Jørgen Birger Jensen

Ion exchange and membrane potentials in cellulose acetate membranes separating solutions of mixed electrolytes

The properties of (almost) symmetrical cellulose acetate membranes are studied by measuring the electromotive force (EMF) of concentration cells with the membrane as separator. One or two 1:1 salts with a common anion (Cl−) were used in different concentrations on each side of the membrane and AgAgCl were used as electrodes. The concentration(s) on one side of the membrane is fixed, whereas one concentration is varied on the other side. A theory is developed based upon ideal Nernst—Planck transport equations in the membrane, Donnan equilibrium at the membrane interfaces and Nernst equilibrium at electrodes. Furthermore, Hendersons continuous mixture hypothesis is used in the case of two different electrolytes. Comparing measurements and theory for pure salts (NaCl and KCl), the fixed charge of the membrane divided by the intrinsic binding constant for the salt can be evaluated. At low variable concentrations, however, considerable deviations from the one-electrolyte theory are observed. The reason is the competition of the H+ ion from the autoprotolysis of water with the Na+ or K+ ion. The measured values of EMF are therefore highly sensitive to pH at low variable concentrations. The variations with pH (pH between 5 and 8) are well described by the theory assuming unaltered fixed charge and a binding constant for H+ to the membrane which is around 50 times as great as the binding constant for Na+ or K+. The H+ ion is distributed almost evenly between aqueous phase and membrane phase, whereas K+ and Na+ are sterically excluded from the membrane. Comparison between theory and experiment further shows that half of the negative fixed charge is titrated at pH 4 and almost all has been titrated at pH 3. This indicates that the fixed charge in cellulose acetate membranes is caused by carboxylic acid groups (glucuronic acids) as has been reported also in earlier work. A certain asymmetry in the EMF measurements with pure NaCl was observed at high variable concentrations (up to 10 mV), when the membrane sides were changed. The asymmetry is ascribed to the evaporation asymmetry during preparation of the membrane. No asymmetry is observed at low or intermediate variable concentrations.

Electroosmosis in filter cakes of activated sludge

Abstract An experimental apparatus has been developed which fulfils the conditions for measuring the electroosmotic transport of water in filter cakes of activated sludge. A number of different experiments were made on activated sludge treated in different ways, with a dry matter content of approx. 10–30%. The electroosmotic coefficient, i.e. the factor of proportionality between volume flow and applied electric field strength, was found to be independent of, for example, dry matter content or conditioning of the sludge. The experimental results can be explained by assuming a picture of the filter cake as an exopolymer matrix with sludge particles embedded and residual pore solution in isolated pores.

Experimental activity coefficients in aqueous mixed solutions of KCl and KF at 25 °C compared to Monte Carlo simulations and mean spherical approximation calculations

A system of three different ions in solution has been studied experimentally and theoretically. Mean molar ionic activity coefficients have been measured in pure and mixed, aqueous solutions of KF and KCl at 25 °C and 1 atm by means of valinomycin, LaF3 and Ag / AgCl electrodes. More than 200 independent electrometric measurements were considered. The ionic strength varied from 0.0005 to 4 mol dm–3. The activity coefficients were close to unity for pure KF than for KF in equimolar mixture with KCl at the same ionic strength for ionic strengths higher than 1 mol dm–3. The activity coefficients for KCl in pure and mixed solutions could not be statistically separated up to 4 mol dm–3. The Harned coefficients are estimated to be 0 ± 0.0025 dm3 mol–1 for KCl and 0.055 ± 0.025 dm3 mol–1 for KF. The Debye–Huckel limiting law is obeyed within 1.5% in the region from 0.0005 to 0.01 mol dm–3, indicating that the ions involved are small.Comparison with calculations for the primitive electrolyte model using the Kirkwood–Buff equations and the generalized DHX theory has shown, that the experimental data are approximately fitted using diameters of 2.9, 2.9, and 3.4A for the K+, Cl–, and F– ions, respectively. The same values fit approximately the data in the mean spherical approximation (MSA). The MSA calculations demonstrate the validity of Harneds rule. From the latter theory we also obtain single-ion activity coefficients. Monte Carlo (MC) simulations of single-ion activity coefficients have been performed for the primitive, electrolyte model for the above-mentioned ionic diameters and in addition for a diameter of the F– ion equal to 3.7A. Widoms test-particle method is used in conjunction with the extrapolation procedure suggested by Sloth and Sorensen. The MSA as well as the MC calculations support earlier suggestions, that the single-ion activity coefficient of F– in KF–KCl mixed solutions is almost independent of the salt ratio. The same is approximately true for the Cl– ion. Increasing the diameter of the F– ion from 3.4 to 3.7A does not alter this conclusion, but the separation between single-ion activity coefficients becomes larger.

