Homogeneous crystallization in four-dimensional Lennard-Jones liquids.

We observe 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 (LJ) liquids maintained at zero pressure and constant temperatures 0.59

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 two-dimensional ellipse packings over a much wider range of particle aspect ratios (α, the ratio of the major and minor axis lengths) than has been previously attempted. We determine the jamming densities ϕJ(α) to high precision, and find empirical analytic formulae that predict ϕJ(α) to within less than 0.1% for all 1≤α≤10, for three different particle dispersities. Then we explore how these packings' local structural order varies with α. We find that the densest packings possess unusually-well-defined nearest-neighbor shells, including both a higher fraction fZ=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 ZJ → Ziso ≡ 6) with increasing α is interrupted and then reversed as local nematic order increases: ZJ(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 ϕJ/ϕs (where ϕs is the saturated RSA packing density) is nearly α-independent for systems that do not develop substantial local hexatic or nematic order during compression.

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_{final} over a time τ_{ramp} settle at packing fractions given by an inverse-logarithmic rate law, ϕ_{settled}(τ_{ramp})=ϕ_{settled}(∞)+A/[1+Bln(1+τ_{ramp}/τ_{slow})]. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that τ_{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_{settled}(τ_{ramp}), with ϕ_{settled}(∞)=ϕ_{ALP} and A=ϕ_{settled}(0)-ϕ_{ALP}, where ϕ_{ALP}≡.135 is the "adhesive loose packing" fraction found by Liu et al. [Equation of state for random sphere packings with arbitrary adhesion and friction, Soft Matter 13, 421 (2017)SMOABF1744-683X10.1039/C6SM02216B].

Structure of saturated random-sequential-adsorption 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_{s}(α) to high precision, finding an empirical analytic formula that predicts ϕ_{s}(α) to within less than 0.1% for all α≤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_{TS}≃2.4. At this aspect ratio, the peak value g_{max} of packings' positional-orientational pair correlation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) α, g_{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 three. For α≳5, single-layer lamellae become more prominent and long-wavelength density fluctuations increase with α as packings gradually approach the rodlike limit.

Unexpected Ductility in Semiflexible Polymer Glasses with Entanglement Length Equal to Their Kuhn Length.

Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers, are expected to be brittle because classical formulas for their craze extension ratio λ_{craze} and fracture stretch λ_{frac} predict that systems with N_{e}=C_{∞} have λ_{craze}=λ_{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_{craze}≃N_{e}^{1/4}≃C_{∞}^{1/4}, and that they fracture at λ_{frac}=(3N_{e}^{1/2}-2)^{1/2}≃(3C_{∞}^{1/2}-2)^{1/2}. We argue that the classical formulas for λ_{craze} and λ_{frac} fail to describe SPGs' mechanical response because they do not account for Kuhn segments' ability to stretch during deformation.

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. The scalings of simulation runtimes with the number of particles N and number of simulation threads n_{threads} are comparable to popular molecular dynamics 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.

Validation and Refinement of Unified Analytic Model for Flexible and Semiflexible Polymer Melt Entanglement.

We combine molecular dynamics simulations and topological analyses (TA) to validate and refine a recently proposed unified analytic model [Hoy, R. S.; Kröger, M. Phys. Rev. Lett. 2020, 124, 147801] for the reduced entanglement length, tube diameter, and plateau modulus of polymer melts. While the functional forms of the previously published expressions are insensitive to the choice of the TA method and N e -estimator, obtaining better statistics and eliminating all known sources of systematic error in the N e -estimation alters their numerical coefficients. Our revised expressions quantitatively match bead-spring simulation data over the entire range of chain stiffnesses for which systems remain isotropic, semiquantitatively match all available experimental data for flexible, semiflexible, and stiff polymer melts (including new data for conjugated polymers that lie in a previously unpopulated stiffness regime), and outperform previously developed unified scaling theories.

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

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (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 ≃ 40Ne and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 106 time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓK and entanglement length Ne.

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 [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. 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 [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.

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 < ρS except when the attractive forces are long-ranged. For moderate- and short-ranged attractions, stable liquids with ρ > ρS 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 > ρS liquids emerge is ∼0.84ϵ/kB 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 ρS. Overall, our results suggest that the barriers to cavitation in most simple liquids under ambient conditions for which 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.

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 θ0. All systems undergo two discrete, first-order-like transitions: entanglement at φ = φE(θ0) followed by jamming at φ = φJ(θ0) ≃ (4/3 ± 1/12)φE(θ0). For φ < φE(θ0), systems are in a "gas" phase wherein all chains remain free to translate and reorient. For φE(θ0) ≤ φ ≤ φJ(θ0), 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 φJ(θ0). At and slightly above φJ, 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 φJ(θ0) can be characterized via chains' effective aspect ratio αeff. Large-αeff (small-θ0) systems' jamming is bending-dominated and is similar to that observed in systems composed of straight fibers. Small-αeff (large-θ0) systems' jamming is dominated by the degree to which individual chains' dihedrals can collapse into compact, tetrahedron-like structures. For intermediate θ0, 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.

