Interaction indexes for prediction of retention in ... - ACS Publications

cavity in the solvent to accommodate for solute molecules. E(m-x)P is associated to the specific interaction between the solute and the mobile phase. ...
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Anal. Chem. 1902, 54, 435-441

435

Interaction Indexes for Prediction of Retention in Reversed-Plhase Liquid Chromatography P. Jandera Department of Analyflcal Chemlstty, Unlverslty of Chemlcal Technology, Leninovo ”am. 565, Pardubice, Czechoslovakia

H. Colin” and G. Gulochon Laboratolre de Chimie Analyfique Physique, Ecole Polytechnique, Route de Saclay, 9 1 126 Palalseau CGdex, France

A simple model for reversed-phase llquld chromatography Is descrlbed. It Is based on the predomlnant role of the moblle phase In the retentlon rrrechanlsm. The retentlon of a solute can be characterlzed by a slngle parameter: Its Interaction Index. The derlvatlon, dlscusslon, and verlflcatlon of the model are presented. The model Is slmple to use and makes posslble the predlctlon of retentlon data In varlous systems.

It has become quite trivial to write that reversed-phase liquid chromatography (RPLC) is certainly the most popular chromatographic technique. This is so true that Melander and Horviith (I) have recently suggested that one call normal-phase chromatography “reversed-reversed phase”. The consequence of such popularity is that much work has been devoted to develop tools allowing the prediction and the justification of retentilon data in RPLC. It is remarkable, however, that the models that have been proposed up to now are either too general and complex for practical applications or too limited (and more or less simple) to allow for a rapid and rather accurate pirediction of the retention in various conditions. The most exhaustive treatment of the retention mechanism in RPLC is that of IIorvdth and co-workers (2). Their thermodynamic model is based on the solvophobic theory of Sinanoglu (3). It is very rigorous and takes into account both the interactions in the mobile and stationary phases. It is also applicable to various modes of RPLC such as ion pairing for instance (4).Unfortuna1;ely such a rigorous model necessarily introduces a number of physicochemical constants which are often not known and are difficult and time-consuming to determine. This is not very convenient for a rapid prediction of the retention data. The situation seems to be similar with the molecular statistical theory of liquid adsorption chromatography recently presented by Martire and Boehm (5). Various less theoretical approaches have also been developed. They are more simple and easy to use for the analyst, but they are also less general. Either they are limited to certain classes of compounds or they require the previous knowledge of some characteristics of the solutes that necessitates some extra chromatographic measurements. Among these approaches, the most interesting are probably the use of the molecular connectivity introduced by Karger et al. (6) and of the solubility parameters suggested by Tijssen et al. (7). Baker (8)has also introduced the retention indices, similar to Koviits’ indices in gas chromatography, useful to tabulate retention data, but with[ a seemingly limited predictability. Various attempts have also been made to correlate retention data in RPLC with those in gas chromatography (9) or with partition coefficients in 1-octanol-water systems. It must be noted that a numerical approach based on a mathematical treatment, of retention data collected in some selected systems has recently been published by Kirkland et 0003-2700/82/0354-0435$0 1.25/0

al. (IO). It gives remarkably accurate estimates of the capacity ratios and is particularly well suited for mobile phase optimization. It necessitates, however, relatively important computer facilities which are not readily accessible to everybody. The model we want to present here is not theoretical but rather, at that stage, empirical. It has the advantage of being simple and it makes possible the prediction of retention data with an acceptable accuracy (5-20%), at least with the “simple” solutes (benzene ring substituted by one or two functional groups) we have used up to now. Because of its simplicity, the model is less rigorous and thus less accurate than a sophisticated one. It requires some simplifications and some basic assumptions which necessarily limit its range of application. The authors wish to point out that although some of the assumptions made in the derivation of the basic equations may be questionable, the agreement between the calculated and experimental values of the capacity ratios is often surprisingly good. The model is restricted to pure reversed-phase chromatography on nonpolar chemically bonded phases. No attempt has yet been made to extend it to such techniques as ion pairing and ligand exchange. The retention can be predicted in an absolute or relative manner. The absolute prediction requires the knowledge of the interaction index of the solute and of several characteristic parameters of the solvent. The relative prediction is more simple and often more accurate. It only requires the knowledge of the solute interaction index and of the calibration line (log k* vs. I) determined with some test solutes (three or four).

