Stationary phases, thermodynamics

Although the chiral recognition mechanism of these cyclodexttin-based phases is not entirely understood, thermodynamic and column capacity studies indicate that the analytes may interact with the functionalized cyclodextrins by either associating with the outside or mouth of the cyclodextrin, or by forming a more traditional inclusion complex with the cyclodextrin (122). As in the case of the metal-complex chiral stationary phase, configuration assignment is generally not possible in the absence of pure chiral standards. 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

The concentration profiles of the solute in both the mobile and stationary phases are depicted as Gaussian in form. In due course, this assumption will be shown to be the ideal elution curve as predicted by the Plate Theory. Equilibrium occurs between the mobile phase and the stationary phase, when the probability of a solute molecule striking the boundary and entering the stationary phase is the same as the probability of a solute molecule randomly acquiring sufficient kinetic energy to leave the stationary phase and enter the mobile phase. The distribution system is continuously thermodynamically driven toward equilibrium. However, the moving phase will continuously displace the concentration profile of the solute in the mobile phase forward, relative to that in the stationary phase. This displacement, in a grossly... 

An interesting and practical example of the use of thermodynamic analysis is to explain and predict certain features that arise in the application of chromatography to chiral separations. The separation of enantiomers is achieved by making one or both phases chirally active so that different enantiomers will interact slightly differently with the one or both phases. In practice, it is usual to make the stationary phase comprise one specific isomer so that it offers specific selectivity to one enantiomer of the chiral solute pair. The basis of the selectivity is thought to be spatial, in that one enantiomer can approach the stationary phase closer than the other. If there is no chiral selectivity in the stationary phase, both enantiomers (being chemically identical) will coelute and will provide identical log(Vr ) against 1/T curve. If, however, one... 

For the GPC separation mechanism to strictly apply, there must be no adsorption of the polymer onto the stationary phase. Such adsorption would delay elution of the polymer, thereby resulting in the calculation of too low a molecular weight for the polymer. The considerable variety of undesirable interactions between polymers and column stationary phases has been well reviewed for GPC by Barth (1) and this useful reference is recommended to the reader. Thus, the primary requirement for ideal GPC is that the solvent-polymer interaction be strongly thermodynamically favored over the polymerstationary phase interaction. 

The problem of transport of molecules through swollen gels is of general interest. It not only pertains to catalysis, but also to the field of chromatographic separations over polymeric stationary phases, where the partition of a solute between the mobile phase (liquid phase) and a swollen polymeric stationary phase (gel phase) is a process of the utmost importance. As with all the chemical and physicochemical processes, the thermodynamic and the kinetic aspect must be distinguished also in partition between phases. 

Many chromatographic systems show linear relationships between the logarithm of the capacity factor and the reciprocal of the column temperature (van t Hoff plots) [255,258-261]. In thermodynamic terms the interaction of the solute with the stationary phase can be described by... 

If stationary phase interactions are negligible the lattice statistical thermodynamic model and the solvophobic model predict similar results. The strength of the lattice statistical thermodynamic model is that it can explain the shape selectivity observed for certain stationary phases and can accommodate silanophllic interactions. 

Guillaume et al. [69] presented a high performance liquid chromatographic method for an association study of miconazole and other imidazole derivatives in surfactant micellar using a hydrophilic reagent, Montanox DF 80. The thermodynamic results obtained showed that imidazole association in the surfactant micelles was effective over a concentration of surfactant equal to 0.4 pM. In addition, an enthalpy-entropy compensation study revealed that the type of interaction between the solute and the RP-18 stationary phase was independent of the molecular structure. The thermodynamic variations observed were considered the result of equilibrium displacement between the solute and free ethanol (respectively free surfactant) and its clusters (respective to micelles) created in the mobile phase. 

Put in ordinary terms, the more successful we are in causing a separation, the more propensities there are for a re-mixing of the components. There are many ways this can occur but there are a fewer number of important routes to mixing. It seems reasonable that we examine these before we consider all the possible ways in which thermodynamics can be controlled in general terms. In almost all equilibrium separation systems, the separation can occur either in a packed bed of particles or fibers or in an open channel or tube. The stationary phase is either coated on the walls of the channel or on the particles/fibers of the packed bed. If there were no mixing mechanisms an infinitely narrow packet containing the components would become a series of infinitely narrow packets of pure components moving at different velocities toward the end of the packed bed or tube. 

The retention of the band or peak beyond what V0 predicts depends on the magnitude of the equilibrium constant and logically on the volume Vs or area As of the stationary phase. The equation of importance is Vr — V0+KVS and the net retention V/ = KVS. Two main factors influence the value of the equilibrium constant and these are the chemical nature of the mobile and stationary phases. Chemistry is molecules and while true thermodynamics knows no molecules or forces between molecules, chemists think in terms of molecular properties. Among those properties, there is a consideration of the kinds of forces that exist between molecules. Granted that thermodynamics are energy not force considerations but it is useful to understand the main forces involved in the interaction between molecules. Put another way,... 

The equilibrium constant is then connected to the thermodynamics of the mobile phase-stationary phase transfer process using classical expressions. 

It is apparent from early observations [93] that there are at least two different effects exerted by temperature on chromatographic separations. One effect is the influence on the viscosity and on the diffusion coefficient of the solute raising the temperature reduces the viscosity of the mobile phase and also increases the diffusion coefficient of the solute in both the mobile and the stationary phase. This is largely a kinetic effect, which improves the mobile phase mass transfer, and thus the chromatographic efficiency (N). The other completely different temperature effect is the influence on the selectivity factor (a), which usually decreases, as the temperature is increased (thermodynamic effect). This occurs because the partition coefficients and therefore, the Gibbs free energy difference (AG°) of the transfer of the analyte between the stationary and the mobile phase vary with temperature. 

Haroun, M. et al.. Thermodynamic origin of the chiral recognition of tryptophan on teicoplanin and teicoplanin aglycone stationary phases, J. Sep. ScL, 28, 409, 2005. 

Enantioselective separation by supercritical fluid chromatography (SFC) has been a field of great progress since the first demonstration of a chiral separation by SFC in the 1980s. The unique properties of supercritical fluids make packed column SFC the most favorable choice for fast enantiomeric separation among all of the separation techniques. In this chapter, the effect of chiral stationary phases, modifiers, and additives on enantioseparation are discussed in terms of speed and resolution in SFC. Fundamental considerations and thermodynamic aspects are also presented. 

In this chapter, approaches to fast chiral separations using SFC, including fundamental considerations, influences of chiral stationary phases, modifiers, and additives are discussed. The thermodynamic aspects of SFC are also presented. 

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