We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $\exp(-2r/\sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $\exp(-(t/τ_L)^{1/2})$, where $t$ is the time and $τ_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $\mathcal{L}(t_w) \sim t_w^{1/2}$ and $\mathcal{R}(t_w) \sim t_w^{1/4}$; the spatial correlation function decays as $\exp(-r/ \mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.
Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/τ)^β]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corté et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $β$ that depends on the strain amplitude: $0.25 < β< 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional …
We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential …
Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain…
Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a funct…
The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition that spatial averaging over a heterogeneous distribution of locally exponential relaxation processes leads to stretching. Here we perform simulations of model polymeric and small-molecule glass-formers in the isoconfigurational ensemble to show that stretching instead emerges from a combination of spatial averaging and locally nonexponential relaxation. Res…
The polymer relaxation dynamic of a sample, stretched up to the stress hardening regime, is measured, at room temperature, as a function of the strain $λ$ for a wide range of the strain rate $\dotγ$, by an original dielectric spectroscopy set up. The mechanical stress modies the shape of the dielectric spectra mainly because it affects the dominant polymer relaxation time $τ$, which depends on $λ$ and is a decreasing function of $\dotγ$. The fastest dynamics is not reached at yield but in the softening regime. The dynamics slows down during the hardening, with a progressive increase of $τ$. A …
We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$η$} = 0.2) and intermediate ($η$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneo…
We report experimental evidence that a polymer stretched at constant strain rate $\dotλ$ presents complex memory effects after that $\dotλ$ is set to zero at a specific strain $λ_w$ for a duration $t_w$, ranging from $100$s to $ 2.2\times10^5$s. When the strain rate is resumed, both the stress and the dielectric constant relax to the unperturbed state non monotonically. The relaxations depend on the observable, on $λ_w$ and on $t_w$. Relaxation master curves are obtained by scaling the relaxation time as $t/\ln (t_w)$. The dielectric evolution also captures the distribution of the relaxation t…
Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the…
The stretched exponential function, $\exp[-(t/τ_{K})^β]$, describes various relaxation processes while it has been suggested that the power exponent, $β$ is derived from the non-uniformity of the process. In this paper, we attempted to estimate this non-uniformity by introducing Shannon entropy. Shannon entropy evaluates the average information contents of the distribution function, which reflects statistical homogeneity. We investigated the relaxation process of shear induced multilamellar system, which is described with the stretched exponential function. Three types of shear (constant, squa…
Particle-based simulations are performed to study the post-relaxation dynamics of functionalized (patchy) colloids adsorbed on an attractive substrate. Kinetically arrested structures that depend on the number of adsorbed particles and the strength of the particle-particle and particle-substrate interactions are identified. The radial distribution function is characterized by a sequence of peaks, with relative intensities that depend on the number of adsorbed particles. The first-layer coverage is a non-monotonic function of the number of particles, with an optimal value around one layer of ad…
We use computer simulations to study the relaxation dynamics of a model for oil-in-water microemulsion droplets linked with telechelic polymers. This system exhibits both gel and glass phases and we show that the competition between these two arrest mechanisms can result in a complex, three-step decay of the time correlation functions, controlled by two different localization lengthscales. For certain combinations of the parameters, this competition gives rise to an anomalous logarithmic decay of the correlation functions and a subdiffusive particle motion, which can be understood as a simple …
We use large-scale computer simulations to explore the non-equilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically-arrested phase separation is accompanied by `anomalous' particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatio-temporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is the first microscopically-resolved model reproducing all features of the spo…
Employing wide-angle neutron spin echo spectroscopy, we measured the Q-dependent coherent intermediate scattering function of the prototypical ionic glass former Ca0.4K0.6(NO3)1.4, in the equilibrium and supercooled liquid states beyond the hydrodynamic regime. The data reveal a clear two-step relaxation: an exponential fast process, and a stretched exponential slow alpha process. de Gennes narrowing is observed in all characteristic variables of the alpha process: the relaxation time, amplitude, and stretching exponent. At all length scales probed, the relative amplitude of the alpha-relaxati…
We study the relaxation dynamics of a binary liquid mixture near a light-absorbing Janus particle after switching on and off illumination using experiments and theoretical models. The dynamics is controlled by the temperature gradient formed around the heated particle. Our results show that the relaxation is asymmetric: the approach to a nonequilibrium steady state is much slower than the return to thermal equilibrium. Approaching a nonequilibrium steady state is a two-step process leading to the behavior of the spatial variance of concentration field similar to the initial overshoot in respon…
The molecular mobility of glass and supercooled liquid states of nilutamide has been studied with broadband dielectric spectroscopy for a wide range of temperature and frequency. Besides primary $α$-relaxation an excess wing like secondary relaxation is observed. The temperature dependence of structural $α$-relaxation show non-Arrhenius behaviour, and follows Vogel-Fulcher-Tammann (VFT) empirical formula. The glass transition temperature, T$_{g}$=302K and fragility index, m=76 are obtained from the VFT parameters. The structural $α$-relaxation process is non-Debye with Kohlraush-Williams-Watts…
