Dynamical heterogeneity in a model for permanent gels: different behavior of dynamical susceptibilities

Efficient d-dimensional molecular dynamics simulations for studies of the glass-jamming transition

We develop an algorithm suitable for parallel molecular dynamics simulations in d spatial dimensions and describe its implementation in C++. All routines work in arbitrary d; the maximum simulated d is limited only by available computing resources. These routines include several that are particularly useful for studies of the glass-jamming transition, such as SWAP Monte Carlo and FIRE energy minimization. The scalings of simulation runtimes with the number of particles N and number of simulation threads n_{threads} are comparable to popular molecular dynamics codes such as LAMMPS. The efficient parallel implementation allows simulation of systems that are much larger than those employed in previous high-dimensional glass-transition studies. As a demonstration of the code's capabilities, we show that supercooled d=6 liquids can possess dynamics that are substantially more heterogeneous and experience a breakdown of the Stokes-Einstein relation that is substantially stronger than previously reported, owing at least in part to the much smaller system sizes employed in earlier simulations.

Field induced anisotropic cooperativity in a magnetic colloidal glass

The translational dynamics of a repulsive colloidal glass-former is probed by time-resolved X-ray Photon Correlation Spectroscopy. In this dense dispersion of charge-stabilized and magnetic nanoparticles, the interaction potential can be tuned, from quasi-isotropic to anisotropic by applying an external magnetic field. This powerful control parameter finely tunes the anisotropy of the intricate energy landscape in the colloidal glass-former, which is seen here as a new tunable model-system to probe the dynamical heterogeneities at the approach of the glass transition. Both structural and dynamical anisotropies are reported on interparticle lengthscales associated with highly anisotropic cooperativity, almost two orders of magnitude larger in the field direction than in the perpendicular direction and in zero field.

Non-Gaussian rotational diffusion in heterogeneous media

We employ a simple model for rotational diffusivity DR of dumbbells in porous media in order to study spatially heterogeneous and non-Gaussian dynamics at Fickian time scales. We obtain the distribution P(DR) of DR's of single dumbbells for both ergodic and nonergodic systems. When a pore percolating network disappears beyond the pore percolation transition and the rotational dynamics becomes nonergodic, each single dumbbell undergoes Gaussian rotational dynamics but with different DR, which depends solely on the local pore structure. We also construct a map of heterogeneous dynamic regions and illustrate that such seemingly Fickian but non-Gaussian dynamics could be understood as the linear combination of the Gaussian rotational displacement distribution functions of each dumbbell. With a percolating pore network, the rotational dynamics becomes ergodic, and P(DR) is a δ function at the average value of DR.

Dynamical arrest: interplay of glass and gel transitions

The structural arrest of a polymeric suspension might be driven by an increase of the cross-linker concentration, which drives the gel transition, as well as by an increase of the polymer density, which induces a glass transition. These dynamical continuous (gel) and discontinuous (glass) transitions might interfere, since the glass transition might occur within the gel phase, and the gel transition might be induced in a polymer suspension with glassy features. Here we study the interplay of these transitions by investigating via event-driven molecular dynamics simulation the relaxation dynamics of a polymeric suspension as a function of the cross-linker concentration and the monomer volume fraction. We show that the slow dynamics within the gel phase is characterized by a long sub-diffusive regime, which is due both to the crowding as well as to the presence of a percolating cluster. In this regime, the transition of structural arrest is found to occur either along the gel or along the glass line, depending on the length scale at which the dynamics is probed. Where the two lines meet there is no apparent sign of higher order dynamical singularity. Logarithmic behavior typical of A3 singularity appears inside the gel phase along the glass transition line. These findings seem to be related to the results of the mode coupling theory for the F13 schematic model.

