String-like Collective Motion Research Articles

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting.

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

We show that thermodynamic scaling can be derived by combining the Murnaghan equation of state (EOS) with the generalized entropy theory (GET) of glass formation. In our theory, thermodynamic scaling arises in the non-Arrhenius relaxation regime as a scaling property of the fluid configurational entropy density $s_c$, normalized by its value $s_c^*$ at the onset temperature $T_A$ of glass formation, $s_c / s_c^*$, so that a constant value of $TV^{\gamma}$ corresponds to a \textit{reduced isoentropic} fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of $\tau_{\alpha}$ by the GET holds both above and below $T_A$ and to test whether the extent $L$ of stringlike collective motion, normalized its value $L_A$ at $T_A$, also obeys thermodynamic scaling, as required for consistency with thermodynamic scaling. While the predicted thermodynamic scaling of both $\tau_{\alpha}$ and $L/ L_A$ is confirmed by simulation, we find that the isothermal compressibility $\kappa_T$ and the long wavelength limit $S(0)$ of the static structure factor do not exhibit thermodynamic scaling, an observation that would appear to eliminate some proposed models of glass formation emphasizing fluid `structure' over configurational entropy. It is found, however, that by defining a low temperature hyperuniform reference state, we may define a compressibility relative to this condition, $\delta \kappa_T$, a transformed dimensionless variable that exhibits thermodynamic scaling and which can be directly related to $s_c / s_c^*$. Further, the Murnaghan EOS allows us to interpret $\gamma$ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus.

Fast dynamics in a model metallic glass-forming material.

We investigate the fast β- and Johari-Goldstein (JG) β-relaxation processes, along with the elastic scattering response of glass-forming (GF) liquids and the boson peak, in a simulated Al-Sm GF material exhibiting a fragile-strong (FS) transition. These dynamical processes are universal in "ordinary" GF fluids and collectively describe their "fast dynamics," and we find these relaxation processes also arise in a GF liquid exhibiting a FS transition. String-like particle motion, having both an irreversible and a reversible nature (stringlets) component, occurs in the fast-dynamics regime, corresponding to a ps timescale. String-like collective motion associated with localized unstable modes facilitates irreversible and intermittent particle "jumping" events at long times associated with the JG β-relaxation process, while stringlets associated with localized stable modes and corresponding perfectly reversible atomic motion give rise to the boson peak. To further clarify the origin of the boson peak, we calculate the density of states for both the stringlet particles and the "normal" particles and find that the stringlet particles give rise to a boson peak, while the normal atoms do not. The growth of stringlets upon heating ultimately also leads to the "softening" of these excitations, and the boson peak frequency and shear modulus drop in concert with this softening. The growth of string-like collective motion upon heating in the fast-dynamics regime is further shown to be responsible for the growth in the intensity of the fast relaxation process. Relaxation in cooled liquids clearly involves a hierarchy of relaxation processes acting on rather different timescales and spatial scales.

Superionic UO2: A model anharmonic crystalline material.

Crystalline materials at elevated temperatures and pressures can exhibit properties more reminiscent of simple liquids than ideal crystalline materials. Superionic crystalline materials having a liquidlike conductivity σ are particularly interesting for battery, fuel cell, and other energy applications, and we study UO2 as a prototypical superionic material since this material is widely studied given its commercial importance as reactor fuel. Using molecular dynamics, we first investigate basic thermodynamic and structural properties. We then quantify structural relaxation, dynamic heterogeneity, and average ion mobility. We find that the non-Arrhenius diffusion and structural relaxation time of this prototypical superionic material can be described in terms of a generalized activated transport model ("string model") in which the activation energy varies with the average string length. Our transport data can also be described equally well by an Adam-Gibbs model in which the excess entropy density of the crystalline material is estimated from specific heat and thermal expansion data, consistent with the average scale of stringlike collective motion scaling inversely with the excess entropy of the crystal. Strong differences in the temperature dependence of the interfacial mobility from nonionic materials are observed, and we suggest that this difference is due to the relatively high cohesive interaction of ionic materials. In summary, the study of superionic UO2 provides insight into the role of cooperative motion in enhancing ion mobility in ionic materials and offers design principles for the development of new superionic materials for use in diverse energy applications.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

String-like collective motion and diffusion in the interfacial region of ice.

We investigate collective molecular motion and the self-diffusion coefficient Ds of water molecules in the mobile interfacial layer of the secondary prismatic plane (112¯0) of hexagonal ice by molecular dynamics simulation based on the TIP4P/2005 water potential and a metrology of collective motion drawn from the field of glass-forming liquids. The width ξ of the mobile interfacial layer varies from a monolayer to a few nm as the temperature is increased towards the melting temperature Tm, in accordance with recent simulations and many experimental studies, although different experimental methods have differed in their precise estimates of the thickness of this layer. We also find that the dynamics within this mobile interfacial ice layer is "dynamically heterogeneous" in a fashion that has many features in common with glass-forming liquids and the interfacial dynamics of crystalline Ni over the same reduced temperature range, 2/3 < T/Tm < 1. In addition to exhibiting non-Gaussian diffusive transport, decoupling between mass diffusion and the structural relaxation time, and stretched exponential relaxation, we find string-like collective molecular exchange motion in the interfacial zone within the ice interfacial layer and colored noise fluctuations in the mean square molecular atomic displacement 〈u2〉 after a "caging time" of 1 ps, i.e., the Debye-Waller factor. However, while the heterogeneous dynamics of ice is clearly similar in many ways to molecular and colloidal glass-forming materials, we find distinct trends between the diffusion coefficient activation energy Ea for diffusion Ds and the interfacial width ξ from the scale of collective string-like motion L than those found in glass-forming liquids.

