帶電球型複合粒子在電解質濃度梯度中之擴散泳運動

Diffusiophoresis of a Spherical Soft Particle in Electrolyte Gradients

黃稟元(Ping-Yuan Huang)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.00175

摘要

本論文以理論探討帶有固定電荷的球型複合粒子在電解質溶液中所進行的擴散泳運動。複合粒子可分成二個部份；一為內部，即中心固體的部分，溶液中的離子與流體皆無法穿透其表面；另一為表面層，即為中心固體周圍吸附的均勻多孔性物質層或高分子層，而離子與流體皆可自由地穿透。本文在解析的過程中，考慮複合球型粒子在任意電雙層厚度但低電位的條件下，求解Poisson-Boltzmann方程式和修正過的Stokes方程式。主導對稱電解質溶液中的電位分佈、離子濃度分佈和流場分佈的電動力方程式可以藉由假設相對於平衡狀態時，系統只有受到微小的擾動來線性化。藉由正規擾動法，這些被線性化的方程式以複合球型粒子之固體核心表面的電荷密度和多孔表面層的固定電荷密度做為二個微小擾動參數，並搭配上適當的邊界條件來求得解析解，進而求得電解質溶液中的電位分佈、流速分佈、壓力分佈以及電化學位能分佈。
求解上述四物理量分布後，再藉由平衡作用於粒子的電力和流體阻力等二力，可以得到帶電複合粒子的擴散泳正規化速度的解析形式，其表示式準確到固體核心表面的電荷密度和多孔表面層的固定電荷密度之第二階。結果顯示：由相異電性但相等電量之固體核心和多孔表面層組合成之電中性複合粒子可進行擴散泳運動(包含電泳和化學泳)，且運動方向是由多孔表面層上的固定電荷所決定。在固體核心和整顆複合粒子的半徑比極限的情況下，帶電複合球型粒子即分別蜕變成球型固體粒子和球型多孔粒子，故亦可得到這二種粒子的擴散泳正規化速度的解析解。

關鍵字

擴散泳 ； 球型複合粒子 ； 電解質濃度梯度 ； 電雙層

並列摘要

An analytical study of the diffusiophoresis (consisting of electrophoresis and chemiphoresis) of a charged soft particle (or composite particle) composed of a spherical rigid core and a surrounding porous shell in an electrolyte solution prescribed with a uniform concentration gradient is presented. In the solvent-permeable and ion-penetrable porous surface layer of the particle, idealized frictional segments with fixed charges are assumed to distribute at a constant density. The electrokinetic equations which govern the electric potential profile, ionic concentration distributions, and fluid flow field inside and outside the porous layer of the particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the surface charge densities on the rigid core surface and the fixed charge densities in the porous shell as the small perturbation parameters.
An analytical expression for the diffusiophoretic mobility of the soft sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the surface charge densities on the rigid core surface and the fixed charge densities in the porous shell, is valid for arbitrary values of , , , and , where is the reciprocal of the Debye screening length, is the reciprocal of the length characterizing the extent of flow penetration inside the porous layer, is the normalized diffusion coefficient of the small ions in the porous structure, is the radius of the soft sphere, and is the radius of the rigid core of the particle. It is shown that a soft particle bearing no net charge can undergo diffusiophoresis (electrophoresis and chemiphoresis), and the direction of its diffusiophoretic velocity is decided by the fixed charges in the porous surface layer of the particle. In the limiting cases of large and small values of , the analytical solution describing the diffusiophoretic mobility for a charged soft sphere reduces to that for a charged rigid sphere and for a charged porous sphere, respectively.

並列關鍵字

Diffusiophoresis ； Spherical soft particle ； Electrolyte gradient ； Double layer

參考文獻

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