Universal features of the free-energy functional at the freezing transition for repulsive potentials

Abstract

The free energy difference between coexisting solid and liquid phases is studied in the context of classical density functional theory (DFT). A bridge function is used to represent the higher-order (n > 2) terms in the perturbative expansion of the excess Helmholtz free energy, and the values of this bridge function within the solid lattice are determined by inversion using literature Monte Carlo simulation results. Four potential models, specifically hard-sphere and inverse 12th-, 6th-, and 4th-power repulsive, are studied. The face-centered cubic (fcc) solid is considered for the hard-sphere and inverse 12th-and 6th-power potentials, while the body-centered cubic (bcc) solid is considered for the inverse 6th-and 4th-power potentials. For a given solid structure there is a remarkable similarity among the bridge functions for different potentials that is analogous to the universality in the sum of elementary diagrams, or bridge functions, of liquid-state theory as originally observed by Rosenfeld and Ashcroft [Physical Review A 20, 1208-1235]. In further analogy with liquid-state theory, the bridge functions in the present problem are plotted as functionals of the second-order convolution term in the perturbative expansion. In each case, the plot indicates a unique functionality in the dense regions of the solid near the lattice sites but a scattered and nonunique behavior in the void regions. Interestingly, knowledge of the functional relationship in the unique region near the lattice sites seems to be sufficient to quantitatively model the solid-fluid phase transition. These qualitative observations are true for both fcc and bcc solid phases, although there are some quantitative differences between them. The findings suggest that pursuit of a closure-based DFT of solid-fluid transitions may be profitable.

Aggregation behavior of nanoparticles: Revisiting the phase diagram of colloids

“…Indeed, the BCC phase was experimentally observed in charged soft colloids with range comparable or exceeding their size (Kanai et al, 2015). For the IPL potential, there are additional symmetries: the thermodynamic behavior can be expressed as a function of a single dimensionless parameter (Verma and Ford, 2011) dependent on a combination of the reduced temperature τ kT/ε and of η γ ρσ 3 τ…”

“…Indeed, the BCC phase was experimentally observed in charged soft colloids with range comparable or exceeding their size ( Kanai et al, 2015 ). For the IPL potential, there are additional symmetries: the thermodynamic behavior can be expressed as a function of a single dimensionless parameter ( Verma and Ford, 2011 ) dependent on a combination of the reduced temperature and of that is a temperature-scaled density. HSY does not display the scaling properties, being a combination of two different functional forms; however, the related point-like Yukawa (PY) without repulsive wall does.…”