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Square-well Fluid Properties

The purpose of these pages is to provide some explicit results from Monte Carlo simulations for various versions of the Square-well fluid [1]. It is intended to provide guides for testing codes. Reproducing these results is a test of the correctness of codes, either written by the user or obtained elsewhere. The explicit conditions for each of the sets of results are supplied so that meaningful comparisons of your results with the ones listed here are possible.

  1. SAT-TMMC: Liquid-vapor coexistence properties obtained by grand-canonical transition-matrix Monte Carlo and histogram re-weighting [2]. Mean values and uncertainties of the saturation pressure and coexisting liquid and vapor densities, energies, and activities are reported.
    A. SW Potential with well parameter λ=1.5 over the reduced temperature range 0.80 to 1.15 at increments of 0.05.
  2. Equations of state: pressure as a function density at various temperatures.

As is usually the case, temperature, density (number density), pressure, etc., are given in reduced units (denoted by *). That is, these properties are expressed in terms of the well-depth energy, ε, and length scale, σ, defined by the Square-well potential:

$$ \Large V_{sw} \left(r\right) = \left\{ \begin{array}{cc} \infty & r < \sigma \\ - \epsilon & \sigma \leq r < \lambda \sigma \\ 0 & r \geq \lambda \sigma  \end{array} \right. $$

The reduced temperature T*, density ρ*, and pressure p* are kBT/ε, ρσ3, pσ3/ε, respectively. In the Square-well potential, λ is the parameter that sets the well width and, by necessity, is greater than 1.


  1.  A. Rotenberg, J. Chem. Phys. 43, 1198 (1965).
  2. J. R. Errington, J. Chem. Phys. 118, 9915 (2003). 
Created September 8, 2014, Updated July 31, 2018