The effect of temperature on thermoosmosis

Thermoosmosis through a collodion membrane (cm) and a poly(styrenesulfonic acid)—collodion interpolymer membrane (im) was observed, and changes in the mean temperature of the bulk solutions on both sides of the membrane and the KCl molality were recorded. The absolute value of the thermoosmotic coefficient, D, increased with increasing mean temperature. This was due to an increase in the fluidity of the KCl solutions. In all cases the direction of thermoosmosis was from the cold side to the hot side. For the charged membrane (im), the molality dependence of D was larger than that for the collodion membrane (cm).     

On the separation mechanism of gel permeation chromatography

The separation mechanism of gel permeation chromatography was investigated by static experiments. It was found that the solute molecule is excluded from part of the inner space of the gel particle, which is entirely available to the solvent molecule. The excluded volume, ΔV, increases with increase of molecular size of the solute. A linear relationship was observed between the ΔV and the logarithm of molecular size. Excluded volume was found to be independent of solute concentration as was expected. Absorption effect was negligible with polystyrene gel. However, a strong effect was observed between acids and polydextran gel. The possibility of using absorption effects to increase the separability of GPC is suggested.     

Analytical theory for permeation of condensable gases in a nanopore

The permeation of a condensable gas mixture in a pressure gradient is examined within a dynamic density functional theory (DDFT). The non-equilibrium density and flux profiles of gas molecules trapped within a nanopore are calculated for each species as a function of feed gas density. Because of important fluid–fluid interaction close to condensation the flux and density gradients are not related by constant transport diffusivities with the thermodynamic correction of uniform density. For long narrow pores the relation of the selectivity to the equilibrium adsorption isotherms is validated. Improved separation is achieved by combining preferential wall interaction and advantageous attraction between gas molecules of different species and examples are discussed. Results from experiments and simulations of permeation in binary mixtures near condensation are still rare and the theory provides a simple basis to study qualitative trends using known parameters.     

On the CO2 permeation of uniaxially drawn polymers

The CO₂ permeation coefficient and the difficient were measured using the permeation time-lag method for films of atactic polystyrene and high-density polyethylene, each as a function of uniaxial draw ratio. The reduction of permeability with draw ratio is observed for polystyrene and for polyethylene. In the latter it is associated with an increase in crystallinity. In both cases the premeability decreases and the solubility constant remains unchanged. The reduction of permeability is thus caused only by the reduction in diffusion of CO₂ in the drawn polymers. The mechainism is different for the two polymers, as is confirmed by measurements of birefringence, glass transition temperature, and crystallinity.     

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.     

On the simultaneous optimization of pressure and layout for gas permeation membrane systems

We present a methodology for the simultaneous optimization of pressure and network configurations for gas separation membrane permeators. The methodology targets and refines pressure clusters for efficient operation of membrane networks and follows a three-stage strategy. The first stage produces a pressure target curve (PTC) that allows the identification of Pareto optimal pressure cluster combinations. This is followed by a second stage, where the different optimal pressure ratios are used in an optimal search for process structures to identify the performance of the individual clusters. The third stage processes the information generated in the first two stages in a generalized process superstructure model. Throughout the methodology, a modified process synthesis model for membrane network optimization and design is employed which can be optimized robustly using the simulated annealing algorithm. Three illustrative examples are presented to demonstrate the proposed methodology for simultaneous pressure and layout optimization.     

On the equivalence between the microscopic frictional theory and transition-state theory

The generalized Langevin equations are presented by considering such microscopic motions of molecules described by the microscopic Hamiltonian whose potential function is quadratic and internal degree of freedom is multidimensional. Considering the long time behavior of the reactive mode, the Grote-Hynes equation has been derived from the generalized Langevin equations. Furthermore, we have proved that solving the Grote-Hynes equation is equivalent to solving the eigenvalue problem for the whole system, and then the Grote-Hynes treatment coincides with the transition-state theory for the whole system. © 1996 John Wiley & Sons, Inc.     

Gel permeation chromatography: On the shape of the calibration plot and molecular size separability

Data obtained from the calibration of GPC columns of different permeabilities with standard polystyrenes are reported. For single columns the logarithm molecular weight–elution volume plot is linear for approximately one and one-half decades in molecular weight. GPC separations are such that the separability of two samples of similar molecular weight improves as their mean molecular weight decreases. Because of this the analysis of high molecular weight polymers can best be accomplished on a series of columns in which each column has a high permeability limit. The elution volume for columns in series is shown to be the sum of the elution volumes of the individual columns. As higher molecular weights are eluted a pronounced tailing effect is observed.     

