Chern. AnaL (Warsaw), 41,157 (1996) REVIEW

Electrochromatography

by l.S.Kowalczyk

Technical University ofGdallSk, 80-952 Gdansk, Poland

Key words: electrochromatography, electroosmotically driven , pressure driven

The principles of separation of the mixture of chemical compounds by means of electrochromatography are described. Interphase reactions and electric field influence - for selection of separation conditions, are taken into consideration. Application of electroosmotically and pressure driven flows of moving phase, are also characterized. Some examples ofseparation results, also by comparison of the results ofseparation by means of thin-layer and capillary electrochromatography, capillary electrophoresis and liquid chromatography in microcolumns - are demonstrated.

Opisano zasady rozdzielania mieszanin zwii\.zkow chemk~nych metodami elektro­ chromatografii, uwzgh;dniaji\.c rowlloczesnie wystt;puji\.ce oddzialyw3nia mit;dzyfazo­ we oraz wplyw pola elektrycznego na zwii\.zki rozdzielane. Ponadto scharakteryzowano przeplyw e1ektroosmotyczny oraz przeplyw laminarny, wymuszony pompowaniern, wykorzystywane jako przyczyny ruchu fazy ruchomej. Przedstawiono przyklady roz­ dzielania substancji metodami elektrochromatografii cienkowarstwowej ikapilarnej. zarazem porownano otrzymane wyniki z uzyskanymi po zastosowaniu elektroforezy i chromatografii cieczowej kapilarnej.

Electrochromatography is a separation method of mixture of chemical com­ pounds which uses simultanously occurring interphase reactions and electric field influence. Theelectroosmotically driven flow is employed in the discussed systems. Sometimes a pressure-driven flow is ,also used. Various types of interactions, men­ tioned above provide the new separation possibilities. However, a selection of separation conditions cannot be only limited to generally known methods aschroma­ tography and electrophoresis. Mutual relations between interactions in both kinds of systems, mentioned above, should be also considered. For example, selecting the chemical composition of both phases - the electrical properties (e.g. conductivity) 158 l.S. Kowalczyk should be taken into account at the same time. Therefore, there is still basic question to resolve: what is actual relation between the two kinds of influences. This is the fundamental problem.

Thin-layer electrochromatography The first papers on electrochromatography or electroosmotically driven chroma­ tography were probably published in 1963-65 [1-5]. It was thin-layer electrochro­ matography. For investigation of the electrophoretic mobility, in thin-layer electrochromatography (electrophoresiswith chromatographic phenomena) the fol­ lowing relationship [2,5J has been used:

U= X~Xi( £).2 = JX-Xi)(l + T) (1) tE i Et where x denotes apparent (macroscopic) length of migration, under the influence of electric field and solution movement measured along the medium surface, Xi ­ apparent length of electroosmotically driven flow indicator (non-charged compound e.g. glucose),E -electric fieldstrength, i-apparent (macroscopic) length ofthe pore (capillary), measured along the medium layer, i' - actual length of the tortuos pore (capillary) of the medium layer, and T = (i'/i) - 1 is the path length parameter or structure coefficient for the layer. But in thin-layer electrochromatography, when "chromatognlphic phenomena" (adsorption, partition, etc.) influence the rate of migration 'of compounds moving under the action ofelectric field the coefficient RD analogous to the chromatographic coefficient RF, should be taken into account. Therefore we obtain for the length of migration [2,5]: .

Xs x' x=-­ Xi= --, (2) RD,s RD,i where xs' x' denote apparent length of migration of the particles influenced by "chromatographic phenomena". Because the above mentioned phenomena retard the movement ofthe substances subject to electric field strength and/or solution flow action - the RD,i,s coefficients should be lower than unity (RD,i,s < 1.0). Table 1 gives, for some cases, the experimen­ tally obtained values of coefficient RD [1]. Plots in Fig.l represent electroosmotic solution flow velocities as a function of thin-layer porous media compositions [2]. Kowalczyk and CzapliIiski [6] proposed the use ofa hydraulic flow (electrolyte cells on various levels) as additional to electroosmotic one for separation ofsubstan­ ces by means of thin-layer electrophoresis. The increased flow of the liquid phase, obtained in that way can be useful for separation optimization also for electrochro- Electrochromatography 159

matography, instead of pressure-driven flow (see further discussion in this paper). Ten years later also Pretorius and coworkers [7] have been using thin-layer electroch­ romatography and discussed the advantages of this technique over conventional chromatography and electrophoretic methods of separation.

