Department of Chemical and Materials Engineering, California State University, Pomona, California 91768, USA.
J Chem Phys. 2010 Feb 21;132(7):074505. doi: 10.1063/1.3308648.
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.
我们通过探索（K(1)、Z(1) 和 Z(2)）的参数空间（即相互作用强度和相互作用范围的参数），研究了具有两个 Yukawa 项（一个吸引项和一个排斥项）和硬心的势能的流固转变。我们应用 Giaquinta 和 Giunta（1992）的单相结晶规则，通过寻找残余熵达到零的条件来实现这一目标。为了获得准确的熵性质，我们采用了零分离类型的自洽封闭理论。这种封闭给出了准确的热力学性质。通过求解奥恩斯坦-泽尔尼克方程来获得相关函数。我们考察了结构因子 S(q)相对于其团簇-团簇峰的情况，根据 Hansen 和 Verlet（1969）的说法，团簇-团簇峰的值是相变的另一个指示。我们发现，参数 Z(1)（决定吸引力范围）在晶体形成中很重要，只要存在足够的吸引力（参数 K(1)）。如果吸引力的范围太窄，仅靠强度不足以满足 Giaquinta 规则或在给定浓度和温度下凝固。排斥范围的控制取决于 Z(2)参数。其变化可以在零波数（即 q=0）处使 S(q)产生高峰值。讨论了对蛋白质和胶体溶液结晶的影响。
