Anal. Chem. 1996, 68, 2580-2589
Classical Retention Mechanism in Ion Exchange Chromatography. Theory and Experiment Gyo 1 rgy Fo´ti, Gabriella Re´ve´sz, Pe´ter Hajo´s,† Gabrielle Pellaton, and Ervin sz. Kova´ts*
Laboratoire de Chimie Technique, Ecole Polytechnique Fe´ de´ rale de Lausanne, CH-1015 Lausanne, Switzerland
The classical model for ion exchange chromatography is characterized by firmly adsorbed driving ions at the surface of the stationary phase in an amount required by electroneutrality and stoichiometric ion exchange between the bulk of the eluent electrolyte and this immobilized Stern layer. Retention equations have been derived for system peaks, labeled eluent ions, and analytes in a system containing only strong electrolytes by strictly respecting this model. It is shown that the classical model described dependence of retention data on concentration and composition of the binary eluent with excellent precision, but the resulting system parameters were not self-consistent. Inconsistency of the results might be due to contributions from another retention mechanism. A firmly immobilized layer of driving ions and a stoichiometric exchange between the layer and ions in the bulk of the electrolyte characterize the generally accepted model for ion exchange chromatography.1-5 Any textbook on colloid chemistry confirms that this model is unrealistic (see, e.g., ref 6). Above the immobile Stern layer, there must be a diffuse Gouy-Chapman layer, in which ions are mobile and are carried along the column bed by the movement of the eluent, whereby a streaming potential is generated. This picture is confirmed by capillary electrophoretic experience.7 Electroosmotic movement of the electrolyte in the applied electric field in the capillary is due to mobile excess charge in the diffuse layer. A model for ion exchange chromatography based on the Gouy-Chapman theory has recently been attempted.8 In spite of these arguments, equations derived from the Stern model seem to describe retention in ion exchange chromatography, at least in simple cases, with a very good precision. In a recent report,9 the retention of strong electrolytes on strong ion exchangers has been treated by assuming only the existence of a Stern layer. Based on the model, retention volumes of system peaks, of analytes, and of labeled eluent components † Permanent address: Department of Analytical Chemistry, University of Veszpre´m, H-8201 Veszpre´m, Hungary. (1) Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962. (2) Incze´dy, J. Analytical Applications of Ion Exchangers; Pergamon Press: Oxford, 1966. (3) Gjerde, D. T.; Fritz, J. S. Ion Chromatography, 2nd ed.; Hu ¨ thig: Heidelberg, 1987. (4) Tarter, J. G. Ion Chromatography; Marcel Dekker: New York, 1987. (5) Haddad, P. R.; Jackson, P. E. Ion Chromatography; Elsevier: Amsterdam, 1990. (6) Hunter, R. J. Foundations of Colloid Science; Oxford University Press: Oxford, 1992. (7) Capillary Electrophoresis: Principles and Practice; Kuhn, R., Hoffstetter-Kuhn, S., Eds.; Springer: Berlin, 1993. (8) Ståhlberg, J. Anal. Chem. 1994, 66, 440. (9) Fo´ti, G.; Hajo´s, P.; sz. Kova´ts, E. Talanta 1994, 41, 1073.
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have been related to working variables such as eluent composition and concentration, the charge of driving ions and analytes, and the exchange capacity of the stationary phase. One early and m - 1 late system peaks have been predicted in an eluent containing m driving ions, and an explicit retention equation was derived for the one late system peak in binary eluents (m ) 2). The objective of the present paper is to compare the theoretical considerations of ref 9 with experiment. Hence, it was intended to construct a system that approches the model of ref 9 as closely as possible with the simplest multicomponent system: binary eluent with all counterions (driving ions, E1 and E2, and analytes, su) having charge number of unity (zE1 ) zE2 ) zsu ) 1). In particular, (i) the ion exchanger with a flat surface was approximated by a wide-pore silica-based adsorbent with quaternary ammonium groups immobilized at its surface; (ii) as multicomponent strong eluent was taken a binary solution of ethane- and propane-sulfonate, EtS and PrS, in water, W; and (iii) labeled eluent components were approximated by perdeuterated alkane sulfonates, EtS* and PrS*, and deuterium oxide, W*. The necessary surface concentration of the ionic groups at the surface of the stationary phase as well as the concentration domain of the eluent electrolyte was elucidated in preliminary experiments.10 A commercial wide-pore silica was chemically modified with a mixture of (3,3-dimethylbutyl)dimethyl(dimethylamino)silane