Lynne Wong's PhD thesis

5.6.4.4 Fitting of sorption models to the experimental EMC data
In order to determine which isotherm model best described the experimental EMC data
obtained, fifteen of the isotherm models listed in Table 5.1 (all except the last two) and the
modified Chung-Pfost and modified GAB models in Table 5.2 were fitted to the data. The
parameters of the first seven models in Table 5.1 (namely, the Bradley, Caurie I, Caurie II,
Halsey, Henderson, Kuhn and Smith models) were estimated by linear regression with
Microsoft Excel software whereas those of the GAB model were estimated with the aid of
the WATER ANALYSER PROGRAM (Webbtech@bigpond.com). Those of the
remaining nine models (namely, BET, modified BET, Day-Nelson, Hailwood-Horrobin,
Iglesias-Chirife, Mizrahi, Oswin, modified Chung-Pfost and modified GAB) were
estimated by making use of the non-linear regression procedure of SigmaPlot (SPSS Inc.).
The values of these parameters together with the calculated regression criteria, i.e. the
coefficient of determination R 2 , the mean deviation modulus P and the standard error of the
estimate E s , for each model and for each of the nine sugar cane components aged 52 and 36
weeks are shown in Tables 5.19 – 5.27. The BET, Day-Nelson and modified Chung-Pfost
models yielded spurious results; they would undoubtedly give poor fit of the experimental
results and were not included in the Tables.
From Tables 5.19 – 5.27, it can be seen that for the first ten isotherm models, namely the
GAB, Hailwood-Horrobin, Henderson, Bradley, Caurie I, Smith, Oswin, Halsey, Caurie II
and modified GAB models, the coefficient of determination R 2 approaches one for most
temperatures studied (30, 45, 55 and 60 °C) and for all the nine cane component parts of
both ages. However, for the last four isotherm models, namely the Kuhn, Iglesias-Chirife,
Mizrahi and modified BET models, this was not the case, R 2 was low and mostly below
0.90, and the mean relative deviation modulus P was much greater than 10. They therefore
gave a poor fit of the experimental results. As mentioned earlier in Section 5.3.4, for a
good fit, R 2 must approach one, the P value must be between 5 and 10, and the standard
error of the estimate, E s , must be as small as possible.
The poor fit of the last four isotherm models was confirmed from inspection of the
isotherm plots for the EMC of stalk fibre of variety R 570 aged 52 weeks shown in Fig
5.10. The complete set of isotherm plots for all the nine components is included on the CD
(file: Isotherm plots.xls).
The isotherm plots show that in general, apart from the bad fit of the four models
mentioned above, the Bradley and Smith models are only applicable within the activity
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