THEORY The basic assumption of the model is that the contribution of the stationary phase to the retention is much smaller than the contribution of the mobile phase as will be discussed below. This is in agreement with the idea-first developed by Locke (11) some years ago and now widely accepted-that the selectivity in RPLC is mainly controlled by the mobile phase. It is then possible to treat the retention in RPLC in a fashion very similar to the one used by Snyder for normal-phase chromatography (12). Snyder considers that the energy of transfer of the solute from the mobile to the stationary phase is mainly the result of polar interactions in (or at the surface of) the stationary phase. He assumes that the interactions in the mobile phase are to first approximation basically nonpolar and that the nonpolar part of the various interactions cancel each other

[E(s-x)~’ - E ( M - S )-~[E(M-x)~’ ~I - E (M-M)NPl

r=

0

(1)

E(M+), E ( M - ,and ~ , E ( M - are ~ ) stationary phase-solute, mobile phase-stationary phase, mobile phase-mobile phase, and solute-mobile phase interactions, respectively. Superscript NP indicates the nonpolar contribution of these interactions. If it can be assumed that the stationary phase in RPLC can only induce nonpolar forces (see below), then the energy 0 1982 Amerlcan Chemical Soclety

436

ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982

change, hE, associated with the transfer of 1 mol of solute from the mobile to the stationary phase is given by where superscript P stands for polar. Equation 2 is analogous to Snyder’s basic equation for normal-phase chromatography, where, however, the polar interactions are considered only in the stationary (more polar) phase. The situation is reversed for reversed-phase systems. Equation 2 is very important and deserves some comments. This equation is in perfect agreement with the solvophobic concept which postulates that the hydrophobic effect plays a fundamental role in RPLC. It indicates that the main contribution to solute retention originates from the mobile phase (E(M-M)‘). E(M-M)’ is directly related to the energy of cohesion between the solvent molecules and thus it represents the energy necessary to create a cavity in the solvent to accommodate for solute molecules. E(M-X)’ is associated to the specific interaction between the solute and the mobile phase. It appears with a negative sign in eq 2 which means that the larger the affinity of the solute for the solvent (the larger E(M-x)p) the smaller the energy change, AE. From the thermodynamic point of view, eq 2 does not involve a particular retention mechanism. The interactions associated with aqueous RPLC may involve dipole-dipole, hydrogen bonding, and dispersive forces. As seen above, each of the interactions E(,-,), E(M-x), ... can be divided in two contributions (i) the nonpolar part which should be nonspecific and approximately equal for all common organic molecules of similar size and (ii) the polar part which is associated with the presence of polar and/or polarizable functional groups (heteroatoms and multiple bonds). The energy of interaction between two molecules A and B is related to the charge distribution in each molecule. Unfortunately, none of the existing physical parameters such as dipole moment, dielectric constant, and so on can be directly used to quantify these interactions. In the particular case of charged species, the energy of interaction is proportional to the product of the electrical charge of each species. As far as neutral but polar or polarizable molecules are concerned, it is necessary to use some parameter other than the dipole moment to describe the charge distributions at the instant of interaction. Indeed, for a given molecule, the charge distribution depends on the nature of the other molecules interacting with it. To solve this problem, it could be useful to use some kind of polarity indices like those introduced by Snyder. However, it may be not possible to use Snyder’ indexes in such a medium as the aqueous mobile phase in RPLC. Therefore, it seems necessary to define a new parameter-the interaction index I-to describe the very peculiar polar interactions between the solute molecules and the aqueous media. As it wiU be seen below, it often turns out that the interaction index is similar to the polarity index. These indexes will be determined from retention data measured in aqueous/organic solutions. By definition, the energy of polar interaction between two molecules A and B whose interaction indexes are I* and IB, respectively, is given by Equation 3 introduces two coefficients CA and CB. This is necessary for two reasons. First, the coefficients correct for the scale chosen for the Is. Second, as it is the case for polarity indexes, it will perhaps be necessary at a further stage to define different selectivity classes. This originates from the fact that a given molecule A can interact with another molecule B in different ways, depending on the relative chemical functionalities of A and B. This cannot be fully accounted for by the indexes IAand IB and it thus requires the introduction of the Coefficients CAand CB. Because a given solute is characterized by a unique value of I, the distinction between the different

selectivity classes will appear at the level of the coefficients C. Investigations are in progress in this direction. Let Ix and I M be the interaction indexes of solute and mobile phase, respectively. IM is a function of the nature and concentration of the organic solvent. The free energy of transfer, AG,of one solute mole of volume Vx from the mobile to the stationary phase can be derived from eq 2 and 3 (4)

The coefficient C M characterizes the ability of the molecules of mobile phase to undergo polar interaction between each other via their specific functional groups. Cx is an analogous coefficient for solute molecules. It may be different from CM but should be constant at least for solutes in a given class of selectivity. The logarithm of the capacity ratio is related to AG by the well-known equation

AG

log k’= log 4 - 2.3RT

(5)

where 9 is the phase ratio. The mobile phase in RPLC is most often a mixture of water and an organic solvent. In analogy to Snyder’s polarity indexes in binary solvent mixtures (13),the interaction index of such a binary mixture can be written

