O. Kedem

Thermodynamic analysis of the permeability of biological membranes to non-electrolytes.

The application of the conventional permeability equations to the study of biological membranes leads often to contradictions. It is shown that the equations generally used, based on two permeability coefficients—the solute permeability coefficient and the water permeability coefficient—are incompatible with the requirements of thermodynamics of irreversible processes. The inconsistencies are removed by a thermodynamic treatment, following the approach of Staverman, which leads to a three coefficient system taking into account the interactions: solute-solvent, solute-membrane and solvent-membrane. The equations derived here have been applied to various permeability measurements found in the literature, such as: the penetration of heavy water into animal cells, permeability of blood vessels, threshold concentration of plasmolysis and relaxation experiments with artificial membranes. It is shown how the pertinent coefficients may be derived from the experimental data and how to choose suitable conditions in order to obtain all the required information on the permeability of the membranes. The significance of these coefficients for the elucidation of membrane structure is pointed out.

Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes

Abstract A theory of hyperfiltration, based on non-equilibrium thermodynamics, is presented, in which authors combine elements of their own previous work with important contributions of other investigators. The theory pinpoints criteria for salt-rejecting membranes; it does not deal with concentration polarization. The equations for water and salt flux across a differential membrane layer are derived from first principles, and integrated across the membrane, assuming constancy of three coefficients, viz. the specific hydraulic permeability, p1, the local solute permeability, P, and the reflection factor, σ. which is known to be a quantitative index of salt rejection, varying from zero to unity (for non-rejecting to perfect membranes respectively). This procedure is justified by considerations based on the friction model of membrane transport processes. It is shown that 1-σ is the product of an equilibrium term and a kinetic term. The first characterizes the static salt exclusion and hydrophilic properties of the membrane. The second is a quantitative expression for the kinetic characteristics of the membrane.

Role of the membrane surface in concentration polarization at ion-exchange membrane

Abstract A thin convection-free cell was constructed for the characterization of cation-exchange membranes, with CuSO4 solutions confined between thick copper electrodes. Current—voltage curves were recorded for several homogeneous membranes. The limiting current, i.e. the flat portion of the curve, was 1.5–4 times lower than the theoretical prediction. At high voltage the current increases approximately linearly above its limiting value. Onset of noise and noise frequency were determined. It was suggested that the ion conductance of the membrane surface is not uniform. This inhomogeneity decreases the available area and, at high voltage, gives rise to local mixing of the unstirred layer by electroconvection. High limiting current was observed with a composite membrane comprising a porous heterogeneous layer and a highly permselective dense homogeneous layer (sulfonated polysulfone). This may be due to electroconvection in the porous part of the layered structure. The drastic difference of polarization at homogeneous sulfonated polysulfone membranes and at the composite membrane was confirmed in a laboratory electrodialysis stack.

Graded Autocatalysis Replication Domain (GARD): kinetic analysis of self-replication in mutually catalytic sets.

A Graded Autocatalysis Replication Domain (GARD) model is proposed, which provides a rigorous kinetic analysis of simple chemical sets that manifest mutual catalysis. It is shown that catalytic closure can sustain self-replication up to a critical dilution rate, λc, related to the graded extent of mutual catalysis. We explore the behavior of vesicles containing GARD species whose mutual catalysis is governed by a previously published statistical distribution. In the population thus generated, some GARD vesicles display a significantly higher replication efficiency than most others. GARD thus represents a simple model for primordial chemical selection of mutually catalytic sets.

Hyperfiltration in charged membranes: the fixed charge model

Abstract Salt rejection, R , in charged membranes was evaluated according to the fixed charge model as described by Teorell-Meyer-Sievers. Taking into account the concentration dependence of the transport coefficients, it was found that R at given J r , is a function of the ratio between membrane charge and salt concentration, the mobilities of the ions, and the effective thickness of the membrane. The limiting salt rejection at high flow rates, R ∞ , is given by the reflection coefficient corresponding to the salt concentration in the feed solution R ∞ = σ . Concentration profiles at high flow rates confirm this conclusion. The reflection coefficient,σ , is completely determined by the ratio between membrane charge and feed concentration, the valencies of the ions and the transport number of the counter-ion in free solution. R ∞ was calculated for a wide region of relative charge densities, and several transport numbers corresponding to some common electrolytes. High transport number of the co-ion decreases R ∞ . For divalent counter-ions salt rejection is lower, as a consequence of the different ion distribution. Negative values for R ∞ are obtained in a considerable part of the region. High salt rejection is obtained for divalent co-ions.

