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

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

Connectivity effects in the segmental self- and cross-reorientation of unentangled polymer melts

The segmental (bond) rotational dynamics in a polymer melt of unentangled, linear bead-spring chains is studied by molecular dynamics simulations. To single out the connectivity effects, states with limited deviations from the Gaussian behavior of the linear displacement are considered. Both the self and the cross bond-bond correlations with rank ℓ=1,2 are studied in detail. For ℓ=1 the correlation functions are precisely described by expressions involving the correlation functions of the chain modes. Several approximations concerning both the self- and the cross-correlations with ℓ=1,2 are developed and assessed. It is found that the simplified description of the excluded volume static effects derived elsewhere [D. Molin et al., J. Phys.: Condens. Matter 18, 7543 (2006)] well accounts for the short time cross-correlations. It also allows a proper modification of the Rouse theory which provides quantitative account of the intermediate and the long time decay of the rotational correlations with ℓ=1

Non-local cooperative atomic motions that govern dissipation in amorphous tantala unveiled by dynamical mechanical spectroscopy

The mechanisms governing mechanical dissipation in amorphous tantala are studied at microscopic scale via Molecular Dynamics simulations, namely by mechanical spectroscopy in a wide range of temperature and frequency. We find that dissipation is associated with irreversible atomic rearrangements with a sharp cooperative character, involving tens to hundreds of atoms arranged in spatially extended clusters of polyhedra. Remarkably, at low temperature we observe an excess of plastically rearranging oxygen atoms which correlates with the experimental peak in the macroscopic mechanical losses. A detailed structural analysis reveals preferential connections of the irreversibly rearranging polyhedra, corresponding to edge and face sharing. These results might lead to microscopically informed design rules for reducing mechanical losses in relevant materials for structural, optical, and sensing applications

Coincident correlation between vibrational dynamics and primary relaxation of polymers with strong or weak johari-goldstein relaxation

The correlation between the vibrational dynamics, as sensed by the Debye-Waller factor, and the primary relaxation in the presence of secondary Johari-Goldstein (JG) relaxation, has been investigated through molecular dynamics simulations. Two melts of polymer chains with different bond length, resulting in rather different strength of the JG relaxation are studied. We focus on the bond-orientation correlation function, exhibiting higher JG sensitivity with respect to alternatives provided by torsional autocorrelation function and intermediate scattering function. We find that, even if changing the bond length alters both the strength and the relaxation time of the JG relaxation, it leaves unaffected the correlation between the vibrational dynamics and the primary relaxation. The finding is in harmony with previous studies reporting that numerical models not showing secondary relaxations exhibit striking agreement with experimental data of polymers also where the presence of JG relaxation is known