Mixture Design is a Design of Experiments (DOE) tool used to determine the optimum combination of chemical constituents that deliver a desired response (or property) using a minimum number of experimental runs. While the approach is sufficient for most experimental designs, it suffers from combinatorial explosion when dealing with the multi-component mixtures found in pharmaceutical excipient design. To circumvent this problem, a recently developed design technique called Property Clustering is applied. In this type of design the properties are transformed to conserved surrogate property clusters described by property operators, which have linear mixing rules even if the operators themselves are nonlinear. Product and process property targets are then used to describe a feasibility target region. To solve the mixture design, components are mixed according to property operator models in a reverse problem format until the mixture falls within the feasibility target region. Once candidate solutions are found, they can be screened with additional criteria per the experimenter's preference.

The degree of accuracy of this modeling technique depends heavily on the ability of the property operator models to adequately describe the property within the studied design space. This work focuses on the utilization of linear, or first order, Scheffe canonical and Cox polynomial models as the property operators. It is shown that the Scheffe models can be used in the existing clustering format, while Cox models require the clusters to be rewritten in terms of standard and a pseudo clusters. While both models result in identical solutions, it is shown that use of the Cox model reduces collinearity between the chemical constituents and leads to a set of interpretation opportunities unrealized when using Scheffe models. It is also shown that the use of statistically derived property operators may lead to negative property cluster space for which techniques are presented on how to quantify and qualify such regions.

In situations of high collinearity, property clustering is applied to the latent variables associated with Principal Component Regression (PCR). It is shown that representing the principal latent properties in the cluster domain not only reduces the number of plots required to illustrate the latent variable space, but also provides a medium from which components and component mixtures can be selected for experimental design. In situations where a component or component mixture does not meet the selection criteria, new molecules can be created based on group contribution methods. In addition, it is shown that process constraints can be mapped into the latent variable space to facilitate a more efficient design.

Selected case studies in mixture and molecular design will be used to illustrate the techniques.