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, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{3}], semiflexible [Edwards-de Gennes: Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{2}], and tightly entangled [Morse, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{1+ϵ}] regimes, where ℓ_{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.

Densest versus jammed packings of bent-core trimers.

We identify putatively maximally dense packings of tangent-sphere trimers with fixed bond angles (θ=θ_{0}), and contrast them to the disordered jammed states they form under quasistatic and dynamic athermal compression. Incommensurability of θ_{0} with three-dimensional (3D) close packing does not by itself inhibit formation of dense 3D crystals; all θ_{0} allow formation of crystals with ϕ_{max}(θ_{0})>0.97ϕ_{cp}. Trimers are always able to arrange into periodic structures composed of close-packed bilayers or trilayers of triangular-lattice planes, separated by "gap layers" that accommodate the incommensurability. All systems have ϕ_{J} significantly below the monomeric value, indicating that trimers' quenched bond-length and bond-angle constraints always act to promote jamming. ϕ_{J} varies strongly with θ_{0}; straight (θ_{0}=0) trimers minimize ϕ_{J} while closed (θ_{0}=120^{∘}) trimers maximize it. Marginally jammed states of trimers with lower ϕ_{J}(θ_{0}) exhibit quantifiably greater disorder, and the lower ϕ_{J} for small θ_{0} is apparently caused by trimers' decreasing effective configurational freedom as they approach linearity.

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 θ0. Using molecular dynamics simulations, we examine how varying θ0 affects their thermal solidification. By examining trends with θ0, comparing these to the trends in trimers' jamming phenomenology, and then focusing on the six θ0 that are commensurable with close-packed crystalline order, we obtain three key results: (i) the increase in trimers' solidification temperature Ts(θ0) as they straighten (as θ0 → 0°) is driven by the same gradual loss of effective configurational freedom that drives athermal trimers' decreasing ϕJ(θ0) [where ϕJ(θ0) is the packing fraction at jamming]; (ii) θ0 that allow formation of both FCC and HCP order crystallize, while θ0 that only allow formation of HCP order glass-form; and (iii) local cluster-level structure at temperatures slightly above Ts(θ0) is highly predictive of whether trimers will crystallize or glass-form.

Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory.

We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.

From sticky-hard-sphere to Lennard-Jones-type clusters.

A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.

Isostaticity and the solidification of semiflexible polymer melts.

Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The configurational freedom associated with bond angles (θ) can be associated with the characteristic ratio C∞ = (1 + 〈cos(θ)〉)/(1 - 〈cos(θ)〉). We find that the dependence of the average coordination number at solidification [Z(Ts)] on chains' characteristic ratio C∞ has the same functional form [Z ≃ a - b ln(C∞)] as the dependence of the average coordination number at jamming [Z(ϕJ)] on C∞ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification.

Jamming of Semiflexible Polymers.

We study jamming in model freely rotating polymers as a function of chain length N and bond angle θ_{0}. The volume fraction at jamming ϕ_{J}(θ_{0}) is minimal for rigid-rodlike chains (θ_{0}=0), and increases monotonically with increasing θ_{0}≤π/2. In contrast to flexible polymers, marginally jammed states of freely rotating polymers are highly hypostatic, even when bond and angle constraints are accounted for. Large-aspect-ratio (small θ_{0}) chains behave comparably to stiff fibers: resistance to large-scale bending plays a major role in their jamming phenomenology. Low-aspect-ratio (large θ_{0}) chains behave more like flexible polymers, but still jam at much lower densities due to the presence of frozen-in three-body correlations corresponding to the fixed bond angles. Long-chain systems jam at lower ϕ and are more hypostatic at jamming than short-chain systems. Implications of these findings for polymer solidification are discussed.

Thermalized formulation of soft glassy rheology.

We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully thermal and nearly athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.

Effect of chain stiffness and temperature on the dynamics and microstructure of crystallizable bead-spring polymer melts.

We contrast the dynamics in model unentangled polymer melts of chains of three different stiffnesses: flexible, intermediate, and rodlike. Flexible and rodlike chains, which readily solidify into close-packed crystals (respectively, with randomly oriented and nematically aligned chains), display simple melt dynamics with Arrhenius temperature dependence and a discontinuous change upon solidification. Intermediate-stiffness chains, however, are fragile glass-formers displaying Vogel-Fulcher dynamical arrest, despite the fact that they also possess a nematic-close-packed crystalline ground state. To connect this difference in dynamics to the differing microstructure of the melts, we examine how various measures of structure, including cluster-level metrics recently introduced in studies of colloidal systems, vary with chain stiffness and temperature. No clear static-structural cause of the dynamical arrest is found. However, we find that the intermediate-stiffness chains display qualitatively different dynamical heterogeneity. Specifically, their stringlike motion (cooperative rearrangement) is correlated along chain backbones in a way not found for either flexible or rodlike chains. This activated "crawling" motion is clearly associated with the dynamical arrest observed in these systems, and illustrates one way in which factors controlling the crystallization versus glass formation competition in polymers can depend nonmonotonically on chain stiffness.