Character defect theory

As suggested by Figure 1, an interesting aspect of the quantum defect theory is that the value of the quantum defect determines not only the energy of the state but also the spatial character of the wave function. Thus the properties in Table 1 may be applied to any atom if the effective quantum number n = n - fi is used instead of n. 

B( n) is the contribution to Bn of all the configurations in which n defects are assigned to m sites. The summation over m in Eq. (205) is essentially similar in character to that employed in 0. Retention of only m = 1, 2 corresponds to the familiar quasichemical approximation of order-disorder theory.33... 

Another model applied for the calculation of the OMC pore size distribution is the density functional theory (DFT). This model assumes that the micro- and mesopores are sht-shaped and that the pore walls consist of defect-free basal planes of graphene sheets [35]. Both assumptions might be justified to a certain degree for micropores in activated carbons. However, they are certainly not valid for mesopores in OMCs. As mentioned above, the OMC mesopores correspond to the voids in between the carbon rods. Thus, their shape is not slit-like. Furthermore, the graphitic character strongly depends on the OMC synthesis temperature. For OMC synthesized at low temperature (i.e., < 1300°C), the graphene layer contain numerous defects (see below). Finally, in some pitch-based OMC, the graphene layers are orientated perpendicular to the OMC... 

Several possible responses of block copolymer microstructure to an electric field have been considered by us and other groups. We investigated the possibility of alignment by selective disordering and alignment by movement or creation of defects for a lamellar microstructure. Gurovich [60] proposed that the polymer chains are distorted by an electric field, changing the conditions for stability and the character of the ordered phases. Onuki and Fukuda [78] developed a theory for a ripple instability in a lamellar block copolymer like the one seen in smectic A... 

As already mentioned, the layered structure of cholesteric materials imposes certain limitations on the topological classification of defects based on ho-motopy groups a more general theory is still lacking. In this section we discuss macroscopic defects such as focal conic domains and oily streaks whose existence depends crucially on the layered character of ordering. 

First-principles calculations including electron-electron interactions beyond the mean field theory have shown the excitonic character of optical transitions in SWNTs with large exciton binding energies (of up to 1 eV for the (8,0) SWNT) (Spataru et al. 2004). These predictions have been corroborated by experiments (Shaver et al. 2007 Wang et al. 2005), Unfortunately, these calculations are too demanding for routine calculations in large diameter tubes, and unlikely to be practical to study the effect of defects and functionalization. 

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