retention volume of second system peak

8/14/2019 Retention Volume of Second System Peak

1/4

381NALYTICAL SCIENCES JUNE 1996, VOL. 12

Retention Volume of the Second SystemIon-Exchange Chromatography withMonobasic Acid Eluent Systems

Peak inOriginal Papers

Hideki WATANABE Yukio YOKOYAMA and Hisakuni SATOtLaboratory of Analytical Chemistry,Hodogaya, Yokohama 240, Japan

Faculty of Engineering, Yokohama National University

A general, functional relationship between the retention volume of the 2nd system peak and the chromatographicparameters (the acid dissociation constant of the eluent component, the eluent concentration, the acid/salt ratio in theeluent, the acid-partition coefficient) in ion chromatography with monobasic acid eluent systems (acids, salts, and theirmixtures) have been derived. The relations precisely reproduced the results by computer simulation based on the platetheory, and were confirmed with independent experiments. By using these relations, the partition isotherm of eluentacids to the stationary phase can be obtained easily.Keywords System peak, ion-exchange chromatography, computer simulation, monobasic acid eluent system

Computer simulations''2 based on the plate theory andthe acid partition model have revealed the origin andfundamental behavior of the system peaks3-5 oftenobserved in ion-exchange chromatography with bulk-property detectors. By these simulations, however, wecan only obtain a chromatogram (concentration profilevs. the volume of mobile phase) for a set of parametervalues after calculations taking several tens of minutes,and the calculation sometimes is terminated because theequilibrium calculation in a certain plate does notconverge. In the calculation of 1000 theoretical plates,even the use of quadruple-precision variables with amainframe computer was sometimes unsuccessful.2etailed evaluation of the retention characteristics ofthe second system peak is thought to be impossible unlesswe know the functional relationships between theretention volume and such chromatographic parametersas the acid dissociation constant of the eluent, as well asthe eluent concentration, pH or acid/salt ratio in aneluent, acid-partition coefficient, and so on.lthough Yamamoto et al.6 tried to obtain such afunctional relationship, they considered the capacityratio of the 2nd system peak only for acid eluents.Because the appearance of the 2nd system peak is notlimited to acid eluents, the equation is not utilized ingeneral. So, we have derived a general relationshipconsistent with the results obtained by the computersimulations) for monobasic acid eluent systems (acids,salts, and their mixtures), and have confirmed therelation experimentally.

Theoretical Premise and Computer Simulationmonobasic acid eluent system contains HB, B-, H+and A+ (some cation other than H+). The total concen-tration of B species in the mobile phase of a theoretical

plate is represented as CBand the concentration of A+ sCA. A+ was assumed to be indifferent to the acid-basereaction.The acid-base equilibrium in the mobile phase isrepresented as:B~H+ + B-: Ka = [H+]m[B-]m/[HB]m (1)he ion-exchange equilibrium is represented as:-+B-RIB-+X-R: Ke=[X-]S[B-]m/[X-]m[B-]5,

2)where X- is the analyte ion and R is the skeleton of ion-exchanger. The suffixes, m and s represent mobile andstationary phases, respectively.The acid partition equilibrium can be represented as:

HB)m!(HB)S: Kd=[HB]S/[HB]m (3)nother reaction equilibrium is the auto-protolysis of

solvent water.2O~H++OH-: KW=[H+][OH-] (4)ass balances in a theoretical plate can be representedTo whom correspondence should be addressed .


2/4

382 ANALYTICAL SCIENCES JUNE 1996, VOL. 12

as:

Ce= [B-]S+ [X-]S (5)Tx = [X ]m+ [X ]s (6)CB= [B-]m+ [HB]m (7)CA= [A+]m= [B-]m+ [X-]m+ [OH-]m - [H+]m (8)

where Ce is the ion-exchange capacity of the stationaryphase. The phase ratio was assumed to be 1.0 for thesimplicity in the computer simulation. Values of Tx,CB, and CA n ith plate at jth transfer of the mobile phaseare given from the initial conditions and the previousprocesses (transfer 1-* j-1).t was assumed in the present theoretical treatment andcomputer simulation based on the plate theory (denotedbelow by "PT calculation") that the above 8 equationshold for every theoretical plate. Other than thesesimplifications, we tried to treat the systems as rigorouslyas possible.The computer program for the simulation of mono-basic acid eluent systems was written in MS-FORTRAN"and run on an IBM personal computer (PS/V,80486DX). The scheme of the programs was shown inthe previous paper.' The theoretical plate number wasset at 100 for almost all calculations for the convenienceof computer time. Source program lists are available onrequest.

