Eigenmobilities in background electrolytes for capillary zone electrophoresis: IV. Computer program PeakMaster

We are introducing a computer implementation of the mathematical model of zone electrophoresis (CZE) described in Stedry, M., Jaros, M., Hruska, V., Gas, B., Electrophoresis 2004, 25, 3071-3079 program PeakMaster. The computer model calculates eigenmobilities, which are the eigenvalues of the matrix tied to the linearized continuity equations, and which are responsible for the presence of system eigenzones (system zones, system peaks). The model also calculates other parameters of the background electrolyte (BGE)-pH, conductivity, buffer capacity, ionic strength, etc., and parameters of the separated analytes--effective mobility, transfer ratio, molar conductivity detection response, and relative velocity slope. This allows the assessment of the indirect detection, conductivity detection and peak broadening (peak distortion) due to electromigration dispersion. The computer model requires the input of the BGE composition, the list of analytes to be separated, and the system instrumental configuration. The output parameters of the model are directly comparable with experiments; the model also simulates electropherograms in a user-friendly way. We demonstrate a successful application of PeakMaster for inspection of BGEs having no stationary injection zone.     

Optimization of background electrolytes for capillary electrophoresis I. Mathematical and computational model

A mathematical and computational model is introduced for optimization of background electrolyte systems for capillary zone electrophoresis of anions. The model takes into account mono- or di- or trivalent ions and allows also for modeling of highly acidic or alkaline electrolytes, where a presence of hydrogen and hydroxide ions is significant. At maximum, the electrolyte can contain two co-anions and two counter-cations. The mathematical relations of the model are formulated to enable an easy algorithmization and programming in a computer language. The model assesses the composition of the background electrolyte in the analyte zone, which enables prediction of the parameters of the system that are experimentally available, like the transfer ratio, which is a measure of the sensitivity in the indirect photometric detection or the molar conductivity detection response, which expresses the sensitivity of the conductivity detection. Furthermore, the model also enables the evaluation of a tendency of the analyte to undergo electromigration dispersion and allows the optimization of the composition of the background electrolyte to reach a good sensitivity of detection while still having the dispersion properties in the acceptable range. Although the model presented is aimed towards the separation of anions, it can be straightforwardly rearranged to serve for simulation of electromigration of cationic analytes. The suitability of the model is checked by inspecting the behavior of a phosphate buffer for analysis of anions. It is shown that parameters of the phosphate buffer when used at neutral and alkaline pH values possess singularities that indicate a possible occurrence of system peaks. Moreover, if the mobility of any analyte of the sample is close to the mobilities of the system peaks, the indirect detector signals following the background electrolyte properties will be heavily amplified and distorted. When a specific detector sensitive on presence of the analyte were used, the signal would be almost lost due to the excessive dispersion of the peak.     

Eigenmobilities in background electrolytes for capillary zone electrophoresis: II. Eigenpeaks in univalent weak electrolytes

We analyze in detail a mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are eigenvalues of the matrix tied to the linearized continuity equations. Our model considers CZE systems, where constituents are weak electrolytes and where pH of the background electrolyte may reach the full range from 0 to 14. Both hydrogen and hydroxide ions are taken into account in relations for conductivity and electroneutrality. An electrophoretic system with N constituents has N eigenmobilities. We reveal that two of the eigenmobilities have a special meaning as they exist due to the presence of hydrogen ions and hydroxide ions (in water solutions). These two eigenmobilities are responsible for the existence of two corresponding system zones (system peaks). We show that the stationary zone (injection zone, water zone, gap, peak, dip) is in many common background electrolytes composed of these two eigenzones which overlap, due to their very low electrophoretic mobility, into one zone. Other eigenmobilities give rise to system zones originating due to a possible existence of double (or multiple) coconstituents in the background electrolyte. The last group of eigenmobilities is connected with the movement of eigenzones accompanying analytes and enabling their indirect UV or conductivity detection. The model allows assessing experimentally available quantities such as effective mobility of the analyte, molar conductivity detection response, transfer ratio, and relative velocity slope and gives a picture about migration of analytes, their electromigration dispersion and signals obtained in detectors. It allows computer simulation of electropherograms and enables optimization of background electrolytes.     

