INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY MACROMOLECULAR CHEMISTRY DIVISION MACROMOLECULAR CHEMISTRY—9 Specially invited and selected symposium lectures presented at the INTERNATIONAL SYMPOSIUM ON MACROMOLECULES held in Aberdeen, Scotland 10-14 September 1973 Symposium Editor L. C. CROSS The Chemical Society, London L O N D ON BUTTERWORTHS ENGLAND: BUTTERWORTH & CO (PUBLISHERS) LTD. LONDON: 88 Kingsway, WC2B 6AB AUSTRALIA: BUTTERWORTHS PTY. LTD. SYDNEY: 586 Pacific Highway, Chatswood, NSW 2067 MELBOURNE: 343 Little Collins Street, 3000 BRISBANE: 240 Queen Street, 4000 CANADA: BUTTERWORTH & CO. (CANADA) LTD. TORONTO: 2265 Midland Avenue, Scarborough, M1P 4S1. NEW ZEALAND: BUTTERWORTHS OF NEW ZEALAND LTD. WELLINGTON: 26-28 Waring Taylor Street, 1 SOUTH AFRICA: BUTTERWORTH & CO. (SOUTH AFRICA) (PTY) LTD. DURBAN: 152-154 Gale Street The contents of this book appear in Pure and Applied Chemistry, Vol. 39, Nos. 1-2 (1974) Suggested U.D.C. number: 541-64(063) © International Union of Pure and Applied Chemistry 1974 ISBN 0 408 70654 6 Printed in Great Britain by Page Bros (Norwich) Ltd., Norwich EXECUTIVE AND PROGRAMME COMMITTEES Chairman: Sir HARRY MELVILLE Members: G. ALLEN E. H. ANDREWS C. H. BAMFORD J. W. BARRETT C. E. H. BAWN G. M. BURNETT J. I. CUNEEN J. F. GIBSON J. R. RUCK KEENE D. W. SAUNDERS I. M. WARD E. F. T. WHITE A. H. WlLLBOURN vi THERMODYNAMIC ASPECTS OF POLYMER COMPATIBILITY R. KONINGSVELD, L. A. KLEINTJENS and H. M. SCHOFFELEERS Central Laboratory, DSM, Geleen, The Netherlands ABSTRACT Polymer compatibility, to be understood here in the sense of thermodynamic stability, depends in a subtle way on molecular parameters. Some of these are traceable with the aid of model calculations based upon Flory and Huggins' expression for the free enthalpy of mixing. It appears that, in oligomeric mixtures in particular, the average chain lengths and the distributions of chain lengths in the two constituents markedly affect the location and shape of the miscibility gap. The entropy of mixing tends to shift the gap towards the composition region in which the constituent with the smaller average chain length dominates. The interaction parameter, if depending on concentration, can outweigh this effect. Examples, taken from literature and our own data, indicate that this situation does occur in practice. Hence, the lattice-based free enthalpy ex- pression is an accurate tool for describing actual phase relations; however, it cannot quantitatively predict their temperature, chain length, and concentra- tion dependence. In the last respect Flory's equation of state theory appears to be very superior. This was recently shown by McMaster, who analysed Flory's new free enthalpy function and found that small differences inter al. in the thermal expansion coefficients of two compatible polymers will cause the system to become incompatible upon a rise in temperature. The latter pheno- menon is known to occur; examples are given. Compatibility being a subtle phenomenon, the question seems to be justified whether two samples of the same polymer of widely differing chain length might be immiscible. For linear polyethylene and anionic polystyrene the available data point to chain length compatibility. Two methods for the determination of compatibility are dis- cussed, viz. the mutual solvent method and a light-scattering technique. INTRODUCTION Polymer compatibility is a comprehensive subject which has been treated from quite different angles. If one has to deal with practical production problems the processability of a polymer blend naturally offers itself as a useful measure of compatibility. This criterion, however important, does not necessarily coincide with other standards. From the viewpoint of equilibrium thermodynamics, for instance, compatibility means miscibility on a molecular scale, and we cannot say off-hand whether such a state goes with easy processing. 1 PAC—39—1—B R. KONINGSVELD, L. A. KLEINTJENS AND H. M. SCHOFFELEERS In view of the high viscosity of the constituents it seems obvious that one should not expect polymer mixtures prepared by the usual technological procedures to be in an equilibrium state, and kinetic effects will doubtless have a good deal to do with differences in judgment on polymer compatibility. It is of considerable importance to recognize the parameters that determine the equilibrium state of mixed polymers. In those cases where the mixture has not yet reached equilibrium such insight will be needed, or at least be helpful, in understanding the change of properties with time. A mixture of two miscible polymers will gradually increase its degree of dispersion so as eventually to become a one-phase system. On the other hand, thermodynamically incompatible polymers will in course of time reduce the degree of dispersion. This illustrative example was given by Gul', Penskaya, Kuleznev and Arutyunova1 who suggested use of the conditions of thermo- dynamic stability as a criterion for compatibility. We follow their line of SOLVENT (1 ) - SOLVENT (2) N = n j + n 2 17^=10 m=10 2 Figure 1. Schematical illustration of the numbers of possible arrangements in a small-molecule mixture (top), a polymer solution (middle) and a polymer mixture (bottom). The polymer chains each contain 10 segments of the size of the solvent molecules. 