ExperimentalApparatusThe chromatographic system consisted of a Tosoh(Tokyo, Japan) CCPM pump, a Rheodyne (Cotati, CA,USA) 8125 sample injector with a 100 l sample loop, aTosoh CM-8000 conductivity detector, and a Tosoh UV-8000 absorbance detector. The separation column wasa Tosoh IC-anion PW (4.6X50 mm).ReagentsAll chemicals were of analytical grade and werepurchased from Wako (Osaka, Japan) or Tokyo Kasei(Tokyo, Japan), and were used without further purifica-tion. Water was purified by using a mixed-bed ion-exchange column and a Milli-Q Labo water purificationsystem.Chromatographic procedure

ater solutions of salicylic acid, sodium salicylate,and salicylic acid+sodium salicylate were flowed with apump at 1 ml/min. The acidity of the eluent waschanged with the mixing ratio of the acid and the salt.As the sample, water or an aqueous solution of sodiumchloride was injected. All experiments were performedat about 22 C. Output from a detector was stored in thedisk memory of a personal computer (Fujitsu, FM-R50)

and processed with homemade software written inBASIC.Measurement of partition isothermhe quantities of acids adsorbed by a separationcolumn were measured for the salicylic acid-sodiumsalicylate system by using the method described in aprevious paper.'

Results and DiscussionDerivation of the unctional relationshiphe second system peak is thought to be caused by theperturbation of the adsorption equilibrium of the eluentacid in the analytical column after the sample intro-duction."6 Although this case is a sort of vacancychromatography', the retention volume of the secondsystem peak ( V2) s thought to be given by the well-knownrelations for usual partition chromatography as,

2 Vm+ Kd' VS (9)where, Vm nd VSepresent the volumes of the mobile andstationary phases, respectively, in a column. In Fig. 1,some results by computer simulation are plotted. Eachgroup of the same Ka value and acidity shows a linearrelation, but a different slope. Therefore, Eq. (9) isinvalid for the present case.hen the partition isotherm is not linear at a certain

Fig. 1 Consistency between the results of PT calculationssymbols) and Eq. (15) (lines). Parameters: CB=0.005, Vm==0.5, Kex=1.0*, Ce=0.01, acid sample. 0, Ka=5.0X10-4

acid eluent); ~, Ka 5.OX 0-4 (salt eluent); Q, Ka 5.OX10-3acid eluent); (, Ka 5.OX10-3 (salt eluent); ~, Ka5.OX 10-2acid eluent); /, Ka5.OX 10-2 (salt eluent). * Selectivityoefficient of ion-exchange reaction between B- and a sampleon.


3/4

383NALYTICAL SCIENCES JUNE 1996, VOL. 12

temperature, the partition coefficient (Kd) is given9 as

da[HB]S (10)[HB mwhere, [HB]m and [HB]S are the concentrations of HB inthe mobile and stationary phases, respectively.ecause the acid molecule in the eluent dissociatespartly (weak electrolyte) or perfectly (strong electrolyte),the retention behavior of the 2nd system peak becomescomplicated. The sample injection causes the concen-tration change of the total concentration of the eluent ion(CB). Therefore the coefficient to VS n Eq. (9) waspresumed to be given by the partial differential co-efficient, a[HB]S/a CB.6'8 Thus,

[HB]S2= Vm+ CB VS (11) a

The differential coefficient in Eq. (11) can be representedas:

a[HB]S a[HB]S a[HB]mCB a[HB]m aCB

[HB]maCB Kd (12)

The differential coefficient to Kd in Eq. (12) may beconsidered as a sort of correction term for Kd.rom the basic relations, Eqs. (1), (7) and (8), weobtain the next relation between [HB]m and CB,neglecting [X-] and [OW] terms as small.

