Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed.     

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.     

Slip length of water on graphene: limitations of non-equilibrium molecular dynamics simulations

Data for the flow rate of water in carbon nanopores is widely scattered, both in experiments and simulations. In this work, we aim at precisely quantifying the characteristic large slip length and flow rate of water flowing in a planar graphene nanochannel. First, we quantify the slip length using the intrinsic interfacial friction coefficient between water and graphene, which is found from equilibrium molecular dynamics (EMD) simulations. We then calculate the flow rate and the slip length from the streaming velocity profiles obtained using non-equilibrium molecular dynamics (NEMD) simulations and compare with the predictions from the EMD simulations. The slip length calculated from NEMD simulations is found to be extremely sensitive to the curvature of the velocity profile and it possesses large statistical errors. We therefore pose the question: Can a micrometer range slip length be reliably determined using velocity profiles obtained from NEMD simulations? Our answer is "not practical, if not impossible" based on the analysis given as the results. In the case of high slip systems such as water in carbon nanochannels, the EMD method results are more reliable, accurate, and computationally more efficient compared to the direct NEMD method for predicting the nanofluidic flow rate and hydrodynamic boundary condition.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Ionic Transport Triggered by Asymmetric Illumination on 2D Nano-Membrane

Ionic transport and ion sieving are important in the field of separation science and engineering. Based on the rapid development of nanomaterials and nano-devices, more and more phenomena occur on the nanoscale devices in the field of thermology, optics, mechanics, etc. Recently, we experimentally observed a novel ion transport phenomenon in nanostructured graphene oxide membrane (GOM) under asymmetric illumination. We first build a light-induced carriers’ diffusion model based on our previous experimental results. This model can reveal the light-induced ion transport mechanism and predict the carriers’ diffusion behavior under different operational situations and material characters. The voltage difference increases with the rise of illuminate asymmetry, photoresponsivity, recombination coefficient, and carriers’ diffusion coefficient ratio. Finally, we discuss the ion transport behavior with different surface charge densities using MD simulation. Moderate surface charge decreases the ion transport with the same type of charge due to the electrostatic repulsion; however, excess surface charge blocks both cation and anion because a thicker electrical double layer decreases effective channel height. Research here provides referenced operational and material conditions to obtain a greater voltage difference between the membrane sides. Also, the mechanism of ion transport and ion sieving can guide us to modify membrane material according to different aims.     

Polymer chain dynamics at interfaces: role of boundary conditions at solid interface

Using classical molecular dynamics simulations, we study the dynamical properties of a single polymer chain dissolved in an explicit solvent and strongly adsorbed at solid-liquid interface. To circumvent a serious challenge posed by finite size effects due to long-range hydrodynamic effects, we developed a correction procedure that substantially limits the finite size effects. Concurrently, we provide an analysis of distinctly different size effects in the directions transverse and normal to the interface. We find that on analytically smooth interfaces, corresponding to the slip boundary condition, the motions of the polymer chain and the surrounding solvent are hydrodynamically coupled. This leads to the chain diffusion coefficient D scaling with the chain degree of polymerization N as D approximately N(-3/4), consistent with the Zimm dynamics for strongly adsorbed chains. Introduction of transverse forces at the interface results in loss of correlation between the motion of the polymer chain and the solvent. Consequently, D approximately N(-1), which is a characteristic of the Rouse dynamics.     

Anomalous transport in molecularly confined spaces

We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.     

Diffusivity of asphaltene molecules by fluorescence correlation spectroscopy

Using fluorescence correlation spectroscopy (FCS) we measure the translational diffusion coefficient of asphaltene molecules in toluene at extremely low concentrations (0.03-3.0 mg/L): where aggregation does not occur. We find that the translational diffusion coefficient of asphaltene molecules in toluene is about 0.35 x 10(-5) cm(2)/s at room temperature. This diffusion coefficient corresponds to a hydrodynamic radius of approximately 1 nm. These data confirm previously estimated size from rotational diffusion studied using fluorescence depolarization. The implication of this concurrence is that asphaltene molecular structures are monomeric, not polymeric.     

