Frequency dependence, microscopic systems

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

As microscopic systems, these oscillators have a zero-point energy (ZPE) equal to hvc aii and the difference in zero-point energies for a particular vibration in isotopomers depends upon vibrational frequencies. These, in turn, depend on the force constant (the same for... 

Langevin et al. [35,71] have proposed a simplified hydrodynamic model of thinning of microscopic foam films that accounts for the influence of surface elasticity on the rate of thinning in a large range of thicknesses and Ap. However, as noted by the authors, in view of the rapid loss of surfactant molecules at the surface during film drainage, the elasticity would not correspond to the actual bulk surfactant concentration but to lower values since the system is very far from equilibrium. Frequency dependence of surface elasticity has been considered by Tambe and Sharma [72]. 

In all real systems, some deviation from ideal behavior can he observed. If a potential is applied to a macroscopic system, the total current is the sum of a large number of microscopic current filaments, which originate and end at the electrodes. If the electrode surfaces are rough or one or more of the dielectric materials in the system are inhomogeneous, then all these microscopic current filaments would be different. In a response to a small-amplitude excitation signal, this would lead to frequency-dependent effects that can often be modeled with simple distributed circuit elements. One of these elements, which have found widespread use in the modeling of impedance spectra, is the so-called constant phase element (CPE). A CPE is defined as... 

Schmidt, et al. studied the rheological properties of solutions of fd-virus, using classical mechanical and magnetic tweezers rheometry to determine G and G" (101). Macroscopic and microscopic measurements were in reasonable agreement. The observed frequency dependence of G at low frequency was much weaker than predicted by some modem theoretical calculations(102). Comparison was made with actin solutions to separate fundamental properties from single-system peculiarities. Actin aggregation is extremely sensitive to a wide variety of factors. 

Extended nonequilibrium thermodynamics is not based on the local equilibrium hypothesis, and uses the conserved variables and nonconserved dissipative fluxes as the independent variables to establish evolution equations for the dissipative fluxes satisfying the second law of thermodynamics. For conservation laws in hydrodynamic systems, the independent variables are the mass density, p, velocity, v, and specific internal energy, u, while the nonconserved variables are the heat flux, shear and bulk viscous pressure, diffusion flux, and electrical flux. For the generalized entropy with the properties of additivity and convex function considered, extended nonequilibrium thermodynamics formulations provide a more complete formulation of transport and rate processes beyond local equilibrium. The formulations can relate microscopic phenomena to a macroscopic thermodynamic interpretation by deriving the generalized transport laws expressed in terms of the generalized frequency and wave-vector-dependent transport coefficients. 

For an individual system D depends on the parameters in the Hamiltonian. One expects D to increase with increasing coupling strength between the molecular modes, all else being the same. The relevant rate near the transition is a microscopic frequency of local motion, o>, that depends on the local density of states. Thus in this regime,... 

Abstract Theoretical, experimental principles and the applications of the frequency response (FR) method for determining the diffusivities in microporous and bidispersed porous solid materials have been reviewed. Diffusivities of hydrocarbons and some other sorbates in microporous crystals and related pellets measured using the FR technique are presented, and the FR data are analysed to demonstrate the identification of the FR spectra. These results display the ability of the FR method to discriminate multi-kinetic mechanisms, including a surface resistance or surface barrier occurring simultaneously in the systems, which are difficult to be determined using other microscopic or macroscopic methods. The FR measurements also showed that the diffusivity of a system depends significantly on the subtle differences in molecular shape and size of sorbates in various... 

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