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The equations of ionic currents in the parallel composite membrane-NaCl system were derived from the phenomenological equations presented by Kedem and Katchalsky. The elements of the conductance matrix for the composite membrane system, gαβ, as well as those for the single membrane systems with cation-exchange or anion-exchange membranes, or , respectively, were determined by the measurements of membrane potential, membrane conductance, and salt flux. It was found that gαβc or gαβa for the constituent elements of the composite membrane system was different from or for the single membrane systems, respectively. These differences may be attributed to the situation that gαβc and gαβa represent the intra- and intermembrane transport phenomena, while and represent the former phenomena only. The composite membrane system is characterized by the large cross coefficient which is comparable in the magnitude to the straight coefficients, i.e., gNa·Cl ≈ gNa·Na ≈ gCl·Cl. Kedem and Katchalsky have predicted that the s...

Reverse transport in a liquid membrane system was studied on the basis of nonequilibrium thermodynamics. The electrochemical affinities which drive the ion flux in the system accompanying the chemical reaction were described in the form of the dissipation function. The system was confirmed to be a typical physicohemical system. In addition, using the equations developed in this study, several membrane parameters were estimated and the correlation between the diffusional ion conductance and ion concentration within the liquid membrane was discussed.

A theory for the ion transport across liquid ion-exchange membrane was presented on the basis of nonequilibrium thermodynamics with the assumptions that the carrier ions and complexes were present ...

Basic ion transport characteristics of a homogeneous amphoteric ion exchange membrane (Kanegafuchi Chem. Ind. 1.0-PA-29) were studied by measuring the membrane potentials and conductances. Concentration cell systems of NaCl, KCl, CaCl2, and SrCl2 with a concentration range of 10−1–10−3 mol dm−3 were studied and the electroconductive membrane permeabilities were estimated from the electrochemical data. Generally, Cl− is slightly more permeable than cations under the present experimental conditions, except the result that K+ is more permeable at low concentrations. Unlike the usual uniform cation exchange membrane of which transport characteristics to ions strongly depend upon the number of ionic charges, a “1.0-PA-29” amphoteric membrane exhibits different transport properties for the NaCl and KCl systems. In the NaCl system, the membrane was constantly anionic selective, while in the KCl system, biphasic ion selectivities were observed depending upon the external KCl concentration. Fundamental electrochem...

Basic electrochemical properties of an amphoteric ion-exchange membrane (1.0—PA—29), in which almost equal numbers of cationic and anionic sites are distributed homogeneously over the functionalized polymer networks, were studied for a variety of concentration-cell systems. Unlike the usual uniform ion-exchange membrane, potentiometric permselectivities were demonstrated even for ions of the same charge, as shown by the result that distinctive potential responses were observed for a series of alkali metal chloride, sodium salt, and tetra-alkylammonium chloride systems. The sequence of membrane permeabilities to cations and anions calculated from the electrochemical data could well be correlated to the sequence of the hydrated radii of the respective ions. So the potentiometric responses to any electrolyte system can be predicted from the permeability data or hydrated radius values of individual cations and anions. The present results suggest that the homogeneous amphoteric ion-exchange membrane functions effectively as an ion sieve, sifting out the sizes of permeating hydrated cations and anions.

The ionophoretic activity of dipalmitoyl-DL-α-phosphatidylcholine (DPPC) was investigated on the system in which two aqueous NaCl solutions are separated by a porous support membrane impregnated with a 1-octanol solution of DPPC. Transmembrane potential and conductance measurements were carried out with changing temperature to estimate the membrane permeability to ions. To clarify the mechanism of ion transport through an immobilized DPPC-1-ctanol membrane, differential scanning calorimetry and photon correlation spectroscopy were employed to investigate the molecular properties of DPPC in a water-saturated 1-octanol system. An endothermic peak was detected at around 18°C in the water-saturated 1-octanol system, but not in the pure 1-ctanol system. Laser light scattering study indicated that DPPC molecules form aggregates, ca. 0.1 μm in diameter, in water-saturated 1-octanol, but not in pure 1-octanol. Temperature dependences of the relaxation time estimated by the light scattering study changed above and below 18°C. The critical temperature, 18°C, correlates well with that at which modes of the temperature dependences of membrane permeability are altered. Results obtained by these three types of experiments indicate that inverted micellar aggregates of DPPC function as an ionophore.

