arXiv subjects

Jack F. Douglas

Publications and source records attributed to Jack F. Douglas.

At least 19 recordsLinked to original sources

arXiv2026

String Model Predicts Relaxation in Sheared Glass-Forming Liquids

Understanding how structural relaxation evolves from equilibrium to nonequilibrium conditions remains a central problem in glass physics. Using simulations of model glass formers under steady shear, we show that the String Model, which links stringlike cooperative rearrangements to relaxation in equilibrium glass-forming liquids, predicts the structural relaxation time across the full range of temperatures and shear rates investigated without additional nonequilibrium fitting parameters, when combined with a shear-dependent effective temperature that is captured by a generalized fluctuation-dissipation relation. These results indicate that equilibrium and nonequilibrium relaxation are governed by the same underlying cooperative mechanism, but they occur under different effective thermodynamic conditions under steady shear. More broadly, our study provides a unified microscopic description of thermal and mechanically driven dynamics in glass-forming liquids.

cond-mat.soft↗

arXiv2026

Tunable Cooperative Motion, Rigidity, and Glassy Dynamics in Knotted Ring Polymer Melts

We present a molecular dynamics study of the influence of knot complexity and molecular mass on glass formation upon cooling in knotted ring polymer melts. We find that cooperative motion, rigidity, and glassy dynamics can be tuned over a wide range by knots. By leveraging these knotting constraints, we assess the validity of prevalent models of glass formation, including the string model based on cooperative particle motion, the localization model emphasizing fluctuations in local particle mobility, and the shoving model derived from emergent elastic properties in relation to material stiffness. In line with our previous findings on polymeric and other glass-forming liquids, we demonstrate that all these models of glass formation provide a quantitative description of segmental relaxation as a function of knot complexity, molecular mass, and temperature, despite their apparently distinct conceptual foundations. Our study thus provides additional evidence for an underlying unity among various theoretical frameworks and for the presence of quantitative relations between the characteristic properties emphasized by these models. Furthermore, we discuss dynamic and elastic heterogeneities in relation to fragility and stiffness variations of knotted ring polymer melts, with a focus on how these trends relate to other glass-forming liquids where fragility is tuned over a large range.

cond-mat.soft↗

arXiv2025

Atomistic mechanisms of dynamics in a two-dimensional dodecagonal quasicrystal

Quasicrystals have been observed in a variety of materials ranging from metal alloys to block copolymers. However, their structural and dynamical properties cannot be readily described in terms of conventional solid-state models of liquids and solids. We may expect the dynamics of this specific class of quasicrystalline materials to be more like glass-forming liquids in the sense of exhibiting large fluctuations in the local mobility ("dynamic heterogeneity") and non-Arrhenius temperature dependence of relaxation and diffusion. In this work, we investigate a model dodecagonal quasicrystal material in two dimensions (2D) using molecular dynamics (MD) simulations, with a focus on heterogeneous dynamics and non-Arrhenius relaxation and diffusion. As observed in glass-forming liquids and heated crystals, we observe a two-stage relaxation dynamics in the self-intermediate scattering function $F_s(k,t)$ of our quasicrystal material. It involves a fast $β$-relaxation and $α$ relaxation process having a highly temperature dependent relaxation time whose activation energy varies in concert with the extent of string-like collective motion, a phenomenon recognized to occur in glass-forming liquids at low temperatures and crystalline materials at elevated temperatures. After examining the dynamics of our dodecagonal quasicrystalline material in great detail, we conclude that the dynamics of these materials more closely resembles observations on metallic glass-forming liquids than crystalline materials.

cond-mat.mtrl-sci↗

arXiv2025

Quantitative relations between nearest-neighbor persistence and slow heterogeneous dynamics in supercooled liquids

