Kraus model compounds

Krause, A.A. and Niemczyk, H.D. Gas-liquid chromatographic analysis of chlorthal-dimethyl herbicide and its degradates in turfgrass thatch and soil using a solid-phase extraction technique, J. Environ. Sci Health, B25(5) 587-606, 1990. Kresheck, G.C., Schneider, H., and Scheraga, H.A. The effect of DzO on the thermal stability of proteins. Thermod3mamic parameters for the transfer of model compounds from HzO to DzO, J. Phys. Chem., 69(9) 3132-3144, 1965. 

Analogous to the spherical filler of radius R in the Kraus model, Bhattacharya and Bhowmick [31] consider an elliptical filler represented by R(1 + e cos 0), in the polar coordinate. The swelling is completely restricted at the surface and the restriction diminishes radially outwards (Fig. 40 where, qt and q, are the tangential and the radial components of the linear expansion coefficient, q0). This restriction is experienced till the hypothetical sphere of influence of the restraining filler is existent. One can designate rapp [> R( 1 + e cos 0)] as a certain distance away from the center of the particle where the restriction is still being felt. As the distance approaches infinity, the swelling assumes normality, as in a gum compound. This distance, rapp, however, is not a fixed or well-defined point in space and in fact is variable and is conceived to extend to the outer surface of the hypothetical sphere of influence. 

Sippola, V., Krause, O., and Vuorinen, T., Oxidation of lignin model compounds with cobalt-sulphosalen catalyst in the presence and absence of carbohydrate model compound. Journal Of Wood Chemistry And Technology 2004,24 (4), 323-340. 

Sippola, V. O. and Krause, A. O. I., Oxidation activity and stability of homogeneous cobalt-sulphosalen catalyst -Studies with a phenolic and a non-phenolic lignin model compound in aqueous alkaline medium. J Molecular Catalysis A-Chemical 2003, 194 (1-2), 89-97. 

Polyimides have excellent dielectric strength and a low dielectric constant, but in certain electrolyte solutions they can electrochemically transport electronic and ionic charge. Haushalter and Krause (5) first reported that Kapton polyimide films derived from 1,2,4,5-pyromellitic dianhydride (PMDA) and 4,4 -oxydianiline (ODA) undergo reversible reduction/oxidation (redox) reactions in electrolyte solutions. Mazur et al., (6) presented a detailed study of the electrochemical properties of chemically imidized aromatic PMDA- derived polyimides and model compounds in nonaqueous solutions. Thin films of thermally... 

Simell, P.A., Hirvensalo, E.K., Smolander, V.T. and Krause, A.O.I. (1999) Steam reforming of gasification gas tar over dolomite with benzene as a model compound. Industrial and Engineering Chemistry Research, 38,1250-1257. 

Kraus model as modified by Ulmer on SBR/carbon black (60 phr) compounds. 

From a theoretical point of view, the Lion et al. model has the merit to approach the DSS effect by applying constitutive laws formulated on the basis of fractional calculus, in other terms by formulating the behavior of materials with respect to fractional time derivatives of stress and strain an approach that in principle requires only a small number of material constants to express the material properties in the time or the frequency domain. However, deriving model parameters from experimental data is not straightforward and, for instance Lion et al. had to use a stochastic Monte Carlo method to estimate the model parameters for a comparison with experimental data on 60 phr CB filled rubber compound. Moreover, mathematical handling of the above equations (see Appendix 5.5) shows that, like the Kraus model, this one exhibits also horizontal symmetry for the G curve and vertical symmetry for the G" curve, and is therefore not expected to perfectly meet experimental data, at least in its present state of development. 

Figure 6.10 shows typical dynamic properties of vulcanized PDMS-silica systems, as investigated through strain sweep experiments at constant frequency and temperature. As can be seen, dynamic strain softening is observed in a qualitatively similar manner to other filled polymers. It follows that models, which successfully fit conventional filled rubbers (e.g., carbon black filled compounds), are expected to well suit such data. This is indeed the case, as shown by the curves in Figure 6.10, drawn by fitting the Kraus-Ulmer equations, i.e.. 

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