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Fundamental-measure free energy density functional for hard spheres:
Dimensional crossover and freezing Y. Rosenfeld, M. Schmidt, H. Löwen, and P. Tarazona, Phys. Rev. E 55, 4245 (1997). Locate in [bare] [illustrated] list. Get [full paper] as pdf. Extract. We show that the fundamental-measure geometrically based theory provides a free-energy functional for 3D hard spheres with the correct properties of dimensional crossover and freezing. After a simple modification of the functional, as we propose, it retains all the favorable D=3 properties of the original functional, yet gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D drastically. [more]  Read the [full paper] as pdf. |
Basic model fluids
Density functionals were constructed for hard spheres [5] [6], penetrable spheres that interact with a step-function pair potential [7] (see [14] for more discussion), the Asakura-Oosawa-Vrij model of colloid-polymer mixtures [11], the Widom-Rowlinson model [17], and non-additive hard sphere mixtures [53].DFT for soft potentials
Based on the hard sphere case [5] [6], a density functional theory (DFT) for soft (i.e. continuously varying as a function of interparticle distance) potentials was obtained by considering dimensional crossover [8], and subsequently extended to mixtures [10]. Applications concern the liquid structure of model fluids [13], and structure and freezing of star polymer solutions [15] (see also [16].)Hard spheres
The hard sphere system freezes between [2] and [3], and in ~[23] dimensions (tags as contents!), as well as on stripe-patterned substrates [26]. Deep relations to dimensional crossover exist [5] [6]. Hard spheres were immersed in emulsions [9], confined to a flexible container [18], exposed to surfaces of other quenched spheres [37] and of random fiber networks [39], and subject to gravity [51]. Recently, the Rosenfeld functional [5] [6] was generalized to non-additive mixtures [53].[more]