IM= (1- X)IH,O+ XIOR,

(6)

where X is the volume fraction of organic solvent. I H z o and are the interaction indexes of water and the organic solvent, respectively. The combination of eq 4 , 5 , and 6 yields

IORG

log

k’= log f#J + -[IHzO - x ( I H z O - IORG)] 2.3RT (cM[IH,O - x ( l H , O - IORG)] - CXIxI (7) cM vX

Equation 6 can be rearranged as follows: log

k’= log

f#J

+ VXIH,OCM 2.3RT [CMIH,O- CxIxl -

Or more simply

+

log k’= a - TZX dX2

(9)

Equation 9 indicates that there is a quadratic relationship between log k’ and the volume composition of the mobile phase. Several workers have already reported and discussed such a dependence (14-16). The quadratic term dX2 can often be neglected as a first approximation because X is smaller than 1. Moreover, the ratio d l n is smaller than (IH~o - IoRcJ/(ZIH@ - Ix) which is not very different from (IHzo - I O ~ J J / Z I H ~ The values of dln are about 0.25, 0.31, and 0.38 for methanol, acetonitrile, and tetrahydrofuran, respectively (see below). In order to illustrate the effect of the quadratic term, we give on Figure 1 the plots of Y = X - p X 2 for p = 0.25 and 0.31. Because the capacity ratios are usually measured in a more or less restricted range of organic volume fraction (typically between X = 0.8 and 0.3), the plots log k’vs. X can be approximately fitted by an apparently satisfactory straight line. This is illustrated on Figure 1. The regression coefficients of these lines are quite good: 0.999 and 0.998 for p = 0.25 and 0.31, respectively. Accordingly, the quadratic term would have often been overlooked by the analysts. Equation 8 shows that the influence of the nature of the solute on the retention appears at two levels: (i) the intensity

ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982 tY 0.71

4 t

0,3

v

de h T Flgure 1. Plots of Y = X - pX2 for p = 0.25 (1) and p = 0.30 (2) The dotted lines are linear regressions of the points between X = 0.3 and X = 6.8. 0.2

04

0.6

of interaction (CxIx) and (ii) the volume of interaction (Vx). Equation 8 also indicates that the relative importance of the quadratic term increases with decreasing polarity of the organic solvent. This is in agreement with experimental observations. Equation 9 suggests that the coefficient a should increase with increasing size of the solute ( Vx), decreasing polarity of the solute (I),and decreasing temperature. Similarly, the coefficient n should increase with increasing size of the solute, decreasing polarity of the solute, decreasing temperature, and decreasing polarity of the organic solvent. The relationship between the capacity ratio and the interaction index can be derived from eq 7

Because Cx is constant for solutes belonging to the same selectivity group, then for such solutes, eq 10 is equivalent to log k‘/Vx - log 4/Vx

A

BIx

(11)

When second-order terms (with respect to X) can be neglected, A and B are given by A G C Y - C Y ~ XB = p - @ i X

(12)

The combination of eq 10 and 12 gives 2.3RTa = CM21Hzo2

2.3RTCYl =2cM2IHzO(IHZO- IORG)

2.3RTP = CMCXIH~O 2.3RTP1= CMCX(IH,o - IORG) (13) The following relationship can be derived from eq 13

W/P1

= a/a1

(14)

Equation 11predicta a linem variation of the specific logarithm of the capacity ratio log 12* = (log k’ - log 4)/Vx of a series of compounds (belonging to the same selectivity class) on a given system with the interaction index. This equation can be used either to estimate the capacity ratio of solutes whose Is are known (assuming that A and B have been measured) or to calculate the values of interaction indexes from the retention data. Equation 1.4 can be used to check the model. Two assumptions made in the derivation of the above equations can be argued with. First, it is a rather crude approximation to consider that only dispersion forces are involved

437

in the stationary phase. It is indeed well-known that, on the one hand, all the OH groups on the silica matrix cannot be derivatized and, on the other hand, as recently shown by McCormick and Karger (18)and Slaats et al. (19),a significant amount of the organic solvent is extracted by the stationary phase. This organic solvent can sometimes play a very significant role (20) on the retention. The free OH groups can also induce particular retention patterns (21). Second, it is sometimes incorrect to neglect the second-order terms in eq 10; the coefficient A being in fact, a quadratic function of the solvent composition. It is remarkable, however, that the experimental plots of A vs. X can be most often fitted by straight lines with very good regression coefficients (>0.9999). It must be kept in mind, in any case, that extrapolations of the plots A and B vs. X far from the range where measurements have been made can give large errors, especially close to X = 1and X = 0 where significant deviations from linearity have often been observed.

