Glasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here.

Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic model in the mean-field limit of infinite spatial dimension, and numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner and jamming transitions. Comparing meanfield predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.

This article describes how the dimensions of nanowires affect the transmittance and sheet resistance of a random nanowire network. Silver nanowires with independently controlled lengths and diameters were synthesized with a gram-scale polyol synthesis by controlling the reaction temperature and time. Characterization of films composed of nanowires of different lengths but the same diameter enabled the quantification of the effect of length on the conductance and transmittance of silver nanowire films. Finite-difference time-domain calculations were used to determine the effect of nanowire diameter, overlap, and hole size on the transmittance of a nanowire network. For individual nanowires with diameters greater than 50 nm, increasing diameter increases the electrical conductance to optical extinction ratio, but the opposite is true for nanowires with diameters less than this size. Calculations and experimental data show that for a random network of nanowires, decreasing nanowire diameter increases the number density of nanowires at a given transmittance, leading to improved connectivity and conductivity at high transmittance (>90%). This information will facilitate the design of transparent, conducting nanowire films for flexible displays, organic light emitting diodes and thin-film solar cells.Indium tin oxide (ITO) is the material of choice for transparent conducting films in flat-panel displays, organic solar cells, and organic light emitting diodes because, with a sheet resistance of 10 U sq À1 at a transmittance of 90% (l ¼ 550 nm), it is highly conductive and transparent. However, indium is a scarce element, ITO is brittle, and ITO film is expensive because it is produced with a vapor-phase coating process that is 1000 times slower than newspaper printing.1,2 These problems have motivated a search for alternatives to ITO that are flexible and can be deposited from liquids at high coating rates.3-9 As discussed in recent reviews, promising solution-processed alternatives to ITO include poly(3,4-ethylenedioxythiophene)poly(styrenesulfonate), carbon nanotubes, graphene, ITO nanowires, and metal nanowires.10-15 Of these alternatives, films of silver nanowires currently have the highest conductance and transmittance. 4,16-18For example, Leem et al. have recently reported obtaining silver nanowire films with a sheet resistance of 10 U sq À1 at a transmittance of 89.3% (l ¼ 550 nm), nearly matching ITO. Although silver ($1000 kg À1) is more expensive than indium ($800 kg À1 ), the fact that silver nanowire films can be produced with highthroughput wet-coating processes allows them to achieve lower costs. 19,20Here we report a simple polyol synthesis that enables control over the length and diameter of silver nanowires, as well as their production on the gram scale. By measuring the properties of films composed of nanowires with distinct ranges of dimensions, we have obtained the first quantitative confirmation of theoretical predictions for the effect of nanowire length and number density on the conductance of 2D...