On the theory of thermometric titration

The general equation defining the change in solution temperature DeltaT during a thermometric titration is DeltaT = T - T(0) = - AV 1 + BV where A and B are constants, V is the volume of titrant used to produce temperature T, and T(0) is the initial temperature. There is a linear relation between the inverse values of DeltaT and V: 1 Delta T = - a V - b where a = 1/A and b = B/A, both a and b being constants. A linear relation between DeltaT and V is usually a special case of this general relation, and is valid only over a narrow range of V. Graphs of 1/DeltaTvs. 1/V are more suitable for practical calculations than the usual graphs of DeltaTvs. V.     

On the theory of polarographic maxima

The theory of polarographic maxima is presented taking into account the interaction of momentum transport, the electrostatic potential field, the adsorption—desorption and the faradaic processes. Several earlier results are generalised. The systems approach employed here is also extended to quasi-linear situations.     

On the theory of steady-state electrodiffusion

The problem of the electrical field strength distribution outside the boundary layer under on passing of steady-state current through electrolyte is considered. The solution is obtained as a small-parameter reciprocal-power expansion; however, the expansion of the solution in terms of positive powers of this parameter, by using of the method of splicing of asymptotic solutions, is divergent. For the region under consideration, an expression for the field strength is obtained, which differs from the corresponding expression obtained from the electrical neutrality conditions.     

On the theory of solvent effects

A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding. New features of this model are found. The classical aspects are discussed and secondly the quantal implications are considered. A correct Hartree-Fock-like operator is derived which represents an electron in a molecular orbital subjected to the average effect of the other electrons and to the reaction field produced by the virtual charges on the atomic centers.A general formalism based on the preceding model is presented in appendix. The final equations have a form similar to Newton's equation to represent a solvated electron. Unlike some other theories in this field, there is no cut-off involved in the evaluation of the molecular integrals.     

On the theory of the electrochemical diode

Russian Chemical Bulletin -     

On the permeation time lag for different transport equations by Frisch method

A constructive application of Frisch method for deriving permeation time lags for different transport equations is shown. Two main classes, i.e. parabolic and hyperbolic diffusional mass transport equations, are presented and compared. An influence of drift and chemical reaction terms on the time lag is discussed.     

Moment theory for the analytical determination of rate constants for solute permeation at the interface of spherical molecular aggregates

Moment equations were developed on the basis of the Einstein equation for diffusion and the random walk model to analytically determine the rate constant for the interfacial solute permeation from a bulk solvent into molecular aggregates (k_in) and the inverse rate constant from the molecular aggregates to the bulk solvent (k_out). The moment equations were in good agreement with those derived in a different manner. To demonstrate their effectiveness in one concrete example, the moment equations were used to analytically determine the values of k_in and k_out of three electrically neutral solutes, i.e. resorcinol, phenol, and nitrobenzene, from the first absolute (μ_1A) and second central (μ_2C) moments of their elution peaks, as measured by electrokinetic chromatography (EKC), in which the sodium dodecyl sulfate (SDS) micelles were used as a pseudostationary phase. The values of k_in and k_out should be determined with no chemical modifications and no physical action with the molecular aggregates because they are dynamic systems formed through weak interactions between the components. The moment analysis of the elution peak profiles measured by EKC is effective to unambiguously determine k_in, k_out, and the partition equilibrium constant (k_in/k_out) under appropriate experimental conditions.     

On the dielectric theory and computer simulation of water

The static dielectric properties of ST2 water are carefully examined by means of a computer-adapted Kirkwood theory. “Experimental” data are provided by various molecular dynamics simulations involving 216. 500 and 1000 water molecules and corresponding to a variety of boundary conditions. It is shown that the integral of the respective modified T tensor plays the central role in matching different boundary conditions. Thus a unique dielectric constant σ = 82 ± 15 is obtained for a density p = 1 g/cm³ and a temperature T = 120°C. Furthermore, it is found that the constitutive relation P = [(σ - 1)/4 – is already fulfilled in a sample of a few hundred molecules. Finally, R-dependent Kirkwood g factors are discussed, which give a vivid picture, how different boundary conditions influence orientational correlations between water dipoles.