Ion-exchange membranes in extraction processes

Extraction processes aided by ion-exchange membranes are reported. Extraction of metal cations was carried out with a cation-exchange membrane separating the feed from the extractant. It is shown that the components of the extraction medium are very well retained in the organic phase. Stripping was carried out either through a second, identical, membrane, or by direct re-extraction. In the extraction of copper by LIX the ion transport is sensitive to the rate of stirring in the organic extractant phase. In a flow cell the copper transport is 5.6 × 10−9 mol/cm2-sec from a mixture of copper and nickel salt, 4.5 mM each. No nickel transfer was observed. Silver was selectively extracted by di(2-ethyl-hexyl)dithiophosphoric acid from a solution containing an excess of sodium thiosulfate. Extraction of acid with a long chain amine was carried out with an anion-exchange membrane separating the feed and the extractant and a second anion-exchange membrane separating the extractant and receiving solution in a three compartment cell. The aqueous solutions were not contaminated by the amine. Flux of acid was 4.7 × 10−9 mol/cm2-sec from an 0.57 M solution of sulfuric acid.

Water transport in porous and non-porous membranes

Abstract Osmotic water flow, giving the filtration coefficient, and the diffusion of isotopic water were measured in a number or membranes. It is shown that the ratio, g , between osmotic and self-diffusion flux, observed under forces of equal magnitude, may serve as a measure for the mutual interaction between water molecules penetrating the membrane, as compared to the interaction with the membrane constituents. High values were found for g in porous films. In liquid membranes, g is small but does not equal unity. Hence, in diffusion of water through these organic liquids, water-water interactions are of the same order as water-solvent interactions. In one polymer membrane, polyethylacrylate, g is close to one, as would be expected for molecular diffusion in dilute solulion. In cellulose acetate films, g is only slightly higher than in an analogous liquid membrane (triacetine) indicating that here water transport is essentially diffusion in a homogeneous phase.

Studies in irreversible thermodynamics III. models for steady state and active transport across membranes

Abstract If a lattice model can exchange molecules with two baths, it becomes a membrane model. With this point of departure, we study in this paper the steady state flux properties of 20 membrane models. Although we start with lattice gas models, the type of treatment is more general than this. It applies to any membrane made up of independent units, each of which can exist in a finite number of discrete states. The transition probabilities between states are assumed to be “unimolecular”. In biological cases, at least, the states include different macromolecular configurations. In a number of models a “carrier” is introduced. In others, the transport of one or two species across the membrane is coupled to a chemical free energy source such as ATP → ADP + P (“active transport”). Each of the models studied can be represented by a diagram which shows the allowed transitions between states. There is a close relationship between the diagram on the one hand and the steady state force-flux relations on the other. The over-all reciprocal relations for a model are compounded from more fundamental reciprocal (“equal susceptibility”) relations for individual cycles (closed paths) in the diagram of the model.

The role of coupling in pervaporation

Abstract In some pervaporation systems coupling between flows may play an important role. Specifically, this appears to apply to the pervaporation of water and alcohol through ion-exchange membranes. Transport equations including a mutual drag coefficient are discussed and a procedure for the measurement of this coefficient is described. It is shown that a concave concentration profile for the less permeable species may be a consequence of coupling. Coupling may explain the close agreement between pervaporation selectivity and sorption selectivity in a range of concentrations observed in ion-exchange membranes.

Transport coefficients and salt rejection in unchanged hyperfiltration membranes

Abstract Flow equations for salt and water in double-layer membranes are suggested and salt rejection as a function of transport coefficients is derived. Salt rejection at given volume flow is completely determined by the reflection coefficient and salt permeability of the dense layer. Salt rejection was measured as a function of flow rate for modified cellulose-acetate membranes heat-treated at different temperatures. The maximal salt rejection observed with these membranes ranged from 69–99%. Salt-rejection curves were calculated from the independently measured transport-coefficients. Good agreement between the calculated and observed curves was found. This approach makes it possible to separate the influence of flow rate on salt rejection from eventual pressure-induced changes in membrane structure.