Role of the Solvent in Liquid-Solid Chromatography-A
Review
L. I?.Snyder Technicon instruments Corp., Tarrytown, N. Y. 1059 1
During the past 10 years, several different physical models have been proposed for adsorption in liquid-solid chromatography (LSC), in an effort to explain the role of the solvent in this separation method. A comparison is made here of three of these models, and a critical evaluation is given of their respective advantages and limitations. It Is concluded that the original models of Snyder and Soczewinski are complementary in providing good descriptions of two llmiting cases: adsorption on silica from strong solvent mixtures (Soczewinski) and adsorption on alumina (Snyder). Minor modification of the derived equations from each of these two models leads to essentially equivalent predictions of the effect of a change in solvent on solute retention. However the model of Soczewinskl Is somewhat limited in its range of application. A third model, that of Scott and Kucera, appears to be in disagreement with reported experimental data. As a result, the approach outlined by these authors for the selection of a "rational series of solvents" for gradient elution seems open to question. A practlcal summary of what is now known concerning solvent effects in LSC Is given, with attention to the problem of designing solvent programs for use in gradient elution.
The way in which a given solvent affects separation in liquid-solid chromatography (LSC) is of .obvious practical importance. For adequate resolution in either isocratic or gradient elution, solute retention is normally controlled by choosing the right solvent(s); e.g., see ( 1 ) .An adequate understanding of the role of the solvent in determining LSC retention must in turn be based on a realistic physical model of the adsorption process in practical LSC systems. One such model was developed by myself during the early 1960's [see (2) for a review]. Somewhat later, an alternative approach was suggested by Soczewinski ( 3 ) .More recently, a third description of the role of the solvent in LSC has been offered by Scott and Kucera ( 4 ) ,for use in the design of a solvent series for gradient elution. So far little attempt has been made to compare or contrast these three treatments with respect to their validity or universality [but see (511. I t is my goal here to provide a critical comparison of these various LSC models, with emphasis on their practical implications. Experimental tests of each model will be attempted, since comparisons of experiment with theory provide the ultimate test of the validity of a given model. I will not attempt an exhaustive review of the relevant experimental literature in this connection, but will rely largely on previous data summaries and selected published work. Aside from the question of the relative adequacy of these various theories of solvent effects in LSC, I hope also to point out some limitations in our present knowledge. Hopefully this will encourage further experimental work in criti(1) L. R. Snyder and J. J. Kirkland, "Introduction to Modern Liquid Chromatography," Wiley-lnterscience, New York, N.Y., 1974, Chap. 8, 13. (2) L. R. Snyder, "Principles of Adsorption Chromatography," Marcel Dekker, New York, N.Y., 1968, Chap. 8. (3) E. Soczewinski, Anal. Chem., 41, 179 (1969). (4) R. P. W. Scott and P. Kucera, Anal. Chem., 45, 749 (1973). (5) L. R. Snyder, Quoted in ref. ( 3 )
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This article is a special review which, although not appropriate for periodic review, makes a contribution by integrating, evaluating, or correlating past research. Such reviews are not regular features in the technical section: however. they are not arbitrarily excluded just because they deal with new evaluations of past data rather than presentation of new data. cal areas. Finally, I will summarize some practical conclusions which now appear well established as valid guides for the selection of solvents in isocratic or gradient elution.
THE THREE LSC MODELS: A REVIEW The various LSC models under discussion are summarized in Table 1. The basic Snyder model (I) can be successively modified (Ia and Ib) to.give more general and accurate predictions of solvent effects, as indicated in Table I. The starting Soczewinski model (11) can likewise be extended (model IIa) for increased generality. The Scott and Kucera model (111)so far exists in a single version. Snyder Model I. All three models of the adsorption process (2-4) assume that the adsorbent surface (or adsorption sites) is completely covered by adsorbed solute molecules X and/or solvent molecules S; i.e., an adsorbed monolayer is postulated. Model I further assumes normally flatwise adsorption of all molecules, so that if the molecular areas of solute and solvent are A , and A,, respectively, and n = A,/ A,, the stoichiometry of the adsorption equilibrium becomes
x, + It s,
x, + )i s,
F===
(1)
Here m and a refer, respectively, to molecules in the mobile and adsorbed phases. Thus adsorption of a molecule of X results in the displacement of n molecules of initially adsorbed solvent. The next assumption of model I is an effectively homogeneous adsorbent surface, so that the adsorption energies of solvent molecules a t different positions on the surface are constant. This is usually true for adsorption on alumina (except for binary solutions of certain very strong solvents), but it is less often true for silica as adsorbent. However we will see that this complication can be handled rather easily (model 1a)-without departing from the conceptual simplicity of model I. The final assumption is that solution energy terms, involving interactions between X and S in the mobile phase, are cancelled by similar interactions in the adsorbed phase. This premise is difficult to accept by those trained in classical solution thermodynamics, but a large mass of experimental data suggests its reliability as a first approximation, in the case of the common polar absorbents (e.g., silica, alumina, and other inorganic solids). Given the above starting premises, we can derive an expression (2) for the variation of solute retention as a function of solvent strength:
log ( k 2 / h , ) = @ ' A ,( € 1
~
€2)
(2 1
According to Equation 2, the ratio of capacity factors ( k 2 / kl) for a solute X and solvents 1 and 2 is given as a function of an adsorbent activity parameter cy', the solute molecular
ANALYTICAL C H E M I S T R Y , VOL. 46, NO. 1 1 , S E P T E M B E R 1974
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Table I. S u m m a r y of Various Adsorption Models f o r Use in LSC I. Snyder ( 2 )
Assumes monolayer adsorption, continuous and homogeneous surface, and cancellation of solute-solvent interactions in solution and adsorbed phases. Adsorption equilibrium given by Equation 1, and role of solvent given by Equations 2 and 3. Applicable for alumina as adsorbent (most cases), or for silica and weakly adsorbed solutes and solvents. Useful for predicting solvent strength or solvent programs for gradient elution. la. Snyder ( 2 )
Same as model I, except values of A , and nb are larger than calculated molecular areas. This largely corrects for surface inhomogeneity, and extends the approximate applicability of Equations 2 and 3 t o all LSC systems (including silica with strong solvents). Useful for solvent strength and solvent program predictions. Ib. Snyder ( 2 )
Same as model Ia, except secondary solvent effects are taken into account. This removes any assumptions of surface homogeneity or cancellation of solvent-solute interactions. Role of solvent is given by Equations 3 and 4, with secondary solvent term ( 3 2 - A l ) given by additional relationships such a s Equation 5. I n principle, this approach allows the very accurate prediction of solvent effects for all LSC systems. Useful for solvent strength, solvent program, and solvent selectivity predictions. 11. Soczewinski (3)
Assumes monolayer adsorption, discrete adsorption sites of equal energy, cancellation of solute-solvent interactions in solution and adsorbed phases, and complete coverage of adsorption sites by one component B of a so!vent binary (for N I , 2 0.25). Adsorption equilibrium given by Equation 6, role of solvent given by Equation 7. Applicable for silica as adsorbent, monofunctional solutes, and solvent binaries which consist of a strong solvent B and a weak solvent A. Useful for predicting solvent strength. IIa. Soczewinski ( 6 )
