PS A = 2 0 x 10 -1° m, ~=0.93 x 10 -3 ma/kg, ML=104/2"52 x x10-1°=41"27x101°. The mean value V1=0.9+0.2 obtained well agrees with the magnitude p'l determined from the molecular-mass function of Tcr. In considering the data on the temperature dependence of [r/] for the polyalkylstyrenes (the initial slopes in Fig. 3a, b) it is important to bear in mind the presence in them of quite long side chains. The ratio of the contour lengths of the latter to the distance between neighbouring points of their attachment to the main c h a i n / z = 3 (for PHS) and 5 (for PDS). This leads to further far action and may be taken into account in two ways. Firstly, the macromolecules of the polyalkylstyrenes may be regarded as regular comb-like chains consisting of infinitely thin radicals of the main c h a i n - P S and side alkyi radicals. In Flory's lattice model only the volumetric fraction occupied in solution by the polymer molecules, irrespective of their architecture is of significance. Therefore, on breaking down of the macromolecule into portions the collision of which produces a far action it is necessary to consider the total contour length of the comb-like macromolecule LtotaI which is evidently equal to Ltotai=L(/t+l). Consequently, taking into account equation (5), formula (7) must be supplemented by the multiplier (It+ 1)3/2 which in the case of the linear PS polymer is equal to unity (/t--0). At the same time, for the experimental determination of the measure of rigidity A = hg/L (degree of coiling
Intrinsic viscosity of"solutions of PS and polyalkylstyrenes
777
of the macromolecule caused by the near action) it is natural to allow only for the contour length of the main chain L. In passing we would note that in comparing the rigidity of two macromolecular chains with different unit molecular mass Mj. the use as measure of rigidity of the magnitude h2/M may lead to an erroneous conclusion unlike comparison of the A values. Additional construction of the dependence of [tl]/M 1/2 on M 1/2 [15] convinced us that in the temperature interval studied PHS and PDS do not change the value A which might have occurred because of their diphilicity [8, 9]. Substitution of the experimental values in formula (7) taking into account the additional multiplier gives the values of ~p,~presented in the Table which, as in the case of PS, well agree with the P't magnitudes obtained from the dependence of Tcr on M. The approach described does not, however, allow one to judge the transverse dimensions of the macromolecules. Secondly, comb-like macromolecules may be modelled by worm-like chains [3] of finite thickness d with the contour length L. If formula (3) is applied to them it is possible to evaluate the diameter d by regarding the collision of the portions of such a chain as the collision of cylinders of length 1. The excluded volume of such a cylinder is proportional to its own volume [16] and the magnitude flo~//1/l 2 obtained experimentally is proportional to d flote1-412
1+
+
d
(8)
However, the proportionality coefficient is a function of the ratio p =lid. The value in parentheses rapidly tends to unity with rise in p and already f o r p = 6 amounts to 1.5. The presence in eqn. (8) of two unknowns p and d does not allow one to determine the latter quantitatively. Only qualitative comparison of the transverse dimensions of the polyalkylstyrenes and PS is possible. It is natural to carry out division of the worm-like chain into portions of length I=A which gives for the three polymers considered roughly an identical value of p. At any rate, p of the polyalkylstyrenes is always smaller than for PS. Therefore, the ratio of the experimentally observed magnitudes flot~ul/l 2 shows the upper limit of the ratio of diameters clpHs/@s<~l'1 for PHS and ~<1.4 for PDS. This evaluation shows that the transverse dimensions of the polyalkylstyrene macromolecules insignificantly exceed those for PS which agrees with the results of other methods for PDS [9] and indicates the moderate rigidity o f the side alkyl chains. In conclusion, we would emphasize that from the temperatme dependence of [r/] only one thermodynamic parameter-~u~ can be determined. Determination of the other parameter O as was done in references [4, 5] is incorrect since to construct the dependence of a s - c~3 (or %3- 1 ) on l I T it is necessary to know the magnitude [r/]0, i.e. to determine in advance O by another method. This predetermines the point of intersection of the straight line 1 with the axis I/T (Fig. 3).
