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Visco-elastic properties of linear polymers and their mixtures with narrow molecular weight distribution
1194
¥U. G. Y~OVSX~ 6t a/.
Table 6 gives the results of determin~ions of the characteristics of some OAS specimens. On comparing data on the composition of the reaction mixtures obtained at the same time at temperatures 110 and 120 ° it is seen that a 10 ° rise in temperature leads to a marked reduction in the concentration of initial compounds (3 fold reduction) and "dimer" (~ 2.2 fold reduction); the number of terminal P and D units (in fi-mers, where fi~2) varies only slightly, but the concentration of central P and D units is doubled, and the M-W is increased accordingly. The ltTmlx values and degrees of conversion are in good agreement with the results obtained by other methods (chemical analysis, ebullioscopy), which points to the trustworthiness and reliability of the analytical procedures developed on the basis of NMR spectroscopy. Translated by R. J. A. ~-IENDRY REFERENCES 1. I. Ys. SLONIM, L. M. BOLOTINA, Ira. G. URMAN, L. Ye. REITBURD, A. Kh. BULAI a n d M. M. GOL'DER, Vysokomo]. soyed. B22: 644, 1980 (Not translated in Polymer Sci. U.S.S.R.)
PolymerScienceU.S.S.R.Vol. 24, No. 5, pp. 1194-1204,1982 Printed in Poland
0082-8950182/051194-11$07.50/0 © 1983 Pergamon Pros Ltd.
VISCO-ELASTIC PROPERTIES OF LINEAR POLYMERS AND THEIR MIXTURES WITH NARROW MOLECULAR WEIGHT DISTRIBUTION * Yu. G. ¥A~OVSKII, G. V. VINOGRADOVand L. I. IvA~ovA A. V. Topchiyev Institute of Petrochemical Synthesis, U.S.S.R. Academy of Sciences
(Received 14 Jmu~ry 1981) A study was made of visco-elastic, dynamic characteristics of mixtures based on 1,4-polybutadiencs of narrow molecular weight distribution (MWD) with different molecular weights of the matrix a n d additive (from 104 to 106) in the range of low concentrations of the high molecular weight component. Concentration dependences were determined for initial viscosity, the initial coefficient of high-elasticity a n d equilibrium oompliance. I t v ~ s shown t h a t the relative variation of components of the dynamic modulus of the initial mstrix increases with a n increase in MW of the additive and decreases with an increase in MW of the matrix. I t was established that for m i n i m u m
* Vysokomol. coyed. A~4: No. 5, 1057-1065, 1982.
Viseo-elastic properties of linear polymers
1195
oonoontrations of the high moloou]~_r weight component in a low molooular weight mata~ speolal features in the bel~viour of the latter are determined by properties of the viseo-elastic medium. Characteristic values of elastic moduli and the coeffioient of high-elasticity of mixtures (i.e. systems of maximum dilution) were calculated, when the medium is not only viscous, but also elastic. ONE of the most important problems now facing theology is the description of the visco-elastie behaviour of high-molecular weight polymers in a wide range of variation of rates of action and temperature. I t is known [1-4] that special features of visco-elastic behaviour are determined first of all b y molecular parameters such as MW and MWD. One of the most convenient and informative experimental methods of investigating relaxation properties of polymers is the dynamic method, when the behaviour of the system is studied under conditions of cyclic low-amplitude deformation. Using a fairly wide range of variation of the frequency of action and temperature, it is possible to observe in this case special features of the behaviour of the system in a very wide range of properties. Dynamic characteristics are essential to verify various theories. It is important that the behaviour of materials with constant structure is evaluated in dynamic experiments. Insufficiently accurate description available of the distribution of long relaxation times of the system, using well-known theories [5], makes it necessary to develop further theoretical concepts and new experimental data. An explanation is given [6, 7] of monomolecular approximation and the concept of microvisco-elasticity is formulated on this basis, according to which the motion of macromolecules among themselves and the solvent, if it exists, is equivalent to motion n o t in a viscous, b u t in a visco-elastic medium. Characteristics of this effective visco-elastic medium (micro-elasticity) do not agree with characteristics of visco-elasticity of the entire system as a whole (maero-visco-elasticity). CHARACTERISTICS
Additive concentration, %
OF
M ~&__ -M
0.125 0.25 0-5 1.0 3.0 5-0 7.0 10.0 20.0
PB
m__
v
--
A N D C O M P O S I T I O N S OF B I I q A R Y M I X T U R E S
1X
Mixture M~=5X 105
105
,--lX10 1 × 10 ~ M , m__
Bx
EL
B~
E~ --
M ~&__ - - 1 X 10 6
] 10 ~ M vra= l X 1 0
--
A 1
A2 A3 A4
4 M'~v:IX
12.ASED O N T H E M [
4 M ~m _ _- - 1 X 106
B1
I
D1
B2 B3 B4
I
B5 Be
A5
B8 B4
E3
Ae A7
B~
__
.
B 7
Be
-
1
-
t
D~ D. D4 D5 Ds
zVote. M y• - - M W o f a d d i t i v e M ,m - ~ W o f t h e m a t r i x . W h e n M ,m= 1 x 10 a n d i x 10 ~, #. ~ 2"52 x 10 a n d 3 × 105 P a . se¢
realmetively.
Yu. G. Y ~ o v s ~ z
1196
el al.:
One of the experimental confirmations of the validity of this concept is its successful application to describing visco-elastic properties of polymer mixtures. In fact, assuming monomolecular approximation it is natural to assume in this case that one of the components of the mixture in relation to macromolecules of the other component is a medium, which should be regarded as visco-elastic. The simplest example of this system is the mixture of two different linear polymers or a mixture of two fractions of the same linear polymer of different MW. Rheological investigations of similar systems represent one form of studying the type of interaction of maeromolecules with the polymeric environment. This study deals with visco-elastic properties of flexible-chain linear polymer mixtures of different MW with narrow MWD in the range of low concentrations of additives. Polybutadionos (PB) obtained b y anionic polymerization and having relatively low MWD ( M w / M ~ <~1-2) were chosen for investigation. Samples contained a n a p p r o x i m a t e l y equal amount of c/s- and trans-isomors { ~ 45~o), the content of 1,2 structures being 8-10°~. Initial samples had a value of M = I × 104, 1 × l 0 s, 5 × 106 and 1 × 106. Binary mixtures of these samples wore prepared b y joint solution in benzene and b y the addition of a tfighmolecular weight component to the low.molecular weight one. Compositions of mixtures examined are tabulated.
~gG:pa 6 , I)qO.
