Theory for the phase behaviour of a colloidal fluid with competing interactions

Abstract

We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gasliquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behaviour. The amplitude of the density modulations is the order parameter in our theory. The theory predicts that the phase transition from the uniform to the modulated fluid phase can be either first order or second order (continuous). The phase diagram exhibits two tricritical points, joined to one another by the line of second order transitions.

Finite size effects in neutron star and nuclear matter simulations

“…Similar non-homogeneous structures are found in solvated di-block copolymers [18] and are, actually, inherent to any system with competing interacions of different ranges (see [20,21] and references therein). Phenomenologically, this usually manifests as a competition between bulk and surface or interfacial energies which is settled by adopting a geometry such that its surface is minimal [22], while subject to constraints or frustration.…”

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

“…This procedure was applied to pattern formation in systems with competing interactions in two 7 and three 42 dimensions, but in the latter case, the density profile was assumed to vary only along one direction. An algorithm implementing a similar method was also used in SCFT calculations of the structures formed by hard dumbbells with attractive interactions in two dimensions.…”

“…12, at least for one-component systems. A similar mean-field approach has also been employed in the study of microphase formation in a fluid of hard-core particles with competing short-range attractive and longer-range repulsive interactions; 7,42 although in the latter case, the reference part of the free energy contains also the hard-sphere contribution and therefore cannot be treated exactly.…”

Communication: Thermodynamic signatures of cluster formation in fluids with competing interactions

“…13 Upon increasing R or z 1 , particles tend to aggregate into finite clusters, eventually leading to microphase separation which preempts the macroscopic GL transition. [2][3][4][5][6][7][8] The cluster size is determined by a subtle balance between the SA, which favours the onset of aggregation, and the LR, which limits the growth of clusters. A widely used diagnostic of aggregation is provided by the static structure factor S(q) (q = kσ is the reduced wavenumber).…”

“…3,5,8,15 For appropriate choices of z 1 , z 2 , and R, the amplitude of the prepeak increases with K 1 , while its position shifts towards lower wavenumbers. 2,8 In fact, the random phase approximation 2 and a mean field version of density functional theory 6,7 0021-9606/2012/137(1)/011101/4/$30.00…”