[HB]m2-[HB]m(2CB- CA +Ka)+ CB2- CACB=O13)

The partial differential coefficient in Eq. (12) can beobtained by the differentiation of Eq. (13), and by thesubstitution of the mass conservation equation and theelectric neutrality rule.

8[HB]m [H+]mo [Br]moa CB [H+]mo [B-]mo+ Ka (14)

where, [H+]mo nd [B-]mo re the concentrations of H+ andB-, respectively, in the eluent.hus, we obtain the next general relation for theretention volume of the 2nd system peak.KdV2 = Vm + Ka

VS (15)1+

[H+]m0 [B-]moEquation (15) is consistent with all the simulationresults (PT calculation) for monobasic acid eluentsystems (HB+AB) as shown in Fig. 1, where solid lines

were[B-]mo

drawn by using Eq. (15).as in the case of acid eluent

If [H+]mo s equal to, Eq. (15) becomes

KdV2 = Vm + Ka VS (16)1+ 2[H+]m0This is the same relation as that given in the report by

Yamamoto et al.6Experimental confirmationhe general equation (Eq. (15)) for the retentionvolume of the 2nd system peak was confirmedexperimentally for the salicylic acid-salicylate eluentsystem. The partition isotherm for this eluent systemwas first measured independently from the chromatog-raphy.) Because the isotherm (Fig. 2) was not linear,the measured values for [HB]S and [HB]m were adjustedto Freundlich's equation, [HB]S=k[HB]ml/n,by the least-squares method. Although Yamamoto et a1.10 usedLangmuir's equation to the similar system, our measureddata fitted better to the former equation than to the latterone in the present work. By using the k and n valuesthus obtained (1.43 and 3.97, respectively), Kd valueswere calculated for any values of [HB]m with Eq. (10).The retention volume of the 2nd system peak could beestimated by using Eq. (15) and is shown by the solid linein Fig. 3. The values of Vm and VS n Eq. (15) wereobtained from the retention volume of the first systempeak (water dip) and the column size. Experimentalvalues (marks) well fit to the theoretical relation, eventhough the partition isotherm is not linear. Thus,general relationships between the retention volume of the

Fig. 2 Acid-partition isotherm for the salicylic acidodium salicylate system. 0, CB=0.8 mM (constant),B=variable; S, CA/ CB=0.8 (constant), CB=variable.

andCA!


4/4

384 ANALYTICAL SCIENCES JUNE 1996, VOL. 12

2nd system peak and chromatographic parameters havebeen obtained for monobasic acid eluent systems. Nowwe can estimate V2 for any monovalent eluent systemseasily without performing PT calculations if we know Kdand Ka. Although such basic data as the values of Kd arenot yet known sufficiently today, we can easily obtain

these values by measuring V2 in chromatographic ex-periments.The intensity of the 2nd system peak depends on theamounts of the concentration change of eluent species atthe sample injection and on the method of detection.This point will be presented separately.

References1. H. Sato, Anal. Chem., 62, 1567(1990).. H. Sato and H. Watanabe, Reactive Polymers, 17, 1

1992).. D. T. Gjerde and J. S. Fritz, Anal. Chem.,53, 2324(1981).. T. Okada and T. Kuwamoto, Anal. Chem., 56, 20731984).. P. E. Jackson and P. R. Haddad, J. Chromatogr., 46,1251985).. A. Yamamoto, A. Matsunaga, M. Ohto, E. Mizukami,. Hayakawa and M. Miyazaki, J. Chromatogr.,482,45(1989).. C. N. Reilley, G. P. Hildebrand and J. W. Ashley Jr.,nal. Chem.,34, 1198(1962).. A. J. P. Martin and R. L. M. Synge,Biochem. ., 35,13581941).. F. Riedo and E. Kovats, J. Chromatogr., 39, 1(1982).0. A. Yamamoto, A. Matsunaga, E. Mizukami,. Hayakawa and M. Miyazaki, J. Chromatogr.,644,83(1993).1. Product of Microsoft Corporation.

ReceivedJanuary 8, 1996)AcceptedFebruary 26, 1996)

Fig. 3 Experimental cvalues (0) and the theoretical relationline) for the retention volume of the 2nd system peak in thealicylic acid and sodium salicylate system.

retention volume of second system peak

Documents