Rate theory, elution chromatography

The rate theory of chromatography describes the shapes and breadths of elution bands in quantitative terms based on a random-walk mechanism for the migration of molecules through a column. A detailed discussion of the rate theory is beyond the scope of this text. We can, however, give a qualitative picture of why bands broaden and what variables improve column efficiency. ... 

In a chromatographic separation, the individual components of a mixture are moved apart in the column due to their different affinities for the stationary phase and, as their dispersion is contained by appropriate system design, the individual solutes can be eluted discretely and resolution is achieved. Chromatography theory has been developed over the last half century, but the two critical theories, the Plate Theory and the Rate Theory, were both well established by 1960. There have been many contributors to chromatography theory over the intervening years but, with the... 

The essentials of chromatography have been discussed in Section I, A, and are illustrated in Fig. 1. Although saturation operations have been investigated at length by rate-theory approaches, the case of chromatographic elution from an incompletely saturated column has received little attention from the rate standpoint. 

Figure 3.2 The elution curve of a single component, plotted as the analyte concentration at the column exit (proportional to the detector response Rj,) as a function of V, the total volume flow of mobile phase that has passed through the column since injection of the analytical sample onto the column. (V is readily converted to time via the volume flow rate U of the mobile phase.) The objective of theories of chromatography is to predict some or all of the features of this elution curve in terms of fundamental physico-chemical properties of the analyte and of the stationary and mobile phases. Note that the Plate Theory addresses the position of the elution peak but does not attempt to account for the peak shape (width etc.). The inflection points occur at 0.6069 of the peak height, where the slope of the curve stops increasing and starts decreasing (to zero at the peak maximum) on the rising portion of the peak, and vice versa for the falling side the distance between these points is double the Gaussian parameter O. Modified from Scott, www.chromatography-online.org, with permission.

One of these proposed a non-equilibrium process in which the separation was controlled by differing rates of diffusion for different molecular masses [23]. Other workers have proposed a separation by flow mechanism [24, 25] in which the larger molecules are excluded from the surface of the gel particles and remain in the centre of the solvent channels and are thus eluted first. The original theory did not invoke a porous structure for the gel, but this was modified later. The mechanism bears resemblance to that proposed for hydrodynamic chromatography (see Chapter 10). A further model suggested that the pore size distribution of the gel was directly responsible for its ability to separate molecules by size, and that there is a one-to-one correspondence with size of pores and size of molecules [26]. All these theories have been critically reviewed in the book by Yau et al [6]. 

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