2,
'N: Z 0-
0 0
1
2
3
1o9 m , sec "I
0
1
2 J log m, sec-1
-2
0
2 l ~ r.e,sec-~
FIG. 1. Frequency dependences of moduli G' and G" for mixtures on the concentration of the high-molecular weight component: a (series A): •--0; 2--0.125; 3--0.25; 4--0.5; 6-- 1.0; 6--5"0; 7--10.0; 8--20.0; 9--100%; b (series B): 1--0; 2--0.5; 3--1.0~ 4--5.0~/o; v (series C): 1 - - 0 ; 2 - - 0 . 1 2 5 ; 3--0.25; 4--0.5; 5--1.0; 6--5.0; 7~10.0; 8--20.0~o.
Visco-elastic properties of linear polymers
119T
Experiments were carried out in a device used for dynamic investigations of polymers ("mechanical spectrometer" [8]), operated under conditions of forced nonresonant vibrationa in the range of angular frequencies co of 10-3 to 3 x 103 sec -1. Components of the complex dynamic shear modulus-elasticity modulus G' and loss modulus G" were determined. Figure 1 shows frequency dependences of the elasticity modulus G' and loss modulus G" for mixtures based on P B with M = 1 x 104 (matrix) and with additions of high-molecular weight P B with M--~ 1 x 105, 5 x 105 and 1 x l0 s. MW ratios of the initial sample and additives are 10, 50 and 100, respectively. Initial viscosities of the initial sample and additives differed, being 1.2× 104; 7 X 105 and 1.25 x 107. The dependence on rate of G' (~) and G" (co) for the initial P B sample with ~ / ~ 1 x 104 is mainly significant in the Figures. In the entire frequency range examined curves of G'(~o) and G"(o~) show a practically continuous increase (a weak inflexion is only seen on curves of G'(~o). The type of variation observed in dynamic characteristics is typical of polymers with a fairly low MW, for which high-elastic properties are very moderately expressed. I t is well known that this is typical of polymers with M < 5 ~/c, where Me is the critical MW. For P B M c ~ 6000, i.e. for a sample with M-~ 1 x 104 the ratio of M / M e < 2. Figure 1 indicates that according to MW and the concentration of the additive, both qualitative and quantitative variations are observed in the dependences derived. First, a finite zone (flow range) is achieved for all dependences with low frequencies. Here the value of G" ~ and G ' ~ 2. Initial viscosities of mixtures G" G' ~0~ lira ~ and the initial coefficient of high-elasticity A°-~ lira - - m a y be ~-~0
CO
,~0
easily calculated in this range. I t is seen that the higher the ratio of initial viscosities of initial components, the more markedly values of G' and G" v a r y with concentration in the finite zone, the elasticity modulus being the most sensitive characteristic here. I t should be noted t h a t properties show a particularly sudden chage in the range of fairly low Concentrations (~ 1%) of the high-molecular weight component. Values of G' for mixtures A, B and C, on changing concentrations from 0 to 1% of the high-molecular weight additive, v a r y 1.2; 40 and 25,000 times, respectively, while values of G " - - I , 2, 2.5 and 4-fold respectively, i.e. to a much slighter extent. With an increase in the concentration and MW of the high-molecular weight, additive the gradient of curves G'(eo) begins to vary and inflexio~ls appear on them and then, with a higher additive content a plateau is formed, which characterizes transition into the high-elastic state. With m a x i m u m frequencies curves G'(eo) and G"(o~) show a sudden increase, which is due to transition of the system to a "side-like" state. Let us now exami~_e a series o f curves D a d E for mixtures, in which the initial sample-matrix has a value of M = 1 x 105 and additives have a~ value o f M~-5 X 105 and 1 x 10 e, respectively. Initial viscosity ratios of the matrix and additive in this case are 5 . 8 x 1 0 and 1-05x104 (Fig. 2a, Table).
1198
Yu. G. Y~ovs~u e~a/.
In contrast with PB with M = I x 1 0 4 ibr an initial sample of mixtures of this series, the ratio of M/Mc=16 and it shows all signs of a high-molecular weight polymer, i.e. tL~st of all a clear plateau on the curve of G'(co) and a maxi m u m and minimum on G"(~), which corresponds to achieving the high-elastic state. The addition to the initial sample of high-molecular weight additives of ~ifferent concentration changes the gradient of curves G'(o~) and G"(co) in the finite zone and pl~duces inflexions in the transition range to the high-elastic state. As with samples A, B, C the addition of a high-molecular weight component has a more considerable effect on the dependence of G'(co) in the finite zone, however, the scale of variation of the value of G' is much lower than in a previous series of samples. For mixture E, for example, G' and G" change 20 and 2.5-fold, respectively. Results in Figs. 1 and 2~ indicate that the variation in visco-elastic characteristics of polymer mixtures, according to MW of the matrix and additive a n d concentration, is rather complex. To explain the effect of MW of the matrix and MW of the additive on visco-elastic properties of binary mixtures and the ~tifferences of these systems from the bchaviour of polymer solutions, viscoelastic characteristics of PB solutions with ~ f ~ l × l0 s were measured in good and poor solvents, i.e. ~-methylnaphthalene (~-MN) (t/=2.5×10-sPa.sec) and cetane (~=3.95× 10 -8 Pa.sec), respectively. Results of these measurements are given in Fig. 2b. I t can be seen that results obtained for solutions in different solvents are similar from a qualitative point of view (compare curves 1, 2 and 3 ~nd 4). Quantitatively, initial viscosities are 3 times lower in a poor solvent for a 5 ~ solution and 10 times lower for a 2 ~ solution. This difference is in satisfactory agreement with results in the literature [9], from which it follows that for concentrated solutions of flexible-chain polymers the type of solvent has a practically negligible effect on viscosity characteristics. Figure 2c shows the dependence of G'(co) and G"(co) for systems with different matrices, but identical (5%) content of high-molecular weight additive (PB) with M - ~ 1 × l0 s. I t is clear ~ t MW of the matrix has a decisive effect on the type of dependence derived; greatest changes are observed in absolute values of ~iynamic characteristics for the elasticity modulus. I t is also important that the type of curve change, which is apparently, due to the form of molecular interaction in these systems, or the ratio between micro- and macro-viscoelasticity, which determines molecular interaction. I n the case of a purely viscous matrix curves resemble the Rouse dependencse. In the case of a visco, elastic matrix of fairly low MW the system behaves as a tdgh-polymer; there is a range of fluid state, a ldatcau and transition to the skin-like stat~. On increasing MW of the matrix dependences are of a type observed for polymer mixtures--there isa break on cur~es G'(~o)and (~"(co) in the range of low frequencies a a d the maxi m u m and minimum coincide, with m~ximum values for PB with M - ~ I × 105 ~n the range of high freq~tencies. Figure 2d indicates that the most difference in the curves is observed for the
a
b [o9 4-
2
7
I
2
I
I
I
I
t ,
0
Io91 P a
1
~9 ~ ,
I
I
[
I
j
6
0 2 -2
iogG.,ea
I
I i 2 !o9 , ~ , s e c "I
0
C
0
2 l o9
re,see"
_
d to9 G'~pe
2
l~jo',pa
0 -2
0
l~
2 m ,sec "I
1 -2
I
I 0
I
I 2
I
lo 9 w, sec "1
FIG. 2. F r e q u e n c y dependences of m o d u l i G' a n d G" for m i x t u r e s of series D w i t h different c o n c e n t r a t i o n s of t h e high-molecular weight c o m p o n e n t (a), for various solutions of P B w i t h M = I × l 0 s (b), for systems w i t h different M W of m a t r i c e s (c), for m i x t u r e s ba~od on P B w i t h M = I × 104 w i t h different M W of the high-molecular weight a d d i t i v e (d). a: •--0; 2--0.125; 3--0.25; 4--0.5; 5--1.0; 6--3.0; 7 - - 5 - 0 % ; b: 1 - - 2 % solution in eotane; 2 - - 2 % solution in a-MN; 3 - - 5 % solution in cotane; 4 - - 5 % solution in a-MN; c: 1 - - c o t a n o ; 2 - - ~ - M N ; 3--PB with M=l×104; 4 - - P B w i t h M - - l × 1 0 5 ; d: 1 - - M ~ l × 1 0 4 ; 2--M=l×10s; 3-M = 5 × 105; 4--~i----1 × 108 .
