Hierarchical multiscale simulation of electrokinetic transport in silica nanochannels at the point of zero charge

Effects of nanoscale confinement and partial charges that stem from quantum calculations are investigated in silica slit channels filled with 1 M KCl at the point of zero charge by using a hierarchical multiscale simulation methodology. Partial charges of both bulk and surface atoms from ab initio quantum calculations that take into account bond polarization and electronegativity are used in molecular dynamics (MD) simulations to obtain ion and water concentration profiles for channel widths of 1.1, 2.1, 2.75, and 4.1 nm. The interfacial electron density profiles of simulations matched well with that of recent X-ray reflectivity experiments. By simulating corresponding channels with no partial charges, it was observed that the partial charges affect the concentration profiles and transport properties such as diffusion coefficients and mobilities up to a distance of about 3 sigma(O)(-)(O) from the surface. Both in uncharged and partially charged cases, oscillations in concentration profiles of K(+) and Cl(-) ions give rise to an electro-osmotic flow in the presence of an external electric field, indicating the presence of an electric double layer at net zero surface charge, contrary to the expectations from classical continuum theory. I-V curves in a channel-bath system using ionic mobilities from MD simulations were significantly different for channels with and without partial charges for channel widths less than 4.1 nm.     

Solvation force, structure and thermodynamics of fluids confined in geometrically rough pores

The effect of periodic surface roughness on the behavior of confined soft sphere fluids is investigated using grand canonical Monte Carlo simulations. Rough pores are constructed by taking the prototypical slit-shaped pore and introducing unidirectional sinusoidal undulations on one wall. For the above geometry our study reveals that the solvation force response can be phase shifted in a controlled manner by varying the amplitude of roughness. At a fixed amplitude of roughness, a, the solvation force for pores with structured walls was relatively insensitive to the wavelength of the undulation, lambda for 2.3/=0.5. The predictions of the superposition approximation, where the solvation force response for the rough pores is deduced from the solvation force response of the slit-shaped pores, was in excellent agreement with simulation results for the structured pores and for lambda/sigma(ff)>/=7 in the case of smooth walled pores. Grand potential computations illustrate that interactions between the walls of the pore can alter the pore width corresponding to the thermodynamically stable state, with wall-wall interactions playing an important role at smaller pore widths and higher amplitudes of roughness.     

Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface

Prewetting transition is studied for the square-well fluid of attractive-well diameter lambda(ff)sigma(ff)=1.5 in the presence of a homogeneous surface modeled by the square-well potential of attractive well from 0.8sigma(ff) to 1.8sigma(ff). We investigate surface phase coexistence of thin-thick film transition using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Molecular dynamics (MD) and GC-TMMC are utilized to predict the properties of the fluid for various surface fluid affinities. Occurrences of prewetting transition with the variation of surface affinity are observed for a domain of reduced temperature from T(*)=0.62 to 0.75. We have used MD and GC-TMMC+finite size scaling (FSS) simulations to calculate the boundary tension as a function of temperature as well as surface affinity. Boundary tensions via MD and GC-TMMC+FSS methods are in good agreement. The boundary tension increases with the decrease of wall-fluid affinity. Prewetting critical properties are calculated using rectilinear diameter approach and scaling analysis. We found that critical temperature and density increase with the decrease of wall-fluid affinity.     

用密度泛函理论研究Lennard-Jones 流体在狭缝中的相平衡

用改进的基础度量理论(modified fundamental measure theory, MFMT)和密度Taylor展开分别表达过剩自由能中的短程作用和色散作用. 流体分子与狭缝壁之间的相互作用以10-4-3势能函数表达. 由巨势最小原理确定Lennard-Jones (LJ)流体在狭缝中的密度分布和过剩吸附量, 所得结果与分子模拟数据吻合良好. 根据平衡时两相温度, 化学势及巨势相等, 计算了LJ流体在狭缝中的相平衡.     

Nanoscale colloids in a freely adsorbing polymer solution: a Monte Carlo simulation study

A key issue in nanoscale materials and chemical processing is the need for thermodynamic and kinetic models covering colloid-polymer systems over the mesoscopic length scale (approximately 1-100 nm). We have applied Monte Carlo simulations to attractive nanoscale colloid-polymer mixtures toward developing a molecular basis for models of these complex systems. The expanded ensemble Monte Carlo simulation method is applied to calculate colloid chemical potentials (micro(c)) and polymer adsorption (gamma) in the presence of freely adsorbing Lennard-Jones (LJ) homopolymers (surface modifiers). gamma and micro(c) are studied as a function of nanoparticle diameter (sigma(c)), modifier chain length (n) and concentration, and colloid-polymer attractive strength over 0.3 < Rg/sigma(c) < 6 (Rg is the polymer radius of gyration). In the attractive regime, nanocolloid chemical potential decreases and adsorbed amount increases as sigma(c), or n is increased. The scaling of gamma with n from the simulations agrees with the theory of Aubouy and Raphael (Macromolecules 1998, 31, 4357) in the extreme limits of Rg/sigma(c). When Rg/sigma(c) is large, the "colloid" approaches a molecular size and interacts only locally with a few polymer segments and gamma approximately n. When Rg/sigma(c) is small, the system approaches the conventional colloid-polymer size regime where multiple chains interact with a single particle, and gamma approximately sigma(c)2, independent of n. In contrast, adsorption in the mesoscopic range of Rg/sigma(c) investigated here is represented well by a power law gamma approximately n(p), with 0 < p < 1 depending on concentration and LJ attractive strength. Likewise, the chemical potential from our results is fitted well with micro(c) approximately n(q)sigma(c)3, where the cubic term results from the sigma(c) dependence of particle surface area (approximately sigma(c)2) and LJ attractive magnitude (approximately sigma(c)). The q-exponent for micro(c) (micro(c) approximately n(q)) varies with composition and LJ attractive strength but is always very close to the power exponent for gamma (gamma approximately n(p)). This result leads to the conclusion that in attractive systems, polymer adsorption (and thus polymer-colloid attraction) dominates the micro(c) dependence on n, providing a molecular interpretation of the effect of adsorbed organic layers on nanoparticle stability and self-assembly.     

Extending the simple weighted density approximation for a hard-sphere fluid to a Lennard-Jones fluid II. Application

A simple weighted density approximation (SWDA) was extended to nonuniform Lennard-Jones fluids by following the spirit of a partitioned density function theory [S. Zhou, Phys. Rev. E 68 (2003) 061201] and mapping the hard-core part onto an effective hard-sphere fluid whose higher order terms beyond the second order of the functional perturbation expansion are treated by the SWDA. The resultant DFT formalism performs well for Lennard-Jones fluids under the influence of diverse external fields. With the present DFT formalism, we investigate in detail the structure and adsorption properties of a low-density LJ gas in a spherical cavity with a wall consisting of hard-sphere or LJ particles. It was found that when the cavity wall exerts an attractive external potential on the LJ particles in the cavity, the excess adsorption decreases as the temperature increases, while when the cavity wall exerts a hard repulsive external potential on the LJ particles in the cavity, the excess adsorption increases as the temperature increases.     

Density inhomogeneity and diffusion behavior of fluids in micropores by molecular-dynamics simulation

The density profiles and the diffusion behavior of fluid argon confined in micropores were studied by molecular-dynamics simulations. The effects of pore size (width), temperature and number density on the density profiles and the self-diffusion coefficients in micropores were simulated with pore widths from 0.6 to 4.0 nm. The density profiles are greatly affected by the pore size. Strong inhomogeneities in the channel direction and vapor-liquid phase separation in the micropores were observed when initial conditions were chosen in the coexistence region of the fluid. The self-diffusion coefficient in the channel direction in the pores was found to be much lower than in the bulk, and decreasing with decreasing pore size, decreasing temperature, and increasing density.     

Structure of inhomogeneous attractive and repulsive hard-core yukawa fluid: grand canonical Monte Carlo simulation and density functional theory study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.     

