Free Energy Evaluations in Practice

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write... 

Equation (9.53) for the desired molecular field is nonlinear, typically solved iteratively. For this molecular-field approach to become practical, an alternative to this nonlinear iterative calculation is required. A natural idea is that a useful approximation to this molecular field might be extracted from simulations with available generic force fields. Then with a satisfactory molecular field in hand, the more ambitious quasichemical evaluation of the free energy can be addressed, presumably treating the actual binding interactions with chemical methods specifically. This is work currently in progress. 

The procedure adopted to portray the scope and utility of a linear free-energy relationship for aromatic substitution involves first a determination of the p-values for the reactions. These parameters are evaluated by plotting the values of log (k/ka) for a series of substituted benzenes against the values based on the solvolysis studies (Section IV, B). The resultant slope of the line is p, the reaction constant. The procedure is then reversed to assess the reliability and validity of the Extended Selectivity Treatment. In this approach the log ( K/ H) observations for a single substituent are plotted against p for a variety of reactions. This method assays the linear or non-linear response of each substituent to variations in the selectivity of the reagents and conditions. Unfortunately, insufficient data are available to allow the assignment of p for many reactions. It is more practical in these cases to adopt the Selectivity Factor S as a substitute for p and revert to the more empirical Selectivity Treatment for an examination of the behavior of the substituents. 

The London dispersive component of the surface free energy, y, of a solid may be shown to be a predominant property for the prediction of behavior of nonpolar adsorbents such as polyolefins or of practically nonpolar adsorbents like some carbon materials (natural graphites and carbon fibers). In this section, we propose a simple approach for the determination of the ys using nonpolar probes such as n-alkanes in inverse GC at infinite dilution. We also discuss the evaluation of the London dispersive component of the surface energy (or enthalpy, / ), starting from the variation of the adsorption characteristics, of a series of long-chain n-alkanes molecules, with temperature. 

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