Same as model 11, except adsorption equilibrium given by Equation 1 (with n replaced by n‘, the number of functional groups in the solute). Role of solvent given by Equation 7a. Applicable for same LSC systems as model 11, including polyfunctional solutes. 111. Scott and Kucera
(4)
Assumes monolayer adsorption, complete coverage of adsorption sites by one component B of any solvent binary (for N ,> 0.02), mobile phase interactions between solvent and solute are of major importance-particularly dispersion interactions, and dispersion interactions increase with solvent molecular weight. This model has not been verified experimentally, so its range of applicability cannot be stated. It has been used for predicting solvent programs for gradient elution. area A,, and the difference in solvent strengths t o of the two solvents ) q and 6 2 ) . Values of A , can be calculated from the known molecular dimensions of a given solute, and values of t o can then be determined experimentally for various solvents by means of Equation 2. In (2) and elsewhere, CY’is referred to as a. Also, the ratio ( k z l k l ) is replaced there by the equivalent distribution constant ration KZlK1. This same simple model (I) also allows us to derive the solvent strength €ab of a binary mixture composed of pure solvents A and B (2): l o g (Nb 1 0 n b ( E b - E a+ ) 1 - Sb) Cab
Here
t,
ZZ
and
6,
q,
+
(3)
-
refer to the
’?/b to
values of pure A and B
Nb is the mole fraction of B in the solvent binary, and is the molecular area ( A , value) of molecule B. Equations 2 and 3 adequately describe the variation of k’ values with solvent composition in many LSC systems (e.g., (2) and prior references). Experimental and calculated values of k’ usually differ by no more than f25%, even for changes in k’ by 2 to 3 orders of magnitude. S n y d e r Model Ia. Some important exceptions to Equations 2 and 3 do exist, however, particularly for adsorption on silica. Thee have been shown to be related to selective localization of solute and/or solvent molecules on strong adsorption sites (recall that this violates our assumptionmodel I- of an effectively homogeneous and continuous adsorbent surface, with constant solvent adsorption energies a t every point on the surface). Fortunately these apparent failures of Equations 2 and 3 can be handled by a simple mathematical expedient: the use of A , or flb values which are somewhat larger than the actual molecular areas of the molecules involved. Since these corrected values of A, or nb are now known or calculable for most solutes and common solvents (2), Equations 2 and 3 can be used to predict reliable k’ values us. solvent composition in most LSC systems. Thus, from a practical standpoint, Equations 2 and 3 yield acceptable accuracy for a wide range of experimental conditions. S n y d e r Model Ib. Equations 2 and 3 are useful for selecting solvents of the optimum strength in isocratic elution ( I , 2), or for designing a solvent program in gradient elution (7, 8). However Equation 2 is less useful for predicting changes in solvent selectivity [see ( I ) ] .By solvent selectivity, we mean the ability of a change in solvent to create a difference in the relative retention of two similar solutes, particularly when the separation factor cy for the two solutes is initially close to one. The limitations of Equation 2 in this respect arise from our simplifying assumptions. That is, Equation 2 does not recognize certain so-called “secondary solvent effects” that can affect solute retention and separation. Such secondary solvent effects for a given solute and solvent can be lumped into a collective term A, allowing the expansion of Equation 2 as follows: ea),
nb
(Cb
(6) E. Soczewinski and W. Golkiewicz, Chromatographia, 6, 269 (1973).
>
Here 31 and A2 are secondary solvent parameters for the given solute and solvents 1 and 2, respectively. By itself, Equation 4 does not add to our understanding of solvent effects in LSC; it merely recognizes that our original model is a first approximation. A I and A2 then represent correction terms for specific solute-solvent combinations. By comparing experimental data with Equation 4, we can solve for values of ( A 2 - AI) in given cases, and then examine how this term varies with experimental conditions and solute structure. This, in turn, permits us to infer specific adsorption mechanisms for various combinations of solutes and solvents in LSC. Such a study was carried out (9) for a number of solutes and solvents that are incapable of hydrogen bonding with each other (no proton donors included). Here it was possible to correlate these (& - AI) values with high precision in terms of a simple secondary effect: competition of strongly adsorbing solute and solvent molecules for the same strong adsorption sites. The resulting correlational relationship was given as
The term 3’ is a parameter characteristic of the given solute, increasing with the relative tendency of X to localize (7) L. R. Snyder and D. L. Saunders, J. Chromatogr. Sci., 7, 195 (1969) (8) L. R . Snyder, J. Chromatogr. Sci., 8, 692 (1970). (9) L. R. Snyder, J. Chromatogr., 63, 15 (1971).
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onto a strong site. ml and m2 are parameters characteristic of solvents 1 and 2, respectively, increasing with the localization of solvents 1 and 2 on strong sites. In this latter study (9),Equations 4 and 5 predicted over 600 experimental k’ values with a precision that approached the repeatability of the actual measurements. This suggests, therefore, that these secondary solvent effects are almost entirely the result of solute-solvent localization effects. Other effects, including solute-solvent interactions in the mobile phase, appear to play little role in determining solute retention. In LSC systems involving proton-donor solutes or solvents, it is clear that additional interactions are important in affecting solute retention (e.g., 2, 9, 10). One rather welldocumented effect is the so-called “basic solvent anomaly” (2, 9). Here basic solvents (e.g., amines, pyridines, ethers) preferentially increase the retention of proton-donor solutes, as a result of the hydrogen bonding of solvent and solute molecules in the adsorbed phase. Other studies (e.g., 1 0 , I I ) suggest that in other LSC systems involving protondonor solutes and basic solvents, mobile phase interactions dominate, thus decreasing the retention of donor solutes. Therefore, there is some uncertainty a t present in predicting whether hydrogen-bonding effects will increase or decrease solute retention in a given case. However, we can usually expect significant changes in relative solute retention whenever such hydrogen-bonding effects are possible. Soczewinski Model I1 (3).Adsorption sites on silica are generally conceded to be surface silanol groups [(e.g.,( 2 ) ] . Soczewinski has proposed that these interact with protonacceptor solutes and solvents to form discrete, one-to-one complexes of the form A*-X or A*-& where A* is a silanol group. The adsorption equilibrium, corresponding to Equation l, is then
X
or
+
A*-S
x, + s,
e A*-X F=
+
S
x, + s,
(6)
Model I1 leads directly to a simple expression for the effect of solvent composition on solute retention. For the case of binary solvents A-B (B, a proton-acceptor strong solvent; A, a weak solvent that cannot bond):
R M 5 log k ’ =
constant
-
log N,
(7)
Equation 7 is based on premises similar to those used in the derivation of Equation 2; i.e., solute-solvent interactions are ignored, and all sites A* are assumed to be equivalent. The principal difference between models I and I1 is that model I assumes a continuous, constant-energy adsorbent surface, while model I1 assumes discrete adsorption sites which are not closely spaced-with inactive surface in between these sites. The equilibrium equations (Equations 1 and 6) are seen to be similar, except that n equals 1 for model 11. Soczewinski Model IIa (6). More recently Soczewinski has observed in some LSC systems that
RM
= constant - n’ log,V,
(7a)
where n’ > 1. The constant n’ (which we will compare with n in Equation 1) appears to correlate with the number of equivalent, strongly adsorbing groups in the solute molecule ( e . g . , hydroxyls substituted onto a benzene ring). In these cases Soczewinski has assumed that a solute with n’ such substituents is capable of interacting simultaneously with n’ adsorbent sites A*, (10) S. Hermanek, V. Schwartz, and 2. Cekan, Collect Czech. Cbem. Commum, 28, 2031 (1963). (1 1) W. Nienstedt, Acta Endocrinol., Suppb. 1967, p. 114.