1200
Y~. G. Y~_~OVSKIIe$ a/.
dependence o'f G'(eo); the higher the MW of the additive, the more marked this difference. For a P B additive with M = - I × 1 0 6 dependences show a clearly expressed range of high-elasticity. Dependences of G"(co) in this case show a particularly marked variation.
l°g#o,Pa'sec
o..o.~
q ~C ~
5
a
b
5
#
1°9A°,Pa'$ecz 3 G
J
//" /
' o
--1
o l'/' I
o
I
I. zogc,%
I
-I
o
I
I
I logo,%
FxG. 3. Dependence on concentration of the high-molecular weight component of maximum Newtonian viscosity t/o (a) and of the initial coefficient of high-elasticity A~ (b). a: 1--PB with M = l × 10~ in cetane; 2--same in ~-MN; 3-6--series A, B, C, E, respectively; b: 1-3series A, C and E, respectively. Summarizing special features in the behaviour of linear polymer mixtures described in the range of low additive concentrations of one of the components it m a y be concluded t h a t there are enormous qualitative and quantitative differences in visco-elastic properties, particularly in the finite zone. These differences are mainly determined by characteristics of the matrix of the mixture and then, b y MW and concentration of additives introduced. I t is significant t h a t the variation of the parameters described first of all affects dependences of the elasticity modulus on frequency. I t is w e l l - k n o ~ from the literature [1] that in the finite zone (i.e. in the low frequency range, or in the range of long relaxation times) with a change in MW elastic properties of the material, particularly the initial coefficient of high,elasticity A~, changes very suddenly as a function of MW (in proportion to the seventh-eight power), i.e. much more markedly than initial viscosity. Experimental results indicate that elastic properties of the material are, in the end zone, also much more sensitive, compared with viscosity, to molecular heterogeneity of the system. This is particularly clear from a comparison of dependences of ~0(c) and A°(c).
Visco-elastic properties of linear polymers
1201
Figure 3a shows the dependence of T0(c) for PB solutions with M = 1 0 6 in eetane an4 in ~-MN and for polymer mixtures. For solutions the initial viscosity varies in proportion to the square of concentration. This shows satisfactory agreement with results previously derived [9] for PB solutions of the same MW in ~-MN (on curve 2 the upper two points correspond to this, i.e. concentrations of 10 and 15%). For polymer mixtures two groups of dependences of T0(c) may be distinguished. The first group of dependences corresponds to mixtures, for which the matrix has M : 104 (series A, B and C) and indicates that up to given concentrations c~ 0.5% initial viscosity remains practically unchanged and with c > 0.5% the gradient of these dependences increases with an increase in the initial viscosity of the additive (tangent of the gradient varies between 0.7 and 3.0). It should be noted that for concentrated pol)~ner solutions initial viscosity varies according to the fifth power of concentration [10]. The second group is given for mixtures of series E (curve 6). Initial viscosity shows a slight variation with an increase in the concentration of the additive up to c = 1 ~o and then increases in proportion to c°'3. Figure 3b shows dependences of the initial coefficient of high-elasticity A~ on the concentration of the high-molecular weight additive for mixtures type A, C and E. o It can be seen that dependences of A~(c) vary. For mixture A this is a step function A°~~c1"5;for mixtures C and E the dependence shows a break with a concentration of c~0.5 and 1%. When c~0-5% A°~~c2fl in the concentration range studied, where fl is the exponent according to %=f(c). It is important that coefficient A~ varies for all the mixtures according to c to an extent which is twice as high as %(c). It should be noted that, according to a previous study [10], values of A~ ~ cTM for concentrated polymer solutions. 0 Comparison of curves A~(c) and %(c) indicates that when c ~ 0 . 5 % % is practically unaffected by concentration variation, while coefficient A~ changes suddenly in this range. Special features in the variation of A°~(c) and %(c) may, apparently, be a stronger (compared with ordinary solvents) effect of the matrix, i.e. in other words, the specific interaction of the matrix and the high-molecular weight additive. Intrinsic viscosities [~]= lira ~--~0 of mixtures with polymer additives of c~0 r/o"V different MW were calculated from the results. It appeared that [~/]~M °'5, i.e macromolecular conformation of the additive is the same as in a 0-solvent. This conclusion is in agreement with views developed [11], according to which low-molecular weight components in amorphous polymer mixtures are similar to a 0-solvent. A description is given in this paper of measuring the viscosity of PE mixtures of different MW, starting with their oligomers. Furthermore, characteristic values of the initial coefficient of high-elasticity of
1202
Y1y. G. Y~bTOVS~r 6t U/.
the mixtan~ [A °] were calculated. It appeared that [A°]~M 8. This important experimental relation for polymer mixtures with low concentrations of additives of high molecular weight is derived for the first time in this study. After examining the variation of parameters of the system such as initial viscosity and the initial coefficient of high-elasticity, it is interesting to deal with the ratio of these values in mixtures, which may be evaluated from the • 0 0 variation of equilibrium comphance of the system ~=AG/~8. It has been known from studies carried out by Philippoff and Trapeznikov [12, 13] that dilute solutions of high-molecular weight polymers (PIB) may show very high reversible deformations (up to 20,000%). In a later study Graessley [14] pointed out that solutions of high-molecular weight polymers give clearly expressed maxima on the dependence of equilibrium compliance on concentration in the range of low concentrations. OYe'IO"I 100-
50
0
//
3
-
-3
10
-#
3
-'5
5 i
-6
I
0
5
I
0
~£
I0c,% ~.
