System Of Hard Particles Research Articles

Modelling human behaviour in a bumper car ride using molecular dynamics tools: a student project

Amusement parks are excellent laboratories of physics, not only to check physical laws, but also to investigate if those physical laws might also be applied to human behaviour. A group of Physics Engineering students from Universitat Politècnica de Catalunya has investigated if human behaviour, when driving bumper cars, can be modelled using tools borrowed from the analysis of molecular dynamics simulations, such as the radial and angular distribution functions. After acquiring several clips and obtaining the coordinates of the cars, those magnitudes are computed and analysed. Additionally, an analogous hard disks system is simulated to compare its distribution functions to those obtained from the cars’ coordinates. Despite the clear difference between bumper cars and a hard disk-like particle system, the obtained distribution functions are very similar. This suggests that there is no important effect of the individuals in the collective behaviour of the system in terms of structure. The research, performed by the students, has been undertaken in the frame of a motivational project designed to approach the scientific method for university students named FISIDABO. This project offers both the logistical and technical support to undertake the experiments designed by students at the amusement park of Barcelona TIBIDABO and accompanies them all along the scientific process.

Static structural signatures of nearly jammed disordered and ordered hard-sphere packings: Direct correlation function.

The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed "hyperuniformity") has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function c(r), rather than the total correlation function h(r), diverges. We expand on the notion that c(r) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the nth derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c(r) with regards to singularities it inherits from h(r). These relations provide a concrete means of identifying features that must be expressed in c(r) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c(r)∝-1/r as r→0 that accompanies the formation of the delta function at c(D) that indicates the formation of contacts in all cases, and show that this scaling behavior is, in this case, a consequence of the growing long rangedness in c(r), e.g., c∝-1/r^{2} as r→∞ for disordered packings. At densities in the vicinity of the freezing density, we find striking qualitative differences in the structure factor S(k) as well as c(r) between TJ- and LS-generated configurations, including the early formation of a delta function at c(D) in the TJ algorithm's packings, indicating the early formation of clusters of particles in near contact. Both algorithms yield structure factors that tend towards zero in the low-wave-number limit as jamming is approached. Correspondingly, we observe the expected power-law decay in c(r) for large r, in agreement with previous theoretical work. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a sensitive means of monitoring for the appearance of an incipient rigid network.

Lock-and-key dimerization in dense Brownian systems of hard annular sector particles.

We develop a translational-rotational cage model that describes the behavior of dense two-dimensional (2D) Brownian systems of hard annular sector particles (ASPs), resembling C shapes. At high particle densities, pairs of ASPs can form mutually interdigitating lock-and-key dimers. This cage model considers either one or two mobile central ASPs which can translate and rotate within a static cage of surrounding ASPs that mimics the system's average local structure and density. By comparing with recent measurements made on dispersions of microscale lithographic ASPs [P. Y. Wang and T. G. Mason, J. Am. Chem. Soc. 137, 15308 (2015)JACSAT0002-786310.1021/jacs.5b10549], we show that mobile two-particle predictions of the probability of dimerization P_{dimer}, equilibrium constant K, and 2D osmotic pressure Π_{2D} as a function of the particle area fraction ϕ_{A} correspond closely to these experiments. By contrast, predictions based on only a single mobile particle do not agree well with either the two-particle predictions or the experimental data. Thus, we show that collective entropy can play an essential role in the behavior of dense Brownian systems composed of nontrivial hard shapes, such as ASPs.

Structural entropy of glassy systems from graph isomorphism.

Configurational entropy plays a central role in thermodynamic scenarios of the glass transition. As a measure of the number of basins in the potential energy landscape, configurational entropy for a glass-forming liquid can be evaluated by explicitly counting distinct inherent structures. In this work, we propose a graph-theory based method to examine local structure and obtain the corresponding entropy of hard-particle systems. Voronoi diagrams of associated clusters are classified using a graph isomorphism algorithm. The statistics of these clusters reveal structural motifs such as icosahedron-like order, and also allow us to calculate the structural entropy SG. We find the structural entropy of an n-particle subsystem grows linearly with n. Thus the structural entropy per particle can be obtained from the slope dSG/dn. Our results are consistent with previous values for configurational entropy obtained via thermodynamic integration. Structural entropies per particle are measured for hard-disk and hard-sphere polydisperse systems, and extrapolated for monodisperse hard disks, all of which are nonzero at the dynamic glass transition.

Hard convex lens-shaped particles: Densest-known packings and phase behavior.

By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similarity of their shape to that of hard oblate ellipsoids is reflected in a qualitatively similar phase diagram, differences are more pronounced in the high-density crystal phase up to the densest-known packings determined here. In contrast to those non-(Bravais)-lattice two-particle basis crystals that are the densest-known packings of hard (oblate) ellipsoids, hard convex lens-shaped particles pack more densely in two types of degenerate crystalline structures: (i) non-(Bravais)-lattice two-particle basis body-centered-orthorhombic-like crystals and (ii) (Bravais) lattice monoclinic crystals. By stacking at will, regularly or irregularly, laminae of these two crystals, infinitely degenerate, generally non-periodic in the stacking direction, dense packings can be constructed that are consistent with recent organizing principles. While deferring the assessment of which of these dense ordered structures is thermodynamically stable in the high-density crystalline solid regime, the degeneracy of their densest-known packings strongly suggests that colloidal convex lens-shaped particles could be better glass formers than colloidal spheres because of the additional rotational degrees of freedom.

