Cation and anion transport through hydrophilic pores in lipid bilayers

To understand the origin of transmembrane potentials, formation of transient pores, and the movement of anions and cations across lipid membranes, we have performed systematic atomistic molecular dynamics simulations of palmitoyl-oleoyl-phosphatidylcholine (POPC) lipids. A double bilayer setup was employed and different transmembrane potentials were generated by varying the anion (Cl-) and cation (Na+) concentrations in the two water compartments. A transmembrane potential of approximately 350 mV was thereby generated per bilayer for a unit charge imbalance. For transmembrane potential differences of up to approximately 1.4 V, the bilayers were stable, over the time scale of the simulations (10-50 ns). At larger imposed potential differences, one of the two bilayers breaks down through formation of a water pore, leading to both anion and cation translocations through the pore. The anions typically have a short residence time inside the pore, while the cations show a wider range of residence times depending on whether they bind to a lipid molecule or not. Over the time scale of the simulations, we do not observe the discharge of the entire potential difference, nor do we observe pore closing, although we observe that the size of the pore decreases as more ions translocate. We also observed a rare lipid flip-flop, in which a lipid molecule translocated from one bilayer leaflet to the opposite leaflet, assisted by the water pore.     

Concentration dependences of the transport coefficients of rod-like molecules in narrow slit-shaped pores

The concentration dependences of the label transport and shear viscosity coefficients for rod-like molecules in slit-shaped pores were studied. The calculations were carried out using the lattice gas model, which describes a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions were taken into account. The translational and rotational motions of molecules were described in terms of the transition state theory for nonideal reaction systems, which took into account the influence of neighboring molecules on the height of the activation barrier. The model equations reflect the pronounced anisotropy of the distribution of system components along the normal to the pore wall surface and ordering effects of molecules along various directions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1485–1494, September, 2006.     

Freezing of hard spheres confined in narrow cylindrical pores

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.     

Anisotropic dynamics of dipolar liquids in narrow slit pores

We report molecular dynamics simulation results for Stockmayer fluids confined to narrow slitlike pores with structureless, nonconducting walls. The translational and rotational dynamics of the dipolar particles have been investigated by calculating autocorrelation functions, diffusion coefficients, and relaxation times for various pore widths (five or less particle diameters) and directions parallel and perpendicular to the walls. The dynamic properties of the confined systems are compared to bulk properties, where corresponding bulk and pore states at the same temperature and chemical potential are determined in parallel grand canonical Monte Carlo simulations. We find that the dynamic behavior inside the pore depends on the distance from the walls and can be strongly anisotropic even in globally isotropic systems. This concerns especially the particles in the surface layers close to the walls, where the single particle and collective dipolar relaxation resemble that of true two-dimensional dipolar fluids with different in-plane and out-of-plane relaxations. On the other hand, bulklike relaxation is observed in the pore center of sufficiently wide pores.     

Polymolecular adsorption and capillary condensation in narrow slit pores

Capillary condensation and polymolecular adsorption in narrow slits has been calculated, where the fields of surface forces overlap one another. The calculations were carried out on the basis of macroscopic theory of dispersion forces and the isotherms of lone adsorption layers at the free surface. It has been shown that under the effect of mutual attraction through a gap, polymolecular adsorption films lose their stability long before their thickness has approached the half-width of a flat slit. This results in hysteresis of the capillary condensation in an ensemble of plane-parallel slits.

In the case of systems having strong adsorbate-adsorbate interaction, there has been detected the existence of the lower limit of sizes of slit pores, wherein the capillary meniscus can coexist with adsorption films. With a slit width smaller than the critical one, the meniscus is likely to form a finite contact angle with “dry” surfaces of a slit. Thus an explanation has been given of the lower limit of the capillary condensation in an ensemble of flat-surface, slit pores. In the case of strong adsorbate-adsorbent interaction, the coexistence of meniscus with adsorption films within the scope of the approach used is possible in slits of any width.

The value of corrections for the surface forces effect to be entered in the calculations of slit pores dimensions has been analyzed on the basis of the capillary condensation data obtained.

