Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices

Physical Review Letters, vol. 132, pp. 078202

Abstract

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations, and we develop a theoretical description based on mapping interactions onto a linear response model to describe the modes. Our results reveal the importance of entropic steric effects and can be used for developing reconfigurable materials at the colloidal length scale.

Authors 3

1. Julio Melio Aachen Huygens-Kamerlingh Onnes Laboratory

   Leiden University

   Affiliation as printed

   Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands

2. Silke Henkes Aachen Lorentz Institute

   Leiden University

   Affiliation as printed

   Lorentz Institute, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands

3. Daniela J. Kraft Aachen Huygens-Kamerlingh Onnes Laboratory

   Leiden University

   Affiliation as printed

   Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands