Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system

An algorithm in which kinetic lattice grand canonical Monte Carlo simulations are combined with mean field theory (KLGCMC/MF) is presented to calculate ion currents in a model ion channel system. In this simulation, the relevant region of the system is treated by KLGCMC simulations, while the rest of the system is described by modified Poisson-Boltzmann mean field theory. Calculation of reaction field due to induced charges on the channel/water and membrane/water boundaries is carried out using a basis-set expansion method [Im and Roux, J. Chem. Phys. 115, 4850 (2001)]. Calculation of ion currents, electrostatic potentials, and ion concentrations, as obtained from the KLGCMC/MF simulations, shows good agreement with Poisson-Nernst-Planck (PNP) theory predictions when the channel and membrane have the same dielectric constant as water. If the channel and membrane have a lower dielectric constant than water, however, there is a considerable difference between the KLGCMC/MF and PNP predictions. This difference is attributed to the reaction field, which is missing in PNP theory. It is demonstrated that the reaction field as well as fixed charges in the channel play key roles in selective ion transport. Limitations and further development of the current KLGCMC/MF approach are also discussed.     

Adsorption mechanism of carbon dioxide in faujasites: grand canonical monte carlo simulations and microcalorimetry measurements

Molecular simulations have been coupled with adsorption microcalorimetry measurements in order to understand more deeply the interactions between carbon dioxide and various types of faujasite surfaces. The modeling studies, based on newly derived interatomic potentials for describing the interactions within the whole system, provide isotherms and evolutions of the differential enthalpy of adsorption as a function of coverage for DAY, NaY, and NaLSX which are in very good accordance with those obtained experimentally. The microscopic mechanism of CO2 adsorption was carefully analyzed, with different behaviors proposed, depending on the energetic characteristics of each faujasite surface, which are consistent with the trends observed for the differential enthalpies of adsorption.     

Adsorption and structure of water on kaolinite surfaces: possible insight into ice nucleation from grand canonical monte carlo calculations

Grand canonical Monte Carlo calculations are used to determine water adsorption and structure on defect-free kaolinite surfaces as a function of relative humidity at 235 K. This information is then used to gain insight into ice nucleation on kaolinite surfaces. Results for both the SPC/E and TIP5P-E water models are compared and demonstrate that the Al-surface [(001) plane] and both protonated and unprotonated edges [(100) plane] strongly adsorb at atmospherically relevant relative humidities. Adsorption on the Al-surface exhibits properties of a first-order process with evidence of collective behavior, whereas adsorption on the edges is essentially continuous and appears dominated by strong water lattice interactions. For the protonated and unprotonated edges no structure that matches hexagonal ice is observed. For the Al-surface some of the water molecules formed hexagonal rings. However, the a o lattice parameter for these rings is significantly different from the corresponding constant for hexagonal ice ( Ih). A misfit strain of 14.0% is calculated between the hexagonal pattern of water adsorbed on the Al-surface and the basal plane of ice Ih. Hence, the ring structures that form on the Al-surface are not expected to be good building-blocks for ice nucleation due to the large misfit strain.     

Thermodynamic characterization of fluids confined in heterogeneous pores by monte carlo simulations in the grand canonical and the isobaric-isothermal ensembles

Materials presenting nanoscale porosity are able to condense gases in their structure. This "capillary condensation" phenomenon has been studied for more than one century. Theoretical models help to understand experimental results but fail in explaining all experimental features. Most of the time, the difficulties in making quantitative or even qualitative predictions are due to the geometric complexity of the porous materials, such as large pore size distribution, chemical heterogeneities, or pore interconnections. Numerical calculations (lattice gas models or molecular simulations) are of considerable interest to calculate the adsorption properties of a fluid confined in a porous model with characteristic sizes up to several tens of nanometers. For instance, the grand canonical Monte Carlo method allows one to compute the average amount of fluid adsorbed in the porous model as a function of the temperature and the chemical potential of the fluid. However, the grand potential, necessary for a complete characterization of the system, is not a direct output of the algorithm. It is shown in this paper that the use of the isobaric-isothermal (NPT) ensemble allows one to circumvent this problem; that is, it is possible to get in one single Monte Carlo run the absolute grand potential for any given thermodynamic state of the fluid. A simplified thermodynamic integration scheme is then used to evaluate the grand potential over the whole isotherm branch passing through this initially given point. Since the usual NPT technique is a priori limited to homogeneous pores, it is proposed, for the first time, to generalize this procedure to a pore presenting a chemical heterogeneity along its axis. The new method gives the same results as the previous for homogeneous pores and allows new predictions for chemically heterogeneous pores. Comparison with the full integration scheme shows that the proposed direct calculation is faster since it avoids multiple Monte Carlo runs and more precise because it avoids the possible cumulative errors of the integration procedure.     

