中国物理B ›› 2017, Vol. 26 ›› Issue (1): 17801-017801.doi: 10.1088/1674-1056/26/1/017801

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇    下一篇

Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

Hongqing Tian(田洪庆), Zengju Lian(连增菊)   

  1. Faculty of Science, Ningbo University, Ningbo 315211, China
  • 收稿日期:2016-07-24 修回日期:2016-10-31 出版日期:2017-01-05 发布日期:2017-01-05
  • 通讯作者: Zengju Lian E-mail:lianzengju@nbu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11304169), the Natural Science Foundation of Ningbo City, China (Grant No. 2012A610178), the Open Foundation of the Most Important Subjects of Zhejiang Province, China (Grant No. xkzwl1505), and K. C. Wong Magna Fund in Ningbo University of China.

Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

Hongqing Tian(田洪庆), Zengju Lian(连增菊)   

  1. Faculty of Science, Ningbo University, Ningbo 315211, China
  • Received:2016-07-24 Revised:2016-10-31 Online:2017-01-05 Published:2017-01-05
  • Contact: Zengju Lian E-mail:lianzengju@nbu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11304169), the Natural Science Foundation of Ningbo City, China (Grant No. 2012A610178), the Open Foundation of the Most Important Subjects of Zhejiang Province, China (Grant No. xkzwl1505), and K. C. Wong Magna Fund in Ningbo University of China.

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摘要： We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air-water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.

关键词: Poisson-Boltzmann equation, like-charged attraction, basis function expansion, multipoint collection method

Abstract: We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air-water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.

Key words: Poisson-Boltzmann equation, like-charged attraction, basis function expansion, multipoint collection method

中图分类号:  (Theory, models, and numerical simulation)

  • 78.20.Bh
02.70.-c (Computational techniques; simulations) 05.10.-a (Computational methods in statistical physics and nonlinear dynamics) 78.67.Bf (Nanocrystals, nanoparticles, and nanoclusters)