Table 1. Val ues ofcoefticientRD for thin-layer electrochromatography for electcoosmotically driven chroillatography for glucose, analogous toRFin 1'1£, which is the retardation coefficient for substance molecules, subject to interphase phenomena, during the movement in electric field [1] Veronal buffer, Solution: 0.05 mol FI hydrochloric acid pH 8.6 Stationary filter paper glass filter paper glass starch kaolin phases: Whatman1 fiber Whatman 1 fiber Substances: RD-values glucose 0.95 1.0 0.97 0.97 0.97 1.0 1.0 1.0 0.9 ox'albumine 0;91 1.0 Fe3+ 1.0 1.0 0.0 0.37 1.0 0.0 0.0 Cu2+ 1.0 1.0 0.61 0.91 1.0 1.0 0.0 C02+ 1.0 1.0 1.0 1.0 0.0

a) VOt' mmh-f 3 • • III • 10 2 • • •

s 6 • • • • • •• •

-10 .. • • • -IS

b) Ve,mmh""

10 • • • • • Alz°)

S 6 • • • III glassfibcr 5 10 15 20 0 I I I I r,cm • III II· • • starch -5 7 - • • • • • filter pap«Whlb:nan 1 .. • • • III • SiOz -10

Figure 1. Diagrams of electroosmotic flow in different layers: solution flow velocities as a functions along the medium layers. Voltage: 7.5 V cm-I , time: 60 min. a) 0.05 mol I-I hydrochloric acid, b) veronal buffer, pH =8.6 [3] 160 J.S. Kowalczyk

Capillary electrochromatography

In the last years, because of unusual successes of electrophoresis due to the separation in capillaries, the electrochromatography was also conducted in capil­ laries. This provided essential efficiency increase ofthe systems used, in comparison with the thin-layer ones. As it is generally known, high efficiency separation in capillaries results in profitable hydrodynamic conditions, first of all, due to lower effect of eddy diffusion and plug profile instead of parabolic front, known from laminar flow. Knox and Grant [8) demonstrated capillary electroosmotic chromato­ graphy in packed fused-silica capillaries and they observed an improvement in plate height by a factor of 2, in comparison with pressure-driven chromatography in the same column. Tsuda et al. [9) have found, that in capillary tube 30-200 ~mx 30-90 CIU the H value for unretained solute, in gisodium hydrogen orthophosphate-water, is about one thirtieth of that obtained under laminar flow conditions. Also Bruin et al. [10) have stated, that the efficiency of open tubular columns (with inner diameters in the range 5-25 f..llu), with isoelectrically-driven moving phase is better than that of pressure-driven phase, by a factor of ca. 2. Figure 2 shows the plots of H =f(v) for electroosmotically and pressure driven flow, according to Bruin et al. [10) statements. Pfeffer et al. [11) observed in 10 ~m capillaries coated with polymer PS-264 an efficiency of up 230.000 plates, generated in less than 4 min. Yamamoto et al. [12] with 1.6 f..uu ODS in 50 ~m lD. capillaries obtained an efficiency of up to 790 His. The capillary columns of higher efficiency show increase in detector response, what leads to the lower detection limit of separated substances. The same situation is observed in capillary LC [13,14). A plate height equation in general chromatography is [25]

H =Blv + Csv + Cmv + (lIA + l/Cvr1 (3) where A denotes the coefficient for eddy diffusion, B - the coefficient for axial molecular diffusion, Cm - the coefficient for resistance to mass transfer in the mobile phase, Cs - the coefficient for resistance to mass transfer in the stationary phase, v­ mean linear flow velocity of a solute. In eq. (3) only Cmv is affected by the shape ofthe velocity profile in the column. Because the flow pattern of Vmob (flow velocity due to mobility of solute) would be a plug flow profile, the apparent mean linear flow velocity in electroosmotically driven electrochromatography without a pressurized flow is as follow

(4) and hence

(5) Electrochromatography 161

a) 80 -n------:l,..------,

80

§. ... 40 X

20

0.4 1.2 1.8

b) 40 "T"'II------..-;------.

