Home » Formulation Optimization Utilizing DOE Mixture Statistics
Maintaining maximum color development throughout the production process for cellulose acetate butyrate/acrylic-based automotive refinish formulations with high-strength carbon black has always been an issue. Formulators have found that the order of addition can impact the final color of the applied coating. For this reason, it is imperative that the grind formulation provides the highest possible color strength, as it is likely to lose some color development in the course of processing.
This problem can be studied using the traditional scientific approach of isolating independent variables and examining their impact on the desired properties. However, when this is done, it quickly becomes apparent that something is being missed. One by one, the optimal amount of each formulation component is empirically determined through experimentation, but when these components are combined at the determined ratios, the results are far less desirable than predicted.
When evaluating Borchi® Gen 0451 pigment dispersant in CAB/TPA automotive refinish applications, this phenomenon was experienced. Laboratory trials to evaluate Borchers® dispersants produced inconclusive and even conflicting results. The problem lies in the fact that the separate components could have interactions with each other with respect to the desired properties. For example, when the formulator changes the level of dispersant in the grind formulation, the loading of the other components is also changed. If all the components have interactions with the responses, how can you conclude that changes in the desired properties are due only to the change in dispersant level – even if the ratio for the other components remains constant? If one plans traditional experiments, altering the ratios of each component individually and in combination with the other components, the number of trials adds up quickly, and this approach is simply not feasible.
There is a powerful statistical approach that is well suited for formulation optimization. It is a subset to the design of experiment (DOE) technique called mixture statistics. This statistical technique is designed to allow the experimenter to account for all component interactions, and calculate a formulation that is most likely to maximize the desired properties.(1)
Unfortunately, a common response to the mere mention of DOE is skepticism and resistance. It is true that a traditional factorial DOE is very limited in value when applied to formulation development. However, a DOE need not be the all-encompassing, labor-intensive exercise that many have encountered. In fact, the proper application of DOE methods should minimize the amount of time and resources needed to achieve the desired goals.(2-4)