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Oleksiy Starykov Jan Prokeš Ivo Křivka Jaroslav Stejskal 《Macromolecular Symposia》2004,212(1):455-460
Polyaniline (PANI) base was protonated in aqueous solutions of an organic acid, 3-nitro-1,2,4-triazol-5(4H)-one (NTO). The temperature dependence of DC conductivity of PANI-NTO seems to correspond to the theory of variable range hopping (VRH) in three dimensions. The frequency dependence of AC conductivity also reflects the hopping nature of mobile charges. The activation energy for the polymers with protonation degree above 0.12 remains constant with increasing dopant concentration and DC conductivity. The value of this constant may correspond to the energy needed for the ionization of dopant counterion. The fit of the electric relaxation function to the stretched exponential function ϕ(t) = exp[−(t/τ)β] gives the stretch parameter β about 0.35, which shows that the distribution of relaxation times is broad and indicates a high inhomogeneity in the distribution of a dopant. 相似文献
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For and variable exponents and with values in [1, ∞], let the variable exponents be defined by The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space to the variable Lebesgue space for , then where C is an interpolation constant independent of T. We consider two different modulars and generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that and , as well as, lead to sufficient conditions for and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that , are Lipschitz continuous and bounded away from one and infinity (in this case, ). 相似文献