Mean field spin glasses treated with PDE techniques

Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1–RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra’s broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.     

Spectroscopic Investigation of Oxygen- and Water-Induced Electron Trapping and Charge Transport Instabilities in n-type Polymer Semiconductors

We present an optical spectroscopy study on the role of oxygen and water in electron trapping and storage/bias-stress degradation of n-type polymer field-effect transistors based on one of the most widely studied electron transporting conjugated polymers, poly{[N,N9-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,59-(2,29-bisthiophene)} (P(NDI2OD-T2)). We combine results obtained from charge accumulation spectroscopy, which allow optical quantification of the concentration of mobile and trapped charges in the polymer film, with electrical characterization of P(NDI2OD-T2) organic field-effect transistors to study the mechanism for storage and bias-stress degradation upon exposure to dry air/oxygen and humid nitrogen/water environments, thus separating the effect of the two molecules and determining the nature of their interaction with the polymer. We find that the stability upon oxygen exposure is limited by an interaction between the neutral polymer and molecular oxygen leading to a reduction in electron mobility in the bulk of the semiconductor. We use density functional theory quantum chemical calculations to ascribe the drop in mobility to the formation of a shallow, localized, oxygen-induced trap level, 0.34 eV below the delocalized lowest unoccupied molecular orbital of P(NDI2OD-T2). In contrast, the stability of the polymer anion against water is limited by two competing reactions, one involving the electrochemical oxidation of the polymer anion by water without degradation of the polymer and the other involving a radical anion-catalyzed chemical reaction of the polymer with water, in which the electron can be recycled and lead to further degradation reactions, such that a significant portion of the film is degraded after prolonged bias stressing. Using Raman spectroscopy, we have been able to ascribe this to a chemical interaction of water with the naphthalene diimide unit of the polymer. The degradation mechanisms identified here should be considered to explain electron trapping in other rylene diimides and possibly in other classes of conjugated polymers as well.     

Proteins as sponges: a statistical journey along protein structure organization principles

The analysis of a large database of protein structures by means of topological and shape indexes inspired by complex network and fractal analysis shed light on some organizational principles of proteins. Proteins appear much more similar to "fractal" sponges than to closely packed spheres, casting doubts on the tenability of the hydrophobic core concept. Principal component analysis highlighted three main order parameters shaping the protein universe: (1) "size", with the consequent generation of progressively less dense and more empty structures at an increasing number of residues, (2) "microscopic structuring", linked to the existence of a spectrum going from the prevalence of heterologous (different hydrophobicity) to the prevalence of homologous (similar hydrophobicity) contacts, and (3) "fractal shape", an organizing protein data set along a continuum going from approximately linear to very intermingled structures. Perhaps the time has come for seriously taking into consideration the real relevance of time-honored principles like the hydrophobic core and hydrophobic effect.     

Phase equilibria of the Dy–Al–Si system at 500 °C

The isothermal section at 500 °C of the Dy–Al–Si system was studied in the whole concentration range. The alloys were characterized by X-ray powder diffraction, scanning electron microscopy and electron micro-probe analysis. A few samples were analysed by differential thermal analysis. The following intermetallic compounds, some of them showing variable composition, were found: DyAl₂Si₂ (τ₁), hP5-CaAl₂O₂ structure type, Dy₂Al₃Si₂ (τ₂) mS14-Y₂Al₃Si₂ structure type, Dy₂Al_1+x Si_2−x (τ₃), 0 ≤ x ≤ 0.25, oI10-W₂CoB₂ structure type and Dy₆Al₃Si (τ₄), tI80-Tb₆Al₃Si structure type. A number of binary phases dissolve the third element forming ternary solid solutions: Dy(Al_1−x Si _x )₃, 0 ≤ x ≤ 0.5, hP16-Ni₃Ti structure type, Dy(Al _x Si_1−x )₂, 0 ≤ x ≤ 0.1, oI12-GdSi₂ structure type, Dy(Al _x Si_1−x )_1.67, 0 ≤ x ≤ 0.2, oI12-GdSi₂ structure type, DyAl _x Si_1−x , 0 ≤ x ≤ 0.2, oC8-CrB, and Dy₅(Al _x Si_1−x )₃, 0 ≤ x ≤0.3, hP16-Mn₅Si₃ structure type. The melting point of Dy₆Al₃Si was determined.     

Evidence for the applicability of a novel procedure (swelling-poling-deswelling) to produce a stable alignment of second order NLO-chromophores covalently attached to a cross-linked PMMA or polystyrene polymeric network

The “swelling-poling-deswelling” technique is a new procedure of poling crosslinked polymeric network carrying covalently attached NLO (nonlinear optical) chromophores. It is based upon a solvent-swollen crosslinked polymeric network before submission to poling. Under electrical poling, the matrix is deswelled without heating above the polymer Tg (glass transition temperature) obtaining a significant improvement of the stabilization of the alignment of the chromophores and therefore of the SHG (second harmonic generation). We determined the d₃₃ values of DR1 chromophore linked in different manner to PMMA (polymethylmethacrylate) and polystyrene. Crosslinked PMMA gives very good results, in fact the 40% of the d₃₃ value remains after 4 months respect to d₃₃ evaluated a couple of hours after poling. Interestingly the same stability in the time of the d₃₃ is observed with the crosslinked polystyrene matrix. In terms of d₃₃ after poling, the two systems carrying DR1 (Disperse Red 1) moieties covalently attached to the polystyrene matrix (side-chain and crosslinked) behave in a similar manner, but in terms of stability, the linear polymeric system is the best (75%), higher than all systems investigated.     

DMA analysis to predict the performance of waterborne coatings

In previous studies some waterborne coatings, specifically formulated for the scope of the research, were studied during an artificial weathering process by means of dynamic mechanical analysis (DMA) technique. In those studies the chemical and physical parameters which mainly affect the performance of coatings and their evolution during weathering were measured. The aim was to predict the performance of coatings for exterior wood during their service life by means of accelerated artificial tests and instrumental measures. In this study four commercial products were artificially weathered following the European standard EN 927-6. The changes in the mechanical properties were measured by means of the DMA as reported in the previous studies. With this research the authors have verified the capability of this method to predict the performance in use of coatings.     

Self-assembly and two-dimensional spontaneous resolution of cyano-functionalized [7]helicenes on cu(111)

Birds of a feather flock together: STM and DFT studies provide the first example of spontaneous chiral resolution of a helicene on a surface. Racemic 6,13-dicyano[7]helicene forms fully segregated domains of pure enantiomers (2D conglomerate) on Cu(111). The propensity of the system to optimize intermolecular CN???HC(Ar) hydrogen bonding and CN???CN dipolar interactions translates into chiral recognition with preferential assembly of homochiral molecules.