Mixture-Process Design or Response Surface Design

[#1]

Hello everyone,

I am writing to ask for advice on designing an experiment to optimize a somewhat complicated chemical reaction. Here is what it involves:

A substrate (1.0 eq) reacts with a mixture of two reagents called RA and RB.

The total amount of RA and RB is always 0.5 eq.

The proportions of RA and RB vary within the mixture of these two reactants.
RA varies from 38% to 62%, and RB also varies from 38% to 62%.

The reaction is catalyzed by a mixture of two catalysts, CatX and CatY.

The total amount of catalyst varies from 0.1 to 0.5 eq.

The proportions of CatX and CatY vary within the mixture of the two catalysts.
CatX ranges from 0 to 100%, and CatY ranges from 0 to 100%.

Reaction time is a continuous factor studied over a period of 6 to 24 hours.

The objective of the experimental design is to maximize the conversion rate of the substrate into reaction products.

Initially, I attempted to use the Custom Design platform of JMP 18 to define a mixture-process design.

How can I tell JMP that RA + RB constitutes one mixture and CatX + CatY constitutes another?
Indeed, if this specification is not made, JMP considers the four compounds to be four constituents of a single mixture.
I tried to specify linear constraints but without success.

What effects should be included in the model to obtain a response surface design in this case?

In a second attempt, I simplified the problem by considering the proportion of RA as a continuous factor ranging from 38% to 62% without specifying RB. Similarly, I considered the proportion of CatX as a continuous factor ranging from 0 to 100% without specifying CatY. Although RB and CatY do not appear in the table, I know that :
RB = 1 - RA
CatY = 1 - CatX.

In this case, I considered including main, interaction, and quadratic effects to obtain a response surface design.

Is one approach better than another?

Would it be problematic to have the total amount of catalyst as one factor and the proportions of catalysts as the other factors?

Thank you for your help.

[#2 · Accepted solution]

Hi @Kyle_Katarn 

I think your second approach should work best (and is more simple), as some of the raw materials will be perfectly correlated (reagents concentrations and catalyzers ratios).
If you want the reagants and catalyzers proportions to be optimized "independantly" (you don't investigate the ratio of reagants to catalysts), then you may not need a Mixture design : the quantity of RA can be determined by quantity of RB (or the other way around), and same situation for catalyst.

• For reagants, you only need one continuous factor, for example quantity RA, with levels from 0.19eq to 0.31eq (the 38% to 62% ratio applied to the total quantity for reagants : 0.5eq). The other reagant quantity can be deduced from this factor level.
• For catalysts, if you also vary the total amount, you need two continuous factors, one for the ratio of one catalyst, for example CatXfrom 0 to 1, and one for the total amount of catalysts, from 0.1 to 0.5eq.

Is time really a controllable factor in your case ?

May the force be with you,

[#3]

Thank you for your help and advice.

Using directly the number of equivalent of RA as a continuous factor instead of the proportion is a good idea.

Yes, time is a controllable factor. Samples will be collected at the specified times and analyzed to measure the conversion rate.

I will compare the Box-Behnken and Face-Centred Central Composite designs to determine which is more suitable.

May the force be with us all.

[#4]

Hi @Kyle_Katarn,

Ok sounds good.
If you're still searching comparative analysis and discussions between Box-Benhken, Central Composite Design and Custom I-Optimal RSM design, there are already some discussion available in the forum :

Determining Alph : Comparison between Box-Behnken and CCD.

Optimization task with 2 continuous and 1 discrete (2 levels) factors : Advices on the use of Custom vs. Classical RSM designs.

why are no star points in custom design RSM : Comparative evaluation of CCD designs depending on the location of star points (axial value).

Specifying axial value as rotatable in custom design : How to change the default (-1/+1) axial value for Custom I-optimal RSM designs.

Hope these discussions will help you,

"Goodbye, old friend" 

[#5]

Thank you for the links!
It's not always easy to determine which design is more suitable. So, it's interesting to read different opinions about their respective advantages and disadvantages.