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X
+
n’A*-S e X - A , , *
+ n’S
which then leads to Equation 7a rather than Equation 7 [see also discussion of ( 3 ) ] . Note that secondary solvent effects (and the major contributions to solvent selectivity) are ignored in models I1 and IIa Gust as in models I and Ia). Equations 7 and 7a are thus primarily useful for predictions of solvent strength or the form of a two-solvent gradient in gradient elution. Scott and Kucera Model I11 ( 4 ) .Scott and Kucera have described a series of solvents A, B, C, . . . for gradient elution such that “ . . . a single solvent change between any consecutive member of the series (e.g.,A to B, B to C, etc.) will result in an approximately constant incremental change in the logarithm of the distribution coefficient of a solute.” In attempting to set up a rational basis for selecting the individual solvents A, B, C, etc., these authors give a qualitative description of adsorption in gradient elution, thereby advancing certain hypotheses concerning adsorption in LSC and the role of the solvent in affecting solute retention. Thus, although their treatment ( 4 ) is concerned only with gradient elution and is essentially qualitative in nature, Scott and Kucera have in effect presented a new model (111)for the role of the solvent in LSC. Since the main concern of these workers is with gradient elution, the solvent strength of binary mixtures is of primary interest (as in the case of models I1 and IIa). The variation of solvent strength with the composition of a binary A-B (B stronger, as before) is described ( 4 ) as follows: Beginning with pure A, “ . . . as soon as a more polar solv e n t (B) is introduced into the mobile phase, it is selectively adsorbed and partially deactivates the stationary phase so the forces acting on the solutes are all suddenly reduced to a new lower level.” (the authors use the word solute in the original, but apparently mean solvent.) As the concentration of B in the mobile phase increases further, solvent strength increases “almost solely from the gradual change in polarity of the mobile phase.” Finally, Scott and Kucera state “ . . . the dispersion force effect on each solute (should) decrease progressively along the solvent series. Now the dispersion force effect of each solvent can be considered as approximately proportional to its molecular weight. . . .” Thus a model arises which is apparently based on the following premises: 1) Initial addition of solvent B to A causes a very rapid increase in the solvent strength, due to the displacement of most of A from the adsorbent surface by B. This displacement is almost complete after addition of -2% of B to the solvent mixture. 2) Further addition of B (up to a final concentration of 100%B) to the mobile phase causes a more gradual increase in solvent strength, as a result of solvent-solute interactions in the mobile phase. 3) Dispersion forces are important in determining solvent strength, and the contribution of these forces to solvent strength is proportional to the molecular weight of the solvent. DISCUSSION Soczewinski us. Snyder Models. The starting models ( I and 11) in these two approaches, as derived, respectively, from Equations 1 and 6, each represent limiting cases that are known to apply for some LSC systems. Thus, for weakly adsorbing solvents and solutes, and water-deactivated adsorbents, the ideal of a continuous homogeneous surface is closely approached [see discussion of ( 2 ) , Chap. 4 and 101. Equations 2 and 3 are then found to fit experimental k’ values rather well [ ( 2 ) and prior refs.], without the use of
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 11, SEPTEMBER 1974
adjusted values of A , or nb (i.e., model I). Similarly, for the opposite case involving strongly adsorbing solutes and solvents, and discrete (widely separated) surface sites, we can expect that adsorption will be described by Equation 6 rather than Equation 1 (model 11).An illustrative example of such a limiting case would be simple ion exchange, with univalent charged species X and S. Several LSC systems have been reported in which Equation 7 (model 11) applies [(6) and prior refs.]. However a number of LSC systems are not well described by either model I or 11. In model I, most of the differences implied in Equations 1 us. 6 can be bridged in one of two ways. First, the value of n and A , is obviously related to the configuration of the adsorbed solute molecule, which can be either horizontal (flat) or vertical. Vertical adsorption usually means attachment of solute to a strong adsorption site through a single, strongly adsorbing substituent group (e.g., -OH), and smaller values of A , and n. We can in many cases calculate A , values for each of these two configurations; comparison of these values with an experimentally derived value of A , (via Equation 2) then indicates which configuration is in fact preferred (see discussion and examples of 12-15), A general analysis of this type ( 5 ) suggests, for very strong solvents and silica as adsorbent, that the vertical adsorption of many solutes will in this case be favored. In such LSC systems (see below), the value of n in Equation 1 approaches unity, thereby bridging some of the difference between models I and 11. I n m o s t LSC s y s t e m s , however, f l a t adsorption is preferred a n d t h i s complication c a n be ignored. The second way in which the Snyder model recognizes the possibility of preferential adsorption on strong sites is by allowing larger values of A , and nb (model Ia) than are calculated from actual molecular areas. This expedient is equivalent to assuming selective adsorption of the solutes or solvents in question onto the more active regions of the adsorbent surface [Le., strongest sites; see discussion of (Z)]. This adjustment of Equations 2 and/or 3 (model Ia) in turn leads to good agreement of calculated and experimental k’ values in most LSC systems that are not well described by these equations when the normal values of A , and nb are used. This approach (adjustment of A , and nb values) was first suggested by the observation that experimental values of A , and nb (measured via Equations 2 or 3) are, in fact, constant in several systems, but are higher than calculated values. It should be stressed that this adjustment of A , and n b is in no sense an arbitrary “fudge factor,” but is based on the known tendency of certain molecules to localize on strong adsorbent sites. As a result, adjusted values of A , and nb can be estimated in advance for any compound, even those that have not been studied previously [see discussion of (2)]. In the limit of vertical adsorption and strongly adsorbing solutes and solvents, it can be shown that the value of n in Equation 1 becomes equal to 1. The important conclusion is that model Ia is sufficiently flexible and general to include LSC systems of the type first treated by Soczewinski [ ( 3 )and model 111. In similar fashion, the Soczewinski model can be modified to describe LSC systems which fall closer to the model of Equation 1 than Equation 6. This is achieved by postulating multisite attachment of the adsorbed solute, which the leads to model IIa and Equation 7a. We will next examine how well these hybrid models (Ia and IIa) apply for (12) (13) (14) (15)
