Soft and stiff normal modes in floppy colloidal square lattices

TL;DR

This study experimentally demonstrates floppy and stiff normal modes in colloidal square lattices with DNA linkers, revealing size-dependent shear softness and aligning with simulations and theory, advancing reconfigurable colloidal materials.

Contribution

It introduces a well-controlled experimental system for floppy spring networks using colloid-supported lipid bilayers with DNA linkers, and provides a theoretical framework for their normal modes.

Findings

Soft modes with low stiffness emerge alongside stiff modes.

Shear stiffness decreases as lattice size increases.

Experimental results align with Brownian simulations and theoretical models.

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 linear response 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.