Tomoyuki Kinjo

Molecular dynamics simulation of electrokinetic flow of an aqueous electrolyte solution in nanochannels

Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics simulations. The four transport coefficients that characterize the response to weak electric and pressure fields, namely, the coefficients for the electrical current in response to the electric field (M(jj)) and the pressure field (M(jm)), and those for the mass flow in response to the same fields (M(mj) and M(mm)), are obtained in the linear regime using a Green-Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsagers reciprocal relation (M(jm) = M(mj)) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of M(mj) due to the excess co-ions, takes places for very high surface charge density.

Angular Momentum Form of Verlet Algorithm for Rigid Molecules

A new simple algorithm is presented for solving the equations of motion for rigid molecules. These equations are integrated using a Verlet framework in the angular momentum form. This simple algorithm is named “the angular momentum Verlet algorithm”. For obtaining a high accuracy in molecular dynamics (MD) simulations, we introduce the scaling method with the constraint by Lagranges method of undetermined multipliers. The results of MD simulations for carbon tetrachloride using the angular momentum Verlet algorithm are reported. The relative total energy fluctuations for carbon tetrachloride using the angular momentum Verlet algorithm are compared with those using the standard leap-frog and Gear predictor–corrector algorithms. The energy drift using the angular momentum Verlet algorithm is smaller than that using the leap-frog or Gear predictor–corrector algorithm, particularly for large time intervals. The MD simulations for A X n Y 4- n -type models having different moments of inertia are also carried ...

Linkage between atomistic and mesoscale coarse-grained simulation

To reduce computational cost in large scale molecular simulations and to adjust the simulation methods to multiscale nature of complex materials, it is effective to treat several atoms (or molecules) as one element. Dissipative particle dynamics (DPD) and Brownian dynamics (BD) simulations are typical examples of such coarse-graining methods. In the coarse-grained (CG) simulation methods, linkage between molecular and mesoscale parameters is important to assess accuracy and applicability of these methods. For that purpose, we derived equation of motion for the CG particles by using projection operator method which will be appeared on a subsequent paper. In the derived equation, the force acting on the CG particles is divided into the mean force, friction force and random force. In this study, we calculated the mean force between CG particles by molecular dynamics (MD) simulations with constraints. We also showed the universality of the calculated mean forces.

Analysis of electro-osmotic flow in a microchannel with undulated surfaces

Abstract The electro-osmotic flow through a channel between two undulated surfaces induced by an external electric field is investigated. The gap of the channel is very small and comparable to the thickness of the electrical double layers. A lattice Boltzmann simulation is carried out on the model consisting of the Poisson equation for electrical potential, the Nernst–Planck equation for ion concentration, and the Navier–Stokes equations for flows of the electrolyte solution. An analytical model that predicts the flow rate is also derived under the assumption that the channel width is very small compared with the characteristic length of the variation along the channel. The analytical results are compared with the numerical results obtained by using the lattice Boltzmann method. In the case of a constant surface charge density along the channel, the variation of the channel width reduces the electro-osmotic flow, and the flow rate is smaller than that of a straight channel. In the case of a surface charge density distributed inhomogeneously, one-way flow occurs even under the restriction of a zero net surface charge along the channel.

Generic transport coefficients of a confined electrolyte solution

Physical parameters characterizing electrokinetic transport in a confined electrolyte solution are reconstructed from the generic transport coefficients obtained within the classical nonequilibrium statistical thermodynamic framework. The electro-osmotic flow, the diffusio-osmotic flow, the osmotic current, as well as the pressure-driven Poiseuille-type flow, the electric conduction, and the ion diffusion are described by this set of transport coefficients. The reconstruction is demonstrated for an aqueous NaCl solution between two parallel charged surfaces with a nanoscale gap, by using the molecular dynamic (MD) simulations. A Green-Kubo approach is employed to evaluate the transport coefficients in the linear-response regime, and the fluxes induced by the pressure, electric, and chemical potential fields are compared with the results of nonequilibrium MD simulations. Using this numerical scheme, the influence of the salt concentration on the transport coefficients is investigated. Anomalous reversal of diffusio-osmotic current, as well as that of electro-osmotic flow, is observed at high surface charge densities and high added-salt concentrations.

Polarizable Dissipative Particle Dynamics Simulation of Electrolyte Solutions

Solvent polarizability is introduced into a coarse-grained (CG) particle model to represent polar solvents on a mesoscopic level. In our method, the polarization of coarse-grained particles is represented by an oscillator which consists of two oppositely charged particles connected to each other by a spring. The charges and the spring constant are chosen so that the constant of proportionality relating the electric field to the induced dielectric polarization density corresponds to the macroscopic susceptibility. Dissipative particle dynamics (DPD) simulations of polar and the non-polar solvents are carried out to model electrolyte solutions. The cation-anion radial distribution functions (RDFs) for the polar solvent show an oscillatory character, as well as a sharp peak at a distance which corresponds to contact ion pair formation. In contrast, the RDFs for the non-polar solvent shows a monotonic change and a broad peak. This suggests that the introduction of the oscillator model for polar solvents improves the adequacy of the coarse-grained model of electrolyte solutions.

