Phenomenological Criteria

Lewis (1938) was not content with a purely conceptual view of adds and bases, for he also listed certain phenomenological criteria for an add-base reaction. The process of neutralization is a rapid one, an add or base displaces a weaker add or base from its compounds, adds and bases may be titrated against each other using coloured indicators, and both adds and bases have catalytic effects. 

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... 

Three phenomenological criteria can be identified for the exchange reaction on the alloys ... 

Lewis chose four familiar experimental criteria as the basis of his definitions of acids and bases. The four phenomenological criteria are ... 

Some writers have indicated that hydrogen acids require special consideration in the Lewis terminology. No doubt such a misunderstanding arises from the emphasis of the Br0nsted theory upon displacement of one base by another as the only criterion of acid-base phenomena. Actually displacement is only one of the four phenomenological criteria of acids and bases, and the Brpnsted type equation is only one of the two types of acid-base displacement. The Brpnsted theory is thus included in the Lewis theory and requires no special consideration. 

For such blends containing the droplets embedded in matrices, linear viscoelastic moduli can be calculated from several models formulated on the basis of the local stress balance (or other phenomenological criteria). " Among these models, the emulsion model proposed by Palieme appears to be most frequently compared with the experimental data. The complex modulus G =G + iG" deduced from this model can be summarized as ... 

Photophysical effects will here be taken to include light-induced changes in the extent of adsorption as well as photoelectronic effects involving the localisation or delocalisation of electrons at the illuminated interface. They will be differentiated from photochemical effects by the phenomenological criterion that photochemical effects involve rupture and/or rearrangement of bonds other than those between adsorbate and adsorbent. 

Ignition of the reaction is assumed to occur at a critical macroscopic temperature. This assumption provides a simple phenomenological criterion for purposes of displaying the wave propagation behavior, although it may seriously oversimplify the physics of initiation in detail. 

In the case of strong collisions, corresponding to y = 0, inequality (1.88) is reduced to a conventional validity criterion of the binary theory (1.59). However, if collisions are weak (y 1), the actual criterion given in Eq. (1.88) is considerably weakened and Langevin phenomenology is valid at larger densities. 

Lorentzian line shapes are expected in magnetic resonance spectra whenever the Bloch phenomenological model is applicable, i.e., when the loss of magnetization phase coherence in the xy-plane is a first-order process. As we have seen, a chemical reaction meets this criterion, but so do several other line broadening mechanisms such as averaging of the g- and hyperfine matrix anisotropies through molecular tumbling (rotational diffusion) in solution. 

Theoretical studies are primarily concentrated on the treatment of flame blow-off phenomenon and the prediction of flame spreading rates. Dunskii [12] is apparently the first to put forward the phenomenological theory of flame stabilization. The theory is based on the characteristic residence and combustion times in adjoining elementary volumes of fresh mixture and combustion products in the recirculation zone. It was shown in [13] that the criteria of [1, 2, 5] reduce to Dunskii s criterion. Longwell et al. [14] suggested the theory of bluff-body stabilized flames assuming that the recirculation zone in the wake of the baffle is so intensely mixed that it becomes homogeneous. The combustion is described by a second-order rate equation for the reaction of fuel and air. 

The phenomenological ordering of polymers projected for use as constructing materials is not an easy matter. Sometimes the temperature stability is used as a criterion, i.e., the temperature up to which the mechanical properties remain more or less constant. Another attempt for classification, uses the E modulus or the shape of the curve of stress-strain measurements (see Sect. 2.3.5.1). In general one can say that semicrystalline thermoplastics are stiff, tough, and impact-resistant while amorphous thermoplastics tend to be brittle. Their E... 

Within the region of validity of linear phenomenological equations, the theorem of minimal entropy generation at steady state is a general stability criterion. The static head is the natural steady state where the net ATP flow vanishes and a minimum of 1 occurs along the loci of the static-head states... 

Carbon forms with major sp hybridization may be phenomenologically classified into graphitizable and nongraphitizable. The criterion established to differentiate these two classes is too empirical, and there are important exceptions (e.g., polyimide-derived carbons) to this rule. Nevertheless, these two concepts are useful for purposes of classification. 

A general classification scheme for the discussion of the properties of mixed valence compounds has been introduced by Robin and Day 17). Although by no means all the deeply colored transition metal cyanides M [BM(CN) ]2H2O are mixed valence compounds in the strict sense, we will use this classification scheme for the whole group. The classification of the polynuclear cyanides is made on a purely phenomenological basis using the electronic spectra as a criterion. 

A macroscopic theory of strength is based on a phenomenological approach. No direct reference to the mode of deformation and fi acture is made. Essentially, this approach employs the mathematical theories of elasticity and tries to establish a yield or failure criterion. Among the most popular strength theories are those based on maximum stress, maximum strain, and maximum work. 

In contrast to (a) and (b), (c) is not a criterion based on phenomenology but refers to the structure which cannot be recognised at first sight. Nevertheless, it seems desirable to add this criterion to the definition of gels, since a number of systems conforming with (a) and (b) which should not be considered as gels however, can, by direct observation (e.g., with the ultramicroscope) be identified as not conforming with (c). 

Assuming that dominates possible quantum fluctuations, Schilling et al. (1993) used the phenomenological Lindemann melting criterion (Lindemann 1910) to describe the experimentally observed irreversibility line in terms of vortex-lattice melting i.e.. 

The closer the delta parameters of the both components are, the more compatible the components are. In very general and phenomenological terms it can be stated that for a polymer and a monomer (or any other low-molecular-weight-component) the criterion for solvabihty is... 

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