Rheological response of a glass-forming liquid having large bidispersity.

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

Finite-size effects in the diffusion dynamics of a glass-forming binary mixture with large size ratio.

Extensive molecular dynamics computer simulations of an equimolar, glass-forming AB mixture with a large size ratio are presented. While the large A particles show a glass transition around the critical density of mode-coupling theory ρc, the small B particles remain mobile with a relatively weak decrease in their self-diffusion coefficient DB with increasing density. Surprisingly, around ρc, the self-diffusion coefficient of species A, DA, also starts to show a rather weak dependence on density. We show that this is due to finite-size effects that can be understood from the analysis of the collective interdiffusion dynamics.

Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory.

Molecular dynamics computer simulations of a polydisperse soft-sphere model under shear are presented. The starting point for these simulations are deeply supercooled samples far below the critical temperature, Tc, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below Tc, we identify a lifetime τlt that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of τlt can be well described by an Arrhenius law. The existence of transient amorphous solid states below Tc is associated with the possibility of brittle yielding, as manifested by a sharp stress drop in the stress-strain relation and shear banding. We show that brittle yielding requires, on the one hand, low shear rates and, on the other hand, the time scale corresponding to the inverse shear rate has to be smaller or of the order of τlt. Both conditions can only be met for a large lifetime τlt, i.e., for states far below Tc.

On the existence of thermodynamically stable rigid solids.

Customarily, crystalline solids are defined to be rigid since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the metastable state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then used to obtain the equilibrium free energy as a function of this variable. Our results lead to a unique view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable when an external field, which penalizes particle rearrangements, is switched on. This produces a line of first-order phase transitions in the field-strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.

Nucleation Theory for Yielding of Nearly Defect-Free Crystals: Understanding Rate Dependent Yield Points.

Experiments and simulations show that when an initially defect-free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called yield point. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small nonuniversal exponent. We reanalyze a representative set of published data on nanometer sized, mostly defect-free Cu, Ni, and Au crystals in light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid. The single relation derived here, which is not a power law, explains data covering 15 orders of magnitude in timescales.

Active microrheology in two-dimensional magnetic networks.

We study active microrheology in two-dimensional (2D) magnetic networks. To this end, we use Langevin dynamics computer simulations where single non-magnetic or magnetic tracer particles are pulled through the network structures via a constant force f. Structural changes in the network around the pulled tracer particle are characterized in terms of pair correlation functions. These functions indicate that the non-magnetic tracer particles tend to strongly affect the network structure leading to the formation of channels at sufficiently high forces, while the magnetic tracer particles modify the network structure only slightly. At zero pulling force, f = 0, both non-magnetic and magnetic tracer particles are localized, i.e. they do not show diffusive behavior in the long-time limit. Nevertheless, the friction coefficient, as obtained from the steady-state velocity of the tracer particles, seems to indicate a linear-response regime at small values of f. Beyond the latter linear response regime, the diffusion dynamics of the tracer particles are anisotropic with superdiffusive behavior in force direction. This transport anomaly is investigated via van Hove correlation functions and residence time distributions.

Precursors of fluidisation in the creep response of a soft glass.

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Molecular dynamics simulation of charged colloids confined between hard walls: pre-melting and pre-freezing across the BCC-fluid coexistence.

Molecular dynamics (MD) computer simulations are used to study the structure of hard-core Yukawa systems confined between two parallel hard walls. States around the coexistence between a fluid and a body-centered cubic (BCC) crystal are considered. In all cases a pronounced layering in the vicinity of the walls is observed. Using a thermodynamic integration scheme, we determine the wall-fluid interfacial free energy γ which is negative and monotonically decreasing with increasing bulk density of the fluid. In the case of the fluid, the layers next to the walls undergo a transition from a fluid to a hexagonal structure. This pre-freezing transition occurs well below the coexistence bulk density of the fluid. The confined BCC crystal in (111) orientation shows melted regions between crystalline face-centered cubic (FCC) layers close to the wall and the BCC bulk region.

Plastic deformation of a permanently bonded network: Stress relaxation by pleats.

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing "pleats", system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local non-affine displacements, i.e., those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain-field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit, the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

An Ising model for metal-organic frameworks.