Lattice Boltzmann Flow Simulation in Micro-Nano Transitional Porous Media

In order to simulate heat and mass transfer in porous media whose scales range micron to nanometers, this work intends to provide a scheme for flow field simulation for such porous media. Since Navier-Stokes equations are no longer applicable to high Knudsen number (Kn) flow regimes, the conventional lattice Boltzmann method (LBM) cannot be applicable to flows in nanoscale porous media. Hence, a modified lattice Boltzmann method is applied for computing flows in micro-nano porous media in the transitional flow regimes at moderately high Knudsen numbers. The lattice Boltzmann equation applied is an extended version using an effective relaxation time associated with Kn and a regularization procedure coupled with Maxwell’s diffuse-scattering boundary condition for walls. For the flow field where the representative molecular mean free path varies (effectively the Kn varies locally), the locally defined Kn is introduced. In order to verify the LBM scheme, the results are compared with those of the molecular dynamics (MD) simulations by the Leonard-Jones potential. The flow fields considered are in modeled nano-porous media whose porosity is around 0.9. The results of micro-nanoscale porous media flows at Knudsen numbers: Kn = 0.04–0.24 show reasonable agreement in both the simulation methods and confirm the reliability of the presently applied LBM. Interestingly, in complex flow geometry, the advantage of higher order discrete velocity models of the LBM is not notable. Therefore, it is concluded that conventional discrete velocity models, say the D2Q9 and D3Q19 models are reasonably enough for flows in micro-nanoscale porous media.Copyright

Flow Simulations in a Sub-Micro Porous Medium by the Lattice Boltzmann and the Molecular Dynamics Methods

In order to devise and establish a cost-effective strategy to simulate flows in continuum to slip and transitional regimes, present study focuses on evaluating a lattice Boltzmann equation [Niu et al., Phys. Rev. E 76, 036711, 2007] formerly proposed by the present authors’ group. The main test flow case is a flow around a square cylinder situated in a sub-micro channel. Since a rather shorter streamwise domain size and a periodic streamwise boundary condition are imposed, the flow regime is regarded as a part of an infinite cylinder array set in a narrow channel which can be considered as a kind of micro-porous media. For the assessment of the lattice Boltzmann simulations, the molecular dynamics (MD) simulations using Leonard-Jones potential are also performed. In the MD simulations, novel boundary treatments are applied. The results of the square cylinder flow by both the simulations at Knudsen number Kn=0.08 show reasonable agreement and confirm the reliability of the present lattice Boltzmann method (LBM). The fact that the computational time of the present MD simulation to obtain the reliable statistics is 1800 times as much as that of the LBM clearly indicates the usability of the LBM for engineering applications even in the slip and transitional flow regimes.Copyright

Coarse-grained simulations of polyelectrolyte brushes using a hybrid model

We investigate the structure of polyelectrolyte brushes to determine the effects of the charge fraction of the polymers, grafting density, chain length, and salt concentration. A hybrid coarse-grained model is employed, where a soft potential is applied to coarse-grained particles representing the solvent, while a hard potential is used for the polymer beads, and co- and counterions. A steep increase in brush height with charge fraction is observed in the low-to-moderate charge fraction regime, whereas the brush approaches the contour height in the high charge fraction regime. The effects of graft density and chain length on brush height are well explained by the scaling theory based on the balance between the osmotic pressure and chain elasticity, properly taking into account the polymer stiffness. In addition, Pincus’s power law for varying added salt concentration is also reproduced by the simulation.

Topological modelling of the hydrogen bond network of water cluster and proton hopping in a hydrated polyelectrolyte membrane

The water cluster is characteristically constructed through the hydrogen bond formation in various types of aqueous solutions, especially in the pore of nano-materials such as polyelectrolyte membranes. The proton conduction in such a water cluster depends on the topology of the hydrogen bond network, since the movement of the proton is mainly driven by hydrogen bond exchange in the water cluster. The first-principle electronic state calculation should be straightforwardly adopted in order to estimate the proton conductivity because the change in hydrogen bond formation is associated with the change in the electronic states of the cluster. Although the first-principle calculations of proton conductivity are basically available to estimate the rate of proton hopping in the water clusters, it would be extremely time-consuming to simulate the dynamic structure in an inhomogeneous morphology of nanometre length scale such as in the polyelectrolyte membrane based on the electronic structure theory calculations. Here, the characterisation of the hydrogen bond network via a dynamically directed graph was evaluated to calculate the dynamical properties in the global structure of nanometre length scale inhomogeneous morphologies. The static and dynamic properties of the network structure were analysed by following the treatment of the graph theory. The mean rate of Hamming displacement (MHD) was defined to quantitatively express the dynamics of the hydrogen bond network. The average of the differences between the Hamming distances at different time steps, as the definition of the MHD, showed that the relaxation of the hydrogen bond network in polyelectrolyte membranes was slower than in the pure water because of the stronger clustering in a local area due to the mesoscopic morphology or confinement effect in nano-pores. Furthermore, proton hopping was modelled as a random walk on the dynamical hydrogen bond network, and then the diffusion coefficients of proton in the Nafion membranes were estimated as comparable results with the previous literatures.