--- PD e 80 - ED ::a. X...

20 ... _ ,,".-"" .... ,-' , ....-,- ~~ 10 ~ ...... ----fII' .. ',--.... ~ ..-.. --_..-- ---,--.-..- =--_.---...... --~---- ...... _-_..- ... ~t!!I

0.4 0.8 1.2 1.8 Veo,mms-t Figure 2. Theoretical plate height curves for an electrically driven (ED) system (solid lines) and a pressure-driven (PO) system (dashed lines) with a) a 25 J.tm 1.0. capillary and b) a 10 J.tm I.D. capillary, for different capacity factors, IC (reprinted with permission from ref. [10])

The influence of the electric field on mass transfer in the mobile phase (em) and therefore on th~ termH3 in eq. (5) is the most effective. Hence, the tennH3 in eq. (5) for electroosmotically driven capillary electrochromatography is as follow:

(6)

where Wa is a coefficient of a step in molecular diffusion. 162 J.S. Kowalczyk

ElectroosmoticalJy driven capillary eledrochromatography The linear electroosmotic flow velocity is given by

v = DC; E (7) osm 4Jt 11 where D denotes electric pennitivity (dielectric constant), 11 - viscosity ofthe liquid and (; - electrokinetic potential. When an electric field, E, is applied along the axis of a tube containing a liquid an effective electroosmotic flow of linear velocity is as follow [11,17]:

vosm = keEI(zqCfJ.) (8) where k denotes a proportionality constant, e '- the charge per unit surface area 011 the wall, Z- the number of valence electrons per molecule of the electrolyte, C- the concentration of electrolyte, a - an empirical constant. The linear velocity of electroosmosis depends on the physical parameters of the solvent and on the concentration of the electrolyte used. The relative values of the velocities of water, acetonitrile and methanol respectively, following from the ratios of Dill are 7,10and 6. Table 2 gives the linearvelocities ofelectroosmosis ofsomesolutions [18]. One interesting aspect ofelectroosmosis flow is that it generates flat profiles [7,19]. This kind of velocity flow profile, as well as laminar flow profile are shown in Fig. 3.

Table 2. Linear flow velocity of electroosmosis at 100 V cm-1 in glass capillary columns [18] (solute: benzene or pyridine) Solvent Linear velocity, cm-1 Column Distilled water 0.061 Methanol 0.034 A Acetonitrile 0.14 0.05% Methanol-n-hexane 0.0006 0.01 mol 1-1 NazHP04-water 0.13 0.025 mol 1-1 NazHPOrwater 0.093 0.05 mol 1-1 Na2HP04-water 0.087 B 0.075 mol 1-1 Na2HP04-water 0.077 0.1 mol 1-1 Na2HP04-water 0.057 Methanol-benzene (1:9) 0.01 Reprinted with permission from reference [18]. A: 57.6 cmx132 f-tm J.D. B: 60 cmx132 f-tm J.D.

a) b) c)

Figure 3. \!cuious flow profile shapes: a) a hypothetical homogeneous flow, bulk flow or piston flow profile; b) electroosmotical flow profile observed in electrophoretically driven systems; c) laminar flow profile observed in pressure-driven systems Electrochromatography 163

In chromatographic systems this results in lower resistance to mass transfer in the mobile phase. But more important aspect of electroosmotic now is that the velocity now is nearly indppendent of the geometry and size ofthe channels in the packing. Jorgenson et al. [20] have observed that packing irregularities are less important when electroosmotic now is used instead of flow generated by pressure. Moreover Stevens et ale [19] have observed that, along a capillary or through porous media, electroosmotically driven flow rate is independent of column length, with a given potential gradient. In Figure 4, for comparison, are demonstrated the separations by 8) -8A2N.1H4N 4A1N,5A2N-

-2A1N

, , ,, 0 2 6 8 10

b) 1H4N-

f~lN SA2N=1 -8A2N 4A1N-

I 1 I I , , 0 2 4 6

1H4N- c) ~:"1 f~ L .