I
1.0 c~lO ~ZoJ 5
Fro. 4. Dependence of equilibrium compliance of mixtures Ie° on the concentration of the high-molecular weight component in mixture A (1), C (2) and (E) (3). FIe. 5. Determining characteristic values of elasticity moduli for mixtures of series A; when co=l (•); 1.6 (2); 2.5 (3); 4.0 sec-X (4). To develop these views, i t is interesting to compare properties of systems examined, which in the light of studies cited should be regarded as solutions of a high-molecular weight polymer in polymeric and oligomeric solvents. Figure 4 shows the dependence of equilibrium compliance on concentration. It can be seen that in the case of mixture A there is a maximum on the curve
Visco-elastic properties of linear polymors
1203
1°(o) when c~0.5%. For mixtures A and E the maximum is blurred, which is due to closer MW values of the mixed components. The existence of different mechanisms of visco-elastic behaviour of polymer mixtures in various concentration ranges of the high-molecular weight component points to the existence of "critical" concentrations; on exceeding these concentrations the visco-elastic properties of the system change markedly. Critical concentrations corresponding to the initial superimposition of ranges of 1-08 polymer spheres may be determined approximately according to Debye: Car= - -
where [~/] is the intrinsic viscosity of the high-molecular weight component. Calculation shows that the value of ccr for mixtures A, B and C corresponds to 0.5; 0.7 and 1%, respectively, i.e. to approximately the same concentrations, 0 wllere the maximum is observed on the dependence of le(c). Adopting the assessment of critical concentrations proposed, it may be assumed that the dependences shown in Fig, la (curves 1-5) up to concentrations of 0.5% give a description of the behaviour of non-interacting macromolecules of high MW. Special features of their visco-elastic properties are due to interaction with the surrounding polymer matrix, which is interpreted as a visco-elastic medium. It follows from an earlier study [15] that the behaviour of linear polymers diluted to the maximum extent in a solvent, using cyclic low-amplitude deformation, agrees quantitatively with predictions of the Rouge-Zimm theory for good solvents considering average hydrodynamic interaction. The dependence of dynamic characteristics on frequency has a gradient of ½. Characteristic values of elasticity moduli of mixtures were determined for the systems described, i.e. for systems of maximum dilution calculated according to the formula [G']----- lira G'/c [18]. Results of calculation are shown in Fig. 5 coO
for mixture A. It can be seen that with concentrations of c < 0 . 5 % the dependence of G'/c(c) is satisfactorily approximated using a straight line and when c I>0-5 % values of G'/c increase markedly. Characteristic moduli thus calculated indicate that the dependence of [G']=f(~) is close to the dependence of G'(co) for the initial matrix. This is further evidence that in the case of minimum concentrations of the high-molecular weight component in a low-molecular weight matrix special features of the behaviour of the system are determined by properties of the visco-elastic medium. This study therefore gives a generalization for the first time of a well-known extrapolation for polymer solutions to zero concentrations and a calculation of characteristic elasticity moduli and coefficients of high-elasticity for mixtures,. i.e. for the case when the medium is not only viscous, but also elastic.
Translated by E. S~.~R~
1204
Yu. G. Y ~ o v s x ~ I eta/.
REFERENCES 1. G. V. VINOGRADOV, Yu. G. YANOVSKII, A. Ya. M.ALKIN, L. V. TITKOVA, V. V. BA.1L~TCHEYEVA, S. I. SERGEN'KOV, Ye. K. BORISENKOVA, Ye. V. KATSYUTSEVICH and V. V. VOLOSEVICH, Vysokomo]. soyed. A20: No. 11, 2403, 1978 (Translated in Polymer Sei. U.S.S.R. 20: 11, 2701, 1978) 2. S. OI~OGI, T. MASUDA and K. KITAGAWA, Macromolecules 8: 1~o. 2, 109, 1970 3. G. V. VINOGRADOV, Yu. G. YANOVSKII, V. A. TEMNLKOVSKII, V. V. BARANCHEYEVA and K. A. ANDRIANOV, I)okl. AN SSSR 222: No. 4, 855, 1975 4. A. Ya. M A I J £ ~ , G. Zh. ZHANGEREYEVA and M. P. ZABUGINA, Vysokomol. soyed. A16: No. 10, 2360, 1974 (Translated in Polymer Sei. U.S.S.R. 16: 10, 2741, 1974) 5. V. N. POKROVSKY and Yu. G. YANOVSKTI, Rheo]. Aeta 12: No. 4, 280, 1973 6. V. N. POKROVSKII and V. S. VOLKOV, Vysokomol. soyed. A20: No. 12, 2700, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 12, 3029, 1978) 7. V. N. POKROVSKII, V. S. VOLKOV and G. V. VINOGRADOV, Mekhanika polimerov, No. 4, 186, 1977 8. L. P. UL'YANOV, Yu. G. YANOVSKII, V. N. NEIMARK and S. I. SERGEYENKOV, Zavodsk. lab. 39: No. 11, 1402, 1973 9. V. E. DREVAL, A. Ya. M A L K ~ , G. V. VINOGRADOV and A. A. TAGER, Europ. Polymer J. 9: No. 1, 85, 1973 10. G. V. VINOGRADOV, A. Ya. M~T.K1N, Yu. G. YANOVSKII, 1~. K. BLINOVA, S. I. SERGEYENKOV, M. P. ZABUGINA, L. V. TITKOVA, V. G. SHALGANOVA and V. V. BARANCHEYEVA,Europ. Polymer J. 9: No. 11, 1231, 1973 11. L. F. SKALAYEVA Struktura i svoistva polimornykh materialov (In: Structure and Properties of Polymer Materials). p. 95, Zinatne, Riga, 1979 12. W. pH[LIPPOFF, Viskosit/it der Kolloide, T. Steinkoff, Dresden, 1942 13. A. A. TRAPEZNIKOV, Dotd. AN SSSR 155: No. 2, 430, 1964 14. W. W. GRAESSLEY, Advances Polymer Sci. 16: No. 1, 89, 1974 15. R. M. JOHNS01~, J. L. SCHRAG and J. D. FERRY, Polymer Japanese 1: No. 6, 742, 1970
¥U. G. Y~OVSX~ 6t a/.