Specific background electrolytes for nonaqueous capillary electrophoresis

The use of organic solvents or mixture of solvents in capillary electrophoresis is gaining wider attention. The electroosmotic flow mobility of eight organic solvents (acetonitrile, acetone, dimethylformamide, dimetylsulphoxide, propylene carbonate, methanol, ethanol, n-propanol) and of mixtures of several solvents (methanol-acetonitrile, methanol-propylene carbonate, acetonitrile-propylene carbonate) has been studied. The influence of 1,3-alkylimidazolium salts in different solvents on the separation of different analytes has been investigated. Some of these salts have shown usefulness for matrix-assisted laser desorption ionization matrices and off-line analysis of electrophoresis fractions. It also appears that nonaqueous capillary electrophoresis with 1,3-alkylimidazolium salts as background electrolytes is suitable for separation small inorganic ions.     

Multivalent weak electrolytes - risky background electrolytes for capillary zone electrophoresis

Multivalent weak acids and bases are useful components of buffers in electrophoresis. The use of such buffers as background electrolytes (BGEs) in capillary zone electrophoresis (CZE) is, however, risky due to the existence of unsafe regions in the analytical window of the separation. This contribution discusses the problems and shows that multivalent weak species in BGEs bring about the same effects as mixtures of two independent co-ions, i.e., the presence of two centers of symmetry in the electropherograms and the existence of a migrating system zone with a mobility in between these two centers of symmetry. The system zone deteriorates the analytical separation and detection of the analytes in its neighborhood. Illustrative experimental examples for both cationic and anionic CZE are shown and related discussion is given. Finally, some basic rules are formulated to avoid the preparation of risky BGEs.     

Eigenmobilities in background electrolytes for capillary zone electrophoresis. I. System eigenpeaks and resonance in systems with strong electrolytes

A background electrolyte system for capillary zone electrophoresis which is composed of three strong univalent ionic constituents is investigated. The ion 1 is considered as a counter-ion and two ions, 2 and 3, are considered as co-ions in relation to the analyte ion 4. We investigate the linearized model of electromigration in such a system and calculate the eigenvalues of a corresponding matrix. The model is formulated in such a way that the eigenvalues of the system are certain mobilities, which we call eigenmobilites, which characterize specific features of the electrophoretic migration. One of the eigenmobilities is the system eigenmobility u_S causing the rise of the system peak, called here the system eigenpeak. A situation when the analyte has the same mobility as the system eigenmobility, u₄=u_S, is analyzed in detail. We show that it leads to the resonance—the mutual jump in the concentration profile of both co-ions, 2 and 3, has a shape of the spatial derivation of the originally sampled analyte profile and, moreover, it grows linearly with time. After a sufficiently long time it can be “amplified” to any value. The resonance has then a great impact on signals of indirect detection methods, like indirect UV detection or conductivity detection. In the framework of the linearized model the relative velocity slope S_X, a measure of electromigration dispersion, is expressed as S_X=F(u₁+u₄)(u₂−u₄)(u₃−u₄)/[u₄(u_S−u₄)], where u_i is the mobility of the ith ion and F is the Faraday constant. As in practice the concentration of the analyte is not infinitely small and has a certain finite value, the analyte will be at the resonance severely dispersed to a much broader spatial interval. When a specific detector is used, the signal of such an analyte can apparently be missed without any notice.     

Eigenmobilities in background electrolytes for capillary zone electrophoresis: III. Linear theory of electromigration

A mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are the eigenvalues of a matrix M tied to the linearized governing equations is presented. The model considers CZE systems, where constituents, either analytes or components of the background electrolyte (BGE), are weak electrolytes--acids, bases, or ampholytes. There is no restriction on the number of components nor on the valence of the constituents nor on pH of the BGE. An electrophoretic system with N constituents has N eigenmobilities. In most BGEs one or two eigenmobilities are very close to zero so their corresponding eigenzones move very slowly. However, there are BGEs where no eigenmobility is close to zero. The mathematical model further provides: the transfer ratio, the molar conductivity detection response, and the relative velocity slope. This allows the assessment of the indirect detection, conductivity detection and peak broadening (distortion) due to electromigration dispersion. Also, we present a spectral decomposition of the matrix M to matrices allowing the assessment of the amplitudes of system eigenpeaks (system peaks). Our model predicted the existence of BGEs having no stationary injection zone (or water zone, gap, peak, dip). A common practice of using the injection zone as a marker of the electroosmotic flow must fail in such electrolytes.     

