arXiv subjects

Rico Milkus

Publications and source records attributed to Rico Milkus.

8 recordsLinked to original sources

arXiv2023

Vibrational density of states and specific heat in glasses from random matrix 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 $T \sim 1K$, 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.

cond-mat.dis-nn↗

arXiv2020

Scaling up the lattice dynamics of amorphous materials by orders of magnitude

We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the Kernel Polynomial Method (KPM) for the computation of the vibrational density of states (VDOS) and the eigenmodes, including the $Γ$-correlator of the affine force-field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with $N=10^4$ atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to $10^6$ atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with $N$.

cond-mat.dis-nn↗

arXiv2018

Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics

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.

cond-mat.soft↗

arXiv2018

Interpretation of the vibrational spectra of glassy polymers using coarse-grained simulations

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 non-bonding 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.

cond-mat.soft↗

arXiv2017

A unifying model for random matrix theory in arbitrary space dimensions

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, 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 $d\rightarrow\infty$, which for the first time clarifies the physical meaning of space dimension in these models. The approximate results for $d=3$ provided by our method 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.

cond-mat.dis-nn↗

arXiv2017

Nonmonotonic dependence of polymer glass mechanical response on chain bending stiffness

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.

cond-mat.soft↗

arXiv2017

Non-affine lattice dynamics of defective fcc crystals

The mechanical, thermal and vibrational properties of defective crystals are important in many different contexts, from metallurgy and solid-state physics to, more recently, soft matter and colloidal physics. Here we study two different models of disordered fcc crystal lattices, with randomly-removed bonds and with vacancies, respectively, within the framework of non-affine lattice dynamics. We find that both systems feature the same scaling of the shear modulus with the newly defined inversion-symmetry breaking (ISB) parameter, which shows that local inversion-symmetry breaking around defects is the universal root source of the non-affine softening of the shear modulus. This finding allows us to derive analytical relations for the non-affine (zero-frequency) shear modulus as a function of vacancy concentration in excellent agreement with numerical simulations. Nevertheless, due to the different microstructural disorder, the spatial fluctuations of the local ISB parameter are different in the vacancy and bond-depleted case. The vacancy fcc exhibits comparatively a more heterogenous microstructural disorder (due to the broader distribution of coordination number $Z$), which is reflected in a different scaling relation between boson peak frequency in the DOS and the average $\bar{Z}$. These differences are less important at low vacancy concentrations, where the numerical DOS of the vacancy fcc can be well described theoretically by coherent-potential approximation, presented here for the bond-depleted fcc lattice in 3d.

cond-mat.soft↗

arXiv2017

Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids

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 atomic-level 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 inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep $G(t)\sim t^{-1/2}$ 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.

cond-mat.soft↗