A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

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• 作者：Yu Qiao ; Xuejiao Liu ; Minxin Chen ; Benzhuo Lu
• 关键词：Hard sphere repulsion ; Three dimensional fundamental measure theory ; Poisson–Nernst–Planck equations ; Size ; modified PNP ; Equation of state
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：163
• 期：1
• 页码：156-174
• 全文大小：855 KB
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• 作者单位：Yu Qiao (1)
  Xuejiao Liu (1)
  Minxin Chen (2)
  Benzhuo Lu (1)
  
  1. State Key Laboratory of Scientific and Engineering Computing, National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  2. Department of Mathematics, Center for System Biology, Soochow University, Suzhou, 215006, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

The 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.