Department of Applied Physics, University of Fukui, Bunkyo, Fukui, Japan.
J Colloid Interface Sci. 2011 Aug 1;360(1):256-61. doi: 10.1016/j.jcis.2011.04.054. Epub 2011 Apr 24.
This report is concerned with theoretical demonstration of the spontaneous emulsification which has been observed in a soft contact of nitrobenzene with water without surfactant [K. Aoki, M. Li, J. Chen, T. Nishiumi, Electrochem. Commun. 11 (2009) 239]. The demonstration is based on the model of spherical oil droplets with any size in equilibrium. The droplets are composed of the smallest droplets, the total number of which is given. An assembly of small droplets has larger surface energy than that of large ones because the surface energy is proportional to the surface area. The former has larger configurational entropy than the latter because the number of small droplets is bigger than that of the large ones. Since the free energy is determined by the competition between the surface energy and the entropy, it is not clear which assembly has lower free energy. This question was solved numerically here by statistical mechanics calculation of the size distributions, which contained only a parameter of the surface energy. The results of the computation at small number of droplets were used for deriving approximate equations for extremely large number of droplets. The size distribution was localized both to the smallest and the largest droplets. The diameter of the largest droplet was estimated from the dynamics in which coalescence by diffusion of droplets is disturbed by gravitational convection. The size then predicted was of the order of micrometer, being close to experimental values.
本报告关注的是在没有表面活性剂的情况下，硝基苯与水的软接触中观察到的自发乳化的理论证明[K. Aoki、M. Li、J. Chen、T. Nishiumi，电化学通讯 11（2009）239]。该证明基于任何尺寸的球形油滴处于平衡状态的模型。这些液滴由最小的液滴组成，其总数是给定的。由于小液滴的数量比大液滴多，小液滴的集合具有比大液滴更大的表面能，因为表面能与表面积成正比。小液滴的配置熵也比大液滴大，因为小液滴的数量比大液滴多。由于自由能由表面能和熵之间的竞争决定，因此不清楚哪种集合具有更低的自由能。这个问题通过对尺寸分布的统计力学计算得到了数值解，其中只包含一个表面能参数。对少量液滴的计算结果被用于推导出对极大数量液滴的近似方程。尺寸分布既局限于最小的液滴，也局限于最大的液滴。最大液滴的直径是从由于液滴扩散而引起的合并被重力对流干扰的动力学中估计的。预测的尺寸为微米量级，接近实验值。