Practical and theoretical aspects concerning the use of salt bridges in electrochemistry

Abstract The emf of electrochemical cells containing various sorts of salt bridges between various concentrations has been measured. The net diffusion potential over a salt bridge has been treated theoretically. An expression to calculate the net diffusion potential has been derived and tested on values estimated from the emf measurements. A merit factor has been calculated for a saturated KCl bridge separating two HCl solutions and compared with the merit factor estimated from emf measurements on the cell: Pt|Ag|AgCl, HCl( c 1 )|KCl(sat)|HCl( c 2 ), AgCl|Ag|Pt The practical performance of two commonly used reference electrodes with salt bridges has been tested on emf measurements on KBr solutions.

Electromotive force and impedance studies of cellulose acetate membranes: Evidence for two binding sites for divalent cations and for an alveolar structure of the skin layer

Abstract The electromotive force (EMF) has been measured for a great number of concentration cells of the type: Ag | AgCl ⋎ ⪢variable⪡ solution | Cellulose Acetate Membrane | ⪢fixed⪡ solution | AgCl | Ag. The solutions were aqueous solutions of mixed electrolytes at atmospheric pressure and mostly at 25°C (in some few cases 35°C ). The ions considered were the cations H + , Li + , Na + , K + , Mg ++ , Ca ++ , Ba ++ and the anions Cl − and F − (Cl − was always present). The ⪢fixed⪡ solution was the same in each series of experiments, but may be varied from one series to the next. In the ⪢variable⪡ solution, at least one electrolyte concentration was varied during the series of EMF measurements. The variable electrolyte concentration was varied over almost 4 decades (from 10 −4 M to 0.6−1.0 M). The 2.5-Cellulose Acetate (CA) membranes were mostly dense membranes cast by ourselves. A few were asymmetic membranes. The skin layer in asymmetric membranes is assumed to have properties similar to dense membranes. The EMF measurements were interpreted by means of a Donnan-Nernst-Planck (Toorell-Meyer-Sievers) model, which functions quite well due to the low fixed charge in the membrane. The membrane diffusion potential is calculated by the Henderson method and in some cases by solving transcendental equations according to Planck, Pleijel and Schlogl. There is no great difference between the membrane potentials calculated by the two methods, but the ion profiles and the actual rates of electrodiffusion may be found by the latter method. Earlier results are recapitulated, especially the evidence for an alveolar structure found by interpreting the membrane capacitance increase with salt concentration - found by means of impedance measurements - in the light of a combined Trukhan-Bruggemann theory. Alveoles in dense membranes or in the skin layer of asymmetric membranes seem to have a mean radius corresponding to ca. 70 A. The dielectric constant in the alveoles is ca. 30 in contrast to a dielectric constant of ca. 16 in the ⪢lamellar phase⪡ inbetween the alveoles. The dielectric constant of ca. 30 in the alveolar phase is also supported by a simple dielectric calculation of the Nernst distribution of mono- and divalent ions between external water and the alveolar solution. Corrections for activity coefficients only seems important above 0.5 M. The Onsager-Samaras dielectric repulsion from the lamellar wall is of some significance only at low salt concentrations. Measured Nernst distribution coefficients in dense CA-membranes agree roughly with calculated values. We also focus on new results for the binding of divalent cations to the glucuronic acid groups of the CA-chains, which may temporarily transform the membranes from weak cationic exchange membranes to weak anionic exchange membranes. The divalent cations may be washed out, but the rate of dissociation is very low. There seems to be two relaxations, the slower being of the order of weeks, the faster being of the order of days. The dissociation of Ba ++ was followed at 25°C and at 35°C and at different external concentrations of NaCl. The slow relaxation seems connected with the Coulomb interaction between the COO − groups and the Ba ++ ions, whereas the fast relaxation is probably reflecting dissociation from physical dipole-ion bonds.