The membrane potential and conductance of the cation-exchange membrane-aqueous quaternary tetraalkylammonium chloride systems have been measured by using NH4+, tetramethyl-(Me4N+), tetraethyl-(Et4N+), tetrapropyl-(Pr4N+), and tetrabutylammonium ions (Bu4N+). The potential change in the concentration cell with these salts was about 58 mV for a tenfold change of concentration. The membrane conductance in the concentration cell increased with the concentration. The membrane permeability, as estimated from the potential and conductance data, was in the order of NH4+>Me4N+>Et4N+>Pr4N+>Bu4N+; it is proportional to the geometric mean of the activities of exterior solutions. The effective pore size of the membrane was deduced from the conductance data and found to be ca. 10 A. The selective permeation coefficient has been determined from the potential data of the two- and multi-ionic systems. The selectivity data obtained with the two-ionic system were in agreement with those obtained with the multi-ionic system....

In order to clarify the mechanism of ion transport across an amphoteric membrane with sulfonate and N -methylpyridinium groups as exchange sites, membrane potential and membrane conductance measurements were carried out with varying valences of cations and anions of the electrolyte solution. It was shown that the membrane studied behaves as a cation exchange membrane in 1-1 valent and 2-2 valent electrolyte solutions. On the other hand, the membrane function was strongly influenced by the valence of the cation; the membrane in the LaCl 3 system in particular was preferentially anion selective. The permeability coefficients were evaluated according to the theory of nonequilibrium thermodynamics, and ion transport was discussed.

A theory for the ion and solvent transports through membrane has been developed on the basis of nonequilibrium thermodynamics. The fluxes were represented as linear functions of the effective driving potentials. The theory is reduced to that of Katchalsky when the concentration ratio of two aqueous solutions is near unity and the solutions are dilute. The effect of solvent flow on the interionic correlations was discussed. It was pointed out that Despic and Hills’ theory of the electroosmotic effect on the membrane conductance is not valid with respect to both theoretical and experimental aspects. The comparison of the present theory with the previous one was also made. The six independent phenomenological coefficients (elements of the conductance matrix) were experimentally determined as a function of concentration with the concentration cell consisting of the amphoteric ion-exchange membrane and aqueous calcium chloride solutions. The membrane properties were discussed in terms of the conductance matrix...

Transport characteristics of Na+–Ca2+ bi-ionic system with a highly selective cation-exchange membrane were investigated on the basis of nonequilibrium thermodynamic theory. As a principal transport parameter, the membrane permeability matrix or membrane conductance matrix can be estimated from the membrane potential, conductance, and ion flux data. Significances of diffusional and electroconductive processes of ion transport across membrane were systematically discussed in terms of these matrix elements. Partial contributions of inter-cationic (Na+–Na+, Na+–Ca2+, and Ca2+–Ca2+) correlations to the membrane transport process of ions were examined by means of comparing the estimated values of corresponding matrix elements. It was suggested that Ca2+ ions, of which membrane concentrations are kept at high level independently of the Na+/Ca2+ concentration ratio of external aqueous solutions, play a critical role in the membrane transport phenomena. Participations of Cl− transport in the cation-exchange proce...

A theory of membrane ion transport suitable for a self-consistent analysis of transport phenomena is presented on the basis of nonequilibrium thermodynamics. The theory assumes only a steady state and no volume flow across the membrane. Ion flow is expressed as a linear function of the total ion activity difference across the membrane. Coefficients of the flux equation are defined as elements of a permeability matrix. The equations for the membrane properties (e.g., potential and conductance) are derived from the equation of ion flux. The theory is applicable to any multi-ionic system containing ions of various charges. A physical representation of membrane permeability and a correlation between membrane permeability and the elements of a permeability matrix are explained. Transport phenomena are discussed with respect to the theory presented.

Transport properties of a cation-exchange membrane-aqueous sodium chloride solution system have been studied. The membrane used was a sulfonated styrene–divinyl benzene copolymer, Neosepta C66-5T. The salt concentration was kept at 10−1 mol dm−3 on one side of the membrane and varied from 10−3 to 10−2 mol dm−3 on the other. The six elements of a conductance matrix have been experimentally determined according to the previous theory and the membrane properties were discussed in terms of conductance elements. All the elements of the conductance matrix were positive within the concentration range studied. This would be characteristic of a cation-exchange membrane. The electrical ion conductance was greater than the diffusional ion conductance by a factor of 10 to 100. The ion-solvent coupling coefficient was much less than the interionic one, although the electroosmotic conductance was ten-times greater than the membrane conductance. The reflection coefficient was close to unity. The electroosmotic propertie...

