Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures

Abstract

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solidtransition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura–Oosawa (AO) model where the polymer’s degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is η p r = 0.1 and the colloid-polymer size ratio is q ≡ σ p / σ = 0.15 (with σ p and σ as the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquidsystems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box, creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p co is obtained, yielding p co = 11.576 k B T / σ 3 for the hard-sphere system and p co = 8.00 k B T / σ 3 for the AO model (with k B as the Boltzmann constant and T as the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquidinterface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values γ ̃ ≈ 0.49 k B T / σ 2 for the hard-sphere system and γ ̃ ≈ 0.95 k B T / σ 2 for the AO model.