Using molecular dynamics simulations of a binary Lennard-Jones model of glass-forming liquids, we examine how the decay of the normalized neighbor-persistence function $C_{\rm B}(t)$, which decays from unity at short times to zero at long times as particles lose the neighbors that were present in their original first coordination shell, compares with those of other, more conventionally utilized relaxation metrics. In the strongly-non-Arrhenius temperature regime below the onset temperature $T_{\rm A}$, we find that $C_{\rm B}(t)$ can be described using the same stretched-exponential functional form that is often utilized to fit the self-intermediate scattering function $S(q, t)$ of glass-forming liquids in this regime. The ratio of the bond lifetime $τ_{\rm bond}$ associated with the terminal decay of $C_{\rm B}(t)$ to the $α$-relaxation time $τ_α$ varies appreciably and non-monotonically with $T$, peaking at $τ_{\rm bond}/τ_α\simeq 45$ at $T \simeq T_{\rm x}$, where $T_{\rm x}$ is a crossover temperature separating the high- and low-temperature regimes of glass-formation. In contrast, $τ_{\rm bond}$ remains on the order of the overlap time $τ_{\rm ov}$ (the time interval over which a typical particle moves by half its diameter), and the peak time $τ_χ$ for the susceptibility $χ_{\rm B}(t)$ associated with the spatial heterogeneity of $C_{\rm B}(t)$ remains on the order of $τ_{\rm imm}$ (the characteristic lifetime of immobile-particle clusters), even as each of these quantities varies by roughly $5$ orders of magnitude over our studied range of $T$. Thus, we show that $C_{\rm B}(t)$ and $χ_{\rm B}(t)$ provide semi-quantitative spatially-averaged measures of the slow heterogeneous dynamics associated with the persistence of immobile-particle clusters.

cond-mat.soft↗

arXiv2024

Generalized Entropy Theory Investigation of the Relatively High Segmental Fragility of Many Glass-Forming Polymers

We utilize the generalized entropy theory (GET) of glass formation to address one of the most singular and least understood properties of polymer glass-forming liquids in comparison to atomic and small molecule liquids -- the often relatively high fragility of the polymer dynamics on a segmental scale, $m_s$. We first analyze the relation between $m_s$ and the ratio, $S_c^*/ S_c(T_{\mathrm{g}})$. We find that an apparently general nonlinear relation between $m_s$ and $S_c^*/ S_c(T_{\mathrm{g}})$ holds to a good approximation for a large class of polymer models, $m_s \approx 7.9 \exp [0.6S_c^*/ S_c(T_{\mathrm{g}})]$. The predicted ranges of $m_s$ and $S_c^*/ S_c(T_{\mathrm{g}})$ are consistent with experimental estimates for high molecular-mass polymer, oligomeric, small molecule, and atomic glass-forming liquids. In particular, relatively high values of $m_s$ are found for polymers having complex monomer structures and significant chain stiffness. The variation of $m_s$ with molecular mass, chain stiffness, and intermolecular interaction strength can be traced to the variation of $S_c^*$, which is shown to provide a measure of packing frustration defined in terms of the dimensionless thermal expansion coefficient and isothermal compressibility. The often relatively high fragility and large extent of cooperative motion are found in the GET to derive from the often relatively large packing frustration in this class of polymer glass-forming liquids. Finally, we also develop a tentative model of the ``dynamical segmental relaxation time'' based on the GET, in which the polymers on a coarse-grained scale are modeled as strings of structureless ``beads'', as assumed in the Rouse and reptation models of polymer dynamics.

cond-mat.soft↗

arXiv2024

Stringlet Excitation Model of the Boson Peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations (``stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency $ω_{BP}$ in the temperature regime well below the observed glass transition temperature $T_g$. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above $T_g$. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above $T_g$, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

cond-mat.soft↗

arXiv2023

Computation of Riesz $α$-capacity $C_α$ of general sets in $\mathbb{R}^d$ using stable random walks

A method for computing the Riesz $α$-capacity, $0 < α\le 2$, of a general set $K \subset \mathbb{R}^d$ is given. The method is based on simulations of isotropic $α$-stable motion paths in $d$-dimensions. The familiar Walk-On-Spheres method, often utilized for simulating Brownian motion, is modified to a novel Walk-In-Out-Balls method adapted for modeling the stable path process on the exterior of regions ``probed'' by this type of generalized random walk. It accounts for the propensity of this class of random walk to jump through boundaries because of the path discontinuity. This method allows for the computationally efficient simulation of hitting locations of stable paths launched from the exterior of probed sets. Reliable methods of computing capacity from these locations are given, along with non-standard confidence intervals. Illustrative calculations are performed for representative types of sets K, where both $α$ and $d$ are varied.

stat.CO↗

arXiv2023

A quantitative theoretical model of the boson peak based on stringlet excitations

The boson peak (BP), a low-energy excess in the vibrational density of states over the phonon Debye contribution, is usually identified as one of the distinguishing features between ordered crystals and amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery and a consensus on its theoretical derivation has not yet been achieved. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes which involve string-like excitations ("stringlets") having a one-dimensional (1D) nature. In this work, we build on a theoretical framework originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in independent simulation studies. We show that a generalization of this framework provides an analytically prediction for the BP frequency $ω_{BP}$ in the temperature regime well below the glass transition temperature in both 2D and 3D amorphous systems. The final result involves no free parameters and is in quantitative agreement with prior simulation observations. Additionally, this stringlet theory of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in cooled liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes at finite temperature which leads to a large low-frequency contribution to the 3D vibrational density of states, as observed in both experiments and simulations.

