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A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions
Qiao, Yu1; Liu, Xuejiao1; Chen, Minxin2; Lu, Benzhuo1
2016-04-01
Source PublicationJOURNAL OF STATISTICAL PHYSICS
ISSN0022-4715
Volume163Issue:1Pages:156-174
AbstractThe hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al. in Phys Rev Lett 79:435-438, 1997; Kilic et al. in Phys Rev E 75:021502, 2007; Lu and Zhou in Biophys J 100:2475-2485, 2011; Liu and Eisenberg in J Chem Phys 141:22D532, 2014) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.
KeywordHard sphere repulsion Three dimensional fundamental measure theory Poisson-Nernst-Planck equations Size-modified PNP Equation of state
DOI10.1007/s10955-016-1470-7
Language英语
Funding ProjectState Key Laboratory of Scientific/Engineering Computing ; Chinese Academy of Sciences ; China NSF[91230106] ; China NSF[NSFC11001062] ; NSF of Jiangsu Province[BK20130278]
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000372284600008
PublisherSPRINGER
Citation statistics
Cited Times:10[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22302
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
2.Soochow Univ, Dept Math, Ctr Syst Biol, Suzhou 215006, Peoples R China
Recommended Citation
GB/T 7714
Qiao, Yu,Liu, Xuejiao,Chen, Minxin,et al. A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions[J]. JOURNAL OF STATISTICAL PHYSICS,2016,163(1):156-174.
APA Qiao, Yu,Liu, Xuejiao,Chen, Minxin,&Lu, Benzhuo.(2016).A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions.JOURNAL OF STATISTICAL PHYSICS,163(1),156-174.
MLA Qiao, Yu,et al."A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson-Nernst-Planck Equations to Account for Hard Sphere Repulsion Among Ions".JOURNAL OF STATISTICAL PHYSICS 163.1(2016):156-174.
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