Physical Significance of Parameters in Correlations of Rf Solvent Effects SIR: Perisho ( I ) has recently proposed an equation that successfully correlates many R, values for closely related compounds in two solvent systems. Some of these correlations, however, led to values of the parameter p = AM/A8 that are too large or too small to have any physical meaning. In this letter, I attempt to clarify the problem. Perisho's symbolism is used. CY = ratio of solute concentrations in mobile and stationary phases; p = AJv/A8 = ratio of cross-sectional areas of mobile and stationary phases; Ap = free energy of transfer for one mole of solute from S to M ; subscripts x and y refer to different solvent systems X and Y. For the Rf value of a solute in solvent system X , we write R,, = cuZpz/(a,p, 1); a similar expression can be written for R,, for the same solute. Combining these leads to (2)
+
where F = Lyzpz/aupu. F can be expanded by introducing the thermodynamic relation CY = exp(-Ap/RT), giving pz -UP=- A F Y ) / R T
F = - e Pu
(2)
We consider Equations 1 and 2 to be general in scope, and next inquire into the forms that F may take in important special cases. For convenience, and because it appears to be a good assumption (3), we may consider pz/pu to be a constant. Case I. Let (4p2 - Apv) = C, where C is a constant. Then from Equation 2, F = (pz/pv)exp(-C/RT). Clearly F is a constant. This condition leads to correlations between R,, and R,, of the type discussed in an earlier paper (2). Case 11. Let 4pu/4pz = D , where D is a constant. Combining this condition with Equation 2 leads, after some rearrangement, to
Equation 4 is identical with Perisho's equation ( I ) . (Perisho assumed pz = pu in his treatment.) This equation leads to correlations that are qualitatively different from the Case I correlations. The assumption that pz/py is constant is not a necessary one, and in the general case more complicated behavior can arise. For example, F can be constant even if C is not constant, provided that pz/pu also changes; the required condition is easily derived. Minor deviations from the exact Case I and Case I1 equations may be ascribable to changes inwpz/pu. The important point here is that Cases I and I1 are mutually exclusive (except when D = 1). In the original presentation (2) of Equation 1, it was pointed out that F might be a constant (present Case I) or might be a function of Rf (Case 11)) and examples of both cases are numerous ( I , 2). Physical interpretation of the parameters can only follow classification into the appropriate special case. (Other special cases may exist, but the analyses reported to date do not require additional ones.) This classification can be made by plotting R, against Rfz. If the curve given by the data does not cross the diagonal (Le., the line Rf, = Rf,), then the system belongs to Case I. If the curve crosses the diagonal, the system belongs to Case 11. [Generalized plots of these functions have been presented ( I , 2).] Another criterion utilizes the plotting method suggested by Soczewinski ( 4 ) ; one plots RMuagainst R,lrz; if the slope of the straight line is unity, the system is of the Case I type; if the slope differs from unity, it is a Case I1 system. The meaningless number for p obtained by Perisho resulted from applying Equation 4 (Case 11) to chromatographic systems that belong in Case I.
KENNETH A. CoNNoRs (3) Substituting Equation 3 into Equation 1: (1) C. R.Perisho, ANAL.CHEM., 40, 551 (1968). (2) K. A. Connors, ibid., 37, 261 (1965). (3) C. R. Perisho, A. Rohrer, and J. A. Thoma, ibid, 39, 737 (1967).
1386
ANALYTICAL CHEMISTRY
School of Pharmacy University of Wisconsin Madison, Wis. 53706
RECEIVED for review March 13,1968. Accepted May 9,1968. (4) E. Soczewinski, ANAL.CHEM., 37, 1439 (1965).
