Frontal Method

Among the different methods presented,15 the frontal method is of general applicability when the investigation of the evolution of maxima of retention peaks with respect to the injected quantities is attractive when high-efficiency columns are available. 

Figure 3. Sorption Isotherm of Starch Determined at 25°C by Modified Frontal Analysis and Frontal Method.

There are two methods for the chromatographic analysis of the reaction products first, elution analysis, which is used by most workers and provides the basis for all commercial instruments and second, frontal analysis, developed by Rezl and co-workers [12, 24, 25]. The frontal method has a number of advantages over the elution method ... 

An effective means of concentrating light trace components is the frontal method [52, 53]. A modification of this method is frontal chemical concentration, in which a chemical reagent is used instead of the sorbent. The reagent forms with the main component a complex that is completely retained in the reactor. Compared with the method in which common sorbents are used, frontal chemical concentration offers the following potential advantages ... 

There are three possible geometrical arrangements of the cell with respect to the source and the detector. The right-angle arrangement shown in Figure 9.3 is the most common, and the most advantageous for dilute solutions. The other two methods [7] are the frontal method and the in-line method. 

Elution and frontal methods are commonly employed for the determination of adsorption isotherms of different probes on ground solids. The application of the elution techniques is more widespread. The use of one of these methods involves several injections for different amounts of the probe and overlapping of the obtained peaks to check whether the diffusive parts of them superimpose, which is a characteristic feature of the equilibrium conditions of ideal, non-linear models. It is mandatory to select an inert gas with a relatively small kinetic diameter, which is not adsorbed under the chromatographic conditions applied. 

We compared our algorithm GSPAR with FRONTAL, the frontal method of SPEEDUP, using four example matrices arising from dynamic process simulation of chemical plants. The computation time (in CPU sec.) for a Cray Y-MP is given in table 4.1. 

The chromatography can be carried out using either an elution method, where the analysed mixture is placed on the top of the chromatographic column and the separation is arrived at by additions of a suitable solvent at the top of the column, or by using the frontal method, where the sample is dissolved first in the solvent and the solution of the sample in the solvent is added to the top of the column. 

More precise results can be obtained by measurement of the step-height in the frontal method, than by measurement of the surface under a peak in the elution method. However, a greater amount of substance is required for the former method. In elution techniques OT-0-5 mg sample is usually sufficient. When a differential method is used for compensating the effect of oxygen dissolved in the polarographed effluent, as low as 0-004 mg to... 

Hood, P., 1976. Frontal solution program for unsymmetric matrices. Int. J. Numer. Methods Eng. 10, 379-399. 

The most frequently used modifications of the basic Gaussian elimination method in finite element analysis are the LU decomposition and frontal solution techniques. 

SOLUTION ALGORITHMS GAUSSIAN ELIMINATION METHOD 205 6.4.2 Frontal solution technique... 

Irons, B, M., 1970. A frontal solution for finite element analysis, hit. J. Numer. Methods Eng. 2, 5-32,... 

Experiments Sorption equihbria are measured using apparatuses and methods classified as volumetric, gravimetric, flow-through (frontal analysis), and chromatographic. Apparatuses are discussed by Yang (gen. refs.). Heats of adsorption can be determined from isotherms measured at different temperatures or measured independently by calorimetric methods. 

This type of chromatographic development will only be briefly described as it is rarely used and probably is of academic interest only. This method of development can only be effectively employed in a column distribution system. The sample is fed continuously onto the column, usually as a dilute solution in the mobile phase. This is in contrast to displacement development and elution development, where discrete samples are placed on the system and the separation is subsequently processed. Frontal analysis only separates part of the first compound in a relatively pure state, each subsequent component being mixed with those previously eluted. Consider a three component mixture, containing solutes (A), (B) and (C) as a dilute solution in the mobile phase that is fed continuously onto a column. The first component to elute, (A), will be that solute held least strongly in the stationary phase. Then the... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The dynamic olefin insertion process has been modeled using various quantum mechanical methods. A concerted four-center mechanism involving a frontal copla-nar attack of the C=C unit on the Zr-H bond of 1 is associated with a low activation energy of 0-15 kcal mol and has been proposed for the reaction of ethylene (Scheme 8-2) [37]. 

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