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Dimensional crossover and the freezing transition in density functional
theory Y. Rosenfeld, M. Schmidt, H. Löwen, and P. Tarazona, J. Phys.: Condens. Matt. 8, L577 (1996). Locate in [bare] [illustrated] list. Get [full paper] as pdf. Extract. A modified geometrically based free-energy functional for hard spheres is proposed which gives reliable results even for situations of extreme confinements that reduce the effective dimensionality D. It is accurate for hard spheres between narrow plates (D = 2), inside narrow cylindrical pores (D = 1), and is exact in the 0D limit (a cavity that cannot hold more than one particle). This functional also predicts the hard-sphere fluid-solid transition in excellent agreement with the simulations. [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]