Nonextensive Statistical Mechanics, Anomalous Diffusion and Central Limit Theorems

We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of a new central limit theorem, which would play a fundamental role in the foundations and ubiquity of nonextensive statistical mechanics. The basic novelty introduced within this conjectural theorem is the generalization of the hypothesis of independence of the N random variables being summed. In addition to this, we also advance some nonlinear dynamical (possibly exact) relations which generalize the concepts of Lyapunov exponents, entropy production per unit time, and their interconnection as first proved by Pesin for chaotic systems. The article is available online on SpringerLink (www.springerlink.com) using colors instead of greyscales in Figure 4.1. Lecture held in the Seminario Matematico e Fisico on May 21, 2004 Received: December 2004     

Surface-enhanced Raman scattering and micro-Raman imaging of Langmuir-Blodgett films of rhodium phthalocyanine

Rhodium phthalocyanine (RhPc) was synthesized and ultra thin Langmuir-Blodgett (LB) films of RhPc were successfully fabricated. The LB film characterization was carried out using both UV-vis absorption spectra and Raman scattering. The Raman spectroscopy was carried out using 633 and 780 nm laser lines. LB films were deposited onto Ag nanoparticles to achieve the surface-enhanced pre-resonance Raman scattering (pre-SERRS) and surface-enhanced Raman scattering (SERS) for both laser lines, respectively, which allowed the characterization of the RhPc ultra thin films. The morphology of the LB RhPc neat film is extracted from micro-Raman imaging.     

Spectroscopic Studies on the Interaction of Tetramethylpyridylporphyrins and Cationic Clays

In the present work, the interaction between5,10,15,20-tetrakis(1-methyl-4-pyridyl)-21H,23H-porphine (TMPyP) and its metallated form(CoTMPyP) with three cationic clays was investigatedby X-ray diffraction (XRD), UV-VIS and resonance Ramanspectroscopies. Sodium montmorillonites K10 and KSFand a synthetic fluorohectorite (FHT) containingdifferent macrocycle loadings, were prepared by an ionexchange reaction. In nonsaturated KSF and FHT, theCoTMPyP molecule assumes a flat orientation, relativeto the host layers, giving rise to at least twoabsorption bands in the Soret region (ca. 445 and 465 nm)assigned to adsorbed and intercalated CoTMPyP,respectively. For the delaminated K10 sample, a broadband centered around 456 nm, indicates a majorcontribution from the metalloporphyrin on the clayexternal surfaces. The electronic spectra of FHTsamples containing increasing amounts of CoTMPyPshow bands red shifted even when a small amount ofporphyrin is used, suggesting that the electroniclevels of the macrocycle are more affected by theinteraction with the clay than by the metalloporphyrindistortion inside the galleries. The resonance Ramanspectra obtained for all CoTMPyP samples presentedonly minor shifts in peak positions and band width,with the exception of the FHT saturated sample, wherethe bands are clearly broader when compared to otherloadings, suggesting that porphyrin aggregation isoccurring. In the case of TMPyP, the bands at ca. 430and 468 nm were assigned to nonprotonated andprotonated molecules, respectively. This assignment issupported by resonance Raman spectroscopy, which alsoshowed the ₂ mode (ca. 1550 cm^-1) to bethe most sensitive peak to protonation.     

Corrected results for the influence of size,zeta potential,and state of motion of dispersed particles on the conductivity of a colloidal suspension

A correction of a recent work on the dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of dispersed particles (C. Grosse, S. Pedrosa, V.N. Shilov, J. Colloid Interface Sci. 251 (2002) 304) is presented. It is shown that the procedure used in that work to calculate the contribution of the particles to the conductivity of the suspension leads to a result that includes the variation of the conductivity of the dispersion medium. Revised analytical and numerical calculations are presented, which strongly reinforce the conclusions reached in the original work: The expression for the conductivity increment based on the value of the dipolar coefficient of the suspended particles (calculated taking into account their electrophoretic motion) appears to be valid over the whole range of particle sizes.     

Interaction of Co+ and Co2+ with glycine. A theoretical study

Cobalt cations are open shell systems with several possible electronic states arising from the different occupations of the 3d and 4s orbitals. The influence of these occupations on the relative stability of the coordination modes of the metal cation to glycine has been studied by means of theoretical methods. The structure and vibrational frequencies have been determined using the B3LYP method. Single-point calculations have also been carried out at the CCSD(T) level. The most stable structure of Co(+)-glycine is bidentate, with the Co(+) cation interacting with the amino group and the carbonyl oxygen of neutral glycine, and the ground electronic state being (3)A. For Co(2+)-glycine, the lowest energy structure corresponds to the interaction of the metal cation with the carboxylate group of the zwitterionic glycine, the ground electronic state being (4)A'.     

Spectroscopic and electrochemical studies on (2-hydroxypicolinate)-bis(2,2′-bipyridine)ruthenium(II) and related complexes

Summary The synthesis, spectra and electrochemistry of [Ru(bipy)₂-(picOH)]⁺ and -picO-[Ru(bipy)₂]₂ ²⁺ (bipy = 2,2-bipyridine and picOH = 3-hydroxypicolinate ion) are described. The spectroscopic properties in the visible region are dominated by the intense Ru bipy chargetransfer transitions. In the binuclear complex, the two [Ru(bipy)₂L]²⁺ moieties are nonequivalent, exhibiting E _1/2 = 0.69 and 1.20 V versus s.h.e. The partially oxidized species exhibits a weak intervalence transfer band at 1085 nm, and is consistent with a Robin-Day class II mixed valence complex.     

On the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension

The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.