Finite amplitude waves in jammed matter.

Here we use simulations and theory to show that, close to the jamming point, an arbitrary initial distortion of a granular media induces the formation of forward and backward non-linear finite amplitude waves. There are two regimes in the evolution of these waves (near field and far field). Initially, non-linear interactions between forward and backward waves dominate the propagation, leading to complex early evolution (near field). At longer times, forward and backwards waves cease interacting in the far field, and the propagation enters a new regime. Here the waves acquire a triangular-like profile, and evolve in a self-similar fashion characterized by a power law attenuation, whose exponent is weakly dependent on the initial pressure of the system. The finite amplitude waves gradually become linear waves when the amplitude of the initial distortion decreases, or the confining pressure on the system increases.

Macroscopic analogue to entangled polymers.

The entangled structure of polymeric materials is often described as resembling a bowl of spaghetti, swarms of earthworms, or snakes. These analogies not only illustrate the concept, but form the foundation of polymer physics. However, the similarity between these macroscopic, athermal systems and polymers in terms of topology remains uncertain. To better understand this relationship, we conducted an experiment using X-ray tomography to study the structure of arrays of linear rubber bands. We found that, similar to linear polymers, the average number of entanglements increases linearly with the length of the ribbons. Additionally, we observed that entanglements are less frequent near the surface of the container, where there are also more ends, similar to what has been seen in trapped polymers. These findings provide the first experimental evidence supporting the visualization of polymer structures using macroscopic, athermal analogues, confirming the initial intuitive insights of the pioneers of polymer physics.

Shock compression of semiflexible polymers.

We employ molecular dynamics simulations to investigate the shock compression of linear semiflexible polymers. While the propagation velocity of a shock primarily depends on density, both chain rigidity and chain orientation significantly influence the shock width and the final temperature of the system. In general, the shock wave triggers molecular buckling in chains oriented perpendicular to the compression front. Following the passage of the front, the semiflexible chains buckle with a wavelength that decreases with the compression speed as λm ∼ up-0.2, and subsequent relaxation leads to a banana-like liquid crystal phase. In ordered systems with molecules oriented perpendicular to the compression front, the shock width increases by a factor of up to 10 compared to a similar isotropic system, resulting in enhanced shock energy absorption. These findings indicate that chain stiffness plays a critical role in the impact absorption properties of polymeric materials.

Packing structure of semiflexible rings.

Unraveling the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings, but also key to understand biopackaging, such as observed in circular DNA of viruses or genome folding. Here we use X-ray tomography to study the geometrical and topological features of disordered packings of rubber bands in a cylindrical container. Assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, and reveal only minor influence of the container. In the case of longer bands, the confinement causes folded configurations and the bands interpenetrate and entangle. Most of the systems are found to display a threading network which percolates the system. Surprisingly, for long bands whose diameter is more than twice the diameter of the container, we found that all bands interpenetrate each other, in a complex fully entangled structure.

Curvature as a Guiding Field for Patterns in Thin Block Copolymer Films.

Experimental data on thin films of cylinder-forming block copolymers (BC)-free-standing BC membranes as well as supported BC films-strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free-standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.

Smectic block copolymer thin films on corrugated substrates.

In this work we study equilibrium and non-equilibrium structures of smectic block copolymer thin films deposited on a topographically patterned substrate. A Brazovskii free energy model is employed to analyze the coupling between the smectic texture and the local mean curvature of the substrate. The substrate's curvature produces out-of-plane deformations of the block copolymer such that equilibrium textures are modified and dictated by the underlying geometry. For weak curvatures it is shown that the free energy of the block copolymer film follows a Helfrich form, scaling with the square of the mean curvature, with a bending constant dependent on the local pattern orientation. On substrates of varying mean curvature simulations show that topological defects are rapidly expelled from regions with large curvature. These results compare well with available experimental data of poly(styrene)-co-poly(ethylene-alt-propylene) smectic thin films.

Defect formation and coarsening in hexagonal 2D curved crystals.

