Density functional theory study on ion adsorption and electroosmotic flow in a membrane with charged cylindrical pores†

ABSTRACT

Ion adsorption and electroosmotic flow induced by an external electric field have a variety of practical applications, especially for membrane technology. In this work, a partially perturbative density functional theory (DFT) based on the modified fundamental measure theory was applied to investigate the ion density distributions and partitions in a charged cylindrical pore. Different types of electrolyte solutions, including both charge symmetric and asymmetric, were examined using the proposed theory with various pore diameters, bulk densities, ion valencies and surface charge densities. The ion concentration profiles calculated with the theory exhibit good agreements with the results of the Monte Carlo simulations, while the results of the Poisson–Boltzmann equation deviate greatly especially for the high valence electrolytes in narrow cylindrical pores. Some interesting phenomena discovered in both experiments and simulations, such as the reverse distribution of the ions and charge inversion, can be well reproduced with the DFT. Based on the ion concentration distributions obtained from the DFT, the transient velocity profiles of the electroosmotic flow in the charged cylindrical nanopores were calculated with the Navier–Stokes (NS) equation. The characteristics of the electroosmotic flow were discussed under the different bulk electrolyte concentrations and thickness of the electric double layer inside the nanopore. The enhancement of the velocity near the pore wall, which cannot be described by the traditional theory, was well characterised by the DFT combined with the NS equation.     

锥形纳米孔内的电压整流及流体流动

文章以生物纳米通道及纳米孔中的离子传输及化学反应为背景,以离子流整流、电渗流整流、离子积累耗散模型为理论基础,使用有限元数值计算方法研究压力及电场交互作用下的锥形纳米孔孔内离子浓度分布及速度场分布现象.分析了不同电压下压力和电场的交互作用对锥形纳米孔中速度场、流场及浓度分布的影响.结果表明纳米孔孔内氢离子运动方向主要受电场方向影响.由于静电吸附效应,沿着孔壁流动的电渗流中的氢离子浓度会高于体溶液中的氢离子浓度.当电压较小时,流场方向主要受压力流的影响,当电压较大时,流场流动方向由电渗流带动的流体流动和压力驱动的流体流动共同决定.      

Controlling ionic current through a nanopore by tuning pH: a local equilibrium Monte Carlo study

ABSTRACT

The purpose of this work is to create a model of a nanofluidic transistor which is able to mimic the effects of pH on nanopore conductance. The pH of the electrolyte is an experimentally controllable parameter through which the charge pattern can be tuned: pH affects the ratio of the protonated/deprotonated forms of the functional groups anchored to the surface of the nanopore (for example, amino and carboxyl groups). Thus, the behaviour of the bipolar transistor changes as it becomes ion selective in acidic/basic environments. We relate the surface charge to pH and perform particle simulations (Local Equilibrium Monte Carlo) with different nanopore geometries (cylindrical and double conical). The simulations form a self consistent system with the Nernst–Planck equation with which we compute ionic flux. We discuss the mechanism behind pH-control of ionic current: formation of depletion zones.     

利用纳米孔研究DNA

脱氧核糖核酸 (DNA)和蛋白质是构成生命体最为重要的两类生物大分子 .随着科学技术的快速发展 ,越来越多的纳米技术被用来研究这些生物大分子 .文章详细介绍了近来利用纳米孔技术研究DNA的一些进展 .结合作者近期利用聚焦离子束 (FIB)制作纳米孔的工作 ,提出了利用纳米孔解离核小体的设想 .如果能够利用纳米孔将双螺旋DNA从组蛋白八聚体上剥离下来 ,并探测这一过程 ,将揭示核小体中包含的许多生物化学、物理信息 .文章对此进行了较为详细的分析 :处于电场中的核小体在电场的作用下 ,DNA分子穿越纳米孔 ,同时由于纳米孔的阻挡力 ,使组蛋白不能穿越 ,从而诱使DNA从组蛋白八聚体上分离下来 .通过准确检测DNA分子穿孔过程中引起的电流阻塞效应 ,可将DNA与组蛋白的相互作用的一些性质反映出来     

