Investigation of the viscosity of dilute solutions of mixed polymers

Viscosity of dilute solutions of mixed polymers 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

1839

R. P. KAMBOUR, F. E. KARASZ and J. H. DANE, J. Polymer Sci. 4, A-2: 327, 1966 E. T U I ~ K A and W. PRZYGOCKI, Faserforsch. u n d Textiltechn. 18: 91, 1967 L. MAKARUK, J. BOJARSKI and J. P I E N I ~ F . , K , Polymer 13: 341, 1968 W. KOZI~OWSKI, Krystalizacja zeszklonego poliamidu 6 wywotana dziataniem cieczy, Sympozjum Kraj6w RWPG, 1972, IWSS-Lodz B. J. McNULTY, J. Polymer Sci. 7, A-I: 3038, 1969 H. G. ZACH~IANN, Kolloid-Z. u n d Z. ffir Polymere 189: 67, 1963 H. G. ZACHMANN, Makromolek. Chem. 74: 29, 1964; Faserforsch. u n d Textittechn. 18: 427, 1967 H. G. ZACHMANN and W. SHERMANN, Kolloid-Z. und Z. fiir Polymere 241: 916, 1970 E. CALVET and A. PRAT, Microcalorimetry, 1963 J. CHABERT, J. D I ~ S C H , A. BANDERET and J. MEYBECK, J. Text. Inst. 57: T157, 1966 E. BALCERZYK, P. BOIVINET, E. CALVET and K. HEMlaEL, Compt. rend. 256: 3851, 1963 J. H. BRADBURY and J. D. LEEDER, J. Appl. Polymer Sci. 7: 533, 1963 M. PLUTA, Przegl~d WtSk. 19: 261, 1965 T. LOSKE, Methoden der Textilmikroskopie, Stuttgart, 1964

INVESTIGATION OF THE VISCOSITY OF DILUTE SOLUTIONS OF MIXED POLYMERS* V. P. BUDTOV, Yu. B. MO~AKOV, N. V. DUVAKINA and B. E. GELLER Chemistry Institute of the Bashkir Affiliated Branch of the U.S.S.R. Academy of Sciences (Received 9 November 1972) A study was made of the viscosity of solutions of mixed polymer homologues and of incompatible mixtures of polymers in two groups. For the first group of polymers, as well as for the polymer homologues, there is fulfilment of the law of a~lditivity, while for the second group it was found that there were positive and negative deviations of experimentally obtained viscosity values from the calculated values. The experimental results agree well with a theoretical analysis of the viscosity of the solutions of mixed potymer homologues and of the polymers in the first group. For solutions of mixed polymers in the second group anomalies in the relation of viscosity to the composition of the mixtures are due to the formation of supermoleeular structures that have varying stability towards changes in temperature.

II~VESTIGATIO~S of the viscosity of polymer mixtures are of interest to authors from the point of view of solving practical and theoretical problems (for example, determination of the intermoleeular thermodynamic interaction of compatibil* Vysokomol. soyed. 16A: No. 7, 1587-1592, 1974.

1840

V.P. BUDTOVet

al.

ity [1--6]). It has been proposed that qualitative information on the compatibility of polymers should be obtainable by analysis of the concentration dependence of solution viscosity relative to the composition of a mixture of polymers [1]

r/oC

--

c

~-[t/]q-bv~-...,

(1)

where ~ and % are solution and solvent viscosities respectively; c is the total concentration of the polymers. To characterize the viscosity of a mixture of polymers [~/]m it is correct, according to Philippoff [7], to use the formula

[~]m= F X~ [~]~,

(2)

where xt and ~/~ are respectively the weight fraction and intrinsic viscosity of the ith component of a mixture. Formula (2) is valid for non-interacting polymers only. In solutions of mixed polymers which in very dilute solutions are capable of intermolecular interaction (e.g. mixtures of stereoisomers [8]), formula (2) is invalid. It is held by Krigbaum and Wall [1] that for compatible polymers the quantity b in eqn. (1) is equal to

bca~c= (Zx~/~) 2,

(3)

where b~=Kt[~]]~; Ki is Huggin's constant for the ith component characterizing the hydrodynamic and thermodynamic interaction of macromolecules in solution [9-11]. It was assumed that deviations of experimental values of b from the calculated values of bcal6 could provide a basis for determining the compatibility of polymers. It was not made plain, however, which deviations of b from bealc (b>b~ale or b
Viscosity of dilute solutions of m i x e d p o l y m e r s