Translated by A. CRozY
778
D . P . KIRYUKHINet aL
REFERENCES 1. P. J. FLORY, Principles of Polymer Chemistry. N. Y., 1953 2. S. Ya. MAGARIK and G. M. PAVLOV, Vysokomol. soyed. A17: 1691, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 8, 1943, 1975) 3. S. Ya. MAGARIK, G. M. PAVLOV and G. A. FOMIN, Macromolecules I I : 294, 1978 4. T. G. FOX, Jr. and P. J. FLORY, J. Amer. Chem. Soc. 73: 1909, 1951 5. ldem, 1bid 73: 1915, 1951 6. A. R. SHULTZ and P. J. FLORY, Ibid74: 4760, 1952 7. Idem, Ibid, 75: 3888, 1975 8. V. Ye. ESKIN, D. N. ANDREYEV, I. A. BARANOVSKAYA, N. V. D'YAKONOVA, S. Ya. MAGARIK, N. A. SOLOVSKAYA and A. P. FILIPPOV, Vysokomol. soyed. B26: 845, 1984 (Not translated in Polymer Sci. U.S.S.R.) 9. S. Ya. MAGARIK, D. N. ANDREYEV, I. A. BARANOVSKAYA, N. V. D'YAKONOVA, N. A. SOLOVSKAYA, A. P. FILIPPOV and V. Ye. ESKIN, Ibid A28: 1603, 1986 (Translated in Polymer Sci. U.S.S.R. 28: 8, 1783, 1986) 10. F. CANDAU, C. STRAZIELLE and H. BENOIT, Makromolek. Chem. 170: 165, 1973 11. H. YAMAKAWA, Modern Theory of Polymer Solutions. N. Y., 1971 12. H. YAMAKAWA and W. H. STOCKMAYER, J. Chem. Phys. 57: 2843, 1972 13. G. C. BERRY, I bid46: 1338, 1967 14. A. YAMAMOTO, M. FUJII, G. TANAKA and H. YAMAKAWA, Polymer J. 2: 799, 1971 15. W. H. STOCKMAYER and M. FIXMAN, .L Polymer Sci. C, 1,137, 1963 16. A. YSIHARA and T. HAYASGIDA, J. Phys. Soc. Japan 6: 46, 1951
Polymer ScienceU.S.S.R.Vol. 29, No. 4, pp. 778-784, 1987 Printed in Poland
0032-3950/87 $10.00+ .00 © 1988Pergamon Press ple
RADIATION-POLYMERIZATION OF HEPTYLMETHACRYLATE IN PRESENCE OF BUTADIENE-NITRILE RUBBER* D. P. KIRYUKI-IIN, A. I. BOL'SHAKOV an d I. M. BARKALOV Department of the Institute of Chemical Physics, U.S.S.R. Academy of Sciences
(Received 14 August 1985) With increase in the initial concentration of SKN-18 in its composite with heptylmethacrylate auto-acceleration of tile polymerization process shifts to the region of shorter 7-radiation times and for a content of 60 wt. ~ of the rubber polymerization of the monomer proceeds instantly in conditions close to those of the gel effect. The mixed character of termination of the polymer chains is observed and at the final stage of post-polymerization at 295 K linear termination predominates. The rate constant of growth of the polymer chains in the interval 170-180 K has been determined: kp = 2 x 10-13 e x p ( - 6000/R T) cm3/sec. Introduction of small additions of the monomethacrylic ester of ethylene glycol (crosslinking agent) raises the rate of the process. * Vysokomol. soyed. A29: No. 4, 703-708, 1987.
19. 20. 21. 22.
