Phase diagram of a quasi-two-dimensional colloid assembly

We report the results of simulations of the phase diagrams of a quasi-two-dimensional (Q2D) colloid assembly and of a two-dimensional (2D) colloid assembly which have the same colloid-colloid interaction. That interaction is the same as used in the study reported by Zangi and Rice [Phys. Rev. E 58, 7529 (1998)]. Among the goals of the work reported are elucidation of the influence of small amplitude out-of-plane motion on the phase diagram of a system and determination of the effect of that motion on the role of a hexatic phase in the melting process. Both of the systems we have studied undergo a first-order solid I-solid II and solid II-solid III isostructural transition induced by the attractive and repulsive components of the interaction, respectively. Introduction of the out-of-plane motion shifts the low density portion of the phase boundaries involving the solid II phase. The liquid-solid I coexistence line is nearly the same for the two systems. The solid II-solid III transition is shifted to lower temperature and shifted to higher density in the quasi-two-dimensional system. We further use the simulations to calculate the elastic constants, which can be used to predict the location of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting transition. For the Q2D system we find that the first-order melting transition preempts the KTHNY transition for the reduced temperatures T(*)=1.00, 0.60, and 0.50. For the 2D system, when T(*)=0.60, the KTHNY transition barely preempts the first-order melting transition and when T(*)=1.00 and 0.50 the ordinary first-order transition preempts the KTHNY transition.