Electronic and optical features of silicon carbide nanoparticles and nanocomposites
Electron paramagnetic resonance (EPR) investigations were carried out on hybrid Core-Shell nanomaterials associating silicon carbide nanoparticles and conducting polyaniline. The performed experiments compare the paramagnetic centres, the electronic transport features and the interface effects in two classes of materials, bare polymers and core-shell nanocomposites. By EPR, large doping rates were demonstrated in the bare doped polymers through important saturation phenomena which alter significantly the EPR spectrum features. Furthermore, memory effects were involved in the bare doped polymer with regard to the EPR spectrum features depending on the conditions of its thermal treatments. In the hybrid core-shell nanocomposites nor such saturation and nor memory effects were found on the EPR signals even if similar paramagnetic centres exist in both classes of samples. These behaviors were discussed taking into account the thermal stability and the doping efficiency in the considered classes of materials. Optimal doping levels were then realized and their effects on the polymers and the nanocomposites were clarified by using EPR and DRS (dielectric relaxation spectroscopy) measurements. Also, it is demonstrated that the charge carriers consist in polarons in the nanocomposites while bipolarons contributions dominate the electrical conductivity in the bare doped polymers.
Spectroscopic investigation of thermal treatment of doped polypyrrole
The 
 results of a UV/VIS spectroscopic investigation of thin films of oxidized polypyrrole doped with p-toluenesulfonate, dodecylsulfate or copper phthalocyanine tetrasulfonate anions immediately after electrochemical 
 synthesis and during heat treatment are presented. The absorption bands in the resulting spectra were 
 identified with the electronic transitions of the polarons, bipolarons and transverse bipolarons as follows: 
 the absorption bands below ca. 1.4 and at 1.8 eV are both attributed to the sum of the polarons and transverse 
 bipolarons, the band at 2.44–2.5 eV to the sum of polarons, bipolarons and transverse bipolarons and the band 
 around 3.2–3.6 eV to the band gap transition of polypyrrole. The identity of the absorption band above 
 3.8 eV remains uncertain. The absorbance changes of bands in the UV/VIS spectra collected during sample aging 
 and heat treatment were explained as a result of the rearrangement of the polypyrrole structure. The main 
 processes acting during the sample aging are the interchain conversion of polarons into transverse bipolarons 
 and the interaction of polarons with transverse bipolarons yielding bipolarons. The spectral changes 
 induced by sample heating at 80 °C seem to be caused mainly by an interchain dissociation of the transverse 
 bipolarons to polarons and by their slower intrachain recombination into bipolarons and the polypyrrole 
 neutral form. The structural rearrangement induced by the sample heating is a very slow process because 
 the UV/VIS spectra were not stable even after 35 h. The changes taking place in the polypyrrole structure 
 during sample cooling are the opposite of those during the heating but they are only partially reversible 
 in magnitude. The polypyrrole samples doped with p-toluenesulfonate and copper phthalocyanine tetrasulfonate exhibited very similar behavior whereas dodecylsulfate doped samples exhibited an extraordinary 
 behavior owing their liquid-like solid-state micellar structure. The magnitudes of the polypyrrole spectra 
 changes showed that only a relatively small proportion 
 of the 
 species present within 
 the polypyrrole were influenced by these processes.
The Invariance of the Vacuum is the Invariance of the World
The following theorem is demonstrated: If the vacuum is invariant under the group generated by the space integral of the time component of a local vector current, then the Hamiltonian is invariant also. A similar theorem holds for the group generated by the space integral of a space component of a local axial-vector current.