Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming

In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials1. A key assumption underlying the theory was that all jammed packings are equally likely. In the intervening years it has never been possible to test this bold hypothesis directly. Here we present simulations that provide direct evidence that at the unjamming point, all packings of soft repulsive particles are equally likely, even though generically, jammed packings are not. Typically, jammed granular systems are observed precisely at the unjamming point since grains are not very compressible. Our results therefore support Edwards’ original conjecture. We also present evidence that at unjamming the configurational entropy of the system is maximal.S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. D.F. acknowledges support by EPSRC Programme Grant EP/I001352/1 and EPSRC grant EP/I000844/1. K.R. and B.C. acknowledge the support of NSF-DMR 1409093 and the W. M. Keck Foundation

Hollow block copolymer nanoparticles through a spontaneous one-step structural reorganization

The spontaneous one-step synthesis of hollow nanocages and nanotubes from spherical and cylindrical micelles based on poly(acrylic acid)-b-polylactide (P(AA)-b-P(LA)) block copolymers (BCPs) has been achieved. This structural reorganization, which occurs simply upon drying of the samples, was elucidated by transmission electron microscopy (TEM) and atomic force microscopy (AFM). We show that it was necessary to use stain-free imaging to examine these nanoscale assemblies, as the hollow nature of the particles was obscured by application of a heavy metal stain. Additionally, the internal topology of the P(AA)-b-P(LA) particles could be tuned by manipulating the drying conditions to give solid or compartmentalized structures. Upon resuspension, these reorganized nanoparticles retain their hollow structure and display significantly enhanced loading of a hydrophobic dye compared to the original solid cylinders