Accuracy of the Single-mode Model of Controlled Release from Hollow Porous Nanospheres
Abstract
The kinetics of diffusion-controlled release from hollow nanoporous spheres of varying thickness were recently investigated using classical mass transport theory. A new model, expressed in terms of a single diffusive mode, was developed to describe the time-dependent mass transport of a loaded chemical species through the nanosphere shell based on physically reasonable boundary and initial conditions, as well as an assumption of monotonicity during the approach to steady-state diffusive behavior. The purpose of this communication is to demonstrate the validity of these assumptions in the long-time limit and to estimate the error associated with the short-time transport. To this end, the kinetics of the single-mode model are compared with a full solution to the time-dependent diffusion equation obtained using numerical techniques, which demonstrates the utility of the single-mode model for all but the initial moments of the transport process. As a result, it is evident that the single-mode model, which expresses the diffusion of the solute from the nanospheres in terms of a single, universal time constant, is a valid approximate model for describing diffusion in these nanoporous systems for controlled release applications.