In wedge-shaped slits there also exists, besides lower limit the upper limit of capillary hysteresis.     

Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.     

Kinetics and isotherms of asphaltene adsorption in narrow pores

New data relating to the kinetics and adsorption isotherms of asphaltene in consolidated sandstone core samples are reported. The data were obtained from the measurements of electrokinetics of consolidated sandstone core samples in asphaltene/toluene solutions and petroleum oils. The numerical reduction in the (negative) zeta potential of the sandstone samples were attributed to the adsorption of positively charged molecules of asphaltenes. The hydrodynamics thickness δ of adsorption of asphaltene were followed by monitoring the pressure increase that occurred as the adsorbed layer restricted the rock pores and applying Poiseuille's equation. The flow rates indicated a plateau of asphaltene adsorption at a pore blocking thickness of about δ/r = 0.3, which was also the point at which the streaming current reached a plateau. After increasing to about 30% of the pore radius, the adsorbed layer thickness δ stopped growing either with time or with concentration of asphaltene in the flowing liquid. Alternative hypotheses involving asphaltene adsorption isotherms have been investigated. A theoretical treatment advanced describing particle adsorption in the same terms as molecular adsorption and the Langmuir isotherm, with the free energy of asphaltene adsorption on the rock surface (modeled on silica) calculated on the basis of van der Waals attraction. Acceptable agreement was obtained with the electrokinetic measurements.     

Critical temperature of capillary condensation in narrow cylindrical pores

The dependence of the critical temperature of capillary condensation of an adsorbate in cylindrical pores on the diameter of pores is investigated. The calculation is carried out in the quasi-chemical approximation with a calibration function providing the agreement of results for small pores with exact values obtained by the fragment method. The contribution of the size effect to the calibration function as a function of the diameter of pores is considered in terms of the concept of quasi-one-dimensional behavior of the adsorbate in narrow pores. Various adsorbate-adsorbate potentials are considered.     

Electrochemistry of capillary systems with narrow pores V. Streaming potential: Donnan hindrance of electrolyte transport

The electrochemical theory of capillary systems with narrow pores outlined in Part I of this series is applied to the streaming potential and the electrical hindrance of electrolyte transport across ion selective membranes (Donnan hindrance). Both phenomena are related to the fixed ion concentration. Streaming potentials were measured while using collodion membranes of graded porosity and graded fixed ion concentration. The bulk phases consisted of aqueous KCl solutions with a concentration 2×10⁻⁴ n. The streaming potentials were calculated theoretically by using the electrical conductivity data of the membranes given in Part III of this series. The agreement between the experimental results and the predictions of the theory is good. Theory also predicts that a volume flow across the membrane caused by a hydrostatic pressure difference generates a filtration effect the concentration c_s of the electrolyte in the solution leaving the membrane on the low pressure side is lower than the concentration c on the high pressure side. The concentration ratio (c_s/c) is equal to the ratio (κ/κ_i) of the electrical conductivity of the high pressure phase κ and that of the pore fluid κ_i. The hindrance of the electrolyte transport is a transient phenomenon. It disappears slowly if the experiment is continued over a long period of time. This phenomenon, which is of importance in the understanding of ultrafiltration processes using membranes, is discussed in detail. It is compared with the observed changes in the streaming potential as a function of time. The influence of the electrical convection conductivity (electrical surface conductivity) on the streaming potential can be neglected under the chosen experimental conditions. Its influence will be discussed in Part VI of this series.     

Modeling molecular transport in slit pores

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation.     

Monolayer physical adsorption in narrow pores. Apparent surface dimension

Monolayer physical adsorption has been considered, taking into consideration the intrinsic volume of the adsorbate molecules. Since an adsorbed molecule occupies not only the site on the surface but also some of the neighboring volume, it creates steric difficulties for the adsorption of other molecules and leads to underestimation of the measured surface area. As a result, this value depends on the size of the adsorbate molecules and the apparent surface dimension can be introduced, even if the surface of narrow pores has no irregularities of atomic scale size. This effect was shown by simulation of adsorption on the surface of Menger sponge. Experimental data for measuring D-values on silica gels with different pore size distributions are in line with this effect.     

