arXiv subjects

Robert S. Hoy

Publications and source records attributed to Robert S. Hoy.

At least 19 recordsLinked to original sources

arXiv2025

Glassy polymers' strain-hardening moduli scale with their statistical-segment volumes

Using molecular dynamics simulations, we show that a widely-accepted theoretical prediction for glassy-polymeric strain hardening moduli ($G_R \propto ρ_e$, where $ρ_e$ is the entanglement density) fails badly for semiflexible polymers with $N_e \lesssim 4C_\infty$. By postulating that the length, energy and strain scales controlling $G_R$ are the Kuhn length $\ell_K$ and statistical segment length $b = \sqrt{\ell_0 \ell_K}$ (where $\ell_0$ is the backbone bond length), the intermonomer binding energy $u_0$, and the incremental elastic strain $S_{\rm c}$ required to activate Kuhn-segment-scale plastic rearrangements, we develop a scaling theory predicting that $G_R = S_{\rm c}(u_0/\ell_0^3) b^3$ in the athermal limit. This prediction agrees quantitatively (semi-quantitatively) with simulated $G_R$ values for both flexible and semiflexible polymer glasses subjected to athermal uniaxial-stress extension (constant-volume simple shear), over a range of $\ell_K/\ell_0$ that is wider than that spanned by real systems.

cond-mat.soft↗

arXiv2025

Ultrastable jammed sphere packings with a wide range of particle dispersities

We show that for a standard continuously-polydisperse model with particle-diameter distribution $P(σ) \propto σ^{-3}$ and polydispersity index $Δ$, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities $ϕ_{\rm J}(Δ)$ and coordination numbers $Z_{\rm J}(Δ)$, for a wide range of $Δ$. The fractional increase in $ϕ_{\rm J}(Δ)$ obtained by employing these moves first increases rapidly with $Δ$, then plateaus at $6-7\%$ over the range $0.10 \lesssim Δ\leq 50$; the obtained $ϕ_{\rm J}$ are as high as $0.747$ (for $Δ= 0.50$). These density increases are achieved without producing clearly-noticeable crystallization or increased fractionation, despite the fact that the packings are quite hyperstatic for all $Δ> 0$. SWAP and TDOF moves also reduce packings' rattler populations by as much as 99% and increase their bulk moduli by as much as 80%.

cond-mat.soft↗

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

Generating ultradense jammed ellipse packings using biased SWAP

Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $α$, these packings exhibit significantly smaller intermediate-wavelength density fluctuations and greater local nematic order than their less-dense counterparts. The densest packings are disordered despite having packing fractions $ϕ_{\rm J}(α)$ that are within less than 0.5% of that of the monodisperse-ellipse crystal [$ϕ_{\rm xtal} = π/(2\sqrt{3}) \simeq .9069$] over the range $1.25 \lesssim α\lesssim 1.4$ and coordination numbers $Z_{\rm J}(α)$ that are within less than 0.5% of isostaticity [$Z_{\rm iso} = 6$] over the range $1.3 \lesssim α\lesssim 2.0$. Lower-$α$ packings are strongly fractionated and consist of polycrystals of intermediate-size particles, with the largest and smallest particles isolated at the grain boundaries. Higher-$α$ packings are also fractionated, but in a qualitatively-different fashion; they are composed of increasingly-large locally-nematic domains reminiscent of liquid glasses.

cond-mat.soft↗

arXiv2024

Critical slowing down in thermal soft-sphere glasses via energy minimization

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that the terminal relaxation times $τ$ for FIRE energy minimization of soft-sphere glasses exhibit thermal onset as samples become increasingly well-equilibrated. Although $τ(ϕ)$ can decrease by orders of magnitude as equilibration proceeds and the jamming density $ϕ_{\rm J}$ increases via thermal onset, it always scales as $τ(ϕ) \sim (ϕ_{\rm J} - ϕ)^{-2} \sim [Z_{\rm iso} - Z_{\rm ms}(τ)]^{-2}$, where $ϕ_{\rm J}$ is the jamming density and $Z_{\rm ms}(τ)$ is the average coordination number of particles satisfying a minimal local mechanical stability criterion ($Z \geq d+1$) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse $τ$ datasets that look very different when plotted as a function of $ϕ$, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant $ϕ$ and $T$?

