Specific component of free energy

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 specific component of free energy of adsorption is generally determined by the subtraction the dispersive component from the total free energy of adsorption. Several procedures of the calculation of the specific component have been presented in the literature. The differences between the respective procedures lie in the choose of the reference state of the adsorbed molecule. 

Saint Flour and Papirer [48] proposed to determine the specific component of free energy of adsorption AG as the vertical distance between n-alkanes reference line and the point on diagram corresponding to the polar test probe. As the physicochemical property used for definition of the reference state they choose saturated vapour pressure log Pq. Therefore, AG corresponds to the difference in free energies of adsorption between given test probe and hypothetical n-alkane having the same vapour pressure ... 

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... 

Conversely, this equation allows us to calculate the London dispersive component of the adsorbate-adsorbent interaction for a given liquid when the quantity (Avl)1/2 ao,L is defined as a characteristic of the probe considered, as listed in Table 6 from the basis of the polarizability of molecules (in Table 3). For polar probes, the additional or specific component of the Gibbs free energy, — AG P in Eq. (50) resulting from polar interactions is then determined by the distance between the experimental points A and B of same abscissa on the n-alkane lines as illustrated in Fig. 7. 

FIG. 7 Principle of determining the London dispersive and specific components of adsorption Gibbs free energy between untreated carbon fiber (supplied by Soficar, T-300) and all probes, measured at 54.5 °C. 

Thermodynamically, the specific components of adsorption enthalpy [—A/f p] and adsorption enthalpy [—AS P] can be derived from the specific component of Gibbs free energy [—A(j p] expressed as a function of the experimental temperatures in chromatographic process, such as... 

Authors of Ref. [49] proved that the variation of the term RT In Vn as a function of the molar deformation polarization of n-alkanes Pdp is a straight line which slope equal to C Pds is proportional to the surface ability for dispersive interactions. AG = 0 is defined in the same way as in the case of Saint Flour-Papirer s method. However, in this procedure AG = 0 values are always positive while in approach [48] the negative values of the specific component of the free energy of adsorption were observed. Later, Donnet et al. [29] observed that their earlier proposal (i.e. that from Ref.[49]) based on the fundamental London equation gives only a first approximation of the ionization energy of a molecule. They proposed to use Eq.(15) in the form ... 

Finally, there are several approaches to determine the specific component of the surface free energy of carbon materials [71-73]. Among these, that proposed by Donnet et al [73] uses the standard adsorption free energy which is plotted against (hr L) o-10 , where h is the Planck constant, is the characteristic vibration frequency of the electron and a is the deformation polarizability. The method seems to provide reasonable results, although it does not take into account the effect of the surface irregularities. 

Table 8 Specific Components of Surface Free Energy of Adsorption of MSX, SX-I, and SX-I... 

Polar probes have both dispersive and specific components of surface free energy of adsorption. The specific component of surface free energy of adsorption (AGa is determined by subtracting the dispersive contribution from the total free energy of adsorption, and can be obtained from the vertical distance between the alkane reference line [Eq. (30) Figure 21] and the polar probes of interest according to the following equation (60) ... 

Specific Component of the Surface Free Energy of Heat-Treated Silicas. Specific interaction capacities of heat-treated silicas, that is, their ability to interact with polar molecules, were examined with chloroform (Lewis acid probe) and toluene and benzene (amphoteric molecules). Figure 2 provides examples of the evolution of the specific interaction parameter Zsp of the different silicas with chloroform as a probe. 

If RTlnV is plotted versus a(yL ) for a series of alkanes a straight line results and the dispersive contribution of the surface energy can be calculated from the slope. If polar probe molecules are injected, specific interactions can be determined. In the above-mentioned plot, points representing a polar probe are located above the straight line. The distance is equal to the specific component of the free energy JG /. (equation 5). 

Specific Component of the Surface Free Energy of Heat-Treated Silicas... 

Applying the widely-used chemical thermodynamics concept of free energy linearity, it is easy to demonstrate that any characteristic y which linearly depends on free energy or on free activation energy of process in the mixed solvent composed of specifically non-interacting components, shall be linear function of the components with partial molar concentration X. 

All other polar probes exhibit higher net retention volumes, En. and the difference between their net retention volume and that of the n-alkanes for the same value of the dispersive component of surface energy leads to the value of the free energy of desorption, AGjp, corresponding to the specific acid-base interaction, expressed as ... 

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