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Experimental Strategy: Designs for Kinetic Studies

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Invited-icon.jpgA LabAutopedia invited article


Authored by: James N. Cawse, Ph.D.; Cawse and Effect LLC

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Contents

Designs for Kinetic Studies

Many chemical projects simply desire to improve the yield of a process or the purity of a product. In this case, the measurement is typically a straightforward output of an analytical process. The measurement is often of good precision and accuracy, and it can be made better by simple replication and averaging. If, instead, the desire is to improve the rate of a process, several new questions emerge and the precision of the result is more doubtful.

Studies of kinetic processes need to be even more carefully planned than simple yield studies. Please refer to the Experimental Strategy page..  Knowing where to set the highs and lows for the factors is harder when chemical reactions are concerned than it is for other systems. A careful set of rangefinding runs may be the first order of business. Otherwise,  you may have to be clever in coming up with a "Plan B" when you get half way through the experiment and find an inoperable region.

Statistical Issues

Data Regions

If we are measuring a reaction in progress, we are "catching the bird as it flies". The progress of a reaction can be roughly broken down into three regions from an information-centric point of view:

  • Nothing is happening. We are either at the beginning of a reaction, in an induction period, or at the end of a reaction when all the reactants have been exhausted. In either case, taking more than one point in this region is a waste of resources.
  • Things are happening too fast. The concentrations of the reactants or products are changing so rapidly that a very small error in the sample time will result in a large error in the measured result.
  • Things are slow (enough). Reasonably accurate measurements are possible because the change of concentration is relatively small within the variance of the sample time.

Interactions

Two-way interactions are often more important than the main effects in chemical reactions. Chemistry is an inherently non-linear, interactive science, and chemical kinetics is more so. Processes can go off in completely different trajectories, depending on the temperature, mixing conditions, the quantity of a catalyst or reagent used. From a statistical standpoint, these trajectories are interactions, but in chemical essence the data is actually composed of distinctly different data sets from a number of different processes!  It might be a mistake to use the old adage "always throw out the 3-way's if you need degrees of freedom" - there can be real 3FI's.

Designs

Sometimes fairly standard DOE's like factorials and response  surface designs will suffice, but frequently the constrained and non-linear aspects of these systems will require more sophisticated methods. Chemical systems are always mixtures of "stuff" so Formulation designs should be considered. D-Optimal or I-Optimal designs[1] will frequently be required to deal with the constraints and non-linearity. Transformations[2] are likely to be necessary.

Models

There may be sufficient knowledge of chemical first principles for it to be possible to convert DOE data to theoretical models. Box-Tidwell[3] transformations of independent variables may be used to elucidate the non-linear nature of the model and convert it to a non-linear parameter estimation problem, combined with d-optimal designs for iterative refinement. Surface catalytic reactions often follow Langmuir-Hinshelwood[4] kinetics in which the rate law is a function of ratios, so non-linear estimation is inevitable. An algorithmic approach to approximating a rate law of that type is required [5].

Langmuir.png

Bimolecular Langmuir-Hinshelwood equation where CS, CA, and CB are concentrations of surface sites, reactant A, and reactant B.


Chemical Issues

Rate Laws

For a rate measurement to be meaningful we need to know the kinetic profile or rate law of the process. Chemical reactions can be anything from zeroth to first to second order and beyond. The reaction may have an induction period or be a multistep process. This will have a strong influence on the number of points required to get reasonable quality data and also the appropriate spacing of those points in time. In these figures, the circled regions are those of (almost) no information and the arrowed regions are likely to be so fast that good precision is difficult to obtain.

Reactions.png

Scale up

Small scale, high throughput reactors can be used to validate basic relationships and pre-optimize them. During scale up, the optimum is likely to change, and change again at the production scale. At production scale an EVOP[6] design is often a good idea since you can no longer change conditions freely. You may have to baby-sit the reactor for weeks of 24-hour days, but it's usually worth it.  In large scale-ups the controlling mechanism often changes, but the basic relationships determined at the high throughput level will serve as a guide. Some companies such as UOP have gained enough experience with high-throughput research that they are able to skip one or more steps of scaleup because of their confidence in the small scale results.[7]

Mixing and Thermal Issues

In scale-up (even just to a 1-liter flask) the mixing regime is likely to be very different. This could change the reaction greatly! Even more important, the exothermicity of the reaction becomes a critical issue. Controlling the temperature of a 1-ml reactor is easy; there are many tragic instances of reactions in which the heat release could not be controlled at a larger scale, resulting in an explosion or fire. I have watched a nearby lab erupt into uncontrollable flames because of this!!

Summary

Designed experiments are powerful tools for determining the kinetics of a process but absolutely need a strong complement of understanding of the chemistry.



== References ==

  1. www.jmp.com
  2. http://en.wikipedia.org/wiki/Power_transform
  3. Box, G. E. P. and Tidwell, P. W. (1962) Transformation of the independent variables. Technometrics 4, 531-550.
  4. http://en.wikipedia.org/wiki/Langmuir-Hinshelwood_kinetics
  5. J.B.Cropley, A Heuristic Approach to Complex Kinetics, in Chemical Reaction Engineering --Houston, (V.W. Weekman, Jr. and D. Luss, Eds.) ACS Symposium Series 65, American Chemical Society, Washington, D.C., 1978, pg. 293.
  6. http://en.wikipedia.org/wiki/EVOP
  7. M. L. Bricker, J. W. A. Sachtler, R. D. Gillespie, C. P. McGonegal, H. Vega, D. S. Bem and J. S. Holmgren, Strategies and applications of combinatorial methods and high throughput screening to the discovery of non-noble metal catalyst, Applied Surface Science 223(1-3), 15 February 2004, 109-117.
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