Self-assembly and cooperative dynamics of a model colloidal gel network

We study the assembly into a gel network of colloidal particles, via effective interactions that yield local rigidity and make dilute network structures mechanically stable. The self-assembly process can be described by a Flory-Huggins theory, until a network of chains forms, whose mesh size is on the order of, or smaller than, the persistence length of the chains. The localization of the particles in the network, akin to some extent to caging in dense glasses, is determined by the network topology, and the network restructuring, which takes place via bond breaking and recombination, is characterized by highly cooperative dynamics. We use NVE and NVT molecular dynamics as well as Langevin dynamics and find a qualitatively similar time dependence of time correlations and of the dynamical susceptibility of the restructuring gel. This confirms that the cooperative dynamics emerge from the mesoscale organization of the network.

Microscopic picture of cooperative processes in restructuring gel networks

Colloidal gel networks are disordered elastic solids that can form even in extremely dilute particle suspensions. With interaction strengths comparable to the thermal energy, their stress-bearing network can locally restructure via breaking and reforming interparticle bonds. This allows for yielding, self-healing, and adaptive mechanics under deformation. Designing such features requires controlling stress transmission through the complex structure of the gel and this is challenging because the link between local restructuring and overall response of the network is still missing. Here, we use a space resolved analysis of dynamical processes and numerical simulations of a model gel to gain insight into this link. We show that consequences of local bond breaking propagate along the gel network over distances larger than the average mesh size. This provides the missing microscopic explanation for why nonlocal constitutive relations are necessary to rationalize the nontrivial mechanical response of colloidal gels.

Relaxation process and dynamical heterogeneities in chemical gels: critical behavior of self-overlap and its fluctuation

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

Relaxation properties in a diffusive model of k-mers with constrained movements on a triangular lattice

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are k-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of k-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale τ(q(n)) is found to decrease with the wave vector q(n) according to a simple power law. Furthermore, the slowing of the dynamics with density ρ(0) is consistent with the scaling law 1/τ(q(n);ρ(0))∝(ρ(c)-ρ(0))(ϰ), with the same exponent ϰ=3.34±0.12 for all wave vectors q(n). The density ρ(c) is approximately equal to the closest packing limit, θ(CPL)≲1, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient D(s) scales with the same power-law exponent and critical density.

Non-Gaussian dynamics in smectic liquid crystals of parallel hard rods

Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid-crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow interlayer relaxation dynamics over the whole density range of the stable smectic phase which spans a time interval of four time decades. The intrinsic nature of the layered structure yields a hopping-type diffusion which becomes more heterogeneous for higher packing fractions. In contrast, the in-layer dynamics is typical of a dense fluid with a relatively fast decay. Our results on the dynamic behavior agree well with that observed in systems of freely rotating hard rods but differ quantitatively as the height of the periodic barriers reduces to zero at the nematic-smectic transition for aligned rods, while it remains finite for freely rotating rods.

Dynamical heterogeneities in irreversible gels: analogy with spin glasses

We describe the sol-gel transition by introducing an order parameter, defined as the average of local variables, and its fluctuations. It can be shown that these quantities are related to percolation quantities, but in principle they can be measured without resorting to connectivity properties. In this framework it appears that the dynamical transition associated with gelation is a real thermodynamic transition, as happens in spin glasses. The strong analogies between the sol-gel transition and the spin glass transition are also discussed.

Anisotropic spatially heterogeneous dynamics on the alpha and beta relaxation time scales studied via a four-point correlation function

We examine the anisotropy of a four-point correlation function G4(k[over ],r[over ];t) and its associated structure factor S4(k[over ],q[over ];t) calculated using Brownian dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles. We examine the time and temperature dependences of the anisotropy in both functions. We find that the anisotropy is strongest at nearest-neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter alpha_{2}(t)=3deltar;{4}(t)/[5deltar;{2}(t);{2}]-1 but is still pronounced around the alpha relaxation time. We find that the structure factor S4(k[over ],q[over ];t) is anisotropic even for the lowest wave vector accessible in our simulation, suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the q[over ]-->0 limit of the structure factor. We find that the determination of a dynamic correlation length from S4(k[over ],q[over ];t) is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small q behavior of S4(k[over ],q[over ];t) .