Kondrashova, Daria

Valiullin, Rustem

Zeigermann, Philipp

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The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and ApplicationPropagation of solid-liquid interfaces under disordered confinementsDaria Kondrashova∗, Philipp Zeigermann, Rustem ValiullinFaculty of Physics and Earth Sciences, Universita¨t Leipzig, Leipzig, Germany∗daria.kondrashova@rz.uni-leipzig.deRecent progress in the synthesis of nanoporous materials with controlled structural properties madeit possible to address various phenomena occurring in mesoscalic systems. Among them, differentaspects of fluid phase transitions can now be related to the structural properties of the mesoporousmatrices. In this work, we present the results of our experimental studies of crystal growth processesin mesoporous silicon, which was fabricated to have linear, macroscopically long pores. Notably, in anideal cylindrical pore one expects a reduction of the freezing temperature in proportion to the pore size.In the material under study, however, freezing is found to start already before the transition temperature,determined by the average pore size, is reached. The kinetics of this process is found to be very slowand to depend on the temperature. In particular, power-law dependencies of the ice phase invasion intothe pores were observed. These findings we have associated with the fact that the material under studypossesses a substantial degree of disorder, namely there exist a distribution of the pore diameters alongthe pore axis. In light of this, the results obtained have been discussed assuming that the crystal growthprocesses under such strong confinements is an activated process, requiring overcoming of the poresize-dependent barriers in the free energy, rendering the overall process to occur under the occurrenceof the disordered transition rates.To justify the macroscopic model for the ice invasion kinetics, we have developed a simple lattice-fluidmodel [2], which is capable to model the freezing and melting processes of fluids confined to poreswith arbitrary organizations of their pore spaces. We demonstrate that this microscopic lattice modelreproduces quantitatively most experimental observations obtained using porous materials with verydifferent pore geometries. As an important point, this model shows the occurrence of the confinementsize- and temperature-dependent ice phase propagation rates. This finding, thus, validates the use ofthe macroscopic model with distribution of the free energy barriers along the pore axis, which maybe considered as a coarse-grained version of the microscopic one. Different regimes of the ice phasepropagation, including, in particular, the observation of Sinai-like diffusion, will be discussed [3].This work was supported by the DFG (FOR 877).References[1] M. Dvoyashkin, A. Khokhlov, R. Valiullin, J. Ka¨rger: Freezing of fluids in disordered mesopores.J. Chem. Phys. 129, 154702 (2008)[2] D. Kondrashova, R. Valiullin: Improving structural analysis of disordered mesoporous ma-terials using NMR cryoporometry. Microporous Mesoporous Mat. published online, DOI:10.1016/j.micromeso.2013.02.053 (2013)[3] J.P. Bouchaud, A. Georges: Anomalous diffusion in disordered media – statistical mechanisms,models and physical applications. Phys. Rep. 95, 127–293 (1990)

Propagation of solid-liquid interfaces under disordered confinements

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Propagation of solid-liquid interfaces under disordered confinements

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