Nonlocal ion transport in a weakly ionized nonequilibrium plasma

Nonlocal ion transport in a weakly ionized plasma with a strong electric field is analyzed. It is assumed that charge-exchange interactions are the main mechanism of ion scattering. Ion density and drift velocity are determined for nonuniform time varying electric field by using both the direct solution of the kinetic equation and the Chapman-Enskog-type approach. The ion mean velocity is given by an integro-differential operator applied to the electric field. Ion density and drift velocity exhibit resonant behaviour when ω≃kW0, which corresponds to the resonance between ions moving with average velocity W₀ and wave traveling with the phase velocity ω/k     

Modelling of ions for seeding technique to electrify the atmosphere

There are number of ways in which weak electrification can affect the microphysics of clouds, with consequences for cloud lifetime, radiative properties, and precipitation efficiency. Kauffman [2011] suggested ions produced by direct current generators will add to and enhance the catalysing effects that cosmic ray ions are now known to produce in among other things, lowering nucleation barriers, stimulating charged particle growth and stability and increasing the scavenging rate in clouds. Thus to electrify the atmosphere ions can be generated artificially in abundance along with large electric field.Ions can be generated by the corona effect using Atmospheric electrifiers (a device used to generate negative ions) which makes use of corona discharge phenomenon to charge the air particles. Exact assessment of electric field and charge density distributions and the flow dynamics inside the electrifiers is essential to understand the particle behaviour inside the electrifiers.In this paper, a novel model of governing equations to evaluate the space charge density, electric field intensity and velocity of ionized airflow is suggested as a function of applied voltage. The Poisson and charge conservation equations are derived and hence can be used to estimate the electric field and charge density distributions. Navier stokes equation can be used to get the velocity of ionized airflow because of electric force on the air. Simulation is carried out to validate the proposed model and verify that velocity is function of input voltage and is proportional to it.     

含有带正负电离子的等离子体中的非线性波研究

研究了含有带正负电的冷离子和热电子的磁化等离子体系统.运用约化摄动法从该系统的运动方程中推导出Zakharov-Kuznetsov(ZK)方程、改进的ZK方程和耦合ZK方程.给出了这些方程的一种孤立波解,得到了孤立波的振幅、宽度、传播速度与负离子和正离子的质量比、负离子数密度、磁场强度的关系以及正离子和负离子在运动过程中的位移图像. 关键词： Zakharov-Kuznetsov(ZK)方程 改进的ZK方程 耦合ZK方程 约化摄动法     

Effect of Interaction upon Translocation of Confined Polymer Chain Through Nanopore

运用二维的键长涨落模型和蒙特卡洛方法研究高分子链从一个受限空间到自由空间穿孔过程中,链单体与纳米孔之间的相互作用.结果表明,在不同的链长和纳米孔交互作用下,高分子链成功穿越自由能能垒取决于链长和纳米孔长度,并且由于交互作用降低了自由能能垒,导致高分子链在纳米管的平均捕获时间缩短.     

电解质浓度对胶体粒子表面有效电荷的影响

胶体粒子的表面有效电荷是决定胶体性质的重要物理量,但溶液环境(如电解质溶液浓度)是否影响其数值至今尚无统一认识,近年来的一些研究工作给出了存在争议的不同结果和假设.在直接实验测量方面,由于电解质离子和胶体表面吸附离子的置换,粒子表面基团的不完全电离和胶体粒子对离子吸附的共同作用,使得对这类粒子在不同溶液环境下的表面有效电荷的测量和变化机理的认识极为困难.针对该问题,本文测定了羧基和磺酸基修饰的聚苯乙烯胶体颗粒在不同粒子浓度和HCl浓度下的电导率,由于两种粒子与HCl电离产生的阳离子相同(均为H+),可根据电导率-数密度法(迁移法)得到胶体颗粒表面有效电荷数.通过实验结果分析,明确了HCl浓度以及粒子数密度对胶体粒子表面电荷的影响规律以及表面电荷随HCl浓度增大的原因.除此之外,羧基修饰颗粒比磺酸基修饰颗粒的表面电荷随HCl浓度变化更快;对于同一HCl浓度,磺酸基修饰胶体表面电荷不受粒子数密度影响,而羧基修饰胶体颗粒却与之相关.基于粒子表面电荷的理论模型,对这些问题都给出了相应的解释.     

