Chromatographic processes theoretical plate

The separating power of a chromatographic process arises from the development of many theoretical plates to achieve adsorption equiUbrium within a column of moderate length. Even though the separation factor between two components may be small, any desired resolution may be achieved with sufficient theoretical plates. 

The main difference between the chromatographic process carried out in the linear and the nonlinear range of the adsorption isotherm is the fact that in the latter case, due to the skewed shapes of the concentration profiles of the analytes involved, separation performance of a chromatographic system considerably drops, i.e., the number of theoretical plates (N) of a chromatographic system indisputably lowers. In these circumstances, all quantitative models, along with semiquantitative and nonquantitative rules, successfully applied to optimization of the linear adsorption TLC show a considerably worse applicability. 

Time-dominated processes inherently govern chromatography. The horizontal axis of a chromatogram is time (and not energy as in spectroscopy). To describe the quality of a chromatographic system the concepts of the height equivalent to a theoretical plate, HETP or H, and the number of theoretical plates N are used (Equation 4.1) ... 

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. 

E. Extracolumn Band Broadening or Variance To maximize the effective number of theoretical plates, the contribution of the entire chromatographic system to band broadening (system variance, o-2ys) must be minimized. The system variance may be broken down into contributions from the column variance, a 01, as described above, and extracolumn diffusion and mixing processes, cr2x. As with the case of the column variance, extracolumn variance is an additive property and may be broken down into the major components ... 

Martin and Synge (3) introduced the important concept of theoretical plates into chromatography. Their concept was derived from partition theory and random statistics, and was related to similar ideas developed for extraction and fractional distillation. They supposed that the column could be divided into a number of sections called theoretical plates, and that solutes (dissolved compounds) could be expected to achieve equilibrium between the two phases (mobile and stationary) that exist within each plate. The chromatographic process, like an extraction process, can be visualized to occur when mobile phase (solvent) is transferred to the next plate, where a new equilibrium is established. Theoretical plate numbers of 1000 or more are common for HPLC columns, which means that 1000 separate equilibria must be established to obtain the same degree of separation by solvent... 

When the sample is introduced into the column, usually in the form of a zone of vapor, it takes the form of a narrow band. During transit through the column, various factors influence the width of this band, which is continuously increased due to various dispersion processes. These include diffusion of the solute, resistance to mass transfer between and within phases, and the influence of flow irregularities and pertur-bations.f A simple concept, the theoretical plate, carried over from distillation processes, has been used to compare columns and account for the degree of dispersion that influences bandwidth. A chromatographic column may be considered to consist of numerous theoretical plates where the distribution of sample components between the stationary and mobile phase occurs. Hence, a measure of the efficiency of a GC column may be obtained by calculating the number of theoretical plates, N, in the column from ... 

As previously indicated, this discussion is organized for chromatograms from very narrow polymer standards for which we can consider that the effect of molecular weight distribution is negligible and for which the unique separation process is size exclusion. With these limitations, the contribution to band broadening is conveniently separated into extra column effects, eddy dispersion, static dispersion, and mass transfer. In the most classical chromatographic interpretation, extra-column effects are not discussed and the three other contributions are considered as Gaussian, so there is simply the addition of their variances. The number of theoretical plates is defined as N = VJaY and the influence of v, the linear velocity of the eluent, is summarized by the so-called Van Deemter equation ... 

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. 

An efficient column produces sharp peaks and can separate many sample components in a relatively short time. As seen in most chromatograms, peaks tend to be Gaussian in shape and broaden with time, where wb becomes wider with longer tR. This band broadening inside the column is fundamental to all chromatographic processes.1,612 The number of theoretical plates or plate number (N) is a measure of the efficiency of the column. N is defined as the square of the ratio of the retention time divided by the standard deviation of the peak (o). Since wb is equal to 4a for a Gaussian peak,... 

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