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Many articles in the chemical literature use the words “optimized” or optimal” conditions in the report. Most of these in my experience are NOT optimized but rather a set of conditions were investigated and the best results obtained are then used. Out of curiosity, I looked at articles published in the following American Chemical Society (ACS) journals:

• Journal of Organic Chemistry (JOC)
• Journal of the American Chemical Society (JACS)
• Organic Letters (OL)
• Organic Process Research and Development (OPRD)

I choose these four since they are the major organic journals from the ACS and I happen to have subscriptions to all of them. A search of these journals for “optimized” or optimal” in the title or abstract from Jan 2000 to June 2006 resulted in 1065 hits. Searching within those results for those articles containing the word “statistical” results in 144 articles that actually used design of experiments (DOE) to determine the optimal conditions. This means that only about 13.5% of those claiming to be optimal or optimized actually are. I’m sure that if this was expanded to other journals the results would most likely be even lower. This is because the journal OPRD tends to publish quite a few very good articles describing the use of designed experiments resulting in a bias to the high side. My best guess is that including more journals would give a lower percentage of around 8-10%. It should be obvious that the vast majority of those claiming to be optimal really aren’t. They are probably pretty good, but certainly can’t be said with confidence to be the best conditions.

In the normal practice, a variety of solvents are chosen and then the best one selected and this is used to further optimize the conditions such as base. This “one factor at a time” process is quite common but ignores the interaction between the solvent and other conditions such as concentration, temperature, catalyst, reagent (i.e. base), etc. Also, at the end of an “optimization” performed using one factor at a time, you still don’t know for sure if you have found the best conditions. You only know that this set of conditions of those studied gave better results than the other conditions (but not necessarily the best). If a designed experiment is used, then you can arrive at a model for the system and predict where in the experimental space the best reaction conditions are, even if that set of conditions were not part of the design (however, you should always check and make sure this predict is correct). The use of designed experiments allows for the development of mathematical models (typically a quadratic equation) to predict results within the space studied. You can also study as many results as are of interest.

One reason DOE has not been used extensively is that you typically have to change your system to fit a design from a book or article. More recently, computer generated designs have overcome some of this although my experience is that most compute generated deigns are not of the best quality. They typically are what are called D-optimal designs and these designs concentrate on giving the narrowest confidence limits on the b coefficients. This means they are good at finding out how important a certain factor is, but are not the best for predicting the results which is typically what is of interest in industry. Here is an equation for a hypothetical example of a system looking at temperature (T), concentration (C) and catalyst (K).

Result = b0 + (b1 x T) + (b2 x C) + (b3 x K) + (b4 x T x C) + (b5 x T x K) + (b6 x C x K) + (b7 x T^2) + (b8 x C^2) + (b9 x K^2)

A D-optimal design will give you the best value for each of the b’s. This is good in cases where you may be studying eight or ten factors and you want to know the critical process parameters; say the three most important. They do not necessarily give the best results for the prediction of the result.

I-optimal designs however, are generated such that the best possible prediction of the result is what is of interest. It may not be entirely obvious but these are indeed different. Sometimes they may be the same but that is not necessarily the case.

QD information Services offers you the chance to use I-optimal designs that are specific for your set of circumstances. If you want to study four solvents and concentration as well as only three temperatures then we can provide you with an I-optimal design for that. If you are interested in a customized experimental design, feel free to send me an email and we can discuss your specific needs. We also offer help in analyzing the results and finding the true optimal conditions.

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