EXPERIMENTAL SECTION Three different reversed-phase materials were used Lichrosorb RP 18 and RP 8 (Merck, Darmstadt, GFR) and Hypersil ODS (Shandon, Runcorn, England). The columns (15 or 25 cm long, 4 mm i.d.) were home packed. Various combinations of liquid chromatographic pumps and detectors were used. The pumping systems included Waters Model 6000 A (Waters Associates, Milford, MA) and Tracor Model 995 (Tracor, Austin, TX). UVabsorbing solutes were detected with either a Waters 440 detector or a LDC Spectromonitor I11 operated at 254 mm (LDC, Riviera Beach, FL). Nonabsorbing solutes were monitored with a refractometer R401 from Waters. Injections were made with Rheodyne 7125 sampling valves (Rheodyne, Berkeley, CA). The determination of dead times was made with D20 injections according to McCormick and Karger (18). The mass of material in the column was calculated after emptying the columns and drying and weighing the particles. Solvent mixtures were made with doubly distilled water. Methanol (MeOH), acetonitrile (MeCN),dioxane (DIOX),and tetrahydrofuran (THF) were Lichrosolv quality from Merck. The compositions are given in volume percent of organic. The mixtures were prepared by pipetting. The solute molar volumes, V,, were calculated from the molar weights and densities (22). The unit chosen is 100 cm3. The definition of the phase ratio will be discussed below.

RESULTS AND DISCUSSION (1) Interaction Index Scale. Interaction indexes are not absolute physicochemical quantities and it is necessary to define a scale based on several adequately chosen standard compounds. Rather than to define a scale of I based on arbitrary values, we tried to determine if Snyder’s polarity indexes correlate with log k*. Indeed, because the Ps are a measure of the polarity of the solute, it is reasonable to expect that there is a more or less close relationship between the Is and Ps. But it is also likely that the values of the Ps must be-at least-sightly adjusted to yield the I values, because of the aqueous medium in which the Is are defined (in contrast to the Ps).In order to make this fine tuning, we determined the Is from the lines log k* vs. P and calculated the average value of I for a given solute in as many different mobile phases as possible, using various column packing materials. The solutes chosen for this purpose were UV absorbing (ease of detection) belonging to the same selectivity group as defined by Snyder. The reason for the choice of the same selectivity group was to ensure that the solutes would undergo the same type of interaction with the mobile phase (same value of Cx). The solutes were also selected to give a convenient range of capacity ratios (k’values up to 10-20). The experiments were made with benzene, toluene, nitrobenzene, acetophenone, and anisol. The polarity indexes and molar volumes are given in Table I. The results of the determination of the Is are given in Table 11. The data suggest that the scattering of the values

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ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982

Table I. Polarity Indexes and Molar Volumes of Reference Solutes polarity molar solute indexa volumeb toluene benzene anisol nitrobenzene acetophenone a

According to Snyder ( 1 3 ) .

2.3 3.0 3.9 4.5 5.5

1.063 0.889 1.086 1.023

I

1.169

Unit is 100 cm3.

4 4\

I

\

L5 !

\5

Table 11. Average Values of the Interaction Indexes of Reference Solutes solute

rfr

re1 std dev, %

toluene

2.25a 4.2a 2.25b 1.5b 6.8 benzene 3.08 5.0a anisol 3.92a 3.91b 3.5b 5.0a nitrobenzene 4.46a 4.47b 3.5b 4.6 acetophenone 5.52 a Values obtained by using the five standards. Values obtained by using only toluene, anisol, and nitrobenzene. is rather small (about 4-5% for 53 determinations). It must be noted that the determinations of I were made with 3 stationary phases and about 15 mobile phase combinations of both different concentrations and nature (MeOH, MeCN, THF, DIOX) of the organic modifiers. The comparison of Tables I and I1 seems to indicate that the Is are very similar to the Ps. This is not in fact a general situation, and, for instance, the values are very different in the case of the organic modifiers. The linearity of the plots log k* vs. I is most often very good. The average value of the correlation coefficient for the 53 regressions is 0.985 f 2%. It must be noted that in some cases lower values of regression Coefficients are obtained (< 0.950). This usually happens when the organic concentration is larger than 0.8 or smaller than 0.3. The “nonlinear” behavior also depends on the organic modifier; T H F generally gives poorer regressions than MeOH and MeCN. The linearity is, however, most often fairly good, as in more than 85% of the cases the correlation coefficient is larger than 0.995. A closer examination of the data reveals that some solutes could be omitted in the set of “calibration” standards. Although the results are correct with acetophenone, it is probably better not to use this compound because of the possibility of the acetyl group forming aggregates with water molecules (31). The relatively large standard deviation of the interaction index of benzene (see Table 11) also suggests that this solute is perhaps not a good choice. It was indeed observed that when the organic concentration is larger than 0.6-0.7, the value of Ibmnecalculated from the regression lines log k’/ V , vs. P is often smaller than 3.3. The second set of data on Table I1 is obtained by using only toluene, anisol, and nitrobenzene as calibration solutes. It appears that the values of I are the same as previously (calibration with five compounds). As could be expected, the relative standard deviations of the determinations of the Is are smaller. With this set of 3 standards, the average correlation coefficient for the 53 regressions is 0.993 f 1%. This means that, at least for the compounds used, the interaction indexes make possible the quantification of the retention in various conditions. This does not mean, however, that these solutes are convenient for calibration purposes. The correct selection of reference standard compounds is very important for the predictive power of the present model. In first approximation, the model neglects the specific interactions between the solutes and the

