Plate concepts

The theoretical treatment of temperature perturbations that result from solute phase interactions also affords an excellent example of the use of the plate concept in a... 

As the plate concept is to be employed the volume flow will be measured in plate volumes, i.e.,... 

The continuous annular chromatograph can be described mathematically by a theoretical plate approach similar to the one developed by Martin and Synge [40] and exemplified by Said [41] for stationary columns [5]. The mathematical description results in algebraic expressions for the elution position of each solute relative to the feed point and for the bandwidth of the eluting zone as a function of the elution position or other system parameters. However, a series of simplifications have to be made in order to describe the CAC with the theoretical plate concept ... 

GLUECKAUF, E. Trans. Faraday Soc. 51 (1955) 34. Theory of chromatography, Part 9 the theoretical plate concept in column separation. 

Architecture of stamped metal plate concept with MILAs. (Reprinted with permission from Granier, J. 2004-2005. CLEFS CEA 50/51 76-78.)... 

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. 

The model is directly related to the widely used theoretical plate concept, which, in principle, is only valid for Gaussian peaks. 

The separation can be improved by increasing the column length as this increases the number of theoretical plates which can be generated by the column. The theoretical plate concept is similar to that used in distillation, but in chromatography no actual "plates" are present. However, the concept is a useful one in that it provides a convenient means of expressing the separating power of a column. If... 

The theoretical plate concept in chromatography is a popular approach to determining column efficiency (relative band broadening in the column). The number of theoretical plates, N, is related to the retention time and to the width of the solute peak by... 

The concept of theoretical plates evolved from studies of distillation and countercurrent distribution, where distinct stages frequently exist. The widespread adoption of plate concepts in chromatography can be traced... 

Conventional flat-plate concept Planar anode supported concept... 

The plate concept was first adapted to chromatography by Martin and Synge (1941), who derived the theory and equations that will be shown below. The equations assume the following ... 

The theoretical plate concept is useful in determining the efficiency of any given column, but it does not indicate the effects of various operational parameters. Here, however, the van Deemter rate theory proves valuable. The van Deemter equation is ... 

The concept of theoretical plates in chromatography is described elsewhere, and is not repeated here (18,19). Pieri et al. have described the application of the theoretical plate concept to column scale-up and demonstrated its utility in scale-up of pheromone separation over silica gel (15). We have found this same approach to be useful in separations over ion exchange resins used as chromatographic supports. In essence, this approach gives an estimate of column length for a given separation if the particle size is changed. This is based on empirical correlation of the number of theoretical plates, JV, ... 

The efficiency of a real GPC system depends above all on the rate of mass transfer between mobile phase and gel phase, as well as on the extent of secondary processes. Quantitatively, the efficiency can be expressed by the terms like width (w) or deviation (o) of the chromatographic peak, as well as by other terms of the theoretical plate concept. Since the diffusion rate of solute molecules decreases with an increase of their dimensions, one has to expect generally lower efficiency in gel chromatography of macromolecules in comparison with any other mode of liquid chromatographic separation of low molecular substances. 

A number of theoretical treatments of gel chromatography have been published, including applications of the theoretical plate concept similar to those outlined in Chapter 2. It is appropriate here to mention only a few simple parameters of most value in practical work. 

The transfer unit and theoretical plate concepts are quite similar. When equilibrium relationships and process operating lines can be reduced to simple mathematical forms, in fact, the number of transfer units and the number of theoretical plates can be related algebraically. 

Conventional flat-plate concept with self-supporting electrolyte... 

In the Hexis design, fuel is supplied to the center of the electrolyte-supported circular cell (diameter 120 mm), from where it flows to the outer rim of the cell. Here, the fuel that has not reacted within the cell is burned. Air is supplied from the outside and heats up as it flows towards the center of the cell. It then flows back outside the cell in parallel with the fuel. The stack is typically operated at 900 °C. Between 50 and 70 cells are stacked together, generating a power of 1.1 kW [11]. In order to reduce manufacturing costs, Hexis has since altered the two-layer interconnect design to a one-plate concept [12]. 

Mostafa, H.A., and Said, A.S., Theoretical-plate concept for fixed-bed adsorption and ion-exchange, Trans. IChemE, 54, T132-TI34 (1976). 

Theories of paper chromatography are controversial (173,261-272) and, like that of its adsorption counterpart, they are incomplete in that no theory of this intricate process takes into account all known factors. Martin and Synge (174) drew a parallelism with fractional distillation and introduced the theoretical plate concept to chromatography. The rate of movement of a substance on a paper chromatogram may be defined by its R/ value (71), which is the ratio of the distance moved by the substance to that moved by the solvent front measured from the point of application of the substance. This value remains fairly constant for any one compound under given conditions of temperature, solvent composition, solute concentraticm, pH, and paper, but it cannot be relied upon for purposes of identification (24,70,71, 159). 

The insulator consists of a series of identical plates formed on a radius. The plates are produced such that they cover 50 cm of vertical and 120 degrees of circumferential coverage around the fuel bundle. The plates have beveled edges such that they overlap at intersections vertically and circumferentially (see Fig. 8.13). The use of the plate concept is necessary for plate fabrication and fuel performance considerations. From... 

For column chromatography, a plate number, N (based on the theoretical plate concept of distillation columns), is used as a measure of efficiency. Assuming a Gaussian peak profile, N is defined in terms of the solute retention time, tj(, and the peak width as given by the standard deviation, [Pg.126]

With a few exceptions, industrial applications of zeoUtes involve column operation in feeds containing more than two counterions. In general, therefore, the prediction of column performance involves the prediction of multicomponent equilibria and kinetics under dynamic flow conditions. Considering the complexity and diversity of these models (see Sects. 2.3 and 2.4), it is obvious that simplifications and approximations need to be made for practical coliunn modelling. For engineering pmposes, the most popular approach for coliunn modelling is the linear driving force - effective plate concept [97]. 

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