Effect of salts on water viscosity in narrow membrane pores

The effect of various salts on the viscosity, and by implication structure, of water in polymeric membrane pores of radius approximately 1.69 nm and low charge density has been studied. Permeation of pure water and various electrolyte solutions was analyzed using the Hagen-Poiseuille equation expressed in a ratio form to exclude membrane-specific quantities such as pore radius and length. The analysis produced viscosity ratios of electrolyte to pure water inside the membrane pores. Comparing the viscosity ratios inside the pores with their bulk counterparts showed that confinement significantly increased the sensitivity of water structure to the presence of ions. It has been found that, in relative terms in the pores, Cl- was a strong structure breaker, K+ was a moderately strong structure breaker, Na+ was a weak structure breaker, SO4(2-) was a weak structure maker, and Mg2+ was a strong structure maker. Predictive modeling of membrane separation performance would benefit from such effects being taken into account in cases where the pore ion concentrations may be high.     

Molecular transport in narrow channels

The micro-hydrodynamic method is applid to the calculation of the molecular transport in narrow channels in case of capillary condensation, at the flow anisotropy resulted from the potential of the wall surface and/or of boundary vapor and fluid phases. The mechanisms of molecular transport in the one-phase and two-phase fluid flows as a dependence of fluid density and adsorption potential of channel walls are discussed.     

Calculation of the adsorption of rod-like molecules in narrow slit-shaped pores

The adsorption of rod-like molecules in slit-shaped pores was considered within the frame-work of the lattice-gas model. This model is applicable over a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions are taken into account. The equations of the model reflect the strong anisotropy of the distribution of mixture components along the normal to the pore wall surface and ordering of the rods along various directions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1476–1484, September, 2006.     

Phase equilibria and interfacial tension of fluids confined in narrow pores

Correlation between phase behaviors of a Lennard-Jones fluid in and outside a pore is examined over wide thermodynamic conditions by grand canonical Monte Carlo simulations. A pressure tensor component of the confined fluid, a variable controllable in simulation but usually uncontrollable in experiment, is related with the pressure of a bulk homogeneous system in equilibrium with the confined system. Effects of the pore dimensionality, size, and attractive potential on the correlations between thermodynamic properties of the confined and bulk systems are clarified. A fluid-wall interfacial tension defined as an excess grand potential is evaluated as a function of the pore size. It is found that the tension decreases linearly with the inverse of the pore diameter or width.     

Concentration dependences of heat conductivity coefficients of inert gases in narrow pores

Calculation of the transfer of molecules in porous systems requires self-consistent expressions describing the kinetic transfer coefficients for various concentrations and temperatures. The concentration dependences of heat conductivity and self-diffusion coefficients for fluids with different densities, ranging from rarefied gases to liquids, were considered in terms of a unified model. For monoatomic gases (argon), the model takes into account two energy transfer channels, namely, the vacancy mechanism and energy transfer through collisions of molecules. The former channel is characteristic of rarefied gases, while the latter is noted for condensed phases. The energy parameters of the model were determined on the basis of data on the heat conductivity coefficient in the bulk phase. The heat conductivity coefficient follows a linear temperature dependence for low density; in the medium and large density regions, these dependences follow a more complex pattern that changes depending on temperature. The influence of the interaction of atoms with the pore walls on the concentration dependences of the heat conductivity coefficients was investigated for different total amounts of the adsorbate. These coefficients depend appreciably on the distance to the pore wall and on the direction of heat transfer.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

Amidopyrroles: from anion receptors to membrane transport agents

Amidopyrroles have been employed in a variety of anion receptors and sensors. 2,5-Bisamidopyrroles show selective oxo-anion complexation properties in organic solution whilst bis-amides containing dipyrrolylmethane groups form strong complexes with dihydrogen phosphate anions in mixtures of DMSO-d6 and water. Deprotonation of the 2,5-bisamidopyrrole unit can lead to interesting solid-state structures including the formation of orthogonal hydrogen bonded dimers. Amidopyrrole groups have also been employed in receptors for ion-pairs and in membrane transport agents for HCl.