Generalized concentration dependence of self-diffusion coefficients in poly(allylcarbosilane) dendrimer solutions

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 (T). 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'(phi)/D-0 proportional to phi(0) = 1 in the limit of extremely dilute solutions and to the asymptote D'(phi)/D-0 phi(-3) in the range of concentrated solutions 0.3 < phi < 0.55. Here, D-0 = lim(phi-->0) D(phi) and D(phi) are the self-diffusion coefficients of dendrimer in an extremely dilute solution and in a solution with macromolecular concentration phi, respectively. D'(phi) = D(phi) /L(phi), where L(phi) is a normalizing function, taking into account the change of the local mobility of dendritic branches as the macromolecular concentration increases; the L(T) functions have been experimentally extracted from the concentration dependence of the longitudinal relaxation times for the dendrimers in solutions studied.