0 2 4- S 8 T1me,mIn Figure 4. Comparison of the separation of the five anions having similar electrophoretic mobilities by means of a) capillary electroporesis, 21 kV, b) capillary electrochromatography 21 kV, c) cappilary LC. Substances: 4AIN - 4-amino-l-naphthalenesulfonic acid, 2A1N - 2-amino­ I-naphthalenesulfonic acid, 5A2N - 5-amino-2-naphthalenesulfonic acid, 8A2N ~ 8-amino-2­ naphthalenesulfonic acid, IH4N - I-naphthol-4-sulfonic acid. Capillary columns 50 cm x 10 ~m I.D. Buffer: 10 mmol 1-1 phosphate, pH=7.0, containing 1.25 mmol TBA (reprinted with permission from ref. [21 D 164 J.s. Kowalczyk means of capillary zone electrophoresis, open tubular liquid chromatograph and electroosmotically driven electrochromatography, of the anionic compounds with similar mobilities, by using the difference in their partition coefficients [21 J. In Figure 5 the separation of a group of neutral compounds by means of chromatographic system based on electroosmotic flow, using the polymer-coated capillary column of average plate number 250.000 is shown [11 J.

8 A B D

c

. . o 10 20 30 Time, min

Figure S. Chromatogram obtaiDed by meaDS of electrochromatography, based OD electroosmotic flow, usiDg the polymer-coated capillary columDs: 111 cmx 10 J,tm I.D. Buffer: 1 mmoll-I citricacid cODtainiDg 100 J,tmoll-I cTAB aDd 40% acetonitrile. Voltage 30 kV, v = 3.1 DI miD-I. A- anthracene, B- fluoranthreDe, C- pyreDe, D- 9-methylaDthracene, E- 2~methylaD­ thraceDe, H =250.000-290.000 (reprinted with per mission from ref. [11])

Pressure-driven flow capillary electrocbromatograpby Sometimes, for the optimization of the phase in chromatography (e.g. for appli­ cation of reversed-phase surface in capillary columns) a stationary phase chemically bonded to the wall ofcapillaries orpacked capillaries are used [8,10,11,19]. However, when the highly efficient optimal for chromatography, small diameter packing materials are used, the relative small interparticle pore sizes can cause a significantly reduced electroosmotic flow, used as an altenlative to pressure-driven flow (e.g. for dp =10 J!m, interparticle pore diameter, for a close packed spheres, is =2 J!m) [11,22,23]. The same situation is for the optimal for chromatography open tubular columns, where the inside diameter must be of the same order of magnitude as the diameter of particles optimal for column packing [11,23]. Stevens and Cortes [19] investigated the linear velocity of electroosmotic flow as a function of packing size. The minimum passegeway radius through the silica packing material, for various liquid phases, has been estimated. These relationships can be observed in Fig. 6 [19]. Electrochromatography 165

2.0

1.0

OJ!

0.6

0.4

0.2 0.0 ...... _"""- --"__-'-_--'-_---' g 2 4 8 8 10 r, pm Figure 6. Linear velocity vs. minimum passageway radius for various liquids, obtaine(f for the chroma­ tographic packings: Bio.-Sil A, dp=100 ....m, CorasillI, dp= 5 ....m, PartisillO-Sil, dp=lo ....m (in order of decrease of passegeway radius and electroosmotic flow) (reprinted with permission from ref. (19])

When passageway radius is less than 7fJ (= thickness of double layer or diffuse region on the surface), the velocity pr~file of electroosmotic flow would be similar to laminar flow. Therefore, the reduction ofband spreading with electroosmotic flow is expected only when passageway radius of packed column or the radius of a capillary column is greater than 7fJ [19]. Generally, electroosmotic flow in slurry packed capillary columns is from one fifth to one tenth of flow in open tubular capillary columns ofthe same innerdiameter [15]. In these situations the application ofthe mixed, electroosmotically driven and pressure flow (plug flow mixed with Poiseuille flow) is recommended. Then the equation for apparent flow velocity [vap - see eq. (4)] becomes

