Crystallization limits of the two-term Yukawa potentials based on the entropy criterion

Abstract

We examine the fluid-solid transition for the potential with two Yukawa terms (one attractive and the other repulsive) and a hard core by exploration of the parameter space of (K(1), Z(1), and Z(2)), i.e., the parameters of interaction strength and interaction ranges, respectively. We apply the single-phase crystallization rule of Giaquinta and Giunta (1992) by searching for the conditions where the residual entropy reaches zero. To obtain accurate entropy properties, we adopt the self-consistent closure theory of the zero-separation genre. This closure gives accurate thermodynamic properties. The Ornstein-Zernike equation is solved to obtain the correlation functions. The structure factor S(q) is examined with respect to its cluster-cluster peak, whose value is another indication of phase transition according to Hansen and Verlet (1969). We discover that the parameter Z(1) (which determines the range of attractive forces) is important in crystal formation, so long as sufficient attraction (parameter K(1)) is present. If the range of attraction is too narrow, strength alone is not adequate to satisfy the Giaquinta rule or to solidify at given concentration and temperature. The control of the range of repulsion rests with the Z(2)-parameter. Its variations can bring about a high peak in S(q) at zero wave number (i.e., at q=0). Implications for the crystallization of protein and colloidal solutions are discussed.

Two-dimensional systems with competing interactions: dynamic properties of single particles and of clusters

“…denote the positions of either the particles or the clusters at time t. The averaging in equation (11) includes implicitly an average over all particles (or clusters) in the system. In the following, we show correlation functions evaluated at a wave-vector k close to the position of the main peak in the static structure factor of the clusters, S(k), i.e.…”

Two-dimensional systems with competing interactions: microphase formation versus liquid–vapour phase separation

“…The grid in R and K space is equally spaced, with R and K satisfying the usual relation, R K = π/2 M , imposed by the FFT formalism, where M is a suitably chosen integer. As a consequence of relations (11), the grid in r and k space is no longer equally spaced. Furthermore, a lower bound for the R grid, R m = ln r m , has to be chosen.…”

Effects of non-pairwise repulsion on nanoparticle assembly

“…For starters, the long-ranged van der Waals attraction becomes less important than shortranged interactions like H-bonds and the hydrophobic effect. This has inspired numerous studies of the competition between short-range attraction and long-range repulsion, where the repulsion is modeled using a repulsive Yukawa potential [7][8][9][10][11][12][13] . This qualitatively captures the effects of Coulomb repulsion screened by salt because the Yukawa potential emerges from the small potential limit of the Poisson-Boltzmann (PB) equation.…”