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

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.