I am comparing two exponential decay curves that represent the time response of first order chemical reaction. In one of the curves, I have a temperature delay that I can manipulate and make short with higher heating rates in the reactor. I can get to minuscule delay times, but I don't want to use too high heating rates to achieve that. The question is how short a delay should be to be neglected from the study? 1/2 of the curve characteristic time? 1/10? What?
Thanks for your help guys!
A delay time may (or not) be of first order, but the process that originates such a delay may not be related with the (here also of first order) chemical reaction that may be followed (observed), but rather be dependent on another independent phenomena, such as thermal resistance, for instance, when we think at a non-isothermal reaction observed by differential scanning calorimetry (DSC). The magnitude of the error that results from identifying the observed chemical concentration (affected by first order delay) with the corresponding actual (real) concentration, can be estimated accordingly eq. 2.58 of the following reference (p. 25). A similar equation would apply to another observed quantity (e.g. temperature).
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Of some significance with regards to this question may also be the concept of Deborah number, since the actual physical relevance of the above mentioned first order delay may depend also on the observation time. The concept is further examined at the following references.
http://scitation.aip.org/content/aip/magazine/physicstoday/article/17/1/10.1063/1.3051374
Article Aspects of the non-crystalline state
The answer to your question applies to any situation where you have a small parameter, not just chemistry. Being aware of this can be extremely helpful in many fields.
In your case, the small parameter is a time delay. The outcome of your problem (the chemical composition in a numerical experiment) will become independent of your small parameter as your small parameter shrinks to zero.
The point where (as a function of the size of the small parameter) your outcome of interest becomes independent of the small parameter is the point where you can freeze your small parameter it.
Detecting when this happens is usually easily done by doing a log-log plot of the outcome of interest versus the small parameter (a fractional mass versus the time delay in your case).
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