Dynamical scaling of the structure factor for mesoscopic structures with non-Euclidean fractal morphology

In order to examine the validity of linear and nonlinear theories on dynamics of new phase formation for mesoscopic structures in non-Euclidean geometry, the real-time evolution of mesoscopic structures of light and heavy water hydrated calcium sulphates has been investigated. Unlike the case for hydration of silicates, hydration of sulphates with light and heavy water does not have distinct characteristic as far as the agreement with the dynamical scaling hypothesis is concerned. There is no change of the topographical mesoscopic structure for hydrating sulphates, unlike silicates, with light and heavy water. Real-time scattering measurements on hydration of sulphates are incomprehensible in the light of observed [S. Mazumder , Phys. Rev. Lett. 93, 255704 (2004); Phys. Rev. B. 72, 224208 (2005)] results on hydration of silicates. This reports a disagreement with the hypothesis of dynamical scaling of the structure factor of a non-Euclidean system, maintaining same topographical morphology during temporal evolution of the structure. The present investigation, on dynamics of water in different geometric confinements, is also indicative of the fact that the diffusion in non-Euclidean geometry is far from comprehensible.