{"title":"空间电荷模型。泊松-玻尔兹曼方程的一种新的解析逼近解:扩展齐次逼近","authors":"J. Dweik, H. Farhat, J. Younis","doi":"10.17586/2220-8054-2023-14-4-428-437","DOIUrl":null,"url":null,"abstract":"A BSTRACT 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.","PeriodicalId":18782,"journal":{"name":"Nanosystems: Physics, Chemistry, Mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Space Charge Model. A new analytical approximation solution of Poisson-Boltzmann equation: the extended homogeneous approximation\",\"authors\":\"J. Dweik, H. Farhat, J. Younis\",\"doi\":\"10.17586/2220-8054-2023-14-4-428-437\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A BSTRACT 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.\",\"PeriodicalId\":18782,\"journal\":{\"name\":\"Nanosystems: Physics, Chemistry, Mathematics\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nanosystems: Physics, Chemistry, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17586/2220-8054-2023-14-4-428-437\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"NANOSCIENCE & NANOTECHNOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nanosystems: Physics, Chemistry, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17586/2220-8054-2023-14-4-428-437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"NANOSCIENCE & NANOTECHNOLOGY","Score":null,"Total":0}
The Space Charge Model. A new analytical approximation solution of Poisson-Boltzmann equation: the extended homogeneous approximation
A BSTRACT 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.