On the design and optimization of diffusion-controlled, planar delivery devices

Planar delivery devices are defined as multi-layer assemblies of paints, coatings or films designed to deliver chemicals into an environment at a predetermined rate. A readily manufacturable design that consists of two or three layers having different initial loadings of the chemical is described and optimized. Release of a chemical from the device is modeled as one-dimensional Fickian diffusion. A variety of release profiles, i.e. flux versus time, can be achieved by manipulating device parameters such as the thicknesses and initial chemical loadings of the different layers. The usual objective function is to maximize the utilization of the chemical over the design life of the device. Constraints on this optimization include the minimum effective delivery rate, the time required to achieve the minimum delivery rate, and the maximum allowable delivery rate. An important result is that an approximately constant delivery rate of a chemical into a zero-concentration environment is possible using a nearly universal design. The universal design has two chemical containing layers, each having a scaled thickness of 0.5, and one layer, initially devoid of chemical, with a scaled thickness of 0.14. The scaled initial concentrations in the layers, beginning with the layer farthest from the environment are 1.6, 0.4, and 0. Desired average delivery rates and device lifetimes are achieved by a single, typically empirical step in which the diffusivity is fixed to give an optimized utilization of the chemical over the life of the device. Adjustment of the design parameters, including the use of more than three layers, provides little benefit. The same general design, with adjusted parameters, gives good results when the desired profile includes a controlled initial burst or when the delivery rate is a linearly decreasing or increasing function of time.