Biblioteca Digital

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by [3, 4].; Comment: 21 pages, 15 figures

We investigate the phenomenon of counterion condensation in a solution of highly charged rigid polyelectrolytes within the cell model. A method is proposed which -- based on the charge distribution function -- identifies both the fraction of condensed ions and the radial extension of the condensed layer. Within salt-free Poisson-Boltzmann (PB) theory it reproduces the well known fraction 1-1/xi of condensed ions for a Manning parameter xi>1. Furthermore, it predicts a weak salt dependence of this fraction and a breakdown of the concept of counterion condensation in the high salt limit. We complement our theoretical investigations with molecular dynamics simulations of a cell-like model, which constantly yield a stronger condensation than predicted by PB theory. While the agreement between theory and simulation is excellent in the monovalent, weakly charged case, it deteriorates with increasing electrostatic interaction strength and, in particular, increasing valence. For instance, at a high concentration of divalent salt and large xi our computer simulations predict charge oscillations, which mean-field theory is unable to reproduce.; Comment: 8 pages, 6 figures, using RevTeX style, revised version, 1 figure and more pertinent remarks concerning the failure of the energy criterion

One characteristic feature of soft matter systems is their strong response to external stimuli. As a consequence they are comparatively easily driven out of their ground state and out of equilibrium, which leads to many of their fascinating properties. Here, we review illustrative examples. This review is structured by an increasing distance from the equilibrium ground state. On each level, examples of increasing degree of complexity are considered. In detail, we first consider systems that are quasi-statically tuned or switched to a new state by applying external fields. These are common liquid crystals, liquid crystalline elastomers, or ferrogels and magnetic elastomers. Next, we concentrate on systems steadily driven from outside e.g. by an imposed flow field. In our case, we review the reaction of nematic liquid crystals, of bulk-filling periodically modulated structures such as block copolymers, and of localized vesicular objects to an imposed shear flow. Finally, we focus on systems that are "active" and "self-driven". Here our range spans from idealized self-propelled point particles, via sterically interacting particles like granular hoppers, via microswimmers such as self-phoretically driven artificial Janus particles or biological microorganisms...

The transmission of forces through a disordered granular system is studied by means of a geometrical-topological approach that reduces the granular packing into a set of layers. This layered structure constitutes the skeleton through which the force chains set up. Given the granular packing, and the region where the force is applied, such a skeleton is uniquely defined. Within this framework, we write an equation for the transmission of the vertical forces that can be solved recursively layer by layer. We find that a special class of analytical solutions for this equation are L\'evi-stable distributions. We discuss the link between criticality and fragility and we show how the disordered packing naturally induces the formation of force-chains and arches. We point out that critical regimes, with power law distributions, are associated with the roughness of the topological layers. Whereas, fragility is associated with local changes in the force network induced by local granular rearrangements or by changes in the applied force. The results are compared with recent experimental observations in particulate matter and with computer simulations.; Comment: 14 pages, Latex, 5 EPS figures

We explain in depth the previously proposed theory of the coherent Van der Waals(cVdW) interaction - the counterpart of Van der Waals (VdW) force - emerging in spatially coherently fluctuating electromagnetic fields. We show that cVdW driven matter is dominated by many body interactions, which are significantly stronger than those found in standard Van der Waals (VdW) systems. Remarkably, the leading 2- and 3-body interactions are of the same order with respect to the distance $(\propto R^{-6})$, in contrast to the usually weak VdW 3-body effects ($\propto R^{-9}$). From a microscopic theory we show that the anisotropic cVdW many body interactions drive the formation of low-dimensional structures such as chains, membranes and vesicles with very unusual, non-local properties. In particular, cVdW chains display a logarithmically growing stiffness with the chain length, while cVdW membranes have a bending modulus growing linearly with their size. We argue that the cVdW anisotropic many body forces cause local cohesion but also a negative effective "surface tension". We conclude by deriving the equation of state for cVdW materials and propose new experiments to test the theory, in particular the unusual 3-body nature of cVdW.; Comment: 26 pages...

