Quasi-thermodynamics

Another quasi-thermodynamical model of ion transport in polymers is based on the concept of minimum configurational entropy required for rearrangement of the polymer, giving practically identical o—T and D — T dependences as the preceding model. 

The common disadvantage of both the free volume and configuration entropy models is their quasi-thermodynamic approach. The ion transport is better described on a microscopic level in terms of ion size, charge, and interactions with other ions and the host matrix. This makes a basis of the percolation theory, which describes formally the ion conductor as a random mixture of conductive islands (concentration c) interconnected by an essentially non-conductive matrix. (The mentioned formalism is applicable not only for ion conductors, but also for any insulator/conductor mixtures.)... 

Transition state theory, a quasi-thermodynamic/statistical mechanical approach to the theory of reaction rates was developed in the early 1930s by a number of workers including H. Eyring, E. R Wigner, and J. C. Polanyi and was very quickly applied to the consideration of isotope effects on rates of simple molecular reactions. 

The quasi-thermodynamic assumption is that Xf is in equilibrium with the reactants, despite the continuous leakage of X to products. The quasi-equilibrium constant K is then defined in terms of concentration by... 

Molecular Structure Effects and Detergency. The correlation of surfactant structure with interfacial and colloid properties is a poorly understood science. Much study in this area has been thermodynamic which has been a useful endeavor but which nevertheless fails to provide specific molecular structure/physical property correlations. The following study has also been largely thermodynamic to this point however, since the data has been collected on pure LAS homologs, it provides an opportunity to apply some of the quasi-thermodynamic treatments that have been proffered in the literature to date. 

A final quasi-thermodynamic approach to molecular structure effects has been proposed by Good et al. (17-18) which relates molar volumes and the Girifalco-Good interaction parameter, as... 

C/3 n c, O Table III. Quasi- -Thermodynamic Analysis of Detergency Data For Structure Effects on Detergency Molecular ON 5 o 70 m... 

Another aspect of this quasi-thermodynamic approach is to use Equation 25, along with G values from Table 4, to calculate the molar-attraction constant for the sodium sulfonate molecular group or... 

V x(x) the gradient of the chemical potential energy. However, again, it is, strictly speaking, just a mathematical substitution into a kinetic equation—it is a quasi thermodynamic potential, not an equilibrium thermodynamic potential. Equations (9a) and (9b) are often referred to as the drift and diffusion components, respectively, of the electron current. One can see immediately from Eqs. (6), (9a), and (9b) that WU(x) and V x(x) are independent forces in the photoconversion process and, therefore, that it is possible to drive a solar cell with either one, or both, of these forces. In fact, the different types of solar cell can be classified according to the relative importance of these two forces in the photoconversion process. 

Eqn. 3.2-7 is comparable to the well-known Arrhenius law, d nk/dT = - EJRT, which describes the dependence of the rate constant on the temperature by means of the energy of activation, Ea. For reactions occurring in the liquid phase it is the practice to use molar concentrations instead of mole fractions. This implies some complications. The equilibrium product is now defined by molar concentrations. The quasi-thermodynamic development leads to ... 

When the < s are constant across the membrane, (39) is changed into (36). Equation (38) for the diffusion potential can also be obtained by a quasi-thermodynamic method. 

In general it can be said that the experimental material is not extensive. The experimental material concerns the application of irreversible thermodynamics, the application of refined Nernst-Planck flux equations and the application of quasi-thermodynamics. The latter is used to derive equations for membrane potentials. 

The first of the principal Horn and Jackson results is as follows. If the system obeys the law of mass action (or acting surfaces), then if it has a positive PCB it demonstrates a "quasi-thermodynamic behaviour, i.e. its positive steady state is unique and stable and a global Lyapunov function exists. 

The number of complexes minus that of connected components of the graph for their conversions equals the number of linearly independent reactions (stoichiometric vectors). A second Horn and Jackson condition for quasi-thermodynamic behaviour is the weak reversibility of the graph for complex conversions. This graph is called weakly reversible if any of its connected components contain a route to get from any node to any other moving in the direction of its arrows. For example, the scheme... 

