Direct observation of single molecule mobility in semidilute polymer solutions

We determine the mobility of dye-labeled polystyrene molecules in solution by fluorescence correlation spectroscopy (FCS) over a wide range of concentrations and molecular weights (ranging from $3.9\times {10}^3\text{to}1550\times {10}^3\mathrm{g}∕\mathrm{mol}$). In order to obtain absolute values of the diffusion coefficient, which can be compared to diffusion coefficients determined by other methods, the size of the focal volume has been determined by independent experiments and theoretical calculations. All data demonstrate that FCS is uniquely suited to explore polymer dynamics in solution. The mobility of the chains as expressed through the self-diffusion coefficient is significantly slowed down above the overlap concentration $c^{*}$. The dependence of $c^{*}$ on molecular weight is well described by the power law $c^{*}\propto M_w^{1-3\nu }$ ($\nu$: Flory exponent). A comparison with the data taken from the literature demonstrates that the overlap concentration presents a robust concept that holds for a wide range of molecular weights.