S. YA. MAGAR1K et aL kikh soyedinenii metodonl atomno-absorbtsionnoi spektroskopii (Study of Metal-Containing Organic Compounds by Atomic-Absorption Spectroscopy). p. 27, Moscow, 1982 E. FREY and R. D. PRESTON, Nature 196: 130, 1962 E. D. T. ATKINS, W. MACKIE, K. D. PARKER and E. E. SMOLKO, 1bid. 225: 626, 1970 L.L. RAZUMOVA, A. A. VERETENN1KOVA, G. Ye. ZAIKOV and L. A. VOL'F, Vysokomol. soyed. A25: 2085, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 10, 2418, 1983 Yu. A. FURMANOV, I. M. SAV1TSKAYA, V. P. SIL'CHENKO, L . P . BEZUGLAKYA, Ye. B. DOL'BERG, Ye. L. ILLARIONOVA, T. N. KALININA and L. A. MUKOVSKII, Tez. dokl. VI Vsesoyuz. nauch, simpoz. "Snteticheskiye polimery meditsinskogo naznacheniya" (Summaries of Reports to Sixth All-Union Scientific Symposium "Synthetic Medical Polymers"). p. 167, Alma Ata, 1983
PolymerScienceU.S.S.R, Vul.29, No. 4, pp. 772-778, 1987 Printed in Poland
0032-3950/87 $10.00+.00 © 1988PergamonPress pie
TEMPERATURE DEPENDENCE OF THE INTRINSIC VISCOSITY OF SOLUTIONS OF POLYSTYRENE AND POLYALKYLSTYRENES * S. YA. MAGARIK, A, p. FILIPI'OV a n d N. V. D'YAKONOVA Institutc of High Molccular Weight Compounds, U.S.S.R. Academy of Sciences (Received 12 August 1985)
The experimental findings on the temperature dependence of the intrinsic viscosity of solutions of PS and polyalkylstyrenes treated by the modified Flory equation gave values of the entropic parameter ~ concurring with the magnitudes ~ obtained from the molecular-mass dependence of the critical temperature of mixing. The excluded volume of the macromolecules of the polyalkystyrenes insignificantly exceeds that for PS pointing to the closeness of their transverse dimensions, i.e. the low rigidity of the side chains of the polyalkylstyrenes. STUDY o f the t e m p e r a t u r e d e p e n d e n c e of the intrinsic viscosity [q] o f p o l y m e r solutions gives an idea o f the value o f the e n t r o p i c p a r a m e t e r VI [1] a n d the thickness o f the w o r m like chain m o d e l l i n g the m a c r o m o l e c u l e [2, 3]. T h e first a t t e m p t to d e t e r m i n e by this m e t h o d the m a g n i t u d e VI was m a d e in references [4, 5J. It was b a s e d on the k n o w n F l o r y e q u a t i o n
(1 * Vysokomol. soy'ed. A29: No. 4, 698-702, 1987.
Intrinsic viscosity of solutions of PS and polyalkylstyrenes
773
where ez is the dimensional coefficient of swelling; h2o is the mean square distance between the ends of the unperturbed macromolecule; M is the molecular mass; T is temperature, K; O is the temperature at which the solution becomes ideal; F is the specific partial volume of the polymer; V~ is the molar volume of the solvent molecules; N is Avogadro's number. The ~q values obtained proved to be several times smaller than the gq magnitudes determined from the molecular-mass dependence of the critical mixing temperature Toy [6, 71.
F
T,~' = O - ' L 1 + gt~-' \\~-M,]
2~7J
(2)
In the present work to determine ~1 from the temperature dependence of [r/] we used the equation in reference [2] based on the strict theory of minor volumetric effects and their link with the intrinsic viscosity. This equation was also modified for application to comb-like polymers, as are the polyalkylstyrenes studied by us. Another possible model of the latter is the worm-like chain the diameter of which d is also evaluated here from the temperature dependence of It/]. In the work we investigated fractions of poly-p-hexylstyrene (PHS) and poly-p-decylstyrene (PDS) the preparation and characteristics of which were described earlier 18, 9]. The intrinsic viscosities were measured in an Ostwald viscometer with solvent flow time not less than 40 sec. The mixing temperature T.,~, was determined with an accuracy to 0.1 deg from the clouding of the solution on its slow cooling. Earlier the tbllowing 0-solvents were found by the light scatter method from the temperature dependence of the second virial coefficient: for P H S - M E K at 303.2 K [8] and for PDS a mixture of MEK-butylethylketone (BEK) in the ratio 1 : 1.24 by volume at the temperature 294.2 K [9]. The components of the mixed solvent are ketones of similar structure and, therefore, it may be assumed that the energy of their interaction with the PDS macromolecules is much the same. This justifies [1] the application to the three-component system of the procedure described by equation (2) strictly speaking applicable only to a two-component system. The molar volumes of these solvents V1 = 89.6 x 10- 6 m 3 and V1 = 112.6 x x 10 -6 m 3. The specific partial volume 0=0.93 x 10 -3 m3/kg for PHS and F = 0 . 9 2 x x 10 -a m3/kg for PDS. Figure 1 presents the concentration dependences of Tmi~ for the PHS and PDS fractions the molecular masses M of which are given in the Table. For the smallest PHS fraction M = 1 3 6 x 103. The critical temperatures of mixing Tcr are equal to Tmi, with the condition OTmlx/Oc=0. The construction of the dependence of Tcr on (VI/vM) ~ + Vt/2gM (Fig. 2), according to equation (2), helped in determining the values of O and ~tt. O =302.6 for PHS and 291.3 K for PDS. The values of the entropic parameter gq are 1.15 for PHS and 2.75 for PDS; published data for PS: ~'1 = 1.06 [6] and ~tI =0"7 [10].