Analytical model of transversal cooling and heating of channeled ions

A theoretical model is developed explaining the atomic-number dependence of the velocity at which a transition occurs from the heating of the transverse energy of multiply charged channeled ions to its cooling. The model is based on the previously proposed interpretation of the influence of ion charge exchange on the redistribution of the ion flux passed through a thin single crystal with an isotropic distribution of the incident beam. The transition from heating to cooling is explained by the change in the ratio of the average charge of channeled ions to the average charge of ions with random motion in the crystal. In particular, the absence of such a transition for light ions is explained.     

Generalized Poisson-Boltzmann Equation Taking into Account Ionic Interaction and Steric Effects

Generalized Poisson-Boltzmann equation which takes into account both ionic interaction in bulk solution and steric effects of adsorbed ions has been suggested.We found that,for inorganic cations adsorption on negatively charged surface,the steric effect is not significant for surface charge density 0.0032 Cdm 2,while the ionic interaction is an important effect for electrolyte concentration 0.15 moll in bulk solution.We conclude that for most actual cases the original PB equation can give reliable result in describing inorganic cation adsorption.     

Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Feasibility study of artificial rainfall system using ion seeding with high voltage source

A non-linear computational modelling of ions from the ground station for electrifying the atmosphere to make feasibility study of artificial rainfall system is proposed and analyzed. The model considers generation of intermediate ions and ionized airflow velocity. The governing electro hydrodynamic (EHD) equations of the model shows that the space charge density, electric field intensity and velocity of the ionized airflow are function of high input voltage applied to generate the ions. The number of ions generated and their velocity is proportional to the applied ion generator voltage.These artificial ions will be introduced in the atmosphere which will act in a similar manner as cosmic rays. These ions will ionize the aerosols and catalyze nucleation processes and thus electrify the atmosphere which will form cloud droplets to get artificial rain. The mathematical model to study the feasibility of artificial rainfall is also validated under favourable conditions.     

Structural and electrical properties of pure and NaBr doped poly (vinyl alcohol) (PVA) polymer electrolyte films for solid state battery applications

A sodium ion conducting polymer electrolyte based on poly (vinyl alcohol) (PVA) complexed with sodium bromide (NaBr) was prepared using solution cast technique. Several experimental techniques such as XRD, FTIR, SEM, temperature-dependant conductivity and transference number measurements have been performed. XRD and FTIR studies confirm the complexation of salt with the polymer. Surface morphology was studied using Scanning Electron Microscopy. DC conductivity was measured in the temperature range of 303–373 K, and the conductivity was found to increase with the increase of dopant concentration as well as temperature. Transference number data suggests that the charge transport in this polymer electrolyte system is mainly due to ions. Using these polymer electrolyte films, electrochemical cells were fabricated with configuration Na/(PVA:NaBr)/V₂O₅ and Na/(PVA:NaBr)/(I2+C+electrolyte) and their discharge characteristics like open circuit voltage (OCV), short circuit current (SCC), power density, energy density were evaluated and compared. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006.     

Generalized Poisson-Boltzmann Equation Taking into Account Ionic Interaction and Steric Effects

Generalized Poisson-Boltzmann equation which takes into account both ionic interaction in bulk solution and steric effects of adsorbed ions has been suggested. We found that, for inorganic cations adsorption on negatively charged surface, the steric effect is not significant for surface charge density <0.0032 C/dm², while the ionic interaction is an important effect for electrolyte concentration >0.15 mol/l in bulk solution. We conclude that for most actual cases the original PB equation can give reliable result in describing inorganic cation adsorption.     

离子浓度及表面结构对岩石孔隙内水流动特性的影响

酸性环境引发的岩石孔隙表面溶解增加了孔隙内水溶液的盐离子浓度,破坏了孔隙的表面结构.本文采用分子动力学模拟的方法研究了纳米级岩石孔隙内水溶液的流动特性,分析了盐离子浓度和孔隙表面结构对水流速度分布的影响及原因.研究结果表明:纳米级岩石孔隙内的水溶液流动符合泊肃叶流动特性,流速呈"抛物线"分布;随盐离子浓度增加,水溶液内部氢键网络变得更为致密,水黏度随其呈线性增长;水溶液中离子浓度越大,孔隙表面对水流动的阻力越大,最大流速越小,速度分布的"抛物线"曲率半径越大;岩石孔隙表面结构的破坏改变了流动表面的粗糙程度,增加了孔隙表面对H2O分子的吸引力.随表面结构破坏程度的增大,水溶液在近壁区域的密度增大,流速降低;当表面破坏程度达到50%时,水溶液在近壁区域出现了明显的负边界滑移现象.     

