Phenomenological approach

We now consider how one extracts quantitative infonnation about die surface or interface adsorbate coverage from such SHG data. In many circumstances, it is possible to adopt a purely phenomenological approach one calibrates the nonlinear response as a fiinction of surface coverage in a preliminary set of experiments and then makes use of this calibration in subsequent investigations. Such an approach may, for example, be appropriate for studies of adsorption kinetics where the interest lies in die temporal evolution of the surface adsorbate density N. ... 

For modelling conformational transitions and nonlinear dynamics of NA a phenomenological approach is often used. This allows one not just to describe a phenomenon but also to understand the relationships between the basic physical properties of the system. There is a general algorithm for modelling in the frame of the phenomenological approach determine the dominant motions of the system in the time interval of the process treated and theti write... 

To start, we shall first flash on the phenomenological approach used to interpret the data. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

Values of kH olki3. o tend to fall in the range 0.5 to 6. The direction of the effect, whether normal or inverse, can often be accounted for by combining a model of the transition state with vibrational frequencies, although quantitative calculation is not reliable. Because of the difficulty in applying rigorous theory to the solvent isotope effect, a phenomenological approach has been developed. We define <[), to be the ratio of D to H in site 1 of a reactant relative to the ratio of D to H in a solvent site. That is. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

Phenomenological approach to cation-solvent interactions. U. Mayer and V. Gutmann, Struct. Bonding (Berlin), 1972,12,113-140 (102). 

Mayer U, Gutmann V (1972) Phenomenological Approach of Cation-Solvent Interactions. 12 113-140... 

In the last two decades we have witnessed in photocatalysis, as a science, a continuous shift from phenomenological approaches to studies at the molecular level. With accumulation of information obtained in such studies, the accents in the work aimed at development of new photocatalysts and new photocatalytic reactions and technologies, are expected to more and more shift from empirical search to intentional design. 

Another possible use of atomistic simulations would be the possibility of checking the simplest phenomenological approaches, that is, to validate an alternative description of the system based in a simpler mathematical description. 

Two different approaches have been followed to calculate the lineshapes within a relaxation model. According to a phenomenological approach based on the modified Bloch equations [154, 155], the intensity distribution of the theoretical Mossbauer spectrum may be written as [156] ... 

Mayer, U., Gutmann, V. Phenomenological Approach to Cation-Solvent Interactions. Vol. 12, pp. 113-140. 

Carb6, R. (Ed.) (1995) Molecular Similarity and Reactivity From Quantum Chemical to Phenomenological Approaches, Kluwer Academic Publ., Dordrecht. 

TG Kaufmann, EF Leonard. Studies of intramembrane transport A phenomenological approach. AIChE J 14 110-117, 1968. 

The hydrodynamic interaction is introduced in the Zimm model as a pure intrachain effect. The molecular treatment of its screening owing to presence of other chains requires the solution of a complicated many-body problem [11, 160-164], In some cases, this problem can be overcome by a phenomenological approach [40,117], based on the Zimm model and on the additional assumption that the average hydrodynamic interaction in semi-dilute solutions is still of the same form as in the dilute case. 

More advanced scale was proposed by Kamlet and Taft [52], This phenomenological approach is very universal as may be successfully applied to the positions and intensities of maximal absorption in IR, NMR (nuclear magnetic resonance), ESR (electron spin resonance), and UV-VS absorption and fluorescence spectra, and to many other physical or chemical parameters (reaction rates, equilibrium constant, etc.). The scale is quite simple and may be presented as ... 

It is also evident that this phenomenological approach to transport processes leads to the conclusion that fluids should behave in the fashion that we have called Newtonian, which does not account for the occurrence of non-Newtonian behavior, which is quite common. This is because the phenomenological laws inherently assume that the molecular transport coefficients depend only upon the thermodyamic state of the material (i.e., temperature, pressure, and density) but not upon its dynamic state, i.e., the state of stress or deformation. This assumption is not valid for fluids of complex structure, e.g., non-Newtonian fluids, as we shall illustrate in subsequent chapters. 

The only known alternatives for the analysis of macrosystems are by the phenomenological approach, known as thermodynamics, or by the use of... 

W. B. Davis, M. R. Wasidewski, M. A. Ratner, V. Mujica, A. Nitzan, Electron Transfer Rates in Bridged Molecular Systems - a Phenomenological Approach to Relaxation , J. Phys. Chem. 1997,101, 6158-6164. 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

The phenomenological approach does not preclude a consideration of the molecular origins of the characteristic timescales within the material. It is these timescales that determine whether the observation you make is one which sees the material as elastic, viscous or viscoelastic. There are great differences between timescales and length scales for atomic, molecular and macromolecular materials. When an instantaneous deformation is applied to a body the particles forming the body are displaced from their normal positions. They diffuse from these positions with time and gradually dissipate the stress. The diffusion coefficient relates the distance diffused to the timescale characteristic of this motion. The form of the diffusion coefficient depends on the extent of ordering within the material. 

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