1.0

log q

1.0

k7vx

(D

ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982

439

Table 111. Lichrosorb RIP 18 parameter

methanol-water

XU

0.80, 0.71, 0.60, 0.50, 0.45, 0.40 3.378 3.580 P "b 0.999 R 0.31 5 41 0.188 P *c 0.985 ( ~ / R I)/("/ai) 1.78 IORG 22.25 cx2 x 102d 3.96 c M 2 x 103d 1.77

"

acetonitrile-water

dioxane-water

tetrahydrofuran-water

0.66, 0.59, 0.50, 0.43, 0.35

0.70, 0.60, 0.55, 0.50, 0.40 0.40 3.033 3.572 1.000 0.297 0.175 0.994 2.00 19.46 3.92 1.82

0.60, 0.50, 0.45, 0.40, 0.35

2.783 3.351 1.000 0.225 0.126 0.987 2.15 18.85 2.45 1.67

a Values of X used for the regressions A vs. X and B vs. X. of B vs. X. Unit: kcal :K.

Regression coefficient of A vs. X .

2.733 3.860 0.989 0.229 0.184 0.982 1.76 13.92 2.59 1.64

Regression coefficient

--

Table IV. Lichrosorb RIP 8 parameter methanol-water X

0.70, 0.60, 0.50 0.50, 0.40

3.037 3.540 1.000 0.238 P PI 0.131 P 0.988 (PlOl)(.l"l) 2.1 2 IORG 19.75 cx2 x l o 2 2.52 cM2 x 103 1.82 01

p"'

Table V. Hypersil ODS methanolparameter water

X 01 "1

P

a 6,

0.80, 0.70, 0.60, 0.50, 0.45, 0.40 2.783 3.580 0.999 0.315 0.188 0.985

acetonitrile-water

dioxane-water

tetrahydrofuran-water

0.80, 0.70, 0.60, 0.50, 0.40, 0.35, 0.25 2.472 3.025 0.997 0.182 0.109 0.979 2.04 18.37 2.09 1.48

0.80, 0.50, 0.40, 0.30, 0.20

0.475, 0.45, 0.40 0.35, 0.30, 0.25 2.766 4.488 0.999 0.213 0.204 0.995 1.70 8.95 2.21 1.66

2.459 3.030 0,999 0.221 0.107 0.978 2.06 18.18 2.68 1.62

Table VI, Average Values of Solvent Interaction Indexes acetonitrilewater 0.66, 0.60, 0.50, 0.40, 0.30, 0.20 2.783 3.351 1.000 0.225 0.126 0.957 2.15 17.76 2.45 1.67

influence on the linar regressions of the As than on those of the Bs (mobile phase composition errors for instance). It is thus better to use the vallues of a and a1rather than those of and p1to calculate L ~ R G(eq 15). Some errors in the A and B values (and consequently in a,al,p, and p1values) may be due to the neglection of the quadratic term (with respect to X)in the regressions according to eq 8. The average values of 1,3RG are reported in Table VI. The weakest solvent is MeOH MeCN and DIOX are approximately equivalent, and T H F is much stronger. This is in agreement with usual ob!servation on reversed-phase chromatography. Hydrophobicity increases from MeOH to T H F and the term E(M-M)' in eq 2 decreases from MeOH to TMF. It is also clear from Tablo VI that, except for THF, there is a good agreement between the values of IORG obtained with different materials. Complementary experiments are currently carried out to confirm the value of ITHF (which seems to be closer to 14 than to 9).

F ~ R G re1 std dev, %

solvent methanol acetonitrile dioxane tetrahydrofuran a

21.12 18.33 18.82 11.44a

6.0 3.0 4.8 30.7a

Only two values: 13.92 and 8.95.

It is difficult to explain and justify the values obtained for CM2 and particularly for Cxz because of the more or less good quality of the linear regressions E vs. X.The values calculated for different situations are relatively close (for Cxz on the one hand and CM2 on the other hand) with, however, some small differences. Because these coefficients are only related to mobile phase interactions, they must be independent of the stationary phase. This is approximately observed. The small scattering of the data is perhaps due to the choice of the phase ratio (see below).

