Equilibrium constants size exclusion

Solute movement through soil is a complex process. It depends on convective-dispersive properties as influenced by pore size, shape, continuity, and a number of physicochemical reactions such as sorption-desorption, diffusion, exclusion, stagnant and/or double-layer water, interlayer water, activation energies, kinetics, equilibrium constants, and dissolution-precipitation. Miscible displacement is one of the best approaches for determining the factors in a given soil responsible for the transport behavior of any given solute. 

Using this relationship, the dissociation rate constant, k , was calculated as 3.91 X 10 min with a resultant half time of 177.3 minutes. In order to measure the rate constants for trimer formation, dissociation experiments were performed by rapid dilution of an equilibrated protein solution at association conditions (33 gM protein and 2.0 M GuHCl) to monomer conditions (3.3 mM protein, 2.0 M GuHCl). The diluted protein solution was analyzed by HPLC size exclusion to follow the dissociation over time (Figure 6). TTie distribution shifts to the monomer and dimer after ten minutes and the dimer slowly dissociates to form the monomer. The rate constant for trimer dissociation, k/, was calculated as 0.316 min (ti/2 = 2.19 minutes) from the rate of decrease in trimer concentration. Again, the relationship between the rate constants and the equilibrium constant was utilized. 

In size exclusion chromatography, components are excluded from the resin on the basis of size. By definition, solutes are not absorbed. These supports have a linear equilibrium, since a constant volume within the resin is available for a given size solute. When the support comes to equilibrium with the mobile phase, the volume in the pores available to the solute will have the same molar concentrations as the surrounding mobile phase. 

Fundamentally, V, is the sum of the void volume occupied by all solutes, a portion of the internal pore volume defined by the size exclusion differential equilibrium constant and a portion of the surface of the column packing defined by the distribution coefficient describing interactions between the column and solute K. This condition leads to the general equation... 

In the latter case, separation can be achieved by different means (centrifugation, filtration, size exclusion chromatography, etc...) and it is assumed that the equilibrium state is not modified during the separation step. This condition is not necessarily fullfilled, especially when the dissociation constant is sufficiently high. Separation techniques must then be extremely rapid in the case of loosely bound complexes. 

When considering the possible modes of solute retention in SEC it is important to first define the compartmentalization of volumes found within the size exclusion column. The total geometrical volume of the column, Vg, is defined as the sum of the total mobile phase volume, V, and the volume of the packing material or stationary phase, V. The mobile phase volume is further defined as the sum of the volume external to the beads constituting the packing material or the void volume, Vq, and the volume of the channels within the beads, V. The differential solute distribution between the spaces internal to and external to the pores in the column packing material results in the separation of the solutes on the basis of molecular size. In the absence of reversible adsorption, the average elution volume, Vg, is the sum of the void volume occupied by all solutes and a portion of the internal pore-volume defined by the size exclusion equilibrium constant, [Note that this... 

A cursory review of the literature reveals that the ELC technique with micellar mobile phases has proven to be very beneficial in the characterization of micellar systems (184-186,190-192,227,228). For example, microcolumn exclusion LC has been applied to the determination of the CMC value of surfactants (or micellar-forming proteins), determination of the kinetic rate and equilibrium association constants for surfactant (or protein) micellization (184,192), determination of the size or size distribution of micelles (especially those formed from block copolymers or milk casein) (185,186,191,192,225) as well as for estimation of the time required for formation of micelles (or micelle-forming macromolecules) (186) among others. The size and stability of reversed micelles has also been evaluated using ELC (195). 

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