Asymmetric Fluid Criticality II: Finite-Size Scaling for Simulations

Abstract

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions, $L$, focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded ``complete'' thermodynamic $(L\to \infty )$ scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling $[arXiv:cond-mat/0212145]$, is extended to finite $L$, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when $L\to \infty$, the second temperature derivative, $(d^2{\mu }_{\sigma }/d{T}^2)$, of the chemical potential along the phase boundary, ${\mu }_{\sigma }(T)$, diverges when $T\to\Tc -$. The finite-size behavior of various special {\em critical loci} in the temperature-density or $(T,\rho )$ plane, in particular, the $k$-inflection susceptibility loci and the $Q$-maximal loci -- derived from $Q_L(T,<\rho {>}_L)\equiv <m^2{>}_L^2/<m^4{>}_L$ where $m\equiv \rho -<\rho {>}_L$ -- is carefully elucidated and shown to be of value in estimating $\Tc$ and $\rhoc$. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent $\nu$ that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.

23 pages in the two-column format (including 13 figures) This is Part II of the previous paper [arXiv:cond-mat/0212145]

References in corpus (2)

• Asymmetric Fluid Criticality I: Scaling with Pressure Mixing
• Precise Simulation of Near-critical Fluid Coexistence

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