Novel dynamic polymer coating for capillary electrophoresis in nonaqueous methanolic background electrolytes.

Coated capillaries can be advantageous in many capillary electrophoretic applications where nonaqueous background electrolytes are used. In the present work, a new dynamic polymer coating (poly(glycidylmethacrylate-co-N-vinylpyrrolidone)) for methanol-based background electrolytes is introduced. The magnitude and stability of electroosmotic flow was investigated with coated capillaries at pH* values of 3, 7.8, and 10.4 in methanol. At pH* 7.8 and 10.4 the electroosmotic flow was negligible and repeatable. On the other hand, at pH* 3 a weak, unstable electroosmotic flow was observed, due to a change in the conformation of the polymer under acidic conditions. The dynamically coated capillaries were successfully applied to the separations of cationic drugs, phenols, and benzoic acids. The synthesis and characterization of the polymer are described in detail.     

Computer simulation of affinity capillary electrophoresis

A computer-simulated model of affinity capillary electrophoresis is developed. Unlike existing models, it is able to describe the situation where the concentrations of sample molecules and ligand molecules are commensurable, or even the situation where the zones occupied by these molecules are not mixed initially. The model permits to study the dependence of the spatial and temporal distributions of sample molecules on various parameters such as reaction rate constants, concentrations of sample and reagent, electromigration velocities of sample and reagent and sample injection volume. A collection of peak shapes for different values of parameters is presented. The dependence of peak variance on the ratio of the time of analysis to the characteristic time of reaction is studied.     

Separation of organic cations using novel background electrolytes by capillary electrophoresis

A background electrolyte for capillary electrophoresis containing tris(-hydroxymethyl) aminomethane (THAM) and ethanesulfonic acid (ESA) gives excellent efficiency for separation of drug cations with actual theoretical plate numbers as high as 300,000. However, the analyte cations often elute too quickly and consequently offer only a narrow window for separation. The best way to correct this is to induce a reverse electroosmotic flow (EOF) that will spread out the peaks by slowing their migration rates, but this has always been difficult to accomplish in a controlled manner. A new method for producing a variable EOF is described in which a low variable concentration of tributylammonium- or triethylammonium ESA is added to the BGE. The additive equilibrates with the capillary wall to give it a positive charge and thereby produce a controlled opposing EOF. Excellent separations of complex drug mixtures were obtained by this method.     

The preparation of background electrolytes in capillary zone electrophoresis: golden rules and pitfalls

In this article the methodology of the design of suitable background electrolytes (BGEs) in capillary zone electrophoresis (CZE) is described. The principal aspects of the role of a BGE in CZE are discussed with respect to an appropiate migration behavior of analytes, including the transport of the electric current, the buffering of pH, the Joule heat, the electro-endosmotic flow (EOF) and the principal migration and detection modes. The impact of the composition of the BGE upon migration and detection is discussed. It is shown that the total concentration of the BGE is a principal factor and the adjustment of migrating analyte zones according to the Kohlrausch regulating function (KRF) is the principal effect in most of the sample stacking techniques. The number of co-ions and their properties are of key importance for peak shapes of the analyte peaks and for the existence of system zones. The detection of UV-transparent analytes may advanteously be done in the indirect UV mode, by using UV-absorbing co-ions, however, both peaks and dips may be expected in the UV trace in case of multiple co-ionic BGEs. Properties of BGEs can be predicted applying mathematical models and it is shown that with SystCharts, predictions can be given concerning the existence of system zones, detection modes and the peak shapes of analytes for a given BGE. Practical examples of methodological considerations are given in the design of suitable BGEs for four principal combinations of migration and detection modes. The properties of the BGEs selected are exemplified with experimental results. Golden rules are summarized for the preparation of suitable BGEs in CZE.     

