Second virial coefficients from chromatography

The analysis providing interaction second virial coefficients from chromatography rests upon three principal assumptions 1) vapor-liquid equilibrium exists in the column 2) the solute (component 1) is soluble in both the carrier gas (component 2) and the stationary liquid phase (component 3) 3) the carrier gas and stationary liquid are insoluble. Under assumption 1, we can write... 

Several techniques are available for measuring values of interaction second virial coefficients. The primary methods are reduction of mixture virial coefficients determined from PpT data reduction of vapor-liquid equilibrium data the differential pressure technique of Knobler et al.(1959) the Bumett-isochoric method of Hall and Eubank (1973) and reduction of gas chromatography data as originally proposed by Desty et al.(1962). The latter procedure is by far the most rapid, although it is probably the least accurate. 

Size-exclusion chromatography can be used to analyze protein-protein interactions. Bloustine et al. (2003) presented a method to determine second virial coefficients (B2) of protein solutions from retention time measurements in size-exclusion... 

The value of the second virial coefficient A 2 can also be determined from the retention volume that is obtained from self-interaction chromatography (Aliamed et al., 2005 Winzor et al., 2007 Dumetz et al., 2008). The chromatographic retention factor k is calculated from the retention volume VT using the formula... 

Before considering how the excluded volume affects the second virial coefficient, let us first review what we mean by excluded volume. We alluded to this concept in our model for size-exclusion chromatography in Section 1.6b.2b. The development of Equation (1.27) is based on the idea that the center of a spherical particle cannot approach the walls of a pore any closer than a distance equal to its radius. A zone of this thickness adjacent to the pore walls is a volume from which the particles —described in terms of their centers —are denied entry because of their own spatial extension. The volume of this zone is what we call the excluded volume for such a model. The van der Waals constant b in Equation (28) measures the excluded volume of gas molecules for spherical molecules it equals four times the actual volume of the sphere, as discussed in Section 10.4b, Equation (10.38). 

Gas chromatography is primarily an analytical separation technique. However, since the basic process is an equilibration of a solute between two immiscible phases, the chromatographic technique may be used to measure such physical properties as activity coefficients, second virial coefficients of gas mixtures, partition coefficients, adsorption and partition isotherms, and complex formation constants. Other properties which can be measured with less accuracy, from secondary measurements or from temperature variation studies, include surface areas, heats of adsorption, and excess enthalpies and excess entropies of solution. A number of reviews and discussions on these measurements have appeared in the literature. The present work is restricted to a review of activity-coefficient measurements. 

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