Freezing of a soft-core fluid in a one-dimensional potential: Predictions based on a pressure-balance equation

Abstract

Using concepts from classical density functional theory (DFT) we investigate the freezing of a two-dimensional (2D) system of ultra-soft particles in a one-dimensional (1D) external potential; a phenomenon often called laser-induced freezing (LIF). In the first part of the paper, we present numerical results from free minimization of a mean-field density functional for a system of particles interacting via the GEM-4 potential. We show that the system does indeed display a LIF transition, although the interaction potential is markedly different from the cases studied before. We also show that one may consider the (suitably defined) effective density within the potential wells,ρ eff , as a control parameter of LIF, rather than the amplitude of the external potential as in the common LIF scenario. In the second part, we suggest a new theoretical description of the onset of LIF which bases on the pressure balance equation relating the pressure tensor and the external potential. Evaluating this equation for the modulated liquid phase at effective densityρ eff and combining it with the (known) stability threshold of the corresponding bulk fluid, we can predict the critical effective density or, equivalently, the potential amplitude related to the onset of LIF. Our approach yields very good results for the model at hand, and it is transferable, in principle, to other model systems.

Freezing of a soft-core fluid in a one-dimensional potential: Appearance of a locked smectic phase

“…Due to the mean-field character of our approach, the occurrence of LSm is indeed not an obvious result. Different from other studies, however, we do not see re-entrant melting [31], which is consistent with our previous study of systems at p = 1 [47], but which is in contrast to observations in charged polystyrene spheres [34] and for hard discs [29].…”

“…Our present study is based on the same type of model (ultra-soft colloids) and same method of investigation (classical density functional theory in mean-field approximation) as our earlier study on systems with commensurability parameter p = 1 [47].…”

“…As for the colloidal system, we consider (for reasons outlined below and, in more detail, in Ref. [47]) a 2D system of ultra-soft particles, with the interaction given by the generalized exponential model of index n (GEM-n),…”

“…Until recently, studies of LIF were restricted to systems of particles with strongly repulsive interactions, although it is nowadays possible not only to create soft particleparticle interactions [40][41][42][43], but also to investigate their interaction with a substrate [44][45][46]. This motivated us in an earlier study based on classical density functional theory [47] to investigate the phenomenon of LIF in a system interacting via an ultra-soft potential on cosine and Gaussian substrates, focusing on the case p = 1 (where each potential minimum is equally populated). Despite a mean-field like treatment, we could establish the occurrence of LIF and provide full phase diagrams in the planes spanned by the average density ρ and the parameters controlling the fluidsubstrate potential.…”

“…In the present paper, we extend the methodology of [47] to systems with commensurability parameter p = 2, for which, in the ordered phase, the particle distribution in direction perpendicular to the substrate minima has periodicity 2L s . At p = 2, the theory of Frey, Nelson, and Radzihovsky [14,15] predicts that the (re-entrant) melting of the LFS (with p = 2) upon increasing V 0 occurs through two phase transitions with successive unbinding of dislocation pairs.…”