The salt dependence of the preferential interaction coefficient in dna solutions as determined by grand canonical monte carlo simulations

Grand canonical Monte Carlo simulations have been used to calculate the preferential interaction coefficient for aqueous solutions of sodium DNA. A cell model representation was used in these simulations, which were performed over a range of DNA phosphate (1–31 mM) and NaCl (0.2–111 mM) concentrations. Results are in close agreement with the values of the preferential interaction coefficient calculated using the Poisson-Boltzmann cell model, and with published values of experimental Donnan coefficients. The high degree of non-ideality indicated by the calculated preferential interaction coefficients is interpreted in terms of the classical Donnan equilibrium and the concept of thermodynamic association.     

Macrophase and microphase separations for surfactants adsorbed on solid surfaces: a gauge cell monte carlo study in the lattice model

By combining the gauge cell method and lattice model, we study the surface phase transition and adsorption behaviors of surfactants on a solid surface. Two different cases are considered in this work: macrophase transition and adsorption in a single-phase region. For the case of macrophase transition, where two phases coexist, we investigate the shape and size of the critical nuclei and determine the height of the nucleation barrier. It is found that the nucleation depends on the bulk surfactant concentration. Our simulations show that there exist a critical temperature and critical adsorption energy, below which the transition from low-affinity adsorption to the bilayer structure shows the characteristic of a typical first-order phase transition. Such a surface phase transition in the adsorption isotherm is featured by a hysteresis loop. The hysteresis loop becomes narrower at higher temperature and weaker adsorption energy and finally disappears at the critical value. For the case where no macrophase transition occurs, we study the adsorption isotherm and microphase separation in a single-phase region. The simulation results indicate that the adsorption isotherm in adsorption processes is divided into four regions in a log-log plot, being in agreement with experimental observations. In this work, the four regions are called the low-affinity adsorption region, the hemimicelle region, the morphological transition region, and the plateau region. Simulation results reveal that in the second region the adsorbed monomers aggregate and nucleate hemimicelles, while adsorption in the third region is accompanied by morphological transitions.     

Monte carlo simulations of micellization in model ionic surfactants: application to sodium dodecyl sulfate

A lattice model for ionic surfactants with explicit counterions is proposed for which the micellization behavior can be accurately determined from grand canonical Monte Carlo simulations. The model is characterized by a few parameters that can be adjusted to represent various linear surfactants with ionic headgroups. The model parameters have a clear physical interpretation and can be obtained from experimental data unrelated to micellization, namely, geometric information and solubilities of tail segments. As a specific example, parameter values for sodium dodecyl sulfate were obtained by optimizing for the solubility of hydrocarbons in water and the structural properties of dodecane. The critical micelle concentration (cmc), average aggregation number, degree of counterion binding, and their dependence on temperature were determined from histogram reweighting grand canonical Monte Carlo simulations and were compared to experimental results. The model gives the correct trend and order of magnitude for all quantities but underpredicts the cmc and aggregation number. We suggest ways to modify the model that may improve agreement with experimental values.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Monte carlo simulations of polymer surfaces in a cubic lattice, 1 development of a simulation algorithm and first results

A method is presented which allows to simulate surface properties of a model polymer system (in addition to bulk properties). The decisive parameter which controls the equilibrium concentration of empty sites within the bulk phase as well as the surface properties is the attractive energy operating between nonbonded neighbouring polymer segments. In effect, by varying this parameter between -0,5 and -1,5 the volume fraction of vacancies in the bulk phase changed from 0,183 to 0,003. All the parameters defined in order to characterize the “roughness” of the surface indicate that the surface gets smoother and smoother with increasing attractive segment-segment interaction and, accordingly, also with decreasing bulk equilibrium concentration of vacancies.     

Suppressor current switching: a simple and effective means to reduce background noise in ion chromatography

Background noise in ion chromatography with suppressed conductivity detection was significantly reduced for the period of time when the electric current to an anion self regenerating suppressor (ASRS) running in the recycle mode was turned-off. With high capacity AS11-HC columns, it was possible to maintain current free conditions from the beginning of the run past the chloride peak, which enables routine high sensitivity analysis of early to mid eluting peaks. This suppressor current switching was utilized for the analysis of bromate in drinking water with large volume injection using on-line removal of chloride by an On-Guard Ag+-cartridge. The method detection limit (MDL) was 0.21 microg/l in fortified reagent water. Coelution of bromate with an unknown compound was observed, but it was solved by the optimization of gradient program.     