and [5-(dimethylamino)-3,3-dimethylpentyl]dimethyl(dimethylamino)silane. Quaternization of the product with bromomethane gave a dense mixed surface layer with a total surface concentration of Γtot ) 4.77 µmol m-2 and a concentration of the exposed quaternary ammonium groups (QA) of ΓQA ) 0.74 µmol m-2 (see Figure 1). This surface concentration corresponds to a mean distance between QA groups of about 16 Å. This sparse distribution of the small trimethylammonio substituent, easily accessible at the nonpolar surface, ought to enhance the “Stern character” of the electric double layer. The total driving ion concentration of the EtS/PrS eluent electrolyte, cEtot ) cEtS + cPrS, was planned to be varied between 6 e cEtot e 14 mM by ∆cEtot ) 2 mM equidistant steps, and composition was to be varied between 0 e xEtS e 1 by ∆xEtS ) 0.2 equidistant steps (xEtS ) cEtS/cEtot). In this system, retention volumes of the following signals should be determined at each cEtot/xEtS combination: the early and the late system peaks, labeled driving ions, deuterium oxide, and a restricted number of strong monovalent anions (methanesulfonate, chloride, bromide, and nitrate). Special attention was given to the interpretation of the early and the late system peaks and to the information given by the signals of labeled eluent components, solvent, and driving ions. (10) Pellaton, G. Doctoral Thesis, Ecole Polytechnique Fe´de´rale de Lausanne, 1993; No. 1136. S0003-2700(96)00015-7 CCC: $12.00
© 1996 American Chemical Society
measures the holdup volume of the system, identified as the volume of the mobile phase, Vµ, i.e.,
VR,W ) Vµ
(1)
Experimentally, this peak is best generated by injecting a small volume of water (hence the subscript W). With the resulting holdup volume, the net retention volume of a signal, i, can be calculated:
VN,i ) VR,i - Vµ
(2)
Knowledge of the surface area of the adsorbent in the column, S (m2), permits calculation of the areal retention volume,
VS,i ) VN,i/S Figure 1. Structure of the (3,3-dimethylbutyl)dimethylsilyl, DMB, and of the [5-(trimethylammonio)-3,3-dimethylpentyl]dimethylsilyl, QA, substituent.
usually given in units of µL m-2 ≡ nm. The retention volume of deuterium oxide, VR,W*, measures the total volume of the eluent in the system, Vtot, given by
VR,W* ) Vtot ) Vµ + Vϑ It will be seen that our experiments confirm the basic ideas of Small about the origin of the system peaks.11 They definitely contradict literature reports stating that the late system peak is due to disturbances of the adsorption equilibrium involving electroneutral species.12 Finally, we put forward the question of the limits of the model of ref 9. In fact, it will be seen that the model of a pure stoichiometric ion exchange mechanism between electrolyte and a firmly immobilized layer does not provide self-consistent results. THEORY Derivations of ref 9 are based on the following idealized ion exchange chromatographic model: ionic groups are exposed at the surface of the powder particles of the column packing; coions are expelled from the Stern layer; the amount of driving ions adsorbed at the surface is given by the requirement of electroneutrality and is independent of the concentration of the driving ions in the eluent; driving ion concentrations are infinitesimal compared to the concentration of the solvent (water); analyte concentrations are infinitesimal compared to the concentration of the driving ions; and selectivity coefficients are independent of composition and concentration of the eluent. In the following, retention equations derived in ref 9 will be applied to the case experimentally studied in the present paper, i.e., binary mixture of monovalent driving ions, zE1 ) zE2 ) 1, in water as eluent, and monovalent analyte (i.e., solute) counterions, zsu ) 1. The monovalent co-ion is the same in all experiments. In such an eluent, there are two degrees of freedom for composition change. Therefore, when injecting a sample containing only eluent components, the disturbance of the column equilibrium will be split into two eigenperturbations, traversing the column with different retention times, resulting in two peaks, an early and a late system peak. Retention volumes of such peaks can be clearly interpreted in dilute electrolytes.9 The origin of the early system peak (the “void peak” of Small11) is a perturbation of the eluent characterized by an infinitesimal change of the total ion concentration at constant ionic composition. This perturbation is not retained. Its retention volume, VR,W, (11) Small, H. Ion Chromatography; Plenum Press: New York, 1989. (12) Yamamoto, A.; Matsunaga, A.; Mizukami, E.; Hayakawa, K.; Miyazaki, M. J. Chromatogr. 1993, 644, 183.