Utilizing a liquid membrane-aqueous inorganic electrolyte system, the membrane permeability to ion α estimated from the conductance and potential data, Pα, and that at zero electric current estimated from the salt flow and potential data, Pα0, were determined. A solution of calcium hexadecyl sulfate dissolved in 1-octanol and calcium chloride were used as the liquid membrane and the inorganic electrolyte, respectively. The results showed that Pca0⁄Pcl0≈Pca⁄Pcl≈10 and Pcl0≈Ps0, where subscript s refers to the salt. The latter result indicates that the diffusion of a salt through the membrane is governed by the co-ion permeation. It was shown that Pα0 is smaller than Pα and that Pα decreases with increase in the concentration of external calcium chloride solution while Pα0 is nearly independent of the concentration. The difference between Pα and Pα0 can be explained in terms of the elements of permeability and conductance matrices estimated from the electrical and salt flow data.

Transport characteristics of NH4Cl, (CH3)4NCl (TMA–Cl), (C2H5)4NCl (TEA–Cl), (n-C3H7)4NCl (TPA–Cl), and (n-C4H9)4NCl (TBA–Cl) across homogeneous type amphoteric ion exchange membrane (1.0-PA-29, Kanegafuchi Chem. Ind.) were studied. Membrane potentials and conductances of the concentration cell systems were measured to calculate the membrane permeabilities which represent a measure of ionic permselectivity. Membrane potential changed considerably with cationic species and the membrane tended to behave more anionic selectively with increasing bulkiness of cations. The cationic permeabilities calculated from electrochemical data were PNH4>PTMA>PTEA>PTPA>PTBA. Membrane permeabilities to chloride ions, PCl, were greater than those to cations in all the systems studied and it was interesting that PCl values and their dependencies on external electrolyte concentration were almost unchanged irrespective of the difference in cationic species. The present experiment was designed in order to examine the effects of ...

This paper is concerned with analysis of membrane transport processes on the basis of nonequilibrium thermodynamics. Inter-ionic correlations between permeating ions are quantitatively estimated by applying the membrane permeability matrix theory to the system in which the NaCl and CsCl solution phases are divided by a highly selective cation exchange membrane. The membrane permeability matrix of the system may be expressed by four ionic correlation terms concerning with Na+ and Cs+. The electroconductive and diffusional membrane permeabilities are expressed as a function of the matrix elements having the dimension of permeating speed of ions. The conductive and diffusional permeabilities as well as the matrix elements are estimated from membrane potential, conductance, and ionic flux data. The external electrolyte concentration dependence of these permeability parameters is discussed. The conductive and diffusional permeabilities considerably differ from each other and their ratio changes with the extern...

In an amphoteric ion exchange membrane-electrolyte system, three independent experiments were carried out, that is, the membrane potential, membrane conductance and concentration of ions within membrane were measured, respectively. The electrolytes adopted in the systems were NaCl, CaCl2, LaCl3. From the analysis of the results, the specific conductance attributed to Donnan salt within membrane was separated. As a result, it was pointed out that the dynamic state of Donnan salt is obviously different from that of salt in aqueous solution. Furthermore, the comparison between the ions constituting Donnan salt and the counterions which interact with the ion-exchange sites suggested us the existance of two different dynamic states on the ions within membrane.

Ion-transport processes across an amphoteric ion-exchange membrane were investigated by means of estimating the membrane permeability matrix, a set of modified linear phenomenological coefficients, from the electrochemical and the ion flux data. Systematic comparisons of phenomenological analyses on an amphoteric ion-exchange membrane system with those on an ordinary cation-exchange membrane system were carried out to investigate the correlations of singly- and binary-charged membrane structures to characteristic transport properties. The modes of ion permselectivity of an amphoteric ion-exchange membrane in the metal chloride concentration-cell systems are characterized by the potentiometric selective response due to the ion-sieve effect, the low membrane conductance, and the large ion flux, while those of an ordinary cation-exchange membrane are characterized by the totally charge-dependent potential response, the high conductance, and the extremely small ion flux. The cross elements of the membrane per...

In order to clarify the membrane phenomena in an amphoteric membrane, four different experiments were carried out in a simple electrolyte-amphoteric membrane system. The ion transport numbers obtained from the membrane potential and electrodialysis were approximately in agreement with each other. It was indicated that the transport numbers strongly depended on the ionic valence in electrolyte solution. The membrane permeability coefficient representing the dynamic behavior of ion within membrane was evaluated in terms of membrane potential, transport number, and membrane conductance. In addition, the ionic concentrations within membrane equilibrated with outer electrolyte solution were measured to obtain the mobilities within membrane. The membrane phenomena were discussed on basis of the present experimental results.

