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Register a new userModified Poisson-Nernst-Planck model with Coulomb and hard-sphere correlations
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We develop a modified Poisson-Nernst-Planck model which includes both the long-range Coulomb and short-range hard-sphere correlations in its free energy functional such that the model can accurately describe the ion transport in complex environment and under a nanoscale confinement. The Coulomb correlation including the dielectric polarization is treated by solving a generalized Debye-Huckel equation which is a Greens function equation with the correlation energy of a test ion described by the self Greens function. The hard-sphere correlation is modeled through the modified fundamental measure theory. The resulting model is available for problems beyond the mean-field theory such as problems with variable dielectric media, multivalent ions, and strong surface charge density. We solve the generalized Debye-Huckel equation by the Wentzel-Kramers-Brillouin approximation, and study the electrolytes between two parallel dielectric surfaces. In comparison to other modified models, the new model is shown more accurate in agreement with particle-based simulations and capturing the physical properties of ionic structures near interfaces.
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We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Huckel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, towards the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.
We have investigated ion current rectification properties of a recently prepared bipolar nanofluidic diode. This device is based on a single conically shaped nanopore in a polymer film whose pore walls contain a sharp boundary between positively and negatively charged regions. A semi-quantitative model that employs Poisson and Nernst-Plank equations predicts current-voltage curves as well as ionic concentrations and electric potential distributions in this system. We show that under certain conditions the rectification degree, defined as a ratio of currents recorded at the same voltage but opposite polarities, can reach values of over a 1000 at a voltage range <-2 V, +2 V>. The role of thickness and position of the transition zone on the ion current rectification is discussed as well. We also show that rectification degree scales with the applied voltage.
Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel, {it et al.}, Nucl. Instr. Meth. B {bf 184}, 337 (2001); Z. Siwy, {it et al.}, Europhys. Lett. {bf 60}, 349 (2002)]. Here, the ion current rectification is studied within a reduced 1D Poisson-Nernst-Planck (PNP) model of synthetic nanopores. A conical channel of a few $mathrm{nm}$ to a few hundred of nm in diameter, and of few $mu$m long is considered in the limit where the channel length considerably exceeds the Debye screening length. The rigid channel wall is assumed to be weakly charged. A one-dimensional reduction of the three-dimensional problem in terms of corresponding entropic effects is put forward. The ion transport is described by the non-equilibrium steady-state solution of the 1D Poisson-Nernst-Planck system within a singular perturbation treatment. An analytic formula for the approximate rectification current in the lowest order perturbation theory is derived. A detailed comparison between numerical results and the singular perturbation theory is presented. The crucial importance of the asymmetry in the potential jumps at the pore ends on the rectification effect is demonstrated. This so constructed 1D theory is shown to describe well the experimental data in the regime of small-to-moderate electric currents.
We study global dynamics of the Poisson-Nernst-Planck (PNP) system for flows of two types of ions through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previous studied one-dimensional PNP systems in that it encodes the defining geometry of the three-dimensional membrane channel. To justify this limiting process, we show that the global attractors of the three-dimensional PNP systems are upper semi-continuous to that of the limiting PNP system. We then examine the dynamics of the one-dimensional limiting PNP system. For large Debye number, the steady-state of the one-dimensional limiting PNP system is completed analyzed using the geometric singular perturbation theory. For a special case, an entropy-type Lyapunov functional is constructed to show the global, asymptotic stability of the steady-state.
The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channels charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singular perturbation treatment. The quantities, 1/lambda -- the ratio of the Debye length to a characteristic length scale and epsilon -- the scaled intrinsic charge density, serve as the singular and the regular perturbation parameters, respectively. The role of the boundary conditions is discussed. A comparison between numerics and the analytical results of the singular perturbation theory is presented.
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