Nonaqueous capillary electrophoresis with alcoholic background electrolytes: separation efficiency under high electrical field strengths

The effect of high voltage on capillary electrophoresis (CE) separations of anionic analytes in nonaqueous separation media was investigated. Methanol, ethanol, 1-propanol, and 1-butanol were tested as background electrolyte (BGE) solvents. Experiments were carried out with a laboratory-built CE instrument suitable for high-voltage separations. Potentials up to 60 kV were applied with reversed polarity to generate unusually high field strengths (e.g. 2000 Vcm-1) and so achieve fast and efficient separations. Highest separation efficiencies were obtained with propanol as BGE solvent, and the dependency of the efficiency on the separation voltage was more or less linear. With the other alcohols, separation efficiency decreased or remained roughly constant with increasing absolute voltage. The separation efficiencies are discussed in terms of longitudinal diffusion, Joule heating, and analyte interaction with the capillary wall. Capillary preconditioning had a varied effect on the separations in the different BGEs as the BGE and the conditioning process affected the electroosmotic flow (EOF) velocity and direction.     

Experimental assessment of electromigration properties of background electrolytes in capillary zone electrophoresis

Electromigration dispersion (EMD) properties of background electrolytes (BGEs) used in capillary zone electrophoresis (CZE) are of key importance for the success of an analysis. The knowledge of these properties may serve well for the prediction of the asymmetry of peaks of analytes, for the prediction of unsafe regions where a strong interference of system zones may be expected, and for the selection of optimum conditions where the analytes of interest may give sharp and practically symmetric peaks. Present theories enable one to calculate and predict EMD properties of many BGEs but there is also a lot of BGEs that are beyond the present theoretical models as far as their composition and equilibria involved are considered. This contribution brings a method for assessment of EMD properties of any BGE from easily accessible experimental data. The method proposed is illustrated by model examples both for cationic and anionic separations. Imidazole acetate, histamine acetate, and histidine acetate served as model BGEs for cationic separations; as the model BGE for anionic separations, Tris-borate and sodium-borate BGEs have been selected since these buffers are frequently used and borate is well-known for its complexing equilibria in aqueous solutions.     

Computer simulation of transient states in capillary zone electrophoresis and isotachophoresis.

Transient states in the evolution of electrophoretic systems comprising aqueous solutions of weak monovalent acids and bases are simulated. The mathematical model is based on the system of nonstationary partial differential equations, expressing the mass and charge conservation laws while assuming local chemical equilibrium. It was implemented using a high resolution finite-difference algorithm, which correctly predicted the behavior of the concentration, pH and conductivity fields at low computational expense. Both the regular and the irregular modes of separation in capillary zone electrophoresis and isotachophoresis are considered. It is shown that the results of separation, particularly zone order, strongly depend on pH distribution. Simulation data as well as simple analytical assessments may help to predict and correctly interpret the experimental results.     

Triple-channel portable capillary electrophoresis instrument with individual background electrolytes for the concurrent separations of anionic and cationic species

The portable capillary electrophoresis instrument is automated and features three independent channels with different background electrolytes to allow the concurrent optimized determination of three different categories of charged analytes. The fluidic system is based on a miniature manifold which is based on mechanically milled channels for injection of samples and buffers. The planar manifold pattern was designed to minimize the number of electronic valves required for each channel. The system utilizes pneumatic pressurization to transport solutions at the grounded as well as the high voltage side of the separation capillaries. The instrument has a compact design, with all components arranged in a briefcase with dimensions of 45 (w) × 35 (d) × 15 cm (h) and a weight of about 15 kg. It can operate continuously for 8 h in the battery-powered mode if only one electrophoresis channel is in use, or for about 2.5 h in the case of simultaneous employment of all three channels. The different operations, i.e. capillary flushing, rinsing of the interfaces at both capillary ends, sample injection and electrophoretic separation, are activated automatically with a control program featuring a graphical user interface. For demonstration, the system was employed successfully for the concurrent separation of different inorganic cations and anions, organic preservatives, additives and artificial sweeteners in various beverage and food matrices.     

Separation of anti-tumor peptides by capillary electrophoresis in organic solvent containing background electrolytes

Connections between the calculated and measured electrophoretic mobilities (nu(ep)) determined by capillary electrophoresis as well as connections between the measured and calculated diffusion coefficients of anti-tumor peptides have been investigated in background electrolytes (BGEs) containing different organic solvents (acetonitrile, methanol, ethanol and isopropanol). Comparison of the electrophoretic mobility (nu(ep)) values revealed discrepancies between the measured and calculated values. However, no change in the migration order or selectivity could be expected from the calculated nu(ep) values, variation of both properties was observed applying organic solvents as BGE modifiers. Experimental determination of the diffusion coefficient suggested that the effect of the organic solvents is not restricted to the change of the BGE viscosity. The reason for the discrepancy between the measured and calculated mobility values might be the possible conformation and/or solvation changes of the peptide caused by the different organic solvents.     

