Finite size effect of ions and dipoles close to charged interfaces

doi:10.1088/1674-1056/19/4/048702

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 48702-048702.doi: 10.1088/1674-1056/19/4/048702

Finite size effect of ions and dipoles close to charged interfaces

童朝晖, 诸跃进

Department of Physics, Ningbo University, Ningbo 315211, China

收稿日期:2009-06-20 修回日期:2009-09-27 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~20954001 and 10774079), the Natural Science Foundation of Zhejiang Province of China (Grant No.~Y7080401), the Natural Science Foundation of Ningbo City (Grant No.~2009A6100

Finite size effect of ions and dipoles close to charged interfaces

Tong Chao-Hui(童朝晖)^† and Zhu Yue-Jin(诸跃进)

Department of Physics, Ningbo University, Ningbo 315211, China

Received:2009-06-20 Revised:2009-09-27 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~20954001 and 10774079), the Natural Science Foundation of Zhejiang Province of China (Grant No.~Y7080401), the Natural Science Foundation of Ningbo City (Grant No.~2009A6100

摘要/Abstract

摘要： The modified dipolar Poisson--Boltzmann (MDPB) equation, where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level, is studied numerically for a two-plate system with oppositely charged surfaces. The MDPB equation is solved numerically, using the nonlinear Multigrid method, for one-dimensional finite volume meshes. For a high enough surface charge density, numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density. Furthermore, increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces. This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson--Boltzmann (DPB) equation. This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer. In the weak-coupling regime with the electrostatic coupling parameter (the ratio of Bjerrum length to Gouy--Chapman length) $\varXi < 1$, where the MDPB equation works, the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces. Therefore, there are no physical and computational advantages for the MDPB equation over the modified Poisson--Boltzmann (MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.

Abstract: The modified dipolar Poisson--Boltzmann (MDPB) equation, where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level, is studied numerically for a two-plate system with oppositely charged surfaces. The MDPB equation is solved numerically, using the nonlinear Multigrid method, for one-dimensional finite volume meshes. For a high enough surface charge density, numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density. Furthermore, increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces. This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson--Boltzmann (DPB) equation. This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer. In the weak-coupling regime with the electrostatic coupling parameter (the ratio of Bjerrum length to Gouy--Chapman length) $\varXi < 1$, where the MDPB equation works, the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces. Therefore, there are no physical and computational advantages for the MDPB equation over the modified Poisson--Boltzmann (MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.

Key words: dipole, Poisson--Boltzmann equation, charged interface, polarisation

中图分类号: (Permittivity (dielectric function))

77.22.Ch

73.25.+i (Surface conductivity and carrier phenomena) 41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems)

童朝晖, 诸跃进. Finite size effect of ions and dipoles close to charged interfaces[J]. 中国物理B, 2010, 19(4): 48702-048702.

Tong Chao-Hui(童朝晖) and Zhu Yue-Jin(诸跃进). Finite size effect of ions and dipoles close to charged interfaces[J]. Chin. Phys. B, 2010, 19(4): 48702-048702.

参考文献 32

[1]	Andelman D 1995 Handbook of Biological Physics: Structure and Dynamics of Membranes] (Vol.1B) ed.\ Lipowsky R and Sackmann E (Amsterdam: Elsevier Science) pp.603--642
[2]	Israelachvili J N 1990 Intermolecular and Surface Forces] 2$^{\rm nd}$ ed.\ (London: Academic Press)
[3]	Henderson D 1992 Fundamentals of Inhomogeneous Fluids} (New York: Dekker)
[4]	Netz R R and Andelman D 2003 Phys. Rep. 380 1
[5]	Lan D, Wang Y R, Yu Y, Ma W J and Li C 2007 Chin. Phys. 16 468
[6]	Jiang H Y, Ren Y K, Ao H R and Antonio R 2008 Chin. Phys. B 17 4541
[7]	Debye P and Huckel E 1923 Physik 24 185
[8]	Debye P and Huckel E 1923 Physik 24 305
[9]	Lamperski S, Outhwaite C W and Bhuiyan L B 1996 Mol. Phys. 87 1049
[10]	Kjellander R and Marcelja S 1986 J. Phys. Chem. 90 1230
[11]	Attard P, Mitchell D J and Ninham B W 1988 J. Chem. Phys. 89 4358
[12]	Nordholm S, Penfold R, Jonsson B and Woodward C E 1991 J. Chem. Phys. 95 2048
[13]	Netz R R and Orland H 2000 Eur. Phys. J. E 1 203
[14]	Forsman J 2004 J. Phys. Chem. B 108 9236
[15]	Forsman J 2007 Langmuir 23 5515
[16]	Lau A W C 2008 Phys. Rev.E 77 011502
[17]	Borukhov I, Andelman D and Orland H 1997 Phys. Rev. Lett. 79 435
[18]	Borukhov I, Andelman D and Orland H 2000 Electrochim. Acta 46 221
[19]	Bauer B A and Patel S 2009 J. Chem. Phys. 131 084709
[20]	Zhou X Y and Lu H J 2007 Chin. Phys. 16 441
[21]	Huang J P and Yu K W 2004 Chin. Phys. 13 1065
[22]	Kofinger J and Dellago C 2009 Phys. Rev. Lett. 103 080601
[23]	Zhao H P, Liu Z Y and Liu Y Y 2001 Chin. Phys. 10 35
[24]	Abrashkin A, Andelman D and Orland H 2007 Phys. Rev. Lett. 99 077801
[25]	Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992 Numerical Recipe in Fortran 77: the Art of Scientific Computing} 2$^{\rm nd}$ ed.\ (New York: Cambridge University Press) Chapter 19.6
[26]	Tong C, Wu T and Provatas N 2006 Modelling Simul. Mater. Sci. Eng. 14 1447
[27]	Naji A, Jungblut S, Moreira A G and Netz R R 2005 Physica A 352 131
[28]	Boroudjerdi H, Kim Y W, Naji A, Netz R R and Serr A 2005 Phys. Rep. 416 129
[29]	Koehl P, Orland H and Delarue M 2009 Phys. Rev. Lett. 102 087801
[30]	Wertheim M S 1971 J. Chem. Phys. 55 4291
[31]	Kusalik P G and Patey G N 1988 J. Chem. Phys. 88 7715
[32]	Patra C N and Ghosh S K 1997 J. Chem. Phys. 106 2752

