Chromatographic processes capacity factor

So far the Plate Theory has been used to determine the equation for the retention volume of a solute, calculate the capacity factor of a solute and identify the dead volume of the column and how it should be calculated. However, the equation for the elution curve of a solute that arises directly from the Plate Theory can do far more than that to explain the characteristics of a chromatogram. The equation will now be used in a variety of ways to expand our knowledge of the chromatographic process. 

Obviously, there are many ways to influence the capacity factors. However, the effects described above are predictable (see section 4.2.3) and in a sense trivial. It is worth noticing at this point that certain parameters do not at all affect the capacity factor and therefore do not at all affect chromatographic selectivity. These parameters include column length, flow rate and the diameter of packed columns. This renders these parameters irrelevant to the selectivity optimization process. In some cases they may be considered as parameters... 

As is evident from the preceding discussion, the retention behavior of a polypeptide or protein P- expressed in terms of the capacity factor k is governed by thermodynamic considerations. Peak dispersion, on the other hand, arises from time-dependent kinetic phenomena, which are most conveniently expressed in terms of the reduced plate height he, . When no secondary effects, i.e., when no temperature effects, conformational changes, slow chemical equilibrium, pH effects, etc. occur as part of the chromatographic distribution process, then the resolution Rs, that can be achieved between adjacent components separated under these equilibrium or nearequilibrium conditions can be expressed as... 

The capacity factor is directly connected to the distribution coefficient, K, and thus with the thermodynamic quantities A m s and ASm s, which determine the chromatographic sorption process. (The indices m—>s characterize the mass transfer from the mobile phase to the stationary phase.)... 

A mathematical description of the retention of ions under gradient elution conditions was introduced in 1957 by Schwab et al. [131]. It is based on parameters which are derived from the normal chromatographic elution process for which the eluent composition is kept constant during the separation. Hence, the retention of an ion at isocratic elution may be described according to Eq. (86), taking into account the definitions for the capacity factor, k, and the selectivity coefficient, K, [see Eq. (35) and (36) in Section 3.2] ... 

Fritz and Scott (23) derived simple statistical expressions for calculating the mean and variance of chromatographic peaks that are still on a column (called position peaks) and these same peaks as they emerge from the column (called exit peaks). The classical plate theory is derived by use of simple concepts from probability theory and statistics. In this treatment, each sample chemical substance molecule is examined separately, whereas its movement through the colunm is described as a stochastic process. Equations are given for both discrete- and continuous-flow models. They are derived by calculating the mean and variance of a chromatographic peak as a function of the capacity factor k. 

As can be concluded from this short description of the factors influencing the overall reaction rate in liquid-solid or gas-solid reactions, the structure of the stationary phase is of significant importance. In order to minimize the transport limitations, different types of supports were developed, which will be discussed in the next section. In addition, the amount of enzyme (operative ligand on the surface of solid phase) as well as its activity determine the reaction rate of an enzyme-catalyzed process. Thus, in the following sections we shall briefly describe different types of chromatographic supports, suited to provide both the high surface area required for high enzyme capacity and the lowest possible internal and external mass transfer resistances. 

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