L. R. Snyder. J. Chromatogr., 8, 178, 319 (1962). L. R. Snyder. J. Chromatogr., 16, 55 (1964). L. R. Snyder, J. Chromafogr.,28, 432 (1967). L. R. Snyder and H. D. Warren, J. Chromafogr., 15, 344 (1964)
LSC systems intermediate between models I and I1 (Equa.. tions l and 6). In all cases, the Soczewinski model assumes solvents composed of solutions of a strong solvent B in a weak solvent A. For all but dilute solutions (e.g., Nb < 0.1) of B in such cases, it has been shown ( 2 )that
Now if solvent 1 in Equation 2 is taken as pure B, substitution of Equation 8 for the solvent strength of solvent 2 (into Equation 2) gives
= constant - n log LVb This is seen to be of the same form as Equation 7a. The only difference is that model IIa predicts that the slope m of the plot of log k’ us. log Nb will be equal to -n’ (the number of strongly adsorbing substituent groups in the solute molecule), whereas model Ia assumes that m will be equal to -n (the ratio of adjusted molecular areas of solute and solvent). Consider now some recent data of Soczewinski (6),summarized in Table 11. Here the slopes m are given for several hydroxyl-substituted solutes in different binary solvent systems A-B (A is cyclohexane). Also shown are the number n’ of strongly adsorbed functional groups (-OH) in each solute, along with average experimental values of m for each solute, and calculated values of n [from (21, model Ia]. These data thus provide a practical test of the ability of Equation 7a (model IIa) and Equation 8a (model Ia) to predict experimental LSC data, for s y s t e m s of t h e t y p e described b y Soczewinski’s model (strongly adsorbing solutes, solutions of a strong solvent B in a weak solvent A, silica as adsorbent). It should be apparent from Table I1 that both models Ia and IIa give predicted values of m (i.e., values of n or n’) which are reasonably close to the observed values: the standard deviation between average values of m and n’ is only f 0 . 3 unit, and f0.2 unit for m us. n. Model Ia is therefore slightly more reliable in predicting values of m (and the effect of the solvent on retention), but not markedly so. Of greater significance is the fact that both models Ia and IIa are in reasonable agreement in predicting solvent effects in this study (std dev of n us. n’ is f 0 . 3 unit). This is also true for most of the earlier data reported by Soczewinski in defense of model 11. Note also that model Ia (Table 11) predicts m values for the simpler phenols that approach the limiting value of one (see above). Values of m here for the solutes phloroglucinol and pyrogallol are excluded, because these values are derived from only two experimental points, and are therefore less accurate than the remaining m values of Table I (note the curvature of some of these plots in (6)]. One further comment is in order with respect to the data of Table 11. In support of model IIa us. Ia, Soczewinski has claimed (6) that there is “no noticeable effect of the second ring on the slopes m, which provides further evidence (that) the effect of the molecular size of the solute . . . is negligible.” Model Ia predicts that the second ring will affect A , and m. In fact, comparing the two naphthols with phenol, we see that the average value of m is increased from 1.3 to 1.5; i.e., by 0.2 unit. Model Ia (Table 11) predicts an increase in n (or m ) by the same 0.2 unit. Although the effect is small, and is obscured by the scatter of experimental m values, these data tend to support Equation 8a (model Ia) rather than Equation 7a (model IIa). However the similarity of Equations 7a and 8a for LSC systems such as that
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Table 11. Comparison of Calculated a n d Experimental m Values f o r D a t a of Soczewinski and Golkiewicz (6); Calculated n ValuesRin Parentheses SolventsC(B)-values Solute
ASh
Et20
MeCOEt
(1' 3) 1.4 (1.3) 1.4 (1' 3) 1.3 (1' 3) 1.3 (1 3) 1.4 (1.3) 1.3 (1' 3)
(1' 2)
of rn
EtAce,
EtOH
PrOH
(1.2) 1.3 (1.2)
(1.4) 1.3 (1.4) 1.3 (1.4)
(1' 3) 1.6 (1.3) 1.6 (1.3)
(1.5)
(1.4)
(1' 5)
(1.4)
av
n'
Phenol o-Cresol m-Cresol p-Cresol 2,3-Xylenol 2,4-Xylenol
14.4 14.4 15.2 15.2
'
2,5-Xylenol 2,6-Xylenol 3,4-Xylenol 3,5-Xylenol Pyrocatechol Resorcinol
15.2 15.2 15.2 15.2 21.2 21.2
Hydroquinone
21.2
Phloroglucinold
28.8
Pyrogallold p-Methoxyphenol Orcinol
28.8
18.2 22.0
1-Naphthol
15.7
2-Naphthol
15.7
1,6-Dihydroxy naphthalene 2,7-Dihydroxy naphthalene 1,5-Dihydroxy naphthalene
23.3 23.3 23.3
1.4
1.0
(1.2) 1.1
1.3
(1 2)
(1.2) 1.2 (1.2) 1.2 (1.2)
'
1.0 (1.2) 1.0 (1.2) 1.0 1.0
(1.2)
(1.2)
(1.2)
(1.2)
(1.5) 1.4 (1.5) 1.4 (1.5) 2.0 (2.0) 2.4 (2.0) 2.4 (2.0)
1.8 (2.0) 2.0 (2.0)
(2 7)
(2 ' 7)
(2.3)
(2.7) 1.7
(1.5) 2.2 (1.8) 1.6 (1.3) 1.6
(1.7)
(2.7) 1.6 (1.7) 1.9 (2.0) 1.6 (1.5) 1.6 (1.5)
1.1
(1.7)
1.8
(2.0) 2.3 (2.0) 1.8 (2.0)
e (1.4) e
(1.5)
(1.9)
1.4
e
e
(1.2) 1.2
(1.2) 1.6 (1.7) 2.0
(1.6) 2.4 (1.9) 1.4 (1.4) 1.4 (1.4)
e
e
(1.2)
(1.3) 1.4 (1.3) 1.7 (1.9) 2.0 2.4 (1.9) 4.0 (2.5) 3.8 (2.5)
1.2
e
1.1
3.0 (1I71 4.0 (2.4) 3.3 (2.4) 1.3 (1.5) 2.3 (1.8) 1.4 (1' 3) 1.4 (1.3) 2.3 (1.9) 2.3 (1.9)
2.3 (1.9)
1.3
1.3 (1.2) 1.9 (1.7) 2.2 (1.7) 2.7 (1.7) 3.6 (2.3) e
1.9
(1.3)
2.5 (1.9) 2.8
(1.9) 2.4 (1.9)
e
e '
e
2.4
(2.1)
1.4 (1' 5) 1.5 (1.5) e
(2.2) 2.3 (2.2)
2.3 (2.2)
(1.4) 1.6 (1.4) 1.6 (1.4) 1.6 (2,O)
e e
e
(2.2) 2.0 (2.2) 1.6 (2.2)
(1' 3) 1.3 (1.3) 1.3 (1.3) 1.2 (1.3) 1.2 (1.3) 1.2 (1.3) 1.2 (1.3) 1.4 (1.3) 1.4 (1.3) 1.8 (1.9) 2.1 (1.9) 2.5 (1.9) 3.9 (2.5) 3.5 (2.5) 1.6 (1.6) 2.2 (1.9) 1.5 (1.4) 1.5 (1.4) 2.2
1 1 1 1 1 1
1 1
2 2 2 3 3 1
2 1
1 2
(2.0)
2.3 (2.0) 2.1 (2.0)
2 2
From Equation 8a with A, and n b values calculated from data of Table 8-4 (2). Assumes flat adsorption. Mixtures of indicated strong solvents in cyclohexane; Et.0, ethyl ether ( n b = 11.4); MeCOEt, methyl ethyl ketone ( n b = 12.2); EtAcet, ethyl acetate (nb = 12.5); EtOH ethanol ( n b = 10.5); PrOH, n-propanol ( n b = 10.8). Experimental m values are less accurate, because of fewer data points in plots of R\I us. log N b . e Not reported.