The membrane phenomena in an amphoteric membrane-single-electrolyte or mixed-electrolyte solution systems were examined. The mobilities of the ions within the membrane were evaluated from the relation between the transport number and membrane conductance after determination of the ionic concentration within the membrane. In the single-electrolyte system, the mobilities depending on the ionic charges were observed. The facts supported that ion-transport phenomena were mainly controlled by the electrostatic interaction between the ion-exchange sites and the ions within the membrane. On the other hand, the cation with the smaller valence was always excluded out of the membrane in the mixed-electrolyte system. When comparing the ratios of mobilities in the single-electrolyte system with those in the mixed-electrolyte system, large differences between them could be observed. It is conjectured that one of the reasons may be the difference in the Donnan adsorption salt concentration within the membrane.

The biionic membrane potential was measured with the system in which a solution of calcium chloride was separated by a liquid membrane from a solution of another metal chloride. Four kinds of liquid membranes were prepared by dissolving calcium hexadecyl sulfate, stearate, cholate or deoxycholate in aqueous 1-octanol. All of the membranes studied were nearly permselective to cation. The membrane potential was analysed according to the Goldman-type equation based on the irreversible thermodynamics. The slope of a linear portion of the biionic potential vs. logarithmic activity curve showed fairly good agreement with the theoretical slope, i.e., 2.303×2RT⁄(ZCa+ZM)F per a ten-fold increase in activity, where ZCa and ZM were the valencies of calcium ion and another metal ion M existing across a membrane, respectively. The selective permeation coefficients of various metal ions were estimated for each membrane. The surprisingly small differences in the selective permeation coefficient between uni- and bi-valen...

Reverse transport coupled to a chemical reaction was studied with a liquid membrane-electrolyte system. The liquid membrane was prepared by dissolving 10−2 mol-dm−3 monensin in 1-octanol; it was supported by a Millipore filter. The membrane showed an ideal potential response for Na+ and H+ cations. A system with the same Na+ ion concentrations in both exterior aqueous phases was chosen as the reverse transport system. The membrane potential and the ion flux of the system were measured as functions of time. The results were treated in terms of the membrane equations developed in previous papers. The membrane potential and the ion flux could be described consistently according to equations derived on the assumption of a rapid acid-base reaction taking place at the boundary. It was concluded that the acid-base reaction energy is transformed into an electrochemical potential, and, as a result, the reverse ion flux is apparently driven by the electrochemical potential gradient.

A conductance matrix describing the ion-transport phenomena in the membrane-three ion system has been determined. It was indicated there that six independent experiments were required in order to determine six independent elements of the conductance matrix. The NaCl–CaCl2–amphoteric membrane system was chosen as the three ion system, and three kinds of fluxes, two kinds of transport numbers, and the membrane conductance were measured. Nine elements were experimentally determined on the assumption of Onsager’s reciprocal relation. The results showed that the order of elements in conductance matrix was gCaCa>gClCl>gNaNa>gCaCl>gNaCl>gCaNa. In addition, it was pointed out that the interactions among ions can never be ignored when the ion-transport phenomena across membrane are studied.

Bi-ionic potentials were measured as a function of the mole fraction of a counterion in a membrane where the total concentration of the carrier or site (hexadecyl pyridinium ion) was kept constant. The membranes used were prepared by dissolving two hexadecyl pyridinium salts, each with a different counterion, in nitrobenzene. When chloride ion was the only counterion, all bi-ionic systems showed a potential as expected from an equation derived in a previous paper. The order of selectivity in the system was perchloride > thiocyanate > nitrate > bromide > chloride. It was found that the additivity rule for bi-ionic potentials held when the counterion in the membrane was either the same as that in both external aqueous electrolyte solutions, or a less selective one. However, when two different counterions coexisted in the membrane, the membrane potential showed a strong dependence upon the counterion composition. These phenomena were interpreted in terms of the membrane equation by taking into account the boundary potentials. A detailed discussion of the results will be given in this paper.

Liquid membrane electrodes selective to alkyl sulfate ions were devised for octyl, decyl, and dodecyl sulfate ions, and employed in the study of micellar solutions. A nitrobenzene solution of hexadecyltrimethylammonium—alkyl sulfate complex was used as the liquid membrane. The membrane potential-logarithmic concentration showed a maximum at the critical micelle concentration (CMC), an increase with the Nernstian slope at the lower concentrations and a decrease at the higher concentrations. Below CMC, the presence of excess inorganic salt did not alter the Nernstian slope, i.e., the liquid membrane was more highly permselective to alkyl sulfate ions than to inorganic anions. From a simple thermodynamic consideration of a micellar solution based on the pseudo phase model of the micelle, the change in the activity of alkyl sulfate ions and the dissociation of the micelle were discussed. It has been deduced that the concentration of the singly dispersed surfactant ions above CMC is reduced with concentration,...

