Soczewinski equation

From the general framework of the Snyder and Soczewinski model of the linear adsorption TLC, two very simple relationships were derived, which proved extremely useful for rapid prediction of solute retention in the thin-layer chromatographic systems employing binary mobile phases. One of them (known as the Soczewinski equation) proved successful in the case of the adsorption and the normal phase TLC modes. Another (known as the Snyder equation) proved similarly successful in the case of the reversed-phase TLC mode. 

Apart from enabling rapid prediction of solute retention, the Soczewinski equation allows a moleeular-level scrutiny of the solute — stationary phase interactions. The numeiieal value of the parameter n from Equation 2.14, which is at least approximately equal to unity (n 1), gives evidence of the one-point attachment of the solute moleeule to the stationary phase surface. The numeiieal values of n higher than unity prove that in a given chromatographic system, solute molecules interact with the stationary phase in more than one point (the so-ealled multipoint attachment). 

Likewise, the Soczewinski equation (2) is based on the proportionality of 6° and log A/g for binary-solvent mobile phases A/B, when the concentration of B in the mobile phase is large enough so that Bh 1.0. Since the Soczewinski equation has been confirmed for numerous LSC systems using silica as adsorbent (e.g.,22-27), this constitutes confirmation of Eq. 

Fig. 1 Family of log k versus log Cmod plots for hypothetical solutes 1-20 with capacity factors forming a geometrical progression according to Snyder-Soczewinski equation. For isocratic elution at Cmod 1-0, 0.1, and 0.01. Only seven to eight solutes give Rf values in the range 0.09-0.9 (left-hand ordinate).

The Soczewinski equation [5] [Eq. (11)] is a simple linear relationship with respect to log X, linking the retention parameter (i.e., R ) of a given solute with the quantitative composition of the binary mobile phase used ... 

The adsorption of the solutes by discrete one-to-one complexes was discussed by Soczewinski (77, 78). In this simple model equations for k value are derived by the application of the law of mass action to the competitive adsorption equilibria between solute and solvent molecules for the active sites of the adsorbent. It follows then that with an eluent mixture containing a polar solvent in an inert" nonpolar diluent, a linear relationship holds so that... 

By appropriate choice of the type (or combination) of the organic solvent(s), selective polar dipole-dipole, proton-donor, or proton-acceptor interactions can be either enhanced or suppressed and the selectivity of separation adjusted [42]. Over a limited concentration range of methanol-water and acetonitrile-water mobile phases useful for gradient elution, semiempirical retention equation (Equation 5.7), originally introduced in thin-layer chromatography by Soczewinski and Wachtmeister [43], is used most frequently as the basis for calculations of gradient-elution data [4-11,29,30] ... 

Figure 3.19 shows an example of the linear variation of retention with composition according to eqn.(3.74). In this figure the logarithm of the volume fraction () of the stronger solvent is plotted on the horizontal axis. Plotting In XB will lead to a similar linear plot. The simple equation of Soczewinski (eqn.3.74) often yields a very good description of experimental data in LSC [353,355,356]. 

A single solvent only rarely provides suitable separation selectivity and retention in normal-phase systems, which should be adjusted by selecting an appropriate composition of a two- or a multi-component mobile phase. The dependence of retention on the composition of the mobile phase can be described using theoretical models of adsorption. With some simplification, both the Snyder and the Soczewinski models lead to identical equation describing the retention (retention factor. A) as a function of the concentration of the stronger (more polar) solvent, (p. in binary mobile phases comprised of two solvents of different polarities [,121 ... 

In addition Rm value can be used to characterize molecular hydrophobicity in reversed-phase planar chromatography by elution with water-organic solvent mixtures according to the Soczewinski-Wachtmeister equation ... 

Spiegeleer et al., 1987 De Spiegeleer and De Moerloose, 1988), a graphical method (Matyska and Soczewinski, 1993), numerical taxonomy and Information content derived from Shannon s equation (Medic-Saric et al., 1996), and the PRISMA system (Nyiredy et al., 1988, 1989, 1991 Nyiredy and Fater, 1995 Dallenbach-Toelke et al., 1986) (see Section I.D). All of these optimization procedures involve the use of some form of statistical design to select a series of solvents for evaluation or to indicate the best system by comparing the results obtained from an arbitrarily selected group of solvents (Poole and Poole, 1991). 

The use of the stepwise gradient of the mobile phase which is most convenient, is well described by Soczewinski [46,47] and Markowski [48]. A general equation for the final Rf value of a solute chromatographed under conditions of stepwise gradient elution with one void volume of mobile phase has been derived in the following equation [48]. 

Soczewinski and Markowski (13,70) derived an equation for the values of solute chromatographed under stepwise gradient elution. Assuming a definite relationship between the k value and modifier concentration, the final Rf values of solute j (considering that the last, lith, development step is incomplete) is... 

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