of Table I1 should be stressed, rather than these rather minor differences. Scott-Kucera us. Snyder Models. Let us next examine the three main premises of model 111, as listed in the preceding section. First, consider the assumption that the addition of -2% of the strong solvent B to a weak solvent A results in essentially complete coverage of the adsorbent surface by B, thereby resulting in a rapid, discontinuous increase in solvent strength (relative to further increase in the concentration of B). Examination of a large number of experimental plots of solvent strength €ab us. Nb [e.g., (2, 9) and prior refs.] suggests no such effect for most solvent pairs A and B. Rather, solvent strength increases continuously from pure A to pure B, yielding a convex plot of tab us. N b which is accurately described by Equation 3. Also, it has been shown for most solvent pairs that 50% surface coverage by B occurs only when N b > 0.02 [see example and discussion of (13)].The discontinuous increase in solvent strength plus immediate surface coverage by B predicted by model I11 is approached only for two solvents A and B of greatly dissimilar strength: e.g., the extreme ex1388
ample cited by Scott and Kucera ( 4 ) of heptane (A) and isopropanol (B). Here the adsorption energy of isopropanol is so much greater than that of heptane that 1-2% isopropanol in the solvent is probably sufficient to almost totally cover the adsorbent surface. However the extension of this example to solvent pairs which are closer in strength [e.g., heptane-carbon tetrachloride or propyl acetate-methyl acetate ( 4 ) ] does not seem justified in terms of our present theoretical and experimental knowledge of these LSC systems. The second assumption of model I11 is that mobile phase interactions are responsible for the gradual increase in solvent strength as the concentration of B is increased past -2%. Equations 7a and 8a assume near-complete coverage of the surface by B (but at higher concentrations of B), just as in the case of model 111. However the change in solvent strength (with N b ) predicted by these equations comes solely from the simple mass-action relationship implied by Equations 1 or 6. Thus, it is unnecessary to postulate additional solute-solvent interactions as a contributing factor in affecting solvent strength. One might ask whether secon-
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dary solvent effects-namely, the (A2 - AI) term of Equation 5-are ever important for higher values of Nb. Such data as exist leg., (2, 9 ) ] suggest that the term (A2 - AI) becomes constant in most systems for values of N b > 0.25. That is, even in LSC systems where secondary solvent effects are important, mass-action appears to determine the value of tab for higher concentrations of B in the solvent. The last assumption of model I11 is that dispersion interactions contribute significantly to changes in solvent strength, as a result of mobile phase interactions involving solute and solvent. These contributions to solvent strength are further assumed to increase with solvent molecular weight. However, we have seen in the preceding discussion that the combined mobile phase interactions do not appear to be a major factor in affecting solvent strength, as the composition of a binary A-B is changed-i.e., Equations 2 , 3, and 7a are found to be experimentally valid. This suggests that the fraction of these interactions due to dispersion forces is also unimportant. Such data as indicate the possible importance of mobile phase interactions in some LSC systems (see earlier discussion) emphasize the importance of hydrogen- bonding rather than dispersion interactions (for polar adsorbents). Only for nonpolar adsorbents, such as charcoal, do dispersion interactions play an important role in affecting solvent strength [e.g., see discussion of (16),and note dependence of solvent strength on solvent molecular weight for adsorption on charcoal; ref. 2, Figure 8.31. Here and for related systems such as the bonded-phase "partitioning" packings, mobile phase effects and dispersion interactions each appear to be of potential importance in determining solute retention. The assumption in model I11 that dispersion interactions increase with solvent molecular weight appears to be a misunderstanding of the fundamental theory of these interactions. The basic theory of dispersion interactions between solute and solvent has been elaborated by Hildebrand (his solubility parameter theory) and others [(17,18) and prior refs.]. These treatments make it clear that the total dispersion interaction per mole of solute (the quality of interest) is related to the product of solute polarizability per unit volume, solvent polarizability per unit volume, and solute molecular weight-but not solvent molecular weight. The various polarizabilities per unit volume can in turn be related to the refractive indices of the compounds in question, so that solute-solvent dispersion interactions should increase with solvent refractive index-but be independent of solvent molecular weight. Some data which relate to this question are summarized in Table 111. Here the strengths of several saturated hydrocarbon solvents are listed, along with their refractive indices and molecular weights. For these solvents (and hydrocarbon solutes), only dispersion interactions are possible in the mobile phase, thus providing a reasonable test of the importance of such interactions. There is no correlation of solvent strength with solvent molecular weight, but a rough correlation with refractive index. More important, the changes in solvent strength as a result of changes in dispersion interactions are rather small, (and are probably the result of solvent-adsorbate interactions, rather than mobile phase interactions). To summarize, the data of Table I11 do not support any significant dependence of solvent strength on solvent molecular weight, for adsorption onto polar adsorbents such as alumina and silica. (16) L. R. Snyder, J. Chromatogr., 36,455 (1968). (17) J. H. Hildebrand and R . L. Scott, "Regular Solutions," Prentice-Hall, Englewood Cliffs, N.J., 1962. (18) R . A . Keller, B. L. Karger, and L. R. Snyder, in "Gas Chromatography, 1970." R. Stock and S. G. Perry, Ed., Elsevier. New York, N.Y., 1971, p 125.
Table 111. Dependence of Solvent Strength (on Alumina) on Solvent Refractive Index and Molecular Weight (2) So1vent
Refractive index
Molecular weight
1.36 1.40 1.41
72 114 142 84 70
n-Pentane Isooctane Decane Cyclohexane C yclopentane a
1.43 1.41
0 /1
0 .oo 0.01 0.04 0.04 0.05
Measured with hydrocarbon solutes.
Rational Series of Solvents f o r Gradient Elution. On the basis of model 111, Scott and Kucera have given a detailed account ( 4 ) of the factors they consider important in the selection of a series of pure solvents (A, B, C . . . ) for use in gradient elution. The same question-the selection of an optimum solvent program-had previously been examined in terms of model Ib [e.g., (7, 8, 15, 19-21)]. In view of the differences between models Ib and 111, it is unsurprising to fin corresponding differences in the resulting rules for selecting a "rational" series of solvents for gradient elution. The general requirements on a solvent program for gradient elution can be summarized as follows: 1) A sufficient range in solvent strength, from beginning to end of the program, to allow the elution of all sample components with average k' values in the optimum range (1 < k' < 10). 2 ) An even, continuous change in solvent strength along the program, so as to provide comparable resolution throughout the chromatogram (assuming equal a values) and roughly equal band widths. 3) No "displacement" effects as a result of solvent demixing within the column. Solvent demixing can result in large, discontinuous changes in solvent strength during separation, with elution of some sample components as poorly separated fractions ( i e . , k' values = 0 ) . By solvent demixing, we mean the change in composition of a binary solvent as it passes through the column, due to preferential adsorption of the more polar (more strongly adsorbed) solvent component. For a detailed discussion, see Chap. 8 of (1). 4) No sudden changes in secondary solvent effects (-1 values) as the composition of the solvent is changed. If these do occur, the effect on separation can be similar to solvent demixing as in 3). 5 ) Optimization of other aspects of the solvent program: rate of change of solvent strength (dt"/dt), solvent viscosity, solvent matching for constant detector base line, etc. Let us examine each of these points in order, with particular reference to the recommendations provided by model Ib us. 111. An adequate range in solvent strength (requirement 1) is essential in gradient elution, particularly for the analysis of unknown samples. The solvent program proposed by Scott and Kucera is more than adequate in this respect, spanning an estimated range in solvent strength values e" from 0.00 to 0.85. An even change in solvent strength (requirement 2) implies a linear change in t o with time, as first proposed in 1964 (19).Such linear strength gradients are in fact similar to the criterion proposed by Scott and Kucera, that h' values for later solvents (injected as solutes) increase in (19) L. R. Snyder, J. Chromatogr., 13,415 (1964). (20) L. R. Snyder, Chromatogr. Rev., 7, 3 (1965). (21) L. R . Snyder, in "Modern Practice of Liquid Chromatography," J. J. Kirkland, Ed., Wiley-lnterscience, New York, N.Y., 1971, Chap. 4.
