Basic Equations Describing Chromatographic Separations

We will state or derive a bare minimum of the equations most useful for understanding and describing how the most easily measured or controlled variables affect separations in chromatography. Many of the factors in these equations can be derived or calculated from more fundamental parameters, such as diffusion coefficients of analytes in the two chromatographic phases, column dimensions, or variables defined in the statistical theory of random variation. Such details are covered in more advanced texts. 

Manufacturers of open tubular GC columns often specify column radius and stationary phase film thickness ( /,), which is usually much smaller. Simple geometry enables us to calculate the phase ratio  

How much a component is retained by the stationary phase is better described by,  

The plates may be imagined as distances along the column where a complete equilibration of the sample between the two phases takes place. The greater the number of plates for a given column length, the shorter the HETP, H, and the more efficiently the column operates. This distance along 

Since d in Equation 11.5 equals (tX (Oa we can solve for w, in Equation 11.6, insert it into the second expression of Equation 11.5, and relate resolution to plate number N as follows  

---

Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly (as Giddings points out) at the maximum of a peak (1). As stated before, to circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (2) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a dwell time for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. It has been shown that employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others can be developed that describe the various properties of a chromatogram. Such equations will permit the calculation of efficiency, the calculation of the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. 

This chapter introduces fundamental aspects and basic equations for the characterization of chromatographic separations. Starting from the simple description of an analytical separation of different compounds the influences of fluid dynamics, mass transfer and thermodynamics are explained in detail. The important separation characteristics for preparative and process chromatography, e.g. the optimization of resolution and productivity as well as the differences compared with chromatography for analytical purposes, are described. Especially, the importance of understanding the behavior of substances in the nonlinear range of the adsorption isotherm is highlighted. 

Basic physical phenomena occurring during a chromatographic separation are described in Chapter 2. A quantitative description is possible using suitable mathematical models, which are typically based on material, energy, and momentum balances, in addition to equations that quantify the thermodynamic equilibria of the distribution of the solutes between the different phases. A good model has to be as... 

---