Electrode Vessels Research Articles

Evolution of the theoretical description of the isoelectric focusing experiment: I. The path from Svensson's steady-state model to the current two-stage model of isoelectric focusing.

In 1961, Svensson described isoelectric focusing (IEF), the separation of ampholytic compounds in a stationary, natural pH gradient that was formed by passing current through a sucrose density gradient-stabilized ampholyte mixture in a constant cross-section apparatus, free of mixing. Stable pH gradients were formed as the electrophoretic transport built up a series of isoelectric ampholyte zones-the concentration of which decreased with their distance from the electrodes-and a diffusive flux which balanced the generating electrophoretic flux. When polyacrylamide gel replaced the sucrose density gradient as the stabilizing medium, the spatial and temporal stability of Svensson's pH gradient became lost, igniting a search for the explanation and mitigation of the loss. Over time, through a series of insightful suggestions, the currently held notion emerged that in the modern IEF experiment-where the carrier ampholyte (CA) mixture is placed between the anolyte- and catholyte-containing large-volume electrode vessels (open-system IEF)-a two-stage process operates that comprises a rapid first phase during which a linear pH gradient develops, and a subsequent slow, second stage, during which the pH gradient decays as isotachophoretic processes move the extreme pI CAs into the electrode vessels. Here we trace the development of the two-stage IEF model using quotes from the original publications and point out critical results that the IEF community should have embraced but missed. This manuscript sets the foundation for the companion papers, Parts 2 and 3, in which an alternative model, transient bidirectional isotachophoresis is presented to describe the open-system IEF experiment.

Evolution of the theoretical description of the isoelectric focusing experiment: II. An open system isoelectric focusing experiment is a transient, bidirectional isotachophoretic experiment.

The carrier ampholytes-based (CA-based) isoelectric focusing (IEF) experiment evolved from Svensson's closed system IEF (constant spatial current density, absence of convective mixing, counter-balancing electrophoretic and diffusive fluxes yielding a steady state pH gradient) to the contemporary open system IEF (absence of convective mixing, large cross-sectional area electrode vessels, lack of counter-balancing electrophoretic- and diffusive fluxes leading to transient pH gradients). Open system IEF currently is described by a two-stage model: In the first stage, a rapid IEF process forms the pH gradient which, in the second stage, is slowly degraded by isotachophoretic processes that move the most acidic and most basic CAs into the electrode vessels. An analysis of the effective mobilities and the effective mobility to conductivity ratios of the anolyte, catholyte, and the CAs indicates that in open system IEF experiments a single process, transient bidirectional isotachophoresis (tbdITP) operates from the moment current is turned on until it is turned off. In tbdITP, the anolyte and catholyte provide the leading ions and the pI 7 CA or the reactive boundary of the counter-migrating H3 O+ and OH- ions serves as the shared terminator. The outcome of the tbdITP process is determined by the ionic mobilities, pKa values, and loaded amounts of all ionic and ionizable components: It is constrained by both the transmitted amount of charge and the migration space available for the leading ions. tbdITP and the resulting pH gradient can never reach steady state with respect to the spatial coordinate of the separation channel.

Evolution of the theoretical description of the isoelectric focusing experiment: III. Carrier ampholyte behavior in transient, bidirectional isotachophoresis.

In modern isoelectric focusing (IEF) systems, where (i) convective mixing is prevented by gels or small cross-sectional area separation channels, (ii) current densities vary spatially due to the presence of electrode vessels with much larger cross-sectional areas than those of the gels or separation channels, and (iii) electrophoretic and diffusive fluxes do not balance each other, stationary, steady-state pH gradients cannot form (open-system IEF). Open-system IEF is currently described as a two-stage process: A rapid IEF process forms the pH gradient from the carrier ampholytes (CAs) in the first stage, then isotachophoretic processes degrade the pH gradient in the second stage as the extreme pI CAs are moved into the electrode vessels where they become diluted. Based on the ratios of the local effective mobilities and the local conductivities ( / values) of the anolyte, catholyte, and the CAs, we pointed out in the preceding paper (Vigh G, Gas B, Electrophoresis 2023, 44, 675-88) that in open-system IEF, a single process, transient, bidirectional isotachophoresis (tbdITP) operates from the moment current is turned on. In this paper, we demonstrate some of the operational features of the tbdITP model using the new ITP/IEF version of Simul 6.