cond-mat.soft↗

arXiv2023

Homogeneous crystallization in four-dimensional Lennard-Jones liquids

We report the first observation of homogeneous crystallization in simulated high-dimensional ($d > 3$) liquids that follow physically realistic dynamics and have system sizes that are large enough to eliminate the possibility that crystallization was induced by the periodic boundary conditions. Supercooled four-dimensional (4D) Lennard-Jones liquids maintained at zero pressure and constant temperatures $0.59 < T < 0.63$ crystallized within $\sim 2 \times 10^4τ$, where $τ$ is the LJ time unit. WCA liquids that were maintained at the same densities and temperatures at which their LJ counterparts nucleated did not crystallize even after $2.5\times 10^5τ$, showing that the presence of long-ranged attractive interactions dramatically speeds up 4D crystallization, much as it does in 3D. However, the overlap of the liquid and crystalline phases' local-bond-order distributions is much smaller for LJ than for WCA systems, which is the opposite of the 3D trend. This implies that the widely accepted hypothesis that increasing geometrical frustration rapidly suppresses crystallization as the spatial dimension $d$ increases is only generally valid in the absence of attractive interparticle forces.

cond-mat.soft↗

arXiv2023

Structure of jammed ellipse packings with a wide range of aspect ratios

Motivated in part by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of jammed ellipse packings over a much wider range of particle aspect ratios ($α$) than has been previously attempted. We determine $ϕ_{\rm J}(α)$ to high precision, and find empirical analytic formulae that predict $ϕ_{\rm J}(α)$ to within less than 0.1% for all $1 \leq α\leq 10$, for three different particle dispersities. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction $f_{\rm Z = 6}$ of particles with exactly six contacts and a previously-unreported short-range order marked by ``kinetically suppressed'' regions in their positional-orientational pair correlation function $g(r,Δθ)$. We also show that the previously-reported approach to isostaticity (coordination number $Z_{\rm J} \to Z_{\rm iso} \equiv 6$) with increasing $α$ is interrupted and then reversed as local nematic order increases: $Z_{\rm J}(α)$ drops towards 4 as ellipses are more often trapped by contacts with a parallel-oriented neighbor on either side and a perpendicularly-oriented neighbor on either end. Finally we show that $ϕ_{\rm J}/ϕ_{\rm s}$ (where $ϕ_{\rm s}$ is the saturated RSA packing density) is nearly $α$-independent for systems that do not develop substantial local hexatic or nematic order during compression.

cond-mat.soft↗

arXiv2022

Ultraslow settling kinetics of frictional cohesive powders

Using discrete element method simulations, we show that the settling of frictional cohesive grains under ramped-pressure compression exhibits strong history dependence and slow dynamics that are not present for grains that lack either cohesion or friction. Systems prepared by beginning with a dilute state and then ramping the pressure to a small positive value $P_{\rm final}$ over a time $τ_{\rm ramp}$ settle at packing fractions given by an inverse-logarithmic rate law, $ϕ_{\rm settled}(τ_{\rm ramp}) = ϕ_{\rm settled}(\infty) + A/[1 + B\ln(1 + τ_{\rm ramp}/τ_{\rm slow})]$. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that $τ_{\rm slow}$ is set by the slow dynamics of structural void stabilization rather than the faster dynamics of bulk densification. We formulate a kinetic free-void-volume theory that predicts this $ϕ_{\rm settled}(τ_{\rm ramp})$, with $ϕ_{\rm settled}(\infty) = ϕ_{\rm ALP}$ and $A = ϕ_{\rm settled}(0) - ϕ_{\rm ALP}$, where $ϕ_{\rm ALP} \equiv .135$ is the ``adhesive loose packing'' fraction found by Liu \textit{et al.} [W.\ Liu, Y.\ Jin, S. Chen, H.\ A.\ Makse and S.\ Li, \textit{Soft Matt.} \textbf{13}, 421 (2017)].

