Local structure controls shear and bulk moduli in disordered solids

This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/srep18724Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.This work was supported by the Theoretical Condensed Matter programme grant from EPSRC. M.S. thanks the Konrad-Adenauer-Stiftung for their financial support

Force network ensemble: a new approach to static granular matter

An ensemble approach for force distributions in static granular packings is developed. This framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. We show how the formalism yields realistic results, both for disordered and regular ``snooker ball'' configurations, and obtain a shear-induced unjamming transition of the type proposed recently for athermal media.Comment: 4 pages, 4 figures, changed conten

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a "frozen" degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi-two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity.A.C. acknowledges support from the ETN-COLLDENSE (H2020-MCSA-ITN-2014, grant no. 642774). E.E. and J. Burelbach thank the Winton Programme for the Physics of Sustainability for the Pump Prime Grant and the scholarship award, respectively. D.J. thanks the Udayan Care-VCare grant, the Nehru Trust for Cambridge University, the Schlumberger Foundation’s Faculty for the Future Program, and Hughes Hall Santander Bursary Scholarship. Z.X. thanks the National University of Defense Technology Scholarship at Cambridge. A.S.N., D.E.P.P., and N.A.M.A. acknowledge financial support from the Portuguese Foundation for Science and Technology (FCT) (grants EXCL/FIS-NAN/ 0083/2012, UID/FIS/00618/2013, and IF/00255/2013). J. Brujic thanks the Materials Research Science and Engineering Center program of the National Science Foundation under Award DMR-1420073 and L. L. Pontani

Force-clamp analysis techniques reveal stretched exponential unfolding kinetics in ubiquitin

Force-clamp spectroscopy reveals the unfolding and disulfide bond rupture times of single protein molecules as a function of the stretching force, point mutations and solvent conditions. The statistics of these times reveal whether the protein domains are independent of one another, the mechanical hierarchy in the polyprotein chain, and the functional form of the probability distribution from which they originate. It is therefore important to use robust statistical tests to decipher the correct theoretical model underlying the process. Here we develop multiple techniques to compare the well-established experimental data set on ubiquitin with existing theoretical models as a case study. We show that robustness against filtering, agreement with a maximum likelihood function that takes into account experimental artifacts, the Kuiper statistic test and alignment with synthetic data all identify the Weibull or stretched exponential distribution as the best fitting model. Our results are inconsistent with recently proposed models of Gaussian disorder in the energy landscape or noise in the applied force as explanations for the observed non-exponential kinetics. Since the physical model in the fit affects the characteristic unfolding time, these results have important implications on our understanding of the biological function of proteins

Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial processing. Previous studies have focused on the global structure of external forces (the boundary condition), and on the probability distribution of individual contact forces. The disordered spatial structure of the force network, however, has remained elusive so far. Here we report evidence for scale invariance of clusters of particles that interact via relatively strong forces. We analyzed granular packings generated by molecular dynamics simulations mimicking real granular matter; despite the visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, and thus determine a universality class. Remarkably, the flat ensemble of force configurations--a simple generalization of equilibrium statistical mechanics--belongs to the same universality class, while some widely studied simplified models do not.Comment: 15 pages, 4 figures; to appear in Natur

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Self-assembly of polysaccharides gives rise to distinct mechanical signatures in marine gels

Marine-gel biopolymers were recently visualized at the molecular level using atomic force microscopy (AFM) to reveal fine fibril-forming networks with low to high degrees of cross-linking. In this work, we use force spectroscopy to quantify the intra- and intermolecular forces within the marine-gel network. Combining force measurements, AFM imaging, and the known chemical composition of marine gels allows us to identify the microscopic origins of distinct mechanical responses. At the single-fibril level, we uncover force-extension curves that resemble those of individual polysaccharide fibrils. They exhibit entropic elasticity followed by extensions associated with chair-to-boat transitions specific to the type of polysaccharide at high forces. Surprisingly, a low degree of cross-linking leads to sawtooth patterns that we attribute to the unraveling of polysaccharide entanglements. At a high degree of cross-linking, we observe force plateaus that arise from unzipping, as well as unwinding, of helical bundles. Finally, the complex 3D network structure gives rise to force staircases of increasing height that correspond to the hierarchical peeling of fibrils away from the junction zones. In addition, we show that these diverse mechanical responses also arise in reconstituted polysaccharide gels, which highlights their dominant role in the mechanical architecture of marine gels