2 THERMODYNAMIC ASPECTS OF POLYMER COMPATIBILITY thought here and restrict ourselves to a discussion of the various parameters that determine polymer compatibility in thermodynamic equilibrium. The reader is referred to the literature for more comprehensive reviews2-7. Thermodynamic considerations in this field are often limited to the qualitative statement that the free enthalpy (Gibbs free energy) of mixing (AG) must be negative for a system to be thermodynamically stable. This involves a balance between the enthalpy and entropy of mixing, and a boun- dary between stable and unstable states determined by the condition AG = 0. The usual molecular picture is a lattice representation of the system, illus- trated schematically in Figure 1. In equal volumes, the number of possible arrangements in the binary small-molecule mixture (top) is much larger than that in a polymer solution (middle), obtained by partly stringing the mole- cules of one species together to chain molecules. A similar treatment of the molecules in the other component yields a representation of a polymer mix- ture, and is accompanied by a further drastic decrease of the number of arrangements (bottom). The number of nearest neighbour contacts is only slightly affected in the process so that the energy and, hence, the heat of mixing do not differ much between the three cases. This simple model is very illustra- tive and reveals the principal reason why polymer solutions are less resistant to demixing than representative small-molecule mixtures. We also understand that polymer mixtures have so little entropy of mixing to match energy effects, that very small positive heats of mixing suffice to bring about incompatibility. Slonimskii et a/.8-11 measured heats of mixing in a series of polymer pairs and found most of them to mix endothermally, i.e. AH > 0. An exception to this expected behaviour was provided by the system polystyrene-poly- butadiene which sets heat free upon mixing and yet shows partial miscibility. Slonimskii et al concluded that the actual situation is obviously not at all covered comprehensively by the simple molecular picture outlined above and that entropy of mixing terms other than combinatorial ones are involved. They thought the non-combinatorial entropy terms to be related to molecular packing and, hence, to volume changes accompanying the mixing process. In this way they foreshadowed more recent approaches to improve the theory of liquid mixtures, among which the 'equation of state' treatment by Flory and his co-workers12-14 and its application to polymer mixtures by Mc- Master15 are particularly noteworthy. Alekseyenko16 also considered the packing density of mixed polymers and suggested the packing coefficient K, defined as the ratio of the actual and additive (calculated) volumes of the mixture, to be a useful criterion for compatibility. Expansion (K > 1) would then point to incompatibility, contraction (K < 1) to miscibility. GuY et al.1-17 used the independence of a property of the blend from the path by which it is attained as a criterion for thermodynamic stability. They measured optical densities of mixed films as an illustration. It is evident that heats and volumes of mixing, as well as optical properties, are important parameters for thermodynamic stability but they are not wholly determinative. The free enthalpy of mixing unambiguously determines equilibrium states and we therefore prefer to base discussions of compatibility on this quantity. A consideration of the dependence of AG on composition immediately shows that the boundary condition AG = 0 mentioned above 3 R. KONINGSVELD, L. A. KLEINTJENS AND H. M. SCHOFFELEERS arises from much too crude a picture. Mixtures can be and often are unstable at negative AG (though not, of course, relative to the pure components), and can diminish AG still further by separating into two phases. Figure 2 illustrates this situation for a strictly-binary mixture. The stability of the system is determined by the curvature of AG(<p)18-20 and the stability 2 limit, also called spinodal, is given by (d2AG/dq>2), = 0. (1) 2pT where q> is the volume fraction of the second component. The slight ripple in 2 the AG(<p) curve which goes with partial miscibility may be caused by the heat 2 • cp 2 homogeneous system )inodal : (d2AG/d(p*) = o RT T L -itical point: (d\G/ 9<p)^ = o 2 r RT % %.sP %,sP % AG NT tie -line T binodal h2e tpehroagseesn,e ocup2s a nsdy sctepm2' , T c --ft// / N^V\ aa ssppiinnooddaall 2 /"] 1 N /!/ unstable I I,I1I: ' ^ ^meta-stable 1 %%. 