Accurate and local formulation for thermodynamic properties directly from integral equation method

A local formulation for determination of excess chemical potential is derived out by applying an assumption of linear dependence of correlation function and bridge function on the charging parameter to the Kirkwood charging formula and scaling the bridge function, the scaling parameter is specified by a Gibbs–Duhem relation. The local formulation for the excess chemical potential only requires the correlation function and bridge function of the investigated state as input and is therefore free of an unwieldy thermodynamic integration. A comprehensive comparison between the presently calculated thermodynamic quantities for a Lennard–Jones (LJ) fluid including two key quantities, i.e. the excess chemical potential and excess entropy, corresponding simulation data available in literature, and corresponding calculated results by several other global and local formulations, indicates that the present formulation is the only one capable of predicting locally and excellently all of the thermodynamic properties of the LJ fluid. The GCMC simulation is carried out for a core-softened potential fluid and the LJ fluid near critical state and at subcritical state near the gas–liquid coexistence line to obtain the excess chemical potential which is also in excellent agreement with the theoretical prediction from the present formalism; this indicates that the present formalism is of general interest in fluid statistical mechanics and applicable to parameter space covering over the entire phase diagram.     

Influence of atomistic physics on electro-osmotic flow: an analysis based on density functional theory

Molecular density profiles and charge distributions determined by density functional theory (DFT) are used in conjunction with the continuum Navier-Stokes equations to compute electro-osmotic flows in nanoscale channels. The ion species of the electrolyte are represented as centrally charged hard spheres, and the solvent is treated as a dense fluid of neutral hard spheres having a uniform dielectric constant. The model explicitly accounts for Lennard-Jones interactions among fluid and wall molecules, hard sphere repulsions, and short range electrical interactions, as well as long range Coulombic interactions. Only the last of these interactions is included in classical Poisson-Boltzmann (PB) modeling of the electric field. Although the proposed DFT approach is quite general, the sample calculations presented here are limited to symmetric monovalent electrolytes. For a prescribed surface charge, this DFT model predicts larger counterion concentrations near charged channel walls, relative to classical PB modeling, and hence smaller concentrations in the channel center. This shifting of counterions toward the walls reduces the effective thickness of the Debye layer and reduces electro-osmotic velocities as compared to classical PB modeling. Zeta potentials and fluid speeds computed by the DFT model are as much as two or three times smaller than corresponding PB results. This disparity generally increases with increasing electrolyte concentration, increasing surface charge density and decreasing channel width. The DFT results are found to be comparable to those obtained by molecular dynamics simulation, but require considerably less computing time.     

Computer simulation and theory of the diffusion- and flow-induced concentration dispersion in microfluidic devices and HPLC systems based on rectangular microchannels

The dynamics of formation of solute peaks in microfluidic systems are investigated by computer simulation. A finite-element numerical procedure is applied to analyze the diffusion- and flow-controlled concentration dispersion in a 40 microm-high rectangular flow-through channel. Two-dimensional concentration profiles are shown for channels with cross sections of large aspect ratio. The final shapes of the peaks are formed during a very short time period, ranging from a few milliseconds to about 1s for low and high flow velocities, respectively. The observed standard half-width sigma of the peaks is found to strictly follow a linear function of t(1/2) over the whole time range. The extrapolated long-term peak characteristics are in perfect agreement with theoretical predictions. For comparison, theoretical results on the concentration dispersion for solute peaks in open-channel liquid-chromatography (HPLC) are re-examined and applied.     

