Lai S K, Wu K L
Complex Liquids Laboratory, Department of Physics, National Central University, Chung-li 320, Taiwan, Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 1):041403. doi: 10.1103/PhysRevE.66.041403. Epub 2002 Oct 21.
We model the intercolloidal interaction by a hard-sphere Yukawa repulsion to which is added the long-range van der Waals attraction. In comparison with the Derjaguin-Landau-Verwey-Overbeek repulsion, the Yukawa repulsion explicitly incorporates the spatial correlations between colloids and small ions. As a result, the repulsive part can be expressed analytically and has a coupling strength depending on the colloidal volume fraction. By use of this two-body potential of mean force and in conjunction with a second-order thermodynamic perturbation theory, we construct the colloidal Helmholtz free energy and use it to calculate the thermodynamic quantities, pressure and chemical potential, needed in the determination of the liquid-liquid and liquid-solid phase diagrams. We examine, in an aqueous charged colloidal dispersion, the effects of the Hamaker constant and particle size on the conformation of a stable liquid-liquid phase transition calculated with respect to the liquid-solid coexistence phases. We find that there exists a threshold Hamaker constant or particle size whose value demarcates the stable liquid-liquid coexistence phases from their metastable counterparts. Applying the same technique and using the energetic criterion, we extend our calculations to study the flocculation phenomenon in aqueous charged colloids. Here, we pay due attention to determining the loci of a stability curve stipulated for a given temperature T0, and obtain the parametric phase diagram of the Hamaker constant vs the coupling strength or, at given surface potential, the particle size. By imposing T0 to be the critical temperature T(c), i.e., setting k(B)T0 (=k(B)T(c)) equal to a reasonable potential barrier, we arrive at the stability curve that marks the irreversible/reversible phase transition. The interesting result is that there occurs a minimum size for the colloidal particles below (above) which the colloidal dispersion is driven to an irreversible (reversible) phase transition.
我们通过硬球 Yukawa 排斥来模拟胶体间相互作用，并在此基础上加入长程范德华吸引力。与 Derjaguin-Landau-Verwey-Overbeek 排斥相比，Yukawa 排斥明确纳入了胶体与小离子之间的空间相关性。因此，排斥部分可以解析表达，且具有取决于胶体体积分数的耦合强度。利用这种两体平均力势，并结合二阶热力学微扰理论，我们构建了胶体亥姆霍兹自由能，并用它来计算确定液-液和液-固相图所需的热力学量，即压力和化学势。我们研究了在水相带电胶体分散体系中，哈梅克常数和粒径对相对于液-固共存相计算得到的稳定液-液相变构象的影响。我们发现存在一个阈值哈梅克常数或粒径，其值划分了稳定的液-液共存相与亚稳的对应相。应用相同技术并使用能量判据，我们扩展计算以研究水相带电胶体中的絮凝现象。在此，我们适当关注确定给定温度 T0 规定的稳定性曲线的轨迹，并获得哈梅克常数与耦合强度的参数相图，或者在给定表面势时获得粒径的参数相图。通过将 T0 设定为临界温度 T(c)，即令 k(B)T0（=k(B)T(c)）等于一个合理的势垒，我们得到了标志不可逆/可逆相变的稳定性曲线。有趣的结果是，对于胶体颗粒存在一个最小尺寸，低于（高于）该尺寸时，胶态分散体系会被驱动至不可逆（可逆）相变。