Finite size effect of ions and dipoles close to charged interfaces

Finite size effect of ions and dipoles close to charged interfaces

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Kuiyuan Tian(田魁元), Yong Liu(刘勇), Jiangfeng Du(杜江锋), and Qi Yu(于奇). Design optimization of high breakdown voltage vertical GaN junction barrier Schottky diode with high-K/low-K compound dielectric structure[J]. 中国物理B, 2023, 32(1): 17306-017306.
[2]	Xiaoting Sun(孙小婷), Yadong Zhang(张亚东), Kunpeng Jia(贾昆鹏), Guoliang Tian(田国良), Jiahan Yu(余嘉晗), Jinjuan Xiang(项金娟), Ruixia Yang(杨瑞霞), Zhenhua Wu(吴振华), and Huaxiang Yin(殷华湘). Improved performance of MoS₂ FET by in situ NH₃ doping in ALD Al₂O₃ dielectric[J]. 中国物理B, 2022, 31(7): 77701-077701.
[3]	Yu-Bo Li(李宇博), Hao-Yuan Song(宋浩元), Yu-Qi Zhang(张玉琦), Xiang-Guang Wang(王相光),Shu-Fang Fu(付淑芳), and Xuan-Zhang Wang(王选章). Tunable enhanced spatial shifts of reflective beam on the surface of a twisted bilayer of hBN[J]. 中国物理B, 2022, 31(6): 64207-064207.
[4]	. [J]. 中国物理B, 2021, 30(1): 18102-.
[5]	. [J]. 中国物理B, 2020, 29(12): 127701-.
[6]	李永强, 杜新哲, 龚冬良, 杨綦睿, 张汶良, 谢涛, 冯波, 陈恺, 罗会仟, 刘俊明, 朱劲松. The c-axis complex permittivity and electrical impedance in BaFe₂As₂:Experimental examination on transformation validity[J]. 中国物理B, 2019, 28(5): 57702-057702.
[7]	J Mohammed, A B Suleiman, Tchouank Tekou Carol T, H Y Hafeez, Jyoti Sharma, Pradip K Maji, Sachin Godara Kumar, A K Srivastava. Enhanced dielectric and optical properties of nanoscale barium hexaferrites for optoelectronics and high frequency application[J]. 中国物理B, 2018, 27(12): 128104-128104.
[8]	郭艳艳, 郭云均, 魏通, 刘俊明. Multifold polar states in Zn-doped Sr_0.9Ba_0.1TiO₃ ceramics[J]. 中国物理B, 2015, 24(12): 127701-127701.
[9]	侯志文, 康爱国, 马维清, 赵晓龙. Dimension effects on the dielectric properties of fine BaTiO₃ ceramics[J]. 中国物理B, 2014, 23(11): 117701-117701.
[10]	莫漫漫, 文岐业, 陈智, 杨青慧, 邱东鸿, 李胜, 荆玉兰, 张怀武. Strong and broadband terahertz absorber using SiO₂-based metamaterial structure[J]. 中国物理B, 2014, 23(4): 47803-047803.
[11]	S. Maletic, D. Maletic, I. Petronijevic, J. Dojcilovic, D. M. Popovic. Dielectric and infrared properties of SrTiO₃ single crystal doped by 3d (V, Mn, Fe, Ni) and 4f (Nd, Sm, Er) ions[J]. 中国物理B, 2014, 23(2): 26102-026102.
[12]	吕元杰, 冯志红, 顾国栋, 敦少博, 尹甲运, 王元刚, 徐鹏, 韩婷婷, 宋旭波, 蔡树军, 栾崇彪, 林兆军. Different influences of Schottky metal on the strain and relative permittivity of barrier layer between AlN/GaN and AlGaN/GaN heterostructure Schottky diodes[J]. 中国物理B, 2014, 23(2): 27102-027102.
[13]	T. Ataseven, A. Tataroğlu. Temperature-dependent dielectric properties of Au/Si₃N₄/n-Si (metal–insulator–semiconductor) structures[J]. 中国物理B, 2013, 22(11): 117310-117310.
[14]	吕元杰, 冯志红, 蔡树军, 敦少博, 刘波, 尹甲运, 张雄文, 房玉龙, 林兆军, 孟令国, 栾崇彪. Influence of drain bias on the electron mobility in the AlGaN/AlN/GaN heterostructure field-effect transistors[J]. 中国物理B, 2013, 22(6): 67104-067104.
[15]	卢明明, 袁杰, 温博, 刘甲, 曹文强, 曹茂盛. Carbon materials with quasi-graphene layers: the dielectric, percolation properties and the electronic transport mechanism[J]. 中国物理B, 2013, 22(3): 37701-037701.