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

The role of pressure in rubber elasticity

We describe a series of molecular dynamics computations that reveal an intimate connection at the atomic scale between difference stress (which resists stretches) and pressure (which resists volume changes) in an idealized elastomer, in contrast to the classical theory of rubber elasticity. Our simulations idealize the elastomer as a "pearl necklace," in which the covalent bonds are stiff linear springs, while nonbonded atoms interact through a Lennard-Jones potential with energy epsilon(LJ) and radius sigma(LJ). We calculate the difference stress t(11)-(t(22)+t(33))/2 and mean stress (t(11)+t(22)+t(33))/3 induced by a constant volume extension in the x(1) direction, as a function of temperature T and reduced density rho(*)=Nsigma(IJ) (3)/nu. Here, N is the number of atoms in the simulation cell and nu is the cell volume. Results show that for rho(*)<1, the difference stress is purely entropic and is in good agreement with the classical affine network model of rubber elasticity, which neglects nonbonded interactions. However, data presented by van Krevelen [Properties of Polymers, 3rd ed. (Elsevier, Amsterdam, 1990), p. 79] indicate that rubber at standard conditions corresponds to rho(*)=1.2. For rho(*)>1, the system is entropic for kT/epsilon(LJ)>2, but at lower temperatures the difference stress contains an additional energy component, which increases as rho(*) increases and temperature decreases. Finally, the model exhibits a glass transition for rho(*)=1.2 and kT/epsilon(LJ) approximately 2. The atomic-scale processes responsible for generating stress are explored in detail. Simulations demonstrate that the repulsive portion of the Lennard-Jones potential provides a contribution sigma(nbr)>0 to the difference stress, the attractive portion provides sigma(nba) approximately 0, while the covalent bonds provide sigma(b)<0. In contrast, their respective contributions to the mean stress satisfy Pi(nbr)<0, Pi(nba)>0, and Pi(b)<0. Analytical calculations, together with simulations, demonstrate that mean and difference stresses are related by sigma(nbr)=-APi(nbr)P(2)(theta(b)), sigma(b)=BPi(b)P(2)(theta(b)), where P(2)(theta(b)) is a measure of the anisotropy of the orientation of the covalent bonds, and A and B are coefficients that depend weakly on rho(*) and temperature. For high values of rho(*), we find that [sigma(nbr)]>[sigma(b)], and in this regime our model predicts behavior that is in good agreement with experimental data of D.L. Quested et al. [J. Appl. Phys. 52, 5977 (1981)] for the influence of pressure on the difference stress induced by stretching solithane.     

Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems

The structure of a Lennard-Jones (LJ) fluid subjected to diverse external fields maintaining the equilibrium with the bulk LJ fluid is studied on the basis of the third-order+second-order perturbation density-functional approximation (DFA). The chosen density and potential parameters for the bulk fluid correspond to the conditions situated at "dangerous" regions of the phase diagram, i.e., near the critical temperature or close to the gas-liquid coexistence curve. The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. It is found that the DFA theory presented in this work performs successfully for the nonuniform LJ fluid only on the condition of high accuracy of the required bulk second-order direct correlation function. The present report further indicates that the proposed perturbation DFA is efficient and suitable for both supercritical and subcritical temperatures.     

超临界甲烷在纳米材料中最适吸附压力的确定

用巨正则Monte Carlo (GCMC)方法模拟了超临界甲烷在层柱纳米材料中的吸附.模拟中,层柱纳米材料采用了柱子均匀分布在层板间的模型, 非极性分子甲烷采用Lennard Jones分子模型, 层板墙采用Steele的10 4 3模型, 流体分子与柱子的相互作用采用点 点 (site to site) 的方法计算.得到了甲烷的随着压力先增大后减小的超额吸附等温线.在T=207.3 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力 (即对应于最大吸附量时的操作压力) 分别为2.4、3.1和3.7 MPa.然而,在T=237.0 K时,1.02、1.70和2.38 nm孔宽对应的最适操作压力分别为2.9、3.6和4.9 MPa,分别比T=207.3 K时相同孔宽下对应的最适操作压力至少高0.5 MPa. 模拟结果表明, GCMC方法是研究材料吸附性能的一种强有力的工具.     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

牛血清蛋白在NaCl水溶液中渗透压的研究

将NaCl水溶液中带电蛋白质分子间的静电排斥作用用Yukawa位能函数描述,蛋白质分子间的色散作用用Lennard-Jones位能函数描述,代替了经典DLVO理论。基于McMillan-Mayer渗透压统计理论,将Duh和Mier-Y-Teran的Yukawa状态方程与Cotterman等的Lennard-Jones微扰公式相结合,建立了一个新的状态方程,并采用该状态方程研究了含有NaCl的牛血清蛋白(简称BSA)水溶液的渗透压,依据BSA在0.15mol/LNaCl水溶液中的回归参数可预测其在1～5mol/LNaCl水溶液中的渗透压。该状态方程采用了两个回归参数(硬球直径和LJ参数),具有一定的关联和预测效果,并与己有的其它理论模型进行了比较。