Distribution coefficient retention control

It is important to realize that all static phases will contribute to retention and, as a result, a number of different distribution coefficients will control the retention of the solute. Nevertheless, the situation can be simplified to some extent. The static interstitial volume (Vi(s)) and the pore volume fraction (Vp(i)) will contain mobile... 

It has been shown that, in LC, the size of the distribution coefficient of a solute between the two phases determines the extent of its retention. As a consequence, the difference between the distribution coefficients of two solutes establishes the extent of their separation. The distribution coefficients are controlled by the nature and strength of the molecular interactions that takes place between the solutes and the two phases. Thus it is the choice of the phase system that primarily determines the separation that is achieved by the chromatographic system. 

The same linear relationship between mobile phase composition and retention was noted by Katz et al. [7] for binary mixtures in LC. However, in LC the situation is more complicated, and if strong association occurs between the mobile phase components, the relationship becomes nonlinear. Unfortunately, the technique of using the two columns procedure of Purnell is impractical for mixed mobile phases in LC. Furthermore, as the solvents most commonly used are water, methanol, acetonitrile and tetrahydrofuran, and all form strong associates, the use of the linear relationship demonstrated by Katz et al. is severely limited. An example of the linear relationship between volume fraction of one component of two binary mixtures and retention is shown in figure 3.8. The linear relationship is clearly demonstrated and it is seen that the distribution coefficient (which controls retention) can be adjusted to any selected value by choosing the appropriate mixture of the two solvents. 

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. 

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 theory of solute retention, as controlled by molecular Interactions between the solutes and the phase system is, in fact, not germane to the subject of this book. Nevertheless, as distribution and distribution coefficients together with retention volumes and capacity ratios will be discussed or used in the subsequent theoretical development of column theory, the basic principles of molecular interaction will be given. 

It has already been stated that the retention of a solute depends on the magnitude of the distribution coefficient of the solute between the mobile and stationary phases. Furthermore, according to Vant Hoff s Law, the distribution coefficient will vary according to the exponent of the reciprocal of the absolute temperature. In addition, the dispersion of a solute band in a column will be shown to depend on the dlffusivity of the solute In both phases, the viscosity of the mobile phase and also on the distribution coefficient of the solute, all of which vary with temperature. It follows that, for consistent results, the column must be carefully thermostated. The column and its contents have a significant heat capacity and, consequently, it is of little use trytng to thermostat the column in an air bath for satisfactory temperature control, the thermostating medium... 

The concentration of the counterion can be used to control the retention in IEC. It plays a role similar to that of the eluotropic strength of the eluent in RPLC or LSC, in that it affects retention much more than it does selectivity. The capacity factor can be related to the distribution coefficient of the solute (Dx) ... 

It is obvious from Fig. 1 that the chromatographic separation of components in a mixture is dependent on two factors the difference in retention times of two adjacent peaks, or more precisely, the difference between peak maxima and the peak widths. It was shown in the preceding discussion that the retention of a solute is a thermodynamic process controlled by the distribution coefficient and the stationary-phase volume. The peak width, or band broadening, on the other hand, is a function of the kinetics of the system. 

It is seen that if the standard entropy change and standard enthalpy change for the distribution of any given solute between two phases can be calculated, then the distribution coefficient (K) and, consequently, its retention volume can also be predicted. Unfortunately, these properties of a distribution system are bulk properties, that include, in a single measurement, the effect of all the different types of molecular interactions that are taking place between the solute and the two phases. As a result it is often difficult to isolate the individual interactive contributions in order to estimate the magnitude of the overall distribution coefficient, or identify how it can be controlled. Nevertheless, there are a number of ways in which this can be done and, in any event, the thermodynamic approach can provide valuable information with regard to the nature of the distribution. 

