Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices.

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.

Brownian motion of flexibly linked colloidal rings.

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with n=4-8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for n≲8 and saturates for higher values of n. We show that constraints stemming from the ring structure cause this decrease in flexibility for small n and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

Distribution of block copolymers in drying polymer films.

HYPOTHESIS: Block copolymers (BCP) consisting of a polar block and a surface active apolar block are widely used for surface functionalization of polymer films. The characteristics of the copolymer blocks determine whether surface segregation and/or phase separation occurs, for a given bulk mixture. This data can be used to find the optimal BCP composition where high surface enrichment is obtained without accumulation of phase separated BCP in the bulk. METHODS: The distribution of poly(ethylene oxide)-polydimethylsiloxane (PEO-PDMS) BCP in a polymer formulation relevant for coating applications is systematically investigated. The surface segregation is studied in liquid formulations with surface tension measurements and dried films with X-ray photoelectron spectroscopy (XPS), whereas phase separation is quantified using turbidity measurements. The results are compared with Scheutjens-Fleer self-consistent field (SF-SCF) computations, which are also applied to determine the effect of film drying on BCP phase stability and surface segregation. FINDINGS: Longer PDMS blocks result in lower interfacial tension of the liquid polymer mixture, whereas for the cured films, the largest PDMS concentration at the interface was obtained for intermediate PDMS block lengths. This is explained by the observation that phase separation already occurs at very low BCP concentrations for long PDMS blocks. The SCF predictions qualitatively agree with the experimental results and reveal that the BCP distribution changes significantly during film drying.