可調整電荷多孔球形粒子稀薄懸浮液之沉降速度與電位

Abstract

本論文解析研究任意電雙層下之可調整電荷多孔球形粒子的沉降行為，其多孔粒子通常由離子溶液可穿透之高分子電解質或奈米粒子凝聚體所構成。帶有流體摩擦阻力的可解離之官能基團均勻地分布在多孔球形粒子裡，當結合或解離反應發生在官能基團時會有電荷調整的機制使粒子之固定電荷密度與電位分佈線性相關。本論文使用正規微擾法求解主導離子濃度(或電化學位能)分佈、電位分佈和流體速度分佈之線性化電動力方程式，獲得可調整電荷多孔粒子的沉降速度和多孔粒子稀薄懸浮系統之沉降電位解析式。電荷調整效應會降低電動力對沉降速度阻礙的影響，亦會減少相對於當固定電荷密度為定值的情況下之沉降電位(可分別減少50%和25%之多)，而這些降低電動力對沉降速度阻礙及減少沉降電位的效應皆會消失於粒子的等電點。當決定粒子固定電荷之離子濃度提高並越過等電點濃度時，會改變固定電荷密度的正負值且也因此反轉沉降電位的方向。電荷調整效應對多孔粒子沉降運動之影響基本上有別於硬質粒子。

The sedimentation of a charge-regulating porous sphere surrounded by an arbitrary electric double layer, that usually models a permeable polyelectrolyte coil or aggregate of nanoparticles, is analyzed for the first time. The hydrodynamic frictional segments and ionogenic functional groups uniformly distribute in the porous sphere, and a regulation mechanism for the dissociation and association reactions occurring at these functional groups linearly relates the local electric potential to fixed charge density. The linearized electrokinetic equations governing the ionic concentration (or electrochemical potential energy), electric potential, and fluid velocity fields are solved for the case of a small basic fixed charge density by the regular perturbation method. Analytical formulae for the sedimentation velocity of a porous sphere and sedimentation potential of a dilute suspension of porous spheres are then obtained. The charge regulation tends to reduce the electrokinetic retardation to sedimentation velocity and the sedimentation potential (can be as much as 50 and 25 per cents, respectively) compared to the case that the fixed charge density is a constant. Both the electrokinetic retardation to sedimentation velocity and the sedimentation potential vanish at the isoelectric point of the particles. The increase in the bulk concentration of the potential-determining ions crossing the isoelectric point changes signs of the fixed charges and thus causes a reversal in the direction of the sedimentation potential. The effects of charge regulation on the sedimentation of porous particles differ substantially from those of hard particles.