The motivation of this thesis was to understand the processes affecting the release rate of a chemotherapy drug, doxorubicin, from a mesoporous silica nanoparticle, reported in \cite{Hembury2015} and termed a \textit{Quantum Rattle}. A simple model was developed to produce release profiles that could be compared to the experimental data available. The model describes transport using a classical diffusion equation coupled with one (or several) adsorption/desorption reaction equations. A good fit was achieved for both the bare silica nanoparticle and the Quantum Rattle (which also contains gold) using two adsorption equations to account for the very slow release rate of the last 10$\%$ to 15$\%$ of the drug. Within the present model, the rate limiting process was the desorption of the drug from the gold nanoparticles in the inner cavity. Further work is required to understand the processes related to the presence of the gold and complement the study presented in this thesis that explores the role of the silica shell. \newline
In order to corroborate whether the simple description of the model was valid to describe diffusion within the porous silica, I carried out a detailed molecular dynamics study with classical force fields. The molecule within a slab of water was confined between two amorphous silica surfaces separated by a distance of 2.5nm, similar to a typical pore diameter of the nanoparticle. The transport of the molecule through the silica channel was subdiffusive at all timescales studied: at short timescales the subdiffusive dynamics originates from the negative correlations induced by the silica surface (described by a superposition of Fractional Brownian processes) while at large timescales the dynamics is dominated by the prolonged time intervals during which the molecule has reduced mobility due to its proximity to the surface (described by the Continuous Time Random Walk Model).