Chromatography plate theory

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... 

Vacancy chromatography has some quite unique properties and a number of potentially useful applications. Vacancy chromatography can be theoretically investigated using the equations derived from the plate theory for the elution of... 

So far the plate theory has been used to examine first-order effects in chromatography. However, it can also be used in a number of other interesting ways to investigate second-order effects in both the chromatographic system itself and in ancillary apparatus such as the detector. The plate theory will now be used to examine the temperature effects that result from solute distribution between two phases. This theoretical treatment not only provides information on the thermal effects that occur in a column per se, but also gives further examples of the use of the plate theory to examine dynamic distribution systems and the different ways that it can be employed. 

In chromatography there are at least three equilibria analyte/mobile phase, analyte/stationary phase and mobile phase/stationary phase. The origin of the term theoretical plate in chromatography comes from the adaptation of an older plate theory for distillation described by Martin and Synge (Nobel Prize for Chemistry, 1952). This term which is universally used for historical reasons, has no physical significance. It may have been preferable to call it a Tswett ... 

The concept of plate theory was originally proposed for the performance of distillation columns (12). However, Martin and Synge (13) first applied the plate theory to partition chromatography. The theory assumes that the column is divided into a number of zones called theoretical plates. One determines the zone thickness or height equivalent to a theoretical plate (HETP) by assuming that there is perfect equilibrium between the gas and liquid phases within each plate. The resulting behavior of the plate column is calculated on the assumption that the distribution coefficient remains unaffected by the presence of other... 

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. 

Separation of biomolecules by chromatography relies on different features of the molecule and chromatography system (i.e. stationary and mobile phases). When considering chromatography, two major principles require attention, namely retention and plate theory. 

Plate theory Simply measures the rate of migration of a biomolecule through a stationary phase in a given chromatography system. 

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. 

Martin and Synge published their first description of the plate theory in 1941 [1], at the time when Wicke [10], Wilson [11], and Devault [12] were beginning to study the solution of the mass balance equation of chromatography (Section 6.2). 

The plate theory as applied to chromatography is derived from the mathematical theory of distillation columns. Figure 4.5 shows a distillation column. 

Janson and Hedman (1) recently published an excellent review of large-scale chromatography. Many of the broad process design and operation considerations are the same for affinity chromatography as they are for ion exchange or gel filtration. Most chromatography models, however, are based on the assumption of small feed pulses with linear equilibria (such as the widely-used plate theories (2)) and are not directly useful for affinity separations. In this paper we discuss and compare experimental results with two fixed-bed adsorption models that can be used to predict the performance of affinity columns. These two models differ only in the form of the rate-... 

As mentioned earher, the plate theory has played a role in the development of chromatography. The concept of "plate" was originally proposed as a measmement of the performance of distillation processes. It is based upon the assumption that the column is divided into a number of zones called theoretical plates, that are treated as if there exists a perfect equilibrium between the gas and the Hquid phases within each plate. This assumption imphes that the distribution coefficient remains the same fi-om one plate to another plate, and is not affected by other sample components, and that the distribution isotherm is hnear. However, experimental evidences show that this is not true. Plate theory disregards that chromatography is a dynamic process of mass transfer, and it reveals httle about the factors affecting the values of the theoretical plate number. In principle, once a sample has been introduced, it enters the GC column as a narrow-width "band" or "zone" of its composite molecules. On the column, the band is further broadened by interaction of components with the stationary phase which retains some components more than others. Increasing... 

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