Explanation modes/model

In our approach to membrane breakdown we have only taken preliminary steps. Among the phenomena still to be understood is the combined effect of electrical and mechanical stress. From the undulational point of view it is not clear how mechanical tension, which suppresses the undulations, can enhance the approach to membrane instability. Notice that pore formation models, where the release of mechanical and electrical energy is considered a driving force for the transition, provide a natural explanation for these effects [70]. The linear approach requires some modification to describe such phenomena. One suggestion is that membrane moduli should depend on both electrical and mechanical stress, which would cause an additional mode softening [111]. We hope that combining this effect with nonlocality will be illuminating. 

Schmitz and Lu (12) have also considered coupling of translational and rotational modes for rigid rods in congested solutions as an explanation for the extraordinary diffusion regime. They concluded that, for 350 bp dinucleosomal DNA, the coupled ion model gave better agreement with the data. Since our DNA molecules are even shorter, 150 bp, the coupled translation -rotation model can seemingly be ruled out. 

The thermal properties of AU55 are treated in Sect. 3, using especially the results of MES measurements [24,25,42]. These are discussed in connection with the concept of bulk versus surface modes in small particles. An explanation of the temperature dependence of the MES [42] absorption intensities and the Cv results [25] on the basis of a model using the site coordination and the center-of-mass motion are briefly reviewed. The consequences of the Mossbauer results for surface Debye temperatures and for the melting temperature of small gold particles are also discussed. 

The assignments of the v (CH2) bands in terms of the assumed model are not entirely unambiguous. Two strong a bands and two weak 7t bands [re (CH2)0 is probably close to zero intensity] are predicted. In pure PVdC four bands are found, all apparently of a polarization. Two of these, however, at 2850 and 2930 cm-1, are of highly variable intensity in the copolymer spectra they become quite weak in comparison to the other two at 2948 and 2990 cm-1 [Narita, Ichinohe, and Enomoto (747) quote frequency values of 2966 and 3010 cm-1 for these two bands]. A possible explanation is that the 2850 and 2930 cm-1 bands are associated with amorphous structures, while the 2948 and 2990 cm-1 bands are associated with the Fuller structure. We would then have to assume that the vtt (CH2)0 mode is too weak to be observed. It is clear that these proposals require additional confirmation. 

Despite our natural satisfaction with this explanation, we noted that it nevertheless does not provide a clear physical mechanism for the effect. For example, it was not evident why the frequency exaltation is state selective, i.e., it is not observed in any other state, and the frequency of all other modes are reduced upon excitation. It was deemed necessary, therefore, to articulate the avoided crossing model, derive a clear physical origin of the frequency exaltation of the Kekule mode, its state, and mode specificity, and establish the connection of the phenomenon to the jr-distortivity in the ground state. This was achieved in 1996.209... 

The discussion directly following Eq (6) provides a simple, physically reasonable explanation for the preceding observations of marked concentration dependence of Deff(C) at relatively low concentrations. Clearly, at some point, the assumption of concentration independence of Dp and in Eq (6) will fail however, for our work with "conditioned" polymers at CO2 pressures below 300 psi, such effects appear to be negligible. Due to the concave shape of the sorption isotherm, even at a CO2 pressure of 10 atm, there will still be less than one CO2 molecule per twenty PET repeat units at 35°C. Stern (26) has described a generalized form of the dual mode transport model that permits handling situations in which non-constancy of Dp and Dh manifest themselves. It is reasonable to assume that the next generation of gas separation membrane polymers will be even more resistant to plasticization than polysulfone, and cellulose acetate, so the assumption of constancy of these transport parameters will be even more firmly justified. 

A number of attempts have been made to explain the nonlinear, pressure-dependent sorption and transport in polymers. These explanations may be classified as "concentration-dependent (5) and "dual-mode (13) sorption and transport models. These models differ in their physical assumptions and in their mathematical descriptions of the sorption and transport in penetrant-polymer systems. 

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