Thermodynamic classical approach

There was therefore a clear need to assess the assumptions inherent in the classical kinetic approach for determining surface-catalysed reaction mechanisms where no account is taken of the individual behaviour of adsorbed reactants, substrate atoms, intermediates and their respective surface mobilities, all of which can contribute to the rate at which reactants reach active sites. The more usual classical approach is to assume thermodynamic equilibrium and that surface diffusion of reactants is fast and not rate determining. 

What is statistical thermodynamics How does this approach to understanding the thermodynamic behavior differ from the classical approach ... 

Instead of the classical approaches, a molecular-based statistical thermodynamic theory can be applied to allow a model of adsorption to be related to the microscopic properties of the system in terms of fluid-fluid and fluid-solid interactions, pore size, pore geometry and temperature. Using such theories the whole range of pore sizes measured can be calculated using a single approach. Two simulation... 

Marangoni s group subsequently used a thermodynamic approach to modify the model (Marangoni 2000 Marangoni and Rogers 2003). For spherical clusters using a van der Waals forces approach or a semi-classical approach based on the bluk properties of oils, the Young modulus ( ) becomes, respectively ... 

In the weak-interaction limit, the exchange mechanism can be described in terms of thermodynamic quantities, according to a classical approach which parallels that for nonadiabatic electron transfer (see Eqs. (1) and (2)) [59-63]. 

There have been several approaches to the expression of thermodynamic quantities of solutions. Scatchard published a series of papers (see 1801 and previous papers, especially 1802) based on the classical approach via chemical potentizil. Barker (130, 128, 131) applied the theory of conformal solutions (1254) to some H bonding systems after modifying it to allow for dipole attractions or, more generally, molecular orientations. The curves are similar in both cases. 

The molecular modelisation has also a large potential in process development and has to be coupled with more classical approach. For process integration, the thermodynamic optimisation is very useful mainly for developing new processes (pinch technology). 

The classical approach of organic chemistry to the problem of purity has always been that of fractionation. A preparation has been regarded as pure if all attempts to fractionate it have failed to change its measurable properties. In fact, this viewpoint has recently been stated (7) to constitute the definition of a component in the thermodynamic sense of the phase rule. Irrespective of viewpoints, nearly all fractionation techniques are useful in purity studies. 

Among many classical approaches available in the literature, a method developed by Broekhoff and de Boer (BdB) [47—53] for description of vapor adsorption and desorption in cylindrical pores and slit pores is the most thermodynamically rigorous and elegant for more than 35 years. This method relies on a reference system, which is a flat surface having the same structure and surface chemistry as that of the adsorbent. The pores of the adsorbent can have either... 

The major structural motif of steroids is the decalin unit, which is readily accessible by the Diels-Alder reaction. A famous early example is its masterful application by R. B. Woodward. A methyl quinone was reacted with butadiene to yield cw-decalone, a possible precursor for bile acids and after base treatment the thermodynamically more stable trans diastereomer, which may be applied in hormone syntheses. Another classical approach to substituted decalins is the Robinson annelation (Scheme 1.3.2), consisting of a sequence of aldol and Michael additions. 

This derivation differs significantly from the classical approach embodied in the work of Phillies (76,77) and Batchelor (78) in that the thermodynamic and frictional forces between interacting particles are not separately averaged over particle configurations (79). 

The macroscopic description of the adsorption on electrodes is characterised by the development of models based on classical thermodynamics and the electrostatic theory. Within the frames of these theories we can distinguish two approaches. The first approach, originated from Frumkin s work on the parallel condensers (PC) model,attempts to determine the dependence of upon the applied potential E based on the Gibbs adsorption equation. From the relationship = g( ), the surface tension y and the differential capacity C can be obtained as a function of E by simple mathematical transformations and they can be further compared with experimental data. The second approach denoted as STE (simple thermodynamic-electrostatic approach) has been developed in our laboratory, and it is based on the determination of analytical expressions for the chemical potentials of the constituents of the adsorbed layer. If these expressions are known, the equilibrium properties of the adsorbed layer are derived from the equilibrium equations among the chemical potentials. Note that the relationship = g( ), between and , is also needed for this approach to express the equilibrium properties in terms of either or E. Flere, this relationship is determined by means of the Gauss theorem of electrostatics. 

The classical approach to deducing the thermodynamic properties of a substance has traditionally been combustion calorimetry (18). Here the substance of interest is completely burned, and the heat of... 

Dejak, C., Pastres, R., Pecenik, G., PolengM, I. Classical thermodynamic-statistical approach of open systems deviating from maximum entropy. In C. Rossi, S. Bastianoni, A. Donati, N. Marchettini (eds.) Tempos in Science and Nature Structures, Relations, and Complexity, Annals cf the New York Academy of Sciences, vol. 879, pp. 400-405. Academy of Sciences, New York (1999)... 

We present later a classical approach (based on the macroscopic theory of radiant energy conversion) to such an analysis, which was recently reconciled with the non-equihbrium thermodynamic approach built on the definition of the chemical potential of a photon (Meszena and Westerhoff, 1999). 

We note that the approach described above can be used for thin films and other nonuniform systems where density or composition varies rapidly with position at equilibrium (see Chapter 2). It contrasts sharply with the classical treatment of interfacial thermodynamics givrai in Section 3, which deals with overall properties of the interfacial region without considering density or concentration profiles or even the existence of molecules and intermolecular forces. An advantage of the earlier approach is that its results are independent of molecular properties. The principal disadvantage is that values of interfacial tension cannot be predicted. Hence the role of molecular theory is, as in other areas of thamodynamics, to provide information beyond that obtainable with the classical approach. 

The classical approach to crystal growth considers the thermodynamic changes that occur on crystallization. The overall free energy difference, AG, between a small solid particle, the nucleus, and the solute in solution is the sum of the excess free energy between the surface of the particle and bulk of the particle, AGs, and the excess free energy between a very large particle and solute in solution, AG ... 

The classical approach to nucleation outlined above is subject to criticism on several grounds. In the first place, the thermodynamic properties of small clusters are assumed to be identical to those of the bulk phase at equilibrium. At the same time, the subdivision of free energy terms into bulk and surface... 

The kinetic scheme such as the one shown in figure 4 can be used for an analysis of the thermodynamic aspects of photoredox reactions. In the classical approach, the conversion of the precursor complex [S. ..(2] to the successor complex [S. ..Q ] is treated according to the activated complex formalism ... 

The Kelvin-equation-based methods were found to perform reasonably well for macro-porus and some mesoporous materials. However, it was foimd that the classical approach does not hold trae for micropores, in which case the intermolecular attractive forces between the sorbate and sorbent molecules predominate over bulk fluid forces such as surface tension. The potential energy fields of neighboring sorbent surfaces are known to overlap when the pores are only a few molecular dimensions wide. This results in a substantial increase in the interaction energy of an adsorbed molecule [12], which is not accounted for by simple classical thermodynamic models such as the Kelvin equation. 

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