Erickson D, Li D, Werner C
Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 3G8, Canada
J Colloid Interface Sci. 2000 Dec 1;232(1):186-197. doi: 10.1006/jcis.2000.7153.
In the classical "slope-intercept" method of determining the zeta potential and the surface conductance, the relationship between DeltaP and E(s) is measured experimentally at a number of different channel sizes (e.g., the height of a slit channel, h). The parameter (epsilon(r)epsilon(0)DeltaP/µE(s)lambda(b)) is then plotted as a function of 1/h and linear regression is performed. The y-intercept of the regressed line is then related to the zeta-potential and its slope to the surface conductance. However, in this classical method, the electrical double layer effect or the electrokinetic effects on the liquid flow are not considered. Consequently, this technique is valid or accurate only when the following conditions are met: (1) relatively large channels are used; (2) the electrical double layer is sufficiently thin; and (3) the streaming potential is sufficiently small that the electroosmotic body force on the mobile ions in the double layer region can be ignored. In this paper a more general or improved slope-intercept method is developed to account for cases where the above three conditions are not met. Additionally a general least-squares analysis is described which accounts for uncertainty in the measured channel height as well as unequal variance in the streaming potential measurements. In this paper, both the classical and the improved slope-intercept techniques have been applied to streaming potential data measured with slit glass channels, ranging in height from 3 µm to 66 µm, for several aqueous electrolyte solutions. The comparison shows that the classical method will always overestimate both the zeta-potential and the surface conductance. Significant errors will occur when the classical method is applied to systems with small channel heights and low ionic concentrations. Furthermore, it is demonstrated that traditional regression techniques where the uncertainty is confined only to the dependent variable and each measurement is given equal weight may produce physically inconsistent results. Copyright 2000 Academic Press.
在用于确定zeta电位和表面电导率的经典“斜率-截距”方法中，在多个不同的通道尺寸（例如，狭缝通道的高度h）下通过实验测量ΔP与E(s)之间的关系。然后将参数(ε(r)ε(0)ΔP/µE(s)λ(b))作为1/h的函数进行绘制，并进行线性回归。回归直线的y截距与zeta电位相关，其斜率与表面电导率相关。然而，在这种经典方法中，未考虑电双层效应或对液体流动的电动效应。因此，仅当满足以下条件时，该技术才有效或准确：(1) 使用相对较大的通道；(2) 电双层足够薄；(3) 流动电位足够小，以至于双层区域中移动离子上的电渗体力可以忽略不计。在本文中，开发了一种更通用或改进的斜率-截距方法，以处理上述三个条件不满足的情况。此外，还描述了一种通用的最小二乘法分析，该分析考虑了测量通道高度的不确定性以及流动电位测量中的不等方差。在本文中，经典和改进的斜率-截距技术都已应用于用高度范围从3 µm到66 µm的狭缝玻璃通道测量的几种水性电解质溶液的流动电位数据。比较表明，经典方法总是会高估zeta电位和表面电导率。当将经典方法应用于通道高度小且离子浓度低的系统时，会出现显著误差。此外，还证明了传统的回归技术，其中不确定性仅局限于因变量且每个测量值赋予相等的权重，可能会产生物理上不一致的结果。版权所有2000年学术出版社。
