Stability of jammed packings I: the rigidity length scale

In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low frequency vibrational properties of jammed amorphous sphere packings can be understood in terms of a length scale, called l*, that diverges as the system becomes marginally unstable. Despite the tremendous success of this theory, it has been difficult to connect the counting argument that defines l* to other length scales that diverge near the jamming transition. We present an alternate derivation of l* based on the onset of rigidity. This phenomenological approach reveals the physical mechanism underlying the length scale and is relevant to a range of systems for which the original argument breaks down. It also allows us to present the first direct numerical measurement of l*.Comment: 8 pages, 5 figure

Finite-Size Scaling at the Jamming Transition

We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions, indicating an upper critical dimension of 2.Comment: 5 pages, 3 figure

Enhanced diffusion by binding to the crosslinks of a polymer gel

Creating a selective gel that filters particles based on their interactions is a major goal of nanotechnology, with far-reaching implications from drug delivery to controlling assembly pathways. However, this is particularly difficult when the particles are larger than the gel’s characteristic mesh size because such particles cannot passively pass through the gel. Thus, filtering requires the interacting particles to transiently reorganize the gel’s internal structure. While significant advances, e.g., in DNA engineering, have enabled the design of nano-materials with programmable interactions, it is not clear what physical principles such a designer gel could exploit to achieve selective permeability. We present an equilibrium mechanism where crosslink binding dynamics are affected by interacting particles such that particle diffusion is enhanced. In addition to revealing specific design rules for manufacturing selective gels, our results have the potential to explain the origin of selective permeability in certain biological materials, including the nuclear pore complex.National Science Foundation (U.S.) (through Harvard Materials Research Science and Engineering Center Grant DMR-1420570)National Science Foundation (U.S.). Designing Materials to Revolutionize and engineer our Future (Grant DMR-123869)United States. Office of Naval Research (Grant N00014-17-1-3029)National Institutes of Health (U.S.). National Institute for Biomedical Imaging and Bioengineering (Grant R01 EB017755-04)National Science Foundation (U.S.). Career Award (PHY-1454673)National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (DMR-1419807