Retention thermodynamic significance

It has been shown from an analysis of the thermodynamic significance of retention index [29] that the retention index of a compound i = CH3(CH2) X (cf., eqn. 5) can be expressed as... 

The thermodynamic dead volume would be that of a small molecule that could enter the pores but not be retained by differential interactive forces. The maximum retention volume was recorded for methanol and water which, for concentrations of methanol above 10%v/v, would be equivalent to the thermodynamic dead volume for small molecules viz, about 2.8 ml). It is interesting to note that there is no significant difference between the retention volume of water and that of methanol over the complete range of solvent compositions examined, which confirms the validity of this... 

The thermodynamic dead volume includes those static fractions of the mobile phase that have the same composition as the moving phase, and thus do not contribute to solute retention by differential interaction in a similar manner to those with the stationary phase. It is seen that, in contrast to the kinetic dead volume, which by definition can contain no static mobile phase, and as a consequence is independent of the solute chromatographed, the thermodynamic dead volume will vary from solute to solute depending on the size of the solute molecule (i.e. is dependent on both ( i )and (n). Moreover, the amount of the stationary phase accessible to the solute will also vary with the size of the molecule (i.e. is dependent on (%)). It follows, that for a given stationary phase, it is not possible to compare the retentive properties of one solute with those of another in thermodynamic terms, unless ( ), (n) and (fc) are known accurately for each solute. This is particularly important if the two solutes differ significantly in molecular volume. The experimental determination of ( ), (n) and( ) would be extremely difficult, if not impossible In practice, as it would be necessary to carry out a separate series of exclusion measurements for each solute which, at best, would be lengthy and tedious. 

For those samples that are not compatible with GC, the first question to ask involves the size (molecular weight) of the solute molecules. Their size should be compared to the pores of the packing materials that can be used in LC. If the size of the molecules is not negligible relative to the (average) pore size, then part of the pores and hence part of the stationary phase present in the column will not be accessible to the solute molecules. Hence, the simple relationship between chromatographic retention and thermodynamic distribution (eqn.l. 6) loses its significance. To avoid that, wide pore materials can be used for the separation of large molecules (e.g., proteins) based on their distribution over the two phases [202]. 

The slope of a plot of the log of the retention time versus the inverse of the temperature is proportional to the enthalpy of retention for the probe molecule on the coal. This is a thermodynamic measure of the strength of the interaction between the probe molecule and the coal. The temperatures at which major changes in slope are observed represent the points where the mechanism of retention has changed, indicating that a significant change in the chemical or physical structure of the coal has occurred. 

The interpretation of the retention time as the first moment is more comprehensive than the use of the peak time (fmax). mi indicates the position of the peak center on the time scale that, in the case of unsymmetrical peaks, may deviate significantly from the position of the peak maximum. The thermodynamically correct retention time is actually derived from the position of the Gaussian component in a deconvoluted total peak... 

Haarhoff and Van der Linde [14] have studied the same problem, the determination of the band profile in the case of a moderately overloaded column, a case in which the thermodynamic effect of a nonlinear isotherm perturbs only mildly the band profile. They have used the same approach as Houghton, down to Eq. 10.17. However, since the component concentration is significantly different from 0 only around the band maximum, during a period of time which is only a few times the standard deviation of the Gaussian profile obtained imder linear conditions, they have suggested that the effect of the apparent dispersion term on the band profile can be calculated at the limit retention time, They replaced in Eq. 10.20 by... 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

Consequences of the Snyder and Soczewinski model are manifold, and they are of significant practical importance. The most spectacular conclusions of this model are (a) the possibiUty of quantifying the activity of an adsorbent, and (b) the possibility of defining and quantifying the chromatographic polarity of solvents (known as their elution strength). These two conclusions could be drawn only upon the assumption of the displacement mechanism of solute retention. An obvious necessity in this model was to quantify the effect of displacement, which resulted in the relationship given by Eq. 13 for the thermodynamic equilibrium constant of adsorption, for an active... 

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