The Solvation Parameter Model

There are different models trying to give a theoretical basis for the retention in RP, with the solvation parameter model as the currently most widely accepted. 

The solvation parameter model intends to describe the free energy of transferring a solute from the mobile to the stationary phase as a series of product terms representing cavity formation (of hydrophobic solutes in the aqueous mobile phase) and dispersion interactions, plus dipole interactions, hydrogen bonding, and lone pair interactions between polar groups in the solute and polar groups on the solvated surface. 

System constants for the different interactions have been calculated for different packing materials and are available in large tables in the literature. A small selection is shown in Table 3.3. 

One group of interactions is related to the combined cavity formation and dispersion interactions represented by the parameter m. 

The cavity formation component (which is a measure of the hydrophohidty) and the dispersion interactions increase with the size of the hydrophobic part of the analyte. 

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In initial work, a total of 17 different ILs were evaluated by the solvation parameter model [8]. Ten of these ILs were comprised of imidazolium or pyrolidinium cations paired with different anions. Many of these compounds represent the traditional class of IL solvents that have been used extensively in organic synthesis reactions or in other analytical uses. The remaining seven ILs consisted of substituted ammonium cations that have proven to be successful analyte matrices in matrix-assisted laser desorption ionization (MALDI) mass spectrometry [11]. 

Calculation of solute descriptor values for the solvation parameter model... 

An example of part of the output for fitting the solvation parameter model to a reversed-phase chromatographic system by multiple linear regression analysis... 

Figure 1.3. Variation of the system constants of the solvation parameter model (section 1.4.3) with temperature for 37 % (v/v) propan-2-oI in water on the porous polymer PLRP-S stationary phase. The m constant reflects the difference in cohesion and dispersive interactions, r constant loan-pair electron interactions, s constant dipole-type interactions, a constant hydrogen-bond basicity and b constant hydrogen-bond acidity between the mobile and stationary phases. (From ref. [89] The Royal Society of Chemistry).

The master retention equation of the solvation parameter model relating the above processes to experimentally quantifiable contributions from all possible intermolecular interactions was presented in section 1.4.3. The system constants in the model (see Eq. 1.7 or 1.7a) convey all information of the ability of the stationary phase to participate in solute-solvent intermolecular interactions. The r constant refers to the ability of the stationary phase to interact with solute n- or jr-electron pairs. The s constant establishes the ability of the stationary phase to take part in dipole-type interactions. The a constant is a measure of stationary phase hydrogen-bond basicity and the b constant stationary phase hydrogen-bond acidity. The / constant incorporates contributions from stationary phase cavity formation and solute-solvent dispersion interactions. The system constants for some common packed column stationary phases are summarized in Table 2.6 [68,81,103,104,113]. Further values for non-ionic stationary phases [114,115], liquid organic salts [68,116], cyclodextrins [117], and lanthanide chelates dissolved in a poly(dimethylsiloxane) [118] are summarized elsewhere. 

System constants derived from the solvation parameter model for packed column stationary phases at 121°C... 

Figure 2.7. Principal component score plot with the system constants from the solvation parameter model as variables for 52 non hydrogen-bond acid stationary phases at 121°C. Loading for PC 1 0.996 a + 0.059 s -0.054 / - 0.024 c - 0.014 r. Loading for PC 2 0.940 s + 0.328 / + 0.080 r + 0.027 c - 0.037 a.

Figure 2.8. Nearest neighbor complete link cluster dendrogram for the stationary phases in Table 2.6. The system constants from the solvation parameter model were used as variables.

The system of stationary phase constants introduced by Rohrschneider [282,283] and later modified by McReynolds [284] was the first widely adopted approach for the systematic organization of stationary phases based on their selectivity for specific solute interactions. Virtually all-popular stationary phases have been characterized by this method and compilations of phase constants are readily available [28,30]. Subsequent studies have demonstrated that the method is unsuitable for ranking stationary phases by their selectivity for specific interactions [29,102,285-287]. The solvation parameter model is suggested for this purpose (section 2.3.5). A brief summary of the model is presented here because of its historical significance and the fact that it provides a useful approach for the prediction of isothermal retention indices. 

