interaction indexes and solvent effects in reversed-phase liquid chromatography

5
442 Interaction Indexes and Liquid Chromatography Henri Colin” and Georges Gulochon Anal. Chem. 1983, 55, 442-446 Solvent Effects in Reversed-Phase 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 sig- nificant 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 es- timation 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 ac- curate 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 @)/VB and the interaction index. In the def- inition 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 chroma- tography 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 pro- cedure. 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 Xi are, respectively, the interaction index and volume fraction of solvent Si in the mixture. Equation 1 can be rewritten as follows: (2) 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 Imix = IH~O - XX,(IH~O - 4) I 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

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Page 1: Interaction indexes and solvent effects in reversed-phase liquid chromatography

442

Interaction Indexes and Liquid Chromatography

Henri Colin” and Georges Gulochon

Anal. Chem. 1983, 55, 442-446

Solvent Effects in Reversed-Phase

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 sig- nificant 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 es- timation 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 ac- curate 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. I t 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 @)/VB and the interaction index. In the def- inition 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 chroma- tography 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. I t 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 pro- cedure. 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:

(2)

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

Imix = IH~O - XX,(IH~O - 4) I

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

Page 2: Interaction indexes and solvent effects in reversed-phase liquid chromatography

ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983 443

are smaller (negative deviation) than predicted by the simple weighted sum of log k $ according to

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

( 5 ) log k* = A - BK where A is a quadratic function of the volume fraction of organic solvent in the eluent, and B is a first-order function. I t can be easily demonstrated from eq 3 that the same equation can be written in the case of complex solvent mix- tures. 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 usudy the volume changes observed when mixing common pure solvents are small (<5%).

If the logarithm of the capacity factor of the solute in the binary system containing the organic SI is log k‘,, then it can be shown by using eq 3 and 8 that

log k&,x = log k’, -I- (log@ - EO, log @,) + 1 1

(a, is the phase ratio of the column operated with the binary eluent BS,).

For the sake of simplicity, eq 9 can be rewritten as follows:

log k’rnix = CW, log k : +A@ + ASCE (10) I

The term A@ = log (1) - C,w, log @, is most often very small and can be neglected to a first approximation. Equation 10 indicates that log k d l x is simply related to log k:. The last term in the RHS of eq 10 is the solvent coupling effect term. Because I,* increases with increasing lipopholicity of SI , ASCE is greater for the methanol-tetrahydrofuran-water system than for the acetonitrile-methanol-water system for example. This is in agreement with experimental results. It is difficult to calculate the value of the coupling term since it involves the knowledge of the coefficient C,. I t must be noted, how- ever, that this term is always negative because the w, values are less than unity. This means that the capacity factors in complex systems obtained by mixing various binary eluents

log k’,,, = cwj log k’j i

Our experience is that this happens very often. However, positive deviations do occur, for instance when a methanol- water mixture with a high organic content is mixed with an acetonitrile-water mixture with a low organic content. Positive deviations have also been reported in the literature (5). In any case, the volume contractions upon mixing undoubtedly contribute more or less to the observed deviations. For the sake of simplicity of the treatment, these contractions have not been taken into account, but it is not sure that they are the only reason for the existence of positive deviations. An- other cause of deviations from eq 10 may arise from the as- sumption that A@ is negligible. I t is not difficult to calculate this term once the dead volume of the column is known. This volume depends on the composition of the mobile phase, and so does a. The results of the calculations indicate that in some cases A+ is positive, whereas in others it is negative, its ab- solute value being, however, most often smaller than 0.1. This value is sometimes large enough to correct for a positive de- viation, but there are still some cases where this deviation cannot be explained.

As far as the relationship between log k* and I is concerned, eq 6 and 7 can be rewritten as

where Ai and B; are the coefficients A and B corresponding to the binary system BSi. Equations 12 and 13 show that the coefficients Amix and Bmix for a complex mixture can be cal- culated from those pertaining to the binary solvents used to prepare the mixture. This means that the parameters of the calibration lines log k* vs. I (see ref 2) can be predicted in complex solvent mixtures.

Ternary Systems. In the case of a ternary mobile phase, the solvent coupling effect term is given by

The largest coupling effect (largest IASCEl) is obtained when w1 = w2 = 0.5. I t is obvious that ASCE is zero when w1 or w2 is unity, which corresponds to “pure” binary eluents. Equation 14 indicates that it is possible to define “regular” combinations of binary solvents, that is, combinations yielding ASCE = 0, whatever the value of w1 (and thus w2 since w1 + w2 = 1). This corresponds to

xJ,* = xJ2* (15)

In these conditions, the binary solvents have the same in- teraction index, and log k’rnix is exactly given by eq 11. I t is important to note that mobile phases having the same in- teraction index do not necessarily give identical retention patterns. Actually they are generally associated with sig- nificant selectivity differences that are due to specific solvation effects.

