Displacement model

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

A stoichiometric model can conveniently be invoked to explain the ion-exchange retention process [43 6]. As discussed in detail in these cited papers on ion-exchange theory, useful information about the involved ion-exchange process can be deduced from plots of log k vs. the log of the counterion concentration [X], which commonly show linear dependencies according to the stoichiometric displacement model (Equation 1.1)... 

A thorough study on the ion-exchange mechanism and the effect of distinct counterions in this PO mode was recently presented by Gyimesi-Forras et al. [41]. A large variety of distinct acid additives to methanol, acetonitrile, and tetrahydrofuran (Table 1.1) (without any base added) was investigated in view of the stoichiometric displacement model and their effect on the enantiomer separation of 2-methoxy-2-(l-naphthyl)propionic acid. The stoichiometric displacement model (Equation 1.1) was obeyed also in the PO mode, as revealed by linear plots of log k vs. acid concentration. The slopes and intercepts along with the concentration ranges used with the distinct competitor acids are summarized in Table 1.1. 

Influence of Acid Additives on Retention Characteristics of 2-Methoxy-2-(1-Naphthyl)Propionic Acid on a 0-9-(tert-ButylcarbamoyOQuinine CSP as Assessed by the Characteristic Parameters of the Stoichiometric Displacement Model (Slopes and Interc ... 

Jaroniec, M., Partition and displacement models in reversed-phase liquid-chromatography with mixed eluents, J. Chromatogr. A, 656, 37, 1993. 

Use of the Stoichiometric Solvent Displacement Model in Peptide Isolation by Reversed-Phase Chromatography... 

According to this theoretical treatment, the slope of the plots of In k versus the solvent concentration, [3]m, can be employed to derive the contact area associated with the peptide-nonpolar ligand interaction. The retention and elution of a peptide in RPC can then be treated as a series of microequilibriums between the different components of the system, as represented by eq 6. The stoichiometric solvent displacement model addresses a set of considerations analogous to that of the preferential interaction model, but from a different empirical perspective. Thus, the affinity of the organic solvent for the free peptide P, in the mobile phase can be represented as follows ... 

According to the stoichiometric displacement model, the equilibrium constant for peptide adsorption with the solvated nonpolar ligands can be expressed as follows ... 

Retention on these supports is adaquetely described by the adsorption displacement model. Nevertheless, the adsorption sites are delocalized due to the flexible moiety of the ligand, and secondary solvent effects play a significant role. The cyano phase behaves much like a deactivated silica toward nonpolar and moderately polar solutes and solvents. Cyano propyl columns appear to have basic tendencies in chloroform and acidic tendencies in methyl tertiobutyl ether (MTBE)... 

Although the stoichiometric displacement model does not describe the physical situation rigorously enough, it has been widely used and corrected for some shortcomings. Whitley et al.m 89 have corrected the model since not all charges are accessible for the protein. They have introduced a correction... 

Our miscible-displacement modeling approach was modified in order to describe S04 effluent from the BS (as well as BC) layers. We adjusted the computer code to account for a variable concentration of the input pulse rather than a constant one as is commonly accepted in most column experiments and mathematical solutions. In all our simulations presented here, for each soil column, the S04 input concentrations from our experimental results were incorporated as inputs to the model. In addition, presentations of relative concentrations (C/C0) were based on the respective C0 of the applied solution to the top layer (E). 

Previous treatments of the displacement model have for the most part ignored the effects of interactions between solute and solvent models in... 

Second, previous tests of the displacement model have focused mainly on its ability to correlate and predict retention data in terms of derived correlational equations. Such correlations are based on various free energy relationships, and it is often found that comparisons of this kind can be insensitive to differences in the underlying physical model. That is, correlations of experimental retention data with theory may appear acceptable, in spite of marked deficiencies of the model. In some cases (e.g.. Ref. 12, sorption versus displacement models), radically different models can even yield the same or similar correlational equations. Here we will further test the proposed model for LSC retention in the following ways (1) application of the model to a wide range of LSC systems, involving major variations in solute, solvent, and adsorbent (2) examination of the various free energy terms that individually contribute to overall retention. 

Of course, e" values will be solute-specific, due to the inclusion of solute-specific terms in log Q. The simple displacement model predicts that solvent values are not a function of the solute. 

On balance, the plots of Fig. 21 suggest that calculated values of 0b from the present approach are reasonably close to actual isotherm values. Thus, these isotherm data can be regarded as supporting the present displacement model (and related equations), or at the least, not disproving the model. Whether the present approach can be extended to predict isotherm data with an acceptable accuracy for other purposes (e.g., preparative separations with column overload) remains to be seen. This will require careful studies of the same adsorbent sample, measuring both solvent isotherm data and appropriate solute retention values, with use of the solute retention data to derive solvent parameters for calculations of 6b ... 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

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