najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-4-428-437najo-133Research ArticlePHYSICSФИЗИКАThe Space Charge Model. A new analytical approximation solution of Poisson– Boltzmann equation: the extended homogeneous approximationМодель пространственного заряда. Новое аналитическое приближенное решение уравнения Пуассона-Больцмана: расширенное однородное приближениеhttps://orcid.org/0009-0004-2988-0918ДуйкДж.DweikJ.

Jalal Dweik – Jinan university

 Tripoli Lebanon – Main Campus: Zaytoun Abi-Samra, P. O. Box: 818ORCID 

jalal.douwayk@jinan.edu.lbhttps://orcid.org/0009-0005-4696-9786ФархатХ.FarhatH.

Hassan Farhat – Jinan university

Tripoli Lebanon – Main Campus: Zaytoun Abi-Samra, P. O. Box: 818

hassan.farhat@jinan.edu.lbhttps://orcid.org/0000-0003-0576-4264ЮнисДж.YounisJ.

Joumana Younis – Jinan university

Tripoli Lebanon – Main Campus: Zaytoun Abi-Samra, P. O. Box: 818

joumana.younis@jinan.edu.lbJinan UniversityLebanon202303062025144428437Copyright © Dweik J., Farhat H., Younis J., 20252025Дуйк Д., Фархат Х., Юнис Д.Dweik J., Farhat H., Younis J.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/133

The validity of different analytical approximations solution is studied using the classical Poisson– Boltzmann (PB) equation based on a mean-field description of ions as ideal point charges in combination with the assumption of fully overlapped electrical double layers in the membrane pores. The electrical conductivity is calculated by numerical and approximate analytical methods in order to explain the process of ion transport. In this paper, a new analytical approximation named the extended homogeneous approximation (EH) is presented, which provides better results than the homogeneous approximation based on Donnan theory. Also, the results show that the electrical conductivity calculated by the EH, is coherent with the numerical method within specific limits. 

Обоснованность решения различных аналитических аппроксимаций исследована с использованием классического уравнения Пуассона-Больцмана (ПБ), основанного на среднеполевом описании ионов как идеальных точечных зарядов в сочетании с предположением о полностью перекрывающихся двойных электрических слоях в порах мембраны. Электропроводность рассчитана численными и приближенно-аналитическими методами с целью объяснения процесса ионного транспорта. В этой статье представлено новое аналитическое приближение, названное расширенным однородным приближением (EH), которое дает лучшие результаты, чем однородное приближение, основанное на теории Доннана. Кроме того, результаты показывают, что электропроводность, рассчитанная с помощью EH, согласуется с численным методом в определенных пределах.

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The authors declare that there are no conflicts of interest present.