It is well known that amorphous solids display a phonon spectrum where the Debye ∼ ω 2 law at low frequency melds into an anomalous excess-mode peak (the boson peak) before entering a quasilocalized regime at higher frequencies dominated by scattering. The microscopic origin of the boson peak has remained elusive despite various attempts to put it in a clear connection with structural disorder at the atomic/molecular level. Using numerical calculations on model systems, we show that the microscopic origin of the boson peak is directly controlled by the local breaking of centerinversion symmetry. In particular, we find that both the boson peak and the nonaffine softening of the material display a strong positive correlation with a new order parameter describing the local inversion symmetry of the lattice. The standard bond-orientational order parameter, instead, is shown to be a poor correlator and cannot explain the boson peak in randomly-cut crystals with perfect bond-orientational order. Our results bring a unifying understanding of the boson peak anomaly for model glasses and defective crystals in terms of a universal local symmetry-breaking principle of the lattice. arXiv:1601.03879v3 [cond-mat.dis-nn]
We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approach to the glass transition. These results provide evidence that the mechanical glass transition itself is continuous and thus represents a crossover rather than a true phase transition. The relatively sharp drop of the low-frequency storage modulus across the glass transition temperature can be explained mechanistically within the proposed theory: the proliferation of low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy excitations) is directly responsible for the rapid growth of a negative non-affine contribution to the storage modulus.
The structure and vibrational density of states (VDOS) of polymer glasses are investigated using numerical simulations based on the classical Kremer-Grest bead-spring model. We focus on the roles of chain length and bending stiffness, the latter being set by imposing three-body angular potentials along chain backbones. Upon increasing the chain length and bending stiffness, structural reorganisation leads to volumetric expansion of the material and build-up of internal stresses. The VDOS has two dominant bands: a low frequency one corresponding to inter-and intra-chain nonbonding interactions and a high frequency one corresponding principally to vibrations of bonded beads that constitute skeletal chain backbones. Upon increasing the steepness of the angular potential, vibrational modes associated with chain bending gradually move from the low-frequency to the high-frequency band. This redistribution of modes is reflected in a reduction of the so-called Boson peak upon increasing chain stiffness. Remarkably, the finer structure and the peaks of the high-frequency band, and their variations with stiffness, can, for short chains, be explained using an analytical solution derived for a model triatomic molecule. For longer chains, the qualitative evolution of the VDOS with chain stiffness is similar, although the distinct peaks observed for short chains become increasingly smoothed-out. Our findings can be used to guide a systematic approach to interpretation of Brillouin and Raman scattering spectra of glassy polymers in future work, with applications in polymer processing diagnostics.
A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d, and for arbitrary values of the lattice coordination number Z, are shown and discussed. As a function of these two parameters (and their ratio Z/d), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d. Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d→∞, which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d=3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks.
We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nonaffine lattice dynamics theory. A small increase of polymer chain bending stiffness leads first to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus G with bending stiffness is caused by a competition between additional resistance to deformation offered by stiffer backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counter-intuitive finding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.
We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting Generalized Langevin Equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, that we take from numerical evaluation of a marginally-stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye ∼ ω 2 p law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at T Tg. Good agreement is found for both the reactive (real part) of the response and for the α-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches, especially in the reactive modulus. On the low-frequency side of the α-peak, the fitting supports the presence of ∼ ω 4 p modes at vanishing eigenfrequency as recently shown in [Phys. Rev. Lett. 117, 035501 (2016)]. α-wing asymmetry and stretched-exponential behaviour are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.
Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum-rules for viscoelastic response derived on the basis of non-affine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion-symmetry in disordered lattices. By defining a suitable quantitative and general atomiclevel measure of nonaffinity and inversion-symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversionsymmetry breaking in each system. Close to the isostatic point for central-force lattices, powerlaw creep G(t) ∼ t −1/2 emerges as a consequence of the interplay between soft vibrational modes and non-affine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s' at least, it is a well established experimental fact that the specific heat of glasses is instead just linear in T at T ∼ 1K, and presents a pronounced peak when normalized by T 3 , known as the boson peak. Here we present a new approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus. arXiv:1903.05237v4 [cond-mat.dis-nn]
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