Transfer Kinetics of Cargo Items among Nanocarriers

Nanocarriers such as micelles, liposomes, nanoshells and nanocages, dendrimers, carbon nanotubes, and nanoparticles are used in applications to transport cargo items--often drug molecules--to a target site. When nanocarriers collide with each other, cargo items are able to migrate from one to another nanocarrier. We employ chemical reaction kinetics to characterize how the distribution of cargo items among all nanocarriers in a mixture of different nanocarrier types depends on time. In the continuum limit, valid when each nanocarrier contains a sufficiently large number of cargo items, we express the kinetic equations as a system of partial differential equations--diffusion equations with additional demixing terms--that evolve into Gaussian distributions over time. We solve the partial differential equations and thus determine the kinetic behavior for any initial distribution of cargo in this multi-type nanocarrier system. The model can be generalized to address related problems, including the account of sink conditions, spatial variations analogous to diffusion-reaction phenomena, the release of cargo directly into the solution, and aggregation of cargo items inside carriers.