(4a) where vp is mean linear flow velocity due to pressurized flow. If Vosm is considerably lower than Vmob equation (4a) becomes

(4b) 166 J.S. Kowalczyk

·After taking into account vp in equation (4a) or (4b), the term H 3 in eq. (5) is as follows [15,16]:

(6a)

where w~ is equal to 8VplVp and 8vp is the difference between the extreme and mean velocities [15]. • 1\vo methods of pressurized flow generation can be applied: - by using a LC pump, - by introducing a hydrostatic flow, which occurs, when electrolyte reservoirs are not at the arne height. A velocity flow is easier to control using a LC pump. Analysis times using the gravity method are much longer, owing to the slow flow velocity (about 1-10 h compared with about 30 min by using a LC pump) [24]. Application of pressurized flow in electrochromatography should ensure [24]: - optimal separation efficiency, - reducing the analysis time, - efficient cooling of the column, - removing bubbles generated at the electrodes for elimination of a noise. From the above possibilities ofpressure-driven flow applications from the below described observations can be drawn. The random walk model of chromatography [25] has been well applied to electrochromatography systems. It can be assumed that the length ofthe step is the same as in liquid chromatography, but the number ofsteps is larger or smaller compared with ordinary liquid chromatography. When directions O.OV

2.51cV SkY 7.4kV

IOkV

~~ 1 min Figure 7. Example of separation of uracil and cis-N-methyl-4-f3-styrylpyridinium iodide, by applying high voltage electrochromatograp~ywith pressure-driven flow. Microcolumn 7.4 cmxO.5 mm J.D., packed with ODS 3 mm and methanol (88%) + 1.5xlO-3 mol 1-1 phosphate buffer, pH = 6.7 (12%). Electric currents increased representively to increasing voltage: 0; 2.5; 5.0; 7.5; 1Ol-tA (reprinted with permission from ref. [26]) Electrochromatography 167

of Vmob' Vosmand vp [see eq. (4a)] are the same, the number of steps is larger [24]. When vp is of opposite direction, the number ofsteps is smaller compared with liquid chromatography. When the discussed directions are the same, then H is reduced, especially at lowervalues ofvp and higher values ofvmoband vosm [see eqs (3}-(6)] [24]. When small diameter column (capillary, de < 500 (lm) is used and very low current are applied, then heat generated is effectively dissipated through the wall of the capillary. However, if column with a large diameter is used and a high voltage (e.g. for reducing the analysis time) is applied then, by means of intensive pressure-driven flow, effective cooling of the column should be arranged [24]. Problem of the noise, which occurrs because of the bubbles, generated at the electrodes, can be overcome using pressure-driven flow. This either carries the bubbles outofthecolumnor, becausethe columnis ~eptundera high pressure, causes the disolution of the gases generated at the electrodes [24]. In Figures 7 and 8 the

, I A

B 3

2

4

II A 1

2

-+1 f+- 2 min Figure 8. Chromatograms of phenylthiohydantoiu derivatives of aspargiue (2 unknown peaks) and of 2-naphthalenesulfonic acid (peak 3). Column: 130x0.5 mm J.D. and the mixture of phosphate buffer, pH=6.7 (10-3 mol 1-1 for Aaud 10-4 mol 1-1 for B) and methanol (12/88). Chromatogram IA and IB without applied voltage. Chromatogram IIA: 7.4 kV, lIB: 11.8 kV (reprinted with permission from ref. [15]) 168 J.S. Kowalczyk

chromatograms are presented which show the effects ofapplied pressure-driven flow electrochromatography at different currents and applied voltages [15,26].