S. YA. MAGARIK et al.
774
CHARACTERISTICS OF POLYSTYRENE AND
POLYALKYLSTYRENE FRACTIONS~ THEIR PARAMETERS OF
ENTROPY AND EXCLUDED VOLUME
Polymer
M x 10 -a
[t/]0, ma/kg
H
K
qzx
1270 360 92 4400 1560 1050 620 765 900 715 600 570 360 213
0.089 0.047 0'023 0"171 0.100 0.083 0.062 0.080 0.045 0.038 0"034 0"030 0.023 0.018
8'2 2'8 0"7 40"0 9"09 6'06 4"59 6'67 2"00 1 "40 1'36 1 "09 0"726 0"342
1 '27 1 "22 1"10 1 "30 1"28 1"26 1 '25 1 "25 1"26 1"25 1"24 1"21 1'18 1'14
0'62 0'78 0"89 1"08 0"78 0'77 I "03 0"71 1-33 1 "24 1"41 2'70 3"04 2'45
--~
X IU-
,
m
PS
[51
[131
[141 PHS
PDS
1 "40 1'80 1 '90 1 "86 1 "23 1"22 1'62 1 "62 1 '56 1"52 1"68 2'20 2'47 2"00
1 i .I?
~
°
~
299 -
to3/r~,~ 3.5~.
297 g
1..
4
2954
Z93
8 34
,2 I L
q
i I
4
I
4
L
I
8
(4)
l I
8
I
tz (6)
c, lo -~, kgtm3 FIG. 1
(5)
ff I
I
1 2 3 (1/x '/z + l & z ) , 102 Fro. 2
FIG. 1. Temperature of mixing of solutions T,,,, for PHS (1-3) and PDS (4-6) as a function of their concentrations c. FIG. 2. Reciprocal of the critical temperature of mixing 1/Tc ~for PDS (1) and PHS (2) as a function of the parameter 1Ix ~ + ½x) where x = v M / V ~ .
Intrinsic viscosityof solutions of PS and polyalkylstyrenes
775
Comparison of the ~tI values for the polymers and low molecular weight analogues in reference [7] convincingly showed that this method gives for polymers theoretically substantiated values which must be regarded as standard in determining g/1 by other methods. Therefore, Flory proposed [l ] that the ~'1 values obtained from the temperature dependence of [~/]are well understated because of the incorrect numerical coefficient in the formula (1). In reference [2] on the basis of the exact theory of volumetric effects [11 ] an equation was proposed linking the viscosity coefficient of swelling ~ = [r/]/[r/]o with temperature T, the contour length of the macromolecule L, its rigidity A (length of the Kuhn segment) and the parameter ~q a~-l---0.8K
°'~t, 1
T]A ~
(3)
where K is a tabulated function L/A [12]; floz is the parameter of the excluded volume of a portion of the chain of length I. It must be emphasized that in the theory of far-action for flexible chain polymers the breakdown into portions is arbitrary since the value of the ratio flol/l 2 is invariant [11]. Also valid from this point of view, in particular, is the breakdown into portions in the Flory lattice model [1]: the macromolecule breaks down into x parts such that each of them has the volume -vM/Nx equal to the volume of one molecule of the solvent V,/N, i.e.
x=-vM/Vl
(4)
Accordingly, the contour length may be broken down into x portions of length lx
tx-
LVl
(5)
b-M Equation (1) may be represented in the form \2n]
NR.
\
T]~'
(6)
if it is borne in mind that h2/M=-h2/LML=A/ML, where Mz=Mo/2 is the molecular mass of unit length; Mo is the molecular mass of the monomer unit; 2 is its length in the conformation stretched to the limit. Comparison of expressions (3), (5) and (6) shows 2 2 that the invariant flol/l 2 =flox/l~, = -v- 2 M~,/NVI and the parameter of the excluded volume flox on breakdown of the macromolecule, according to the Flory model, is numerically equal to the volume of the solvent molecule V1/N, which is natural. In the light of all this we propose for the determination of the entropic parameter ~tl the use of the equation H A~N Va ~" -- [q]o (~n)~O"SKL~-62M~ ' (7) which follows from relation (3) differing from the Flory equation in the numerical