Rohrschneider s approach is able to predict retention index values for solute s with known solute constants (a, through e) [283,288]. These are determined from AI values for the solute on at least five phases of known phase constants and solving the series of linear equations. The retention index of the solute on any phase of known phase constants (X through S ) can then be calculated from Eq. (2.8). The theoretical defects of the method for assigning intermolecular interactions do not apply to the prediction of retention index values. A mean error of about 6 index units was indicated in some calculations. The retention or retention index values for thousands of compounds can be calculated from literature compilations of solute descriptors and the system constants summarized in Tables 2.6 and 2.8 using the solvation parameter model [103]. The field of structure-driven prediction of retention in gas chromatography is not well developed at present and new approaches will likely emerge in the future. 

Influence of solvent type on the system constants of the solvation parameter model for a cyanopropylsiloxane-bonded silica sorbent in reversed-phase chromatography (r = 0 in all cases)... 

The solvation parameter model has been extended to include ternary solvent systems using a mixture-design approach [271,272]. The system maps are now smooth three-... 

The cavity model of solvation provides the basis for a number of additional models used to explain retention in reversed-phase chromatography. The main approaches are represented by solvophobic theory [282-286] and lattice theories based on statistical thermodynamics [287-291]. To a lesser extent classical thermodynamics combining partition and displacement models [292] and the phenomenological model of solvent effects [293] have also been used. Compared with the solvation parameter model all these models are mathematically complex, and often require the input of system variables that are either unknown or difficult to calculate, particularly for polar compounds. For this reason, and because of a failure to provide a simple conceptual picture of the retention process in familiar chromatographic terms, these models have largely remained the province of the physical chemist. 

System constants of the solvation parameter model for liquid-solid chromatography... 

For chromatographic applications, the most useful models of solvent properties are the solubility parameter concept, Snyder s solvent strength and selectivity parameters, solvatochromic parameters and the system constants of the solvation parameter model for gas to liquid transfer. The Hildebrand solubility parameter, 8h (total solubility parameter), is a rough measure of solvent strength, and is easily caleulated from the physical properties of the pure solvent. It is equivalent to the square root of the solvent vaporization energy divided by its molar volume. The original solubility parameter concept was developed from assumptions of regular solution behavior in which the principal intermolecular interactions were dominated by dispersion forces. 

System constants from the solvation parameter model for transfer from the gas phase to the solvent at 25°C... 

The solvation parameter model has been used as the basis of a structure-driven retention model for method development in reversed-phase thin-layer chromatography [95,151,161-164]. The model should be applicable to normal-phase separations on chemically bonded layers as well, but not silica gel layers [164]. Solute size differences and site-specific interactions on silica gel are not adequately accounted for by the model, which results in poor predictions of retention. The solvation parameter model is described in section 1.4.3. The Rm value (section 6.3.1) is used as the dependent variable. 

Method development for binary mobile phases using the solvation parameter model is based on the use of system maps. A system map is a continuous plot of the system constants obtained from experimental data fit to the solvation parameter model against mobile phase composition. However, once constructed the system map is a permanent record of system properties. It is used in all calculations and is not restricted to the compounds used to construct the system map. A typical system map for methanol-water mobile phases on a 3-cyanopropylsiloxane-bonded layer is shown in Figure 6.17. System maps for several binary mobile phases on octadecylsiloxane-bonded [95],... 

The solvation parameter model (section 6.8.2) can be considered a suitable model for computer-aided method development. Computer-aided strategies for mobile phase... 

Figure 7.7. System constants of the solvation parameter model for retention on a porous polymer stationary phase with a binary mixture of carbon dioxide and 1,1,1,2-tetrafluoroethane as the mobile phase. Column 25 cm X 4.6 mm I.D. Jordi-Gel RP-C18 with a 5 pm average particle diameter. The total fluid flow rate was 1.0 ml/min, backpressure 200 bar and ternperamre I25°C.

System constant ratios from the solvation parameter model for surfactant micelles (Temperature = 20-25°C except were noted)... 

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