1841

has to be tak en into account. These processes become more probable in cases of

deterioration in solvent quality [20]. In view of the above considerations there is a need for experimental and theoretical analyses of the problem of the viscosity of dilute solutions, both for mixtures of compatible polymers (e.g. mixtures of polymer-homologues) and for incompatible polymers. EXPERIMENTAL* The substances investigated were fractions of polystyrene (PS-1 w i t h M w ~ 12 × 105, PS-2 w i t h M,~,~2'7 × 10 s and PS-3 w i t h M w ~ 2 - 8 x 106), p o l y m e t h y l m e t h a c r y l a t e (PMMA w i t h M , , = 3 . 1 × 10~), p o l y v i n y l a c e t a t e (PVA-1 w i t h Mw:=5"9× 104 and PVA-2 w i t h M,~ = 4 . 8 × 105), p o l y v i n y l alcohol (PVAle w i t h M , , = 5 . 3 × 104), polyethylene oxide (t)EO w i t h M w = l . 2 × 104) and polyacryloifitrile (PAN w i t h M ~ , = 5 . 7 × 104). A s t u d y was ma~tc of m i x t u r e s of p o l y m e r homologues ( P V A - I - P V A - 2 - m e t h y l ethyl ketone (MEK), P S - 1 - P S - 2 M E K - e t h y l ketone) as well as m i x t u r e s of PS-1 and P M M A in toluene and in M E K , PVAlc-1 and P S - I in M E K , P V A l c and P A N in 55O/o ~queous NaCNS, and P V A and P E O in acetic acid.

3

/ 0

0"5

7

z, ,q/d/ FIG. 1. C o n c e n t r a t i o n dependence of rlsp/c (1-6) and ht tlrel/C (1'-6") for solutions of P S - 3 - P V A - 2 mixtures, t h e ratios of the components being 1.00 : 0.00 (•); 0.75 : 0.25 (2); 0-85 : 0.15 (3); 0.50 : 0.50 (4); 0.25 : 0-75 (5); 0.00 : 1.00 (6) in M E K .

T h e c o m m o n solvents for each pair of p o l y m e r s were " g o o d " for t h e i n d i v i d u a l comp o n e n t s of one or o t h e r m i x t u r e (the H u g g i n ' s constants for the p o l y m e r s in a g i v e n solvent had v a l u e s below 0-5, while the e x p o n e n t s a in t h e M a r k - K u h n - H o u w i n k e q u a t i o n w e r e h i g h e r t h a n 0-5). All t h e Systems, a p a r t from P V A - 1 - P V A - 2 and P S - 1 - P S - 2 were i n c o m p a tible, so t h a t c o n c e n t r a t e d (5-10%) solutions gradually s e p a r a t e d into phases w i t h a preferential c o n t e n t of one or o t h e r polymeric c o m p o n e n t irL each phase [5]. * E. S. E d u a r d t o o k p a r t in t h e e x p e r i m e n t a l work.

1842

V . P . BUDTOV et al.

