Rate theory of 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. ... 

The rate theory of chromatography, also known as the van Deemter model, examines the factors affecting band broadening, which is the amount of dispersion of a sample as it migrates through a column. 

Rate Theory of chromatography a theory of the dispersive (nonequUibiium) processes occurring in a chromatographic column that lead to peak broadening, usually associated with the name of Van Deemter, but Giddings, Golay and Knox are also important contributors expressed in terms of the variation of H with u. 

The rate theory of chromatography was introduced some 50 years ago by physicists and chemical engineers (van Deemter 1956). Despite all the work, both theoretical and experimental, that has been done since then on dispersion in chromatographic columns, the van... 

In the rate theory of gas-solid chromatography, the equation for h has essentially the same terms except that Cj, replaces C . Ck is a term characteristic of adsorption kinetics. Equation... 

For the solution of sophisticated mathematical models of adsorption cycles including complex multicomponent equilibrium and rate expressions, two numerical methods are popular. These are finite difference methods and orthogonal collocation. The former vary in the manner in which distance variables are discretized, ranging from simple backward difference stage models (akin to the plate theory of chromatography) to more involved schemes exhibiting little numerical dispersion. Collocation methods are often thought to be faster computationally, but oscillations in the polynomial trial function can be a problem. The choice of best method is often the preference of the user. 

The proportionate-pattern case is a classical one in the theory of chromatography, and was treated by DeVault (D2), Walter (Wl), Wilson (W7), and Weiss (W3). It is assumed that equilibrium is maintained everywhere in the column, that is, that N approaches infinity, due to high mass-transfer rates or to long residence times. 

Rate theory of band broadening. The van Deemter equation in planar chromatography can be reduced to... 

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.

Effective diffusivity can be evaluated in a single pellet (113,168,169) or in a stirred vessel (115,170,171) or in a packed bed (113). The method of moments is usually used in parameter estimation. The method of moments and the theory of chromatography were also used extensively by Smith and coworkers in packed bed systems (113) for estimation of adsorption rate constants, particle diffusivity (172) and kinetic constants (173). Use of... 

The theory of chromatography has been reasonably well established with a kinetic or rate theory that describes the broadening of the bands or zones of separated components on a stationary-phase bed, describes their time of appearance at any particular point, and provides details of the separation power or resolution of the particular system employed. Numerous equations describing zone broadening have been proposed, the simplest being the general form of the van Deemter equation as derived for gas-liquid chromatography,... 

Once the competitive isotherms for solutes are known, the theories of chromatography now allow the rapid optimisation of production rate and, through computer simulations, also allow the rapid prediction of preparative chromatograms under any desired conditions. These facilitate the full optimisation of a production scale method. 

There are two fundamental chromatography theories that deal with solute retention and solute dispersion and these are the Plate Theory and the Rate Theory, respectively. It is essential to be familiar with both these theories in order to understand the chromatographic process, the function of the column, and column design. The first effective theory to be developed was the plate theory, which revealed those factors that controlled chromatographic retention and allowed the... 

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... 

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