A new approach for on-line enrichment in electrophoresis of dilute protein solutions

A method is described for on-line enrichment/zone sharpening of a sample of negatively charged proteins (an analogous method for cationic proteins can be designed). The sample is applied on the top of a 5-mm thick layer of a neutral polyacrylamide gel which rests on another 5-mm thick, large-pore polyacrylamide gel which contains positively charged groups. The latter gel layer is attached to the neutral gel column, used for the electrophoretic separation of the proteins. When a voltage is applied the proteins start migrating and become electrostatically adsorbed at the top of the charged, large-pore gel layer (pH 5.4). With the upper electrode vessel filled with a buffer of a pH higher (pH 7.7) than that employed in the enrichment step and with a voltage between the electrodes, these enriched proteins are released (because the enrichment gel is non-charged at pH 7.7) with zone sharpening and migrate into the 5-cm long column (i.d. 5 mm) of a neutral, large-pore polyacrylamide gel for electrophoretic analysis. Upon the electrophoretic migration from the enrichment gel into the separation gel a second zone sharpening may occur, if the increase in pH from 5.4 to 7.7 in the separation gel is not close to momentary. By employing colored test proteins the efficiency of the enrichment step is visually illustrated by a picture. The principle of the concentration method described has been employed also in chromatographic experiments and can with appropriate modifications also be used in other electrophoretic methods, such as capillary electrophoresis.

On‐line CE‐MS using pressurized liquid junction nanoflow electrospray interface and surface‐coated capillaries

A simple and cost-effective laboratory-made liquid junction interface was used for coupling of CE with MS. In this device the capillary column and the spray tip were positioned in the electrode vessel containing appropriate spray liquid. The electrospray potential was applied on the electrode inside the liquid junction. A stable electrospray was produced at nanoliter per minute flow rates generated in the emitter tip without using an external pump. This arrangement provided high durability of the spray tip and independent optimization of the CE separation (use of coated capillaries) and ESI conditions. CE-MS analysis of mixtures of drugs, peptides, tryptic digests of proteins and biological fluids was optimized with respect to the effects of the distance between the separation capillary and electrospray tip and pressure applied on the liquid junction. The sensitivity of the system, in terms of the LOD (base peak monitoring) was below 10 ng/mL for the beta-blocker drugs and below 200 ng/mL for peptide analysis.

A hybrid microdevice for electrophoresis and electrochromatography using UV detection.

We have designed a new class of microdevices composed of a supporting plastic (polyvinyl chloride, PVC) plate integrated with a groove for a piece of fused silica capillary (the separation channel), a slit for on-tube detection, an "islet" for the application of sample, electrode vessels and platinum electrodes. The design permits electrophoretic, electrochromatographic and chromatographic separations with on-tube UV detection. The efficient heat dissipation allows relatively high field strengths. This article is the first one dealing with microdevices where polymer solutions are replaced by homogeneous gels. A new type of gels synthesized from acrylamide and 2-hydroxy-3-allyloxy-propyl-beta-cyclodextrin (allyl-beta-CD) as a cross-linker was employed for electrophoresis and electrochromatography. 2-Acrylamido-2-methylpropanesulfonic acid was added to the monomer solution to create a high electroendosmotic flow in electrochromatographic runs. These gels have excellent electrochromatographic and electrophoretic properties for low-molecular-weight compounds and DNA, as shown previously, namely high resolution combined with high stability. The unique cross-linker can be used for specific interaction with the alkyl and phenyl groups. The tripeptide glutathione (gamma-L-glutamyl-L-cysteinyl-glycine) and its benzyl conjugates were selected as model compounds to study the resolving power of the gel because they are difficult to separate by free zone electrophoresis. The limit of detection (LOD) for S-benzyl-glutathione was determined (ca. 7 microM). Run-by-run reproducibility was high (the separation factor of glutathione in the gel was 0.3 with 2.5% coefficient of variation, CV). Neutral compounds (acetone, acetophenone, propiophenone and butyrophenone) were separated electrochromatographically in the gel. The influence of organic solvent (acetonitrile) on the electroendosmotic mobility was similar to that in reversed-phase separations, although the separation mechanism is different. ATP, ADP and AMP were separated in less than 10 s by free-zone electrophoresis.