In this work we study the processes of defect formation and coarsening of two-dimensional (2D) curved crystal structures. These processes are found to strongly deviate from their counterparts in flat systems. In curved backgrounds the process of defect formation is deeply affected by the curvature, and at the onset of a phase transition the early density of defects becomes highly inhomogeneous. We observe that even a single growing crystal can produce varying densities of defects depending on its initial position and local orientation with regard to the substrate. This process is completely different from flat space, where grain boundaries are formed due to the impingement of different propagating crystals. Quenching the liquid into the crystal phase leads to the formation of a curved polycrystalline structure, characterized by complex arrays of defects. During annealing, mechanisms of geodesic curvature-driven grain boundary motion and defect annihilation lead to increasing crystalline order. Linear arrays of defects diffuse to regions of high curvature, where they are absorbed by disclinations. At the early stage of coarsening the density of dislocations is insensitive to the geometry while the population of isolated disclinations is deeply affected by curvature. The regions with high curvature act as traps for the diffusion of different structures of defects, including disclinations and domain walls.

A device for studying fluid-induced cracks under mixed-mode loading conditions using x-ray tomography.

We introduce an innovative instrument designed to investigate fluid-induced fractures under mixed loading conditions, including uniaxial tension and shear stress, in gels and similar soft materials. Equipped with sensors for measuring force, torque, and fluid pressure, the device is tailored for compatibility with x-ray tomography scanners, enabling non-invasive 3D analysis of crack geometries. To showcase its capabilities, we conducted a study examining crack-front segmentation in a hydrogel subjected to air pressure and a combination of tension and shear stress.

Shocks near jamming.

Nonlinear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.

Two-dimensional crystalization on spheres: Crystals grow cracked.

Here we study how curvature affects the structure of two-dimensional crystals growing on spheres. The mechanism of crystal growth is described by means of a Landau model in curved space that accounts for the excess of strain on crystal bonds caused by the substrate's curvature (packing frustration). In curved space elastic energy penalization strongly dictates the geometry of growing crystals. While compact faceted crystals are observed when elastic energy contribution can be neglected, cracked crystals with ribbonlike forms appear as the main mechanisms to reduce elastic frustration for highly curved systems.

Shock melting of lamellae-forming block copolymers.

While the propagation of shocks through monoatomic liquids and solids is now well understood, the response of macromolecular systems to shock compression remains far less studied. Here we use molecular dynamics simulations to study the shock compression of diblock copolymers assembled in a lamellae morphology, which may display outstanding ballistic performance. For the first time, we show that the morphologies observed after the passage of the shock resemble those observed at equilibrium, at a temperature dictated by the compression velocity. In copolymers, shock compression leads to a decrease in the lamellae period, favoring the mixing of the polymer blocks, such that strongly segregated initial morphologies evolve into less segregated phases after the passage of the shock, or can even melt into an isotropic phase for strong shocks.

Velocity distributions in a gas-gun microparticle accelerator.

Here, we build and characterize a single-stage gas-gun microparticle accelerator, where a pressurized gas expands and launches particles on a target. The microparticles in the range of 60-250 µm are accelerated by the expansion of pressurized nitrogen. By using a high-speed camera, we study how the velocity distribution of accelerated particles is modified by particle size, pressure in the gas reservoir, valve's opening time, and diaphragm's thickness and composition. We employ this microparticle accelerator to study the impact of glass particles with diameters of (69 ± 6) µm accelerated at moderate velocities ∼ (10-25) m/s, using films of poly-dimethylsiloxane as targets.

Relaxational dynamics of smectic phases on a curved substrate.

We study the dynamics of pattern formation of two-dimensional smectic systems constrained to lie on a substrate with sinusoidal topography. We observe a coupling between defects and geometry that induces the preferential location of positive (negative) defects onto regions with positive (negative) Gaussian curvature. For the curvatures studied here we observe unbinding and self-organization of disclination pairs. The local orientation of the pattern and the location of topological defects can be accurately controlled with the curvature of the underlying substrate. Thus, long-range interactions arising from the geometry of the substrate lead to ordered patterns with potential applications to nanotechnology.

Spinodal-assisted nucleation during symmetry-breaking phase transitions.