DISCUSSION The first results so far obtained with the model are encouraging and seem to indicate that, if the model is contestable from the theoretical point of view, it could be nevertheless useful from the practical point of view. Some new results will be soon published (17) showing that the model can explain the particular behavior of some solutes in reversed-phase systems (homologous series, change in elution order, ternary solvents, ...). The basic assumption that the contribution of the stationary phase to the retention process is negligible can be undoubtly refuted in some cases. We will justify this assumption by discussing two points: the role of the extracted modifier and the contribution of the packing material (unreacted silanols).

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ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982

1. Contribution of the Extracted Modifier. It has been recently shown that the nonpolar stationary phases selectively extract the organic component(s) of the mobile phase (1419). This introduces the theoretical possibility of a particular solvation in the stationary phase or at least of lateral interactions between adsorbed organic molecules and solute molecules. Slaats et al. (30) have already reported that the presence of organic modifier on the stationary phase has a strong influence on the activity of the solute and thus affects retention. Tanaka et al. (20) also believe that the solvent molecules extracted can play a significant role in the retention. The actual situation depends on the organic modifier and on its concentration. In the cme of methanol, the extracted amount is relatively small and not sufficient to build up a complete monolayer (23) assuming flat adsorption of the solvent molecule on the packing. The possibility of lateral interaction with adsorbed methanol is thus limited. Moreover, these interactions are of the same nature than those with water molecules in the mobile phase (same chemical functionality) but they are much weaker. It is thus possible to a first approximation to ignore the adsorbed methanol, although this is probably incorrect in some cases. The situation can be different in the case of acetonitrile and particularly tetrahydrofuran. These solvents have not the same chemical functionality as water and can develop some kind of specific polar interactions. Besides, and especially in the case of tetrahydrofuran, the extracted solvent can behave like a liquid stationary phase with the possibility of much stronger London type interactions than with methanol. The experimental results show that, if the model behaves in general still fairly well with acetonitrile (and dioxane), it often gives erroneous predictions (deviation between expected and predicted values larger than 1620%) with tetrahydrofuran. More generally speaking, it is likely that the more lipophilic the organic modifier, the less accurate is the model. The addition of small amounts of such a modifier (which is often a third component of the mobile phase) can result in large Gibbs surface excesses. It is likely that the chromatographic systems are then closer to liquid-liquid ones (the stationary phase being alkyl bonded silica coated with the hydrophilic modifier) than to "regular" reversed-phase ones. The existence of this new stationary phase can then create a new selectivity. This is probably what happens when McCormick and Karger (24) use hexafluoro-2-propanol, trifluoroethanol, trichlorotrifluoroethane, or chloroform. In such conditions, the model will obviously fail. 2. Contribution of the Packing Material. As far as free OH groups are concerned, theoretical and experimental reasons conclude that it is not possible to react all the silanol groups. Their chromatographic role has been often vaguely discussed but Melander et al. (21) have recently given strong experimental evidence of their role. It is likely, however, that the free silanols contribute significantly to the retention only when very polar solutes are involved. It is not unreasonable to expect that for most solutes chromatographed on good quality packings (in terms of free OH groups, that is, polymeric materials or monomeric ones with high coverage and end capping), unreacted silanols have only a secondary (and often negligible) role. Moreover, when chromatographing very polar solutes capable of interaction with residual OH groups, it is a common practice to add small amounts of adequate compounds in the mobile phase to saturate these groups (such as triethylamine for instance). The addition of such chemicals does not modify the gross properties of the mobile phase while it deactivates the stationary phase. It thus seems reasonable to consider the stationary phase as a passive acceptor of solute molecules which are repelled

Table VII. Comparison of the Retention Pattern ( k ' ) on Three Reversed-Phase Materialsa k' on