Synthesis and characterization of polyrotaxane-based polymeric continuous beds for capillary electrochromatography

The continuous bed technique with its attractive features, such as fritless design, one-step in situ synthesis, low back pressure and no need for pressurising the electrode vessels to suppress bubble formation was applied to form polyrotaxane-based stationary phases for capillary electrochromatography (CEC). Rotaxanes are synthesized from two classes of substances, namely linear reactive monomers and inert cyclic compounds. Upon polymerisation, a gel forms with the cyclic molecules mechanically immobilized (see Fig. 1). We have employed this simple approach, using charged derivatives of cyclodextrins in order to introduce charged groups into continuous beds and thus render them appropriate for electrochromatography. The self-assembly of supramolecular structures to form rotaxanes during the synthesis of the continuous beds is treated. The electroosmotic and chromatographic properties of the various polyrotaxane-based stationary phases synthesized are discussed, as well as the synthesis of the continuous beds, including how to affect their porosity and its influence on the efficiency of the electrokinetic separation. The applicability of the rotaxane-based continuous bed is demonstrated by separation of model compounds by reversed- and normal-phase chromatography. A separation of enantiomers is also presented. This experiment is of particular interest because it indicates that the interaction with the cavity of β-cyclodextrin (β-CD) is not a fundamental requirement for enantioseparations.

Electroosmosis- and pressure-driven chromatography in chips using continuous beds.

The application range of microchips can be extended to any mode of chromatography by filling the narrow channels with continuous polymer beds, exemplified by electrochromatography and ion-exchange chromatography. "Wall effects" are eliminated by anchoring the bed to the wall of the channel, an arrangement which has the additional advantage that no frits to support the bed are required. The design of the equipment is based on a quartz chip with all auxiliary pieces (for example, electrode vessels and fluid transfer fittings) placed in a rack, which permits a flexibility of great importance for automation. The same resolution and van Deemter plots were obtained in experiments performed in fused-silica capillaries and in chips for both low-molecular-weight (alkyl phenones, antidepressants) and high-molecular-weight substances (proteins). A sample of uracil, phenol, and benzyl alcohol was separated by electrochromatography in less than 20 s.

Capillary zone electrophoresis with electroosmotic flow controlled by external radial electric field

A new way of regulation of electroosmotic flow (EOF) in capillary zone electrophoresis (CZE) by external electric field has been developed. A set of three high-voltage power supplies is used to form a radial electric field across the capillary wall. One power supply is applied in the usual way as a driving force of CZE and EOF to the ends of the inner capillary compartment dipped into the electrode vessels and filled with background electrolyte. Two power supplies are connected to the ends of the outer low-conductivity coating of the capillary which is formed by the dispersion of copolymer of aniline and p-phenylenediamine in polystyrene matrix. The difference between electric potentials on the outer capillary surface and inside the capillary determines the voltage of radial electric field across the capillary wall and affects the electrokinetic potential at the solid-liquid interface inside the capillary. The effect of magnitude and polarity of external radial electric field on the flow rate of EOF, on the migration times of charged analytes and on the separation efficiency and resolution of CZE separations of synthetic oligopeptides, diglycine, triglycine and octapeptide fragments of human insulin was evaluated. Through the EOF control by external electric field the dynamic effective length of the capillary was obtained and the speed of analysis and resolution of CZE separations of peptide analytes could be optimized.

A Micellar Electrokinetic Chromatographic Method for Determination of Solubilization Isotherms in Surfactant Micelles

We have devised a new micellar electrokinetic chromatographic method for determination of the solubilization equilibrium constants of neutral solutes in surfactant micelles as functions of the intramicellar mole fraction of the solute. In this method, the running solution in a capillary and in electrode vessels contains the neutral solute as well as the surfactant micelles, and the injected solution contains the surfactant micelles and the dilute marker compounds for aqueous and micellar phases but not the solute. The mobility of the solute can be measured from a negative peak recorded on the chromatogram. The solute concentration in the capillary is established, and the mobility of the micellar phase incorporating the solute, which depends on the intramicellar mole fraction of the solute, can be measured from the migration time of the micelle marker. These merits enable precise determination of the solubilization isotherms. This method has been used to study the solubilization equilibria of benzene, phenol, and a series of aliphatic ketones in sodium dodecyl sulfate solution, and the validity and effectiveness of this method for quantifying solubilization have been verified.

