Virial coefficients and demixing in the Asakura-Oosawa model

TL;DR

This paper investigates the demixing transition in the Asakura-Oosawa colloid-polymer model by calculating virial coefficients up to fifth order and comparing critical constants with Monte Carlo simulation results.

Contribution

It provides analytical expressions for the fourth virial coefficient and numerical estimates for the fifth, enhancing understanding of phase behavior in the model.

Findings

Critical constants vary with virial order considered.

Analytical fourth virial coefficient derived for the first time.

Numerical fifth virial coefficients obtained via Monte Carlo.

Abstract

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out.