Abstracts of papers on phase separation and miscibility

A Theoretical Study of Isotope Blends:

No Concentration Dependence of The SANS χ Parameter

James Melenkevitz, Buckley Crist, and Sanat K. Kumar

Macromolecules 33, 6869-6877 (2000)

ABSTRACT

The small-angle neutron scattering (SANS) interaction parameter χ_NS in isotope blends almost always exhibits pronounced upward curvature when plotted as a function of concentration at any given temperature. Optimized cluster theory (OCT), which accounts for blend compressibility and for fluctuations, is used to address this effect in blends of conventional and perdeuterated polyethylene. Structure factors are calculated for symmetric systems having a concentration independent χ_bare = 2.09H10^-4 and chains of N = 3290 or N = 8746 monomers. When analyzed in terms of incompressible RPA approach, exactly as done in experiments, the model returns an interaction parameter that is practically indistinguishable from χ_bare for all blends concentrations between 0.01 and 0.99. Trivial departures from the energetic χ_bare are attributed to equation of state effects. These results, combined those from compressible lattice models (Kumar et al.¹ and Gujrati²), show clearly that compressibility has no significant role in determining the composition dependence of the interaction parameter. The experimental behavior of isotope blends cannot be ascribed to any theoretical reason (i.e., compressibility or density fluctuations), and is therefore attributed to measurement errors.

Thermodynamic Interactions in Isotope Blends: Experiment and Theory

Buckley Crist

Macromolecules 31, 5853-5860 (1998)

ABSTRACT

Full text at http://pubs.acs.org/isubscribe/journals/mamobx/31/i17/pdf/ma971858k.pdf

Small-Angle neutron scattering (SANS) studies of binary mixtures provide χ_NS, a measure of thermodynamic interactions between dissimilar polymer chains, one of which is usually labeled with deuterium. For polymers differing only in isotopic substitution (isotope blends), χ_NS is seen to diverge strongly upwards (or sometimes downwards) at low concentrations of either blend component. This concentration dependence seems to vanish in the limit of large degree of polymerization N. Experimental results can be described by χ_NS(n,N) = β + γ/Nn(1-n), where n is the volume fraction of deuterated polymer. For SANS from a series of blends with different n it is shown that systematic errors in N and/or the static structure factor S(0) lead to precisely the same χ_NS(n,N) when the Flory-Huggins interaction parameter χ is constant. While results for some isotope blend systems can be accounted for with reasonable error estimates, others appear to have a real dependence of χ_NS on n and N. It is suggested that these "non-Flory-Huggins" effects stem a modified entropy of mixing that is most evident in dilute blends. The concentration dependence of χ_NS(n) has no practical effect on macroscopic phase behavior.

Concentration and Chain Length Dependence of Thermodynamic Interactions in Polyethylene Isotope Blends

Buckley Crist

Journal of Polymer Science: Part B: Polymer Physics 35, 2889-2899 (1997)

ABSTRACT

Small-angle neutron scattering (SANS) measurements of interactions in polymer blends, χ_NS, generally depend on blend concentration φ, even though χ_NS is evaluated with a model that assumes that the thermodynamic interaction parameter χ^FH = χ_NS is independent of φ. Londono et al. have reported χ_NS to increase by ~4x when φ drops below 0.05 in polyethylene isotope blends. The relation between scattering and thermodynamics is addressed with incompressible Flory-Huggins theory wherein the thermodynamic interaction parameter χ may vary with concentration φ and degree of polymerization N; here χ_NS(φ) … χ(φ). For polyethylene isotope and similar polyolefin blends, the strong upward curvature of χ_NS implies a modest (ca. 30%) increase of χ. Macroscopic phase behavior is unaffected because the shape of the binodal remains essentially unchanged. The φ-dependence of χ_NS in turn depends on N, leading to the following empirical expression for the thermodynamic interaction parameter: χ(φ,N) = β - (2γ'/Nφ₁φ₂)(φ₁lnφ₁ + φ₂lnφ₂). For polyethylene isotope blends at 155 ^oC, β = 2.85x10^-4 and γ' = 0.15. Simple Flory-Huggins behavior with χ^FH = β is recovered when N approaches infinity. The source of the φ- and N-dependent second term is not known.

