Analytical ultracentrifugation and combined molecular hydrodynamic approaches for polymer characterization

Metallo-Supramolecular Complexation Behavior of Terpyridine- and Ferrocene-Based Polymers in Solution—A Molecular Hydrodynamics Perspective

“…From the perspective of classical polymer physics/molecular hydrodynamics, in order to understand fundamental structure-property correlations that determine the formation and behavior of the polymer-based metallo-supramolecular assemblies at different metal to ligand ratio ( ) in solution, systematic investigations/determinations of certain solution characteristics that are related to the basic macromolecular parameters (molar mass ( ), size ( ), shape) will be required. Such fundamental solution characteristics Equation (1) will basically include the sedimentation coefficient– , the translation diffusion coefficient and the intrinsic viscosity [ 26 , 27 ]: where —the molar mass, —the hydrodynamic radius, —the partial specific volume, —solvent density, —dynamic viscosity of the solvent, —Avogadro’s number, —Boltzmann constant, —Flory hydrodynamic parameter, —viscosity hydrodynamic size.…”

“…The estimated sedimentation and diffusion coefficients together with the determined partial specific volumes are then can be used to calculated the molar masses via the Svedberg equation Equation (4) ( Table 1 ). The partial specific volume of the initial polymers was determined by the classical density measurements of differently concentrated polymer solutions [ 16 , 27 ] and constitutes and for the TerPol and TerFerCop, respectively. where —intrinsic sedimentation coefficient, —frictional ratio, —partial specific volume, —density of a solvent, —dynamic viscosity of the solvent, —Avogadro’s number.…”

“…The complexes were prepared by mixing equal volumes of corresponding polymer and salt solutions ((Eu(CF 3 SO 3 ) 3 and PdCl 2 (CH 3 CN) 2 ) at appropriate concentrations that cover the following range of metal to ligand molar ratios: . In order to promote formation of individual intra-molecular complexes rather than intermolecular network like structures and to reduce possible non-ideal effects at high polymer concentrations, the complexation was studied in a very dilute polymer solutions were the corresponding Debay parameter— [ 27 ], that characterizes the volume fraction occupied by the macromolecules in solution, was , meaning that only 0.6% of the total solution volume is occupied by the macromolecules. In our further discussion we will first look on the upper half of the range ( ) that correspond to the molar salt concentrations of to .…”

“…from the molar mass, but the value may be influenced by the solvent and charge interactions, solvation rate etc. [ 27 ].…”

Amphiphilic Diblock Copolymers Bearing Poly(Ethylene Glycol) Block: Hydrodynamic Properties in Organic Solvents and Water Micellar Dispersions, Effect of Hydrophobic Block Chemistry on Dispersion Stability and Cytotoxicity

“…While calculating M sD , the precise value of partial specific volume is necessary. Whenever it is possible, it can be determined through standard protocols of densitometry measurements; however, when the highest possible concentration of copolymer micelles is limited and its value is imprecise, then an alternative technique (known as the density variation approach [ 34 , 35 ]) can be implemented. It requires isotopically different solvents that differ in basic solvent parameters (i.e., density and dynamic viscosity), and at the same time the conformational status of macromolecules is not affected.…”