Lichrosolute toluene benzene anisol nitrobenzene acetophenone

sorb RP 18

Lichrosorb RP 8

carbon

3.11

1.76

1.11

1.97 1.82 1.17

1.10 1.04

0.71 1.26 2.95 2.16

0.63 0.51 a Mobile phase = 70:30 MeOH-H,O (v/v). 0.95

from the mobile phase by virtue of strong polar interactions between mobile phase molecules (solvophobic effect). This is a very particular situation and it means that the model is restricted to nonpolar Chemically bonded phases. In the case of more or less polar phases as well as in the case of carbon adsorbents, the stationary phase contribution to the retention can be of great importance. For instance, this appears in Table VI1 where the capacity ratios of the calibration solutes measured on three different columns (silica C18, C8 and carbon) using the same solvent are given. The elution order on the bonded phases is almost the opposite of the one on carbon. The nitro and keto groups strongly enhance the retention of the benzene ring on carbon materials because of the polarizability of the carbon surface (%),whereas these polar groups significantly decrease the retention on CISand Cs packings because of the stronger interactions with the mobile phase. The situation is similar with Spheron materials (26,27), the retention being the sum of a reversed-phase mechanism and the adsorption on one of the functional groups of the stationary phase. Either mechanism can predominate depending on the solutes and the mobile phase polarity. 3. Determination of the Phase Ratio. The process of transfer is usually characterized by the distribution constant K (the ratio of the solute concentration in both phases). The relationship between the capacity factor k' (the ratio of the masses of solute in the two phases) and K is

k'= K $

(17)

where $ is the phase ratio. Although the determination of the phase ratio is relatively easy in pure liquid-liquid chromatography, the situation is much more complex in reversed-phase chromatography with chemically bonded materials. In any case, the choice of 4 must be in agreement with the definition of K . For reversed-phase chromatography, Melander and Horvlth (1) have recently suggested the expression 4 as the ratio of the surface area of the adsorbent (m2)divided by the column dead volume (cm3). Kiselev and co-workers (%), on the other hand, used the mass of material (8) in the column divided by the column dead volume, as is usual in adsorption chromatography. K is thus expressed in g/cm3. Other workers (29) have simplified the problem by choosing 4 = 1. If reversed-phase materials are supposed to be liquid phases deposited on silica supports, then the phase ratio (4LL)is the volume of the organic material divided by the volume of the mobile phase in the column. In the other alternative, the retention mechanism is considered to be of the liquid-solid type and the phase ratio is the ratio of the number of solvent molecules in a monolayer a t the surface of the packing to the number of mobile phase molecules. Regardless of the retention mechanism with chemically bonded phases, the choice of 4 results from the definition of K . This may be done in several different ways and the formal thermodynamic description of the distribution phenomena remains correct. The definition of K should be in agreement

ANALYTICAL CHEMISTRY, VOL. 54, NO. 3, MARCH 1982

with the molecular mechanism of retention (partition-adsorption). This point has not been yet fully elucidated but it is currently investigated (23). From the practical point of view, the choice of $ must be such that it allows a simple use of the model by practicing chromatographers and thus must not require time-consuming additional physicochemical measurements. For the sake of convenience, we have defined the stationary phase as tho fraction of the column that is not occupied by the mobile phase. This results in the following definition of the phase ratio:

d~= ( V G -VM)/VM

(18)

where VG and VM are the geometric (empty column) and dead volume of the column. The phase ratio as defined in eq 18 is a dimensionless quantity and can be rapidly determined, because VGcan be simply calculated from the length and inner diameter of the column. This definition of $ implies that the distribution constant is understood as the ratio of solute concentration in the bulk volume of the packing material (i.e., support bonded phase) to that in the mobile phase contained in the column. Such a formal definition of $ of course does not imply any exact idea of the location of solute molecules on (or in) the layer of the bonded moieties. It is obvious that the solute molecules are located in a more or less thick layer on the surface of the bonded phase or that they penetrate more or less into the bonded hydrocarbonaceous chains but that they are not present in the bulk packing material. However, there is no clear and unambiguous picture of the geometry of this layer, the volumn of which would be thus very difficult (if even possible) to calculate and to use in practical applications of this simple retention model. Therefore, it does not seem that the definition of $ given above for reversed-phase chromatography will give less accurate results than the value in a gram of adsorbent per milliliter of mobile phase, as it is currently done in normal-phase chromatography (where the solute molecules are on the surface of the packing and cannot penetrate into the adsorbent matrix). The use of VM, for VM in eq 18 seems to be justified for the following reason. The dependence of VM (and of $) on the composition of the mobile phase cannot be simply expressed in mathematical terms. VM usually changes within relatively narrow limits (1&20%) and a constant value of VM could be used for the sake of simplicity as a first approximation. Using VM, would yield a minimum and constant contribution of the volume of the occluded liquid (which can be understood as a stagmuit mobile phase) to the volume of the packing material (VG - VM) and thus it seems to be more sutiable for this purpose than other values.

+

CONCLUSION The main assumption of this model is that the retention in reversed-phase liquid chromatography is primarily controlled by the interaction8 in the mobile phase. This seems to be confirmed by variouri solvent conditions, at least for the compounds studied. In most cases, the role of the stationary phase (bonded moieties, organic solvent extracted, and residual silanol groups) is secondary and can be neglected. This is a limitation of the model which cannot be used when lipophilic modifiers are introduced in the solvent. The present model is more empirical than theoretical and it cannot give very accurate retention predictions (about 5-20% accuracy). Particularly, it cannot account for subtle selectivity changes which occur upon addition of small quantities of certain compounds to the mobile phase. Nevertheless, the model is

0

441

simple, requires few calculations and generally gives a good estimate of the retention.

