Shape changes resulting from segmental flexibility are ubiquitous in molecular and biological systems, and are expected to affect both the diffusive motion and (biological) function of dispersed objects. The recent development of colloidal structures with freely jointed bonds have now made a direct experimental investigation of diffusive shape-changing objects possible. Here, we show the effect of segmental flexibility on the simplest possible model system, a freely jointed cluster of three spherical particles, and validate long-standing theoretical predictions. We find that, in addition to the rotational diffusion time, an analogous conformational diffusion time governs the relaxation of the diffusive motion, unique to flexible assemblies, and that their translational diffusivity differs by a small but measurable amount. We also uncovered a Brownian quasiscallop mode, where diffusive motion is coupled to Brownian shape changes. Our findings could have implications for molecular and biological systems where diffusion plays an important role, such as functional site availability in lock-and-key protein interactions.

For biologically relevant macromolecules such as intrinsically disordered proteins, internal degrees of freedom that allow for shape changes have a large influence on both the motion and function of the compound. A detailed understanding of the effect of flexibility is needed in order to explain their behavior. Here, we study a model system of freely-jointed chains of three to six colloidal spheres, using both simulations and experiments. We find that in spite of their short lengths, their conformational statistics are well described by two dimensional Flory theory, while their average translational and rotational diffusivity follow the Kirkwood-Riseman scaling. Their maximum flexibility does not depend on the length of the chain, but is determined by the near-wall in-plane translational diffusion coefficient of an individual sphere. Furthermore, we uncover shape-dependent effects in the short-time diffusivity of colloidal tetramer chains, as well as non-zero couplings between the different diffusive modes. Our findings may have implications for understanding both the diffusive behavior and the most likely conformations of macromolecular systems in biology and industry, such as proteins, polymers, single-stranded DNA and other chain-like molecules.