Phase selection in electrochromatography Because in electrochromatography a solute has been subject to electric field influence and interphase reaction at the same time, the knowledge of principles of phase selection for chromatography is as yet insufficient. Of course, a selection of liquid phase should be connected with selecting ofa stationary phase. However more problems has been caused by the reason of "electrical properties" of moving phase. Therefore, in most cases a cho~ce of moving phase composition has been restricted to aqueous phase composition. Pompowski [1] probably was the first one to investi­ gate the application of the water and organic liquid. Also Walbroehl and Jorgenson [27] succeeded itl separation organic bases by using nonaqueous organic solvent. Thus, the use of organic or aqueous organic medium may extend the applicability of electrochromatography to wider range ofcompounds showing low solubility in water. . According to the opinion ofStevens and Cortes the best eluents would - develop a high C; (zeta) potential (have a high amount ofcounterions in solution beyond the plane of share), - have a shallow () - thickness of double layer (have the counterions distributed near the plane ofshear), - have a low electrical conductivity (low' heat generation), - have a low viscosity. Stevens and Cortes [19] have found, that, "when lower field strengths were required for the higher conductivity eluents to prevent overheating in colUlnn, which at moderate levels resulted in an increase in observed current and, at higher levels

0.004 BIO-SIL A • ,./

0.003

"tI u l: J 0.002 0 .....LtJ > 0.001

0.000 t 0 10" 10- 5 10-4 10-3 10- 2 mol·C [KCl] added to eluent

Figure 9. Ratio of linear velocity of electroosmotic flow to field strength l'S. concentration of electrolyte added to the eluent, for columns with various stationary phases: glass tube 2 cm length x 0.040 in LD. (reprinted with permission from ref. [19]) Electrochromatography 169 resulted in an abrupt decrease in observed current as gassing occurred" in column. In Figure 9 [19] a ratio of linear velocity to field strength versus concentration of electrolyte, for various stationary phases was plotted. Fujiwara and Honda [28] have investigated the effect of addition of organic solvent on the separation ofpositional iSOluers. They, among others, have stated that when a constant electric current was applied, the voltage was gradually increased with increasing concentration oforganic solvent due to reduced ionic strength ofthe medium, as shown in Fig. 10 [28]. Figure.11 [28] shows changes of retention times of positional isomers of substituted benzoic acids as a function of the concentration of methanol or acetonitrile.

'20

~ 15 .... Q) ...G ~ 10

5 o 10 20 30 40 60

Methanol or acetonitrile, "lv/v)

Figure 10. Relation between voltage and concentration oforganicsolvent: 1-methanol, 2 - acetonitrile. Capillary: fused silica 80 cmxO.25 mm J.D. Liquids were mixtures ofabove organic solvents with 0.02 mol 1-1 phosphate buffer, pH=7.0. Applied current: 100 ~A (reprinted with permission from ref. [28])

Preparative application ofelectrochromatography

Sample focusing in the column Tsuda [24] has proposed using different velocities of the substances, migrating in electric field (Vmob) and in pressure-driven liquid phase (v p) for its collection in column. This sample focussing process in column can be used for preparative application of electrochromatography, also for concentration of a minor component in a large mixture. The sample introduced as a plug will remain in the column under the condition vp < -2Vmo b (mobility direction is the reverse of the pressurized flow) because the highest laminar flow velocity is twice the mean linear flow velocity. Here, the centre of the substance zone is positioned at half of vp and t~e sample could be stored .in column under the described condition. 170 J.S. Kowalczyk

60 c)

50

..... e :;: c ~ c• ­ae• 20

10

O~__...I-_~ so o 25 so o 2S so

Methanol or acetonitrile J "lv/v)

Figure 11. Retention times of ortho 0, meta (0) and para (~) izomers of a) aminobenzoic acid, b) hydrobenzoic acid, c) methylbenzoic acid. Open symbols - methanol, closed symbols­ acetonitrile; Conditions were the same as those described in Fig. 10 (reprinted with permission from ref. [28])

After several injections, using the applied voltage and switching off the voltage - the selected substances can be introduced continuouslyinto the head ofthe column. Tsuda [24] has presented the instrumentation for continuous sample focusing and typical examples of its applications.