Table 6 gives the results of determin~ions of the characteristics of some OAS specimens. On comparing data on the composition of the reaction mixtures obtained at the same time at temperatures 110 and 120 ° it is seen that a 10 ° rise in temperature leads to a marked reduction in the concentration of initial compounds (3 fold reduction) and "dimer" (~ 2.2 fold reduction); the number of terminal P and D units (in fi-mers, where fi~2) varies only slightly, but the concentration of central P and D units is doubled, and the M-W is increased accordingly. The ltTmlx values and degrees of conversion are in good agreement with the results obtained by other methods (chemical analysis, ebullioscopy), which points to the trustworthiness and reliability of the analytical procedures developed on the basis of NMR spectroscopy. Translated by R. J. A. ~-IENDRY REFERENCES 1. I. Ys. SLONIM, L. M. BOLOTINA, Ira. G. URMAN, L. Ye. REITBURD, A. Kh. BULAI a n d M. M. GOL'DER, Vysokomo]. soyed. B22: 644, 1980 (Not translated in Polymer Sci. U.S.S.R.)
PolymerScienceU.S.S.R.Vol. 24, No. 5, pp. 1194-1204,1982 Printed in Poland
0082-8950182/051194-11$07.50/0 © 1983 Pergamon Pros Ltd.
VISCO-ELASTIC PROPERTIES OF LINEAR POLYMERS AND THEIR MIXTURES WITH NARROW MOLECULAR WEIGHT DISTRIBUTION * Yu. G. ¥A~OVSKII, G. V. VINOGRADOVand L. I. IvA~ovA A. V. Topchiyev Institute of Petrochemical Synthesis, U.S.S.R. Academy of Sciences
(Received 14 Jmu~ry 1981) A study was made of visco-elastic, dynamic characteristics of mixtures based on 1,4-polybutadiencs of narrow molecular weight distribution (MWD) with different molecular weights of the matrix a n d additive (from 104 to 106) in the range of low concentrations of the high molecular weight component. Concentration dependences were determined for initial viscosity, the initial coefficient of high-elasticity a n d equilibrium oompliance. I t v ~ s shown t h a t the relative variation of components of the dynamic modulus of the initial mstrix increases with a n increase in MW of the additive and decreases with an increase in MW of the matrix. I t was established that for m i n i m u m
* Vysokomol. coyed. A~4: No. 5, 1057-1065, 1982.
Viseo-elastic properties of linear polymers
1195
oonoontrations of the high moloou]~_r weight component in a low molooular weight mata~ speolal features in the bel~viour of the latter are determined by properties of the viseo-elastic medium. Characteristic values of elastic moduli and the coeffioient of high-elasticity of mixtures (i.e. systems of maximum dilution) were calculated, when the medium is not only viscous, but also elastic. ONE of the most important problems now facing theology is the description of the visco-elastie behaviour of high-molecular weight polymers in a wide range of variation of rates of action and temperature. I t is known [1-4] that special features of visco-elastic behaviour are determined first of all b y molecular parameters such as MW and MWD. One of the most convenient and informative experimental methods of investigating relaxation properties of polymers is the dynamic method, when the behaviour of the system is studied under conditions of cyclic low-amplitude deformation. Using a fairly wide range of variation of the frequency of action and temperature, it is possible to observe in this case special features of the behaviour of the system in a very wide range of properties. Dynamic characteristics are essential to verify various theories. It is important that the behaviour of materials with constant structure is evaluated in dynamic experiments. Insufficiently accurate description available of the distribution of long relaxation times of the system, using well-known theories [5], makes it necessary to develop further theoretical concepts and new experimental data. An explanation is given [6, 7] of monomolecular approximation and the concept of microvisco-elasticity is formulated on this basis, according to which the motion of macromolecules among themselves and the solvent, if it exists, is equivalent to motion n o t in a viscous, b u t in a visco-elastic medium. Characteristics of this effective visco-elastic medium (micro-elasticity) do not agree with characteristics of visco-elasticity of the entire system as a whole (maero-visco-elasticity). CHARACTERISTICS
Additive concentration, %
OF
M ~&__ -M
0.125 0.25 0-5 1.0 3.0 5-0 7.0 10.0 20.0
PB
m__
v
--
A N D C O M P O S I T I O N S OF B I I q A R Y M I X T U R E S
1X
Mixture M~=5X 105
105
,--lX10 1 × 10 ~ M , m__
Bx
EL
B~
E~ --
M ~&__ - - 1 X 10 6
] 10 ~ M vra= l X 1 0
--
A 1
A2 A3 A4
4 M'~v:IX
12.ASED O N T H E M [
4 M ~m _ _- - 1 X 106
B1
I
D1
B2 B3 B4
I
B5 Be
A5
B8 B4
E3
Ae A7
B~
__
.
B 7
Be
-
1
-
t
D~ D. D4 D5 Ds
zVote. M y• - - M W o f a d d i t i v e M ,m - ~ W o f t h e m a t r i x . W h e n M ,m= 1 x 10 a n d i x 10 ~, #. ~ 2"52 x 10 a n d 3 × 105 P a . se¢
realmetively.
Yu. G. Y ~ o v s ~ z
1196
el al.:
One of the experimental confirmations of the validity of this concept is its successful application to describing visco-elastic properties of polymer mixtures. In fact, assuming monomolecular approximation it is natural to assume in this case that one of the components of the mixture in relation to macromolecules of the other component is a medium, which should be regarded as visco-elastic. The simplest example of this system is the mixture of two different linear polymers or a mixture of two fractions of the same linear polymer of different MW. Rheological investigations of similar systems represent one form of studying the type of interaction of maeromolecules with the polymeric environment. This study deals with visco-elastic properties of flexible-chain linear polymer mixtures of different MW with narrow MWD in the range of low concentrations of additives. Polybutadionos (PB) obtained b y anionic polymerization and having relatively low MWD ( M w / M ~ <~1-2) were chosen for investigation. Samples contained a n a p p r o x i m a t e l y equal amount of c/s- and trans-isomors { ~ 45~o), the content of 1,2 structures being 8-10°~. Initial samples had a value of M = I × 104, 1 × l 0 s, 5 × 106 and 1 × 106. Binary mixtures of these samples wore prepared b y joint solution in benzene and b y the addition of a tfighmolecular weight component to the low.molecular weight one. Compositions of mixtures examined are tabulated.
~gG:pa 6 , I)qO.