ACKNOWLEDGMENT The authors acknowledge Cs. Horvfith (Yale University, New Haven, CT) for his useful comments.

APPENDIX The interaction index of water cannot be directly determined by injection of water. Because there is a simple relationship between I H ~ and OI ~ R (eqGE), IHzo can be readily obtained from IORG when IoRG is known. IMeOH was calculated from the retention data of linear alcohols. It will be shown that there is a linear relationship between IxVx and the number of carbon atoms (nC)in a homologous series (17). The Is of the alcohols are calculated in five different mobile phases (with the Lichrosorb CIS column) from the calibration lines obtained with the test compounds (including benzene but not acetophenone). The average value of the products IxVx are then used to calculate the regression line IxVx-nC. IMeOH is obtained from this line.

LITERATURE CITED Melander, W.; HorvBth, Cs. In "High Performance Liquid Chromatography. Advances and Perspectives";Horvath, Cs., Ed.; Academic Press: New York, 1980; Vol. 2. HorvBth, Cs.; Melander, W.; MolnBr, I. J . Chromafogr. 1976, 125, 129-156. Sinano@u, 0. I n "Molecular Associations In Biology"; Pullman, B., Ed.; Academlc Press: New York, 1968 HorvBth, Cs.; Melander, W.; Molnlr, I . ; Molnar, P. Anal. Chem. 1977, 49,2295-2305. Martire, D. E.; Boehm, R. E. J. Liq. Chromatogr. 1980, 3 ,753-767. Karger, B. L.; Gant, J. R.; Hartkopf, A,; Weiner, P. H. J . Chromafogr. 1976, 128,65-78. Tijssen, R.; Bllliet, H. A. H.; Schoenmakers, P. J. J . Chromafogr. 1976, 122, 185-203. Baker, J. K. Anal. Chem. 1979, 51, 1693-1697. Slaats, E. H.;Heemstra, S.; Poppe, H., to be submitted for publication. Glaich, J. L.; Kirkland, J. J.; Squire, K. M. J . Chromafogr. 1980. 199, 57-79. Locke, D. C. J. Chromafogr. 1988, 35,24-36. Snyder, L. R. In "Principles of Adsorption Chromatography"; Marcel Dekker: New York, 1968. Snyder, L. R.; Klrkland, J. J. In "Introduction to Modern Liquid Chromatography", 2nd ed.; Wlley-Interscience: New York, 1979. Schoemakers, P. J.; Bllllet, H. A. H.; De Galan, L. J . Chromatogr. 1979, 185, 179-195. Melander, W.; Chen, B. K.; HorvBth, Cs. J. Chromafogr. 1979, 185, 99- 109. Gant, J. R.; Dolan, J. W.; Snyder, L. R. J. Chromafogr. 1979, 185, 153-1 77. Colin, H.; Jandera, P.; Guiochon, G., to be submitted for publication. McCormick, R. M.; Karger, B. L. Anal. Chem. 1980, 52,2249-2257. Slaats, E. H.; Markowsky, W.; Fekete, J.; Poppe, H. J. Chromafogr. 1981, 207,299-323. Tanaka, N.; Sakagaml, K.; Araki, M. J. Chromatogr. 1980, 799, 327-337. Melander. W.; Stoveken, J.; HorvBth, Cs. J . Chromafogr. 1980, 199, 35-56. "Handbook of Chemistry and Physlcs", 6lst ed.;The Chemical Rubber Co. Press: Cleveland, OH, 1980. Colin, H., unpublished results. McCormick, R. M.; Karger, B. L. J . Chromafogr. 1980, 199,259-273. Colln, H. Thesls, Parls, 1980. Jandera, P.; ChurBEek, CBslavskq, J.; VoJBEkovB,M. Chromafographia 1980, 13,734-740. Jandera, P.; ChurBEek; J.; Szabo, D. Chromafographia 1981, 14, 7-12 Davydov, V. Ya; Gonzalez, M. E.; Kiselev, A. V.; Lenda, K. Chromafographia 1981, 1 4 , 13-18. Hemetsberger, H.; Klar, H.; Ricken, E. Chromatographia 1980, 13, 277-286. Slaats, E. H.; Kraak, J. C.; Brugman, W. J. T.; Poppe, H.J. Chromatogr. 1980, 149, 225. Vontor, T.; Drobilic, V.; Socha, J.; Vecera, M. Collect. Czech. Chem. Commun. 1974, 39,281-285.

RECEIVFD for review June 8,1981. Accepted October 21,1981.