Influence of molecular-weight polydispersity on the glass transition of polymers.

It is well known that the polymer glass transition temperature T_{g} is dependent on molecular weight, but the role of molecular-weight polydispersity on T_{g} is unclear. Using molecular-dynamics simulations, we clarify that for polymers with the same number-average molecular weight, the molecular-weight distribution profile (either in Schulz-Zimm form or in bimodal form) has very little influence on the glass transition temperature T_{g}, the average segment dynamics (monomer motion, bond orientation relaxation, and torsion transition), and the relaxation-time spectrum, which are related to the local nature of the glass transition. By analyzing monomer motions in different chains, we find that the motion distribution of monomers is altered by molecular-weight polydispersity. Molecular-weight polydispersity dramatically enhances the dynamic heterogeneity of monomer diffusive motions after breaking out of the "cage," but it has a weak influence on the dynamic heterogeneity of the short time scales and the transient spatial correlation between temporarily localized monomers. The stringlike cooperative motion is also not influenced by molecular-weight polydispersity, supporting the idea that stringlike collective motion is not strongly correlated with chain connectivity.

A unifying framework to quantify the effects of substrate interactions, stiffness, and roughness on the dynamics of thin supported polymer films.

Changes in the dynamics of supported polymer films in comparison to bulk materials involve a complex convolution of effects, such as substrate interactions, roughness, and compliance, in addition to film thickness. We consider molecular dynamics simulations of substrate-supported, coarse-grained polymer films where these parameters are tuned separately to determine how each of these variables influence the molecular dynamics of thin polymer films. We find that all these variables significantly influence the film dynamics, leading to a seemingly intractable degree of complexity in describing these changes. However, by considering how these constraining variables influence string-like collective motion within the film, we show that all our observations can be understood in a unified and quantitative way. More specifically, the string model for glass-forming liquids implies that the changes in the structural relaxation of these films are governed by the changes in the average length of string-like cooperative motions and this model is confirmed under all conditions considered in our simulations. Ultimately, these changes are parameterized in terms of just the activation enthalpy and entropy for molecular organization, which have predictable dependences on substrate properties and film thickness, offering a promising approach for the rational design of film properties.

The relationship of dynamical heterogeneity to the Adam-Gibbs and random first-order transition theories of glass formation

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

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.

Direct observation of stringlike collective motion in a two-dimensional driven granular fluid

Dense ensembles of monodisperse hard spheres spontaneously assemble into regions of local crystalline order (grains) that are separated by relatively disordered grain-boundary (GB) regions. It is well known that grains and grain boundaries (GB) profoundly affect the material properties of polycrystalline materials and plastic deformation and transport in this ubiquitous class of materials can be particularly influenced by GB structure and dynamics. We experimentally investigate the nature of particle motion in the GB regions of a quasi-two-dimensional driven system of hard spheres and find, in accord with recent molecular-dynamics simulations of metallic polycrystalline materials, that particle motion in the GB regions involves a highly cooperative stringlike motion as in glass-forming liquids. Moreover, we show that the addition of small particles to a granular fluid allows the scale of this collective motion to be modulated, a phenomenon that is also observed in simulations and measurements on glass-forming fluids.

Characterization of the potential energy landscape of an antiplasticized polymer

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These "substrings" nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in "superstrings" that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

Hydrogen-induced crystallization of an amorphous metal

The influence of hydrogen on the structural stability of an amorphous nickel has been analyzed by molecular dynamics simulation. We find that the volume of the amorphous metal increases nonlinearly with the hydrogen concentration and that it crystallizes at a certain critical concentration. The crystallization is shown to be caused by hydrogen-induced transition from the amorphous to the supercooled liquid state, and the change of diffusion mechanism from atomic hopping to string-like collective motion is also observed at the transition.

Spatially heterogeneous dynamics in liquids: insights from simulation

In this paper, review of recent theoretical and simulation work on dynamical heterogeneity and correlated particle motion in glass-forming liquids and polymers is presented. Evidence for increasing mobility fluctuations in these systems with decreasing temperature, and the relationship between dynamical heterogeneity and decoupling of diffusion and structural relaxation is described. The relationship between dynamical heterogeneity, string-like collective motion, the clustering of strings, and mode-coupling theory is briefly discussed.

Grain formation, stringlike collective motion, and the onset of diffusion in disordered two-dimensional crystals.

Two-dimensional crystals in random potentials are studied by molecular-dynamics methods. The ground state of the system is characterized by a transition of the random-potential-induced defect configurations, which evolve from a dilute gaslike state at weak random potentials to a grain-boundary state at strong random potentials. The dynamics of the system is strongly affected by the defect structure. Stringlike collective hopping of particles along the grain boundaries greatly assists the onset of diffusion in the system at low temperatures.