Water Activity and Plasticization - Food Shelf Life Stability: Chemical, Biochemical, and Microbiological Changes - page 12

empirical relationship describes the temperature dependence of mechanical proper-
ties of amorphous polymers above T g . The ratio, a T , of relaxation times,

τ 0 ,
of configurational rearrangements at respective temperatures, T and T 0 ,reflects the
temperature dependence of mobility. Literature data for viscosity of a number of
amorphous materials showed that a T followed Eq. (1.8), where C 1 and C 2 are con-
stants, and T 0 is a reference temperature. 58

τ and

− ( )
+−

CT T
CTT

−

1 0

log a = (1.8)

( )

T

2 0

Equation (1.8) is known as the Williams-Landel-Ferry (WLF) relationship, which
was reported to be applicable over the temperature range from T g to T g + 100°C. The
use of T 0 at T g + 50°C instead of using T 0 = T g as the reference temperature was
considered preferable, because experimental data on relaxation times at and below
T g are often scarce or nonexisting. However, Williams et al. 58 reported “universal
values” for C 1 and C 2 , but their use in predicting food behavior at temperatures above
T g has been criticized. 59 Peleg 57,59 has shown that the WLF model may not be useful
within the transition range and he has suggested the use of Fermi's distribution
function to model the rate dependence on a w , water content, and temperature of
changes occurring over the glass transition. The main difference between the curves
obtained is that the WLF prediction has an upward concavity, while Fermi's distri-
bution function gives a downward concavity at and around the transition region. 57

V ISCOSITY

The WLF relationship relates viscosity or any other temperature-dependent mechan-
ical property to T g or some other reference temperature, as suggested by Levine and
Slade, 6,9-11,14 although extrapolation and use of the relationship within the transition
temperature range is not justified. 57 Similarities between the physical properties of
various amorphous materials, however, have shown that the use of the WLF model
for predicting temperature dependence of viscosity allows establishing diagrams
showing isoviscosity states above T g or at least to describe the dramatic effect of
the transition on viscosity or relaxation times of mechanical changes. State diagrams
with isoviscosity lines show effects of both temperature and water content on the
physical state ( Figure 1.8 ). Such diagrams are useful in estimation of effects of
composition on relaxation times, i.e., rates of changes in mechanical properties, at
a constant temperature or to establish critical temperatures in food processing (e.g.,
agglomeration, extrusion, and dehydration) and storage (e.g., storage of low-mois-
ture foods and powders at high relative humidity/temperature environments). 6,53

S TIFFNESS

The term collapse , as defined by Levine and Slade, 10 covers various time-dependent
structural transformations that may occur in amorphous food and other biological
materials at temperatures above T g . These changes reflect the effect of the changes
in relaxation times of mechanical properties and flow that occur over the T g tem-