Ref HAL: hal-00693224_v1
Résumé: We analyze the nature of the Schrödinger equation and of the Dirac equation. Due to the theoretical reversibility of time (see Olivi-Tran [1, 2, 3, 4]), a simple transformation of Scḧrödinger equation leads to that conclusion. In the case of Dirac equation the nature itself of the Dirac matrices leads to a quantization of time when solving this equation with the associated matrices.

Ref HAL: hal-00691320_v1
DOI: 10.1103/PhysRevB.85.115437
Résumé: Using the spectral moment's method, the infrared spectra of single-walled boron nitride nanotubes are calculated. The dependence of these modes has been calculated as a function of the nanotube chirality, diameter (from 0.7 to 5 nm), and length. These predictions are useful for understanding the experimental infrared spectra of boron nitride nanotubes.

Ref HAL: hal-00687512_v1
DOI: 10.1021/la204562t
Résumé: Hybrid polyion complex (HPIC) micelles are nanoaggregates obtained by complexation of multivalent metal ions by double hydrophilic block copolymers (DHBC). Solutions of DHBC such as the poly(acrylic acid)-block-poly(acrylamide) (PAA-b-PAM) or poly(acrylic acid)-block-poly(2-hydroxyethylacrylate) (PAA-b-PHEA), constituted of an ionizable complexing block and a neutral stabilizing block, were mixed with solutions of metal ions, which are either monoatomic ions or metal polycations, such as Al3+, La3+, or Al-13(7+). The physicochemical properties of the HPIC micelles were investigated by small angle neutron scattering (SANS) and dynamic light scattering (DLS) as a function of the polymer block lengths and the nature of the cation. Mixtures of metal cations and asymmetric block copolymers with a complexing block smaller than the stabilizing block lead to the formation of stable colloidal HPIC micelles. The hydrodynamic radius of the HPIC micelles varies with the polymer molecular weight as M-0.6. In addition, the variation of R-h of the HPIC micelle is stronger when the complexing block length is increased than when the neutral block length is increased. R-h is highly sensitive to the polymer asymmetry degree (block weight ratio), and this is even more true when the polymer asymmetry degree goes down to values close to 3. SANS experiments reveal that HPIC micelles exhibit a well-defined core-corona nanostructure; the core is formed by the insoluble dense poly(acrylate)/metal cation complex, and the diffuse corona is constituted of swollen neutral polymer chains. The scattering curves were modeled by an analytical function of the form factor; the fitting parameters of the Pedersen's model provide information on the core size, the corona thickness, and the aggregation number of the micelles. For a given metal ion, the micelle core radius increases as the PAA block length. The radius of gyration of the micelle is very close to the value of the core radius, while it varies very weakly with the neutral block length. Nevertheless, the radius of gyration of the micelle is highly dependent on the asymmetry degree of the polymer: if the neutral block length increases in a large extent, the micelle radius of gyration decreases due to a decrease of the micelle aggregation number. The variation of the R-g/R-h ratio as a function of the polymer block lengths confirms the nanostructure associating a dense spherical core and a diffuse corona. Finally, the high stability of HPIC micelles with increasing concentration is the result of the nature of the coordination complex bonds in the micelle core.