2,
'N: Z 0-
0 0
1
2
3
1o9 m , sec "I
0
1
2 J log m, sec-1
-2
0
2 l ~ r.e,sec-~
FIG. 1. Frequency dependences of moduli G' and G" for mixtures on the concentration of the high-molecular weight component: a (series A): •--0; 2--0.125; 3--0.25; 4--0.5; 6-- 1.0; 6--5"0; 7--10.0; 8--20.0; 9--100%; b (series B): 1--0; 2--0.5; 3--1.0~ 4--5.0~/o; v (series C): 1 - - 0 ; 2 - - 0 . 1 2 5 ; 3--0.25; 4--0.5; 5--1.0; 6--5.0; 7~10.0; 8--20.0~o.
Visco-elastic properties of linear polymers
119T
Experiments were carried out in a device used for dynamic investigations of polymers ("mechanical spectrometer" [8]), operated under conditions of forced nonresonant vibrationa in the range of angular frequencies co of 10-3 to 3 x 103 sec -1. Components of the complex dynamic shear modulus-elasticity modulus G' and loss modulus G" were determined. Figure 1 shows frequency dependences of the elasticity modulus G' and loss modulus G" for mixtures based on P B with M = 1 x 104 (matrix) and with additions of high-molecular weight P B with M--~ 1 x 105, 5 x 105 and 1 x l0 s. MW ratios of the initial sample and additives are 10, 50 and 100, respectively. Initial viscosities of the initial sample and additives differed, being 1.2× 104; 7 X 105 and 1.25 x 107. The dependence on rate of G' (~) and G" (co) for the initial P B sample with ~ / ~ 1 x 104 is mainly significant in the Figures. In the entire frequency range examined curves of G'(~o) and G"(o~) show a practically continuous increase (a weak inflexion is only seen on curves of G'(~o). The type of variation observed in dynamic characteristics is typical of polymers with a fairly low MW, for which high-elastic properties are very moderately expressed. I t is well known that this is typical of polymers with M < 5 ~/c, where Me is the critical MW. For P B M c ~ 6000, i.e. for a sample with M-~ 1 x 104 the ratio of M / M e < 2. Figure 1 indicates that according to MW and the concentration of the additive, both qualitative and quantitative variations are observed in the dependences derived. First, a finite zone (flow range) is achieved for all dependences with low frequencies. Here the value of G" ~ and G ' ~ 2. Initial viscosities of mixtures G" G' ~0~ lira ~ and the initial coefficient of high-elasticity A°-~ lira - - m a y be ~-~0
CO
,~0
easily calculated in this range. I t is seen that the higher the ratio of initial viscosities of initial components, the more markedly values of G' and G" v a r y with concentration in the finite zone, the elasticity modulus being the most sensitive characteristic here. I t should be noted t h a t properties show a particularly sudden chage in the range of fairly low Concentrations (~ 1%) of the high-molecular weight component. Values of G' for mixtures A, B and C, on changing concentrations from 0 to 1% of the high-molecular weight additive, v a r y 1.2; 40 and 25,000 times, respectively, while values of G " - - I , 2, 2.5 and 4-fold respectively, i.e. to a much slighter extent. With an increase in the concentration and MW of the high-molecular weight, additive the gradient of curves G'(eo) begins to vary and inflexio~ls appear on them and then, with a higher additive content a plateau is formed, which characterizes transition into the high-elastic state. With m a x i m u m frequencies curves G'(eo) and G"(o~) show a sudden increase, which is due to transition of the system to a "side-like" state. Let us now exami~_e a series o f curves D a d E for mixtures, in which the initial sample-matrix has a value of M = 1 x 105 and additives have a~ value o f M~-5 X 105 and 1 x 10 e, respectively. Initial viscosity ratios of the matrix and additive in this case are 5 . 8 x 1 0 and 1-05x104 (Fig. 2a, Table).
1198
Yu. G. Y~ovs~u e~a/.
In contrast with PB with M = I x 1 0 4 ibr an initial sample of mixtures of this series, the ratio of M/Mc=16 and it shows all signs of a high-molecular weight polymer, i.e. tL~st of all a clear plateau on the curve of G'(co) and a maxi m u m and minimum on G"(~), which corresponds to achieving the high-elastic state. The addition to the initial sample of high-molecular weight additives of ~ifferent concentration changes the gradient of curves G'(o~) and G"(co) in the finite zone and pl~duces inflexions in the transition range to the high-elastic state. As with samples A, B, C the addition of a high-molecular weight component has a more considerable effect on the dependence of G'(co) in the finite zone, however, the scale of variation of the value of G' is much lower than in a previous series of samples. For mixture E, for example, G' and G" change 20 and 2.5-fold, respectively. Results in Figs. 1 and 2~ indicate that the variation in visco-elastic characteristics of polymer mixtures, according to MW of the matrix and additive a n d concentration, is rather complex. To explain the effect of MW of the matrix and MW of the additive on visco-elastic properties of binary mixtures and the ~tifferences of these systems from the bchaviour of polymer solutions, viscoelastic characteristics of PB solutions with ~ f ~ l × l0 s were measured in good and poor solvents, i.e. ~-methylnaphthalene (~-MN) (t/=2.5×10-sPa.sec) and cetane (~=3.95× 10 -8 Pa.sec), respectively. Results of these measurements are given in Fig. 2b. I t can be seen that results obtained for solutions in different solvents are similar from a qualitative point of view (compare curves 1, 2 and 3 ~nd 4). Quantitatively, initial viscosities are 3 times lower in a poor solvent for a 5 ~ solution and 10 times lower for a 2 ~ solution. This difference is in satisfactory agreement with results in the literature [9], from which it follows that for concentrated solutions of flexible-chain polymers the type of solvent has a practically negligible effect on viscosity characteristics. Figure 2c shows the dependence of G'(co) and G"(co) for systems with different matrices, but identical (5%) content of high-molecular weight additive (PB) with M - ~ 1 × l0 s. I t is clear ~ t MW of the matrix has a decisive effect on the type of dependence derived; greatest changes are observed in absolute values of ~iynamic characteristics for the elasticity modulus. I t is also important that the type of curve change, which is apparently, due to the form of molecular interaction in these systems, or the ratio between micro- and macro-viscoelasticity, which determines molecular interaction. I n the case of a purely viscous matrix curves resemble the Rouse dependencse. In the case of a visco, elastic matrix of fairly low MW the system behaves as a tdgh-polymer; there is a range of fluid state, a ldatcau and transition to the skin-like stat~. On increasing MW of the matrix dependences are of a type observed for polymer mixtures--there isa break on cur~es G'(~o)and (~"(co) in the range of low frequencies a a d the maxi m u m and minimum coincide, with m~ximum values for PB with M - ~ I × 105 ~n the range of high freq~tencies. Figure 2d indicates that the most difference in the curves is observed for the
a
b [o9 4-
2
7
I
2
I
I
I
I
t ,
0
Io91 P a
1
~9 ~ ,
I
I
[
I
j
6
0 2 -2
iogG.,ea
I
I i 2 !o9 , ~ , s e c "I
0
C
0
2 l o9
re,see"
_
d to9 G'~pe
2
l~jo',pa
0 -2
0
l~
2 m ,sec "I
1 -2
I
I 0
I
I 2
I
lo 9 w, sec "1
FIG. 2. F r e q u e n c y dependences of m o d u l i G' a n d G" for m i x t u r e s of series D w i t h different c o n c e n t r a t i o n s of t h e high-molecular weight c o m p o n e n t (a), for various solutions of P B w i t h M = I × l 0 s (b), for systems w i t h different M W of m a t r i c e s (c), for m i x t u r e s ba~od on P B w i t h M = I × 104 w i t h different M W of the high-molecular weight a d d i t i v e (d). a: •--0; 2--0.125; 3--0.25; 4--0.5; 5--1.0; 6--3.0; 7 - - 5 - 0 % ; b: 1 - - 2 % solution in eotane; 2 - - 2 % solution in a-MN; 3 - - 5 % solution in cotane; 4 - - 5 % solution in a-MN; c: 1 - - c o t a n o ; 2 - - ~ - M N ; 3--PB with M=l×104; 4 - - P B w i t h M - - l × 1 0 5 ; d: 1 - - M ~ l × 1 0 4 ; 2--M=l×10s; 3-M = 5 × 105; 4--~i----1 × 108 .
