arXiv subjects

Robert S. Hoy

Publications and source records attributed to Robert S. Hoy.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2018

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.

cond-mat.soft↗

arXiv2018

From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters

A relation $\mathcal{M}_{\mathrm{SHS}\to\mathrm{LJ}}$ between the set of non-isomorphic sticky hard sphere clusters $\mathcal{M}_\mathrm{SHS}$ and the sets of local energy minima $\mathcal{M}_{LJ}$ of the $(m,n)$-Lennard-Jones potential $V^\mathrm{LJ}_{mn}(r) = \frac{\varepsilon}{n-m} [ m r^{-n} - n r^{-m} ]$ 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 $N \gtrsim 10$. While the map from $\mathcal{M}_\mathrm{SHS}\to \mathcal{M}_{\mathrm{SHS}\to\mathrm{LJ}}$ is non-injective and non-surjective, 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 unfavourable 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.

physics.atm-clus↗

arXiv2017

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.

cond-mat.soft↗

arXiv2017

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 dependence of the average coordination number at solidification $Z(T_s)$ on chains' characteristic ratio $C_\infty$ has the same functional form [$Z \simeq a - b\ln(C_\infty)$] as the dependence of the average coordination number at jamming $Z(ϕ_J)$ on $C_\infty$ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification.

cond-mat.soft↗

arXiv2016

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-rod-like chains ($θ_0 = 0$), and increases monotonically with increasing $θ_0 \leq π/2$. 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 3-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.

cond-mat.soft↗

arXiv2016

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

We constrast 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 correlated motion (cooperative rearrangement) is correlated along chain backbones in a way not found for either flexible or rodlike chains. This activated "crawling" motion seems to be the cause of the dynamical arrest observed for these systems, and shows that the factors controlling the crystallization vs.\ glass formation competition in polymers likely depend nonmonotonically on chain stiffness.

cond-mat.soft↗

arXiv2015

Effect of chain stiffness on the competition between crystallization and glass-formation in model colloidal polymers

We map out the solid-state morphologies formed by model soft-pearl-necklace polymers as a function of bending stiffness $k_b$ spanning the range from fully flexible to rodlike chains. The ratio of Kuhn length to bead diameter ($l_K/r_0$) increases monotonically with increasing $k_b$ and yields a one-parameter model that relates chain shape to bulk morphology and yields insights into the packing of anisotropic particles. In the flexible limit, monomers occupy the sites of close-packed crystallites while chains retain random-walk-like order. In the rodlike limit, nematic chain ordering typical of lamellar precursors coexists with close-packing. At intermediate values of bending stiffness the competition between random-walk-like and nematic chain ordering produces glass-formation; the range of $k_b$ over which this occurs increases with the thermal cooling rate $|\dot{T}|$ implemented in our molecular dynamics simulations. Finally, values of $k_b$ between the glass-forming and rodlike ranges produce complex ordered phases such as close-packed spirals. Our results should prove useful for rational design of dense colloidal-polymer phases with desired morphologies.

cond-mat.soft↗

arXiv2015

Structure and dynamics of model colloidal clusters with short-range attractions

We examine the structure and dynamics of small isolated $N$-particle clusters interacting via short-ranged Morse potentials. "Ideally preprared ensembles" obtained via exact enumeration studies of sticky hard sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates $\dot{T}$ differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrival temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed $T$ and a variety of nonequilibrium phenomena.

cond-mat.soft↗

arXiv2013

Nonlinear mechanics of thermoreversibly associating dendrimer glasses

We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work-to-fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, "strong, slow" SBs optimize strength, while "weak, fast" SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner-switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.

cond-mat.soft↗

arXiv2013

Simple crystallizable bead-spring polymer model

We develop a simple coarse-grained bead-spring polymer model exhibiting competing crystallization and glass transitions. For quench rates slower than the critical nucleation rate $|\dot{T}|_{crit}$, systems exhibit a first-order crystallization transition below a critical temperature $T=T_{cryst}$. Such systems form close-packed crystallites of FCC and/or HCP order, separated by domain walls, twin defects, and an amorphous interphase. The size of amorphous regions grows continuously as the quench rate $|\dot{T}|$ increases, producing nearly amorphous structure for $|\dot{T}|>|\dot{T}|_{crit}$. Our model exhibits many features observed in recent studies of crystallization of athermal polymer packings, but also critical differences arising from the softness of the pair interactions and the thermal nature of the phase transition. The model is considerably more computationally efficient than other recent crystallizable coarse-grained polymer models; while it sacrifices some features of real semicrystalline polymers (such as lamellar structure and chain disentanglement), we anticipate that it will serve as a useful model for studying generic features related to semicrystalline order in polymer solids.

