A density-functional model for controlled release.
Polymer diffusion based on density-functional theory is applied to controlled release systems. These models explicitly treat the multiphase characteristics of biomolecule-polymer composites typical of drug delivery devices. Polymer diffusion was modeled using the modified Cahn-Hilliard equation with periodic boundary conditions in one dimension and near-zero concentration boundaries in the second dimension. The diffusional driving forces are differences in chemical potential based in part on the Flory-Huggins free energy of mixing in polymer systems rather than concentration gradients. Release rates from this model were compared to exponential models typically used in the drug delivery literature. Simulations based on this model showed that the diffusional exponent is 1/2; this exponent is consistent with Fickian models at early times. Particle growth, which also occurs in diffusing, dispersed systems, was observed. The particle growth exponent in these systems was 2/3, twice the value typical in bulk ripening systems. The increased growth rate was caused by the elimination of small particles due to diffusion out of the system, which removed the low particle size region of the distribution faster than ripening alone.