Hard-core Yukawa model

Meijer, E. J. Azhar, F. El, Novel procedure to determine coexistence lines by computer simulation, application to hard-core Yukawa model for charge-stabilized colloids, J. Chem. Phys. 1997,106, 4678-4683... 

The Gibbs-Duhem integration method excels in calculations of solid-fluid coexistence [48,49], for which other methods described in this chapter are not applicable. An extension of the method that assumes that the initial free energy difference between the two phases is known in advance, rather than requiring it to be zero, has been proposed by Meijer and El Azhar [51]. The procedure has been used in [51] to determine the coexistence lines of a hard-core Yukawa model for charge-stabilized colloids. 

The phase behavior of the hard-core Yukawa potential has been studied experimentally and by numerical simulation, see e.g. Ref. [65, 66, 67]. The computed phase diagram of Ref. [67] shows a fluid-solid (bcc/fcc) and a solid-solid (bcc-fcc) coexistence line and it exhibits two fluid-bcc-fcc triple points, (see Fig. 19). The main difference between the phase diagram of the hard-core Yukawa model and that of the pure (i.e. point-particle) Yukawa potential [68] is the presence of the second triple point. This triple point sets a lower limit for the strength of the Yukawa interaction for which a bcc phase exists. 

El Azhar F, Bans M, Ryckaert JP, and Meijer EJ. 2000. Line of triple points for the hard-core Yukawa model A computer simulation study. Journal of Chemical Physics 112 5121-5126. 

The calculations that have been carried out [56] indicate that the approximations discussed above lead to very good thermodynamic functions overall and a remarkably accurate critical point and coexistence curve. The critical density and temperature predicted by the theory agree with the simulation results to about 0.6%. Of course, dealing with the Yukawa potential allows certain analytical simplifications in implementing this approach. However, a similar approach can be applied to other similar potentials that consist of a hard core with an attractive tail. It should also be pointed out that the idea of using the requirement of self-consistency to yield a closed theory is pertinent not only to the realm of simple fluids, but also has proved to be a powerful tool in the study of a system of spins with continuous symmetry [57,58] and of a site-diluted or random-field Ising model [59,60]. 

In our model, the colloids interact via a hard-core repulsive Yukawa potential, given by... 

In reference [19], a systematic comparison between the predictions of the SCGLE theory and the corresponding computer simulation data for four idealized model systems was reported. The first two were two-dimensional systems with power law pair interaction, u(r) = Air", with n = 50 (i.e., strongly repulsive, almost hard-disk like) and with n = 3 (long-range dipole-dipole interaction). The third one was the three-dimensional weakly screened repulsive Yukawa potential (whose two-dimensional version had been studied in reference [18]). The last system considered involved short-ranged, soft-core repulsive interactions, whose dynamic equivalence with the strictly hard-sphere system allowed discussion of the properties of the latter reference system. For all these systems G(r, f) and/or F(k, f) were calculated from the self-consistent theory, and Brownian dynamics simulations (without hydrodynamic interactions) were performed to carry out extensive quantitative comparisons. In all those cases, the static structural information [i.e., g(r) and 5(A )] needed as an input in the dynamic theories was provided by the simnlations. The aim of that exercise was to... 

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