Solutions for the viscomctric investigations (1-5-0-5 g/dl) were prepared by joint dissolution of weighed portions of the polymers, taken in the required ratios, in a common solvent directly in the calibrated pycnometer. The viseomeVric measurements were carried out in a capillary viseometer at 20 °. The viscosities of the P E O - P V A mixtures were also measured at 30 and 40 °, and those of PVAlc-PAN at 39, 45 and 60 °. I n all eases the flow time of the solvent exceeded 100 sec. The molecular weights of the selected fractions were such as to ensure the absence of any relationship between viscosity and velocity gradient. The values of [q] and of Huggin's constant K were determined from plots of tlsp/c and in tlrel/C vs. concentration c (Fig. 1). The data obtained were averaged. The error in determining [q] was ,~ (1-3)%, and for the constant K ~ (10-20)%. A s m a y be seen f r o m Fig. 2a a n d b, for t h e m i x t u r e s o f p o l y m e r h o m o l o g u e s t h e intrinsic viscosities a n d H u g g i n ' s c o n s t a n t s are linear f u n c t i o n s o f t h e c o m p o s i t i o n o f t h e m i x t u r e s . F o r t h e P S - 1 - P M M A m i x t u r e (Fig. 2c, d) eqn. (2) is K 0.5 a

0 1

K

8"q

2

8

O'3

Cq] 0.!

1.3

e l

3

0.2

A

I

f'8

0.7

dug 1"6 0.9 l.q 0.5 ~

0.~ 0.5

0 z Iz

0.3 ~5

0

0 xI

Ixz

0'5

0 .rr Ixz

FIG. 2. Dependence of K (a, c, e) and [t/] (b, d, f) on composition of the mixture (xl : x2) for PVA-1-PVA-2 (1, 4); PS-1-PS-2 (2, 3, 5, 6); PS-1-PMMA (7, 8, 10, 11); PS-3-PVA-2 (12, 14) and PS-1-PVA-1 (13, 15) in MEK (1, 3, 4, 6, 8, 11, 12-15) and in toluene {2, 5, 7, 10); 9--theoretical dependence of K (x) calculated by formula (7).

satisfied for. [t/], b u t t h e K - v a l u e s (Fig. 2, c u r v e s 7 a n d 8) are c o n s i d e r a b l y h i g h e r t h a n t h o s e c a l c u l a t e d o n t h e basis o f t h e l a w o f a d d i t i v i t y . F o r P S - P V A , P V A l c P A N a n d P V A - P E O m i x t u r e s (Fig. 2, 3) t h e law o f a d d i t i v i t y is n o t fulfilled f o r [t/], a n d c o n s i d e r a b l e n e g a t i v e d e v i a t i o n s o f t h e e x p e r i m e n t a l v a l u e s o f K f r o m t h o s e c a l c u l a t e d on t h e basis o f t h e l a w o f a d d i t i v i t y are o b s e r v e d . Moreo v e r f o r P V A - P E O t h e d e v i a t i o n s o f [t/] f r o m t h e a d d i t i v e v a l u e s (Fig. 3a) d o n o t v a r y as t h e t e m p e r a t u r e rises, w h i l e for P V A l c - P A N (Fig. 3a) in t h e r e g i o n o f h i g h P V A l e c o n c e n t r a t i o n s there" are d e v i a t i o n s o f [~/] f r o m t h e t h e o r e t i c a l v a l u e s , a n d t h e s e d e v i a t i o n s are o n l y slightly t e m p e r a t u r e - d e p e n d e n t , while

Viscosity of dilute solutions of mixed polymers

1843

w i t h high contents of P A N in the m i x t u r e these deviations become less m a r k e d as t h e t e m p e r a t u r e rises, a n d a t 60 ° there is even a change in the sign of deviat i o n s of the e x p e r i m e n t a l [t/] values from the theoretical. /qJ-f~TJc fq]c 0 ~--:

[?l]c

0"1

~Z

#

xl i i /

// ,~×S[ ,

[ ~lI.

d@

d /" /

2.0

/

I'C

/ /_12

0"8

7"2

1"0

~]'~ ~

i I/

0"0 o.qi.

1"2

,< " L -5"i i . , ~ J

.