Dynamical phase transitions in one-dimensional hard-particle systems

We analyze a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyze two phenomena that are associated with these large deviations of the activity: phase separation (at low activity) and the formation of hyperuniform states (at high activity). We consider a version of the model which operates at constant volume, and a version at constant pressure. In these nonequilibrium systems, differences arise between the two ensembles, because of the extra freedom available to the constant-pressure system, which can change its total density. We discuss the relationships between different ensembles, mechanical equilibrium, and the probability cost of rare density fluctuations.

A comparison of automated scanning electron microscopy (ASEM) and acoustic attenuation spectroscopy (AAS) instruments for particle sizing

The objective of this work is to compare particle size distributions (PSD) measured by automated scanning electron microscopy (ASEM) and acoustic attenuation spectroscopy (AAS) instruments at Oklahoma State University (OSU). The techniques provide quantitative PSD measurements of dispersed systems of both hard and soft particles. Glass spheres, fly ash, and latex spheres are chosen to illustrate the range of materials that can be analyzed with these techniques. The variety of length scales and material property attributes investigated provides some insight about the consistency of the ASEM and AAS measurements for these types of particles. Although both instruments yield internally consistent PSD, rigorous statistical analysis shows that the two instruments can yield different results when measuring samples from the same batch of particles. The difference is not surprising given the different physics of each instrument. Nevertheless, the similarity in PSD hints at the validity of comparing absolute PSD and PSD changes.

Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems.

We analyze biased ensembles of trajectories for diffusive systems. In trajectories biased either by the total activity or the total current, we use fluctuating hydrodynamics to show that these systems exhibit phase transitions into "hyperuniform" states, where large-wavelength density fluctuations are strongly suppressed. We illustrate this behavior numerically for a system of hard particles in one dimension and we discuss how it appears in simple exclusion processes. We argue that these diffusive systems generically respond very strongly to any nonzero bias, so that homogeneous states with "normal" fluctuations (finite compressibility) exist only when the bias is very weak.

Superadiabatic Forces in Brownian Many-Body Dynamics

Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces. Application of the method to a system of one-dimensional hard particles reveals the importance for the dynamics, as well as the complexity, of these nontrivial out-of-equilibrium contributions. Our findings help clarify the status of dynamical density functional theory and provide a rational basis for the development of improved theories.

Memory effect in uniformly heated granular gases.

We evidence a Kovacs-like memory effect in a uniformly driven granular gas. A system of inelastic hard particles, in the low density limit, can reach a nonequilibrium steady state when properly forced. By following a certain protocol for the drive time dependence, we prepare the gas in a state where the granular temperature coincides with its long time value. The temperature subsequently does not remain constant but exhibits a nonmonotonic evolution with either a maximum or a minimum, depending on the dissipation and on the protocol. We present a theoretical analysis of this memory effect at Boltzmann-Fokker-Planck equation level and show that when dissipation exceeds a threshold, the response can be called anomalous. We find excellent agreement between the analytical predictions and direct Monte Carlo simulations.

Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

Numerous recent investigations have been devoted to the determination of the equilibrium phase behavior and packing characteristics of hard nonspherical particles, including ellipsoids, superballs, and polyhedra, to name but just a few shapes. Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities, verifying the result of a previous qualitative study [ J. Chem. Phys. 2011 , 135 , 151101 ]. The freezing- and melting-point packing fractions for this transition are respectively ϕF = 0.496 ± 0.006 and ϕM = 0.591 ± 0.005. At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal, with coexistence densities in the range ϕ ∈ [0.780 ± 0.002, 0.802 ± 0.003]. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. Specifically, we systematically study the structural characteristics of the MRJ packings, including the centroidal pair correlation function, structure factor and orientational pair correlation function. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (≈ 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers.

Communication: From rods to helices: Evidence of a screw-like nematic phase

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C2 symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry, Z. Hensel, Z. Dogic, M. Shribak, and R. Oldenbourg, Phys. Rev. Lett. 96, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.

Emergent Collective Phenomena in a Mixture of Hard Shapes through Active Rotation

We investigate collective phenomena with rotationally driven spinners of concave shape. Each spinner experiences a constant internal torque in either a clockwise or counterclockwise direction. Although the spinners are modeled as hard, otherwise noninteracting rigid bodies, their active motion induces an effective interaction that favors rotation in the same direction. With increasing density and activity, phase separation occurs via spinodal decomposition, as well as self-organization into rotating crystals. We observe the emergence of cooperative, superdiffusive motion along interfaces, which can transport inactive test particles. Our results demonstrate novel phase behavior of actively rotated particles that is not possible with linear propulsion or in nondriven, equilibrium systems of identical hard particles.

