Hydrodynamic invariant of polymer molecules

Abstract The theories of hydrodynamic properties of macromolecules in solution leading to an invariant relationship between the values of the intrinsic viscosity, η, the molecular weight, M , and the translational friction coefficient of the molecule, f , have been considered. The review of experimental data comprising as much as about 2000 fractions of various polymers suggests that for all flexible‐chain and moderately rigid‐chain molecules the hydrodynamic parameter A 0 = k η 0 (Mη/100) 1/3 f −1 is actually an invariant independent of the chain length and the thermodynamic strength of the solvent and for moderately polydisperse samples also independent of the degree of their polydispersity. For polymers with very rigid chains the parameter A 0 has a high value over the experimentally investigated range of M . These conclusions make it possible to recommend the use of the following average experimental values of the invariant A 0 for the determination of M of polymers from the values of η and f : for flexible‐chain and synthetic polymers with moderately high chain rigidity (3.2 ± 0.2) · 10 −10 , for polymers with high chain rigidity (3.7 ± 0.4) · 10 −10 , and for cellulose derivatives and other polysaccharides with molecular dispersity of nonelectrolyte solutions (3.30 ± 0.30) · 10 −10 erg deg −1 mol −1/3 . The fact that the experimental value of A 0 = 3.2 · 10 −10 does not coincide with the value of A ∞ = 3.8 · 10 −10 erg deg −1 mol −1/3 predicted by the theories of translational friction and viscosity of macromolecules implies that the theoretical values of P ∞ = 5.11 and Φ ∞ = 2.8 · 10 23 mol −1 are mutually incompatible and these theories require further development.