# [R] almost logistic data evaluation

Stephen Ellison S@E|||@on @end|ng |rom LGCGroup@com
Wed Jun 10 17:46:29 CEST 2020

```I'm not sure this is really a statistical problem, in the sense of looking for a convenient but arbitrary statistical function; to do it well is more of a physicochemical modelling problem.
I can't give you an answer but maybe a direction I'd consider if I wanted to take it seriously ...

You have a steady heat input (which is initially a straight line but becomes asymptotic as cooling rate approaches heating rate),  plus an exothermic reaction whose rate will almost certainly depend on temperature (I guess close to the usual 'double every 10K' rule of thumb for chemistry, but of course there are plenty of exceptions and diffusion control doesn't follow Arrhenius rate dependence. ). On a bad day it may self-catalyse as well, but it's already self-accelerating in the sense that the rate will go up with the temperature and the temperature will go up faster at higher rates.

To model that you would ideally set up a kinetic model for the chemistry, with coefficients for (probably) an activation energy rather than a simple rate constant, enthalpy of reaction, heat input and at least one arbitrary heat capacity so that you have something that relates heat input and enthalpy to temperature. There'll be another term (probably based on newton's law of cooling) to model external heating and cooling, again with that system heat capacity to convert energy to temperature.

That'll be a moderately awkward differential equation.  For the common exponential relation of temperature and rate (assuming an Arrhenius relationship for the rate constant), with temperature not constant, it will almost certainly need numerical solution with something like the deSolve package. That can give you an integrated change at different times. After that 'all' you need to do is wrap that in a function to return a residual sum of squares and then plug that into something like optim() or perhaps nls() to fit the curve.

You may want to set I say 'all you need ...'; obviously, that's a fair bit of work...

________________________________________
From: PIKAL Petr [petr.pikal using precheza.cz]
Sent: 10 June 2020 07:59
To: Stephen Ellison; r-help using r-project.org
Subject: RE: [R] almost logistic data evaluation

Hi

External heating. Normally I would use TA instrumentation but for technical
reasons it is impossible. And other complicating factor is that temperature
rise is from beginning almost parabolic (it's derivation is straight line).

Therefore I started with double exponential fit, which is sometimes
satisfactory but sometimes gives nonsense result. After help from R
community I got in almost all cases reasonable fit.

However I want to concentrate on just the reaction part and to find some
more simple way how to get slope for temperature rise and maybe other
parameters related to changes in experiments.

I was advised to look at "growth curve analysis" which I will try to, but I
wonder if due to twisted data is appropriate.

Thanks.
Petr

> -----Original Message-----
> From: R-help <r-help-bounces using r-project.org> On Behalf Of Stephen Ellison
> Sent: Tuesday, June 9, 2020 7:11 PM
> To: r-help using r-project.org
> Subject: Re: [R] almost logistic data evaluation
>
> > Actually "y" is growing temperature, which, at some point, rise more
rapidly
> due to exothermic reaction.
> > This reaction starts and ends and proceed with some speed (hopefully
> different in each material).
>
> Are you applying external heating or is it solely due to reaction
kinetics?
>
>
> Steve E
>
> *****************************************************************
> **
> This email and any attachments are confidential. Any u...{{dropped:19}}

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