Thermodynamic descriptions based on the adsorption approach to retention in RP HPLC work pretty well in explanations of all effects. Special attention in using thermodynamic theory has to be placed on the actual value of the surface area of the adsorbent. As we have discussed in the adsorbent section, there is a significant changes in the adsorbent surface area after bonding the hydrophobic ligands.
The presence of accessible residual silanols usually introduces highly energetic specific interactions, which cause nonuniform behavior of specific components in the column.
The entropy and enthalpy changes associated with the competitive adsorption of analyte on the reversed-phase adsorbent are defined by van't Hoff equation
where K is the thermodynamic equilibrium constant, is an excess free Gibbs energy of surface interactions of analyte over eluent and compared to standard state, same for enthalpy , and entropy, R is the gas constant.
or as a first approximation we can write
From the above equation we can conclude that the dependencies of the logarithm of the capacity factor vs. the inverse temperature should be linear. Experimental data are shown below.
Dependencies of the logarithm of the capacity factors vs. inversed temperature for alkylbenzenes homologous series. (from bottom to top: benzene, toluene, ethylbenzene (C2), propylbenzene (C3), C5, C7, C9, C11, C13, C15)
According to the above equation, the slope of the line represents an excess adsorption enthalpy, and the intercept represents the entropy value for the particular component.
The longer the alkyl chain, the higher the entropy, and the stronger surface interactions. But the energetic increment for each -CH2- group is not the same for each component, as it can be seen from the graph below.
These dependencies are shown here to illustrate the possibility of thermodynamic measurements of surface interactions using HPLC. Deeper consideration is out of the scope of this book and can be found in special literature.