Simulation estimates of cloud points of polydisperse fluids

Matteo Buzzacchi*, Peter Sollich, Nigel B. Wilding, Marcus Müller

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

24 Citations (Scopus)


We describe two distinct approaches to obtaining the cloud-point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand-canonical ensemble. The first method determines the chemical potential distribution μ (σ) (with σ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution ρ (σ) match a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p (n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns μ (σ) such that an equal-peak-weight criterion is satisfied for p (n) for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining μ (σ). We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are exponentially small in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a polydisperse lattice-gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.

Original languageEnglish
Article number046110
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - 18 Apr 2006

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