The rate theory of chromatography

In all of the previous discussion and particularly in the plate theory, the velocity of the mobile phase in the column and solute diffusion are, perhaps surprisingly, never taken into account. Of all things, the speed should have an influence upon the progression of the analytes down the column, hence their dispersion and by consequence, upon the quality of the analysis undertaken. 

Rate theory is a more realistic description of the processes at work inside a column which takes account of the time taken for the solute to equilibrate between the two phases. It is the dynamics of the separation process which is concerned. The first kinetic equation for packed columns in gas phase chromatography was proposed by Van Deemter. 

This equation is based on a Gaussian distribution, similar to that of plate theory. Its simplified form, proposed by Van Deemter in 1956, is well known (expression 

The three experimental basic coefficients A, B and C are related to diverse physico-chemical parameters of the column and to the experimental conditions. If H is expressed in cm, A will also be in cm, B in cm /s and C in s (where velocity is measured in cm/s). 

This equation reveals that there exists an optimal flow rate for each column, corresponding to the minimum of H, which predicts the curve described by Equation 1.30. 

---

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. 

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. 

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. 

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... 

Dispersion in Columns and Mobile Phase Conduits, the Dynamics of Chromatography, the Rate Theory and Experimental Support of the... 

The air oxidation of 2-methylpropene to methacrolein was investigated at atmospheric pressure and temperatures ranging between 200° and 460°C. over pumice-supported copper oxide catalyst in the presence of selenium dioxide in an integral isothermal flow reactor. The reaction products were analyzed quantitatively by gas chromatography, and the effects of several process variables on conversion and yield were determined. The experimental results are explained by the electron theory of catalysis on semiconductors, and a reaction mechanism is proposed. It is postulated that while at low selenium-copper ratios, the rate-determining step in the oxidation of 2-methylpropene to methacrolein is a p-type, it is n-type at higher ratios. 

The efficiency of a column is a number that describes peak broadening as a function of retention, and it is described in terms of the number of theoretical plates, N. Two major theories have been developed to describe column efficiency, both of which are used in modern chromatography. The plate theory, proposed by Martin and Synge,31 provides a simple and convenient way to measure column performance and efficiency, whereas the rate theory developed by van Deemter et al.32 provides a means to measure the contributions to band broadening and thereby optimize the efficiency. 

The brief historical development in the last chapter noted that the early theoretical papers described chromatography in terms similar to distillation or extraction and were known as the plate theory. Useful as it may have been in the development of chromatography, the plate theory is of little value in modern chromatography and has been replaced by the rate theory. Any of the early books on gas chromatography can be consulted for a discussion of the plate theory, and Giddings1 has written a good historical summary of the concurrent development of the plate and rate theories. 

The open-tubular column or capillary column is the one most commonly used in gas chromatography (GC) today. The equation that describes dispersion in open tubes was developed by Golay [1], who employed a modified form of the rate theory, and is similar in form to that for packed columns. However, as there is no packing, there can be no multipath term and, thus, the equation only describes two types of dispersion. One function describes the longitudinal diffusion effect and two others describe the combined resistance to mass-transfer terms for the mobile and stationary phases. 

The rate theory examines the kinetics of exchange that takes place in a chromatographic system and identifies the factors that control band dispersion. The first explicit height equivalent to a theoretical plate (HETP) equation was developed by Van Deemter et al. in 1956 [1] for a packed gas chromatography (GC) column. Van Deemter et al. considered that four spreading processes were responsible for peak dispersion, namely multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase, and resistance to mass transfer in the stationary phase. 

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. 

To apply this equation to different situations and not exclusively to gas chromatography, it needs to be modified. The rate theory was developed and showed that term A was negligible and that term C corresponds to the sum of mass transfer in the stationary phase and in the mobile phase. 

---