Poisson-Boltzmann-Nernst-Planck model

Journal Article · Sat May 21 04:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3581031· OSTI ID:21560243

Qiong, Zheng ^[1]; Guowei, Wei ^[1]

---

1. Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 (United States)

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

• OSTI ID: 21560243
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 19 Vol. 134; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
60 APPLIED LIFE SCIENCES
APPROXIMATIONS
BIOCHEMISTRY
BOLTZMANN EQUATION
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CHARGE EXCHANGE
CHEMISTRY
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
DIRICHLET PROBLEM
ELECTRIC POTENTIAL
EQUATIONS
EVALUATION
FORECASTING
INTEGRO-DIFFERENTIAL EQUATIONS
INTERACTIONS
ION EXCHANGE
KINETIC EQUATIONS
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
NANOSTRUCTURES
ORGANIC COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
PROTEINS
RELAXATION
SEMICONDUCTOR DEVICES
SIMULATION
VARIATIONAL METHODS