Capillary zone electrophoresis in a hydrodynamically closed separation system with enhanced sample loadability

Some phenomena linked with capillary zone electrophoresis (CZE) performed in a hydrodynamically closed separation system with enhanced sample load capacity via the use of capillary tubes of larger I.D.s were studied. Calculations of the plate heights for varying amounts of the analytes loaded onto 50 and 300 μm I.D. columns under identical CZE separating conditions revealed that the analytical advantages of using columns of larger I.D. include significantly reduced contributions of electromigration dispersion. At higher concentrations of the carrier electrolytes this gain, however, can be partially lost due to increased thermal dispersive effects. Calculated resolutions for a varying ratio of a pair of the analytes loaded onto 50 and 300 μm I.D. columns favoured the use of the latter I.D. in situations when the ratio of the analytes was higher than ca. 102:1. CZE experiments were carried out in a 300 μm I.D. capillary tube made of fluorinated ethylene–propylene copolymer (FEP) with a porous cellophane membrane serving as a hydrodynamic barrier to prevent a flow of the solution in the separation compartment due to a pressure difference between the electrode vessels. Movement of the membrane was found to be a source of undesired flows in the separation compartment, which adversely affected both the reproducibilities of migration times of the analytes and their separation efficiencies. Mechanical support eliminated these problems. Dispersive phenomena associated with electroosmosis in the closed separation compartment were effectively suppressed by using high molecular weight derivatives of water soluble polymers (methylhydroxyethylcellulose and polyethyleneglycol) in the carrier electrolyte solutions. Examples from the separations of various groups of analytes (synthetic food colourants, some inorganic anions, alkali and alkaline earth metal cations and glycoforms of erythropoietin) are given to illustrate a practical utility of the studied CZE approach.

Vacancy Capillary Zone Electrophoresis and Differential Capillary Zone Electrophoresis: Variations on a Well-Known Theme

Two new variants on capillary zone electrophoresis (CZE) are described and experimentally investigated. In vacancy CZE the sample, diluted with a background electrolyte, fills the electrode vessels and the separation capillary. When pure background electrolyte is injected, the resulting electropherogram represents the composition of the sample. The electropherogram is almost identical with the result of a conventional CZE experiment. In differential CZE the sample again fills the electrode vessels and the separation compartment. After injection of a slightly different sample, a differential electropherogram is obtained that represents the differences between the two samples. The retention times of both new variants are comparable with conventional CZE, the separation efficiency, in terms of theoretical plates, is marginally lower, and both show good quantitative characteristics. The concept of vacancy electrophoresis explains the origin of unexpected system peaks in conventional CZE when multiple co-ions in the background electrolyte are used.

New approaches in the design of capillary electrophoresis experiments.

This paper gives a survey of recent methodological studies of capillary electrophoresis at the Department of Biochemistry, Uppsala University. Several methods for on-and off-tube concentration of solutes have been developed. These methods also permit desalting of the sample, which is necessary for the creation of narrow starting zones in zone electrophoresis and to reduce the risk of precipitation and narrowing of the separation window in isoelectric focusing (IEF). A unique method designed particularly for desalting of samples for IEF is also discussed. To obtain high resolution the adsorption of solutes to the capillary wall must be eliminated. A pH stable, hydrophilic polymer coating has, therefore, been developed. Although polymer solutions give lower resolution than do gels they are often used as molecular-sieving media because they are replaceable and thus permit repetitive automated analyses in the same capillary. We have shown that low-melting methoxylated agarose gels are also replaceable and give the same high resolution as do polyacrylamide and dextran gels. Following an electrophoresis the methoxylated agarose gels can be displaced in the stationary capillary past the detection window. This scanning technique has several advantages. A capillary with strong electroendosmosis permits, in principle, separation of both acidic and basic proteins in one run. However, depending on whether the capillary wall is negatively or positively charged either the basic or the acidic proteins most often migrate with strong tailing caused by the electrostatic interaction with the capillary wall. The distortion of the zones is much less if the electroendosmotic flow is replaced by a hydrodynamic flow and the electrophoresis is performed in a coated electroendosmosis-free capillary to suppress adsorption of both basic and acidic proteins. By a unique technique we can prepare chromatographic beds with diameters as small as 5-25μm. These beds, which are more homogeneous than conventional beds built up of preformed beads, can be used with advantage for electrochromatography and for different modes of capillary chromatography of fractions obtained from micropreparative HPCE experiments. There is a general trend and desire to decrease the analysis time without sacrificing resolution. Therefore, we have developed low-conductivity buffers with satisfactory buffering capacity which permit field strengths as high as 2, 000V/cm with attendant very short run times. Many enantioselective agents gave strong UV-absorption. Therefore, the experimental conditions must be chosen so that they do not pass the detection window. Otherwise, the noisy background is very disturbing. When a zone migrates from a straightinto a curved section of a capillary the molecules at the outer lane will lag behind those at the inner lane. The attendant loss in resolution, which all commercial apparatus exhibits, can be decreased considerably by coiling the capillary into the figure-of-eight or a serpentine path. A straight capillary is, however, preferable. Methods for the determination of pH and electrical conductivity in small volumes are discussed. A technique for micropreparative HPCE and HPLC is presented. An HPCE apparatus designed according to new principles is described (straight capillary; one electrode vessel is closed to avoid hydrodynamic flow in the capillary; electroendosmotic pump for washing of the capillary; thermostated slit for the UV beam to obtain a straight base line; only a small part of the capillary is not cooled actively; thermal application of the sample; the sample rests as a small droplet on a carousel; the droplet is covered by a cap which can be lifted by a magnet; effective insulation for field strengths up to at least 2, 000V/cm).