cond-mat.soft↗

arXiv2013

Particle-scale reversibility in athermal particulate media below jamming

We perform numerical simulations of athermal repulsive frictionless disks and spheres in two and three spatial dimensions undergoing cyclic quasi-static simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction ϕand maximum strain amplitude per cycle γ_{\rm max}. Point-reversible states, where particles do not collide and exactly retrace their intra-cycle trajectories, occur at low ϕand γ_{\rm max}. Particles in loop-reversible states undergo numerous collisions and execute complex trajectories, but return to their initial positions at the end of each cycle. Loop-reversible dynamics represents a novel form of self-organization that enables reliable preparation of configurations with specified structural and mechanical properties over a broad range of ϕfrom contact percolation to jamming onset at ϕ_J. For sufficiently large ϕand γ_{\rm max}, systems display irreversible dynamics with nonzero self-diffusion.

cond-mat.soft↗

arXiv2013

Minimal energy packings of nearly flexible polymers

We extend recent studies of the minimal energy packings of short flexible polymers with hard-core-like repulsions and short-range attractions to include bond-angle interactions with the aim of describing the collapsed conformations of `colloidal' polymers. We find that flexible tangent sticky-hard-sphere (t-SHS) packings provide a useful perturbative basis for analyzing polymer packings with nonzero bending stiffness only for {\it small} ratios of the stiffnesses for the bond-angle ($k_b$) and pair ($k_c$) interactions, i.e. $k_b^{\rm crit}/k_c \lesssim 0.01$ for $N<10$ monomers, and the critical ratio decreases with $N$. Below $k_b^{crit}$, angular interactions give rise to an exponential (in $N$) increase in the number of distinct angular energies arising from the diversity of covalent backbone paths through t-SHS packings. As $k_b$ increases above $k_b^{crit}$, the low-lying energy landscape changes dramatically as finite bending stiffness alters the structure of the polymer packings. This study lays the groundwork for exact-enumeration studies of the collapsed states of t-SHS-like models with larger bending stiffness.

cond-mat.soft↗

arXiv2012

Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction $f$ of nuclei with order compatible with the bulk (RHCP) crystal decreases sharply with increasing $N$ due to a high propensity for stacking faults, 5- and near-5-fold symmetric structures, and other motifs that preclude RHCP order. While $f$ increases with increasing $H$, a significant fraction of hyperstatic nuclei for $N$ as small as 11 retain non-RHCP structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of $N\lesssim 10$ particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.

cond-mat.soft↗

arXiv2011

Glassy dynamics of crystallite formation: The role of covalent bonds

We examine nonequilibrium features of collapse behavior in model polymers with competing crystallization and glass transitions using extensive molecular dynamics simulations. By comparing to "colloidal" systems with no covalent bonds but the same non-bonded interactions, we find three principal results: (i) Tangent-sphere polymers and colloids, in the equilibrium-crystallite phase, have nearly identical static properties when the temperature T is scaled by the crystallization temperature T_{cryst}; (ii) Qualitative features of nonequilibrium relaxation below T_{cryst}, measured by the evolution of local structural properties (such as the number of contacts) toward equilibrium crystallites, are the same for polymers and colloids; and (iii) Significant quantitative differences in rearrangements in polymeric and colloidal crystallites, in both far-from equilibrium and near-equilibrium systems, can be understood in terms of chain connectivity. These results have important implications for understanding slow relaxation processes in collapsed polymers, partially folded, misfolded, and intrinsically disordered proteins.

cond-mat.soft↗

arXiv2011

Why is Understanding Glassy Polymer Mechanics So Difficult?

In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled vs. well-entangled systems and (ii) melts vs. glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary vs. binary and (iv) cooperative vs. nonccoperative relaxation dynamics. I discuss the applicability of (iii-iv) to understanding the functional form of glassy strain hardening. Results from molecular dynamics simulations show that the "dramatic" strain hardening observed in densely entangled systems is associated with a crossover from unary, noncooperative to binary, cooperative relaxation as strain increases; chains stretch between entanglement points, altering the character of local plasticity. Promising approaches for future research along these lines are discussed.

cond-mat.soft↗

arXiv2010

Minimal energy packings and collapse of sticky tangent hard-sphere polymers

We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions, and compare them to corresponding results for monomer packings. We define and identify ``dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry over high and low symmetries. We also examine the packing-preparation dependence for longer single chains using molecular dynamics simulations. For slow temperature quenches, chains form crystallites with close-packed cores. As quench rate increases, the core size decreases and the exterior becomes more disordered. By examining the contact number, we connect suppression of crystallization to the onset of isostaticity in disordered packings. These studies represent a significant step forward in our ability to predict how the structural and mechanical properties of compact polymers depend on collapse dynamics.

cond-mat.soft↗

arXiv2010

Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening

A simple theory for glassy polymeric mechanical response which accounts for large scale chain relaxation is presented. It captures the crossover from perfect-plastic response to strong strain hardening as the degree of polymerization $N$ increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain activated relaxation arising from the need to maintain constant chain contour length reduces the $N$ dependence of the characteristic relaxation time by a factor $\sim \dotεN$ during active deformation at strain rate $\dotε$. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.

cond-mat.soft↗