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Tzyy-Leng Horng

2013-12-25
16:30:00 - 17:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

PNP-steric model was developed from MPNP model [1] by Eisenberg and Lin [2]. PNP-steric model simplifies the Lennard-Jones (LJ) potential of MPNP model by a band-limited function, which turns the non-local LJ integral into a local derivative. This makes the computation more efficient by avoiding the time-consuming convolution when dealing with non-local LJ potential. One may think of the localization of LJ potential in PNP-steric model as a low-frequency-mode approximation of it. PNP-steric model has been successfully applied to study the selectivity in Ca channel [3]. However, a pitfall was observed that it causes high-frequency instability as the inter-species LJ parameters gets somewhat larger than their intra-species counterparts. This would set a constraint on those important parametric values, that might further fail to describe significant physics related to electrolyte. One example is the over-screening phenomenon of charged-wall problem with 1:2 electrolyte, which has been depicted by many molecular dynamics studies. Motivated by by the single-file diffusion observed in a narrow single-walled carbon nanotube (SWCNT) [4], a bi-Laplacian diffusion is added to PNP-steric model to account for over-crowdedness of particles. This bi-Laplacian diffusion can suppress the high-frequency instability mentioned above that Fickian diffusion fails to. The new model was tested on the over-screening phenomenon of charged-wall problem happening at 1:2 electrolyte, and the result agrees well with [5] by choosing a larger inter-species LJ coupling parameter. Multiple over-screening loops in ionic concentration distributions were also observed when further increasing inter-species LJ coupling parameter, which was also observed by some MD studies. The new model was also tested on the single-file diffusion case of [4]. Discarding Fickian diffusion and choosing appropriate LJ parameters, simulation showed out-of-phase traveling concentration waves of particles that mimics the single-file transportation of particles in a narrow SWCNT as shown in [4]. All these imply that a better application to ion channel is expected by using this newly modified model.

[1] Eisenberg, B., Y. Hyon, and C. Liu, Energy Variational Analysis EnVarA of Ions in Water and Channels: Field Theory for Primitive Models of Complex Ionic Fluids. Journal of Chemical Physics, 2010. 133: p. 104104.
[2] Eisenberg, B. and T. C. Lin, A New Approach to the Lennard-Jones Potential and a New Model: PNP-Steric Equations, to appear in Communications in Mathematical Sciences.
[3] T.-L. Horng, T.-C. Lin, C. Liu and B. Eisenberg, PNP Equations with Steric Effects: a Model of Ion Flow through Channels, Journal of Physical Chemistry B, 2012. 116: 11422-11441.
[4] Q. Chen, J. D. Moore, Y.-C. Liu, T. J. Roussel, Q. Wang, T. Wu, and K. E. Gubbins, Transition from Single-File to Fickian Diffusion for Binary Mixture in Single-Walled Carbon Nanotubes, J. Chem. Phys., 2010. 113, 094501. [5] D. Boda, W. R. Fawcett, D. Henderson and H. Sokolowski, Monte Carlo, Density Functional Theory, and Poisson-Boltzmann Theory Study of the Structure of an Electrolyte near an Electrode, J. Chem. Phys., 2002. 116: 7170-7176.

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