Analytic reference interaction site model-mean spherical approximation theory of flexible polymer blends: Effects of spatial and fractal dimensions

Journal Article · Fri Mar 01 00:00:00 EST 1991 · Journal of Chemical Physics; (USA)

DOI:https://doi.org/10.1063/1.460704· OSTI ID:6223343

Schweizer, K S; Curro, J G ^[1]

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1. Sandia National Laboratories, Albuquerque, New Mexico 87185 (US)

Recently developed methods for obtaining exact and approximate analytical solutions of the reference interaction site model-mean spherical approximation (RISM-MSA) integral equations for liquid mixtures composed of long, flexible polymers are applied to study the critical temperature {ital T}{sub {ital c}} for phase separation of symmetric isotopic binary blends as a function of degree of polymerization {ital N}, spatial dimension {ital D}, and fractal dimension {ital d}{sub {ital f}} of the individual macromolecules. For ideal random walk coils, the theory predicts a nonclassical behavior given by {ital T}{sub {ital c}}{proportional to}{ital N}{sup ({ital D}{minus}2)/2} in two and three dimensions, and the classical Flory--Huggins mean field {ital T}{sub {ital c}}{proportional to}{ital N} law is recovered in four and higher dimensions. For arbitrary interpenetrating polymeric fractals, the theory predicts {ital T}{sub {ital c}}{proportional to}{ital N}{sup ({ital D}{minus}{ital d}{sub {ital f}})/{ital d}{sub {ital f}}} for spatial dimensions below 2{ital d}{sub {ital f}} and Flory--Huggins behavior for {ital D}{gt}2{ital d}{sub {ital f}}. These novel scaling laws for isotopic mixtures are a consequence of a consistent treatment of chain connectivity on all length scales, intermolecular excluded volume, and a short range unfavorable interaction between hydrogenated and deuterated polymers. A general, closure-independent physical argument based on a renormalization of the bare chi parameter by relatively long range correlated fluctuations in the blend is proposed which reproduces all the qualitative predictions of the RISM-MSA integral equation theory. Analogies with nonclassical critical fluctuation effects are established. Application of the analytical approach to purely athermal blends is also presented.

• DOE Contract Number: AC04-76DP00789
• OSTI ID: 6223343
• Journal Information: Journal of Chemical Physics; (USA), Vol. 94:5; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
MIXTURES
CRITICAL TEMPERATURE
POLYMERS
PHASE STUDIES
ANALYTICAL SOLUTION
DIMENSIONS
FRACTALS
INTEGRAL EQUATIONS
LIQUIDS
DISPERSIONS
EQUATIONS
FLUIDS
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
400201* - Chemical & Physicochemical Properties