Theoretical treatments of the membrane process in the steady state were presented by using the rate equation in the preceding paper (Kimizuka & Koketsu,1964). It was shown that the equation for the ion conductance and transport number were expressed as functions of the membrane permeability, the composition and the membrane potential. The transport numbers of ions to the membrane of frog's sartorius muscle in normal Ringer's solution were calculated according to the derived equation. The membrane potential calculated according to the Nernst equation by using the transport numbers and the equilibrium potentials of potassium, sodium and chloride ions was in agreement with the observed value. The membrane conductance was shown to be a function of the applied potential, by which the difference between the calculated membrane resistance at rest and the observed one, could be explained. The equation for the passive ion flux at rest was given as a function of the composition and the membrane permeability, and it was shown that the calculated passive movements of ions were consistent with the directions of the active transports. The equation for the resting potential, as well as the membrane conductance, were obtained for the case in which the external solution contains the bivalent ions. The prolonged action porential of the crustacean muscle fibers (Fatt & Ginsborg, 1958) in the presence of strontium ions could be expressed in terms of the derived equation, and the membrane permeabilities to the ions were evaluated according to the proposed relationships. It was shown that the current-voltage relation measured with the giant axon of loligo (Hodgkin, Huxley & Katz, 1952) could be expressed by the derived equations. The discussion for the states of the membrane was given in terms of the proposed theory. The current-voltage relation for the cable has also been derived.

1. The surface viscometer, the main part of which consisted of a fine vertical thread of glass carrying a horizontal platinum wire at its lower end, was devised for the measurement of the surface viscosity of solutions. 2. The measurements of the surface viscosity as well as some other surface properties of solutions of a number of dyes and saponin were carried out. The effect of coexisting alcohol and inorganic electrolyte for the saponin solution were also examined. The results showed a close correlation between the surface viscosity, the life of foam and so called membrane effect.

(1) The rupture of aqueous saponin film was studied by measuring the variation of the frequency of the breaking with tension as well as by measuring the breaking time as a function of stress. The results showed that the irreproducibility of the observed data upon surface tension was due to the breaking of the solid film and this mechanism was also responsible for the nature of the stability of such a foam as that produced by saponin, which was also considered to consist of solid film. (2) A new method for the measurement of surface tension, applicable to the solution forming a solid adsorbed layer,was presented. (3) It was shown that the membrane effect is a breaking stress of the adsorbed layer.

The bi-ionic membrane potential has been studied on a system consisting of electrolyte solutions separated from another one by an ion exchange membrane. The slope of the linear portion of the curve of potential vs. log activity ratio, log aMaN, was found to be 118(zM+zN) mv at 20°C, where aM and zM denote respectively the activity and the charge of permselective ion M present on one side of the membrane and aN and zN, those of the ion N on the other side. This was in good agreement with the theoretical prediction provided that the membrane is permselective to either cations or anions and the relative membrane permeability is a constant.

The self-diffusion coefficient of an ion and the membrane permeability were studied with a system consisting of two identical electrolyte solutions separated by a cation exchange membrane. The membrane permeability to cation was estimated from the membrane conductance data. The result indicated that the membrane permeability increased with a decrease in electrolyte concentration. The self-diffusion coefficients and the concentrations of Na+, Cs+, and Ca2+ in the membrane were also measured by the radiotracer method. At concentrations less than 0.1 M, the self-diffusion coefficients more or less increased with increasing concentrations, while the concentrations within membrane remained almost constant. The membrane permeability to ion estimated from the conductance data was in excellent agreement with that calculated by the relation in which the membrane permeability is given as the self-diffusion coefficient times the partition coefficient divided by the membrane thickness.

The self-diffusion coefficient of an ion and the membrane permeability were studied with a system consisting of two identical electrolyte solutions separated by a cation exchange membrane. The membrane permeability to cation was estimated from the membrane conductance data. The result indicated that the membrane permeability increased with a decrease in electrolyte concentration. The self-diffusion coefficients and the concentrations of Na+, Cs+, and Ca2+ in the membrane were also measured by the radiotracer method. At concentrations less than 0.1 M, the self-diffusion coefficients more or less increased with increasing concentrations, while the concentrations within membrane remained almost constant. The membrane permeability to ion estimated from the conductance data was in excellent agreement with that calculated by the relation in which the membrane permeability is given as the self-diffusion coefficient times the partition coefficient divided by the membrane thickness.