On the relation between hierarchical morphology and mechanical properties of a colloidal 2D gel system

We study a bidimensional gel system formed by a Langmuir film of gold nanoparticles. Its morphology is thoroughly characterized by AFM, SEM, and ellipsometric imaging techniques and shows a complex structure with features on a hierarchy of different sizes following a Levy distribution. The mechanical response arising after the gel point is investigated by Interfacial Shear Rheometry. The film is found to be mainly elastic, with the mechanical moduli scaling as a power law of the reduced concentration, in the same way as the fluctuation time which was measured in a recent X-ray Photon Correlation Spectroscopy experiment. The frequency dependence of the moduli is well described in the framework of the Soft Glass Rheology model (SGR) [Sollich et al. Phys Rev Lett 78, 2020 (1997)]. In this theory a power law distribution of relaxation times is postulated, whose exponent is experimentally determined for the present case. Such a distribution may reflect - in the dynamics - the hierarchical nature of the morphology of the film evidenced by microscopy. A mastercurve can be built, extending time-temperature to a time-concentration superposition principle as in [Cicuta et al. Phys Rev Lett 90, 116103(2003)]. This allows to describe the mechanical response over a frequency range slightly larger than that experimentally accessible. Besides the SGR component, a viscous term is always present, whose origin is investigated also taking into account samples with different preparation histories.