New approaches to concentration on a microliter scale of dilute samples, particularly biopolymers with special reference to analysis of peptides and proteins by capillary electrophoresis II. Applications

On theoretical grounds several approaches for the concentration of ionic solutes are suggested in ref. 1. The methods are of general applicability. In this paper we describe how they can be employed in high-performance capillary electrophoresis (HPCE) for 1000-fold manual and automated on-line concentration from microliters down to nanoliters. The risk that the solutes may escape detection —the obvious disadvantage of HPCE— is, accordingly, reduced considerably. Briefly, the whole capillary (and for more than 1000-fold concentration also an electrode vessel or a vessel in contact with an electrode vessel) is filled with the dilute sample solution. The sample becomes concentrated as it migrates toward a pH gradient, a small-pore gel, a dialysis tubing attached to one end of the capillary, or by displacement electrophoresis combined with a hydrodynamic counterflow. These concentration steps (except the last) require a short mobilization step to prevent the narrow, concentrated sample zone from broadening in the initial phase of the final analysis step (free zone electrophoresis).

New approaches to concentration on a microliter scale of dilute samples, particularly biopolymers with special reference to analysis of peptides and proteins by capillary electrophoresis I. Theory

New methods are described for the concentration of ionic analytes, particularly ampholytes, such as peptides and proteins. In most of these methods the sample is depleted (partially) of strong electrolytes concomitantly with the concentration. The methods are based on the fact that electrophoretic migration velocities decrease upon decreasing the absolute value of the zeta potential of a solute and the pore size of the electrophoresis medium and upon increasing the cross section of the electrophoresis chamber, the viscosity and the electrical conductivity of the electrophoresis medium. We have also utilized the zone-sharpening properties of displacement electrophoresis in combination with a hydrodynamic counter flow to create a stationary zone where the sample solutes can be collected continuously. In practice, the whole electrophoresis tube is filled with the sample solution to be concentrated. When a voltage is applied the solutes begin to migrate, but finally cease to move as they approach the end of the tube, provided that the above-mentioned parameters in that section of the tube have been given appropriate values. By means of this technique the sample can be concentrated into a zone of a width of 0.2–0.5 mm. Accordingly, a 400–1000 fold concentration is obtained when a 200 mm long tube is filled completely with the sample and still more if also an electrode vessel (or a vessel connected to this electrode vessel) is loaded with sample. The narrow sample zone can be withdrawn from the tube and subjected to further studies or used as a starting zone for an in-tube zone electrophoresis. The tendency for broadening of the very narrow starting zone during the initial phase of this electrophoresis step can be counteracted by a short mobilization step involving displacement electrophoresis, electrophoresis in a steep pH gradient, or on-tube dialysis against a (diluted) buffer. This step can be omitted when the concentration is accomplished by a combination of displacement electrophoresis and a counter flow. In Part II we show how the theory developed in this paper can be utilized practically.

Electrophoresis of gliadins in long acrylamide gels: Method and nomenclature

Gliadins, defined as wheat kernel storage proteins soluble in 70% ethanol, possess an electrophoretic diversity permitting us to identify different varieties. Because of genetic proximity, however, it sometimes proves impossible to distinguish between different varieties using standard methods. An electrophoresis method, utilizing a discontinuous buffer system with aluminum lactate and potassium lactate in the gel and sodium lactate in the electrode vessels, is described for two types of gels 18 cm and 32 cm in length. The number of bands is higher than with standard methods, and is significantly increased with long gels, facilitating the distinction between varieties. A nomenclature for the new bands is presented for several widely different cultivars.

