442
Anal. Chem. 1983, 55, 442-446
Interaction Indexes and Solvent Effects in Reversed-Phase Liquid Chromatography Henri Colin” and Georges Gulochon Laboratoire de Chimie Analytique Physique, Ecole Polytechnique, 9 I 128 Palaiseau Cedex, France
Pave1 Jandera University of Chemical Technology, Department of Analytical Chemistry, Leninovo NZm, 565 Pardubice, Czechoslovakia
The retention model for reversed-phase llquld chromatography based on Interaction Indexes Is extended to complex solvent mixtures and, more particularly, to ternary systems. I t Is shown that when blnary eluents are mixed to give a complex solvent, the capacity ratio of a solute In this solvent Is related to the capacity ratio in each binary eluent. The relationship between log k’ in the complex solvent and log k’ in the binary eluents allows one to define “regular” combinations of binary mixtures yielding complex solvents in whlch the predlction of retentlon is very simple. The theoretlcal treatment is verlfied experimentally with ternary systems.
A simple approach to quantitative prediction of retention in reversed-phase liquid chromatography (RPLC) has been recently proposed ( I ) . It is based on the observation of the predominant role of mobile phase interactions compared to those in the stationary phase. The basic equations of the model agree well with the characteristic features of retention in RPLC. A new parameter was introduced-the interaction index I-to describe the solute and the solvent behavior. This index is somewhat similar to Snyder’s polarity index, P. Very significant differences are, however, observed, particularly with polar compounds. Recent work (2) has shown that RPLC specific stationary phase interactions involving unreacted silanol groups and the adsorbed solvent layer may, in some cases, make a very significant contribution to retention. This indicates that an absolute prediction of retention based solely on mobile phase interactions is questionable. As has been seen, however (3), the correct choice of calibration compounds makes possible a fairly accurate relative prediction, even in complex solvent mixtures. A relative prediction of retention means the estimation of the capacity ratios in a given solvent from data obtained in another solvent, or with other solutes in the same solvent. The reason why the present model gives fairly accurate results is that the stationary phase interactions are more or less taken into account in the calibration lines. In a previous publication ( I ) , the model was derived in the case of a binary eluent composed of water and an organic modifier. It was shown that there is a quadratic relationship between the logarithm of the capacity ratio and the volume fraction of organic solvent in the eluent. Another important consequence of the model is that there is a linear relationship between the corrected logarithm of the capacity ratio log k* = (log k ’ - log @)/VBand the interaction index. In the definition of the corrected logarithm, Q, is the phase ratio and V , the molar volume of the solute. Although binary eluents are very popular in RPLC, it is a general trend in today’s practice of reversed-phase chromatography to use ternary or even more complex mobile phases. The usefulness of such eluents has already been demonstrated several times (see ref 4 for instance).
The purpose of this work is to extend the model to complex mobile phases, with a particular emphasis to ternary eluents. It will be shown that, in certain conditions, the retention in such mobile phase conditions can be easily predicted from the retention in binary water-organic systems.
THEORY A complex mobile phase (water + organic solvents SI, S1, ..., S,, ...) can be prepared in two different ways. First, one can mix the required volumes of the pure liquids (“general procedure”), and second, one can mix adequate volumes of binary systems BS; (water + S,),provided their compositions and relative amounts are conveniently chosen (“binary system procedure”). In the following, we will derive the equations giving the capacity ratio by using the two approaches of a complex solvent: the general procedure and the binary system procedure. We will then particularly focus on the examination of ternary solvents. General Approach. Snyder’s equation for the calculation of the polarity of a mixture of solvents ( 4 ) can be extended to our system in the following form:
where I; and X i are, respectively, the interaction index and volume fraction of solvent Si in the mixture. Equation 1 can be rewritten as follows: Imix
= IH~O - XX,(IH~O - 4)
(2)
I
By use of the same approach as that used for binary solvents ( I ) , it can be shown that the logarithm of the capacity ratio in the mixture (log k’,J is given by T,
n
where I,* = IHZ0 - I,. The necessity of the coefficient C, is explained in ref 1 where it was found that the value of C, practically does not depend on the nature of the organic solvent, and therefore to first approximation, a single constant C, may be used for a complex mixture. Equation 3 can be rewritten under the form log k’mix = a - m(X,) d(X,) ASCE (4)
+
+
where m(X,) and d ( X , ) are first-order and second-order functions, respectively, of the variables X,.ASCE is a solvent coupling effect term, which characterizes the interactions between the molecules of organic solvents in the mobile phase. Equation 4 shows that the expression for the capacity ratio in a complex solvent system is actually very similar to that
0003-2700/83/0355-0442$01.50/0@ 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL.
