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.pi...@precheza.cz]
Sent: 10 June 2020 07:59
To: Stephen Ellison; r-help@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-boun...@r-project.org> On Behalf Of Stephen Ellison
> Sent: Tuesday, June 9, 2020 7:11 PM
> To: r-help@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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