Sedimentation parameter of linear polymers

Abstract

Relationship between the sedimentation coefficient S ₀ and its concentration coefficient K _S obtained in experiments on velocity sedimentation are discussed. The values of S ₀, K _S, and independently determined molecular masses reported by different researchers for different linear unchanged polymers are considered. It was established that the scaling index K ∼ S{ie101-1} unambiguously related to scaling index S ₀ ∼ M ^b. The generalization of experimental data, which is based on Svedberg’s equation for S ₀ and on the expression K _S=B(h ²)^3/2 M ⁻¹ made it possible to introduce the dimensionless sedimentation parameter β _S. The average experimental values of β _S were calculated for different polymer types and, to the first approximation, do not depend on molecular mass. Therefore, it is possible to write the generalized Wales-van Holde equation M _KS=(N _A/β _S)^3/2[S]^3/2 K ^1/2_S .

The adequacy of evaluation of M is illustrated taking as an example the determination of equilibrium rigidity of a polymer chain (flexible-chain polymers under ϑ-conditions and flexible-chain polymers in a thermodynamically good solvents) and of the unit length mass of the polymer chain (rigid-chain polymers). A rigorous theory of the concentration dependence of the sedimentation coefficient should take into account quantitatively the relationship between polymer chain draining and the solvent counterflow in the sedimentation of macromolecules.