in a binary eluent where ASCE is zero, The analogy between binary systems and more complex ones also appears in the relationship between log k* and the interaction index I. It has been shown in ref 1 that there is a linear relationship lbetween these two quantities
log k* = A - BK
(5) where A is a quadratic function of the volume fraction of organic solvent in the eluent, and B is a first-order function. It can be easily demonstrated from eq 3 that the same equation can be written in the case of complex solvent mixtures. The coefficients A and B are given by
i#J
(7) Equations 6 and 7 indicate that A is a second-order function of the solvent composiition, whereas B is a firsborder function. The effect of the interactions of the organic components of the mobile phase appears in the parameter A . Binary System Approach. We have indicated above that a complex solvent mixture can be prepared by using a certain combination of binary solvents, provided certain conditions are satisfied. The details of the calculations and the conditions are given in the Appendix in the case of a ternary mixture. The complex mixture containing the organic solvents S1, S2,..., S,, ..., and water is thus prepared by mixing adequate quantities of the binary systems BS1,BSz,...,BS,, .,., containing water and the organic solvents S1,S2, ,.., S I , ..,,respectively. The volume fraction of S, in the binary mixture BS, is x,. It is clear that there exisiri a simple relationship between X , (the volume fraction of S, in the complex mixture), x,,and w, (the volume fraction of the binary BS, in the complex mixture)
X I = x,w,
(8)
Equation 8 assumes that the mixing volume excess is zero. This is incorrect in most cases, but u s u d y the volume changes observed when mixing common pure solvents are small (
x1
(21)
and x1
> X d ( 1 - XZ)
(22)
Registry No. MeOH, 67-66-1; MeCN, 75-05-8;THF, 109-99-9; dioxane, 123-91-1.
LITERATURE C I T E D Jandera, P.;Colin, H.; Guiochon, G. Anal. Chem. lD82, 54, 435-441. Colln, H.; Krstulovic, A.; Yun, 2.; Gulochon, Q. J . Chromatogr., In press. Colin, H.; Guiochon, Q,;Jandera, P. Chromatographla,in press. Snyder, L. R.; Klrkland, J. J. I n Introduction to Modern Liquid Chromatography", 2nd ed.; Wiley-Interscience: New York, 1979. Glaich, J. L.; Kirkland, J. J.; Squire, K. M. J. Chromatogr. lD80, 199, 57-79. "Handbook of Chemistry and Physics", 61st ed.; CRC Press: Boca Raton, FL, 1980. McCormlck, R. M.; Karger, B. L. Anal. Chem. ID81, 52,741-744. Colin, H.; Schmlner, J. M.; Guiochon, G. Anal. Chem. lD81, 53, 625-632.
RECEIVED for review February 26,1982. Resubmitted August 19, 1982. Accepted November 18, 1982.
Retention Behavior of Some Aromatic Compounds on Chemically Bonded Cyclodextrin Silica Stationary Phase in Liquid Chromatography Kazuml Fujlmura, * Teruhisa Ueda, and Telichi Ando Department of Industrial Chemistry, Faculty of Engineering, Kyoto University, Sakyo-ku, Kyoto 606, Japan
The retentlon behavior of some aromatic compounds on silica gels wlth chemically bonded cyclodextrin molecules has been studied. The capacity factor of the sample generally increased by virtue of the specific Interaction between cyclodextrin units and sample molecules. The effects of (a) the substituents and thelr relative positlon on the benzene or naphthalene ring, (b) the spacer length, (c) the mobile phase, and (d) the variety of cyclodextrin were examlned. The parameters of the mobile phase were the kind of organic solvent used and the water content. The effect of addltlon of cyclodextrin to the mobile phase was also Investigated under conventional reversed-phase hlgh-performance liquid chromatography conditions In order to confirm the existence of inclusion equilibrium between cyclodextrln and sample molecules.
Cyclodextrins (CD's), which are known to be cyclic oligosaccharides consisting of six or more a-(1,4)-linked D-glucopyranose units, form inclusion complexes with a variety of organic molecules both in the solid state and in an aqueous solution. The stability of such inclusion complexes is, in general, most closely related to the fitness of the size of guest molecules to that of the cavity of cyclodextrin units, although many other factors such as van der Waals forces, dipole-dipole interaction, hydrogen bonding, and hydrophobic interaction
also play a role in determining the ease of complex formation (1-4). Many attractive features of cyclodextrins, such as found in covalent or noncovalent catalysis and enantiomeric catalysis, arise from these specific interactions between cyclodextrin units and guest molecules (1-4). The recent application of cyclodextrins as models for enzymes is also based on this specific inclusion property. In the field of chromatography, much attention is now being paid to the use of cyclodextrins as an additive in the mobile phase and/or the stationary phase bonded to a suitable support. Three review articles dealing with this subject have been published recently (5-7). In an attempt to use cyclodextrin as a stationary phase, several kinds of polymer gels have been prepared (6, 7). These polymer gels, however, require a long analytical time because of their low mechanical strength, and hence the application of these gels to modern high-performance liquid chromatography (HPLC) seems to be difficult. This paper describes a preparation of silica gels with chemically bonded cyclodextrins and the retention behavior of some aromatic compounds on these bonded silica gels. EXPERIMENTAL SECTION Reagents and Materials. a- and P-cyclodextrinsused were purchased from Nakarai Chemicals Co. (Kyoto, Japan). All aromatic compounds and silanes were of the highest quality available and were purchased from various suppliers. These
0003-2700/83/0355-0446$01.50/0C2 1983 American Chemical Society
