Stationary phase distribution coefficient

In liquid elution chromatography, separation is based on adsorption on the solid or on partition to a stationary or bonded liquid phase. Distribution coefficients are modest so that solutes migrate through the column as shown in Figs. 14.1-2 and 14.1-3. Gradients can be used but usually are not since the column has to be reequilibrated afterward. Two somewhat different approaches have bMn taken ... 

Distribution Coefficients. Gel-permeation stationary-phase chromatography normally exhibits symmetrical (Gaussian) peaks because the partitioning of the solute between mobile and stationary phases is linear. Criteria more sophisticated than those represented in Figure 8 are seldom used (34). 

The distribution coefficient, represents the fractional volume of a specific stationary phase explored by a given solute, represented by equation 3 ... 

A separation process that is achieved by the distribution of the substances to be separated between two phases, a stationary phase and a mobile phase. Those solutes, distributed preferentially in the mobile phase, will move more rapidly through the system than those distributed preferentially in the stationary phase. Thus, the solutes will elute in order of their increasing distribution coefficients with respect to the stationary phase."... 

Xs) is the concentration of solute in the stationary phase, and (K) is the distribution coefficient of the solute between the two phases. 

The extent to which two solutes are separated depends exclusively on the relative magnitudes of their individual distribution coefficients (K(a)) and (K(b)) and the amount of stationary phase with which they can interact, (V(a)) and (V(b)). Consequently, for them to be separated, either their distribution coefficients must differ (choose appropriate phase systems), the amount of stationary phase with which they interact must differ (choose a stationary phase with exclusion properties), or a subtle combination of both. 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

The primary factors that govern retention are the distribution coefficient (K) and the volume of stationary phase (Vs)). It is now necessary to identify those parameters that control the magnitude of the distribution coefficient itself and the volume of available stationary phase in a column. A study of these factors will be the subject of the next chapter. 

Although, for most moderators, the surface of a stationary phase in LC can be considered stable at moderator concentrations above about 5%v/v, the results from the same experiments as those carried out by Purnell and his group could still be considered invalid and, at best, would not lead to unambiguous conclusions. Katz et al. [9] avoided this problem by examining liquid/liquid distribution systems using water as one phase and a series of immiscible solvent mixtures as the other and by measuring absolute distribution coefficients as opposed to retention volumes. 

For chromatography purposes the product of the distribution coefficient and the volume of stationary phase, or stationary phase surface area, gives the corrected retention volume,/, e.,... 

It should be recalled that the distribution coefficients are referenced to the solvent mixture and not the stationary phase and are thus the inverse of the distribution coefficient employed in the chromatography elution equation. 

K(2)) is the distribution coefficient of solute (2) with respect to the stationary phase,... 

When the relationship between the distribution coefficient of a solute and solvent composition, or the corrected retention volume and solvent composition, was evaluated for aqueous solvent mixtures, it was found that the simple relationship identified by Purnell and Laub and Katz et al. no longer applied. The suspected cause for the failure was the strong association between the solvent and water. As a consequence, the mixture was not binary in nature but, in fact, a ternary system. An aqueous solution of methanol, for example, contained methanol, water and methanol associated with water. It follows that the prediction of the net distribution coefficient or net retention volume for a ternary system would require the use of three distribution coefficients one representing the distribution of the solute between the stationary phase and water, one representing that between the stationary phase and methanol and one between the stationary phase and the methanol/water associate. Unfortunately, as the relative amount of association varies with the initial... 

It is seen from the above equation that the band velocity is inversely proportional to the distribution coefficient with respect to the stationary phase. It follows that any changes in the distribution coefficient (K) will result directly in changes in the band velocity (Z). Consequently, if the isotherm is linear, then all concentrations will travel at the same velocity and the peak will be symmetrical. 

The isotherm will be close to linear at very low concentrations of solute in the mobile phase and thus, again, all concentrations in the peak will travel at the same speed and the resulting peak is symmetrical. However, when the points y, x and y", x" are reached, the concentration of solute in the stationary phase is increasing more rapidly with the solute concentration in the mobile phase and thus the distribution coefficient at the higher concentrations is larger. It follows that, as the peak velocity is inversely proportional to the distribution coefficient, then the higher concentrations in the peak will migrate more slowly than the lower concentrations. 

Consequently, the solutes will pass through the chromatographic system at speeds that are inversely proportional to their distribution coefficients with respect to the stationary phase. The control of solute retention by the magnitude of the solute distribution coefficient will be discussed in the next chapter. 

Solute retention, and consequently chromatographic resolution, is determined by the magnitude of the distribution coefficients of the solutes with respect to the stationary phase and relative to each other. As already suggested, the magnitude of the distribution coefficient is, in turn, controlled by molecular forces between the solutes and the two phases. The procedure by which the analyst can manipulate the solute/phase interactions to effect the desired resolution will also be discussed in chapter 2. 

The chromatographic column has a dichotomy of purpose. During a separation, two processes ensue in the column, continuously, progressively and virtually independent of one another. Firstly, the individual solutes are moved apart as a result of the differing distribution coefficients of each component with respect to the stationary phase in the manner previously described. Secondly, having moved the individual components apart, the column is designed to constrain the natural dispersion of each solute band (i.e. the band... 

Thus, to achieve the required separation either (1) the distribution coefficient (K) of all the solutes must be made to differ, or (2) the amount of stationary phase (V s) available to each component of the mixture interacts must be made to differ. A further alternative (3)... 

Chemical forces are normally irreversible in nature (at least in chromatography) and thus, the distribution coefficient of the solute with respect to the stationary phase is infinite or close to infinite. Affinity chromatography is an example of the use of chemical forces in a separation process. The stationary phase is formed in such a manner that it will chemically interact with one unique solute present in the sample and thus, exclusively extract it from the other materials... 

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