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

The nonlinear Poisson-Boltzmann equation is solved by using Debye-Hu ckel linearizing approximation.A surface charge density（σ）/surface potential（ψ₀） 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.