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geometric progression from one solvent (A, B, C, . . . ) to the next, along the solvent series. Linear solvent strength gradients yield bands of approximately constant width, provide equivalent resolution at all parts of the chromatogram, and have a number of further advantages [see discussion of (18) and examples of (7,8,22)]. Note, however, that if we accept Equation 3 (rather than model 111) as a valid expression for the change in solvent strength with composition, it is unnecessary that the strengths t o of the pure solvents A, B, C, . . . differ by constant increments along the series. For example, the three solvents pentane ( t o = O.OO), 2-chloropropane ( t o = 0.28), and ethyl ether ( t o = 0.38) have been used without difficulty for a linear strength program covering the range 0.00 5 c o 50.38. A desire to avoid solvent demixing and displacement effects (requirement 3) seems to be the main reason Scott and Kucera have chosen a total of 12 different solvents for their solvent program. These authors have correctly appreciated the need for more than two or three individual solvents to span a wide range in solvent strength, since solvent demixing is favored by large differences in solvent strength for two adjacent solvents in a gradient elution series. However, the use of too many individual solvents in a gradient program also has its disadvantages. With a large number of solvents, it becomes difficult to simultaneously meet the requirements of an even change in solvent strength (requirement 2) a n d the other requirements 4 and 5 above. A quantitative treatment of solvent demixing and displacement in gradient elution has been given (18),and has since been validated in various ways [e.g., (15) and separations of (7)]. This work suggests that far fewer than 12 solvents are required to span the solvent strength range between heptane and water-without encountering solvent demixing as a problem. Thus comparison of the data of ( 4 ) with previous c o values on silica (2) indicates a range of solvent strength in the Scott-Kucera program of roughly 0.00 5 t o 50.85. Three solvents (pentane, 2-chloropropane, and ethyl ether) suffice for the range 0.00 5 t o I 0.38 (see above), suggesting that six should be adequate for the entire range (e.g., the latter three solvents plus acetonitrile, ethanol, and water). As we will see, this has important advantages with respect to optimizing other aspects of the solvent program. In this previous study (7) of gradient elution, the chromatograms show no evidence of solvent demixing, and band widths were constant with an average standard deviation of only rtl5%. By comparison, the chromatograms of ( 4 ) show as much as a 4-fold variation in band width within a given separation. The reader may find it helpful to compare the quality of the chromatograms reported in ( 4 ) us. (7), keeping in mind the time required for individual separations. The successive pure solvents used in a total solvent program should not exhibit sudden changes in secondary solvent effects (requirement 41, as these can cause large, sudden changes in k’. Such changes are undesirable, particularly when they lead to lower k’ values for certain compounds. Scott and Kucera have addressed this problem by focusing attention on the importance of dispersion interactions, suggesting that these should decrease regularly along the solvent series. As discussed previously, however, dispersion forces do not appear to contribute seriously to these secondary solvent effects. Rather, hydrogen bonding effects should be controlled so far as possible to provide a regular increase in the proton donor and acceptor characteristics of successive solvents in the program. This requirement with regard to optimum solvent programs has already been discussed, and practical guides for use in this (22) L R. Snyder, J. Chromatogr. Sci., 7, 595 (1969). 1390
connection have been summarized (21). Interestingly, the solvent series reported by Scott and Kucera ( 4 ) does show a reasonable progression of solvent acceptor and donor properties from heptane to water, as measured by so-called specific solubility parameter values [(a, and 6h, 21)]. That is, values of 6, and 6h for these 12 solvents increase regularly along the solvent series. Consider finally, the various requirements on the solvent program summarized under point 5. The optimum value of dco/dt has been derived and verified experimentally (7, 8). The quantity dc’ldt in gradient elution is precisely analogous to llk’ in isocratic elution. Therefore an optimum, intermediate value of dt’ldt exists, just as for k’ in isocratic elution [e.g., see Chap. 13 of ( I ) ] . All solvents used in a gradient program should be as nonviscous as possible. A rough rule-of-thumb states ( I ) that a doubling of solvent viscosity in either isocratic or gradient elution means a doubling in the time required for a given separation, other factors equal. In this regard, the choice in ( 4 ) of such relatively viscous solvents as carbon tetrachloride and nitropropane is unfortunate. Using a smaller number of total solvents in the program (e.g., six), it would be possible to maintain solvent viscosity below 0.4 CP over most of the program. There is, of course, no reason to use higher viscosity solvents (e.g., heptane) simply to maintain a regular decrease in solvent molecular weight along the solvent series [as in ( 4 ) ] . Scott and Kucera claim that it is not possible to adequately span a wide range in solvent strengths without resorting to solvents that are opaque in the ultraviolet (specifically a t 254 nm). This unfortunately limits their solvent series to the relatively insensitive and cumbrous wiretransport detector. Actually, many workers are now using gradient elution in LSC with UV detectors, which are much more sensitive and convenient; e.g., see examples of (7,21). Using the 6-solvent series proposed earlier (pentane, 2chloropropane, ethyl ether, acetonitrile, ethanol, water), it should be possible to operate the UV detector at wavelengths as low as 230 nm, and substitution of isopropyl ether for 2-chloropropane would extend this lower limit further. When using several solvents with moderate UV absorption (e.g., 0.1-0.2 absorbance), base-line constancy at high sensitivity can be attained by adding small quantities of a weakly-adsorbing, strongly-absorbing compound to each pure solvent (A, B, C, . . . ) in the series, so as to achieve constant absorbances for each pure solvent. Mixing of these solvents in the solvent program (without demixing of the added substance) would then give a constant base line. One such compound that appears promising in this respect is 2,6-di-tert-butyl-4-methyl phenol (BHT).
SUMMARY AND CONCLUSIONS Four areas have been examined in the present discussion: 1) the physical validity of different models of adsorption; 2) the accuracy of estimates or calculations of solvent strength; 3) secondary solvent effects and solvent selectivity; and 4) optimum solvent series for gradient elution Let us now proceed to a practical summary. Physical Models of Adsorption in LSC. There is no single “best” model, since the adsorption mechanism changes with major variations in solute structure, solvent strength, and/or adsorbent type. Model I appears to provide a good description for alumina as adsorbent, and it also works well for silica when the solutes and solvents are not strongly adsorbing. Model I is less satisfactory in describing strong solvent systems for silica as adsorbent. Model I1 (or IIa) comes closest to physical reality in those LSC systems where model I is most deficient. Modification of model I to yield model Ia is equivalent to recognizing
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
~
~~~
~
~
~~~~~~
Table IV. Examples of Solvent Selectivity in LSC (Alumina) (a) Concentration of B i n a solvent binary A-B (nondonor solutes/solvents) (9)
k’ Solvent
50 vol % benzene/pentane 23 vol % CH*Cl?/pentane 0.05 vol % dimethylsulfoxide/pentane
Acetonaphthalene
Dinitronaphthalene
5.1 5.5
2.5 5.8 3.5
1.0
a
2.0 1.05 3.5
(b) Relative basicity of B (proton-donor solutes) ( 1 8 , 13)
k’ Solvent
CH,Cl, Benzene 20 vol % diethyl amine/pentane
Quinoline
Aniline
a
2.1
1.3
1.6
5.4 0.4
5.6 3.5
1.04 8.7
6,
0 0.5
4
(c) Relative acidity of B( proton-acceptor solutes) ( 1 0 )
k’
Solvent
Ether 1,2-Dichloroethane CHCls 5 vol % ethanol/benzene 10 vol % ethanoliheptane 20 vol % ethanol/heptane
38-dimethylaminocholestene-5 R-N (CH1)2
Cholesterol R-OH
0.3 2.8 1.4 1.1 4.0 2.2
0.9 9.0
1.7
1.2 2.0 0.8
a
3.0 3.2 1.2 1.1 2.0
2.8
