Elastic steric stabilization in polymer melts

Elastic Steric Stabilization in Polymer Melts J~Lckel (1) was perhaps the first to recognize the probable importance of an elastic contribution to steric stabilization. Although Ottewill (2, 3) stressed the need to evaluate the magnitude of the elastic term on several occasions, it is only recently (4) that a first-order analytic theory was developed which permits this to be done readily. The simplest way to consider the behavior of polymers that provide steric stabilization is to regard them as occupying two separate spaces: one, a thermodynamic space that arises because the centers of mass of the segmental elements are unable to locate themselves spontaneously in a thermodynamic excluded volume that may be positive, zero, or negative, depending upon the solvent; the other, a real space in which the centers of mass of the segments can distribute themselves in a finite number of ways over the real available volume, which is always positive. Using Flory's (5) nomenclature, we may say that the former space gives rise to the mixing contribution to steric stabilization (which may be positive, zero, or negative, depending upon the solvent) whereas the latter space gives rise to the elastic term (which is always positive). Note, however, that the elastic contribution to steric stabilization is likely to be negligibly small (4) unless the minimum distance of particle separation is less than the contour length of the stabilizing chains. Thus the elastic term is only important in the interpenetration plus compression domain (4). Even the demonstration of the existence of an elastic contribution to steric stabilization is not without experimental difficulties. The reason for this is that, except for very close approach, the mixing term is usually dominant (4). There are, in principle, at least two ways of overcoming this problem. First, if it were possible to use a theta-solvent, the mixing term would be zero (or near zero) and only the elastic term should be observed (6). However, the precise location of the exact theta-point is experimentally difficult and the contributions of the fourth and higher virial coefficients remain uncertain so that this approach is likely to prove inconclusive. An alternative way of rendering the mixing term small is to use a solvent with a very large molar volume because the mixing term is inversely proportional to this parameter. Indeed, it is for this very reason that polymer molecules in a melt of identical molecules are predicted by Flory (7) to adopt their theta-solvent (i.e., unperturbed) dimen-

sions. Hence, although the interaction parameter x~ is equal to zero and not ½ as in a theta-solvent, a polymer in its own melt behaves to a good approximation as if it were in a theta-solvent. There is now direct experimental evidence to support this prediction (8). This approach appears to provide a more direct method of demonstrating elastic steric stabilization. In what follows we describe the preparation of sterically stabilized latexes in polymer melts. As the foregoing discussion indicates, the mixing contribution to stability for such latexes is likely to be negligibly small. The primary origin of stability is inferred, from comparisons with theory, to arise from elastic effects as defined by Flory (5). EXPERIMENTAL Four poly(ethylene oxide) (PEO) samples were studied: Fluka 600, Merck 1500 and 6000, and an ICI 6000. Here the number represents the molecular weight of the polymer. The two samples of molecular weight 6000 gave essentially identical results. Three initiators were used: benzoyl peroxide, lauryl peroxide, and azobisisobutyronitrile were all purum grade. Latexes were successfully prepared with each of these initiators but the first two were more effective, perhaps because of their greater propensity to hydrogen abstract from PEO. The styrene was vacuum redistilled before use. The latexes were prepared by dissolving initiator (0.05 g) in the molten polymer (20 g) and heating to 80°C for 30 rain. Further initiator (0.1 g) was then added and, after 15 rain, the styrene (0.2 cm *) was dissolved in the melt. If no latex was evident after 1 hr, further monomer (0.1 cm 3) and initiator (0.01 g) were added. Further additions of monomer and initiator were made if no turbidity was evident at subsequent half-hourly intervals. After preparation the latexes were stored at 70°C. Particle sizes were controlled by limiting the amount of added monomer or by adding the chain transfer agent n-dodecyl mercaptan. The particle sizes were measured by either light scattering or electron microscopy. RESULTS AND DISCUSSION Latexes stabilized by PEO 6000 in molten PEO 6000 were in general extremely stable. Only latexes