Recent Developments in Phase Separation of Polyolefin

Melt Blends

Buckley Crist and Mary J. Hill

Journal of Polymer Science: Part B: Polymer Physics 35, 2329-2354 (1997)

ABSTRACT

Saturated hydrocarbon polymers may be differentiated by the relative amount and placement of methylene, methyl, methine and quaternary carbon moieties. While it has been known or suspected for some time that polyolefins of conventional molecular weight (M_w . 100 kg/mol) with dissimilar chemical microstructures are most often immiscible in the liquid state, recent experiments with binary blends of model polyolefins have increased greatly our understanding of thermodynamic interactions between unlike chains. Model systems with methyl (-CH₃) and ethyl (-C₂H₅) short-chain branches give results, expressed as the Flory-Huggins interaction parameter χ, that are nearly universal; repulsive interactions (χ > 0) are more pronounced at low temperatures, leading to liquid-liquid phase separation at an upper critical solution temperature. Phase behavior of more complex systems (with distributions of chain microstructures and/or molecular weight) is generally consistent with predictions from model systems. An interesting exception is from work at Bristol on blends of lightly branched ethylene - α-olefin copolymers with unbranched polyethylene as the minority species. Here the presence of two liquid phases is inferred under conditions not expected from model studies; effects of copolymer composition and molecular weight are also unusual. Recent theoretical work points to the importance of chain stiffness (established by short-chain branching) in determining the thermodynamics of model blends. Nonrandom mixing of chains with different stiffness gives rise to an enthalpic χ, which may be negative under certain conditions. Other limitations of the Flory-Huggins approach to describing blend energetics are considered. At present there is no theoretical basis for liquid-liquid phase separation reported by the Bristol group.

Is Compressibility Important in the Thermodynamics of Polymer Mixtures?

Sanat K. Kumar, Boris A. Veytsman, Janna K. Maranas and Buckley Crist

Physical Review Letters 79, 2265-2268 (1997)

ABSTRACT

Full text at http://ojps.aip.org/journal_cgi/getpdf?KEY=PRLTAO&cvips=PRLTAO000079000012002265000001

The effect of compressibility on the static scattering from polymer mixtures is critically evaluated through a general thermodynamic analysis. We find that compressibility plays an important role for blends comprised of chains with disparate chemical structures, and that it is effectively irrelevant for blends with similar chemical structures.

Comments on "Ambiguities in the interpretation of small-angle neutron scattering from blends of linear and branched polyethylene"

Buckley Crist

Polymer 38, 3145-3147 (1997)

ABSTRACT

Small-angle neutron scattering has recently been applied to study liquid-liquid phase separation in blends of branched and linear polyethylenes. While experimental results from two groups are basically the same, interpretations differ strongly. The analyses of Schipp et al., which favor phase separation, are shown to be incorrect. There is no contraction of chain dimensions in blends of linear and branched polyethylene chains. The postulate that large domain sizes in two-phase blends obscure the presence of phase separation is correct in principle, but requires dimensions some ten times larger than the ~1μm sizes reported for the systems in question. Thus neutron scattering does not support liquid-liquid phase separation inferred from indirect studies of polyethylene blends.

On "Pinning" Domain Growth in Two-Phase Polymer Liquids

Buckley Crist

Macromolecules 29, 7276-7279 (1996)

ABSTRACT

Full text at http://pubs.acs.org/isubscribe/journals/mamobx/29/i22/pdf/ma960527p.pdf

What has been reported as "pinning" or severely reduced growth rates of phase separated domains in off-critical polymer blends is shown to be the normal effect of crossover between two kinetic regimes associated with morphology of the liquid-liquid system. The bicontinuous liquid microstructure formed by spinodal decomposition grows rapidly by hydrodynamic coarsening where size ~ Lt until the percolated system dissociates into droplets. The droplets then grow by classical coarsening with radius increasing as ³ ~ Kt, where K may be calculated for Ostwald ripening and/or coalescence with no impediments to mobility at any size scale. Apparent pinning persists for the induction period Δt . ³/K required for the slower particle growth to be observed, and the characteristic % t^1/3 behavior is not recovered for approximately 10Δt. Numerical simulations of spinodal decomposition in polymer blends, which to date omit hydrodynamics, are unable to capture the change in growth mechanism and rate on switching from percolated to droplet morphology.

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