Yield phenomenology

Just as in the case of equilibrium thermodynamics, thermodynamics of irreversible processes yields phenomenological equations which in principle are independent of the molecular nature of the system. In contrast, statistical mechanics derives transport properties from the microscopic picture of the solution. Considerable progress has been made in this latter type of approach during recent years. 

There is a large volume of contemporary literature dealing with the structure and chemical properties of species adsorbed at the solid-solution interface, making use of various spectroscopic and laser excitation techniques. Much of it is phenomenologically oriented and does not contribute in any clear way to the surface chemistry of the system included are many studies aimed at the eventual achievement of solar energy conversion. What follows here is a summary of a small fraction of this literature, consisting of references which are representative and which also yield some specific information about the adsorbed state. 

In this section, the general inelastic theory of Section 5.2 will be specialized to a simple phenomenological theory of plasticity. The inelastic strain rate tensor e may be identified with the plastic strain rate tensor e . In order to include isotropic and kinematic hardening, the set of internal state variables, denoted collectively by k in the previous theory, is reduced to the set (k, a) where k is a scalar representing isotropic hardening and a is a symmetric second-order tensor representing kinematic hardening. The elastic limit condition in stress space (5.25), now called a yield condition, becomes... 

Frieden s theory is that any physical measurement induces a transformation of Fisher information J I connecting the phenomenon being measured to intrinsic data. What we call physics - i.e. our objective description of phenomenologically observed behavior - thus derives from the Extreme Physical Information (EPI) principle, which is a variational principle. EPI asserts that, if we define K = I — J as the net physical information, K is an extremum. If one accepts this EPI principle as the foundation, the status of a Lagrangian is immediately elevated from that of a largely ad-hoc construction that yields a desired differential equation to a measure of physical information density that has a definite prior significance. 

Phenomenological evidence for the participation of ionic precursors in radiolytic product formation and the applicability of mass spectral information on fragmentation patterns and ion-molecule reactions to radiolysis conditions are reviewed. Specific application of the methods in the ethylene system indicates the formation of the primary ions, C2H4+, C2i/3+, and C2H2+, with yields of ca. 1.5, 1.0, and 0.8 ions/100 e.v., respectively. The primary ions form intermediate collision complexes with ethylene. Intermediates [C4iZ8 + ] and [CJH7 + ] are stable (<dissociation rate constants <107 sec.-1) and form C6 intermediates which dissociate rate constants <109 sec. l). The transmission coefficient for the third-order ion-molecule reactions appears to be less than 0.02, and such inefficient steps are held responsible for the absence of ionic polymerization. 

A phenomenological correlation of CHF can be developed by combining the subcooling effect and the flow friction effect on the CHF. This is done by substituting Eq. (5-19) into Eq. (5-18), yielding... 

The results are shown in Fig. 5. We notice that the EOS calculated with the microscopic TBF produces the largest gravitational masses, with the maximum mass of the order of 2.3 M , whereas the phenomenological TBF yields a maximum mass of about 1.8 M . In the latter case, neutron stars are characterized by smaller radii and larger central densities, i.e., the Urbana TBF produce more compact stellar objects. For completeness, we also show a sequence of stellar configurations obtained using only two-body forces. In this case the maximum mass is slightly above 1.6 M , with a radius of 9 km and a central density equal to 9 times the saturation value. 

It is the nature of the activator that holds the answer to the inherent question If the polymerisations initiated by protonic acids, e.g., CF3S03H, and by syncatalytic systems, such as that consisting of the same acid + thiolan [25] or Me2S [26] are both pseudo-cationic, why does the one yield a product whose DP is determined by proton transfer to monomer, whilst the other produces a living system A review of the facts shows a simple phenomenological distinction, from which a mechanistic explanation can be deduced. The distinction is this ... 

As noted by Carberry in 1987, only phenomenological values can be measured in the laboratory since it is not possible to a priori distinguish between A (the catalytic area) and A (exposed measurable area), per volume of catalyst agent. This yields a structure-sensitive reaction that is dependent on crystallite size. While it is clear that a mechanism cannot be determined from purely kinetic measurements, a proposed mechanism is only accepted after it can predict the observed kinetic measurements. The dominant issue of the observed measurements is whether A or A is being measured. This correct measurement will yield the proper intrinsic kinetics, but will not reveal much insight into the mechanism. Thus, it is imperative to identify and obtain as much information as possible on the nature of intermediate chemical species. 

Thus, the perhaps unfamiliar constitutive relations (2.23)-(2.25) yield familiar results when the fields are time harmonic moreover, because of (2.26) and (2.27), physical meaning can now be attached to the phenomenological coefficients even for arbitrarily time-dependent fields. 

More successful attempts to interpret yielding on a molecular level were based on an extension of the Eyring phenomenological flow theory by incorporating molecular characteristics [132,133]. The modification is based on changes in distribution of rotational conformation states of segments upon stress action and the effect of temperature on them. 

Since the molecular crazing criteria require a substantial amount of detailed information about the molecular structure of the solid polymer and no clear correlation to the macroscopic phenomena observed experimentally exists, phenomenological criteria analogous to those for shear yielding were proposed. The... 

All formulas mentioned above are fulfilled for any phenomenological photoconduction model. Microscopic description needs detailed research of the quantum yield, parameters of the generation, recombination and transport processes. 

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