Short-Time Elasticity of Polymer Melts: Tobolsky Conjecture and Heterogeneous Local Stiffness

An extended Molecular-Dynamics study of the short-time "glassy" elasticity exhibited by a polymer melt of linear fully-flexible chains above the glass transition is presented. The focus is on the infinite-frequency shear modulus $G_\infty$ manifested in the picosecond time scale and the relaxed plateau $G_p$ reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbours of each monomer exhibits marked distribution with average value given by $G_\infty$. In particular, the neighbourhood of the end monomers of each chain are softer than the inner monomers, so that $G_\infty$ increases with the chain length. $G_p$ is not affected by the chain length and is largely set by the non-bonding interactions, thus confirming for polymer melts the conjecture formulated by Tobolsky for glassy polymers.Comment: 18 pages, 6 figure

Cage rattling does not correlate with the local geometry in molecular liquids

Molecular-dynamics simulations of a liquid of short linear molecules have been performed to investigate the correlation between the particle dynamics in the cage of the neighbors and the local geometry. The latter is characterized in terms of the size and the asphericity of the Voronoi polyhedra. The correlation is found to be poor. In particular, in spite of the different Voronoi volume around the end and the inner monomers of a molecule, all the monomers exhibit coinciding displacement distribution when they are caged (as well as at longer times during the structural relaxation). It is concluded that the fast dynamics during the cage trapping is a non-local collective process involving monomers beyond the nearest neighbours.Comment: 15 pages, 6 figure

Competition of the connectivity with the local and the global order in polymer melts and crystals

The competition between the connectivity and the local or global order in model fully-flexible chain molecules is investigated by molecular-dynamics simulations. States with both missing (melts) and high (crystal) global order are considered. Local order is characterized within the first coordination shell (FCS) of a tagged monomer and found to be lower than in atomic systems in both melt and crystal. The role played by the bonds linking the tagged monomer to FCS monomers (radial bonds), and the bonds linking two FCS monomers (shell bonds) is investigated. The detailed analysis in terms of Steinhardt's orientation order parameters Q_l (l = 2 - 10) reveals that increasing the number of shell bonds decreases the FCS order in both melt and crystal. Differently, the FCS arrangements organize the radial bonds. Even if the molecular chains are fully flexible, the distribution of the angle formed by adjacent radial bonds exhibits sharp contributions at the characteristic angles {\theta} = 70{\deg}, 122{\deg}, 180{\deg}. The fractions of adjacent radial bonds with {\theta} = 122{\deg}, 180{\deg} are enhanced by the global order of the crystal, whereas the fraction with 70{\deg} < {\theta} < 110{\deg} is nearly unaffected by the crystallization. Kink defects, i.e. large lateral displacements of the chains, are evidenced in the crystalline state.Comment: J. Chem. Phys. in pres

A study of the deep structure of the energy landscape of glassy polystyrene: the exponential distribution of the energy-barriers revealed by high-field Electron Spin Resonance spectroscopy

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field Electron Spin Resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). The exponential distribution of the energy-barriers for the rotational motion of the spin probe is unambigously evidenced at both 240K and 270K. The same shape for the distribution of the energy-barriers of PS was evidenced by the master curves provided by previous mechanical and light scattering studies. The breadth of the energy-barriers distribution of the spin probe is in the range of the estimates of the breadth of the PS energy-barriers distribution. The evidence that the deep structure of the energy landscape of PS exhibits the exponential shape of the energy-barriers distribution agrees with results from extreme-value statistics and the trap model by Bouchaud and coworkers.Comment: Final version in press as Letter to the Editor on J.Phys.:Condensed Matter. Changes in bol

Support vector machines with quantum state discrimination

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification

Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination

Méthodes MCMC pour la décomposition en paquets d'ondelettes de signaux transitoires

Les bases de paquets d'ondelettes fournissent un cadre approprié à la recherche d'une représentation optimale des processus stochastiques. Dans cet article, nous abordons le problème du choix de la "meilleure base" sous un angle bayésien, lorsque l'observation est un signal transitoire bruité, en considérant cette base optimale comme l'un des paramètres du modèle. Des distributions a priori non-homogènes sont introduites sur les coefficients de décomposition du signal, nécessitant la mise en oeuvre d'algorithmes de Monte Carlo par chaînes de Markov à sauts réversibles. Diverses méthodes d'estimation, pouvant dépendre de plusieurs représentations, sont évaluées au travers de simulations

Non-gaussian effects in the cage dynamics of polymers

The correlation between the fast cage dynamics and structural relaxation is investigated in a model polymer system. It is shown that the cage vibration amplitude, as expressed by the Debye-Waller factor, and the relaxation time $\tau_\alpha$ collapse on a single universal curve with a simple analytic form when the temperature, the density, the chain length and the monomer-monomer interaction potential are changed. For the physical states with the same $\tau_\alpha$ coincidence of the mean-square displacement, the intermediate scattering function and the non-Gaussian parameter is observed in a wide time window spanning from the ballistic regime to the onset of the Rouse dynamics driven by the chain connectivity. The role of the non-Gaussian effects is discussed.Comment: 8 pages, 5 figure