The surprising recent discoveries of quasicrystals and their approximants in soft matter systems poses the intriguing possibility that these structures can be realized in a broad range of nano- and micro-scale assemblies. It has been theorized that soft matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly-specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity...

We introduce a "Hamiltonian"-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed systems. At the microscopic level, we show that the volume function is the Voronoi volume associated to each particle and in turn we provide an analytical formula for the Voronoi volume in terms of the contact network, valid for any dimension. We then develop a statistical theory for the probability distribution of the volumes in 3d to calculate an average volume function coarse-grained at a mesoscopic level. The salient result is the discovery of a mesoscopic volume function inversely proportional to the coordination number. Our analysis is the first step toward the calculation of macroscopic observables and equations of state using the statistical mechanics of jammed matter, when supplemented by the condition of mechanical equilibrium of jamming that properly defines jammed matter at the ensemble level.; Comment: 23 pages, 8 figures

We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using volume fluctuation analysis and graph theoretical methods. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter. At the mesoscopic level the entropy vanishes at random close packing. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits.; Comment: 5 pages, 1 figure

We introduce and simulate a two dimensional probabilistic model of granular matter at vanishing pressure. The model exhibits a perfectly sharp random loose packing density, a phenomenon that should be verifiable for real granular matter.; Comment: 27 pages, 13 figures. Future versions may be found at: http://www.ma.utexas.edu/users/radin/papers.html

The fast-growing field of soft matter research requires increasingly sophisticated tools for experimental studies. One of the oldest and most widely used tools to study soft matter systems is optical microscopy. Recent advances in optical microscopy techniques have resulted in a vast body of new experimental results and discoveries. New imaging modalities, such as nonlinear optical microscopy techniques that were developed to achieve higher resolution, enable soft matter research at length scales ranging from the molecular to the macroscopic. The aim of this chapter is to introduce a variety of optical microscopy techniques available to soft matter researchers, starting from basic principles and finishing with a discussion of the most advanced microscopy systems. We describe traditional imaging techniques, such as bright field and polarizing microscopy, along with state-of-the-art three-dimensional (3D) imaging techniques, such as fluorescence confocal and nonlinear optical microscopies. Different approaches are discussed along with their applications in the study of soft matter systems by providing typical examples.; Comment: Total 41 pages (double spaced) including 18 figures, Soft Materials book chapter

We numerically examine the transport of active run-and-tumble particles driven with a drift force over random disordered landscapes comprised of fixed obstacles. For increasing run lengths, the net particle transport initially increases before reaching a maximum and decreasing at larger run lengths. The transport reduction is associated with the formation of cluster or living crystal states that become locally jammed or clogged by the obstacles. We also find that the system dynamically jams at lower particle densities when the run length is increased. Our results indicate that there is an optimal activity level for active matter transport through quenched disorder, and could be important for understanding biological transport in complex environments or for applications of active matter particles in random media.; Comment: 7 pages, 6 postscript figures

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schr\"odinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the $s-$wave. The lowest frequency of the collective mode is determined through the Fourier transform of the time dependent solution and its dependences on the number of atoms and the strength of the three-body force are studied. We show that the addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force.; Comment: Contribution to the "Internationl Workshop on Collective Excitations in Fermi and Bose Systems", Serra Negra, Brazil, September 14-17, 1998. To be published by World Scientific, Singapore

Years ago Edwards proposed a thermodynamic description of dense granular matter, in which the grains (the `atoms' of the system) interact with inelastic forces. The approach is intriguing but is not justified from first principles, and hence, in the absence of conclusive tests of its validity, it has not been widely accepted. We perform a numerical experiment with a realistic granular matter model specially conceived to be reproducible in the laboratory. The results strongly support the thermodynamic picture.; Comment: 4 pages, 3 figures

Active systems, or active matter, are self-driven systems which live, or function, far from equilibrium - a paradigmatic example which we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The nonequilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one which has recently been the subject of intense interest among biological and soft matter physicists is that of the so-called "motility-induced phase separation", whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions - we will briefly discuss at the end their role, which is not currently fully understood in this context.; Comment: Contribution to the special issue "Coarsening dynamics"...

