Band broadening plate theory

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 plate theory assumes that an instantaneous equilibrium is set up for the solute between the stationary and mobile phases, and it does not consider the effects of diffusional effects on column performance. The rate theory avoids the assumption of an instantaneous equilibrium and addresses the diffusional factors that contribute to band broadening in the column, namely, eddy diffusion, longitudinal diffusion, and resistance to mass transfer in the stationary phase and the mobile phase. The experimental conditions required to obtain the most efficient system can be determined by constructing a van Deemter plot. 

Clearly, departures from equilibrium—along with the resultant zone spreading—will decrease as means are found to speed up equilibrium between velocity states. One measure of equilibration time is the time defined in Section 9.4 as teq, equivalent to the transfer or exchange time between fast- and slow-velocity states. Time teq must always be minimized this conclusion is seen to follow from either random-walk theory or nonequilibrium theory. These two theories simply represent alternate conceptual approaches to the same band-broadening phenomenon. Thus the plate height from Eqs. 9.12 and 9.17 may be considered to represent simultaneously both nonequilibrium processes and random-walk effects. 

A variety of surfaces such as metals, plastics, and glass can retain proteins during a separation process. In CE, a problem is manifested in the adsorption of proteins by fused silica capillaries (see Section IV). This problem is attributed to the adsorption of positively charged sites of proteins on negatively charged sites (silanol groups) on the capillary wall—a process that leads to band broadening and a much lower number of theoretical plates than would be expected on the basis of theory. 

An analyte is injected into the column in the form of very small zone with even distribution of the analyte within this zone. While this zone is moving through the column, it gets broadened. The degree of this band-broadening is called the efficiency. There are several different theories (or mathematical approaches) used for the description of the band broadening. Martin and Synge [8] introduced the plate theory for the evaluation of the column efficiency. Plate theory assumes that the analyte is in the instant equilibrium with... 

The process of band broadening (Figure 2.1) is measured by the column efficiency or the number of theoretical plates N, equation (2.24)), which is equal to the square of the ratio of the retention time to the standard deviation of the peak. In theory, the value of N for packed columns has only a small dependency on k and may be considered to be a constant for a particular column. Column efficiency in open-tubular systems decreases markedly with increased retention. For this reason open-tubular liquid chromatography systems must be operated at relatively low kf values (see section 2.5.S.2). 

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... 

In theory, millions of theoretical plates per metre can be achieved with electrophoresis making this technique superior to LC, where the number of plates per column is typically in the order of tens of thousands (section 2.2). In practice, however, lower plate numbers are observed in electrophoresis. Band broadening is... 

Rate theory describes the contribution of different band broadening processes as a function of mobile-phase flow rate, The original rate theory developed by van Deemter in 1956 [1], relates the plate height to the three major band broadening terms. This theory is used to minimize peak width in terms of plate height (//) and was further refined to the Hawkes equation, which is shown in Eq. 8. 

Although a detailed theory of band broadening is complicated, it can be presented in a simple form through the van Deemter equation, which expresses the plate height H or the reduced plate height h as a function of A, B, C, and the linear flow velocity of the mobile phase ... 

The earliest attempts to explain chromatographic band broadening were based on an equilibrium model which came to be known as the Plate Theory. While it was of some value, it did not deal with the nonequUibrium conditions that actually exist in the column and did not address the causes of band broadening. However, an alternative approach describing the kinetic factors was soon presented it became known as the Rate Theory. 

The van Deemter rate theory identified three major factors that cause band or zone broadening during the chromatographic process the eddy diffusion or the multi-path effect (A-term), longitudinal diffusion or molecular diffusion of the analyte molecules (B-term), and resistance to mass transfer in the stationary phase (C-term). The broadening of a zone was expressed in terms of the plate height, H, and was described as a function of the average linear velocity of the mobile phase, u. 

Relation of such empirical calibration to quantitative spectroscopic theory was pursued with two of the different source lamps by determining their spectral distributions from high resolution spectro-graphic plates made by repeated flashes, combined with numerical evaluation of Tji via equation (2.3) using the band transition probability factor or /-number, and the pressure broadening factor, as well as the absorber temperature, as selectable parameters. Uncertainty concerning the presence of continuum radiation between the OH lines in the source spectrum ultimately limited the definiteness of this calibration procedure. 

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