Horn and Jackson [50], M. Feinberg [51], Horn [52] and Feinberg and Horn [53] showed that if the scheme of complex conversions is weakly reversible and (most essential) the conditions (169) is fulfilled, the system always has a PCB and hence demonstrates "quasi-thermodynamic behaviour. The weak reversibility condition seems to be less essential since, for its fulfilment, it is sufficient to suggest that all steps are reversible assuming, if necessary, the rate constant for a reversible step to be sufficiently low. Hence the main difficulty for the application of the results of Horn, Jackson and Feinberg to a concrete reaction system can be the impossibility of fulfilling eqn. (169), which cannot be overcome by small additions to the equations. 

The quasi-thermodynamic approach outlined above will obviously remain applicable to future coal conversion technologies as well, because the underlying thermodynamic principles are universal and invariant. Figure 2 is illuminating in this context it shows that by-product waters of liquefaction processes can be differentiated from their gasification counterparts by their redox potential and pH characteristics (13). 

We finally contrast the preceding de ivation with the quasi thermodynamic approach initiated by Tolman (8). In his work, the surface tension is assumed to be given by... 

The term transition state is sometimes used interchangeably with the term transition structure, although in a strict sense the two are not identical. Transition state is the quasi-thermodynamic state of... 

The concentration of majority carriers in the depletion layer will depend on a quasi-thermodynamic term iVD exp (v), and a transport term. It will be shown below that the first term is likely to dominate under normal conditions [131],... 

It can be seen that the quasi-thermodynamic boundary condition of Wilson and Memming is satisfied if Dp is large, LD is small and the light intensity is low. Explicitly, we have... 

McLennan, D. J. Semianpirical calculation of rates of Sn2 Finkelstein reactions in solution by a quasi-thermodynamic cycle, Aust. J. Chem. 1978,31,1897-1909. 

We see that the rate of production of products is determined by two quantities, the first a quasi-thermodynamic quantity, the equilibrium concentration of free radicals, and the second a kinetic quantity, namely, the rate at which each radical can go through a chain cycle. When the cycle is made up of two steps of disproportionate speed as in the present case, it is the slower step (in this case Br + H2) which is of importance in determining the over-all rate. It is this feature which explains in this case the specific inhibition by HBr even though the over-all reaction is essentially not reversible. The slow step in a chain will in general (though not always) be endothermic. This implies that its reverse is exothermic and hence of lower activation energy, and so faster. We can thus always expect inhibition by products in chain reactions except in those cases in which the fast steps are of unusual speed. 

The transition state is in quasi-thermodynamic equilibrium with the reactants, and the removal of the products does not affect the reactants equilibrium up to the transition state. 

D. J. McLennan, Aust. J. Ghent., 31, 1897 (1978). Semi-Empirical Calculation of Rates of 5 2 Finkelstein Reactions in Solution by a Quasi-Thermodynamic Cycle. 

Quasi-thermodynamic approaches. Effects of temperature and pressure. Corresponding states... 

The term transition state refers to a hypothetical quasi-thermodynamic state. Transition structure... 

If this equation is compared with Eq. (33), we readily conclude that the more general quasi-thermodynamic treatment presented in section 3 takes into account the dipole-dipole interactions among the normal components of the dipole moment of the adsorbed species. 

Thus, in the quasi-thermodynamic approximation considered here the occurrence of nonequilibrium electrons and holes in the bands can be described as the splitting of the initial Fermi level F into two quasi-levels F and Fp. 

The quasi-thermodynamic approach enables one to obtain a criterion for finding out whether a semiconductor is liable to (photo)corrosion and suggest a way of preventing it. For example, in the case of a binary semiconductor MX (where M denotes the electropositive and X the electronegative components) the equation for a partial electrochemical reaction of cathodic decomposition with conduction electrons involved can be written in the form... 

Equation IV. 18 splits the heat of transport into two terms, the first of which is quasi-thermodynamic in that it involves only averages over equilibrium ensembles, and the second of which arises from the deviation of the distribution function in pair space from the equilibrium distribution function. Qn corresponds to the expressions for the heat of transport found by previous authors who have neglected the nonequilibrium perturbation to the distribution function. 

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