Abstract
The Helmholtz free energy and pressure for binary Lennard-Jones chain mixtures are derived using a variational first-order perturbation theory. The reference system consisting of a binary mixture of freely jointed tangent hard sphere chains is solved in the Percus-Yevick approximation. The optimal diameter of segments in the hard sphere chain reference system is determined by minimizing the Helmholtz free energy for the chain mixture through the Gibbs-Bogoliubov inequality. The Lennard-Jones potential is introduced via a perturbation on the reference system and uses only the interchain radial distribution function, which is solved in the Percus-Yevick approximation. This simplification is compensated for by introducing a state-independent parameter κ
B
for pure components to account for intrachain (three-body) effects included in the simulation but omitted from the theory. A simple mixing rule is proposed to calculate mixture integrals appearing in the perturbation term. New simulation data are presented for binary Lennard-Jones chain mixtures for a range of temperatures T*, chain lengths m and chain fraction, plus Lennard-Jones size (σ) and energy (ε) parameters. Six physical systems are studied: a 4-mer/4-mer mixture with ε
22
/ε
11
= 1.2 and equal size parameters; a 4-mer/4-mer mixture with σ
22
/σ
11
= 1.5 and equal energy parameters; a 4-mer/8-mer mixture with equal parameters; a 4-mer/8-mer mixture with ε
22
/ε
11
= 1.2 and equal size parameters; an 8-mer/8-mer mixture with ε
22
/ε
11
= 1.2 and equal size parameters; and an 8-mer/8-mer mixture with σ
22
/σ
11
= 1.5 and equal energy parameters. All six systems are simulated at three segment densities (ρ = 0.2, 0.4 and 0.8), two reduced temperatures (T* = kT/ε
11
= 4 and 8) and six chain fractions (X
1
= 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0). Good agreement is obtained between simulation and theory over a range of parameters and conditions.