We present a three-dimensional Ising model where lines of equal spins are frozen such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH4) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.

Equilibrium and dynamic pleating of a crystalline bonded network.

We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the homogeneous phase, a number of heterogeneous "pleated" phases, which can be stabilised by an external field. This field is conjugate to a global collective variable quantifying "non-affineness," i.e., the deviation of local particle displacements from local affine deformation. In the pleated phase, stress is localised in ordered rows of pleats and eliminated from the rest of the lattice. The kinetics of the phase transition is unobservably slow in molecular dynamics simulation near coexistence, due to very large free energy barriers. When the external field is increased further to lower these barriers, the network exhibits rich dynamic behaviour: it transforms into a metastable phase with the stress now localised in a disordered arrangement of pleats. The pattern of pleats shows ageing dynamics and slow relaxation to equilibrium. Our predictions may be checked by experiments on tethered colloidal solids in dynamic laser traps.

Two-dimensional magnetic colloids under shear.

Complex rheological properties of soft disordered solids, such as colloidal gels or glasses, inspire a range of novel applications. However, the microscopic mechanisms of their response to mechanical loading are not well understood. Here, we elucidate some aspects of these mechanisms by studying a versatile model system, i.e. two-dimensional superparamagnetic colloids in a precessing magnetic field, whose structure can be tuned from a hexagonal crystal to a disordered gel network by varying the external field opening angle θ. We perform Langevin dynamics simulations subjecting these structures to a constant shear rate and observe three qualitatively different types of material response. In hexagonal crystals (θ = 0°), at a sufficiently low shear rate, plastic flow occurs via successive stress drops at which the stress releases due to the formation of dislocation defects. The gel network at θ = 48°, on the contrary, via bond rearrangement and transient shear banding evolves into a homogeneously stretched network at large strains. The latter structure remains metastable after switching off of the shear. At θ = 50°, the external shear makes the system unstable against phase separation and causes a failure of the network structure leading to the formation of hexagonal close packed clusters interconnected by particle chains. At a microcopic level, our simulations provide insight into some of the mechanisms by which strain localization as well as material failure occur in a simple gel-like network. Furthermore, we demonstrate that new stretched network structures can be generated by the application of shear.

On the Gaussian approximation in colloidal hard sphere fluids.

We study the behaviour of the self-intermediate scattering function and self-van Hove correlation function for quasi-two-dimensional colloidal hard sphere fluids at a range of area fractions. We compute these functions first directly from the particle coordinates and secondly from the mean squared displacement via the Gaussian approximation. This allows us to test the validity of this approximation over a range of length and time scales, where we find that the Gaussian approximation holds if the hydrodynamic limits are appropriately probed. Surprisingly, only small deviations from Gaussian behaviour are seen at intermediate times, even for dense fluids. We next consider these deviations from Gaussian behaviour firstly via the non-Gaussian parameter and secondly by considering the relaxation times of the intermediate scattering function. From these measurements we develop a scaling relation in order to directly determine the combinations of wavevectors and times at which the non-Gaussian behavior is seen. This allows for the clear identification of the hydrodynamic regimes and thus provides new insight into the crossover between long- and short-time self-diffusion.

Condensation of Methane in the Metal-Organic Framework IRMOF-1: Evidence for Two Critical Points.

Extensive grand canonical Monte Carlo simulations in combination with successive umbrella sampling are used to investigate the condensation of methane in the nanoporous crystalline material IRMOF-1. Two different types of novel condensation transitions are found, each of them ending in a critical point: (i) a fluid-fluid transition at higher densities (the analog of the liquid-gas transition in the bulk) and (ii) a phase transition at low densities on the surface of the IRMOF-1 structure. The nature of these transitions is different from the usual capillary condensation in thin films and cylindrical pores where the coexisting phases are confined in one or two of the three spatial dimensions. In contrast to that, in IRMOF-1 the different phases can be described as bulk phases that are inhomogeneous due to the presence of the metal-organic framework. As a consequence, the condensation transitions in IRMOF-1 belong to the three-dimensional (3D) Ising universality class.

Effect of Hydrodynamic Interactions on Self-Diffusion of Quasi-Two-Dimensional Colloidal Hard Spheres.