cond-mat.soft↗

arXiv2022

Structure of saturated RSA ellipse packings

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of (asymptotically) saturated RSA ellipse packings. We determine the packing fractions $ϕ_{\rm s}(α)$ to high precision, finding an empirical analytic formula that predicts $ϕ_{\rm s}(α)$ to within less than $0.1\%$ for all $α\leq 10$. Then we explore how these packings' positional-orientational order varies with $α$. We find a transition from tip/side- to side/side-contact-dominated structure at $α= α_{\rm TS} \simeq 2.4$. At this aspect ratio, the peak value $g_{\rm max}$ of packings' positional-orientational paircorrelation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) $α$, $g_{\rm max}$ increases exponentially with deceasing (increasing) $α$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $α$ increases beyond $3$. For $α\gtrsim 5$, single-layer lamellae become more prominent, and long-wavelength density fluctuations increase with $α$ as packings gradually approach the rod-like limit.

cond-mat.soft↗

arXiv2022

Unexpected ductility in semiflexible polymer glasses with $N_e = C_\infty$

Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers (SCPs), are expected to be brittle because classical formulas for their craze extension ratio $λ_{\rm craze}$ and fracture stretch $λ_{\rm frac}$ predict that systems with $N_e = C_\infty$ have $λ_{\rm craze} = λ_{\rm frac} = 1$ and hence cannot be deformed to large strains. Using molecular dynamics simulations, we show that in fact such glasses can form stable crazes with $λ_{\rm craze} \simeq N_e^{1/4} \simeq C_\infty^{1/4}$, and that they fracture at $λ_{\rm frac} = (3N_e^{1/2} - 2)^{1/2} \simeq (3C_\infty^{1/2} - 2)^{1/2}$. We argue that the classical formulas for $λ_{\rm craze}$ and $λ_{\rm frac}$ fail to describe SPGs' mechanical response because they do not account for Kuhn segments' ability to stretch during deformation.

cond-mat.soft↗

arXiv2022

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. Scaling of simulation runtimes with the number of particles $N$ and number of simulation threads $n_{\rm threads}$ is comparable to popular MD 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.

cond-mat.soft↗

arXiv2021

Thermodynamic stability of hard sphere crystals in dimensions 3 through 10

Although much is known about the metastable liquid branch of hard spheres--from low dimension $d$ up to ${d\to\infty}$--its crystal counterpart remains largely unexplored for $d>3$. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to $d=10$, and the dimensional trends suggest that crystal stability likely persists well beyond that point.

cond-mat.stat-mech↗

arXiv2021

Facile equilibration of well-entangled semiflexible bead-spring polymer melts

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [R. Auhl et al., J. Chem. Phys. v. 119, p. 12718, 2003] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with $N \simeq 40 N_e$ and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 million timesteps. For semiflexible chains, our method is several times faster than standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length $\ell_K$ and entanglement length $N_e$.

cond-mat.soft↗

arXiv2020

Does the Sastry transition control cavitation in simple liquids?

We examine the Sastry (athermal cavitation) transitions for model monatomic liquids interacting via Lennard-Jones as well as shorter- and longer-ranged pair potentials. Low-temperature thermodynamically stable liquids have $ρ< ρ_S$ except when the attractive forces are long-ranged. For moderate- and short-ranged attractions, stable liquids with $ρ> ρ_S$ exist at higher temperatures; the pressures in these liquids are high, but the Sastry transition may strongly influence their cavitation under dynamic hydrostatic expansion. The temperature $T^*$ at which stable $ρ> ρ_S$ liquids emerge is $\sim 0.84ε/k_B$ for Lennard-Jones liquids; $T^*$ decreases (increases) rapidly with increasing (decreasing) pair-interaction range. In particular, for short-ranged potentials, $T^*$ is above the critical temperature. All liquids' inherent structures are isostructural (isomorphic) for densities below (above) the Sastry density $ρ_S$. Overall, our results suggest that the barriers to cavitation in most simple liquids under ambient conditions where significant cavitation is likely to occur are primarily vibrational-energetic and entropic rather than configurational-energetic. The most likely exceptions to this rule are liquids with long-ranged pair interactions, such as alkali metals. The most likely exceptions to this rule are liquids with long-ranged pair interactions, such as alkali metals.