this duality of adsorption mechanisms in LSC systems, and leads to correlative equations that accurately predict changes in k’ with solvent composition for all LSC systems (as in Table 11). Model I11 does not appear to agree with available experimental data, and no new evidence has been cited in its behalf. Predictions of Solvent Strength. Model IIa provides reasonable estimates of relative solvent strength for solvent binaries of the type described earlier (on silica). However Equations 7 and 7a are basically limited relationships which apply to a narrow range of possible LSC systems. Furthermore, they do not describe how solvent strength varies between different binaries (e.g., A-B us. A-C). Model Ia provides essentially complete coverage of all possible cases in practical LSC systems, although experimental t o values are lacking for some common solvents (particularly for silica as adsorbent). Therefore there is a definite need for additional measurements of co values on silica. In this connection, the experimental difficulty of such measurements should not be underestimated. In my opinion, it is quite difficult to achieve accurate measurements of solvent strength via thin-layer chromatography. Column chromatography under carefully controlled conditions is normally required; e.g., see discussion of (2) Chap. 13, as well as (23), and consider the experimental precautions observed in (9). It should be apparent from the present discussion that the relative solvent strengths of binary mixtures (same components A and B) are more accurately predicted than are the strengths of different pure solvents (C, D, . . . ). Secondary solvent effects, when large enough, can appear as apparent reversals in solvent strength for different solutes. Fortunately, these secondary solvent effects normally change continuously and evenly as the composition of a given binary solvent A-B is varied. As a result, changes i n solvent strength are most conveniently and accurately controlled by varying t h e composition of a given binary solvent mixture, rather than by using various pure solvents or their mixtures with other solvents. This will also avoid discontinuous changes in a values when adjusting solvent
strength for optimum k’ values (i.e., in the range 1 < h’ < 10). For an extensive listing of the solvent strengths of pure and binary solvents, see (1,2,21, 24). Secondary Solvent Effects. Although this is a very complex area, we are beginning to achieve a good understanding of the factors that relate a values to the composition of the solvent in LSC. Most of these secondary solvent effects appear to be controlled by solute-solvent-adsorbent interactions within the adsorbed phase. A few examples of secondary effects that may be based on mobile phase interactions have been reported, but these are so far limited in number and are restricted to proton-donor solutes and/or solvents. For nondonor solutes and solvents, an adequate theory of secondary solvent effects now exists [model Ib and send see (9)]. The data of Table IVa illustrate how selectivity varies with the solvent in these cases. If we consider several binary solvents A-B of roughly the same strength, selectivity changes regularly as the concentration of the strong solvent component B decreases. In Table IVa, for example, the concentration of B goes from 50 vol% (benzene) to 23 vol% (CH2C12) to 0.05 vol% (dimethyl sulfoxide), while, in this same sequence, the retention of dinitronaphthalene relative to acetonaphthalene is successively increased. As a result, maximum separation factors a (easiest separation) are found either for dilute solutions of B as solvent, or for concentrated solutions of B. Intermediate concentrations of B generally give a values closer to unity, and are therefore less desirable. If the first attempt a t separation gives an a value near one, solvents of similar strength but different concentration of B (both larger and smaller) should be tried for improved solvent selectivity. Some examples of the importance of hydrogen bonding for change in solvent selectivity are shown in Tables IVb and IVc. In Table IVb data are shown which illustrate the importance of the basicity of B [measured by the parameter 6,, (21)] in providing preferential retention of protondonor solutes. In this case, as solvent basicity increases, the
(23)H.Schlitt and F. Geiss. J. Chromatogr., 67, 261 (1972).
(24) D. L. Saunders, Anal. Chem., 46, 470 (1974) A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 1 1 , SEPTEMBER 1974
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relative retention of aniline (a proton-donor) increases relative to the nondonor solute quinoline. As in the case of Table IVa, maximum values of a are predicted either for very basic or nonbasic solvents B, with intermediate basicities giving values of a closer to unity. Table IVc is another example of hydrogen-bonding effects, presumably due to preferential interaction in the mobile phase of very basic (proton acceptor) solutes with strong-donor solvents (IO). In this case, the dimethylamino analog of cholesterol is preferentially eluted by solvents of increasing acidity or proton-donor ability (Le., solvent acidity increases downward in Table IVc, from ether to 20% ethanol/heptane). Again we see that solvents of intermediate acidity (e.g., CHC13, 5 vol% ethanol) give cy values nearer one, with maximum solvent selectivity obtained either with relatively acidic (e.g., 20 vol% ethanol) or nonacidic (e.g., ether) solvents. The factors which determine solvent selectivity in systems such as that of Table IVc are less well understood, and it is not possible to make firm predictions concerning how selectivity will vary with different solute/ solvent combinations. Nevertheless, it is apparent that attention to maximum differences in solvent acidity or basicity (very large or small values of 6, and &) can yield large cy values for many pairs of solutes. At present our understanding of hydrogen bonding effects in LSC is incomplete, and quantitative predictions of changes in solvent selectivity for given solute pairs are not generally possible. Hopefully, further study of such LSC systems (in the context of model Ib) will lead to a basis for reliable estimates of solvent selectivity in most cases. As in the case of experimental measurements of solvent strength (discussed above), carefully controlled studies by column chromatography offer the best approach for obtaining the necessary data with sufficient accuracy. Optimum Solvent Series for Gradient Elution. Gradient elution LSC is a most powerful technique for the separation of complex samples. By rather straightforward extrapolation, we can anticipate the separation of hundreds of individual sample components from a given sample in less than two hours, using presently available columns. Thus we have demonstrated ( 7 ) separations with a peak capacity of 50 for separation times of less than 50 min, using a 20-11 silica column and a solvent strength range of 0.00 5 t o 5 0.38. Extending the solvent strength range to maximum polarity solvents, as in the case of Scott and Kucera's program (0.00 5 eo -< 0.85), should then lead to a peak capacity of about 100 for a 100-min separation. Now replacing the 20-11 silica column (N,ff = 2.5/sec) with a 5-11 silica column [(Neff = 25/sec, see ( I ) ] should multiply peak cam or a factor of three, to a final value of pacity by d three hundred. This is equivalent to the best separations now being reported by temperature-programmed gas chromatography. To attain this level of performance, the basic guidelines presented in the preceding section must be followed. Some of these guidelines are more important than others. Displacement effects must be avoided, and there must be a constant rate-of-change of solvent strength throughout separation (constant dt"/dt). Similarly, the t o range covered by the solvent program must cover a sufficiently wide range (e.g., pentane through methanol or water). Secondary solvent effects can lead to poor resolution of some solute pairs, but by themselves probably do not much affect the peak capacity of the separation. Some representative solvent series that meet the above requirements have been given elsewhere ( 1 , 21), and many more can be assembled from the detailed recommendations given here. Since many of these solvent programs have not been experimentally evaluated, however, it can be antici1392
pated that some of them will require minor modification for optimum performance in actual practice. Despite the apparent incorrectness of model 111, and the inappropriateness of many of the solvent program recommendations given in ( 4 ) , the solvent series proposed by Scott and Kucera should be useful in some applications with the wire-transport detector. Thus this series meets the primary requirements of an extended t o range, an even increase in t o with time (dt"/dt roughly constant), an absence of solvent demixing, and a continuous increase in the proton-donor and acceptor characteristics of the solvent. Its main limitations are its incompatibility with the UV detector and the use of higher viscosity components. It could, of course, by further improved by attention to the optimization of the value of dc'ldt as described in (7,8). Aside from the question of what constitutes an optimum solvent program for gradient elution, other practical problems exist which we have not discussed. Thus, the equipment needed for full-range optimum gradients must be capable of handling up to six individual solvents, and to blend adjacent solvents so as to yield constant dto/dt. Most commercial solvent programmers for liquid chromatography are unsatisfactory in this respect. The device of Scott (25) comes close to meeting this need, since stepwise elution with enough (e.g., 12) individual steps [i.e., solvents of increasing t o , as in Table 13.9 of ( I ) ]approaches the performance of a true continuous gradient [see discussion of ( 7 ) ] , particularly when a mixing chamber between the gradient device and column is provided. Another practical problem is that of maintaining the water content of the LSC column roughly constant during separation and column regeneration, as discussed in ( 7 ) . Regeneration of the column is most usefully achieved with a simple reverse gradient, where the solvent program is run in reverse, at a more rapid rate (larger value of dto/dt) (26).