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and shown difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the defnition of a volume function dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, that explores states with volume fractions below those achievable by existing simulation protocols...

Phase separation is a fundamental phenomenon that produces spatially heterogeneous patterns in soft matter. In this Lecture Note we show that phase separation in these materials generally belongs to what we call "viscoelastic phase separation", where the morphology is determined by the mechanical balance of not only the thermodynamic force (interface tension) but also the viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry between the components of a mixture, which can be caused by either a size disparity or a difference in the glass transition temperature between the components. We stress that such dynamic asymmetry generally exists in soft matter. The key is that dynamical asymmetry leads to a non-trivial coupling between the concentration, velocity, and stress fields. Viscoelastic phase separation can be explained by viscoelastic relaxation in pattern evolution and the resulting switching of the relevant order parameter, which are induced by the competition between the deformation rate of phase separation and the slowest mechanical relaxation rate of a system. We also discuss an intimate link of viscoelastic phase separation, where deformation fields are spontaneously generated by phase separation itself...

We study theoretically the unzipping of a double stranded DNA from a condensed globule state by an external force. At constant force, we find that the double stranded DNA unzips an at critical force Fc and the number of unzipped monomers M goes as M~(Fc-F)^{-3}, for both the homogeneous and heterogeneous double stranded DNA sequence. This is different from the case of unzipping from an extended coil state in which the number of unzipped monomers M goes as M~(Fc-F)^{-chi}, where the exponent chi is either 1 or 2 depending on whether the double stranded DNA sequence is homogeneous or heterogeneous respectively. In the case of unzipping at constant extension, we find that for a double stranded DNA with a very large number N of base pairs, the force remains almost constant as a function of the extension, before the unraveling transition, at which the force drops abruptly to zero. Right at the unraveling transition, the number of base pairs remaining in the condensed globule state is still very large and goes as N^{3/4}, in agreement with theoretical predictions of the unraveling transition of polymers stretched by an external force.; Comment: 17 pages, 4 figures

A systematic expansion of the many-body master equation for active matter, in which motors power configurational changes as in the cytoskeleton, is shown to yield a description of the steady state and responses in terms of an effective temperature. The effective temperature depends on the susceptibility of the motors and a Peclet number which measures their strength relative to thermal Brownian diffusion. The analytic prediction is shown to agree with previous numerical simulations and experiments. The mapping also establishes a description of aging in active matter that is also kinetically jammed.; Comment: 2 figures

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviours of the mean toroidal and cross sectional radii, $r_c$ and $r_{cross}$, as functions of the contour length L: $(r_c, r_{cross}) \sim L^{\nu(N_c)}$ with $\nu=(1/5, 2/5)$ for the van der Waals type, $\nu=(-1/3, 2/3)$ for the Coulomb type, $\nu=(-1, 1)$ for the delta function type attractions in the asymptotic limit. For the toroids with finite winding number $N_c=100 \sim 400$, we find $\nu \simeq 0$ for the Yukawa interaction with screening parameter $\kappa=0.5 \sim 1.0$, and $\nu=0.1 \sim 0.13$ for the van der Waals type interactions. These findings could provide possible explanation for the experimentally well known observation $\nu \simeq 0$ of the condensed DNA toroids. Conformational transitions are also discussed.; Comment: 5 pages (double column), 1 table and 3 figures (colour)

Recent years have witnessed a great research boom in soft matter physics. by now, most advances, however, are of either empirical results or purely mathematical extensions. The major obstacle is lacking of insights into fundamental phsysical laws underlying fractal mesostructures of soft matter. This study will use fractional mathematics, which consists of fractal, fractional calculus, fractional Brownian motion, and Levy stable distribution, to examine mesoscopic quantum mechanics and time-space structures governing "anomalous" behaviors of soft matter. Our major results include fractional Planck quantum energy relationship, fractional phonon, and time-space scaling transform.; Comment: Welcome comments to chen_wen@iapcm.ac.cn