Phenomenological coefficients activation energies

In order to develop a consistent free-volume diffusion model, there are some issues which must be addressed, namely i) how the currently available free-volume for the diffusion process is defined, ii) how this free-volume is distributed among the polymer segments and the penetrant molecules and iii) how much energy is required for the redistribution of the free-volume. Any valid free-volume diffusion model addresses these issues both from the phenomenologic and quantitative points of view such that the diffusion process is described adequately down to the microscopic level. Vrentas and Duda stated that their free-volume model addresses these three issues in a more detailed form than previous diffusion models of the same type. Moreover, it was stated that the model allows the calculation of the absolute value of the diffusion coefficient and the activation energy of diffusion mainly from parameters which have physical significance, i.e. so-called first principles . In the framework of this model the derivation of the relation for the calculation of the self-diffusion coefficient of the sol-... 

The parameter AP accounts for a specific contribution of the plastic material to the diffusion process. Phenomenologically speaking AP has the role of a conductance of the polymer matrix towards the diffusion of the migrant (Chapter 6). Higher values of AP in such polymers as PE lead to increased DP-values while in stiff chain polymers such as polyesters and polystyrenes lower AP-values account for smaller diffusion coefficients for the same migrant. The parameters b and c account for the specific contributions of the migrant and the diffusion activation energy respectively. 

The phenomenological coefficients in a one-plus rate equation derived for a specific mechanism are composites of individual rate coefficients of steps. Activation energies for them can be established from their temperature dependence with the Arrhenius equation. With regard to their activation energies, two types of phenomenological coefficients can be distinguished those consisting entirely of products, ratios, or ratios of products of individual rate coefficients and those which also involve additive terms. 

A significant variation of the activation energy of a phenomenological coefficient with temperature indicates that the coefficient involves additive terms of individual rate coefficients of steps. 

Phenomenological coefficients in reduced rate equations are combinations of individual rate coefficients of steps. If a phenomenological coefficient consists entirely of a product, a ratio, or a ratio of products of individual rate coefficients, its activation energy is essentially temperature-independent. In contrast, if the phenomenological coefficient involves additive terms, its activation energy varies with temperature unless the terms have similar activation energies or one of them dominates. 

The first term describes the dependence of the coercivity on the anisotropy field. In an ideal system, the phenomenological coefficient c would be one and is reduced to about 0.1 in a real system. The second term describes the thermal activation effects. denotes the anisotropy energy, is the molecular field and c is a phenomenological coefficient, which gives an account for the decrease of anisotropy and/or exchange interactions at defect position. The experimental data show that - has a quadratic-like behaviour which means... 

A phenomenological approach. Sect. 9.2.2 was implemented for ultrafast reactions (UFR) RX + e —> R + X — also in polar media, i.e for the estimation of the cathodic E1/2 ([173], pp 122-136 [225]). Gas-phase activation energy being also considered as the decisive factor in this case. Assuming that the activation energies En = m for the UFR processes in one and same polar media (solvent + electrolyte, coefficient 0 [Pg.294]

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