1200
Y~. G. Y~_~OVSKIIe$ a/.
dependence o'f G'(eo); the higher the MW of the additive, the more marked this difference. For a P B additive with M = - I × 1 0 6 dependences show a clearly expressed range of high-elasticity. Dependences of G"(co) in this case show a particularly marked variation.
l°g#o,Pa'sec
o..o.~
q ~C ~
5
a
b
5
#
1°9A°,Pa'$ecz 3 G
J
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' o
--1
o l'/' I
o
I
I. zogc,%
I
-I
o
I
I
I logo,%
FxG. 3. Dependence on concentration of the high-molecular weight component of maximum Newtonian viscosity t/o (a) and of the initial coefficient of high-elasticity A~ (b). a: 1--PB with M = l × 10~ in cetane; 2--same in ~-MN; 3-6--series A, B, C, E, respectively; b: 1-3series A, C and E, respectively. Summarizing special features in the behaviour of linear polymer mixtures described in the range of low additive concentrations of one of the components it m a y be concluded t h a t there are enormous qualitative and quantitative differences in visco-elastic properties, particularly in the finite zone. These differences are mainly determined by characteristics of the matrix of the mixture and then, b y MW and concentration of additives introduced. I t is significant t h a t the variation of the parameters described first of all affects dependences of the elasticity modulus on frequency. I t is w e l l - k n o ~ from the literature [1] that in the finite zone (i.e. in the low frequency range, or in the range of long relaxation times) with a change in MW elastic properties of the material, particularly the initial coefficient of high,elasticity A~, changes very suddenly as a function of MW (in proportion to the seventh-eight power), i.e. much more markedly than initial viscosity. Experimental results indicate that elastic properties of the material are, in the end zone, also much more sensitive, compared with viscosity, to molecular heterogeneity of the system. This is particularly clear from a comparison of dependences of ~0(c) and A°(c).
Visco-elastic properties of linear polymers
1201
Figure 3a shows the dependence of T0(c) for PB solutions with M = 1 0 6 in eetane an4 in ~-MN and for polymer mixtures. For solutions the initial viscosity varies in proportion to the square of concentration. This shows satisfactory agreement with results previously derived [9] for PB solutions of the same MW in ~-MN (on curve 2 the upper two points correspond to this, i.e. concentrations of 10 and 15%). For polymer mixtures two groups of dependences of T0(c) may be distinguished. The first group of dependences corresponds to mixtures, for which the matrix has M : 104 (series A, B and C) and indicates that up to given concentrations c~ 0.5% initial viscosity remains practically unchanged and with c > 0.5% the gradient of these dependences increases with an increase in the initial viscosity of the additive (tangent of the gradient varies between 0.7 and 3.0). It should be noted that for concentrated pol)~ner solutions initial viscosity varies according to the fifth power of concentration [10]. The second group is given for mixtures of series E (curve 6). Initial viscosity shows a slight variation with an increase in the concentration of the additive up to c = 1 ~o and then increases in proportion to c°'3. Figure 3b shows dependences of the initial coefficient of high-elasticity A~ on the concentration of the high-molecular weight additive for mixtures type A, C and E. o It can be seen that dependences of A~(c) vary. For mixture A this is a step function A°~~c1"5;for mixtures C and E the dependence shows a break with a concentration of c~0.5 and 1%. When c~0-5% A°~~c2fl in the concentration range studied, where fl is the exponent according to %=f(c). It is important that coefficient A~ varies for all the mixtures according to c to an extent which is twice as high as %(c). It should be noted that, according to a previous study [10], values of A~ ~ cTM for concentrated polymer solutions. 0 Comparison of curves A~(c) and %(c) indicates that when c ~ 0 . 5 % % is practically unaffected by concentration variation, while coefficient A~ changes suddenly in this range. Special features in the variation of A°~(c) and %(c) may, apparently, be a stronger (compared with ordinary solvents) effect of the matrix, i.e. in other words, the specific interaction of the matrix and the high-molecular weight additive. Intrinsic viscosities [~]= lira ~--~0 of mixtures with polymer additives of c~0 r/o"V different MW were calculated from the results. It appeared that [~/]~M °'5, i.e macromolecular conformation of the additive is the same as in a 0-solvent. This conclusion is in agreement with views developed [11], according to which low-molecular weight components in amorphous polymer mixtures are similar to a 0-solvent. A description is given in this paper of measuring the viscosity of PE mixtures of different MW, starting with their oligomers. Furthermore, characteristic values of the initial coefficient of high-elasticity of
1202
Y1y. G. Y~bTOVS~r 6t U/.
the mixtan~ [A °] were calculated. It appeared that [A°]~M 8. This important experimental relation for polymer mixtures with low concentrations of additives of high molecular weight is derived for the first time in this study. After examining the variation of parameters of the system such as initial viscosity and the initial coefficient of high-elasticity, it is interesting to deal with the ratio of these values in mixtures, which may be evaluated from the • 0 0 variation of equilibrium comphance of the system ~=AG/~8. It has been known from studies carried out by Philippoff and Trapeznikov [12, 13] that dilute solutions of high-molecular weight polymers (PIB) may show very high reversible deformations (up to 20,000%). In a later study Graessley [14] pointed out that solutions of high-molecular weight polymers give clearly expressed maxima on the dependence of equilibrium compliance on concentration in the range of low concentrations. OYe'IO"I 100-
50
0
//
3
-
-3
10
-#
3
-'5
5 i
-6
I
0
5
I
0
~£
I0c,% ~.
