Quasi one-dimensional variable range

Hydrochloric acid as well as camphor sulfonic acid doped polyaniline prepared in chloroform often have [59] log a proportional to T as expected for quasi-one-dimensional variable range hopping, Equations (3) and (4). Generally, the higher conductivity samples have a weaker temperature dependence at low temperatures (Tq 700-1000 K for T<80 K), and lower conductivity samples a stronger temperature dependence (To 4000 K). The smaller Tq for the more highly conducting samples has been associated with weaker localization due to improved intrachain and interchain order. 

Hydrochloric acid as well as camphor sulfonic acid doped polyaniline prepared in chloroform often have log a proportional to as expected for quasi-one-dimensional variable range hopping (VRH), Fig. 46.11, [73,121,143] ... 

Epstein et al. [41, 54, 71] suggested that the sulfonated polyanilines have much stronger temperature dependence conductivity than emeraldine hydrochloride due to greater electron localization. The temperature dependence of the conductivity of 50 % [41], 75 % [54] and fully ring sulfonated polyanilines [71] was best fit by the quasi one-dimensional variable range hopping model described by Equation (2.1) ... 

DC current passing through the ER fluid was found to sinusoidally oscillate with the applied mechanical field [63,64], This phenomenon was theoretically addressed [65] on the basis of the fibrillated chain structure framework and the quasi-one-dimensional variable range hopping conductive model. An ER sensor for real-time monitoring the mechanical field based on this phenomenon was thus proposed. It can be primarily used as a detector of seismography and a monitor for bridge vibration conditions... 

For PPy(S-PHE), which has the least structural order of the doped PPy samples studied here, o-dc(T) shows the highest degree of localization, with a large resistivity ratio [p(4 K)/p(300 K) — 10 ]. The temperature dependence is that of quasi-one-dimensional variable range hopping. 

Fogler, M.M., S. Teber, and B.l. Shklovskii. 2004. Variable-range hopping in quasi-one-dimensional electron crystals. Phys Rev B 69 035413. 

Quantum Hall edge states, 16-7 Quantum mechanical calculations, 12-3-12-6 Quasi-ID arrays, 16-16 Quasi-ID polymer nanofibers, 16-9 Quasi-ID variable range hopping, 8-32, 8-33 Quasi-one-dimensionality (quasi-ID), 15-8, 15-10-15-13, 15-15, 15-29, 15-55, 15-57, 15-67... 

Furthermore, mathematical procedures can be applied to the detailed mechanism or the skeletal mechanism which reduces the mechanism even more. These mathematical procedures do not exclude species, but rather the species concentrations are calculated by the use of simpler and less time-consuming algebraic equations or they are tabulated as functions of a few preselected progress variables. The part of the mechanism that is left for detailed calculations is substantially smaller than the original mechanism. These methods often make use of the wide range of time scales and are thus called time scale separation methods. The most common methods are those of (i) Intrinsic Low Dimensional Manifolds (ILDM), (ii) Computational Singular Perturbation CSF), and (iii) level of importance (LOl) analysis, in which one employs the Quasy Steady State Assumption (QSSA) or a partial equilibrium approximation (e.g. rate-controlled constraints equilibria, RCCE) to treat the steady state or equilibrated species. 

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