467 Copyright ~) 1976 by Academic Press. Inc. All rights of reproduction in any form reserved.

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of very large particle size (of order, say, 1000 nm radius) appeared to aggregate and then only after a period of several weeks. The aggregates formed could be redispersed by shaking. Reduction of the molecular weight to 1500 resulted in a similar pattern of behavior, except that only particles whose radii were less than ca. 100 nm exhibited long-term stability. Larger particles coagulated slowly over several days to form flocs that could be broken up readily by shaking. The preparation of latexes stabilized by PEO 600 in liquid PEO 600 proved to be extremely difficult. Even after careful control of the amount of styrene added or the addition of chain transfer agent, any moderately sized latex coagulated in a period of from 4 hr to 4 days, despite appearing to be stable at very small particle sizes. Note that the molar volume of PEO 600 may not be large enough to render the mixing term totally negligible; however, any mixing term would contribute to stability, not instability. To show that the stable latexes were in fact stabilized by PEO anchored to the particle surface, a melt latex was poured into a large excess of water at the same temperature and then cooled. The resuiting latex was found to undergo reversible flocculation in 0.39 M MgSO, at ca. 321°K. This is close to the theta-temperature for PEO under those conditions (9) and, from previous studies (10), implies that the latexes were stabilized by PEO strongly attached to the particle surface. Moving boundary electrophoresis of the same particles in distilled water showed that their zeta-potentials were very small (ca. 5 mV). This suggests that electrostatic effects could be eliminated as a source of stability. To demonstrate that the difference between the PEO 600 and 6000 systems was not the result of different viscosities of the melt, a small volume of the PEO 6000 latex was diluted with a large excess of PEO 600. No particle coagulation was observed, even on standing for several weeks. Stable melt latex particles also displayed aggregation on the addition of small amounts of water. This would be expected from the studies of Li-in-on el al. (ll), who prepared PEO stabilized latexes in water and subsequently dissolved PEO into the dispersion medium. Curiously enough, we found that such aggregation could not be reversed by shaking at room temperature but was rapidly reversed by the addition of more water or by heating to 50°C. To explain the observed pattern of results, we have carried out calculations on the magnitude of the elastic repulsion in the systems studied. We assumed that the stabilizing chains could be regarded as Gaussian tails so that the elastic free energy (zXG~1) could be calculated from (4) : AG oi = 27rvLakT(~ -- ~o~/6 -- ~o/2 + ~o In ~o). [1]

Here v = number of attached chains per unit area,

L = steric barrier layer thickness, a = particle radius and a0 = do~L, where do = minimum distance of separation of the surfaces of the two particles. Strictly speaking, the value of L to be used in Eq. ['1~ is the contour length (i.e., the fully extended zig-zag length) of the chains; the reason for this is that if do < L an elastic contribution to stability appears because of the decrease in the real volume available to some of the chains. Ottewill and Walker (12) have presented experimental evidence that appears to show that low molecular weight poly(ethylene oxide) chains are approximately fully extended when anchored at the surface of colloidal particles. If this is correct then the value of L to be used in Eq. rl-I is indeed the fully extended length of the stabilizing chains. It would seem unlikely that higher molecular weight chains would also be fully extended so we have performed Monte Carlo calculations (13) on tails sandwiched between two parallel flat plates. These calculations suggest that the dimensions of such chains are not altered significantly unless the distance of separation is less than 1.5 times the 3-D rms end-toend length of the chains in free solution. The Monte Carlo calculations imply that a more realistic value to be used in Eq. [-11 for higher molecular weight chains in a polymer melt is 1.5 times the unperturbed rms end-to-end length. Because we were uncertain which value of L was appropriate for our systems, calculations were performed using both assumptions. However, as will be seen, the Monte Carlo value for L appeared to give better agreement with experiment. The approximate unperturbed dimensions were calculated from data available in the literature (14). Admittedly, there is some doubt associated with the applicability of such data to the lowest molecular weight chains studied; however, this uncertainty is significantly less than that associated with the choice of the value of L to be used in Eq. V1-]. The value of v was calculated by assuming that the polymer chains were hexagonally close packed on the surface so that each hexagon contained an inscribed circle of radius equal to one-half of the unperturbed rms end-to-end length of the chain. The approximate validity of this assumption was checked against the experimental data of Doroszkowski and Lambourne (15) for polystyrene stabilized systems. Whereas our assumption, with due allowance for intramolecular expansion, predicts a specific adsorption weight of 3.6 X 10-a g cm-2, the measured value was 5.2 )< 10-a g cm-~. The London dispersion attraction between the core particles was calculated using the procedures described previously (16). The ionization potential of condensed PEO was estimated to be 7.0 eV from the literature value (17) of 9.2 eV for gaseous diethyl ether, together with values of 0.7 eV to allow for polymerization effects and 1.5 eV to allow for condensation (16).

