(255z) Modeling Controlled Release from Hollow Porous Nanospheres

The kinetics of diffusion-controlled release from hollow nanoporous spheres of varying thickness were investigated using classical mass transport theory. A new model was developed to describe the time-dependent mass transport through the shell. The model was compared with experimental kinetic profiles of transport of glyphosate in hollow silica nanosphere systems. The silica spheres were synthesized via a sacrificial method using Poly-(styrene-methyl acrylic acid) spheres as templates, thereby producing shell/core nanospheres with diameters ranging from roughly 367.6 to 406.8 nm and shell thicknesses spanning 22.0 to 32.8 nm. These nanosphere systems were loaded with glyphosate and then exposed to a reservoir of distilled water. Periodic sampling allowed determination of the glyphosate release kinetics as a function of shell thickness: the release rate decreased and the release period was prolonged by increasing shell thickness. The model was used to estimate the effective diffusivity and predict the concentration profile within the shell as well as the amounts of retained and released glyphosate. By rescaling the concentration profile in dimensionless form, it was observed that the amounts of released and retained glyphosate as functions of time could each be superimposed on a universal curve that was independent of shell thickness. Furthermore, the rate of the diffusive process with respect to shell thickness was determined by a single time constant that quantified the kinetics of the diffusive transport. It was also demonstrated that the associated diffusion coefficient of the mass transport must be calculated on a per-sphere rather than a per-mass basis. These results suggest that accurate predictions of time-released drugs and agrochemicals in diffusion-controlled nanosphere systems can be achieved via a single determination of an associated material rate constant. Predictions of the diffusion kinetics of hypothetical nanosphere systems were computed for a variety of experimental parameters, such as shell thickness and porosity.