cond-mat.soft↗

arXiv2023

Parallel Emergence of Rigidity and Collective Motion in a Family of Simulated Glass-Forming Polymer Fluids

The emergence of the solid state in glass-forming materials upon cooling is accompanied by changes in both thermodynamic and viscoelastic properties and by a precipitous drop in fluidity. Here, we investigate changes in basic elastic properties upon cooling in a family of simulated polymer fluids, as characterized by a number of stiffness measures. We show that $τ_α$ can be expressed quantitatively both in terms of measures of the material ``stiffness'', $G_p$ and $\langle u^2 \rangle$, and the extent $L$ of cooperative particle exchange motion in the form of strings, establishing a direct relation between the growth of emergent elasticity and collective motion. Moreover, the macroscopic stiffness parameters, $G_p$, $B$, and $f_{s, q^*}$, can all be expressed quantitatively in terms of the molecular scale stiffness parameter, $k_{\mathrm{B}}T / \langle u^2 \rangle$ with $k_{\mathrm{B}}$ being Boltzmann's constant, and we discuss the thermodynamic scaling of these properties. We also find that $G_p$ is related to the cohesive energy density $Π_{\mathrm{CED}}$, pointing to the critical importance of attractive interactions in the elasticity and dynamics of glass-forming liquids. Finally, we discuss fluctuations in the local stiffness parameter as a quantitative measure of elastic heterogeneity and their significance for understanding both the linear and nonlinear elastic properties of glassy materials.

cond-mat.soft↗

arXiv2023

Approach to Hyperuniformity in a Metallic Glass-Forming Material Exhibiting a Fragile to Strong Glass Transition

We investigate a metallic glass-forming (GF) material (Al90Sm10) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of OGF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, Tg. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. In particular, we quantify the 'hyperuniformity index' H of our liquid which provides a quantitative measure of molecular 'jamming'. To gain insight into the T-dependence and magnitude of H, we also estimated another more familiar measure of particle localization, the Debye-Waller parameter $ $ describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and $ $ for heated crystalline Cu. This comparative analysis between H and $ $ for crystalline and metallic glass materials allows us to understand the critical value of H on the order of $10^{-3}$ as being analogous to the Lindemann criterion for both the melting of crystals and the 'softening' of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative assembly process in the GF liquid.

cond-mat.soft↗

arXiv2022

Thermodynamic-Dynamic Interrelations in Glass-Forming Polymer Fluids

We utilize the lattice cluster theory (LCT) of polymer fluids to show that the configurational entropy, enthalpy, and internal energy are all closely interrelated, as suggested by recent measurements by Caruthers and Medvedev, so that the generalized entropy theory (GET) of glass formation, a combination of the LCT and Adam-Gibbs model, can be recast in terms of any of these thermodynamic properties as a matter of convenience. Thermodynamic scaling, a form of density-temperature scaling exhibited by dynamic and some thermodynamic properties, is used to assess which thermodynamic properties are most naturally linked to dynamics, and we explore the origin of this scaling by both direct calculations based on the GET and molecular dynamics simulations of a coarse-grained polymer model. Through a combination of our comprehensive modeling of thermodynamic properties using the LCT and the highly predictive GET model for how the fluid thermodynamics relate to its dynamics, along with simulation results confirming these theoretical frameworks, we obtain insights into thermodynamic aspects of collective motion and the slow $β$-relaxation processes of glass-forming liquids.

cond-mat.soft↗

arXiv2021

The Initiation of Shear Band Formation in Deformed Metallic Glasses from Soft Localized Domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively 'soft' regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying 'soft' regions and their evolution as the material is deformed to varying degrees, where the metric of 'softness' must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale , the 'Debye-Waller factor', provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this 'softness' metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition of SB formation occurs when the softness ( ) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being 'interfacial' in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

cond-mat.mtrl-sci↗

arXiv2021

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 $TV^γ$ 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 $τ_α$ 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 $τ_α$ and $L/ L_A$ is confirmed by simulation, we find that the isothermal compressibility $κ_T$ 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, $δκ_T$, 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 $γ$ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus.

cond-mat.soft↗

arXiv2021

Dynamic Heterogeneity, Cooperative Motion, and Johari-Goldstein $β$-Relaxation in a Metallic Glass-Forming Material Exhibiting a Fragile to Strong Transition

