Partition coefficient, chromatographic thermodynamic

Schantz, M.M., Martire, D.E. (1987) Determination of hydrocarbon-water partition coefficients from chromatographic data and based on solution thermodynamics and theory. J. Chromatogr. 391, 35-51. 

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. 

It is illustrated in Figure 5.1a. Clearly, both Rr and Rr can be easily calculated from their respective chromatograms, making them very useful measures for describing chromatographic results. Recall also that Rr = 1/(1 + k) and that k is proportional to the partition coefficient K, the basic thermodynamic variable in chromatographic theory. 

The driving force in chromatography for the. separation of an analyte is the equilibrium between the stationary and the mobile phases. As it was di.scus.sed in Chapter 11 in more detail, the chromatographic equilibrium can be related to the chemical potential of the compound. Unfortunately, the relationship between retention parameters and the quantities related to the chemical structure cannot be solved in. strictly thermodynamic terms. Therefore, the extra-thermodynamic approach is applied to reveal the relationships. During chromatography we do not achieve a proper equilibrium, the separation is still a result of the difference of equilibrium constants for the compounds in the stationaiy and the mobile phases. The.se equilibrium con.stants can be related to measured retention data as was discussed in the previous chapter. So whenever our chromatographic system (the stationary and the mobile phase) can be considered as two immiscible phases the retention data (equilibrium data) will provide a partition coefficient. 

Shake-flask measurements are often employed to design a suitable LLPC system for a given sample mixture by assisting in the selection of the two phases in which the compound of interest shows a partition coefficient sufficiently different from those of the impurities. One of the two phases is then immobilized on a suitable support that is packed into the column, and the second phase is used as the mobile phase. In general, partition coefficients of solutes obtained from static experiments compare favorably with those obtained from chromatographic experiments [3]. A comprehensive thermodynamic treatment of LLPC can be found in Ref. 4, and the prediction and control of zone migration is discussed extensively in Ref. 5. 

A large value means the analyte spends more time in the stationary phase and thus spends more time on the column and has a longer retention time (Figure 11.3). The partition coefficient can be assumed to be constant for a compound under a given set of chromatographic conditions and represents the thermodynamic... 

The thermodynamic partition constant, Ki, has to be employed for calculating the free energy of adsorption of any adsorbate, which differs in nature from the chromatographic partition constant, K. Actually, the thermodynamic partition coefficient, Ki, is the ratio of the partial pressure of the chromatographed solute p, to its molar fraction in the stationary phase, jc,-. For designing chemical processes the thermodynamic Ki values are usually expressed as ... 

Thermodynamic partition coefficient. In chromatographic applications the Nernst distribution constant it of a component i, referred to as the... 

The thermodynamic and chromatographic partition coefficients are related by the equation ... 

Eqn (2.42) expresses the correlation between the retention parameter F,v of a column and the equilibrium thermodynamic properties of the system represented by the chromatographic partition coefficient K. 

The quantitative interpretation of chromatographic data often becomes more intricate because of adsorption at one or both interfaces (liquid-solid and gas-liquid) present in the system it is obviously assumed that the whole support surface area is covered by stationary phase and therefore there is no gas-solid interface. Provided that one can evaluate and then eliminate the contribution of interface adsorption to the net retention volume, the partition coefficient reflects only the solute-solvent interaction and it allows the determination of thermodynamic properties of solution to a greater degree of irrecision. 

The numerical values of chromatographic partition coefficient, regarded as a constant of physical equilibrium, depend on the standard states chosen for the solute in the two phases that participate in the distribution process. Consequently the standard thermodynamic properties take values which depend on this choice. A standard thermodynamic property should always be accompanied by an explicit definition of standard states. 

Up to this point we have discussed the optimization of gas chromatographic separations by manipulation of the column variables that do not affect peaks relative retentions. Changing the column dimensions, the stationary-phase film thickness or the carrier-gas velocity will affect retention times, but the peaks thermodynamic partition coefficients (K) remain constant a long as the colunm temperature and the stationary-phase chemistry remain unchanged. As a result, the peaks relative retentions—the ratios of their adjusted retention times (t )—also will not be affected by such manipulations, and so the peaks elution order and relative separations remain unchanged. This makes prediction of the effects of modifying these variables fairly simple to compute using relationships such as those presented thus far in this chapter. 

Where K is the surface partition coefficient and A is the total surface area of the polymer powder in the chromatographic column. Thermodynamically, the molar free energy of adsorption,.AGi , of solute on the polymer layer can be related to Vg by the following relationship ... 

The partition and activity coefficients are used for determining the excess thermodynamic functions of the mixing of chromatographed substances on stationary phase free... 

The basic assumption in any chromatographic theory is that retention is determined by the thermodynamic factors. In such a way, mobile and stationary phases are interpreted as true thermodynamic phases with volumes Vm and Vs, respectively, so that retention volume depends on the partition (distribution) equilibrium coefficient A" of the solute in these two phases Vr = Vm +KVs-By definition, all enthalpic and entropic interactions between the macromolecules and the chromatographic surface occur in the stationary phase. If the size of macromolecules in solution is comparable with the internal diameter of pores, the entire pore volume represents the stationary phase. Vs = Vp, yet the mobile phase is formed by the interstitial volume only, Vm = Vq. This is not always the case for... 

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