0

~~I /"./.47

0.1t

t

r 0"5

.,'5>+<2

08

t¢

J

/

O'q

//~

////9 'J

i

¢. e i i

~'/

I

z~ 1 me

0"5 0

0 .r 1 1 me

Fro. 3. Dependence of ([0] [/]]m)/[/l]m(a, c) and (b, d) on composition (x~ : x~) of PVAlc-PAN mixtures in an aqueous 55°,o NaCNS solution (a, b) and of PEO-PVA irt acetic acid (c, d) at 60 (1), 45 (2), 30 (3), 40 (4) and 20° (5). I n t h e light of e x p e r i m e n t a l results one m a y therefore subdivide the incompatible m i x t u r e s of polymers into groups. I n the case of the incompatible polymers m a k i n g up t h e first group the mixing of the polymers has little effect on t h e viscosity of the solutions, and eqn. (2) is satisfied for [~/]. In the case of the second group of p o l y m e r m i x t u r e s there are deviations of [r/] from the values calculated on the basis of formul~ (2). DISCUSSION OF RESULTS

I t was shown in papers [6, 11] t h a t the concentration d e p e n d e n c e of solution viscosity [t/] is d e t e r m i n e d b y intermolecular h y d r o d y n a m i c and t h e r m o d y n a mic interactions. I n the region of low concentrations the solution viscosity is e x p r e s s e d as 1

~--q0 _ [,fl+ ~ 7 ~/0c

c[,712+... '

(4)

1844

V. :P. BUDTOV

et al.

where 7 is a parameter characterizing intermolecular thermodynamic interaction. For a 0-solvent 7 = 0 , and as the solvent quality improves ? rises, tending towards saturation. The value of 7 is related to the "excluded volume" u of the macromolecule [9, ll] u

7=0.5----L(u), v

where v is the volume of the macromolecule, and L (u) is a certain function of u [9]. To obtain a quantitative solution of the problem of the viscosity of a polymer mixture we will assume that intermolecular hydrodynamic interactions do not depend on the type of polymer, and are analogous to hydrodynamic interactions in solutions of a single polymer [16]. All further theoretical relationships and the final results are therefore valid only for mixtures of macromolecules without specific interactions. Let us analyse the behaviour of the first group of mixtures of incompatible polymers. For the viscosity of the polymer mixtures, in view of eqn. (4) and the law of additivity for the viscosity of the components of a mixture, we obtain

/]rel----~X~/Trel= 1 -~-G~Xi [t]]l >{

)<(l+c~xj~[tl],+...)=l+c[tl]md-C2[tl]2m(Km+~)-~...

(5)

For Huggin's constant Km we obtain 1

. . . . .

Km[ff]em=[ff]m ~x,[oJ,K, + ~j- ~ x, xj[~], [q]j (x/1--2Kj--x/1--2K~) 2

(6)

As the second term in eqn. (6) is much lower, for Huggins' constant for a mixture of compatible polymers the following expression is correct: Km -

[/~]m

(7)

This formula gives a method of calculating Km that is similar to that proposed in paper [1] (eqn. (3)) (Fig. 2, curve 9). The parameter g characterizing the deviation fromad ditivity in the behaviour of a system is expressed as

~=[,1]~ ~ ~ x~xj[@ [@ (',/7~TJ-7~J)

(s)

By experimental determination of the values of g, [r]Jm, [r]]], and 7~ one may also find the value of 7ij which characterizes the thermodynamic interaction of heterogeneous polymers. Major difficulties stand in the way of strict solutions of the relationship between ? and the interaction of heterogeneous macromolecules. An equation

1845-

Viscosity of dilute solutions of mixed polymers

for the above relationship may be more easily derived, however, if one assume~ in view of the extensive data in [16] that ? ~ u in "poor" solvents, and that y is practically independent of u in "good" solvents. Krigbaum and Flory [21] investigated the "excluded volume" ua, for a triple mixture of two polymers in relation to the composition of the mixture. Provided that the partial volumes of the polymers were equal, it was found that u T = x l u2 ~ ÷ 2 x ~ x 2 u ~ 2 ÷ x 2 u ~2 2 ,

(9~

where u~ are "excluded volumes" of the components, and ~2

u12: 2

(10)

- - (1 - - Z l o - - Z2o-~ Z 1 2 ) m l m 2 F O0

Here v0 is the molar volume of the solvent; ~ is the partial volume of the polymer; m~, m., -- the mass of the macromolecules; X~k -- Flory-Huggins parameters characterizing the fraction of the chemical potential of the solvent that is dependent on intermolecular interactions; F -- a complex function of size, molecular weight and X~e (for a 0-solvent F = l). For chains with similar thermodynamic flexibility, when at the same time there is no great difference in the molecular weights of the components of a mixture, we obtain ?Z12~

N/Ul12t22

-~ ~.:

~__

(1]).