(3)
(4)
if an isotope effect on retention can be neglected and the molar concentration of water both in the mobile phase and in the stationary layer is about equal to the concentration of pure water (both are dilute solutions). Consequently, knowledge of the retention volumes of water and deuterium oxide allows experimental determination of the volume of the mobile phase, Vµ, and of the stationary phase, Vϑ ) VN,W*, respectively. Experimentally, the retention volume of deuterium oxide is difficult to determine due to its unsufficient separation from the early system peak. It is best generated without the latter by injecting an eluent sample prepared in water containing a small amount of deuterium oxide. The late system peak originates from a perturbation by a sample having the same driving ion concentration but a different ionic composition than the eluent. This perturbation is always retained; it has a positive net retention volume, VN,E. Equation 26 of ref 9 gives, after rearrangement,
Q/cEtot VN,E ) KE1/E2 (mL) [1 + (KE1/E2 - 1)xE1]2
(5)
where Q (µmol) is the exchange capacity of the column, cEtot (mM) is the total concentration of the eluent, and xE1 is the mole fraction of driving ion E1 in the eluent (xE1 + xE2 ) 1). The intereluent selectivity coefficient, KE1/E2, is defined for our specific case (zE1 ) zE2 ) 1) by
KE1/E2 )
ΘE1/ΘE2 cE1/cE2
(6)
where Θ is the relative surface coverage (ΘE1 + ΘE2 ) 1). Experimentally, the late system peak is best generated by injecting a sample having the same concentration but a slightly different composition than the eluent. With the injection of an analyte counterion into the binary eluent, the number of degrees of freedom for composition change rises to three; hence, three peaks are expected: the early and the late system peaks, and the third peak, which is clearly attributed to the solute. If the concentration of the solute of unit charge is infinitesimal compared to those of the driving ions, its net retention volume, VN,su, is given by eq 7 (eq 23 of ref 9 after rearrangement): Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
2581
Q/cEtot VN,su ) Ksu/E2 1 + (KE1/E2 - 1)xE1
(7)
The selectivity coefficient of the solute with respect to one of the driving ions (e.g., E2), Ksu/E2, is given by
Ksu/E2 )
Θsu/ΘE2 csu/cE2
(8)
Experimentally, this peak is easily generated by injecting a dilute solution of the solute. The net retention volumes of two particular analytes, the labeled driving ions, VN,E*1 and VN,E*2, are given by a relationship analogous to eq 7:
Q/cEtot VN,E*1 ) KE1/E2 ) KE1/E2VN,E*2 1 + (KE1/E2 - 1)xE1
(9)
if isotope effects on retention can be neglected. Equation 9 shows that determination of the retention volumes VN,E*1 and VN,E*2 in an eluent of known composition would provide an easy means to fully characterize the chromatographic system. In fact, knowledge of these data allows the calculation of both the column capacity, Q,
Q ) cE1VN,E*1 + cE2VN,E*2 and the intereluent selectivity coefficient, KE1/E2,
KE1/E2 ) VN,E*1/VN,E*2 Unfortunately, in many cases, conductometric detection of the corresponding signals is difficult. These peaks are best generated by injecting a sample having the same concentration and ionic composition as the eluent but prepared with the labeled driving ion. (Because of detection difficulties, it may be necessary to inject a sample that contains the labeled driving ion at a concentration higher than its unlabeled counterpart in the eluent. This implies generation of the late system peak, which may interfere with the signal of the labeled driving ion.) Let us insist that retention eqs 5, 7, and 9 are valid only when the selectivity coefficients defined in eqs 6 and 8 are independent of concentration and composition of the eluent. Finally, let us note that, at constant eluent composition, eqs 5, 7, and 9 may all be written in the form
log VN,i ) const - log cEtot well known from literature,5 where the slope of the resulting linear plot is the ratio of the charge numbers of the concurrent ions. In our case, this ratio is equal to unity. EXPERIMENTAL SECTION Materials. The precipitated silica for the preparation of the ion exchanger was Nucleosil 300 from Macherey-Nagel (Du¨ren, F.R.G.), with nominal particle diameter of 5 µm and pore diameter of 300 Å. BET evaluation of the nitrogen adsorption isotherm at 77 K in the relative pressure range of 0.05 < Pe/Po < 0.23 gave a specific surface area of s ) 98 ( 2 m2 g-1, using a recently reported value of 13.5 Å2 for the surface requirement of an adsorbed nitrogen molecule.13 Nitrogen for adsorption experiments (99.999%) and liquid nitrogen for thermostating (99.8%) were from Carbagas (Lausanne, Switzerland). The silylating agents, (3,3-dimethylbu(13) Jelinek, L.; sz. Kova´ts. E. Langmuir 1994, 10, 4225.
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Analytical Chemistry, Vol. 68, No. 15, August 1, 1996
tyl)dimethyl(dimethylamino)silane (dimethylamino-DMB) and [5-(dimethylamino)-3,3-dimethylpentyl]dimethyl(dimethylamino)silane (dimethylamino-DMPA), were synthetized in our laboratory.14 The solvents, research grade cyclohexane and ethanol from Fluka (Buchs, Switzerland) and HPLC grade 2-propanol and methanol from Romil Chemicals (Leics, U.K.) were used as received; research grade diethyl ether from Merck (Darmstadt, F.R.G.) was freshly distilled before use. The eluent components, monohydrates of sodium ethanesulfonate (NaEtS) and sodium 1-propanesulfonate (NaPrS), the analytes, sodium methanesulfonate (NaMeS), NaCl, NaBr, and NaNO3, and the reagents, methyl bromide, HNO3, and AgNO3, were research grade chemicals from Fluka (Buchs, Switzerland) and were used as received. Doubly distilled water (W) was prepared by distilling deionized water over KMnO4 in a Pyrex glass still from Bu¨chi (Flawil, Switzerland; Model Fontavapor-285). Research grade deuterium oxide (W*), isotope purity > 99.5%, was from Chemie Uetikon (Uetikon, Switzerland). Monohydrates of perdeuterated sodium ethanesulfonate (NaEtS*) and sodium 1-propanesulfonate (NaPrS*), purity > 98%, were synthetized in our laboratory. Instrumentation. Silicon dioxide was stored and handled in a Model GB-80 glovebox from Mecaplex (Grenchen, Switzerland) in an argon atmosphere containing