Equation 11 can thus be used to optimize the composition of a ternary mixture (or a more complex one), provided the retention data are known in binary solvents with the same interaction index. I t must be noted that such solvents gen- erally give the same range of capacity factors, and this suggests that this approach to complex solvents is very similar to the one of Glajch et al. (5 ) . The difference between their treat- ment and ours is that we assume eq 11 to be valid, whereas

Page 3: Interaction indexes and solvent effects in reversed-phase liquid chromatography

444 ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983

Table I. Various Combinations Investigated To Prepare the Ternary System 50: 20: 30 Water-Methanol- Acetonitrile

combination

A 501MeOH-H,O (40:60)1 t 50[MeCN-H2O (60:40)]

B 40[MeOH-H20 (50:50)] + 6O[MeCN--H,O (50:50)]

C 33.3[MeOH-H20 (60:40)] t 66.7 [ MeCN-H,O (4 5: 5 5) ]

D 28.61MeOH-H,O (70:30)1 + 71 .h [ MeCN-H ,O ( 4 2: 5 8 ) ]

E 25[MeOH-H20 (80:20)] + 75 IMeCN-H,O (40: 60) 1

Glajch et al. (5) use a modified simplex algorithm to relate log k’to the eluent composition. This necessarily gives more accurate predictions but requires rather sophisticated equipment. The possibility to optimize ternary and quater- nary mixtures with eq 11 and “regular” combinations of binary solvents will be soon reported (3).

EXPERIMENTAL SECTION The column was 15 cm X 4 mm home-packed with Lichrosorb

RP18, 5 pm (Merck Darmstadt, GFR). The pumping system was a Waters Model 6000A (Waters

Associates Milford, MA). Solutes were detected with a Waters 440 photometer. Injections were made with a Rheodyne 7125 sampling valve (Rheodyne, Berkeley, CA).

Solvent mixtures were prepared with doubly distilled water and Lichrosolv grade solvents (Merck) by pipetting. The mo- bile-phase compositions are given in volume percentages. The molar volumes of the solutes were calculated from the molecular weights and densities (6). The determinations of dead times were made with DzO (7).

RESULTS AND DISCUSSION In order to check the binary system approach to characterize

ternary mixtures, we carried out two series of experiments. First the “regularness” of various combinations of binary solvents yielding the same ternary mixture was examined. Second, the variations of ASCE with the composition of the ternary solvent were evaluated. From the results obtained during the second experiment, the validity of eq 12 and 13 was also tested. These experiments were carried out by using six solutes (phenylacetylene, p-dichlorobenzene, m-chloro- toluene, m-bromonitrobenzene, nitrobenzene, and benzonitrile) and various methanol-water and acetonitrile-water mixtures. The choice of the solutes is not arbitrary since they correspond to a set of calibration compounds (3). These solutes cover a rather large range of polarity.

“Regularness” of Combinations of Binary Solvents. The composition of the ternary solvent investigated is 5020:30 water-methanol-acetonitrile. This mobile phase can be prepared from several combinations. Each of them is char- acterized by the composition of the two binary solvents (xl and x 2 ) and in the relative amounts in the mixture (wl and w2). A given combination yields a given solvent coupling effect.

The “regularness” of a combination is estimated in terms of the average relative difference (%RSD) for the six solutes between the experimental capacity factors and those calculated from eq 11. The various combinations investigated are re- ported in Table I and the values of % RSD, as well as those of Aldz =

The general trend that can be seen in Table I1 is an increase of % RSD with increasing A1-2. This is in agreement with eq 9 which predicts that the larger the Al-2 values, the less “regular” the combination and then the less accurate the prediction given by eq 11. % RSD is very small for the combination B for which A1-2 is almost zero. This combination is almost perfectly “regular”. In the case of combinations A

- x212*)2 are given in Table 11.

Table 11. Accuracy of Precision of Capacity Factors with Ternary System ( 5 0 : 20: 30 Water-Methanol-Acetonitrile) from the Retention Data in Various Binary Systems

combination A B C D E

A 1-2 12.7 0.7 1.1 6.3 14.1 % RSD 23.3 2.2 3.6 1 5 19.1

OICHLOROBEUZENE

i

0 . 6 . e . 2 . 4

0 .L . 4 . 6 . a 1

Figure 1. Variation of the solvent coupling effect (ASCE) with the solvent composition w (=%e in the mixture A-B), where A = 50:50 methanol-water: (0) B = 44.355.7 acetonitrile-water; (A) B = 59.3:40.7 acetonitrile-water; (0) B = 74.3:25.7 acetonitrile-water.

and E on the other hand, is large, as well as % RSD. The large value of Al-2 for these two systems is due to the large difference between the interaction indexes of the binary solvents.

