Methods and apparatus for characterizing a polymer sample and in preferred embodiments, libraries of polymer samples, in a comprehensive, directly-coupled multi-dimensional liquid chromatography system are disclosed. The first and second dimensions are preferably high-performance liquid chromatography dimensions, such as for example, a first dimension adapted for determining composition (e.g. adapted for mobile-phase gradient elution chromatography, including reverse phase chromatography, adsorption chromatography and the like), and a second dimension adapted for determining molecular weight or particle size (e.g., adapted for size exclusion chromatography, including gel permeation chromatography).