On the Apparent SEC Molecular Weight and Polydispersity Reduction upon Intramolecular Collapse of Polydisperse Chains to Unimolecular Nanoparticles

Abstract

When unimolecular particles of molecular weight M are formed by intramolecular cross-linking of individual polymer chains, a significant reduction in hydrodynamic radius and, hence, apparent molecular weight (Mapp) is found by size exclusion chromatography (SEC) with traditional calibration. A concomitant reduction in polydispersity index (PDI) is often observed. This work tries to clarify the relationship between the molecular weight decrease and the simultaneous PDI narrowing reported by SEC for collapsed polymeric nanoparticles. A power-law expression is derived by assuming that fractal, soft nano-objects are formed upon intramolecular collapse: Mapp ∝ Mβ where β = (1 + αF)/(1 + αL), αF being a parameter related to the fractal degree of the soft nanoparticle and αL the Mark–Houwink–Sakurada exponent of the precursor polymer. Two limiting cases provide the expected minimum and maximum β values: β ≈ 0.56 for perfectly compact nanoparticles and β ≈ 1 for nano-objects equivalent to flexible chains in good solvent. Results available in the literature for intramolecular cross-linked nanoparticles of different chemical composition have been analyzed in terms of this simple scaling law. Its direct effect on SEC polydispersity reduction is addressed for a precursor displaying a log-normal molecular weight distribution. The apparent polydispersity of the nanoparticles is given by PDIapp = (PDI)β2. Because of the heterogeneous nature of the collapsing process and/or the potential presence of marginal, minor amounts of intermolecular byproducts, some deviation of experimental PDIapp data from theoretical predictions is observed.