Martin and Synge plate model

The Martin and Synge plate model [1] is a continuous plate model. It assumes that the column is equivalent to a series of continuous flow mixers. Mobile phase is transferred from one vessel to the next one as new mobile phase is added to the first vessel. Hence, the mobile phase flows continuously, and in each mixer the volumes of the mobile phase, Vm, and of the stationary phase, Vs, remain constant. The model is also based upon the assumption that, at the beginning of the experiment, only the first plate (rank / = 0) is loaded with the sample and that there are no sample components in the other plates. Said [13] has extended the theory of the continuous plate model to the case in which the solute is initially distributed on several plates, according to a certain distribution fimction. 

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where... 

The difference between the two plate models has been discussed by Klinkenberg and Sjenitzer [16]. In both models, we have a series of identical mixers, each containing the same amoimt of mobile and stationary phases. In the Martin and Synge model, by contrast with the Craig model, the mobile phase flows continuously. The result is that we have two different distributions, but both of them tends toward the same limit (Eq. 6.5) when the number of stages increases indefinitely. 

The concept of plate number and plate height in chromatography was developed by Martin and Synge who used an analogous model and theory of mass distribution as that adapted for the elucidation of processes occurring in a distillation column. 

Armstrong and Nome [1] extended to micellar media the classic model of Martin and Synge, and Herries et al. [8]. The model describes the situation that a solute experiences in an ideal system formed of a number of identical plates, where partitioning equilibria take place. The transitions that can occur in the three environments that exist in a micellar chromatographic system i.e., the aqueous phase, the micelles and the stationary plmse) were considered (Fig. 5.1). The mass fraction of solute in each environment and each theoretical plate was obtained from P m and Pws The P s coefficient was not included in the model, since it can be obtained by combination of the two former (P g Pws/Pwm)-... 

These models assume that the chromatographic column can be divided into a series of a finite number of identical plates. Each plate contains volumes and of the mobile and stationary phases, respectively. The sample is introduced as a solution of known concentration in the mobile phase used to fill the required number of plates. Plate models are essentially empirical, and cannot be related to first principles. Depending upon whether one assumes continuous or batch operation. two plate models can be considered The Craig model and the Martin and Synge model. 

Note that, although both models lead to the same profile, the resulting relationships between number of plates in the column and standard deviation differ. The conventional plate number as defined in chromatography is equal to N for the Martin and Synge model, and to N (l+ k o)lk o for the Craig model. In any discussion of column efficiency it is convenient to consider the height equivalent to a theoretical plate (or HETP). 

A second model, the theory of plates, was developed by Martin and Synge in 1941. This is based on the functioning of a fractionating column, then as now a widely used separation technique. It is assumed that the equilibrium between two phases on each plate of the column has been fully established. Using the plate theory,... 

The 1952 Nobel Prize was awarded to two Englishmen, A. J. P. Martin and R. L. M. Synge, for their work in the development of modern chromatography. In their theoretical studies, they adapted a model that was first developed in the early 1920s to describe separations on fractional distillation columns. Fractionating columns, which were first used in the petroleum industry to separate closely related hydrocarbons, consisted of numerous interconnected bubble-cap plates (see Figure 30F-2) at which vapor-liquid equilibria were established when the column was operated under reflux conditions. 

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