Monte Carlo calculations of thermodynamic properties of the restricted, primitive model of electrolytes at extreme dilution using 32, 44, 64, 100, 216 and 512 ions and ca. 106 configurations per simulation

Monte Carlo (MC) simulations have been performed for the restricted primitive electrolyte model at a Bjerrum parameter B= 1.546 and three extremely small concentrations. The precision of the obtained thermodynamic properties (the excess energy, the heat capacity and the osmotic coefficient) is unprecedented in the literature. The objective is to study the first deviations from the Debye-Huckel limiting law (DHLL) without any assumptions. The values of the mentioned thermodynamic properties are significantly different from the values obtained from the extended Debye-Huckel expression (DH). MC values are situated between DH and DHLL values and are close to the values of the DHX theory (which uses a DH screened potential as the effective potential connected with the radial distribution functions). However, the MC values are also significantly different from the DHX values. The MC values of the radial distribution functions at contact are statistically identical to the values given by the DHX theory, but the contact values are quite uncertain because of the rare close encounters at extreme dilution. Nevertheless, the osmotic coefficients are well determined, since the contact term is vanishingly small in comparison to the third of the excess energy. The excess Helmholtz free energy has been calculated in the same Metropolis sampling by means of the Salsburg–Chesnut method. For an infinite Metropolis Markov chain, this method is shown to lead to the correct result for the excess electrostatic free energy. However, the method has not quite converged even with 106 configurations, and the electrostatic free energies are found to be ca. 5% higher than the DHLL values. The DH theory predicts up to 5% lower values. Because of the present systematic deviation, the electrostatic entropies calculated by the difference between the excess energy and the electrostatic free energy are 15–20% lower than the DHLL values.

Electromotive force studies of cellulose acetate membranes. Binding of divalent cations and membrane potentials of KCl–KF mixtures

Cellulose acetate (CA) membranes cast in our laboratory were characterised electrochemically by EMF measurements. Henderson and Schlogl integrations are used for calculating the membrane potential. Experiments with divalent ions (BaCl2, MgCl2 in HCl) have been performed, and it is shown that the divalent ions bind strongly to the glucuronic acid groups in the CA membrane, transforming the cation exchanger into an anion exchanger. It takes more than one month for the bound divalent cations to dissociate fully from the glucuronic acid groups at 25 °C. The four-ion system KCl–KF–HCl is studied, and it is shown that the F– ion has a lower diffusion coefficient in the membrane than the Cl– ion. The differences between Schlogl and Henderson integration are less than the experimental uncertainty for the KCl–KF–HCl measurements. The membrane concentration profiles and fluxes of ions are calculated for the system KCl–KF–HCl.

Anomalous behavior of saturated aqueous tungstate solutions

Potentiometric measurements on a freshly prepared saturated silver tungstate solution at 25°C indicate the existence of at least four different ionic tungstate species in this solution leading to the formation of a four-component precipitate. Solubility measurements have been carried out on saturated aqueous silver tungstate solutions at 25°C at different ionic strengths and at various pH. An attempt is made to explain the appearance of the solubility curves. Conductivity measurements on saturated sodium tungstate solutions indicate a phase transition of solid sodium tungstate at 36.5±1.0°C. The assumption of a phase transition is supported by DTA and TGA measurements.