Modeling of retention

Drager, R. R. and Regnier, F. E., Application of the stoichiometric displacement model of retention to anion-exchange chromatography of nucleic acids,... 

Bonded stationary phases for NPC are becoming increasingly popular in recent years owing to their virtues of faster column equilibration and being less prone to contamination by water. The use of iso-hydric (same water concentration) solvents is not needed to obtain reproducible results. However, predicting solute retention on bonded stationary phases is more difficult than when silica is used. This is largely because of the complexity of associations possible between solvent molecules and the chemically and physically heterogeneous bonded phase surface. Several models of retention on bonded phases have been advocated, but their validity, particularly when mixed solvent systems are used as mobile phase, can be questioned. The most commonly accepted retention mechanism is Snyder s model, which assumes the competitive adsorption between solutes and solvent molecules on active sites... 

In spite of widespread applications, the exact mechanism of retention in reversed-phase chromatography is still controversial. Various theoretical models of retention for RPC were suggested, such as the model using the Hildebrand solubility parameter theory [32,51-53], or the model supported by the concept of molecular connectivity [54], models based on the solvophobic theory [55,56) or on the molecular statistical theory [57j. Unfortunately, sophisticated models introduce a number of physicochemical constants, which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. 

Two models have been proposed to describe the process of retention in liquid chromatography (Figure 3.3), the solvent-interaction model (Scott and Kucera, 1979) and the solvent-competition model (Snyder, 1968 and 1983). Both these models assume the existence of a monolayer or multiple layers of strong mobile-phase molecules adsorbed onto the surface of the stationary phase. In the solvent-partition model the analyte is partitioned between the mobile phase and the layer of solvent adsorbed onto the stationary-phase surface. In the solvent-competition model, the analyte competes with the strong mobile-phase molecules for active sites on the stationary phase. The two models are essentially equivalent because both assume that interactions between the analyte and the stationary phase remain constant and that retention is determined by the composition of the mobile phase. Furthermore, elutropic series, which rank solvents and mobile-phase modifiers according to their affinities for stationary phases (e.g. Table 3.1), have been developed on the basis of experimental observations, which cannot distinguish the two models of retention. 

Figure 3.3 Comparison of the (a) solvent-interaction and the (b) solvent-competition models of retention in liquid chromatography.

If one assumes the dynamic ion-exchange model, then equation (3.26) is obtained, which is identical in form to equation (3.24), demonstrating that retention data alone cannot distinguish these two models of retention and that more detailed studies are necessary (Horvath et al., 1977b). 

Garcfa-Alvarez-Coque, M.C. Torres-Lapasio, J.R. Baeza-Baeza, J.J. Modelling of retention behaviour of solutes in micellar liquid chromatography. A review. J. Chromatogr., A 1997, 780, 129-148. 

For proteins, a mathematical model of retention has been developed that works well for Sephadex gels.5 The solute is treated as a sphere of radius rs, while the gel is a network represented by infinitely long, straight rods of radius rx. The rods are randomly distributed, and have an average density of L units of rod length per unit volume of gel. The values of L and rx may be calculated from known dimensions of dextran chains, and then Km may be found from Eq. 14.13 ... 

One popular model of retention has been the solvophobic theory, which relates retention to the surface tension of the mobile-phase solvents (103). As important as the solvophobic theory has been to the development of modern LC, it is based on an incorrect model of the relevant solution processes. It supposes that retention can be modeled in terms of the association of two solute molecules in a single solvent rather than on the transfer of a solute from one solvent to another. Hence the solvophobic theory does not take cognizance of the interactions of the solute with the second solvent, the cavity in the stationary phase it takes into account only the cavity in the mobile phase. 

Assuming positive answers to the preceding three questions, can an appropriate model of retention and band broadening for these macromolecules be used for the systematic and reliable development of a final separation procedure and/or for the design of better column... 

Table 6.6 Parameter for the model of retention (fc ) of anthranilic acid in HPLC according to Eq. (6.112).

G. Kowalska Model of Retention with Use of Multicomponent Mobiie Phases... 

The most accurate assessments of internal dose can be made when the distribution and total body content of an incorporated radionuclide can be determined reliably by direct in vivo counting of emissions from the body. Nevertheless, biokinetic modelling of retention and biophysical modelling of energy deposition may still be needed to calculate the intake and the committed effective dose, so direct methods can also depend on the interpretation of rates of excretion, which often vary markedly over time and between individuals. 

SKRABLE, K.W., CHABOT, G.E., FRENCH, C.S., LABONE, T.R., Use of multicompartment models of retention for internally deposited radionuclides . Internal Radiation Dosimetry (RAABE, O.G., Ed.), Medical Physics Publishing, Madison, WI (1994)271-354. 

Kowalska model of retention with use of multi-component mobile phases, 64-65... 

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