Zeta电位计算过程中Henry函数的优化表达式
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摘要
利用电泳光散射法可以确定带电颗粒的电泳迁移率,由电泳迁移率计算颗粒的Zeta电位需要准确确定Henry函数的数值。为此,利用最小二乘算法对精确Henry函数值进行拟合,获得优化Henry函数表达式;基于Gouy-Chapman-Stern双电层模型理论,求解不同浓度、不同类型电解质溶液中颗粒的双电层厚度,从而获得准确的颗粒半径a与双电层厚度k-1的比值ka;最后利用优化的函数表达式获得准确的Henry函数值。使用该方法分别计算4种不同浓度电解质下颗粒的Zeta电位,实验结果表明,利用优化的Henry函数可以有效提高颗粒Zeta电位的计算精度,计算结果的相对误差小于1.0%。
The electrophoretic mobility of a charged particle can be determined using the electrophoretic light scattering method.To accurately determine the particles Zeta potential from the mobility requires the use of Henry function.An optimal expression for Henry function can be fitted by using the least squares algorithm.The thickness of the electric double layer in different concentrations and different types of electrolyte can be calculated using the Gouy-Chapman-Stern double layer model.An accurate value of kais obtained,here k-1 is the thickness of the double layer and ais the particle radius.The value of ka can be used in the optimal expression to determine an accurate value of Henry function.The particles Zeta potentials for four different concentrations are measured using this approach.The experimental results show that the optimal Henry function can be used to improve the calculation precision of particles Zeta potential,and the relative error of the calculation results is less than 1.0%.
The electrophoretic mobility of a charged particle can be determined using the electrophoretic light scattering method.To accurately determine the particles Zeta potential from the mobility requires the use of Henry function.An optimal expression for Henry function can be fitted by using the least squares algorithm.The thickness of the electric double layer in different concentrations and different types of electrolyte can be calculated using the Gouy-Chapman-Stern double layer model.An accurate value of kais obtained,here k-1 is the thickness of the double layer and ais the particle radius.The value of ka can be used in the optimal expression to determine an accurate value of Henry function.The particles Zeta potentials for four different concentrations are measured using this approach.The experimental results show that the optimal Henry function can be used to improve the calculation precision of particles Zeta potential,and the relative error of the calculation results is less than 1.0%.
引文
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[10]Henderson D,Blum L.The Gouy-Chapman theory as a special case of the hypernetted chain approximation[J].Journal of Electroanalytical Chemistry and Interfacial Electrochemistry,1978,93(2):151-154.
[11]Miller J F.The determination of very small electrophoretic mobilities of dispersions in non-polar media using phase analysis light scattering[D].Bristol:University of Bristol,1990.
[12]Ohshima H.A simple expression for Henry′s function for the retardation effect in electrophoresis of spherical colloidal particles[J].Journal of Colloid and Interface Science,1994,168(1):269-271.
[13]Coleman T F,Li Y Y.An interior trust region approach for nonlinear minimization subject to bounds[J].SIAMJournal on Optimization,1994,6(2):418-445.
[14]Hunter R J.Zeta potential in colloid science:principles and applications[M].London:Academic Press,2013.
[15]Brookhaven Instruments Corporation.Zeta Plus:Zeta potential analyzer instruction manual[M].[2017-05-17].New York:1997.http:∥docplayer.net/2200719-Brookhaven-instruments-corporation-zetaplus-zeta-potential-analyzer-instructionmanual-brookhaven-instruments-corporation.html.
[16]Liu Wei,Zhang Shanshan,John C.Thomas,et al.Zeta potential measurement method of electrophoretic light scattering based on Chirp Z-transform[J].Acta Optica Sinica,2017,37(2):0229001.刘伟,张珊珊,John C.Thomas,等.基于频谱细化算法的电泳光散射Zeta电位测量方法[J].光学学报,2017,37(2):0229001.
[2]Thomas J C,Hanton K L,Crosby B J.Measurement of the field dependent electrophoretic mobility of surface modified silica/AOT suspensions[J].Langmuir,2008,24(19):10698-10701.
[3]Greatz L.Handbuch der elektrizitt und des magnetismus[M].Leipzig:1921.
[4]Hückel E.Die kataphorese der kugel[J].Physik Z,1924,25:204-210.
[5]Henry D C.The cataphoresis of suspended particles.PartⅠ.The equation of cataphoresis[C].Proceedings of the Royal Society of London,A:Mathematical,Physical and Engineering Sciences.The Royal Society,1931,133(821):106-129.
[6]Overbeek J T G.Quantitative interpretation of the electrophoretic velocity of colloids[J].Advances in Colloid Science,1950,3:797-823.
[7]Wiersema P H,Loeb A L,Overbeek J T G.Calculation of the electrophoretic mobility of a spherical colloid particle[J].Journal of Colloid and Interface Science,1966,22(1):78-99.
[8]O′Brien R W,White L.Electrophoretic mobility of a spherical colloidal particle[J].Journal of the Chemical Society,Faraday Transactions 2:Molecular and Chemical Physics,1978,74(1):1607-1626.
[9]Ohshima H,Healy T W,White L.Approximate analytic expressions for the electrophoretic mobility of spherical colloidal particles and the conductivity of their dilute suspensions[J].Journal of the Chemical Society,Faraday Transactions 2:Molecular and Chemical Physics,1983,79(11):1613-1628.
[10]Henderson D,Blum L.The Gouy-Chapman theory as a special case of the hypernetted chain approximation[J].Journal of Electroanalytical Chemistry and Interfacial Electrochemistry,1978,93(2):151-154.
[11]Miller J F.The determination of very small electrophoretic mobilities of dispersions in non-polar media using phase analysis light scattering[D].Bristol:University of Bristol,1990.
[12]Ohshima H.A simple expression for Henry′s function for the retardation effect in electrophoresis of spherical colloidal particles[J].Journal of Colloid and Interface Science,1994,168(1):269-271.
[13]Coleman T F,Li Y Y.An interior trust region approach for nonlinear minimization subject to bounds[J].SIAMJournal on Optimization,1994,6(2):418-445.
[14]Hunter R J.Zeta potential in colloid science:principles and applications[M].London:Academic Press,2013.
[15]Brookhaven Instruments Corporation.Zeta Plus:Zeta potential analyzer instruction manual[M].[2017-05-17].New York:1997.http:∥docplayer.net/2200719-Brookhaven-instruments-corporation-zetaplus-zeta-potential-analyzer-instructionmanual-brookhaven-instruments-corporation.html.
[16]Liu Wei,Zhang Shanshan,John C.Thomas,et al.Zeta potential measurement method of electrophoretic light scattering based on Chirp Z-transform[J].Acta Optica Sinica,2017,37(2):0229001.刘伟,张珊珊,John C.Thomas,等.基于频谱细化算法的电泳光散射Zeta电位测量方法[J].光学学报,2017,37(2):0229001.