Simulation of Phase Transitions in Highly Asymmetric Fluid Mixtures

We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle-size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs ensemble, we are able to probe directly the density and concentration fluctuations that drive phase transitions, but that are inaccessible to conventional simulation algorithms. We develop a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multicomponent fluids. Several illustrative examples are presented.

Figure 1

Measured iso-$Q^{*}$ points (symbols) for a pure LJ fluid, together with parabolic fits (curves). The maxima of the curves (shown for $L/\sigma =10$, 20, 30) in the ${\tilde{\rho }}_0\mathrm{\text{−}}\tilde{T}$ plane correspond to the critical point. The data collapse in the inset confirms the scaling prediction [Eq. (6)].

Figure 2

Iso-$Q^{*}$ curves for size-asymmetric binary mixtures consisting of a LJ fluid (particle size $\sigma$) and small additives (particle diameter $\sigma /10$, volume fraction ${\varphi }_s$). All curves pertain to a linear system size $L=8.06\sigma$. For additives that interact with the fluid as hard spheres (diamonds, upper curve), the critical temperature and density increase compared to the pure fluid (open circles), whereas the critical temperature decreases strongly if the additives have a weak attraction with the fluid (squares, filled circles, triangles).

Figure 3

Variance of $P^{\mathrm{RG}}(x)$ for a LJ mixture with size asymmetry $\sigma /{\sigma }_s=10$, as a function of total number density ${\tilde{\rho }}_0$. Each (isothermal) curve is obtained from simulations at selected densities, but with constant additive volume fraction ${\varphi }_s=0.005$, and is parabolic (see fits), confirming Eq. (7). The maxima locate the coexistence curve diameter.

Figure 4

(a) Example of a $P^{\mathrm{RG}}$ at ${\rho }_0={\rho }_d$, for the fluid mixture described in Fig. 3. (b) Corresponding phase diagram; the open circle indicates the critical point of a pure LJ fluid. The full line is a fit of the form ${\rho }^{\pm }-{\rho }^c=ut+v{t}^{\beta }$.