Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores. VI. Convection conductivity (theoretical considerations)

Generally, the electrical convection current and the electrical convection conductivity (Smoluchowski's surface conductivity) have to be taken into account to describe transport phenomena across membranes with narrow pores although the electrical charge distribution within the pores cannot be described as a Helmholtz electrical double layer. In collodion membranes, which have a comparatively low fixed ion concentration, the contribution of the convection conductivity to the electrical conductivity of the pore fluid may be neglected. This assumption was made tacitly in the analysis of our data obtained with this type of membrane.

In this communication equations are derived which take the convection conductivity into account. They are in agreement with the phenomenological transport equations developed by Staverman on the basis of the thermodynamics of irreversible processes.

The electrical convection conductivity can be considered to be the contribution of the fixed ion concentration to the electrical conductivity. It is argued that this contribution cannot be neglected in ion exchange membranes with a high fixed ion concentration and a high mechanical permeability. Neglecting the electrical convection conductivity in such systems could lead to considerable differences between experimental conductivity data and the theoretical predictions. An electrical conductivity term for the fixed ions is proposed which can be used as a correction factor in the equations in which the contribution of the electrical convection conductivity has been neglected. Suggestions are made for the measurement of the electrical convection conductivity in systems with narrow pores and high electrical conductivity (e.g. ion exchange resins). The consequences of the electrical convection conductivity in practical applications of ion-exchange resins are discussed (acceleration of the rates of ion exchange; improvement of the separation properties by the application of a direct electrical current flow).     

Electrochemistry of capillary systems with narrow pores. IV. Dialysis potentials

The dialysis potentials of different collodion membranes with graded pore sizes and electrochemical activities have been measured in dilute aqueous KCl solutions as functions of concentration. It is possible to predict the value of the diffusion potential within a few millivolts on the basis of electrical conductivity data obtained with the same membranes. In general, the measured values are lower than those calculated. It is assumed that this difference is caused by the membranes having a distribution of pore sizes.     

Electrochemistry of capillary systems with narrow pores. II. Electroosmosis

Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz–Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz–Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.     

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.     

Electrochemistry of capillary systems with narrow pores III. Electrical conductivity

The extension of the Teorell–Meyer–Sievers theory of the dialysis potential to a general theory of capillary systems with narrow pores outlined in Part I of this series of publications has been applied to electroosmotic phenomena in Part II. In this Part, the electrical conductivity, including the electrical convection conductivity, will be treated in terms of the new theory. The corresponding equations already referred to in Part I are derived. In addition, results of measurements of the electrical conductivity of collodion membranes with graded porosity and graded electrochemical activity in aqueous KCl solutions of different concentrations are reported. They are used to test the new theory. It will be shown that it is possible to determine the fixed ion concentration A of the membranes by using electrical conductivity data. The theory predicts that the value of A should be identical with the `selectivity constant' of the Meyer–Sievers theory of the dialysis potential. This prediction will be checked in Part IV of this series of contributions.     

Electrochemistry of capillary systems with narrow pores. VI. Convection conductivity (theoretical considerations)

Generally, the electrical convection current and the electrical convection conductivity (Smoluchowski's surface conductivity) have to be taken into account to describe transport phenomena across membranes with narrow pores although the electrical charge distribution within the pores cannot be described as a Helmholtz electrical double layer. In collodion membranes, which have a comparatively low fixed ion concentration, the contribution of the convection conductivity to the electrical conductivity of the pore fluid may be neglected. This assumption was made tacitly in the analysis of our data obtained with this type of membrane.In this communication equations are derived which take the convection conductivity into account. They are in agreement with the phenomenological transport equations developed by Staverman on the basis of the thermodynamics of irreversible processes.The electrical convection conductivity can be considered to be the contribution of the fixed ion concentration to the electrical conductivity. It is argued that this contribution cannot be neglected in ion exchange membranes with a high fixed ion concentration and a high mechanical permeability. Neglecting the electrical convection conductivity in such systems could lead to considerable differences between experimental conductivity data and the theoretical predictions. An electrical conductivity term for the fixed ions is proposed which can be used as a correction factor in the equations in which the contribution of the electrical convection conductivity has been neglected. Suggestions are made for the measurement of the electrical convection conductivity in systems with narrow pores and high electrical conductivity (e.g. ion exchange resins). The consequences of the electrical convection conductivity in practical applications of ion-exchange resins are discussed (acceleration of the rates of ion exchange; improvement of the separation properties by the application of a direct electrical current flow).     

Electrochemistry of capillary systems with narrow pores. II. Electroosmosis

Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz–Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz–Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.     

Electrochemistry of capillary systems with narrow pores. IV. Dialysis potentials

The dialysis potentials of different collodion membranes with graded pore sizes and electrochemical activities have been measured in dilute aqueous KCl solutions as functions of concentration. It is possible to predict the value of the diffusion potential within a few millivolts on the basis of electrical conductivity data obtained with the same membranes. In general, the measured values are lower than those calculated. It is assumed that this difference is caused by the membranes having a distribution of pore sizes.     

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.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Size-exclusion separation of proteins using a biocompatible polymeric monolithic capillary column with mesoporosity

Biocompatible poly(ethylene glycol methyl ether acrylate-co-polyethylene glycol diacrylate) monoliths were prepared for size exclusion chromatography (SEC) of proteins in the capillary format using Brij 58P in a mixture of hexanes and dodecanol as porogens. The monolithic columns provided size separation of four proteins in 20 mM sodium phosphate buffer (pH 7.0) containing 0.15 M NaCl, and there was a linear relationship between the retention times and the logarithmic values of the molecular weights. Compared to SEC monoliths previously synthesized using a triblock copolymer of polyethylene oxide and polypropylene oxide, an increase in mesoporosity was confirmed by inverse size exclusion chromatography. As a result, improved protein separation in the high molecular weight range and reduced column back-pressure were observed.     

Running buffers for determination of chromium(VI)/(III), cobalt(II) and zinc(II) in complex matrices by capillary electrophoresis with contactless conductivity detection

Complex matrices and rather high acidity in environmental samples are often the impelling challenges for the used running buffers of capillary electrophoresis. Twelve binary acid-base buffers were evaluated for separation of Cr(VI)/Cr(III), Co²⁺ and Zn²⁺ in a sample containing various salts by capillary electrophoresis with contactless conductivity detector. The malic acid (MA) systems including MA-His (histidine), MA-Arg (arginine) and MA-Tris (tris(hydroxymethyl)aminomethane) were selected as the candidates with powerful separation efficiency and good response sensitivity. In the MA-Tris buffer, optimization were further carried out in terms of the pH value and the concentration of MA, and the optimal conditions were obtained as 6 mM MA-Tris and 2 mM 18-crown-6 at pH 3.5. Furthermore, a real application was demonstrated by analyzing the plating rinse water (pH 0.8), in which the Ca²⁺, Na⁺, Cr(VI)/Cr(III), Co²⁺ and Zn²⁺ were all detected by adjusting at pH 3.5 with 5% (v/v) diluent ammonia. Both the cations, e.g., K⁺, Ca²⁺, Na⁺, Mg²⁺, and the common high concentration anions in the sample, e.g., Cl⁻, SO₄²⁻ and NO₃⁻ did not cause any disturbance to the concerned analytes.