Variations of ASCE with Composition. In these ex- periments, the retention of the six solutes was measured in various ternary solvents obtained by mixing two given binary eluents in various proportions. Thus, in the equation giving ASCE (eq 14), the term (xlll* - X , I ~ * ) ~ is constant and the variation of ASCE with the composition of the ternary solvent is only due to wl (and w2). Since w1 + w2 = 1, the product w1w2 is maximal when w1 = w2 = 0.5, and it is equal to zero when wl or w 2 = 1.

The experiments were carried out with three pairs of binary solvents (one solvent being a mixture of water and methanol and the other a mixture of water and acetonitrile). In each pair, the methanol-water mixture contained 50% organic, and the composition of the acetonitrile-water mixture was adjusted in such a way that different values of (xJ,* - ~ ~ 1 ~ ” ) ~ were obtained, The composition of each pair, as well as the cor- responding values of ( x l I l * - ~ ~ 1 ~ * ) ~ , are given in Table 111. The variations of ASCE with the composition are shown in Figure 1 for the three pairs investigated. They deal only with three solutes, but the results obtained with the others were very similar.

The first observation that can be made is that, as predicted by the model, IASCEl is maximal when equal volumes of the

Page 4: Interaction indexes and solvent effects in reversed-phase liquid chromatography

ANALYTICAL CHEMISTRY, VOL. 55, NO. 3, MARCH 1983 445

Table 111. Characteristics of the Three Pairs of Binary Solvents Investigated

percentage organic modifier

methanol- acetonitrile- water water ( x , I , * -

pair mixture mixture x ,I, *IZ I 50 44.3 0.1 I1 50 59.3 16.8 I11 50 74.3 71.4

Table IV. Accuracy 07 the. Prediction of Retention (RSD) in Complex Mobile Phasesa

system I system I1 system I11 50(A) t 85(A) + 33.3(A) + 33.3(B) t

50(B) 15(C) 33.3(C) % RSD 1.9 7.1 4.0 A i - 2 0.54 1.57 0.95

(1 Key: (A) = methanol-water (60:4O), (B) = dioxane- water (50:50), (C) = tetrahydrofuran-water (30:70).

binary mixtures are used (wl = wz) . Moreover, the curve is almost symmetrical relaitive to the line w = 0.5. The values of (xlI1* - X J , * ) ~ given in Table I11 indicate that (i) for a given composition, ASCE must increase when going from pair I l,o pair 111, and (ii) ASCE must be zero for all ternary solvents prepared from the pair I , independently of their compositions. This is in agreement with the experimental data. From eq 14 it can be also predicted that ASCE is proportional to the molar volume of the solute. Thus, ASCE must be the largest for m-bromonitrobenzene and the smallest for p-dicholoro- benzene, although there must not be a large difference between the values obtained with the different solutes since their molar volumes are quite similar. The experimental results indicate that the largest effect is actually obtained with the di- chlorobenzene and the smallest with benzonitrile. I t thus seems that there exists il certain relationship between ASCE and k’which is not accounted for by the model. This suggests that the accuracy of the model is limited, especially when subtle effects are considered. This is also confirmed when one tries to calculate the value of the coupling term. From the data given in ref 1, it can be calculated that the value of ASCE corresponding to w1 = w2 I= 0.5 is about -0.05 (for V, = 1). The experimental values are 2 to 4 times larger. As previously mentioned, the model also predicts only negative values of ASCE whereas positive ones are sometimes observed. Nev- ertheless, a considerable advantage of this approach is that it permits the calculation of the composition of binary solvents yielding “regular” combinations, the interest of which is clear for optimization purposes.

The validity of eq 13--which was first suggested by ex- perimental results-is illustrated with the retention data of aromatic nitrogen bases. ‘I’hirty-six compounds were used for these experiments. The capacity factors of the compounds have been measured in vsu4ous solvents (8) and we only report in Table IV the average relative standard deviations (% RSD) between the experimental capacity factors and the calculated ones, along with the value of The calculation of % RSD is made according to

where n is the number of ;solutes and h iXPtl and k h&d are the experimental and calculated values of h’. The binary systems used had almost the same interaction index. It must be noted that for many azaarenes very large selectivity changes were observed when going from one solvent to the other (see ref

Table V. Values of A and B in Ternary Mobile Phases

Comparison of Experimental and Predicted

composition of the % %

Pair I ( x , I , * - x , I , * ) 2 = 0.1 solvent‘ Acalcd Aexptl RSD Bcalcd Bexptl RSD

80A- 20B 2.118 2.146 0.260 0.260 60A- 40B 1.887 1.901 0.237 0.232 0.7 40A- 60B 165 1.660 0.213 0.208 20A- 80B 1.424 1.420 0.190 0.190

