Brownian dynamics of self-similar macromolecules

M. E. Cates

A theory is presented of the dynamics of a solution of flexible chain macromolecules of arbitrary self-similar connectivity (« polymeric fractals »). The methods used are a Kirkwood approximation/effective medium theory of hydrodynamics, and a scaling theory of fractal correlations based on the idea of the spectral dimension. The resulting relaxation spectra at high and low concentrations are the generalizations (to the case of arbitrary polymeric fractals) of the well-known Rouse-like and Zimm-like spectra for linear polymers. The effective medium theory is extended to include an approximate dynamical description of excluded volume effects (but not entanglements) and also to account for polydispersity. In the presence of a power-law mass distribution (with a high mass cutoff) an « anomalous screening » regime is possible in which the effective fluid propagator G(k) ∼ k-α, with 0 < α < 2. In most cases, both α, and an exponent describing the divergence of the zero-frequency viscosity with the high mass cutoff, are determined uniquely by a self-consistency requirement. However, there are notable exceptions, including the percolation model. The theory is used to calculate various exponents describing the dynamical behaviour of a polymer sol-gel system close to its critical point.

Mots clés: Brownian motion; fractals; gels; polymer solutions; sols

Domaines: Articles anciens

M. E. Cates. Brownian dynamics of self-similar macromolecules. Journal de Physique, 1985, 46 (7), pp.1059-1077. ⟨10.1051/jphys:019850046070105900⟩. ⟨jpa-00210050⟩