# Dynamics of fractal sol-gel polymeric clusters Academic Article

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### abstract

• The dynamics of flexible polymeric fractals in solutions is discussed using a linearization self-consistent approximation. When hydrodynamic interaction is not screened (Zimm model) we find that the mean square displacement $〈\ensuremath{\Delta}{(t)}^{2}〉$ of a monomer is anomalously increasing with time, $〈\ensuremath{\Delta}(\mathcal{t}{)}^{2}〉D\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$ with a universal exponent $\ensuremath{\alpha}=2/d$ in $d$ dimensions, independent of the fractal ${(d}_{f})$ and spectral dimensions. The viscoelastic modulus behaves as $G(\ensuremath{\omega})\ensuremath{\sim}(i\ensuremath{\omega}{)}^{u},$ with ${u=d}_{f}/d.$ When hydrodynamics is screened (Rouse model) we find $\ensuremath{\alpha}{=2/(2+d}_{f})$ and ${u=d}_{f}{/(2+d}_{f}).$ We conclude that measurements of $\ensuremath{\alpha}=2/d$ indicate unambiguously that the Zimm model is applicable and thus should be correlated with ${u=d}_{f}/d$ in rheology measurements.

### publication date

• January 1, 1998