S. YA. MAGARn( et al.
776
coefficient 3s/2/0"8 K ~ 5, and also the form of the functional dependence of the swelling coefficient in the left-hand part. Here, the viscosity swelling coefficient eqa is used and not the dimensional e2 =R2/R g, where/~2 and/~g are the mean square radius of the swollen and unperturbed macromolecule determined from the asymmetry of light scatter. t) /[r/] In equation (7) instead of ~a _ 1 is substituted the value H = ( ~ 1- - O T o ,equalto the initial slope of the experimental dependence of [r/] on the parameter 1 - O/T.
[ql,"s/l~9 0.035
a
~
o o o
0 o
1 1 2 / 1
t)
l
0025
[
[ .
o.os
o oq
.
.
.
.
.
. o.o5
,
1_
z-o/r
olo
F~a. 3. Instrinsic viscosity [~/]as a function of the parameter I - O/Tfor PDS solutions in the mixture M E K : BEK = 1 : 1.24 (a) and PHS in MEK (b). The Table indicates the treatment of the published data from formula (7) taking into account the fact that for PS A = 2 0 x 10 -1° m, ~=0.93 x 10 -3 ma/kg, ML=104/2"52 x x10-1°=41"27x101°. The mean value V1=0.9+0.2 obtained well agrees with the magnitude p'l determined from the molecular-mass function of Tcr. In considering the data on the temperature dependence of [r/] for the polyalkylstyrenes (the initial slopes in Fig. 3a, b) it is important to bear in mind the presence in them of quite long side chains. The ratio of the contour lengths of the latter to the distance between neighbouring points of their attachment to the main c h a i n / z = 3 (for PHS) and 5 (for PDS). This leads to further far action and may be taken into account in two ways. Firstly, the macromolecules of the polyalkylstyrenes may be regarded as regular comb-like chains consisting of infinitely thin radicals of the main c h a i n - P S and side alkyi radicals. In Flory's lattice model only the volumetric fraction occupied in solution by the polymer molecules, irrespective of their architecture is of significance. Therefore, on breaking down of the macromolecule into portions the collision of which produces a far action it is necessary to consider the total contour length of the comb-like macromolecule LtotaI which is evidently equal to Ltotai=L(/t+l). Consequently, taking into account equation (5), formula (7) must be supplemented by the multiplier (It+ 1)3/2 which in the case of the linear PS polymer is equal to unity (/t--0). At the same time, for the experimental determination of the measure of rigidity A = hg/L (degree of coiling
Intrinsic viscosity of"solutions of PS and polyalkylstyrenes
777
of the macromolecule caused by the near action) it is natural to allow only for the contour length of the main chain L. In passing we would note that in comparing the rigidity of two macromolecular chains with different unit molecular mass Mj. the use as measure of rigidity of the magnitude h2/M may lead to an erroneous conclusion unlike comparison of the A values. Additional construction of the dependence of [tl]/M 1/2 on M 1/2 [15] convinced us that in the temperature interval studied PHS and PDS do not change the value A which might have occurred because of their diphilicity [8, 9]. Substitution of the experimental values in formula (7) taking into account the additional multiplier gives the values of ~p,~presented in the Table which, as in the case of PS, well agree with the P't magnitudes obtained from the dependence of Tcr on M. The approach described does not, however, allow one to judge the transverse dimensions of the macromolecules. Secondly, comb-like macromolecules may be modelled by worm-like chains [3] of finite thickness d with the contour length L. If formula (3) is applied to them it is possible to evaluate the diameter d by regarding the collision of the portions of such a chain as the collision of cylinders of length 1. The excluded volume of such a cylinder is proportional to its own volume [16] and the magnitude flo~//1/l 2 obtained experimentally is proportional to d flote1-412
1+
+
d
(8)
However, the proportionality coefficient is a function of the ratio p =lid. The value in parentheses rapidly tends to unity with rise in p and already f o r p = 6 amounts to 1.5. The presence in eqn. (8) of two unknowns p and d does not allow one to determine the latter quantitatively. Only qualitative comparison of the transverse dimensions of the polyalkylstyrenes and PS is possible. It is natural to carry out division of the worm-like chain into portions of length I=A which gives for the three polymers considered roughly an identical value of p. At any rate, p of the polyalkylstyrenes is always smaller than for PS. Therefore, the ratio of the experimentally observed magnitudes flot~ul/l 2 shows the upper limit of the ratio of diameters clpHs/@s<~l'1 for PHS and ~<1.4 for PDS. This evaluation shows that the transverse dimensions of the polyalkylstyrene macromolecules insignificantly exceed those for PS which agrees with the results of other methods for PDS [9] and indicates the moderate rigidity o f the side alkyl chains. In conclusion, we would emphasize that from the temperatme dependence of [r/] only one thermodynamic parameter-~u~ can be determined. Determination of the other parameter O as was done in references [4, 5] is incorrect since to construct the dependence of a s - c~3 (or %3- 1 ) on l I T it is necessary to know the magnitude [r/]0, i.e. to determine in advance O by another method. This predetermines the point of intersection of the straight line 1 with the axis I/T (Fig. 3).
