Phenomenological mobility

From Eqns (6.58) to (6.63), the reduced phenomenological mobilities are obtained as... 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

One could assume that this characteristic behavior of the mobility of the polymers is also reflected by the typical relaxation times r of the driven chains. Indeed, in Fig. 28 we show the relaxation time T2, determined from the condition g2( Z2) = - g/3 in dependence on the field B evidently, while for B < B t2 is nearly constant (or rises very slowly), for B > Be it grows dramatically. This result, as well as the characteristic variation of with B (cf. Figs. 27(a-c)), may be explained, at least phenomenologically, if the motion of a polymer chain through the host matrix is considered as consisting of (i) nearly free drift from one obstacle to another, and (ii) a period of trapping, r, of the molecule at the next obstacle. If the mean distance between obstacles is denoted by ( and the time needed by the chain to travel this distance is /, then - (/ t + /), whereby from Eq. (57) / = /Vq — k T/ DqBN). This gives a somewhat better approximation for the drift velocity... 

The dependence of drift mobility on the external field must be interpreted by a theoretical model, and as such it can elucidate the transport mechanism in a given case. In this section, we will only describe the phenomenological and experimental aspects. Their theoretical significance will be taken up in Sect. 10.2. 

Nowadays attention is turned also to the supermolecular level, that is, to the morphologic aspects, to the nature of interfaces, to the formation of new phases, or of particular aggregates (liquid crystals, gels, etc.). Interest has also been directed to the study of chain mobility for its influence on frictional properties of polymers. In recent years there have been many successful approaches to a microscopic theory (in contrast to a phenomenological approach) of the physi-comechanical behavior of macromolecular materials. 

The Phenomenology of Mobile Electrified Interfaces Electrokinetic Properties... 

PVC-TPA systems the phenomenological equality l/Tef — 1/T — 1/T0 was established, where T0 - experimental temperature which characterize the transport properties of the system. The molecules securing the weak dependence of the mobility on the electric field may be characterized by low Tc (high Tef). 

Chemical diffusion has been treated phenomenologically in this section. Later, we shall discuss how chemical diffusion coefficients are related to the atomic mobilities of crystal components. However, by introducing the crystal lattice, we already abandon the strict thermodynamic basis of a formal treatment. This can be seen as follows. In the interdiffusion zone of a binary (A, B) crystal having a single sublattice, chemical diffusion proceeds via vacancies, V. The local site conservation condition requires that /a+/b+7v = 0- From the definition of the fluxes in the lattice (L), we have... 

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

Each particle of defect species s will respond to this force, but the degree of response will be dependent upon the species in question and the diffusion medium. The proportionality factor is termed the mobility coefficient, B(s), of the species in question. The current, J(s), produced by a given force, Fw, per defect particles will be larger for a greater number of particles per unit volume, since then more particles are set into motion by the force. Thus, from a phenomenological standpoint, it is reasonable to write... 

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