2 solvent solute consolute (critical) state, 2 identical phases Figure 2. Free enthalpy (Gibbs free energy) of mixing as a function of concentration in a binary liquid system showing partial miscibility. of mixing, but could equally well spring from a deviation of the entropy of mixing from mere combinatorial terms. In the latter case one may have partial miscibility even if AH is negative. Wolf recently reviewed entropically and enthalpically induced demixing21. A free enthalpy of mixing expression that has proved useful in describing liquid-liquid phase relations is that by Flory22,23 and Huggins24'25, based on the lattice model of the liquid state. For quantitative descriptions it must be slightly extended2326-28 by a semi-empirical correction term. Further, the fact that actual polymers are generally characterized by a chain-length distribution rather than a single species must be taken into account22'2629 Leaving chain-branching and copolymerisation out of consideration we can 4 THERMODYNAMIC ASPECTS OF POLYMER COMPATIBILITY write AGJRT =yL(p ml\In<p + Z (p,/n^)Incp j + T(p, T, (p) (2) ui u t 2 2> 2 * j where AG^ is the free enthalpy of mixing per mole of lattice sites, <p and Xji (p are the volume fractions of species i in polymer 1 and species j in polymer 2J 2, and m and m are the relative chain lengths of the same, expressed in lti 2j the number of lattice sites they occupy. RT has the usual meaning, and p stands for pressure. The correction term T can be written as T = g(p, T, <p) <pcp (3) 2 1 2 where <p and cp are the volume fractions of the whole polymers 1 and 2, x 2 i.e. = 1 — cp. For the moment we ignore a possible chain-length depen- 2 dence of interaction parameter g. If g goes not depend on concentration we have the familiar Van Laar interaction term30. Using the multicomponent version of equation (1) one finds for the stability limit of a system obeying equation (2)31-33: -(d2r/dq>l) = (l/m, i<Pi) + (Vm,<p) (4) PtT w w2 2 where m and m are the weight-average chain lengths of the two poly- Wt t w 2 mers. Within the range of validity of equation (2) the stability limit of a two- polymer mixture is determined by the concentration dependence of T (or g\ and the chain length distributions of the polymers reveal themselves in terms of the two weight averages only. In some of the cases we shall discuss presently this simple approach seems to work satisfactorily even though relatively small chain lengths are involved. The simple lattice theory supplies descriptive expressions for g in terms of temperature, concentration and chain lengths33-35, but it cannot predict how g will depend on pressure and temperature. For that purpose the theory by Flory and his co-workers12-14 and Patterson and Delmas36-38 have proved to be powerful tools. A striking example of the usefulness of Flory's theory has recently been given by McMaster who applied it to mixtures of two polymers15. Both Flory's and Patterson's free enthalpy expressions are very complicated and contain many parameters that, although readily obtainable from independent measurements on the constituents of the mixture, make these expressions less suitable for the present purpose. Moreover, they are mainly concerned with the dependence of T on temperature, pressure and concentration and attribute the effect of the chain length distributions to the same two combinatorial entropy terms that are used in the lattice theory [first two terms in equation (2)]. Since we are primarily interested here in the effect molecular weight distributions have on the location of miscibility gaps in polymer mixtures we prefer the simpler expressions (2) and (3). The impli- cations of 'equation of state' parameters will be discussed briefly on the basis of McMaster's results. Very recently, Derham, Goldsbrough and Gordon39 expressed serious doubts about the adequcy of equation (2), in as much the influence of the molecular weight distribution is concerned. They carried out very accurate measurements of stability limits in the system cyclohexane-polystyrene, using 5 R. KONINGSVELD, L. A. KLEINTJENS AND H. M. SCHOFFELEERS the pulse-induced critical scattering method developed in their institute. The spinodals were found to depend on the molecular weight distribution of polystyrene in an intricate manner, much more complicated than is suggested by equation (4) which restricts the influence of the distribution to the weight average alone. It is possible to introduce an arbitrary, empirical dependence on the chain length distribution into equation (3), and work out the stability limit33'35. An improved theoretical treatment of the free enthalpy, however, would be preferable. With the systems on hand in particular we are not yet in a position to discuss such subtleties and we shall have to proceed on the basis of the simple expression (2) for the time being. It has been noted before40-42 that the stability condition (1) supplies a convenient means of investigating phase behaviour of liquid systems. This is because all AG functions in current use allow equation (1) to be worked out and the result be written in closed form. This is not possible with the equilibrium conditions for the concentrations of the two coexisting phases (Figure 7), (p' and (p. The latter conditions (arising from the equality of the chemical 2 2 potential of each component in