Diffusion dynamics of star-shaped macromolecules in dilute solutions

Polymer chains dissolved in a solvent take random conformations due to large internal degrees of freedom and are characterized geometrically by their average shape and size. The diffusive dynamics of such large macromolecules play an indispensable role in a plethora of engineering applications. The influence of the size of the polymer chain on its diffusion is well studied, whereas the same cannot be said for the shape of the polymer chain. In the present work, the influence of shape on the center-of-mass diffusion of the star-shaped chains in solution is investigated using Multi-particle Collision Dynamics. Star-shaped chains of varying degrees of functionality are modeled in a good solvent at infinite dilution. The radius of gyration($R_g$) of the star-shaped chains follows a functionality-independent scaling law with the chain length($N$), $R_g \sim N^{\nu}$, where $\nu \sim 0.627$. The shape of the polymer chains is calibrated by relative shape anisotropy. Highly anisotropic star-shaped polymer chains are found to have a faster rate of diffusion along the translational direction due to a slower rate of rotational diffusion when the radius of gyration of the polymer chains is maintained constant.