Pair I1 ( x , I , * - X , I , * ) ~ = 16.8 80A- 20C 2.030 1.955 0.249 0.247 60A-40C 1.712 1.584 6.5 0.214 0,217 0.7 40A- 60C 1.393 1.221 0.179 0.178 20A-80C 1.075 1.020 0.169 0.170

Pair I11 ( x , I , * - X ~ I , * ) ~ = 71.4 80A- 20D 2.229 2.300 0.269 0.279

40A- 60D 1.990 2.019 0.239 0.243 20A- 80D 1.871 1.882 0.224 0.225

60A-40D 2.110 2.135 0.254 0.258 1.7

Key: A = methanol-water (50:50), B = acetonitrile- water (44.3:55.7), C = acetonitrile-water (59.3:40.7), D = acetonitrile-water (74.3: 25.7).

8). From these solvents, two ternary mobile phases and a quaternary one were prepared (see Table IV). It is predictable from Table IV that the smallest % RSD should be obtained with system I, whereas the largest one should be obtained with system 11. This is indeed what is evident from Table IV. However, for the three mixtures, AI+ is always very small, and since V,Cm2/2.3RT is usually less than 0.01, the coupling effect is negligible. This is confirmed by the small values of % RSD in Table IV.

Prediction of t he Parameters A,,, a n d B,,,. The va- lidity of eq 12 and 13 was evaluated by using the data obtained during the last series of experiments devoted to the variation of ASCE with the composition. The coefficients A and B were determined for all the ternary solvents prepared from the pairs I, 11, and 111 (see Table 111). They were also calculated using eq 12 (in which the coupling term was neglected) and 13. The results are reported in Table V.

The data indicate that the prediction of the coefficient B is remarkably accurate for all mixtures, whatever the system composition. As far as the coefficient A is concerned, the accuracy decreases when going from pair I to pair 111 and pair 11. This is not exactly what could be expected from the value of (xlIl* - X J ~ * ) ~ . We have no explanation for this fact. The very small values of % RSD obtained with pairs I and 111 reveal that very accurate estimations of the calibration lines can be made in complex solvent mixtures.

-

GLOSSARY A, B

k* to I C interaction constant I interaction index I R gas constant T temperature V molar volume x2 a, d , m

k’ capacity ratio k*

x2

parameter appearing in the equation relating log

corrected interaction index (=IHzo - I )

volume fraction of organic solvent S, in a complex

parameter appearing in the equation relating log mixture

k’ to the solvent composition

corrected capacity ratio (log k* = (log k’ - log

volume fraction of organic solvent S, in the binary @)/V*)

mixture water-S,

Page 5: Interaction indexes and solvent effects in reversed-phase liquid chromatography

446 Anal. Chem. 1083, 55, 446-450

wi

0 phase ratio

respectively.

volume fraction of the binary solvent containing

Subscripts m and s represent mobile phase and solute,

the organic S i in the complex mixture

APPENDIX The discussion will be limited to ternary solvents. It is

assumed that they are prepared by mixing the binary systems BS1 and BSz composed of water and the organic modifier SI and water and the organic modifier Sz, respectively. The volume fraction of Si in BSi is x i , the volume fraction of Si in the ternary is X i and the volume fraction of BSi in the ternary is win Taking into account the fact that w1 + wz = 1, it can be written that

w l x l = XI (17)

(1 - w1)xz = xz (18) If the composition of one of the binary systems is fixed (for

instance xl), then the composition of the other binary mixture and the value of w1 can be calculated by using the following equations:

w1 = XJXl (19)

x 2 = x1Xz/(x1- Xl) (20)

x1> x1 (21)

(22)

Equation 20 precludes that

and

x1 > X d ( 1 - XZ) Registry No. MeOH, 67-66-1; MeCN, 75-05-8; THF, 109-99-9;

dioxane, 123-91-1.

LITERATURE CITED 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,

"Handbook of Chemistry and Physics", 61st ed.; CRC Press: Boca 57-79.

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 in- creased by virtue of the specific Interaction between cyclo- dextrin 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 pa- rameters of the mobile phase were the kind of organic solvent used and the water content. The effect of addltlon of cyclo- dextrin to the mobile phase was also Investigated under conventional reversed-phase hlgh-performance liquid chro- matography conditions In order to confirm the existence of inclusion equilibrium between cyclodextrln and sample mole- cules.

Cyclodextrins (CD's), which are known to be cyclic oligo- saccharides consisting of six or more a-( 1,4)-linked D-gluco- pyranose 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

0003-2700/83/0355-0446$01.50/0

also play a role in determining the ease of complex formation

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 cyclo- dextrin 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

(1-4).

Reagents and Materials. a- and P-cyclodextrins used 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

C2 1983 American Chemical Society