Schwarz theory

Note that the critical relaxation time is predicted to depend upon the square of the particle radius, as observable. This bound-ion-layer model of Schwarz was remarkably successful in several ways. The magnitude of the dielectric increment and its frequency shift with particle radius were reasonably in agreement with observation. Despite this welcome advance in the understandings of dispersions, the Schwarz theory deliberately excluded the possibility of bound counterion exchange with the surrounding medium. It also neglected any contribution to the particle polarizability that arises from the distortion of the outer or surrounding portions of the diffuse double layer. 

Schwarz theory provides a practical tool for analyzing measured data, but the theory has been criticized for neglecting the diffusion of ions in the bulk solution near the surface. Efforts have been made by, among others, Dukhin, Fixman and Chew, and Sen to employ Gouy-Chapman theory on particle suspensions, but the resulting theories are very complex and difficult to use on biological materials. Mandel and Odijk (1984) have given a review of this work. 

The observed excess absorption was attributed to the helix-coil equilibrium and the results interpreted by means of Schwarz theory for this process (l7a). This attribution was checked by performing comparative absorption measurements on aqueous solutions of poly-L and DL-lysine (10). Identical absorption vs pH curves were obtained for these two compounds, even though poly-DL-lysine undergoes no transition in the pH range 3 13. Comparative... 

A separate aspect of the Schwarz theory [6] covers electrical property changes due to chemical reactions in the bulk solution. Some reactions lead to formation of molecules of very different size and electrical properties than the original reactants, leading to a change in measured permittivity of the system. This effect, however, can be observed only if chemical process occurs faster than rotational diffusion, which is not the case for small molecules but may... 

Methane-to-methanol conversion by gas-phase transition metal oxide cations has been extensively studied by experiment and theory see reviews by Schroder, Schwarz, and co-workers [18, 23, 134, 135] and by Metz [25, 136]. We have used photofragment spectroscopy to study the electronic spectroscopy of FeO" " [47, 137], NiO [25], and PtO [68], as well as the electronic and vibrational spectroscopy of intermediates of the FeO - - CH4 reaction. [45, 136] We have also used photoionization of FeO to characterize low lying, low spin electronic states of FeO [39]. Our results on the iron-containing molecules are presented in this section. 

Hertwig, R.H., Hrusak, J., Schroder, D., Koch, W. and Schwarz, H. (1995) The metal-ligand bond strengths in cationic gold(l) complexes. Application of approximate density functional theory. Chemical Physics Letters, 236, 194-200. 

Blochl, P. E., Margl, P, Schwarz, K., 1996, Ab Initio Molecular Dynamics With the Projector Augmented Wave Method in Chemical Applications of Density Functional Theory, Laird, B. B., Ross, R. B., Ziegler, T. (eds.), American Chemical Society, Washington DC. 

Holthausen, M. C., Fiedler, A., Schwarz, H., Koch, W., 1996, How Does Fe+ Activate C-C and C-H Bonds in Ethane A Theoretical Investigation Using Density Funcional Theory , J. Phys. Chem., 100, 6236. 

It has been suggested that a sensitive test of the diffusion model would be found in the evolution of the eh yield (Schwarz, 1969). Early measurements by Hunt and Thomas (1967) and by Thomas and Bensasson (1967) revealed -6% decay within the first 10 ns and 15% decay in 50 ns. The diffusion theory of Schwarz predicts a very substantial decay ( 30%) in the first nanoseconds for instantaneous energy deposition. Schwarz (1969) tried to mitigate the situation by first integrating over pulse duration (-4.2 ns) and then over the detector response time (-1.2 ns). This improved the agreement between theory and experiment somewhat, but a hypothesis of no decay in this time scale would also agree with experiment. Thus, it was decided that a crucial test of the diffusion theory would... 

R. K. Agarwal and J. A. Schwarz, Analysis of High-Pressure Adsorption of Gases on Activated Carbon by Potential-Theory, Carbon, 26, 873-887 (1988). 

To account for the difference between experiment and theory, Schwarz suggested that electrostriction includes the formation of a glassy shell of 7 to 9 solvent molecules around the ion [102]. This phase transition provides a substantial density increase, and the observed volume changes can then be accounted for. 

M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, Cambridge, Univ. Press, Cambridge, UK, 1987. 

At thermal equilibrium, the helical fraction and all other quantities characterizing the conformation of a helix-forming polypeptide are fluctuating from time to time about certain mean values which are uniquely determined by three basic parameters s, a, and N. The rates of these fluctuations depend on how fast helix units are created or disappear at various positions in the molecular chain. Recently, there has been great interest in estimating the mean relaxation times of these local helix-coil interconversion processes, and several methods have been proposed and tested. In what follows, we outline the theory underlying the dielectric method due to Schwarz (122, 123) as reformulated by Teramoto and Fujita (124). 

Wada et al. (120) reported the observation of a secondary dielectric dispersion with a high-molecular-weight sample of PBLA in wi-cresol and showed that the resulting values of t as a function of / were interpretable in terms of their own theory essentially identical to Schwarz s one. 

Schwarz, G. (1962) A theory of the low-frequency dielectric dispersion of spherical colloidal particles in electrolyte solution, Journal of Physical Chemistry 66, 2636-2642... 

That is, Schwarz et al., loc. cit.y obtain by extrapolation to infinite moderator, A4A2 = 0.04 exp (4500/127 ) which represents, presumably, the reaction rate constants for thermaP species. There is, however, no theoretical basis for expecting such a low ratio of steric factors (0.04), contrary to the statements by the authors. Transition-state theories would on the contrary predict a ratio of steric factors of about unity. In fact these values would then predict that the frequency factors for the reverse reactions, i.e.,... 

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