24
THEORY
Figure 23 Working and full isotherm for wood pulp
3.6 ISOTHERM MODELS
Several different isotherm models have been proposed and compared in the literature.
These models are necessary to predict the moisture content at a given water activity and
are used to evaluate thermodynamic functions of water in foods. The models are necessary
when using isotherm methods with low data resolution to interpolate between isotherm data
points. While there are 270 proposed isotherm models, the most commonly used models are
the Guggenheim-Andersen-de Boer (GAB) and Brunauer-Emmett-Teller (BET). Since the BET
model is only applicable up to 0.50 a
w
, the GAB model is widely accepted as the most useful
for characterizing isotherms across the entire water activity range. Its coefficients also have
theoretical physical meaning such as providing monolayer moisture content. A new empirical
model called the Double Log Polynomial (DLP) or Chi plot has proven to be even better than
the GAB at characterizing complex isotherms. The model equations are shown below.
Equation 5
Where m is the moisture in g/100 solids or g/g solids at water activity a
w
and m
o
is the
monolayer value in the same units. Calculate the constant c with:
Equation 6
Where Q
s
is the surface interaction energy in J/mole, R is the gas constant (8.314 J/mol K)
and T(K) is the temperature.
Equation 7
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