I
1.0 c~lO ~ZoJ 5
Fro. 4. Dependence of equilibrium compliance of mixtures Ie° on the concentration of the high-molecular weight component in mixture A (1), C (2) and (E) (3). FIe. 5. Determining characteristic values of elasticity moduli for mixtures of series A; when co=l (•); 1.6 (2); 2.5 (3); 4.0 sec-X (4). To develop these views, i t is interesting to compare properties of systems examined, which in the light of studies cited should be regarded as solutions of a high-molecular weight polymer in polymeric and oligomeric solvents. Figure 4 shows the dependence of equilibrium compliance on concentration. It can be seen that in the case of mixture A there is a maximum on the curve
Visco-elastic properties of linear polymors
1203
1°(o) when c~0.5%. For mixtures A and E the maximum is blurred, which is due to closer MW values of the mixed components. The existence of different mechanisms of visco-elastic behaviour of polymer mixtures in various concentration ranges of the high-molecular weight component points to the existence of "critical" concentrations; on exceeding these concentrations the visco-elastic properties of the system change markedly. Critical concentrations corresponding to the initial superimposition of ranges of 1-08 polymer spheres may be determined approximately according to Debye: Car= - -
where [~/] is the intrinsic viscosity of the high-molecular weight component. Calculation shows that the value of ccr for mixtures A, B and C corresponds to 0.5; 0.7 and 1%, respectively, i.e. to approximately the same concentrations, 0 wllere the maximum is observed on the dependence of le(c). Adopting the assessment of critical concentrations proposed, it may be assumed that the dependences shown in Fig, la (curves 1-5) up to concentrations of 0.5% give a description of the behaviour of non-interacting macromolecules of high MW. Special features of their visco-elastic properties are due to interaction with the surrounding polymer matrix, which is interpreted as a visco-elastic medium. It follows from an earlier study [15] that the behaviour of linear polymers diluted to the maximum extent in a solvent, using cyclic low-amplitude deformation, agrees quantitatively with predictions of the Rouge-Zimm theory for good solvents considering average hydrodynamic interaction. The dependence of dynamic characteristics on frequency has a gradient of ½. Characteristic values of elasticity moduli of mixtures were determined for the systems described, i.e. for systems of maximum dilution calculated according to the formula [G']----- lira G'/c [18]. Results of calculation are shown in Fig. 5 coO
for mixture A. It can be seen that with concentrations of c < 0 . 5 % the dependence of G'/c(c) is satisfactorily approximated using a straight line and when c I>0-5 % values of G'/c increase markedly. Characteristic moduli thus calculated indicate that the dependence of [G']=f(~) is close to the dependence of G'(co) for the initial matrix. This is further evidence that in the case of minimum concentrations of the high-molecular weight component in a low-molecular weight matrix special features of the behaviour of the system are determined by properties of the visco-elastic medium. This study therefore gives a generalization for the first time of a well-known extrapolation for polymer solutions to zero concentrations and a calculation of characteristic elasticity moduli and coefficients of high-elasticity for mixtures,. i.e. for the case when the medium is not only viscous, but also elastic.
Translated by E. S~.~R~
1204
Yu. G. Y ~ o v s x ~ I eta/.
REFERENCES 1. G. V. VINOGRADOV, Yu. G. YANOVSKII, A. Ya. M.ALKIN, L. V. TITKOVA, V. V. BA.1L~TCHEYEVA, S. I. SERGEN'KOV, Ye. K. BORISENKOVA, Ye. V. KATSYUTSEVICH and V. V. VOLOSEVICH, Vysokomo]. soyed. A20: No. 11, 2403, 1978 (Translated in Polymer Sei. U.S.S.R. 20: 11, 2701, 1978) 2. S. OI~OGI, T. MASUDA and K. KITAGAWA, Macromolecules 8: 1~o. 2, 109, 1970 3. G. V. VINOGRADOV, Yu. G. YANOVSKII, V. A. TEMNLKOVSKII, V. V. BARANCHEYEVA and K. A. ANDRIANOV, I)okl. AN SSSR 222: No. 4, 855, 1975 4. A. Ya. M A I J £ ~ , G. Zh. ZHANGEREYEVA and M. P. ZABUGINA, Vysokomol. soyed. A16: No. 10, 2360, 1974 (Translated in Polymer Sei. U.S.S.R. 16: 10, 2741, 1974) 5. V. N. POKROVSKY and Yu. G. YANOVSKTI, Rheo]. Aeta 12: No. 4, 280, 1973 6. V. N. POKROVSKII and V. S. VOLKOV, Vysokomol. soyed. A20: No. 12, 2700, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 12, 3029, 1978) 7. V. N. POKROVSKII, V. S. VOLKOV and G. V. VINOGRADOV, Mekhanika polimerov, No. 4, 186, 1977 8. L. P. UL'YANOV, Yu. G. YANOVSKII, V. N. NEIMARK and S. I. SERGEYENKOV, Zavodsk. lab. 39: No. 11, 1402, 1973 9. V. E. DREVAL, A. Ya. M A L K ~ , G. V. VINOGRADOV and A. A. TAGER, Europ. Polymer J. 9: No. 1, 85, 1973 10. G. V. VINOGRADOV, A. Ya. M~T.K1N, Yu. G. YANOVSKII, 1~. K. BLINOVA, S. I. SERGEYENKOV, M. P. ZABUGINA, L. V. TITKOVA, V. G. SHALGANOVA and V. V. BARANCHEYEVA,Europ. Polymer J. 9: No. 11, 1231, 1973 11. L. F. SKALAYEVA Struktura i svoistva polimornykh materialov (In: Structure and Properties of Polymer Materials). p. 95, Zinatne, Riga, 1979 12. W. pH[LIPPOFF, Viskosit/it der Kolloide, T. Steinkoff, Dresden, 1942 13. A. A. TRAPEZNIKOV, Dotd. AN SSSR 155: No. 2, 430, 1964 14. W. W. GRAESSLEY, Advances Polymer Sci. 16: No. 1, 89, 1974 15. R. M. JOHNS01~, J. L. SCHRAG and J. D. FERRY, Polymer Japanese 1: No. 6, 742, 1970