Snyder 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. 

The following Snyder equation is another simple linear relationship with respeet to cp, whieh links the retention parameter (i.e.. In k) of a given solute with the volume fraetion of the organic modifier in the aqueous binary mobile phase (cp) ... 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

According to Snyder [28], the solvent strength 8° is the standard free energy of adsorbed solvent molecules in a standard state, and it is given by Equation 4.11 ... 

Prus and Kowalska [75] dealt with the optimization of separation quality in adsorption TLC with binary mobile phases of alcohol and hydrocarbons. They used the window diagrams to show the relationships between separation selectivity a and the mobile phase eomposition (volume fraction Xj of 2-propanol) that were caleulated on the basis of equations derived using Soezewiriski and Kowalska approaehes for three solute pairs. At the same time, they eompared the efficiency of the three different approaehes for the optimization of separation selectivity in reversed-phase TLC systems, using RP-2 stationary phase and methanol and water as the binary mobile phase. The window diagrams were performed presenting plots of a vs. volume fraetion Xj derived from the retention models of Snyder, Schoen-makers, and Kowalska [76]. 

Because of the assumptions underlying its derivation, the Kozeny-Carman equation is not valid at void fractions greater than 0.7 to 0.8 (Billings and Wilder, op. cit.). In addition, in situ measurement of the void fraction of a dust layer on a filter fabric is extremely difficult and has seldom even been attempted. The structure of the layer is dependent on the character of the fabric surface as well as on tfie characteristics of the dust, whereas the application of Eq. (17-12) implicitly assumes that K2 is dependent only on the properties of the dust. A smooth fabric surface permits the dust to become closely packed, leading to a relatively high value of K2. If the surface is napped or has numerous extended fibrils, the dust cake formed will be more porous and have a lower value of K2 [Billings and Wilder, op. cit. Snyder and Pring, Ind. Eng. Chem., 47, 960 (1955) and K. T. Semrau, unpublished data, SRI International, Menlo Park, Calif., 1952-1953]. 

Equation (2) shows that the resolution is a function of three different factors (1) the resolving power of the column as measured by the plate number that expresses the relative width of bands (2) the relative retention of the two compounds that measures how far apart the bands are from each other and (3) the magnitude of retention, as separation is a result of retention. The relative influence of these factors has been discussed by Snyder (72,13) in a form very easy to use in practice. 

The concept of eluotropic strength has been invoked here without a rigorous definition. Snyder (130) developed a series of eluotropic values for solvents by using retention values measured on alumina columns. Colin and Guiochon (86) used a definition similar to that of Snyder to evaluate eluotropic strengths of methanol-water mixtures on various column surfaces. The eluotropic strength, e, was calculated by using the equation... 

The most important features of this equation are the emergence of a eluotropic series, i.e., an eluent-strength series based on e°. The key solvent-strength parameter, e°, which relates to the eluotropic series, was calculated by Snyder (14) for a wide variety of pure solvents. Table 2 lists some values. 

GRADIENT ELUTION. The separation of proteins in RPC is carried out by gradient elution and the chromatographic results are influenced by the gradient conditions and flow rate. According to Snyder (13), a measure of retention in gradient elution is given by the equation,... 

The main strength of the Snyder scheme is for the classification of solvent selectivity. We have seen from table 2.8 that solvents that are chemically similar yield similar selectivity parameters. This type of classification can be made on the basis of structural information alone. However, the Snyder scheme goes one step further, in that it classifies different chemical classes into a single selectivity group. From the definition equations (2.14 through 2.17) we see that the three selectivity parameters are correlated by the equation... 

A minimum of four experimental data points is required to estimate the parameters in eqn.(3.58), similar to the experimental design employed by Snyder et al. [337]. Of course, eqn.(3.58) can only be applied over a limited range of compositions, for example the range over which 1 < k < 10. To describe retention as a function of both temperature and composition over wider ranges of the latter, more complicated equations need to be used. A quadratic equation for the relationship between retention and composition (eqn.3.38) can be combined with eqn.(3.57) to yield... 

Snyder [350] formulated the following equation to describe the above effect quantitatively ... 

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