In order to learn how to achieve the selectivity required to resolve a pair of enantiomorphs, the mechanism of retention must be fully understood. This means that the molecular forces that control retention must be defined, their mode of action identified, and their effect on the distribution coefficient (K) examined. The magnitude of (K) depends on the relative affinity of the solute for the two phases. Consequently, the stationary phase must be chosen to interact strongly with the solutes to achieve a separation i.e. the intermolecular forces between solute and stationary phase must be relatively large). In contrast, the interactions between the solute molecules and the mobile phase should be chosen to be relatively weak, to allow the stronger forces to dominate in the stationary phase and produce the required retention and selectivity. This will naturally occur in GC, as the probability of interaction (collision between solute and gas molecules) is very small compared with that in a liquid, and due to the small mass of the mobile phase molecules, the strength of any interactions that do occur will be extremely weak. This will not be true in LC, and the mobile phase must be chosen so that the type of interactions that take place with the solute will be weaker than those that take place between the solute and the stationary phase. This will become clearer when the different types of molecular interactions are understood. 

These workers examined the effect of mixed stationary phases on solute retention in GC during the late 1970s and early 1980s. They found that, for a wide range of binary mixtures, the corrected retention volume of a solute was linearly related to the volume fraction of either one of the two phases. These results produced considerable controversy which still persists in many contemporary academic circles. The major point of argument arose from the fact that as the corrected retention volume, and thus the distribution coefficient, was linearly related to the volume fraction of either phase, this meant the distribution coefficient was linearly controlled by the volume fraction of the stationary phase component and not exponentially related to it. This does not seem to be surprising, as the volume concentration will control the probability of interaction and thus if the concentration is doubled, the probability of interaction will be expected to double and also the distribution coefficient. However, this linear relationship only holds for binary mixtures. It will be seen that for ternary mixtures, that result from associations of the stationary phase components with one another, the relationship breaks down. 

The same type of molecular forces are involved as those in GC, except that, as the solutes no longer need to be volatile, ionic interactions can now be used to control retention, in addition to dispersive and polar interactions, as in GC. It will be seen that temperature can also be used to control retention in LC, in a somewhat similar manner to GC. The distribution coefficient of a solute between the two phases in LC will always result from both standard free entropy and enthalpy changes during distribution, as in GC. In addition, the separation of enantiomers will also depend primarily on a difference in the standard free entropy between the two isomers, that results from spatial variations and which are then augmented by standard free enthalpy differences. 

For both SFC and SEC, the solute distribution coefficient between stationary and mobile phases is K, which is related to the standard free energy difference for a solute in the two phases. SFC is an enthalpy-controlled process, so that the retention parameter k is positive, and retention volumes, Fr, for the members of a homologous series in SFC are related to molecular mass, M ... 

Theoretically, chromatography may be described as a combination of thermodynamic and kinetic processes. The thermodynamic aspects control the retention and shape of the peak whilst the kinetic aspects control the sharpness of the band. Together they define the resolution between components. The fundamental thermodynamic parameter is the distribution coefficient of the solute between the phases. This is given as the ratio between the concentrations of a solute in the stationary and mobile phases. 

The situation is simpler for SEC. Since the hydrodynamic radius (which gives the diffusion coefficient D) is often considered to be the governing parameter for SEC, we conclude that the one factor (D) controlling retention in SEC can be identified with one of the two parameters controlling retention in thermal FFF. This offers the possibility of combining thermal FFF and SEC as elements of a two-dimensional separation system capable of determining both the molecular mass distribution and the compositional distribution within complex polymeric materials such as copolymers or blends [28]. 

IGC measurements can be carried out using a pulse or continuous technique. The pulse of probe molecule is introduced into the carrier gas stream. This pulse is transported by the carrier gas through the system to the column with the solid sample. On the stationary phase, adsorption and desorption occur and the result is a peak in the chromatogram. The ratio of adsorption/desorption is governed by the partition coefficient. At fixed conditions of temperature and flow rate, the time of retention of a compound is characteristic of the system. An alternative is the fi ontal technique. This is carried out by injection into the carrier gas stream of a continuous stream of the probe molecule. When the sample enters into the column, there is a distribution between phases, and the concentration profiles takes the shape of a plateau, preceded by a breakthrough curve. The shape of this curve is characteristic of each system [3]. The benefit of the frontal technique is that equilibrium can be always established due to its continuous nature while pulse chromatography requires the assumption of a fast equilibration of the probe molecule adsorption on the surface. Between both techniques, the main part of publications describes pulse experiences, since they are faster, easier to control and more accurate, especially if interactions between probe molecules and the adsorbent are weak. 

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