the two phases) lead to implicit equations that must be solved with numerical methods. Every miscibility gap, however, comprises a spinodal and the occurrence of such a limit of stability is there- fore indicative of a range of two-liquid-phase equilibria in the system. In case of doubt one might use the sign of the curvature of AG((p) to decide on 2 which side of the spinodal the unstable states are located. Changing from a heterogeneous to a homogeneous mixture by a change in temperature or pressure, the system passes through the consolute or critical state in which the points of inflection as well as the double tangent points of AG(q>) coincide (Figure 2). The critical state is characterized by equation 2 (1) in conjunction with (d3AG/dq>X = 0 (5) T The multicomponent version of this condition leads to -(d3T/d(p3), = ( m i/ m2,- (m /m2 (pl) (6) 2pT z > Zf2 Wt2 c where m stands for the z-average chain length, and cp is the critical con- z c centration. Equation (6) is subject to the assumptions underlying equation (4). A critical point is located on the spinodal. It coincides with the latter's maximum in a strictly-binary system and shifts away from the maximum if one of the constituents or both contain more than one component32. Estimations of the shape of miscibility gaps are greatly helped if the location of the critical point on the spinodal, calculated with equation (6), is included. In the following discussions the experimental evidence will mainly be derived from literature and our own data on mixtures of low-molecular- weight polymers. Allen, Gee and Nicholson43, who studied the system poly- isobutene-poly(dimethylsiloxane), realized that, owing to their relatively low viscosity, oligomeric systems allow investigation of phase equilibria with the usual means, and yet have some of the properties characteristic for long-chain constituents. For related reasons Mclntyre, Rounds, and Campos- Lopez44 investigated the system polyisoprene-polystyrene to which data we have added some of our own. 6 THERMODYNAMIC ASPECTS OF POLYMER COMPATIBILITY Many experimental methods are in use for establishing the miscibility. of polymers2-7. We limit ourselves to some general remarks which might justify the choice of the methods discussed here in some detail. Alekseyenko warns against methods using solutions of the mixed polymer in a common solvent (mutual-solvent method)16. We agree with him that reliable con- clusions about the properties of the solvent-free polymer mixture cannot be drawn from its behaviour in more or less dilute solution, no matter whether the solvent is good or poor. Procedures based upon solvent-free mixtures are not without danger of misinterpretation either. It has been established that polymer mixtures can sometimes follow temperature changes with an amazing speed. Direct observation of blends with the light microscope has shown that demixing of even high-molecular-weight constituents can set in quite rapidly upon a change of temperature15,45,46. Hence, if the sample has to be frozen in, as for instance in the preparation for the electron microscope, the picture taken is not necessarily representative of the system at room temperature but may be determined by what happened during the heat treatment. Similarly, mechanical loss peaks, in wide use to detect the number of glass transitions (number of separate phases) in a blend, have only significance in the temperature range where the peaks occur and may easily not be representative for the system at other temperatures. In this connection the system natural rubber-SBR might offer an interesting example. Mechanical loss measurements reveal two peaks below 0 °C47, yet microscopic investiga- tion at room temperature shows transparent films only. One could conclude that the system exhibits upper critical solution behaviour upon cooling below room temperature. This conclusion however depends entirely on whether the refractive indices of the constituents differ enough to make the microscopic observation significant. This is the main limitation of the microscopic determination of compatibility. Scholte48,49, Chu et al.50,51 and others have shown that light-scattering measurements provide direct access to the stability limit and thus yield basic thermodynamic information. As in light microscopy, the constituents should have sufficiently different refractive indices for the method to be applicable but the amount of information is much greater. This, however, seems to be the only limitation of the light-scattering method which, in particular in the elegant variation by Gordon et al. (pulse-induced critical scattering39'52), will doubtless prove to be of great value in thermodynamic studies of polymer compatibility. MISCIBILITY GAPS IN MIXTURES OF POLYDISPERSE POLYMERS 1. Concentration-independent interaction parameter If g in equation (3) depends on p and Tonly, we have -{d2T/dcp2) = 2g = (l/m, + (l/m,cp) (7) 2T w w2 2 (spinodal). The location of the critical points on the spinodal is determined by -(d3r/d(p3), = (m^JmlMj ~ (m,2/<2<plc) = 0. (8) 2 pT z 7