Measuring the size of polymers with negative radii using MALS/QELS: an exploration of the thermodynamic radius

The concept of 'size' in polymer science can have several interpretations, including definitions that rely on either statistical or equivalent-hard-sphere measures of the spatial extent of macromolecules in solution. A definition such as that of the equivalent thermodynamic radius (R(T)), which relies on the second virial coefficient of the polymer solution, offers the possibility of a zero or even a negative size parameter for macromolecules, depending on whether the polymer solution is in a theta or poor thermodynamic state, respectively. Here, we present the results of multi-angle light scattering measurements of R(T) for polystyrene and poly(methyl methacrylate), showing positive, negative, and zero values for this radius, depending on dilute solution thermodynamics. These results are augmented with measurements of the hydrodynamic radius, using quasi-elastic light scattering, and with random-walk-based calculations of the root-mean-square and viscometric radii. Re-examination of the literature provides additional examples of negative radii of polymers and oligomers.