NOMENCLATURE A, B, C = various pure solvents; also, a series of such solvents for use in a gradient program A* = an adsorption sit (surface silanol group, for silica) A*-S = a solvent-site complex (model 11) A*-X = a solute-site complex (model 11) A , = molecular area of an adsorbed solvent molecule A , = molecular area of an adsorbed solute molecule dc"/dt = rate of change of solvent strength e o with time in gradient elution k' = capacity factor; equal to total quantity of solute in stationary phase divided by total quantity of solute in mobile phase (isocratic elution) kl, kz = values of k' for solvents 1 and 2, respectively m = slope of experimental plots of RM us. Nb ml, m2 = solvent selectivity parameters; see Equation 5 and related discussion n = number of solvent molecules displaced by one adsorbing solute molecule; Equation 1 nb = molecular area of an adsorbed solvent molecule B; A , value for B n' = number of strongly adsorbing functional groups in a solute molecule; Equation 7a Nb = mole fraction of strong solvent B in a binary A-B R M = log [ ( ~ - R F ) / Rwhere F ] , RF is the fractional solute migration in thin-layer chromatography S,,S, = a solvent molecule S in the adsorbed or mobile phases, respectively t = separation time X,, X, = a solute molecule X in the adsorbed or mobile phases, respectively X-A*,, = adsorbed solute molecule X interacting with n' surface silanol groups 00 = adsorbent activity parameter, varying with adsorbent water content; see (2) (25) R. W. P. Scott and P. Kucera, J. Chromatogr. Sci., 11, 83 (1973). (26) R. E. Majors, in "Advances in Chromatography. 1973," A. Zlatkis, Ed., Chromatography Symp., Univ. of Houston, Houston, Texas, 1973, p 372.
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a = separation factor; equal to r a t i o of k' values f o r t w o solutes in same LSC system A I , 6 2 = secondary solvent parameters ( E q u a t i o n 4), v a r y i n g w i t h solvent a n d solute, f o r solvents 1 a n d 2 a n d same solute Ao = a solute parameter measuring t h e e x t e n t of solute localization; E q u a t i o n 5 t o = solvent s t r e n g t h parameter t l , t2, e,, €b, Cab = values o f € 0 f o r solvents 1 , 2 , A, B, or b i n a r y solv e n t A-B, respectively
ACKNOWLEDGMENT I am much indebted for the critical evaluation of the present manuscript by D. L. Saunders of the Union Oil Co. of California, J. J. Kirkland and J. J. DeStefano of DuPont, and E. Soczewinski. RECEIVEDfor review January 21, 1974. Accepted May 7 , 1974.
Theoretical Comparison of Chromatography and Spectrometry as Methods of Measuring Weak CompIexation Constants Claude Eon and Georges Guiochon Laboratoire de Chimie Analytique Physique, €cole Polytechnique, 7 7, rue Descartes, Paris 5', France
This paper gives a theoretical approach to the rneasurement of complexation constants by gas-liquid chrornatography and establishes some similarities with the spectrometric methods. It is shown that the difference usually found between the results given by these different methods can be explained by a misinterpretation of chromatographic measurements. When corrections are made, we can expect the two kinds of methods to give reliable results in good agreement, provided that the solvent used has the same refractive index as the main additive and that none of the species studied is strongly polar. I n all cases, however, complexation constants do depend on the nature of the inert solvent used and there is no direct access to the absolute constants.
During the past few years, chemistry of charge transfer complexes has been very intensively investigated by means of various spectrometric methods (UV, NMR, IR, etc.). Many data have been reported (1, 2 ) and the large discrepancy found between results obtained by different authors and methods is striking. One can be perplexed about the reliability of these numerical results, especially when dealing with weak molecular complexes. Have we not seen even negative equilibrium constants reported ( 3 )! More recently, a chromatographic method that allows one to measure complexation constants has been described ( 4 , 5 ) . We have shown previously that this method could lead to large errors when the non-ideality of the solution is neglected and we have given a new set of equations to correct for this effect (6-8). At that time, it (1j R . Foster, "Organic Charge Transfer Complexes," Academic Press, New York, N . Y . , 1969. (2) J. Rose, "Molecular Complexes,'' Pergamon Press, New York, N . Y 1967 (3) M. W Hanna and A. L Ashbaugh, J , Phys. Chem.. 68,811 (1964). ( 4 ) B W Bradford, D Harvey, and D. E. Chalkley, J . Inst. Petroi., London, 41, 80 (1955). ( 5 ) J H Purnell, "Gas Chromatography 1966," A. B Littlewood, Ed , The Institute of Petroleum, London (G B ) , 1967, p 3. (6) C Eon. C Pommier, and G Guiochon, Chromatographia, 4 , 235 (1971) (7) C Eon. C. Pommier, and G Guiochon, Chrornafographia, 4, 241 (1971) ( 8 ) C. Eon, C Pommier and G. Guiochon. J . Phys. Chem., 75, 2632 (19711.
seemed that the chromatographic method would be more useful than the spectrometric ones, not only because measurements are faster and can be carried out accurately a t very low concentrations, but mainly because this method appears to derive from a direct thermodynamic approach. However, there are cases where the chromatographic method cannot be used, particularly when none of the solutes is volatile. Thus, it is necessary to investigate the extent of agreement between data derived by both kinds of methods. In one of the rare comparative studies of the same chemical reaction by chromatography and UV spectrometry, a good agreement (20%) between the results of the two methods was found (9), but a much larger discrepancy was recently observed for other chemical reactions by Purnell et al. (IO).On the basis of these last results, Purnell et al. concluded that chromatography was much better than all the spectrometric methods. As no theoretical study of this problem has been made so far, the basic question remains: can chromatographic and spectrometric methods lead to the same value of the complexation constants as they basically measure quite different physical properties? In what conditions and within which range can we expect their results to agree? There are many reasons that could explain the disagreement between the results. Among them, however. the most important is probably that activity coefficients are most often neglected and, moreover, they vary with the composition of the solution. This is especially important as sets of solutions of largely different composition are used in all methods of measurements of complexation constants. In other words, all physical interactions are neglected and it is assumed that all the deviation from ideal solution behavior comes from the chemical reaction. Obviously, this is certainly not valid when dealing with weak molecular complexes. Consequently, the role of the solvent which makes up the activity coefficients is not really taken into account and the measured complexation constants are often meaningless. This approximation, which is bad in any case, can hardly be understood when applied to chromatographic methods which precisely measure the complexation constants from activity coefficients. The aim of this paper is to clarify those points and to (9) C. Eon, C. Pommier, and G. Guiochon, C.R.Acad. Sci., 168, 1553 (1969) (10) J. H . Purnell and 0. P. Srivastava.Ana/. Chem., 4 5 , 1111 (19731
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