The kinetics of spinodal-assisted crystallization in a region of the phase diagram where the dynamics is controlled by the critical slow down was studied by means of a Cahn-Hilliard model. The length-scale selectivity conducted by the spinodal process led to the formation of a filamentary network of density fluctuations that resemble the scarred states found in quantum-chaos systems. The present work reveals that the early structure of density fluctuations acts such as a precursor for crystallization and deeply affects the orientational and translational correlation between growing crystals. At deep quenches the network of fluctuations is deeply modified and the classical picture of spinodal decomposition is recovered.

Thermal properties of vortices on curved surfaces.

We use Monte Carlo simulations to study the finite temperature behavior of vortices in the XY model for tangent vector order on curved backgrounds. Contrary to naive expectations, we show that the underlying geometry does not affect the proliferation of vortices with temperature respect to what is observed on a flat surface. Long-range order in these systems is analyzed by using two-point correlation functions. As expected, in the case of slightly curved substrates these correlations behave similarly to the plane. However, for high curvatures, the presence of geometry-induced unbounded vortices at low temperatures produces the rapid decay of correlations and an apparent lack of long-range order. Our results shed light on the finite-temperature physics of soft-matter systems and anisotropic magnets deposited on curved substrates.

Phase nucleation in curved space.

Nucleation and growth is the dominant relaxation mechanism driving first-order phase transitions. In two-dimensional flat systems, nucleation has been applied to a wide range of problems in physics, chemistry and biology. Here we study nucleation and growth of two-dimensional phases lying on curved surfaces and show that curvature modifies both critical sizes of nuclei and paths towards the equilibrium phase. In curved space, nucleation and growth becomes inherently inhomogeneous and critical nuclei form faster on regions of positive Gaussian curvature. Substrates of varying shape display complex energy landscapes with several geometry-induced local minima, where initially propagating nuclei become stabilized and trapped by the underlying curvature.

Crystallization dynamics on curved surfaces.

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassylike ordering dynamics may completely inhibit the appearance of the ground-state structures.

Uniform shock waves in disordered granular matter.

The confining pressure P is perhaps the most important parameter controlling the properties of granular matter. Strongly compressed granular media are, in many respects, simple solids in which elastic perturbations travel as ordinary phonons. However, the speed of sound in granular aggregates continuously decreases as the confining pressure decreases, completely vanishing at the jamming-unjamming transition. This anomalous behavior suggests that the transport of energy at low pressures should not be dominated by phonons. In this work we use simulations and theory to show how the response of granular systems becomes increasingly nonlinear as pressure decreases. In the low-pressure regime the elastic energy is found to be mainly transported through nonlinear waves and shocks. We numerically characterize the propagation speed, shape, and stability of these shocks and model the dependence of the shock speed on pressure and impact intensity by a simple analytical approach.

Amorphous precursors of crystallization during spinodal decomposition.

A general Landau's free energy functional is used to study the dynamics of crystallization during liquid-solid spinodal decomposition (SD). The strong length scale selectivity imposed during the early stage of SD induces the appearance of small precursors for crystallization with icosahedral order. These precursors grow in densely packed clusters of tetrahedra through the addition of new particles. As the average size of the amorphous nuclei becomes large enough to reduce geometric frustration, crystalline particles with a body-centered cubic symmetry heterogeneously nucleate on the growing clusters. The volume fraction of the crystalline phase is strongly dependent on the depth of quench. At deep quenches, the SD mechanism produces amorphous structures arranged in dense polytetrahedral aggregates.

Lifshitz-Safran coarsening dynamics in a 2D hexagonal system.

The coarsening process in a two-dimensional hexagonal system in the region close to both spinodal and order-order transitions was investigated through the Cahn-Hilliard model. We found a distinctive region of the phase diagram where the pinning of dislocations plays only a minor role and the dynamics is led by the triple points. In this region, we found configurations of domains with the same features as those proposed by Lifshitz. As a consequence, different correlation lengths grow logarithmically in time, in good agreement with the predictions of coarsening at low temperatures proposed by Safran.