Fillers infinite” dilution

Inverse gas chromatographic measurements may be carried out both at infinite dilution and at finite solute concentrations [1]. In the first case vapours of testing solutes are injected onto the colurtm and their concentrations in the adsorbed layer proceed to zero. Testing substances interact with strong active sites on the examined surface. The retention data are then converted into, e.g. dispersive component of the surface free energy and specific component of free energy of adsorption. In the second case, i.e. at finite solute concentrations, the appropriate adsorption isotherms are used to describe the surface properties of polymer or filler. The differential isosteric heat of adsorption is also calculated under the assumption that the isotherms were obtained at small temperature intervals. 

The diffusion coefficient in the mixed matrix is affected by the presence of the filler not only through the effects on polymer FFV but also through changes in the diffusive path the particles are impermeable and act as an obstacle in the path of the gas molecules through the membrane, increasing its tortuosity. The value of the infinite dilution apparent diffusion coefficient in the mixed matrix, A,m(0), can then be related to A,p(0) using a tortuosity factor x, as usually made ... 

The FFV value in the polymer phase of the mixed matrix can be calculated through Equation (7.11) based on the unpenetrated polymer density pi in the polymer phase of the MMM, obtained from the solubility data as indicated above. Since different filler loadings will induce different FFV in the polymer phase, one can use Equation (7.16) to obtain the parameters A and B virtually from as little as two different mixed matrices with two different filler loadings then the same Equation (7.16) can be applied to calculate or correlate the infinite dilution apparent diffusivity Dim for any other filler loading in the same glassy polymer. 

In Figure 7.8c the ratio between the permeability in the composite and that in the pure polymer at infinite dilution for the two penetrants is reported as calculated from Equation (7.18), and clearly the addition of inorganic filler to the polymer enhances the permeability of the material. 

The technique can be considered as complementary to FMC, although it is constrained by the need to use volatile probes, a number of experimental factors usually result in more accurate thermodynamic data being obtained. The most important difference between IGC and FMC is that in the former technique, the probe is at infinite dilution, therefore, only the most active sites on the filler surfaces are likely to be probed. As adsorption from the gas phase occurs during IGC, only weakly bound molecules of carrier gas need to be displaced during the adsorption process, it is this aspect that may lead to production of more accurate thermodynamic data. 

The net retention volume is related to the free energy of the acid-hase interaction G, between the probe and the surface of the filler by Equation (3.6). This relationship is valid only at infinite dilution when interactions between the probe molecules are zero, it is therefore essential that very small volumes of the probe are injected into the carrier stream to get as close to the ideal state as possible. Of course the detector sensitivity dictates the minimum volume, it is usual to operate close to this limit of sensitivity ... 

This justifies the use of inverse gas chromatography (IGC) for filler surface energy characterization. This technique can be used in two very different modes infinite or finite dilution. 

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