Excerpted from:

Molecular Simulation

Molecular Simulation is an international, multidisciplinary, academic journal which covers all aspects of research related to, or of importance to, molecular modelling and simulation (including informatics, theoretical and experimental work). Molecular Simulation exists to bring together the most significant papers concerned with applications of simulation methods, and original contributions to the development of simulation methodology from biology and biochemistry, chemistry, chemical engineering, materials and nanomaterials, medicine, physics and information science. The aim is to provide a forum in which cross fertilization between application areas, methodologies, disciplines, as well as academic and industrial researchers can take place and new developments can be encouraged.

Electric Potential Distribution in Nanoscale Electroosmosis: from Molecules to Continuum
    from Taylor & Francis Journal 'Molecular Simulation'

An international team of nanoscale researchers have published a paper that illustrates differences in using non-equilibrium molecular dynamics (NEMD) and the Poisson–Boltzmann equation when looking at electric potential distribution in nanoscale electro-osmosis.  The author team includes

M. WANG
--Nanomaterials in the Environment, Agriculture and Technology (NEAT), University of California, Davis, CA, USA
--Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, USA;

J. LIU
--Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, USA
--College of Engineering and LTCS, Peking University, Beijing, People’s Repbulic of China

S. CHEN
--Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, USA
--College of Engineering and LTCS, Peking University, Beijing, People’s Republic of China

Abstract-Conclusion
Electric potential distribution in nanoscale electroosmosis have been numerically investigated using both the atomistic method of non-equilibrium molecular dynamics (NEMD) and the continuum theory Poisson–Boltzmann equation (PBE). The applicability of the continuum-based PB theory in nanoscale is discussed by comparing the results from the two different methods.

Results show that: if the bin size of the MD simulation is no smaller than a molecular diameter of solvent and the focusing region is limited to the diffusion layer, the ion distribution profiles calculated by MD simulations agree well with PB predictions at low and moderate bulk ionic concentrations.  The PB theory totally breaks down for high bulk ionic concentrations, which is also consistent with the macroscopic description.

Introduction
Electroosmotic transport (EOT) plays a fundamental role in many biochemical and biophysical processes, such as transports in ion channels in cells. Similar applications can also be found in NEMS/MEMS devices A complete understanding of these physical and chemical processes need correct mathematical descriptions and accurate solutions of the electrostatic potential distributions. One of the most widespread models for the electrostatic interactions is the Poisson–Boltzmann equation (PBE).

The linearized PBE (LPBE) and non-linearized PBE (NLPBE) have been used successfully in predictions and modeling of the EOT at microscales

However, there are three main defects in the pure continuum approach

1. the finite sizes of the ions are neglected;
2. the non-Coulombic interaction between counter- and co-ions and surface is disregarded; and
3. the image forces between ions and the surface are neglected.

Although the image charges have been introduced in extensions of Poisson–Boltzmann (PB) theory and more sophistical statistical mechanical treatments of the double layer, it was generally thought that the PBE broke down in nanoscale EOT.

Much work has been done using the molecular-based simulations with comparisons with the continuum-based PB theory in the last decade. Especially, most of the recent papers based on the first principle have reported the PB theory deviates from the MD results in nanoscale electroosmosis [notations]. Much higher ionic concentration distributions near wall surfaces predicted by MD were reported than those predicted by the PB theory. Qiao and Aluru modified the PBE by introducing an electrochemical potential correction extracted from the ion distribution in a smaller channel using MD simulations. The modified PBE predicted the ion distribution in larger channel widths with good accuracies

Cui and Cochran [notation] found that the PBE agreed quantitatively well with the MD results at moderate ionic concentrations around 20mM and failed at low ionic concentration and higher zeta potential over 50mV. Dufreche et al. [notation] simulated the electroosmosis in clays, which was simplified as Naþ ions in water and declared that the PB theory and MD simulation only agreed only when the interlayer spacing was large enough, and that a slipping modification must be considered for the hydrodynamics.

Such phenomena can not be explained by the classical electrokinetic transport theories and were ascribed to the water transport properties change near the charged surfaces. In this paper, we simulate the electroosmosis in nanochannels using the nonequilibrium molecular dynamics (NEMD). The atomic-based results are compared with the continuum based PBE so that the applicability of the continuum assumption is therefore discussed.

This paper also presents evidence and explores Continuum models; NEMD method; Bin size effect; Stern layer effect; Concentration effect.

Excerpted from:

Molecular Simulation

Molecular Simulation is an international, multidisciplinary, academic journal which covers all aspects of research related to, or of importance to, molecular modelling and simulation (including informatics, theoretical and experimental work). Molecular Simulation exists to bring together the most significant papers concerned with applications of simulation methods, and original contributions to the development of simulation methodology from biology and biochemistry, chemistry, chemical engineering, materials and nanomaterials, medicine, physics and information science. The aim is to provide a forum in which cross fertilization between application areas, methodologies, disciplines, as well as academic and industrial researchers can take place and new developments can be encouraged.