Translated by A. CRozY
778
D . P . KIRYUKHINet aL
REFERENCES 1. P. J. FLORY, Principles of Polymer Chemistry. N. Y., 1953 2. S. Ya. MAGARIK and G. M. PAVLOV, Vysokomol. soyed. A17: 1691, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 8, 1943, 1975) 3. S. Ya. MAGARIK, G. M. PAVLOV and G. A. FOMIN, Macromolecules I I : 294, 1978 4. T. G. FOX, Jr. and P. J. FLORY, J. Amer. Chem. Soc. 73: 1909, 1951 5. ldem, 1bid 73: 1915, 1951 6. A. R. SHULTZ and P. J. FLORY, Ibid74: 4760, 1952 7. Idem, Ibid, 75: 3888, 1975 8. V. Ye. ESKIN, D. N. ANDREYEV, I. A. BARANOVSKAYA, N. V. D'YAKONOVA, S. Ya. MAGARIK, N. A. SOLOVSKAYA and A. P. FILIPPOV, Vysokomol. soyed. B26: 845, 1984 (Not translated in Polymer Sci. U.S.S.R.) 9. S. Ya. MAGARIK, D. N. ANDREYEV, I. A. BARANOVSKAYA, N. V. D'YAKONOVA, N. A. SOLOVSKAYA, A. P. FILIPPOV and V. Ye. ESKIN, Ibid A28: 1603, 1986 (Translated in Polymer Sci. U.S.S.R. 28: 8, 1783, 1986) 10. F. CANDAU, C. STRAZIELLE and H. BENOIT, Makromolek. Chem. 170: 165, 1973 11. H. YAMAKAWA, Modern Theory of Polymer Solutions. N. Y., 1971 12. H. YAMAKAWA and W. H. STOCKMAYER, J. Chem. Phys. 57: 2843, 1972 13. G. C. BERRY, I bid46: 1338, 1967 14. A. YAMAMOTO, M. FUJII, G. TANAKA and H. YAMAKAWA, Polymer J. 2: 799, 1971 15. W. H. STOCKMAYER and M. FIXMAN, .L Polymer Sci. C, 1,137, 1963 16. A. YSIHARA and T. HAYASGIDA, J. Phys. Soc. Japan 6: 46, 1951
Polymer ScienceU.S.S.R.Vol. 29, No. 4, pp. 778-784, 1987 Printed in Poland
0032-3950/87 $10.00+ .00 © 1988Pergamon Press ple
RADIATION-POLYMERIZATION OF HEPTYLMETHACRYLATE IN PRESENCE OF BUTADIENE-NITRILE RUBBER* D. P. KIRYUKI-IIN, A. I. BOL'SHAKOV an d I. M. BARKALOV Department of the Institute of Chemical Physics, U.S.S.R. Academy of Sciences
(Received 14 August 1985) With increase in the initial concentration of SKN-18 in its composite with heptylmethacrylate auto-acceleration of tile polymerization process shifts to the region of shorter 7-radiation times and for a content of 60 wt. ~ of the rubber polymerization of the monomer proceeds instantly in conditions close to those of the gel effect. The mixed character of termination of the polymer chains is observed and at the final stage of post-polymerization at 295 K linear termination predominates. The rate constant of growth of the polymer chains in the interval 170-180 K has been determined: kp = 2 x 10-13 e x p ( - 6000/R T) cm3/sec. Introduction of small additions of the monomethacrylic ester of ethylene glycol (crosslinking agent) raises the rate of the process. * Vysokomol. soyed. A29: No. 4, 703-708, 1987.