Analytic integral equation theory for the critical properties of homopolymer fluids

Abstract

We apply the analytic version of the polymer reference interaction site model theory to determine the critical properties of homopolymer fluids. The Gaussian thread model is used throughout, together with a Yukawa form for the attractive interaction between chain segments. Atomiclike as well as molecular closures are employed, and results are presented using both the compressibility and free-energy route approaches to the thermodynamics. Predictions derived based on different closure approximations for the chain length (N) dependence of the theta and critical temperatures, and of the critical density, are compared with the results of simulations of the liquid-vapor equilibrium in homopolymer systems, as well as with experimental results for the demixing transition in polymer solutions. The large N asymptotic scaling laws, and finite size corrections, for the critical properties depend strongly on the closure employed for treating attractive interactions, and for all cases studied significant deviations from the mean-field Flory-Huggins lattice theory are found. The importance of simultaneously including fluctuation effects associated with both the repulsive and attractive interactions is demonstrated. Model calculations are also presented for the liquid-vapor spinodal and coexistence curves.

Critical properties of long-chain substances from the hypothesis of functional self-similarity

“…The numerous empirical equations predict different types of behaviour [2,9,14,[16][17][18]20]. As for the analogy between polymer-solvent and polymer liquid-vapor systems, Chatterjee and Schweizer [36] point out that this analogy cannot be full due to the presence of large density fluctuations and attractive forces in low density critical fluids in contrast with dense multicomponent blends. Using various closure approximations to the RISM theory and thermodynamic routes they found that either the critical temperature diverges at n → ∞ or α = 1/3 or 1/4.…”

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

“…By invoking the polymer+solvent and polymer+vacuum analogy, one would expect from the FH theory that the pure polymer fluid should reach an asymptotic critical temperature, whereas the critical mass density should become vanishingly small. However, in a recent paper, Chatterjee and Schweizer 30 have pointed out that this analogy cannot be taken for granted because the FH scaling predictions are determined by imposing equal chemical potentials, whereas the critical point of pure polymer fluids is related to a phase equilibria that results from the condition of equal pressure at a given temperature.…”

“…In a recent paper, the PRISM was employed in an attempt to solve the question in the framework of an analytical tractable theory, leading to different predictions depending on the closure employed to solve the PRISM equation. 30 Other previous studies using TPT1 plus a mean field attractive contribution suggested that the critical mass density should vanish in the infinite chain length limit. 45 However, such a conclusion relied on the assumption that the mean field contribution increases linearly with the chain length, a point which at present cannot be taken for granted.…”

An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale

“…Recently, we demonstrated in detail how our coarse-graining procedure is thermodynamically consistent with the atomistic description, within polymer integral equation theory, for a soft-sphere coarse-grained representation where we used the PRISM thread model to parameterize the atomistic model. [16,17]. We also presented a detailed, formal study of the effective potential, when a polymer is represented as a chain of soft blobs with variable size.…”