Gibbs free energy, chromatography

The application of liquid chromatography at the critical point of adsorption to block copolymers is based on the consideration that Gibbs free energy AGab of a block copolymer AnBm is the sum of the contributions of block A and block B, AGa and AGB respectively. 

The equilibrium constant, K, thermodynamically could be described as the exponent of the Gibbs free energy of the analyte s competitive interactions with the stationary phase. In hquid chromatography the analyte competes with the eluent for the place on the stationary phase, and resulting energy responsible for the analyte retention is actually the difference between the analyte interaction with the stationary phase and the eluent interactions for the stationary phase as shown in equation (1-5)... 

Figure 14.11. Plots of the Gibbs free energy per unit area, AG/Ap, as a function of the distance between the two oppositely charged surfaces, L, at different ionic strengths. The results were calculated using 8r = 80, and by setting —0.16 and +0.03 C/m2 as the charge densities of the stationary and mobile phases, respectively.13 [Reprinted, with permission, from J. Stahlberg, B. Jonsson, and C. Horvath, Anal. Chem. 63, 1991, 1867-1874. Theory for Electrostatic Interaction Chromatography of Proteins . 1991 by American Chemical Society.]...

The theory of adsorption at porous adsorbents predicts the existence of a finite critical energy of adsorption e, where the macromolecule starts to adsorb at the stationary phase. Thus, at > the macromolecule is adsorbed, whereas at e < e the macromolecule remains unadsorbed. At e = Ec the transition from the unadsorbed to the adsorbed state takes place, corresponding to a transition from one to another separation mechanism. This transition is termed critical point of adsorption and relates to a situation, where the adsorption forces are exactly compensated by the entropy losses TAS = AH [2, 7]. Accordingly, at the critical point of adsorption the Gibbs free energy is constant (AG = 0) and the distribution coefficient is Kj = 1, irrespective of the molar mass of the macromolecules. The critical point of adsorption relates to a very narrow range between the size exclusion and adsorption modes of liquid chromatography. It is, therefore, very sensitive towards temperature and mobile phase composition. 

For any form of (gas or liquid) chromatography, one can define the distribution of solute between the stationary and mobile phases by an equilibrium (2). At equilibrium the chemical potentials of each solute component in the two phases must be equal. The driving force for solute migration from one phase to the other is the instantaneous concentration gradient between the two phases. Despite the movement of the mobile phase in the system, the equilibrium exists because the solute diffusion into and out of the stationary phase is fast compared with the flow rate. Under dilute solution conditions, the equilibrium constant (the ratio of solute concentrations in the stationary to the mobile phases) can be related to the standard Gibbs free-energy difference between the phases at constant temperature and pressure ... 

Standard Gibbs free energy change in interaction chromatography... 

It should be borne in mind that chiral chromatography is a dynamic process of forming transient noncovalent diastereomeric complexes between chiral solutes and immobilized chiral selectors. Enantioselectivity (a) is a measurement of the thermodynamic stability (A AG) of the two diastereomeric enantiomer/chiral selector complexes. The A AG parameter is the Gibbs free energy difference of the two complex selector-selectand formation. It includes both an enthalpic AAH) and an entropic (TAAS) contributions (Eq. (1)) ... 

Assumption 5 In the definition of the isotherm, the convention is adopted that the solvent (if pure) or the weak solvent (in a mixed mobile phase) is not adsorbed [8]. Riedo and Kov ts [9] have given a detailed discussion of this problem. They have shown that the retention in liquid-solid i.e., adsorption) chromatography can best be described in terms of the Gibbs excess free energy of adsorption. But it is impossible to define the surface concentration of an adsorbate without defining the interface between the adsorbed layer and the bulk solvent. This in turn requires a convention regarding the adsorption equilibrium [8,9]. The most convenient convention for liquid chromatography is to decide that the mobile phase (if pure) or the weak solvent (if the mobile phase is a mixture) is not adsorbed [8]. Then, the mass balance of the weak solvent disappears. If the additive is not adsorbed itself or is weakly adsorbed, its mass balance may be omitted [30]. 

---