Molecular Thermodynamic Model of Multicomponent Chainlike Fluid Mixtures Based on a Lattice Model

Abstract

The molecular thermodynamic model of polymer solutions based on a close-packed lattice model presented in a previous work has been generally extended to multicomponent chainlike fluid mixtures. The Helmholtz function of mixing contains three terms, i.e., the contribution of athermal mixing of polymer chains, which is calculated by Guggenheim's theory; the contribution of nearest-neighbor interactions between monomers, which is calculated by Yang et al.'s model of the Helmholtz function of mixing for a multicomponent Ising lattice; and the contribution of the formation of polymer chains from monomers, which is obtained according to the sticky-point theory of Cummings, Zhou, and Stell. The liquid-liquid phase equilibria of ternary chainlike mixtures predicted by this model are in good agreement with Monte Carlo simulation results and superior to the results calculated by Flory-Huggins (FH) theory and revised Freed theory (RFT) obviously. This model not only can describe types 1-3 phase separations of Treybal classification satisfactorily, but can also correlate well the coexistence curves of binary polymer blends systems with an upper critical solution temperature (UCST) or a lower critical solution temperature (LCST). Meanwhile, model parameters correlated from the binary system can be further extended to predict the corresponding liquid-liquid equilibrium of ternary mixtures, including systems of ionic liquids.

Possible Way to Study Cononsolvency in Confinement: A Lattice Density Functional Theory Approach

“…The above approximations are directly extended from the PLDFT for binary polymer solutions. The function expressions can be obtained from the equation of state for a corresponding uniform system, , where λ L = ( L – 1)­( L – 2)­( aL + b )/ L 2 is a factor accounting for long-range correlations of polymers and constant c = 1.1. The reduced exchange interaction energies (measuring the immiscibility) between particles of types i and j are It should be noted that Flory parameter χ ij = zε̃ ij /2 is quite convenient for mimicking the coarse-grained effective interactions between segments i and j for real fluids − containing nonpolar or polar interparticle interactions.…”

“…The function expressions can be obtained from the equation of state for a corresponding uniform system, , where λ L = ( L – 1)­( L – 2)­( aL + b )/ L 2 is a factor accounting for long-range correlations of polymers and constant c = 1.1. The reduced exchange interaction energies (measuring the immiscibility) between particles of types i and j are It should be noted that Flory parameter χ ij = zε̃ ij /2 is quite convenient for mimicking the coarse-grained effective interactions between segments i and j for real fluids − containing nonpolar or polar interparticle interactions. When ε̃ i 0 = βε ii ≡ ε̅ ii < 0, the effective excluded volume of a monomer i can be larger than a single lattice site because the enhanced binding of a particle to vacuum implies an enlarged depletion zone around the particle to exclude surrounding particles or an enlarged effective volume occupied by the particle.…”

“…The above approximations are directly extended from the PLDFT for binary polymer solutions. The function expressions can be obtained from the equation of state for a corresponding uniform system, 23,24 ∑ ∑…”

The effect of saccharides on equilibrium swelling of thermo-responsive gels

“… 32 To ameliorate the accuracy of fitting, three approaches were suggested: (i) introduction of prescribed dependencies of the coefficients χ ij on volume fractions of constituents, 33 (ii) extension of eqn (2) to account for size and shape of solvent molecules and segments of chains, as well as for attractive and repulsive interactions between them, 34 and (iii) inclusion of higher-order terms with respect to ϕ 1 , ϕ 2 , ϕ n into eqn (2) . 35 Although these refinements improve the quality of matching experimental data, they lead to a strong increase in the number of adjustable parameters, which makes questionable the ability of the models to predict the thermo-mechanical behavior of TR gels in mixtures of solvents.…”

Liquid–liquid equilibria for ternary polymer mixtures

“…To make Freed's LCT more accessible for engineering purposes, Hu et al [23][24][25] revised the Freed theory (RFT) and proposed a double lattice model. Recently, Yang et al [26] developed a mixing Helmholtz function model for a multicomponent Ising lattice, and Liu et al [27,28] constructed a molecular thermodynamic model for ternary polymer systems.…”