We compare experimental results from a quasi-two-dimensional colloidal hard sphere fluid to a Monte Carlo simulation of hard disks with small particle displacements. The experimental short-time self-diffusion coefficient D(S) scaled by the diffusion coefficient at infinite dilution, D(0), strongly depends on the area fraction, pointing to significant hydrodynamic interactions at short times in the experiment, which are absent in the simulation. In contrast, the area fraction dependence of the experimental long-time self-diffusion coefficient D(L)/D(0) is in quantitative agreement with D(L)/D(0) obtained from the simulation. This indicates that the reduction in the particle mobility at short times due to hydrodynamic interactions does not lead to a proportional reduction in the long-time self-diffusion coefficient. Furthermore, the quantitative agreement between experiment and simulation at long times indicates that hydrodynamic interactions effectively do not affect the dependence of D(L)/D(0) on the area fraction. In light of this, we discuss the link between structure and long-time self-diffusion in terms of a configurational excess entropy and do not find a simple exponential relation between these quantities for all fluid area fractions.

Rounding of the localization transition in model porous media.

The generic mechanisms of anomalous transport in porous media are investigated by computer simulations of two-dimensional model systems. In order to bridge the gap between the strongly idealized Lorentz model and realistic models of porous media, two models of increasing complexity are considered: a cherry-pit model with hard-core correlations as well as a soft-potential model. An ideal gas of tracer particles inserted into these structures is found to exhibit anomalous transport which extends up to several decades in time. Also, the self-diffusion of the tracers becomes suppressed upon increasing the density of the systems. These phenomena are attributed to an underlying percolation transition. In the soft potential model the transition is rounded, since each tracer encounters its own critical density according to its energy. Therefore, the rounding of the transition is a generic occurrence in realistic, soft systems.

Crystal growth kinetics in Lennard-Jones and Weeks-Chandler-Andersen systems along the solid-liquid coexistence line.

Kinetics of crystal-growth is investigated along the solid-liquid coexistence line for the (100), (110), and (111) orientations of the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) fcc crystal-liquid interface, using non-equilibrium molecular dynamics simulations. A slowing down of the growth kinetics along the coexistence line is observed, which is due to the decrease of the melting enthalpy with increasing coexistence temperature and pressure. Other quantities such as the melting pressure and liquid self-diffusion coefficient have a comparatively lesser impact on the kinetic growth coefficient. Growth kinetics of the LJ and WCA potentials become similar at large values of the melting temperature and pressure, when both resemble a purely repulsive soft-sphere potential. Classical models of crystallization from the melt are in reasonable qualitative agreement with our simulation data. Finally, several one-phase empirical melting/freezing rules are studied with respect to their validity along the coexistence line.

Crystal-liquid interfacial free energy via thermodynamic integration.

A novel thermodynamic integration (TI) scheme is presented to compute the crystal-liquid interfacial free energy (γcl) from molecular dynamics simulation. The scheme is applied to a Lennard-Jones system. By using extremely short-ranged and impenetrable Gaussian flat walls to confine the liquid and crystal phases, we overcome hysteresis problems of previous TI schemes that stem from the translational movement of the crystal-liquid interface. Our technique is applied to compute γcl for the (100), (110), and (111) orientation of the crystalline phase at three temperatures under coexistence conditions. For one case, namely, the (100) interface at the temperature T = 1.0 (in reduced units), we demonstrate that finite-size scaling in the framework of capillary wave theory can be used to estimate γcl in the thermodynamic limit. Thereby, we show that our TI scheme is not associated with the suppression of capillary wave fluctuations.

Localization dynamics of fluids in random confinement.

The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we find delocalized tracer particle dynamics at small matrix area fractions and localized motion of the tracers at high matrix area fractions. In the delocalized region, the dynamics is subdiffusive at intermediate times, and diffusive at long times, while in the localized regime, trapping in finite pockets of the matrix is observed. These observations are found to agree with the simulation of an ideal gas confined in a weakly correlated matrix. Our results show that Lorentz gas systems with soft interactions are exhibiting a smoothening of the critical dynamics and consequently a rounded delocalization-to-localization transition.