Piperazine quaternary diammonium salts as additives to background electrolytes in capillary zone electrophoresis

The differential behavior of five different quaternary mono- and diammonium salts, among the 18 investigated, in modulating the electroendoosmotic flow (EOF) and analyte separations in capillary zone electrophoresis is evaluated. It is found that quaternary diammonium salts with positive charges separated by more than four carbon atoms, while exhibiting a very strong affinity for chromatographic silica beads, to the point of exhibiting Rf values close to zero, display, on the contrary, a very poor affinity for the silica wall of capillaries. Compounds separated only by a C2 unit (i.e., 1,4-dialkyl-1,4-diazoniabicyclo[2,2,2,]octane, salts 17 and 18) show high Rf values due to strong ion pair association. The unique behavior of quaternary monoammonium salts possessing an iodinated alkyl (butyl or octyl) tail (i.e., 1, 6, and 7) is attributed to their ability to be covalently affixed to the silica wall via alkylation of ionized silanols at alkaline pH values. They thus strongly modulate and typically invert the EOF, even when not present in the background electrolyte. On the contrary, all diammonium salts, devoid of such alkyl tails, are unable to modulate the EOF and to prevent analyte binding to the silica wall, since they are rapidly removed from the wall by the voltage gradient. However, if added in small amount to the background electrolyte, they offer excellent separations of mixtures of very similar organic acids and prevent any interaction with the capillary wall.     

High speed electrophoresis simulation for optimization of continuous flow electrophoresis and high performance capillary techniques: Part I. Computer model.

A computer program for high-speed simulation and optimization of electrophoretic processes has been developed for carrier-free systems of all kinds. The calculations are based on the one-dimensional dynamic (transient-state) model. The three-dimensional geometry of the simulation space can be chosen deliberately. With a highly efficient transport algorithm instead of complicated integration schemes for the transport equations, the calculation time can be effectively spent on various important parameters such as ionic strength, temperature, Joule heat, activity coefficients and concentration changes due to membranes. The parameter set of any carrier free electrophoretic method (i.e., continuous-flow electrophoresis, capillary isotachophoresis and high performance capillary zone electrophoresis) can be imported directly into the computer program by means of a graphic user interface. The program performs overnight-simulation of any electrophoretic system containing up to 15 components.     

Highly reproducible capillary zone electrophoresis of humic acids in cyclodextrin- or oligosaccharide-modified background electrolytes

Capillary zone electrophoresis has been used for the characterization and separation of humic acids. It was found that addition of saccharides like alpha-, beta-, gamma-cyclodextrins, maltose, hydroxyethylcellulose or dextran sulfate in the background electrolyte (50 mM Na2 B4 O7, pH 9.6) yields better separation patterns and highly reproducible electropherograms. Electropherograms with higher numbers of peaks and high reproducibility were obtained with alpha- and beta-cyclodextrins or with a mixture of alpha- + gamma-cyclodextrin-modified background electrolytes. Separation was carried out with the cathode at the detector end of the column. Adsorption of humic acids to the capillary wall was diminished using an epoxy-coated capillary tube.     

Physicochemical characterization of phosphinic pseudopeptides by capillary zone electrophoresis in highly acidic background electrolytes

Phosphinic pseudopeptides (i.e., peptide isosteres with one peptide bond replaced by a phosphinic acid moiety) were analyzed and physicochemically characterized by capillary zone electrophoresis in the pH range of 1.1-3.2, employing phosphoric, phosphinic, oxalic and dichloroacetic acids as background electrolyte (BGE) constituents. The acid dissociation constant (pK(a)) of phosphinate group in phosphinic pseudopeptides and ionic mobilities of these analytes were determined from the pH dependence of their effective electrophoretic mobilities corrected to standard temperature and constant ionic strength of the BGEs. It was shown that these corrections are necessary whenever precise mobility data at very low pH are to be determined. Additionally, it was found that the ionic mobilities of the phosphinic pseudopeptides and pK(a) of their phosphinate group are affected by the BGE constituent used. The variability of migration behavior of the pseudopeptides can be attributed to their ion-pairing formation with the BGE components.