Pushing the glass transition towards random close packing using self-propelled hard spheres

Although the concept of random close packing with an almost universal packing fraction of approximately 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest packing is that states with packing fractions beyond the glass transition at approximately 0.58 are inherently non-equilibrium systems, where the dynamics slows down with a structural relaxation time diverging with density; hence, the random close packing is inaccessible. Here we perform simulations of self-propelled hard spheres, and we find that with increasing activity the relaxation dynamics can be sped up by orders of magnitude. The glass transition shifts to higher packing fractions upon increasing the activity, allowing the study of sphere packings with fluid-like dynamics at packing fractions close to RCP. Our study opens new possibilities of investigating dense packings and the glass transition in systems of hard particles.

Liquid crystalline and solid phases for a system of hard zigzag particles with Lennard-Jones sites in two-dimensions

The map of low and high density phases of an idealized system, the infinitely hard zigzag line model with two Lennard-Jones (LJ) sites is presented. LJ sites are added to a previous model composed of the infinitely hard zigzag line shape particles, R.A. Perusqía, J. Peón, J. Quintana, Physica A 345 (1) (2005) 130–142. The attractions and the molecular volume added to this system through the LJ sites create a more realistic model and, as a consequence, a richer phase behavior is obtained. Although the volume of the LJ sites is quite small it is enough to produce solid phases, absent in the original model. On the other hand the smectic phase that was present in the hard system was not found in this case. Two molecular conformations are chosen to provide a comparison with the previous model. The isothermal–isobaric is used to establish the thermodynamic regions of the different molecular self aggregations and to compare them to already published results.

The isotropic-to-nematic phase transition in hard helices: Theory and simulation

We investigate the isotropic-to-nematic phase transition in systems of hard helical particles, using Onsager theory and Monte Carlo computer simulations. Motivation of this work resides in the ubiquity of the helical shape motif in many natural and synthetic polymers, as well as in the well known importance that the details of size and shape have in determining the phase behaviour and properties of (soft) condensed matter systems. We discuss the differences with the corresponding spherocylinder phase diagram and find that the helix parameters affect the phase behaviour and the existence of the nematic phase. We find that for high helicity Onsager theory significantly departs from numerical simulations even when a modified form of the Parsons-Lee rescaling is included to account for the non-convexity of particles.

A Counterexample Concerning to the Phase Space Multi-Histogram Method

The phase space multi-histogram method is a new technique to study phase transitions in hard particle systems. The method constrains the phase space using a Monte Carlo approach by smoothly varying a potential between the ideal gas and the hard particle limit. Using a small sphere system, we give an example of computing chemical potential at the liquid state. However, we find that the method fails for a dense sphere system at the coexisting liquid-solid state. We conclude that the method is appropriate for dilute hard particle systems, but it fails when the volume fraction of the system is too high.

Communication: Fundamental measure theory for hard disks: Fluid and solid

Two-dimensional hard-particle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semi-quantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for two-dimensional hard-disk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional.

Computing Chemical Potential Using the Phase Space Multi-Histogram Method

We present a new simulation method to calculate the free energy and the chemical potential of hard particle systems. The method relies on the introduction of a parameter dependent potential to smoothly transform between the hard particle system and the corresponding ideal gas. We applied the method to study the phase transition behavior of monodispersed infinitely thin square platelets. First, we equilibrated the square platelet system for different reduced pressures with a usual isobaric Monte Carlo (MC) simulation and obtained a reduced pressure-chemical potential plot. Then we introduce the parametrized potential to interpolate the system between the ideal gas and the hard particles. After selecting the potential, we performed isochoric MC runs, ranging from the ideal gas to the hard particle limit. Through an iterative procedure, we compute the free energy and the chemical potential of the square platelet system by evaluating the volume of the phase space attributed to the hard particles, and then we find the coexistence pressure of the system. Our method provides an intuitive approach to investigate the phase transitions of hard particle systems.

Effect of bond and asymmetry of 2D-dumbbells on their structure in high concentration regime

Particle shape is one of the major parameters governing the structure in hard-particle systems. A 2D-dumbbell, which consists of a pair of binary disks connected to each other, has two geometrical characteristics: the existence of a bond and asymmetry due to a size difference. We investigate the effects of the geometry of 2D-dumbbells on the packing structure at an air–water interface under short-range attractions, varying the area fraction φ of the particles. We observe that although the systems at low φ exhibit the characteristic structure of attractive particle systems, the short-range attraction between the particles due to capillary interaction does not affect the local structure at the maximally random jammed (MRJ) packing fraction. We investigate the influence of a rigid bond on the packing structure by comparing 2D-dumbbell systems with binary-disk systems; we also investigate the effects of asymmetry by controlling the diameter ratio (γ) of the small and large disks of the dumbbell. First, we find that the existence of a bond restricts local segregations between similar kinds of disks, so that phase-separated glass states are forbidden, contrary to the case of binary-disk systems. Second, we observe that varying γ causes a structural order–disorder–order change at high φ. While the crystalline structures of disks (γ = 0) and symmetric dimers (γ = 1) are similar in local contacting and ordering behaviors despite their shape differences, the amorphous structures of asymmetric dimers (γ = 0.3, 0.5, and 0.7) exhibit distinct features depending on γ.