On the determination of molecular weight distributions from sedimentation–diffusion equilibrium data at a single rotor speed

The problem of inferring molecular weight distributions from concentration gradient data taken at sedimentation-diffusion equilibrium for a single rotor speed is ill posed: significantly different distributions correspond to concentration gradients which differ so slightly that they cannot be distinguished by the experiment. It is this intrinsic property of the problem which accounts for the lack of success of the several schemes proposed for its solution. Integral equation theory is applied to show explicitly just what can be inferred with bounded error. Several methods for recovering this information are discussed and applied to example problems.