球状胶粒表面电荷密度/表面电势的一个近似解析式

A Surface Charge Density/Surface Potential Approximate Analytic Expression for Spherical Colloidal Particle

应用Ｄｅｂｙｅ－Ｈüｃｋｅｌ线性化近似求解非线性Ｐｏｉｓｏｎ－Ｂｏｌｔｚｍａｎｎ方程（ＰＢＥ），获得一个混合、非对称电解质溶液中球状胶粒表面电荷密度（σ）／表面电势（Ψ０）的近似解析式，近似解析式适合于大κα的情形，但对于小κα的情形，数值试验表明：只要满足κα≥０．０３，即使表面电势高达３３４ｍＶ（２５℃），近似解析式最大相对误差也低于５％；而文献上报道的其它近似解析式对κα值的下限要求通常高达０．５，甚至于２；本文提出的近似解析式还具有结构简单，适合于分析目的的特点。

The nonlinear Poisson-Boltzmann equation is solved by using Debye-Hu ckel linearizing approximation.A surface charge density(σ)/surface potential(ψ 0) approximate analytic expression is obtained for the spherical colloidal particle immersed in the mixed non-symmetrical electrolyte solution.The expression is fit for the case of large κα,but,in the case of small κα,numerical test shows that only if the condition of κα≥0.03 is met,expression gives a maximal relative error less than 5% even if the scaled surface potential is high up to 13 (equivalent to 334mV at 25)℃).However,the approximate analytic expressions available in literature have a requirement for the low limit of καup to 0.5 or even 2.The expression reported in the present article has a simple structure that can be easily subjected to analysis.