Insight into the origins of the barrier-less knock-on conduction in the KcsA channel: molecular dynamics simulations and ab initio calculations

Since the pioneering work of Zhou et al. (Y. Zhou, J. H. Morais-Cabral, A. Kaufman and R. MacKinnon, Nature, 2001, 414, 43-48) it is now well established that the streptomyces lividans potassium channel (KcsA) can accommodate more than one ion, namely between 2 and 3. As a result, it is usually assumed that the conduction of ions proceeds through a barrier-less knock-on mechanism. This one is an alternation of two sequences containing either 2 or 3 ions which have nearly the same energies. However, the origin of such knock-on mechanism is not clearly known. The entry and the exit of ion in or out of the selectivity filter are suspected to be due to the repulsive interactions between ions. In this work, molecular dynamics simulations running over nanoseconds have been done in order to identify such events. Two specific situations, namely (S(1), S(3)) containing 2 ions and (S(2), S(4)) containing 3 ions, have been investigated regarding the different locations that ions can occupy during their diffusion through the selectivity filter of KcsA. We show that contractions of the (S(1), S(3)) file and dilation of the (S(2), S(4)) file are at the origin of the passage from one sequence to the other. The comparison between the experimentally observed diffusion rate and the occurrence's frequency of such contractions or dilation confirm the importance of such events. Ab initio calculations have also been conducted in order to examine the effect of ion polarization in the filter of KcsA. During the contraction of the ion/water file, one charge at the extra-cellular mouth of the channel strongly deviates from the others. This behavior could guide the diffusion direction to a certain extent since the contraction of the (S(1), S(3)) is favored.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

瞬时离子释放扩散模型及熔盐电解固态WS_2制备纳米W的液相扩散研究

固态化合物熔盐电解冶金在21世纪初被提出后受到学术界和工业界的广泛关注.根据固态化合物电解的动态三相电化学界线模型,固态金属氧(硫)化物阴极在电解还原过程中,涉及O2?(S2?)在电解生成的多孔金属层中的液相扩散,但由于一直以来缺乏方便可靠的理论和实验方法,相关传质过程动力学的研究鲜有文献报道.本文引入多孔电极瞬时离子释放扩散模型,以粉末微腔电极为微型多孔电极,设计双电势阶跃实验研究了WS2在等摩尔比NaCl+KCl熔盐中电解时固态阴极中的液相扩散.实验结果与理论模型符合良好,973 K时,硫离子在孔隙率为69%的多孔金属钨层中的扩散系数为0.92×10?5 cm2/s,扩散活化能为53.4 kJ/mol.研究表明,二硫化钨在NaCl+KCl混盐体系中能够快速电解还原生成纳米金属钨,其中,S2?的扩散传质是整个电解过程的速度控制步骤.     

Coupled ion and network dynamics in polymer electrolytes: Monte Carlo study of a lattice model

Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions. The ions interact attractively with specific beads in the host chains, while polymer beads repel each other. Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion. Diffusion constants for ions and chains as a function of temperature follow the Vogel-Tammann-Fulcher (VTF) law with a common VTF temperature at low ion concentration, but both decouple at higher concentrations, in agreement with experimental observations. Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation, and to detect an exponential pressure dependence of the ionic diffusion.     

Brownian dynamics simulation of the diffusion of rods and wormlike chains in a gel modeled as a cubic lattice: application to DNA

The translational diffusion constant of a particle, D, in a congested medium or a gel can be written as the product of two terms that account for long-range hydrodynamic interaction between the gel or congested medium and the particle, DEM, and a short-range "steric" term, S. For particles of arbitrary shape, DEM has been examined previously within the framework of the effective medium, EM, model (S. Allison et al., J. Phys. Chem. B 2008, 112, 5858-5866). In the present work, we examine S for rod- and wormlike chain models of duplex DNA in the size range of 100 to over 2000 base pairs. The gel is modeled explicitly as a cubic lattice, and Brownian dynamics simulation is used to examine S for a wide range of rod/wormlike chain and gel parameters. For wormlike chains with P = 50 nm, an empirical formula is derived for S that should be valid over a wide range of wormlike chain/gel parameters. For duplex DNA in the size of several hundred to several thousand base pairs in an agarose gel of 2% or less, fair agreement between modeling and experiment is obtained. However, modeling overestimates the length dependence of D observed experimentally. Finally, the reduction of D of DNA (100 to over 1000 base pairs in length) in cytoplasm relative to water can be accounted for quite well using the effective medium plus steric correction approach.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Experimental and numerical model study of the limiting current in a channel flow cell with a circular electrode

We describe first measurement in a novel thin-layer channel flow cell designed for the investigation of heterogeneous electrocatalysis on porous catalysts. For the interpretation of the measurements, a macroscopic model for coupled species transport and reaction, which can be solved numerically, is feasible. In this paper, we focus on the limiting current. We compare numerical solutions of a macroscopic model to a generalization of a Leveque-type asymptotic estimate for circular electrodes, and to measurements obtained in the aforementioned flow cell. We establish that on properly aligned meshes, the numerical method reproduces the asymptotic estimate. Furthermore, we demonstrate that the measurements are partially performed in the sub-asymptotic regime, in which the boundary layer thickness exceeds the cell height. Using the inlet concentration and the diffusion coefficient from literature, we overestimate the limiting current. On the other hand, the use of fitted parameters leads to perfect agreement between model and experiment.