Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan.
J Colloid Interface Sci. 2010 Sep 15;349(2):641-4. doi: 10.1016/j.jcis.2010.05.094. Epub 2010 Jun 1.
It is known that the electrophoretic mobility of a spherical rigid particle in an electrolyte solution with large kappaa (where kappa=Debye-Hückel parameter and a=particle radius) and large Dukhin number (Du>>1) tends to a nonzero constant value in the limit of high zeta potentials. A highly charged liquid drop exhibits the same limiting mobility value. That is, a liquid drop behaves as if it were a rigid particle (the solidification effect). In the present paper we derive the corresponding mobility expression for a highly charged spherical soft particle (i.e., a polyelectrolyte-coated particle) consisting of the particle core of radius a covered with an ion-penetrable surface layer of thickness d in a symmetrical electrolyte solution of valence z. It is shown that for kappaa>> and kappad>>1, the magnitude of the scaled limiting mobility mu((infinity)) is given by |mu((infinity))|=2epsilon(r)epsilon(o)kT/3etaze x (1+a(3)/2b(3)) x 2 ln 2, where epsilon(r) is the relative permittivity of the electrolyte solution, epsilon(o) is the permittivity of a vacuum, e is the elementary electric charge, and kT is the thermal energy. When a approximately b, the obtained limiting mobility expression tends to the result for a rigid sphere. That is, the solidification effect is observed also for a soft particle.
已知，在卡帕值较大（其中卡帕=德拜-休克尔参数，a=粒子半径）和杜欣数较大（Du>>1）的电解质溶液中，球形刚性粒子的电泳迁移率在高 zeta 势极限下趋于非零常数值。高度带电的液滴表现出相同的极限迁移率值。也就是说，液滴的行为就好像它是一个刚性粒子（凝固效应）。在本文中，我们推导出了相应的高电荷球形软粒子（即带电聚合物涂层粒子）的迁移率表达式，该粒子由半径为 a 的粒子核心组成，核心表面覆盖有厚度为 d 的不可穿透离子的表面层，处于带价 z 的对称电解质溶液中。结果表明，对于卡帕值>>和卡帕值>>1，标度极限迁移率 mu((无穷大))的大小由 |mu((无穷大))|=2epsilon(r)epsilon(o)kT/3etaze x (1+a(3)/2b(3)) x 2 ln 2 给出，其中 epsilon(r)是电解质溶液的相对介电常数，epsilon(o)是真空的介电常数，e 是基本电荷，kT 是热能。当 a 约等于 b 时，得到的极限迁移率表达式趋于刚性球体的结果。也就是说，凝固效应也适用于软粒子。
