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

摘要

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition 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-liquid systems 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-liquid interface, 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.