We investigate the Johari-Goldstein (JG) $β$-relaxation process in a model metallic glass-forming (GF) material (Al90Sm10), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG $β$-relaxation time $τ_{JG}$ and the lifetime of the mobile particle clusters $τ_M$, defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the $α$-relaxation time $τ_α$ and the lifetime of immobile particle clusters $τ_{IM}$. Moreover, we find that the average diffusion coefficient D nearly coincides with D$_{Al}$, of the smaller atomic species (Al), and that the hopping time associated with D coincides with $τ_{JG}$ to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG $α$-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG $β$-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that Al90Sm10 exhibits fragile-to-strong (FS) glass-formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties.

cond-mat.mtrl-sci↗

arXiv2021

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

We provide a perspective on polymer glass formation, with an emphasis on models in which the fluid entropy and collective particle motion dominate the theoretical description and data analysis. We first discuss the dynamics of liquids in the high temperature Arrhenius regime, where transition state theory is formally applicable. We then summarize the evolution of the entropy theory from a qualitative framework for organizing and interpreting temperature-dependent viscosity data by Kauzmann to the formulation of a hypothetical `ideal thermodynamic glass transition' by Gibbs and DiMarzio, followed by seminal measurements linking entropy and relaxation by Bestul and Chang and the Adam-Gibbs (AG) model of glass formation rationalizing the observations of Bestul and Chang. These developments laid the groundwork for the generalized entropy theory (GET), which merges an improved lattice model of polymer thermodynamics accounting for molecular structural details and enabling the analytic calculation of the configurational entropy with the AG model, giving rise to a highly predictive model of the segmental structural relaxation time of polymeric glass-forming liquids. The development of the GET has occurred in parallel with the string model of glass formation in which concrete realizations of the cooperatively rearranging regions are identified and quantified for a wide range of polymeric and other glass-forming materials. The string model has shown that many of the assumptions of AG are well supported by simulations, while others are certainly not, giving rise to an entropy theory of glass formation that is largely in accord with the GET. As the GET and string models continue to be refined, these models progressively grow into a more unified framework, and this Perspective reviews the present status of development of this promising approach to the dynamics of polymeric glass-forming liquids.

cond-mat.soft↗

arXiv2021

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 fragile-strong transition. String-like particle motion, having both an irreversible and reversible nature ('stringlets') component, occurs in the fast-dynamics regime, corresponding to a ps timescale. String-like collective motion associated with localized unstable modes facilitate 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 time and spatial scales.

cond-mat.mtrl-sci↗

arXiv2020

Impact of Particle Arrays on Phase Separation Composition Patterns

We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components. Our phase-field simulations indicate that the phase separation morphology in the presence of particle arrays can be tuned to have a continuous, droplet, lamellar, or hybrid morphology depending on the interparticle spacing, blend composition, and time. In particular, when the interparticle spacing is large compared to the spinodal wavelength, a transient target pattern composed of alternate rings of preferred and non-preferred phases emerge at early times, tending to adopt the symmetry of the particle configuration. We reveal that such target patterns stabilize for certain characteristic length, time, and composition scales characteristic of the pure phase separating mixture. To illustrate the general range of phenomena exhibited by mixture-particle systems, we simulate the effects of single-particle, multi-particle, and cluster-particle systems having multiple geometrical configurations of the particle characteristic of pattern substrates on phase separation. Our simulations show that tailoring the particle configuration, or substrate pattern configuration, a relative fluid-particle composition should allow the desirable control of the phase separation morphology as in block copolymer materials, but where the scales accessible to this approach of organizing phase-separated fluids usually are significantly larger. Limited experiments confirm the trends observed in our simulations, which should provide some guidance in engineering patterned blend and other mixtures of technological interest.

physics.chem-ph↗

arXiv2019

Collective Motion in the Interfacial and Interior Regions of Supported Polymer Films and its Relation to Relaxation

To understand the role of collective motion in the often large changes in interfacial molecular mobility observed in polymer films, we investigate the extent of collective motion in the interfacial regions of a thin supported polymer film and within the film interior by molecular dynamics simulation. Contrary to commonly stated expectations, we find that the extent of collective motion, as quantified by string-like molecular exchange motion, is similar in magnitude in polymer-air interfacial layer to that in the film interior, and both are generally distinct from the bulk material. This finding is consistent with Adam-Gibbs description of the segmental dynamics within mesoscopic film regions where the extent of collective motion is related to the configurational entropy of the film as whole rather than a locally defined extent of collective motion or configurational entropy.

cond-mat.soft↗