Interpretation of apparent activation energies for electron transport in dye-sensitized nanocrystalline solar cells

Electron transport in dye-sensitized nanocrystalline solar cells appears to be a slow diffusion-controlled process. Values of the apparent electron diffusion coefficient are many orders of magnitude smaller than those reported for bulk anatase. The slow transport of electrons has been attributed to multiple trapping (MT) at energy levels distributed exponentially in the band gap of the nanocrystalline oxide. In the MT model, release of immobile electrons from occupied traps to the conduction band is a thermally activated process, and it might therefore be expected that the apparent electron diffusion coefficient should depend strongly on temperature. In fact, rather small activation energies (0.1-0.25 eV) have been derived from time and frequency resolved measurements of the short circuit photocurrent. It is shown that the MT model can give rise to such anomalously low apparent activation energies as a consequence of the boundary conditions imposed by the short circuit condition and the quasi-static relationship between changes in the densities of free and trapped electrons. This conclusion has been confirmed by exact numerical solutions of the time-dependent generation/collection problem for periodic excitation that provide a good fit to experimental data.     

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.     

Interfacial slip friction at a fluid-solid cylindrical boundary

Recently we proposed a method to calculate the interfacial friction coefficient between fluid and solid at a planar interface. In this work we extend the method to cylindrical systems where the friction coefficient is curvature dependent. We apply the method to methane flow in carbon nanotubes, and find good agreement with non-equilibrium molecular dynamics simulations. The proposed method is robust, general, and can be used to predict the slip for cylindrical nanofluidic systems.     

Numerical Analysis of 3‐D Flow Past a Stationary Sphere with Slip Condition at Low and Moderate Reynolds Numbers

Computations are performed to determine the steady 3‐D viscous fluid flow forces acting on the stationary spherical suspended particle at low and moderate Reynolds numbers in the range of 0.1≤Re≤200. A slip is supposed on the boundary so that the slip velocity becomes proportional to the shear stress. This model possesses a single parameter to account for the slip coefficient λ (Pa.s/m), which is made dimensionless and is called Trostel number (Tr=λ a/μ). Decreasing slip, increases drag in all Reynolds limits, but slip has smaller effects on drag coefficient at lower Reynolds number regimes. Increasing slip at known Reynolds number causes to delay of flow separation and inflect point creation in velocity profiles. At full slip conditions, shear drag coefficient will be zero and radial drag coefficient reaches to its maximum values. Flow around of sphere at full‐slip condition is not equal to potential flow around a sphere. Present numerical results corresponding to full slip (Tr→0) are in complete accord with certain results of flow around of inviscid bubbles, and the results corresponding to no‐slip (Tr→∞) have excellent agreement with the results predicted by the no‐slip boundary condition.     

石英玻璃分子动力学模拟中的原子电荷转移与系综选择

介绍了SiO2体系分子动力学模拟中的Si、O原子电荷转移问题;采用Morse势函数研究了原子电荷转移对石英玻璃模拟的影响,发现原子电荷转移在影响模型密度的同时,还直接影响着原子的最近邻距离.NPT和NVT系综下的模拟结果对比显示,系综对模型中原子最近邻情况影响不大,但在NVT系综下模拟结果表明实际玻璃中存在的较大的空隙结构,找到了以往模拟中密度结果偏高的原因,提出了一种较好的石英玻璃分子动力学建模的方法.该方法不但解决了在调整电荷时维持原子最近邻距离与保证模型密度之间的矛盾,而且可以很好地描述石英玻璃在远程结构上密度不均、存在较大空隙的无序结构.此外,原子自扩散系数的计算结果展示了空隙结构在石英玻璃扩散性质研究中的作用.     

Fluorescence photobleaching to evaluate flow velocity and hydrodynamic dispersion in nanoslits

Velocity measurement is a key issue when studying flows below the micron scale, due to the lack of sensitivity of conventional detection techniques. We present an approach based on fluorescence photobleaching to evaluate flow velocity at the nanoscale by direct visualization. Solutions containing a fluorescent dye are injected into nanoslits. A photobleached line, created through laser beam illumination, moves through the channel due to the fluid flow. The velocity and effective diffusion coefficient are calculated from the temporal data of the line position and width respectively. The measurable velocity range is only limited by the diffusion rate of the fluorescent dye for low velocities and by the apparition of Taylor dispersion for high velocities. By controlling the pressure drop and measuring the velocity, we determine the fluid viscosity. The photobleached line spreads in time due to molecular diffusion and Taylor hydrodynamic dispersion. By taking into account the finite spatial and temporal extensions of the bleaching under flow, we determine the effective diffusion coefficient, which we find to be in good agreement with the expression of the two dimensional Taylor-Aris dispersion coefficient. Finally we analyze and discuss the role of the finite width of the rectangular slit on hydrodynamic dispersion.     

Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.