Theoretical interpretation density

Thus, the recombination theory provided the first theoretical interpretation of the linear relation between polarization and the logarithm of current density that had been established experimentally. It is true, though, that the preexponential factor in Eq. (15.12) [2303(RTI2FI) 0.03 V] is four times smaller than the experimental values of slope b but it has been shown in later work that factors closer to the experimental values can be obtained when an inhomogeneous surface is assumed. 

In contrast to crystalline solids characterized by translational symmetry, the vibrational properties of liquid or amorphous materials are not easily described. There is no firm theoretical interpretation of the heat capacity of liquids and glasses since these non-crystalline states lack a periodic lattice. While this lack of long-range order distinguishes liquids from solids, short-range order, on the other hand, distinguishes a liquid from a gas. Overall, the vibrational density of state of a liquid or a glass is more diffuse, but is still expected to show the main characteristics of the vibrational density of states of a crystalline compound. 

One important condition is constituted by the fact that certainly in symmetric nuclear matter no phase transition is observed below 3po- In fact some theoretical interpretation of the heavy ion experiments performed at the CERN SPS [30] points to a possible phase transition at a critical density pc ss 6po ss 1/fm3. We will in the following take this value for granted and use an extended MIT bag model [31] (requiring a density dependent bag constant ) that is compatible with this condition. 

The moments of a charge distribution provide a concise summary of the nature of that distribution. They are suitable for quantitative comparison of experimental charge densities with theoretical results. As many of the moments can be obtained by spectroscopic and dielectric methods, the comparison between techniques can serve as a calibration of experimental and theoretical charge densities. Conversely, since the full charge density is not accessible by the other experimental methods, the comparison provides an interpretation of the results of the complementary physical techniques. The electrostatic moments are of practical importance, as they occur in the expressions for intermolecular interactions and the lattice energies of crystals. 

In our opinion, this book demonstrates clearly that the formalism of many-point particle densities based on the Kirkwood superposition approximation for decoupling the three-particle correlation functions is able to treat adequately all possible cases and reaction regimes studied in the book (including immobile/mobile reactants, correlated/random initial particle distributions, concentration decay/accumulation under permanent source, etc.). Results of most of analytical theories are checked by extensive computer simulations. (It should be reminded that many-particle effects under study were observed for the first time namely in computer simulations [22, 23].) Only few experimental evidences exist now for many-particle effects in bimolecular reactions, the two reliable examples are accumulation kinetics of immobile radiation defects at low temperatures in ionic solids (see [24] for experiments and [25] for their theoretical interpretation) and pseudo-first order reversible diffusion-controlled recombination of protons with excited dye molecules [26]. This is one of main reasons why we did not consider in detail some of very refined theories for the kinetics asymptotics as well as peculiarities of reactions on fractal structures ([27-29] and references therein). 

C. Cohen-Addad et al., Nature of S—O interaction in short X-S—O contacts Charge density experimental studies and theoretical interpretation. J. Chem. Soc. Perkin Trans. 2, 191-196 (1984)... 

Another approach that can help in getting hydration numbers is the study of dielectric constants—both the static dielectric constants and the dielectric constant as it depends on frequency. Such measurements give a large amount of information about the surrounds of the ion but a good deal more has to be done before the theoretical interpretation can bear the weight of clear structural conclusions. Density, mobility, and entropy measurements may also be informative. 

The theoretical interpretation of the first voltage drop at low current is based on the Butler-Volmer equation, which is derived by an analysis of electrode kinetics and provides a general description of the relationship between current density and surface overpotential for an electrochemical converter [46] ... 

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