Control of ammonium concentration in Escherichia coli fermentations

A control system has been devised for the maintenance of stable ammonium concentrations throughout a fedbatch fermentation. The control system is based on an ammonia gas-sensing electrode that monitors a pH-adjusted effluent stream from the fermentor. To overcome the time lag between the fermentor and the electrode, feedback control included metered flows of ammonium to both the fermentor and the electrode vessel. The system was used to study the growth of Escherichia coli B (ATCC 11303) at controlled ammonium concentrations of 5 to 200mM. Apparent specific growth rates, biomass and protein production, and glucose yields were essentially constant from 5 to 170mM. Above 170mM ammonium growth was inhibited. As ammonium concentration decreased from 170 to 5mM, ammonium yields increased from 1 to 24 g cell dry wt/g ammonium utilized. The results demonstrate that control of ammonium concentrations at levels so low that ammonium would be exhausted in batch fermentations can significantly increase overall ammonium yields.

A density‐gradient column for rapid preparative isoelectric focusing

AbstractIn this paper a 112‐ml density‐gradient column is described, which allows a rapid, low‐resolving pre‐focusing over its shorter dimension (20 mm), followed by a high‐resolving fine‐focusing over the longer dimension (112 mm) when the column is turned through 90°. This is possible due to the rectangular cross‐sectional shape of the column and to a special design of the electrode vessels. Test runs made with sperm whale myoglobin have shown that very good separations can be obtained in as little as four hours.

Agarose Gel Electrophoretic Separation of Blood Serum Proteins in Cattle

The agarose gel electrophoresis described by Johansson (1972) was modified so that a buffer of pH 7.9 was used in the gel, whereas the buffer in the electrode vessels had a pH of 8.6. The cattle blood serum protein picture is described in detail. The β1-globulin zone shows a very distinct picture of the genetically polymorphic bovine transferrins. The region between the α- and β-globulins shows a number of faint and often very distinct bands. A faint background staining over the whole electrophoretogram may partly be caused by a rather strong lipoprotein in the α1-region, lipids thus having migrated all over the electrophoretogram. The modified method described is well suited as a “screen electrophoresis” for cattle serum and is also useful e.g. in studying bovine transferrin polymorphism.

Displacement electrophoresis

The method of displacement electrophoresis is described and its analogy with displacement chromatography shown. The apparatus consists basically of a capillary tube, a few tenths of a millimetre bore and thin walled, uniting two vessels, each containing an electrode. For the analysis of anions the cathode vessel contains an anion less mobile than any in the sample mixture to be analysed. The capillary tube is filled with a solution of a salt of an anion more mobile than any in the sample and a buffering cation. The anode vessel contains the buffering cation. The electrodes must not produce interfering ions or gas. To reduce disturbance by electroendosmosis a long chain soluble polymer is used to increase the viscosity of the solution in the capillary tube, and the electrode vessel is closed at the end to which electroendosmosis would cause flow if it were open. The sample is introduced between the cathode and the capillary, and a constant current is passed between the elec­trodes. The anions in the sample move initially at different speeds until they are separated in order of their mobility. Then all the anions in the apparatus move down the capillary at the same speed, assuming the tube to be of constant bore, since the concentrations so adjust themselves that the potential gradient at any point is inversely proportional to the mobility of the anions at that point. The boundary between each successive pair of ions is more or less sharp, depending upon the diffusion constants, the potential gradient, the difference in mobility, and the disturbance caused by electroendosmosis, temperature difference across the capillary, and flow of liquid. Each zone has a characteristic pH. Once the train of anions has separated it proceeds down the capillary unchanged. Since each zone has a particular potential gradient, it has also a particular rate of heat generation per unit length and a particular temperature. It is thus possible to follow the separation by means of fixed thermocouples on the outside of the tube, which will record the fronts as they pass under the thermocouple. A thermocouple measuring the temperature of the capillary relative to its surroundings plots a series of steps on a recorder, the height of a step from the baseline being a measure of the mobility. The length of the step is preferably measured from the distance between the peaks of the record provided by a differential thermocouple measuring the difference in temperature along a short length of the tube, which gives a record which is the differential of the step curve. The length of step is proportional to the length of tube occupied by that species of ion and hence to the quantity. A qualitative and quantitative analysis is thus possible. A theory is given of the points mentioned above. An experimental paper will follow.