Generalized Concentration Dependence of Self-Diffusion Coefficients in Poly(allylcarbosilane) Dendrimer Solutions

Abstract

Self-diffusion of three high generations (the fifth, sixth, and seventh) of poly(allylcarbosilane) dendrimer in solutions with deuterated chloroform has been studied over a wide range of macromolecular concentrations (φ). Diffusivity has been measured by NMR with a pulsed gradient of the magnetic field. It is shown that concentration dependences of the dendrimer self-diffusion coefficients ( D ) can be reduced to the generalized concentration dependence. Over the range of volume concentrations from 0.01 up to 0.55, the curve of the generalized dependence of D for dendrimers coincides with the analogous dependence for globular protein in aqueous solutions. Analogous to the universal concentration dependence of D for linear polymers in solvent, the generalized concentration dependence of dendrimers tends to the asymptote D ‘ ( φ ) / D 0 ∝ φ 0 = 1 in the limit of extremely dilute solutions and to the asymptote D ‘ ( φ ) / D 0 ∝ φ -3 in the range of concentrated solutions 0.3 < φ < 0.55. Here, D 0 = lim φ → 0 D (φ) and D ( φ ) are the self-diffusion coefficients of dendrimer in an extremely dilute solution and in a solution with macromolecular concentration φ, respectively. D ‘ ( φ ) = D ( φ ) /L ( φ ), where L ( φ ) is a normalizing function, taking into account the change of the local mobility of dendritic branches as the macromolecular concentration increases; the L ( φ ) functions have been experimentally extracted from the concentration dependence of the longitudinal relaxation times for the dendrimers in solutions studied.