cond-mat.soft↗

arXiv2020

Two-stage athermal solidification of semiflexible polymers and fibers

We study how solidification of model freely rotating polymers under athermal quasistatic compression varies with their bond angle $θ_0$. All systems undergo two discrete, first-order-like transitions: entanglement at $ϕ= ϕ_E(θ_0)$ followed by jamming at $ϕ= ϕ_J(θ_0) \simeq (4/3 \pm 1/10)ϕ_E(θ_0)$. For $ϕ< ϕ_E(θ_0)$, systems are in a "gas" phase wherein all chains remain free to translate and reorient. For $ϕ_E(θ_0) \leq ϕ\leq ϕ_J(θ_0)$, systems are in a liquid-like phase wherein chains are entangled. In this phase, chains' rigid-body-like motion is blocked, yet they can still locally relax via dihedral rotations, and hence energy and pressure remain extremely small. The ability of dihedral relaxation mechanisms to accommodate further compression becomes exhausted, and systems rigidify, at $ϕ_J(θ_0)$. At and slightly above $ϕ_J$, the bulk moduli increase linearly with the pressure $P$ rather than jumping discontinuously, indicating these systems solidify via rigidity percolation. The character of the energy and pressure increases above $ϕ_J(θ_0)$ can be characterized via chains' effective aspect ratio $α_{\rm eff}$. Large-$α_{\rm eff}$ (small-$θ_0$) systems' jamming is bending-dominated and is similar to that observed in systems composed of straight fibers. Small-$α_{\rm eff}$ (large-$θ_0$) systems' jamming is dominated by the degree to which individual chains' dihedrals can collapse into compact, tetrahedron-like structures. For intermediate $θ_0$, chains remain in highly disordered globule-like configurations throughout the compression process; jamming occurs when entangled globules can no longer even locally relax away from one another.

cond-mat.soft↗

arXiv2020

Unified analytic expressions for the entanglement length, tube diameter, and plateau modulus of polymer melts

By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length $N_e$, the plateau modulus $G$, and the tube diameter $a$ in melts that span the entire range of chain stiffnesses for which systems remain isotropic. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^3$], semiflexible [Edwards/de Gennes: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^2$], and tightly-entangled [Morse: $G\ell_K^3/k_\textrm{B}T \sim (\ell_K/p)^{1+ε}$] regimes, where $\ell_K$ and $p$ are respectively the Kuhn and packing lengths. We also find that maximal entanglement (minimal $N_e$) coincides with the onset of local nematic order.

cond-mat.soft↗

arXiv2019

Factors influencing thermal solidification of bent-core trimers

Bent-core trimers are a simple model system for which the competition between crystallization and glass-formation can be tuned by varying a single parameter:\ the bond angle $θ_0$. Using molecular dynamics simulations, we examine how varying $θ_0$ affects their thermal solidification. By examining trends with $θ_0$, comparing these to trends in trimers' jamming phenomenology, and then focusing on the six $θ_0$ that are commensurable with close-packed crystalline order, we obtain three key results: \textbf{(i)} the increase in trimers' solidification temperature $T_s(θ_0)$ as they straighten (as $θ_0 \to 0^\circ$) is driven by the same gradual loss of \textit{effective} configurational freedom that drives athermal trimers' decreasing $ϕ_J(θ_0)$; \textbf{(ii)} $θ_0$ that allow formation of both FCC and HCP order crystallize, while $θ_0$ that only allow formation of HCP order glass-form; \textbf{(iii)} local cluster-level structure at temperatures slightly \textit{above} $T_s(θ_0)$ is highly predictive of whether trimers will crystallize or glass-form.

cond-mat.soft↗

arXiv2018

Densest vs. jammed packings of 2D bent-core trimers

We identify the maximally dense lattice packings of tangent-disk trimers with fixed bond angles ($θ= θ_0$) and contrast them to both their nonmaximally-dense-but-strictly-jammed lattice packings as well as the disordered jammed states they form for a range of compression protocols. While only $θ_0 = 0,\ 60^\circ,\ \rm{and}\ 120^\circ$ trimers can form the triangular lattice, maximally-dense maximally-symmetric packings for all $θ_0$ fall into just two categories distinguished by their bond topologies: half-elongated-triangular for $0 < θ_0 < 60^\circ$ and elongated-snub-square for $60^\circ < θ_0 < 120^\circ$. The presence of degenerate, lower-symmetry versions of these densest packings combined with several families of less-dense-but-strictly-jammed lattice packings act in concert to promote jamming.

cond-mat.soft↗