_ - - _ _ -~

\/(1-2Zlo) (1-2Z~o} /

For a mixture of polymer homologues ZI~=0 and u ~ ~_ \ , u u u 1 2 , while for incompatible polymers u12< \ / u ~ 2 and may even be negative [22, 23]. Using expression (11 ), we obtain for ~,lz 1 -- X10--/~20---Z12

Yx~=w/Yl Y2 , . . . . . . . . . . . . . . V' (1 - - 2Z10) (l --22'20 )

(! 2).

For a mixture of polymer homologues 712= "~/717zand g = 0, while for incompatible polymers v l , < ~/r,~, since ux~< X/Ul~lz. Consequently 6 > 0 , i.e. the viscosity of a mixture of these polymers exceeds that of a mixture of polymer homologues of the same molecular weight. The law of additivity (formula (2)) is valid for the intrinsic viscosity values. of solutions of mixed polymer homologues, and Huggin's constant is calculated by formula (7). As may be seen from Fig. 2a and b, the theoretical and experimental results axe quantitatively in agreement. It is characteristic for solutions of mixed incompatible polymers of the first type that the law of additivity is fulfilled for the intrinsic viscosity values (Fig. 2a, d, P S - I - P M M A in M E K and toluene). This means that in the region of very

1846

v . P . B,TDTOVet al.

lOW concentrations (c -~ 0) the macromolecules of dissimilar p o l y m e r s b e h a v e like isolated Gaussian chains. A t the same time in solutions o f P S - P M M A in M E K there are positive deviations of the K values f r o m those calculated in accordance with formula (7). B y means of these deviations one m a y find t h e value of J, a n d consequently the value of v/}11 7z2--Yi2. The value of Nf~I ~2--~)12 is 0"39 for the s y s t e m P S - P M M A - M E K , and within t h e limits of e x p e r i m e n t a l error, the value in question is i n d e p e n d e n t of c. T h e v a l u e of 712/~/~y2--~0.25, which agrees with theoretical estimates for these solutions of incompatible polymers. The e x p e r i m e n t a l values of b are higher t h a n the theoretical values of be~le. F o r m i x t u r e s of incompatible polymers of the second t y p e ( P V A - P S , P V A P E O and P V A l c - P A N ) there are deviations o f t h e e x p e r i m e n t a l values of [t/] f r o m those c a l c u l a t e d b y formula (2). F o r the same systems one also finds m a r k e d changes in K. Similar e x p e r i m e n t a l results for o t h e r systems are given in papers [1-6]. Similar dependences of [~/] (x) and K (x) characterize the direct and indirect intermolecular contacts in these solutions even in the region of v e r y low concentrations. I t is probable in this case t h a t labile structures m a y appear. I t is interesting to n o t e t h a t the structures formed in solutions of P V A and PVAlc containing small additions of P E O and P A N are t h e r m a l l y stable, while the structures formed in solutions of P E O and P A N with P V A and PVAlc additions are unstable towards changes in t e m p e r a t u r e (Fig. 3). F o r example, structures in solutions of P E O with a PVA addition are b r o k e n down as the t e m p e r a t u r e rises, while structural transitions in solutions of P A N w i t h a PVAlc addition are such t h a t the value of [~/]-[~/]m changes from negative to positive. I t will be necessary to have recourse to other techniques used in the p h y s i c o c h e m i s t r y of p o l y m e r s in order to obtain detailed i n f o r m a t i o n regarding the s t r u c t u r e o f these formations. Translated by R. J. A. HESORY

REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

W. KRIGBAUM and F. WALL, J. Polymer Sci. 5: 505, 1950 N. V. M:IKHAILOV and S. Z. ZELIKMAN, Kolloidn. zh. 19: 465, 1957 B. A. DOGADKIN, V. N. KULEZNEV and S. F. PRYAKHINA, Kolloidn. zh. 21: 174, 1959 V. I. ALEKSEYENKO and I. U. MISHUSTIN, Vysokomol. soyed. 1: 1593, 1959 (Translated in Polymer Sci. U.S.S.R. 2: ]82, 63, 1961) Yu. B. MONAKOV, Dissertation, 1970 B. BOHMER, D. BEREK and S. FLORIAN, Europ. Polymer J. 6: 471, 1970 W. PH]LIPPOFF, Ber. 70: 827, 1937 A. LIQUORI, J. Polymer Sci. 134: 943, 1966 H. JAMAKAWA, J. Chem. Phys. 34: 1360, 1961 J. PETERSON and M. FIX_MAN, J. Chem. Phys. 36: 2516, 1963 ' V. P. BUDTOV, Vysokomol. soyed. 9A: 1511, 1967 (Translated in Polymer Sci. U.S.S.t¢. 9: 7, 1694, 1961) M. FIXMAN, J. Chem. Phys. 23: 1656, 1955 /

Thermophysical chara~teristios of polymers

1847

13. Yu. Ye. EIZNER, Vysokomol. soyed. 3: 748, 1961 (Translated in Polymer Sci. U.S.S.R. 3: 4, 645, 1962) 14. S. WEISSBERG, R. SIMM.A and S. RODHMAN, J. Res. Nat. Bur. Standards 47: 298, 1951 15. V. P, BUDTOV, Vysokomol. soyed. 9A: 2681, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 12, 3034, 1967) 16. V. P. BUDTOV, Vysokomol. soyed. 12A: 1355, 1970 (Translated in Polymer Sci. U.S.S.R. 12: 6, 1537, 1970) 17. V. Ye. ESKIN and I. A. BARANOVSKAYA, Kolloidn. zh. 31: 929, 1969 18. V. Ye. ESKIN and A. N. NESTEROV, Kolloidn. zh. 28: 904, 1966 19. V. A. KARGIN and G. L. SLONIMSKII, Kratkie ocherki po fiziko-khimii polimerov (Short :Notes on the Physico-Chemistry of Polymers). Izd. "Khimiya", 1967 20. S. Ya. FRENKEL, G. K. YEL'YASHEVICH and Yu. Ye. PANOV, Uspekhi khimii i fiziki polimerov (Advances in the Chemistry and Physics of Polymers). p. 87, Izd. " K h i m i y a " , 1970 21. W. KRIGBAUM and P. FLORY, J. Appl. Phys. 20: 873, 1952 22. W. KUHN and H. CANTOW, Makromolek. Chem. 122: 65, I969 23. G. ALLEN, G. GEE and J. NICHOLSON, Polymer 1: 56, 1960

THERMOPHYSICAL CHARACTERISTICS OF POLYMERS IN THE VICINITY OF THE TEMPERATURE OF LIQUID HELIUM* P. D. GOLUB' and I. I. PEREPECHKO Plastics Research Institute

(Received 15 November 1972) The main thermophysical characteristics (Debye temperatures, specific heats, coefficients of thermal expansion and Griineisen parameters) were calculated on the basis of acoustic measurements for a rmmber of polymers, and the results agreed well with the results obtairmd by direct calorimetric measurements. I t is shown that the fmmd thermophysical characteristics are determined b y the chemical constitutions and structures of the polymers. I n the vicinity of 0°K it was found that Griineisen's parameter is greatly ~ncreased, and this sudden rise points to very effective intemnolecular interaction and to an ilarmonic disturbances in the polymers.

~FuRTI-IER progress in aeronautical, space age and cryogenic technology would be inconceivable in the absence of polymeric materials. In view of this the need also arises for data on the thermophysical characteristics of these materials at very low temperatures. At present only very scanty data are available on the thermophysical characteristics of polymers, particularly with regard to their specific heats, which at low temperatures are normally determined by direct * Vysokomol. soycd. A16: No. 7, 1593-1598, 1974.