DoE and Formulation Chemistry

Can I use design of experiments to improve my formulation?

The simple answer is yes, of course. Experimental design can be applied to most industries and applications and formulation is no exception. However, specialist designs are often required for formulation chemistry as a simple factorial design may not always work. In factorial and fractional factorial designs each factor is examined at a high level and a low level; one experiment may require all factors set at a high level and another may have all factors at their lowest level, resulting in different experiments having varying total amounts (below, left). In a formulation, typically the components add up to a set total amount, with some components fixed at certain levels, e.g. a tablet containing a specific amount of API. A mixture design will change the factors proportionally but all runs have the same set total (below, right). In these cases, the response will be a function of the proportions of the factors, not the amounts.

Factorial designs are simple to run and it may be tempting to continue using them for formulation, indeed they can be used to investigate mixtures if there is a filler present which makes up the bulk (>50%) of the blend. However, for a simple 2-component blend there are problems with running a factorial design. Let’s consider making the perfect gin and tonic. Of course, if we were doing a full factor selection we would think about the brand of gin, the brand of tonic, any additives (lemon, lime, cucumber, berries…), the temperature of the drink, the glass it is served in etc, but we can keep it simple and try to understand the best ratio of gin:tonic. A factorial design would consist of 7 experiments (4 runs + 3 centre points, see table below left) varying the amounts of gin and tonic water; the problem comes with experiments 1 and 4. The ratio of gin:tonic is the same, it’s just the total amount which is different. This experiment is just a scale up rather than a different blend. A simplex-based mixture design should be used instead which can be run in 6 experiments and explores different blends of the two components while always totalling 100 mL (see table below right). Do you want to know more about formulation designs? Please get in touch to discuss your requirements. 

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