Three-dimensional soft sphere systems

The second illustrative example refers to a three-dimensional system of Brownian particles interacting through a strongly repulsive and short-ranged, pair potential u(f) of the form 

FIGURE 1.2 Intermediate scattering function F(k, t) for the soft sphere system in Equation 1.29 with p. = 18 and ( ) = 0.5146 at f/fo = 0.006559, 0.02623, and 0.05247. SCGLE theory solid, dashed, and dotted lines BD results open circles, squares, and triangles. (From Yeomans-Reyna, L. et al. 2003. Phys. Rev. E 67 021108. With permission.) 

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To further highlight the differences in the crystalUne and liquid states Table 9.1 lists the entropies of melting calculated in both two- and three-dimensions from the present work (taken at the respective coexistence curve maxima) and from previous work focussed on relatively simple models hard and soft spheres, a Lennard-Jones potential, and the one-component plasma [102]. The absolute values reported here are larger (and consistent with known values for the conformal systems Si and Ge [103]). However, the ratio of the three- and two-dimensional system values appears consistent throughout, reflecting the more ordered nature of the liquid state when confined to two dimensions. 

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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