Multicomponent hard-sphere heterochain fluid: equations of state in a continuum space

Abstract

Simple analytical equations of state have been derived for a mixture of heterochain molecules differing among themselves in both the chain length and primary structure. A model for a polymer chain has been constructed as a sequence of freely jointed tangent hard spheres, whose diameters are not necessarily identical. The statistical mechanical methods previously reported in the literature, namely, a polymeric analog of the Percus-Yevick approximation and the first-order thermodynamic perturbation theory (TPT) of polymerization, have been generalized. According to either of those approaches, the equation of state and residual thermodynamic potentials for the chain fluid are the sum of two terms of which one characterizw a system of disconnected monomers and the other one reflects the effect of monomer bonding in the chain. The specificity of the theories in question shows up in the representation of a second (bonding) term. The quantitative discrepancy in the predictive power of these theories tends to diminish with decreasing packing fraction of the system. As has been found, a version of perturbative theory recently developed by Freed for a homopolymer liquid and the TPT of polymerization lead to essentially the same result in their respective low-order approximations. The general results obtained have been exemplified by a binary copolymer-insolvent system. The copolymer primary structure has been accounted for in the thermodynamic formulas through a weight-average fraction of available chain unit diads, and the chain-length distribution, through anumber-average degree of polymerization. Given the packing fraction, the only necessary molecular parameter in the derived expressions is the ratio of hard-sphere diameters for monomer units and the solvent molecules.

Influence of monomer sequence on microstructure of nonadditive hard chain copolymers: Simulation and equation of state

“…In this work we base our models on the first-order perturbation theory of associating fluids ͑TPT1͒, which was pioneered by Wertheim. 21,22,52 In the literature, the work done using these models was based on additive interactions. In general, the equation of state of m repeat unit chains can be written as…”

Simulation and model development for the equation of state of heteronuclear non-additive copolymer chains

“…The general form of the bonding contribution, Z bond for M multicomponent mixtures and hetero-nuclear chains containing additive hard spherical units was given by Malakhov and Brun: [39] …”

Volume‐explicit equation of state for hard chains, their mixtures, and copolymers

“…Now we can develop equations for chain mixtures by using the general expression given by Eq. 1 and the values of Zhond given by Malakhov and Brun (1992)…”

“…In general, the equation of state of m repeat unit chains can be written as where the first term between the parenthesis is the compressibility factor of the unbonded units, and the second term accounts for the change in Z due to the presence of bonds between the units in a polymer chain. The general form of the theory for multicomponent mixtures and heteronuclear chains containing hard-spherical units in the canonical ensemble was given by Malakhov and Brun (1992). This TPTl theory has been compared to the simulation results of chains of Lennard-Jones segments, with good agreement (Ghonasgi and Chapman, 1994).…”

“…1 with a different expression for Zbond. The general form of the Zbond for multicomponents and heterochains is given by Malakhov and Brun (1992). This model is limited to hard-spherical repeat units.…”