Electrochromatographic solid-phase extraction Electrochromatography, as a selective cleaning procedure, can also be used[24] for saluple preparation. For this purpose a solute should be focused using an applied . voltage and then collected in a small cHrtridge column. This column should be then washed and, afterpH is altered with a buffersolution, and a suitable voltage is applied - the substance can be forced together around the electrode that generated its Inability. The sample substance obtained by the above method is more pure sample than prepared by other conventional cleaning procedure. Electrochromatography 171

Nomenclature ofelectrochromatography

In the first publications [1-6] the term "electrophoresis with chromatographic effects" has been used. In the latest years various nomenclatures, often not equivalent in terms, e.g. pseudoelectrochromatography [29], LC with electroosmotic flow [11] and others may be found. Tsuda [24] has proposed detailed terms for general term "electrochromatography". It seems to me that basic, following terms are sufficient for most cases: - electroosmotically-driven electrochromatography: vap ::: vmob + vosm [eq. (4) [24], -electroosmoticaUy-driven chromatography, electro-driven chromatography, for cases ofelectrochromatography when solute has electrophoretic mobility equal to zero (a solute has not electrical charge): vap ::: vosm or vap ::: vosm + vp [21,24], -pressurized flow-drivenelectrochromatography: vap ::: Vmob + vp [eq. (4b)] [24], - mixed flow-driven electrochromatography: vap ::: vmob + Vosm + vp [eq. (4a)] [24].

REFERENCES

1. Pompowski T., Kowalczyk J. and Son Czun .len" Chem. Anal. (Warsaw), 8, 719 (1963). 2. Kowalczyk J., Wiadomosci Chem., 17,703 (1963). 3. Kowalczyk J., J. Chromatogr., 14, 411 (1964). 4. Kowalczyk J., Chem. Anal. (Warsaw), 9, 29 (1964). 5. Kowalczyk J., Chem.Anal. (Warsaw), 10, 29 (1965). 6. Kowalczyk J. and Czapliriski A, Chem. Anal. (Warsaw), 9,1021 (1964). 7. Pretorius v.:, Hopkins 8.J. and Schieke J.D., J. Chromatogr., 99, 23 (1974). 8. Knox J.H. and Grant I.H., Chromatographia, 24, 135 (1987). 9. Tsuda T., Sweedler J. and zare R.N., Anal. Chem., 62,2149 (1990). 10. Bruin G.J.M., Tock P.P.H., Kraak J.C. and Poppe H., J. Chromatogr., 517, 557 (1990). 11. Pfeffer W.D. and Yeung E.S.,Anal. Chem., 62, 2178 (1990). 12. Yamamoto H., Baumann J. and Erni F.,]. Chromatogr., 593, 313 (1992). 13. Chervet J.P., van Soest RE.J. and Salzmann J.P., LC-GC Int. The Magazine ofSeparation Science, 5, Nr 7, 33 (1992). 14. KingB.W., Westlake J.P., Myers P., Zimina T. and Smith RM.,LC-GCInt. The Magazine ofSeparation Science, 7, Nr 12,702 (1994). 15. Tsuda T.,Anal. Chem., 60,1677 (1988). 16. Tsuda 1: and Maramatsu Y.,]. Chromatogr., 515, 645, (1990). 17. Tsuda T.,]. High Resol. Chl'Omatogr., Chrontatogr. Commun., 10, 622 (1937). 18. Tsuda T., Nomura K and Nagakawa G.,J. Chrontatogr., 248, 241 (1982). 19. Stevens 1:S. and Cortes H.J.,Anal. Chem., 55,1365 (1983). 20. Jorgenson J.W. and DeArman Lukacs K.,J. Chromatogr., 218, 209 (1981). 21. Pfeffer W.D. and Yeung E.S.,]. Chromatogr., 557, 125 (1991). 22. Jorgenson J.W. and Guthrie E.J.,J. Chromatogr., 255, 335 (1983). 23. Nowotny M.,Anal. Chem., 60, 500A (1988). 24. Tsuda T., LC-GC Int. The Magazin ofSeparation Science, 5, Nr 9, 26 (1992). 25. Giddings J.C., Dynamics o/Chromatography, Marcel Dekker, New York 1965. 26. Tsuda T.,Anal. Chem., 59, 521 (1987). 27. Walbroehl Y. and Jorgenson J.W., J. Chromatogr., 315, 135 (1984). 28. Fujiwara S. and Honda S., Anal. Chem., 59, 487 (1987). 29. Verheij E.R, Tjaden U.R and Niessen W.M.A.,J. Chromatogr., 554, 339 (1991).

ReceivedAugust 1995 AcceptedDecember 1995