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The zero frequency dielectric permittivity and micro-. wave relaxation values were also taken from the literature (18) but the refractive index of PEO 600 was measured as 1.47. At large separations the foregoing procedure for calculating Hamaker functions becomes invalid (16). However, at these distances the dispersion attraction is small compared with thermal energy and the Hamaker function (H) may be adequately approximated by the zero frequency contribution alone (19), which is not retarded. For PEO the value of H calculated in this way was 2.2 X 10-21 J. No allowance seemed necessary for the Vold effect in these systems (20). Potential energy diagrams for small (a = 100 nm) and large (a = 1000 nm) polystyrene particles stabilized by PEO 6000 in PEO 6000 melts at 70°C are shown in Figs. 1 and 2, respectively. I t is clear that whichever value we use for L, the elastic repulsion for small particles rises very sharply and is much greater than the core attraction. The core attraction is insignificant compared with thermal energy at distances beyond the range of the elastic term. The potential energy curves shown in Fig. 1 even though they may only be semiquantitative, provide a convincing explanation for the observed long-term stability of the smaller latex particles in PEO 6000. It would seem unlikely that such dispersions could be easily coagulated by, e.g., simply changing the temperature. Particles of 1000 nm radius give somewhat different potential energy curves from those for 100 nm radius, if we use the value for L obtained from Monte Carlo calculations. The potential energy curves for these larger particles show a minimum of order 5kT, which would be sufficient to explain the observed coagulation of larger particles, as well as the ease of redisper-

_

_

i 2O z~G ";0 0

-10~

30 J 3

FIG. 2. Potential energy curves for polystyrene latex particles of radius 1000 nm stabilized by PEO 6000 in PEO 6000 melt at 343°K. The assumed value for u = 3.5 X 10TM cm -2. Curves (1) and (2): &Gel for (1) L = contour length (34.0 nm) and (2) L = 1.5 X rms end-to-end length (8.7 rim). Curve (3) is the van der Waals attractive potential. Curve (4) is the total potential energy derived from craves (2) and (3). sion on shaking. This minimum is exactly analogous to the secondary minimum in electrostatic stabilization, although it cannot strictly be cMled a secondary minimum in steric stabilization because of the absence of a primary minimum. Its origin is quite different from that of the minimum usually accessible to incipiently unstable systems of sterically stabilized particles close to the true theta-point (4); the latter arises from the intermolecular self-attraction of the stabilizing chains in slightly worse than theta-solvents. Shown in Table I are the depths of the minima that occur in the potential energy diagrams of small and large particles for the three PEO systems studied. The Monte Carlo value for L was adopted because it gave significantly better agreement with experiment than the contour length. These data suggest that only relatively small particles (say, of radius <50 nm) TABLE I

1

Predicted Depth of the Potential Energy Minima for Polystyrene Dispersions in PEO Melts

kT

10

20 do/n m 30 /

-!

FIo. 1. Potential energy curves for polystyrene latex particles of radius 100 nm stabilized by PEO 6000 in PEO 6000 melt at 343°K. The assumed value for v = 3,5 X 10TM cm -2. Curves (1) and (2): /',G~1 for (1) L = contour length (34.0 nm) and (2) L = 1.5 )< rms end-to-end length (8.7 ran). Curve (3) is the van der Waals attractive potential. The total potentim energy curves are approximated by curves (1) and (2).

