Supplementary Information for Modus operandi of controlled release from mesoporous matrices: A theoretical prespective†

Subdiffusion or single-file diffusion occurs in crowded media or in the presence of tight spatial confinement. In the particular case of diffusion in a narrow channel, the motion of an assembly of small particles can be so tightly restricted that they arrange themselves into a single file (hence the term single-file diffusion). In such a situation the longitudinal motion of each particle is hindered by its neighbors, which act as impenetrable obstacles. In this respect, inter-particle interactions can suppress Brownian motion in one dimension. However, inter-particle interactions do not affect the normal character of Brownian diffusion as long as particles are able to pass one another, no matter how closely they are confined1. This holds also if attracting particles cluster or condense in the potential wells2,3. Thus, for subdiffusion to occur in the case of drug molecules in mesopores, the diffusing molecules would have to be forced to arrange into a single file. While this should hold in the case of transport in zeolites and molecular sieves, carbon nanotubes and microporous materials, the pore diameter of mesoporous materials (typically lying between 3.5 and 20 nm) is not small enough to enforce subdiffusion of drug molecules with Connolly radii below 10 Å. Without going into an involved mathematical reasoning, the assumption can be justified by considering that loading of pores with drug molecules would be drastically slower than experimentally observed and also the fact that molecules are able to crystallize in mesoporous materials at sufficiently high loading (see for example4,5). Namely, for crystallization to occur, a critical nucleus needs to be formed, which is established by a cooperative density fluctuation in which typically several tens to hundreds of molecules are involved. Needless to say, for this to occur unconstrained diffusion must be possible.