Structural and electrical studies of sodium iodide doped poly(vinyl alcohol) polymer electrolyte films for their application in electrochemical cells

Solid polymer electrolyte films based on poly(vinyl alcohol) (PVA) complexed with sodium iodide (NaI) were prepared using solution cast technique. The structural properties of pure and complexed PVA polymer electrolyte films were examined by X-ray diffraction (XRD) studies. The XRD results revealed that the amorphous domains of PVA polymer matrix was increased with the increase in NaI salt concentration. The variation of film morphology was examined by scanning electron microscopy (SEM) studies. Fourier transform infrared spectral studies for pure and complexed PVA films revealed the vibrational changes that occurred due to the effect of dopant salt in the polymer. Direct current conductivity was measured in the temperature range of 303–373 K, and the conductivity was found to increase with the increase in dopant concentration as well as temperature. Measurement of transference number was carried out to investigate the nature of charge transport in these polymer electrolyte films using Wagner’s polarization technique. Transport number data showed that the charge transport in these polymer electrolyte systems was predominantly due to ions. Using these polymer electrolytes, solid-state electrochemical cells were fabricated. Various cell parameters like open-circuit voltage, short circuit current, power density, and energy density were determined.     

Determining the mobility of ions by transient current measurements at high voltages

We present polarization and transient current experiments that allow an independent determination of the charge carrier density and the mobility of ions in polymer electrolytes at low charge carrier density. The method relies on a complete depletion of ions in the bulk electrolyte achieved by applying high voltages. Based on a qualitative model for the charge dynamics in this nonlinear regime, the method is exemplarily applied to a system of polymethylmethacrylate doped with small amounts of a lithium salt. The independently obtained values for the ionic mobility, the charge carrier density, and the conductivity are consistent for all salt concentrations studied. Criteria for the applicability of the method are discussed.     

非平衡磁控溅射系统的离子束流控制

在非平衡磁控溅射沉积非磁性金属薄膜过程中,离子,原子到达比、沉积速率等参数是影响薄膜结构和性能的重要因素。根据非平衡磁控溅射沉积过程中离子的分布特点,分别考虑离子和中性粒子的传输,导出了对圆形平面靶非平衡磁控溅射沉积薄膜的放电功率、气压和离子束流密度等参数之间的关系,阐明了放电参数对于沉积过程离子束流密度等参数的影响。在Ar放电条件下,测量了系统的伏安特性;采用偏压平面离子收集电极测量了溅射系统轴向离子束流密度随不同的气压、溅射电流和空间位置的变化规律。结果表明模型分析的结论和实验数据的变化趋势相符合。     

Nanopores: A journey towards DNA sequencing

Much more than ever, nucleic acids are recognized as key building blocks in many of life's processes, and the science of studying these molecular wonders at the single-molecule level is thriving. A new method of doing so has been introduced in the mid 1990's. This method is exceedingly simple: a nanoscale pore that spans across an impermeable thin membrane is placed between two chambers that contain an electrolyte, and voltage is applied across the membrane using two electrodes. These conditions lead to a steady stream of ion flow across the pore. Nucleic acid molecules in solution can be driven through the pore, and structural features of the biomolecules are observed as measurable changes in the trans-membrane ion current. In essence, a nanopore is a high-throughput ion microscope and a single-molecule force apparatus. Nanopores are taking center stage as a tool that promises to read a DNA sequence, and this promise has resulted in overwhelming academic, industrial, and national interest. Regardless of the fate of future nanopore applications, in the process of this 16-year-long exploration, many studies have validated the indispensability of nanopores in the toolkit of single-molecule biophysics. This review surveys past and current studies related to nucleic acid biophysics, and will hopefully provoke a discussion of immediate and future prospects for the field.