Molecular weight

Particle radius/nm

Depth of minimum

Stability

6000 6000 6000

20 100 1000

<
stable stable unstable

1500 1500 1500

20 100 500


stable barely stable unstable

600 600

20 100

600

500


stable unstable unstable

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NOTES

would be stabilized by PEO 600 in its melt. Increasing the molecular weight of the PEO to 1500 increases the maximum radius that can be stabilized to ca. 100 nm. These theoretical predictions are, broadly speaking, in agreement with experiment. It must be stressed, however, that the theoretical predictions are semiquantitafive at most. The presence of significant amounts of loops, for example, would lead to the prediction of significantly less stable dispersions. The foregoing results suggest that for small particles and relatively high molecular weight stabilizers, the elastic contribution to steric stabilization is undoubtedly sufficient to impart excellent stability to dispersion in polymer melts. However, for large particles and short stabilizers, coagulation may be observed as a result of the London attraction between the core particles. This pattern of behavior contrasts markedly with that observed for sterically stabilized latexes near to the theta-point. Whereas the onset of instability in the latter case is insensitive to the molecular weight of the stabilizer and the particle radius (10), it is apparent that the stability of melt latexes may well be very dependent upon the molecular weight of the stabilizer and the particle radius. The experimental results presented herein support the suggestion of Doroszkowski and Lambourne (15) that it ought to be possible to prepare stable latices in theta-solvents. This does not yet seem to have been achieved, presumably because quite small deviations from tile theta-point in the direction of a poorer solvent result in the chains becoming selfattracting. As a consequence, the theta-point is the practical limit to stability of many sterically stabilized particles (10). The results are also in agreement with the qualitative concepts advanced by Osmond and Waite (6), which also call for stability in both thetasolvents and polymer melts. ACKNOWLEDGMENTS The first author gratefully acknowledges the award of a Commonwealth Post-Graduate Scholarship. We thank the Australian Research Grants Committee for their support. Mr. R. Evans is thanked for his advice on calculating Hamaker functions. REFERENCES 1. ~ACKEL,K., Kolloid Z. 197, 143 (1964). 2. O]:TIEWlLL, R. H., in "Nonionic Surfactants," Chap. 19. Dekker, New York, 1967.

3. OTTEWtLL, R. H., Kolloid Z. Z. Polym. 227, 115 (1968). 4. EVANS, R., SlV[1THA~,J. B., AND SAPPER, D. H., Kolloid Z. Z. Polym., to appear. 5. FLOR¥, P. J., "Principles of Polymer Chemistry," Chap. 13. Cornell University Press, Ithaca, N. Y., 1953. 6. OS~tOND,D. W. J., AND WAITE, F. A., in "Polymer Colloids." NATO Advanced Study Institute Preprints, Trondheim, 1975. 7. FLOR¥, P. J'., "Principles of Polymer Chemistry," Chap. 14. Cornell University Press, Ithaca, N. Y., 1953. 8. COTTON, J. P., DIECKER, D., BENOIT, H., FARNoux, B., HlOClNS, J., JANNINK, G., OBER, R., ~PICOT, C., AND DES CLOIZEALIX, J., ~facromolecules 7, 863 (1974). 9. BAILEY, F. E., AND CALLARD, R. W., 3". Appl. Polym. Sci. 1, 56 (1959). 10. NAPPIER, D. H., AND HUNTER, R. J., MTP. Int. Rev., Sci. Ser. 1 7, 280 (1972). 11. LI-IN-ON, F. K., VINCIENT,B., AND WAITE, F. A., ACS Symp. Ser. 9, 165 (1975). 12. OTTEWILL, R. H., AND WALKER, T. W., Kolloid Z. Z. Polym. 227, 108 (1968). 13. SMITHA~[, J. B., AND NAPPIER, D. H., to be published. 14. BRANDRUP, ~., AND IMMZERGUT,E. H., "Polymer Handbook," p. IV-58. Interscience, New York, 1966. 15. DOROSZKOWSKI, A., AND LAMBOURNIE, ~., 3". Colloid Interface Sci. 29, 168 (1969). 16. EVANS, R., AND NAPPER, D. H., Y. Colloid Interface Sci. 45, 138 (1975). 17. "Handbook of Chemistry and Physics," 54th ed., p. E-75. CRC Press, Cleveland, 1973. 18. POCI~AN,J. M., AND CRYSTAL, J. G., "Dielectric Properties of Polymers," Plenum, New York, 1972. 19. PARSEOIAN,V. A., Ann. Rev. Biophys. Bioeng. 2, 221 (1973). 20. VOLD, M. J., J. Colloid Sci. 16, 1 (1961). j'. B. Sm~HA~i D. H. NAPPIER

Department of Physical Chemistry University of Sydney N.S.W. 2006, Australia

Journal of Colloid and Interface Science. Vo]. 54. No. 3. March 1976

Received September 18, 1975; accepted October 30, 1975