Slow dynamics in supercooled liquids

Glassy Interfacial Dynamics of Ni Nanoparticles: Part I Colored Noise, Dynamic Heterogeneity and Collective Atomic Motion

Most condensed materials exhibit a significant fraction of atoms, molecules or particles that are strongly interacting with each other, while being configured geometrically at any instant of time in an 'amorphous' state having a relatively uniform density. Recently, both simulations and experiments have revealed that the dynamics of diverse condensed amorphous materials is generally characterized by significant heterogeneity in the local mobility and by progressively increasing collective motion upon cooling that takes the form of string-like collective particle rearrangements. The direct experimental observation of this type of collective motion, which has been directly linked to the growing relaxation times of glass-forming materials, and its quantification under different thermodynamic conditions, has so far been restricted to colloidal and driven granular fluids. The present work addresses the fundamental problem of how to determine the scale of this type of collective motion in materials composed of molecules or atoms. The basic premise of our work is that large scale dynamic particle clustering in amorphous materials must give rise to large fluctuations in particle mobility so that transport properties, especially those related to particle mobility, should naturally exhibit noise related to the cooperative motion scale. In our initial exploratory study seeking a relationship of this kind, we find 1/fα or 'colored noise', in both potential energy and particle displacements fluctuations of the atoms within the glassy interfacial layer of Ni nanoparticles (NPs). A direct relation between the particle displacement (mobility) noise exponent α and the average polymerization index of the string-like collective motion L is observed for a range of NP sizes, temperatures and for surface doping of the NPs with other metal atoms (Ag, Au, Pt) to change of fragility of the glassy interfacial layer at the surface of the Ni NPs. We also introduce a successful analytic model to understand this relationship between α and L.

Free-energy landscape for a tagged particle in a dense hard-sphere fluid

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome, Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.

Free energy landscape and cooperatively rearranging region in a hard sphere glass

Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.

Direct observation of spatiotemporal dependence of anomalous diffusion in inhomogeneous fluid by sampling-volume-controlled fluorescence correlation spectroscopy

The direct observation of a spatiotemporal behavior of anomalous diffusion in aqueous polymer [hyaluronan (HA)] solution was achieved by fluorescence correlation spectroscopy (FCS) using a modified instrument, enabling continuous change of the confocal volume of a microscope, namely, sampling-volume-controlled (SVC) FCS (SVC-FCS). Since HA chains form a mesh structure with a pore size of about 10-40 nm, the observed diffusion coefficient (Dobs) is markedly dependent on the diffusion distance (L). By SVC-FCS, the curve of the distance dependence of diffusion coefficient was directly obtained as a continuous profile in L = 245-600 nm showing evidence of anomalous diffusion. On plotting Dobs against either of the sampling time (tauobs) or the diffusion distance (L), Dobs turnover was observed near the anomalous diffusion area. The appearance of this turnover is attributed to the nonuniform mesh structure that can be observed only by a fast observation and that should be dynamically averaged by polymer motions with large tauobs. This behavior is similar to that revealed in glass, colloidal systems, and gel solutions using dynamic light scattering, neutron scattering, and other techniques.

Order statistics of Rosenstock's trapping problem in disordered media

The distribution of times t(j,N) elapsed until the first j independent random walkers from a set of N>>1, all starting from the same site, are trapped by a quenched configuration of traps randomly placed on a disordered lattice is investigated. In doing so, the cumulants of the distribution of the territory explored by N independent random walkers S(N)(t), and the probability Phi(N)(t) that no particle of an initial set of N is trapped by time t are considered. Simulation results for the two-dimensional incipient percolation aggregate show that the ratio between the nth cumulant and the nth moment of S(N)(t) is, for large N, (i) very large in comparison with the same ratio in Euclidean media, and (ii) almost constant. The first property implies that, in contrast with Euclidean media, approximations of the order higher than the standard zeroth-order Rosenstock approximation are required to provide a reasonable description of the trapping order statistics. Fortunately, the second property (which has a geometric origin) can be exploited to build these higher-order Rosenstock approximations. Simulation results for the two-dimensional incipient percolation aggregate confirm the predictions of our approach.

Crystal phases of a glass-forming Lennard-Jones mixture

We compare the potential energy at zero temperature of a range of crystal structures for a glass-forming binary mixture of Lennard-Jones particles. The lowest-energy ordered state consists of coexisting phases of a single component face centered cubic structure and an equimolar cesium chloride structure. An infinite number of layered crystal structures are identified with energies close to this ground state. We demonstrate that the finite size increase of the energy of the coexisting crystal with incoherent interfaces is sufficient to destabilize this ordered phase in simulations of typical size. Two specific local coordination structures are identified as of possible structural significance in the amorphous state. We observe rapid crystal growth in the equimolar mixture.

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the mth moment <t(m)(j,N)> of the time t(j,N) elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi(M)(t) that no particle of an initial set of M=N,N-1,...,N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi(M)(t), and it is found that for a large range of trap concentrations the mth moment of t(j,N) goes as x(-m) and its variance as x(-2), x being ln(2/d)(1-c)ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for <t(m)(j,N)> for the one-dimensional lattice.

Dynamic heterogeneity of relaxations in glasses and liquids

We report an investigation of the heterogeneity in supercooled liquids and glasses using the non-Gaussianity parameter. We simulate selenium and a binary Lennard-Jones system by molecular dynamics. In the non-Gaussianity three time domains can be distinguished: an increase on the ps scale due to the vibrational (ballistic) motion of the atoms, followed by a growth, due to local relaxations ( beta relaxation) at not too high temperatures, and finally a slow drop at long times. The non-Gaussianity follows in the intermediate time domain a sqrt[t] law. This is explained by collective hopping and dynamic heterogeneity. We support this finding by a model calculation.