Size and average density spectra of macromolecules obtained from hydrodynamic data

It is proposed to normalize the Mark-Kuhn-Houwink-Sakurada type of equation relating the hydrodynamic characteristics, such as intrinsic viscosity, velocity sedimentation coefficient and translational diffusion coefficient of linear macromolecules to their molecular masses for the values of linear density M(L) and the statistical segment length A. When the set of data covering virtually all known experimental information is normalized for M(L), it is presented as a size spectrum of linear polymer molecules. Further normalization for the A value reduces all data to two regions: namely the region exhibiting volume interactions and that showing hydrodynamic draining. For chains without intachain excluded volume effects these results may be reproduced using the Yamakawa-Fujii theory of wormlike cylinders. Data analyzed here cover a range of contour lengths of linear chains varying by three orders of magnitude, with the range of statistical segment lengths varying approximately 500 times. The plot of the dependence of [eta]M on M represents the spectrum of average specific volumes occupied by linear and branched macromolecules. Dendrimers and globular proteins for which the volume occupied by the molecule in solution is directly proportional to M have the lowest specific volume. The homologous series of macromolecules in these plots are arranged following their fractal dimensionality.