order transition. Altogether, some basic problems have not yet been
resolved, and it may well be that there is not just a single classical, second-
order, transition. The values obtained and published for Tg^0 thus are
uncertain by a few degrees.
DSC scans of mixtures of solutes, and particularly of mixtures
including biopolymers, do not show a clear second-order transition. An
easier method of determiningTg^0 then is by dynamic rheology in small
samples as a function of temperature. Figure 16.8b gives an example. Again,
two points can be chosen, at the bend in the curve of the storage modulus, or
the optimum temperature for the loss modulus. Usually, the latter point is
taken, if only because it can be established with greater accuracy. The values
obtained also depend on the rate of temperature increase and on the
deformation frequency during the dynamic measurement (usually 1 Hz).
The greatest uncertainty is in the value of theresidual water contentc^0 W
as determined by DSC. It is obtained by determining the area under the
DSC curve betweenTg^0 andTmand above the (uncertain) base line (cf.
Figure 16.2). It has been shown that this method tends to involve a number
of errors, which altogether lead to considerable overestimation of the value
ofc^0 W. For instance, most values published for sucrose are around 0.36,
whereas 0.17 is now considered to be the best estimate. It must be assumed
that most of the published values for pure substances are too high by a
substantial amount. The best way to obtain the value ofc^0 Wis to findTg^0 ,
e.g., by DSC, and then separately determineTgversuscsfor mixtures of low
FIGURE16.8 Methods of determining the special glass transition temperatureTg^0.
(a) Scan obtained by DSC (differential scanning calorimetry), giving the heat uptake
(e.g., in J?kg^1 ?K^1 ) versus temperatureT. (b) Scan of the storage(G^0 ) and loss
modulus (G^00 ) in Pa versus temperature. (After examples given by Champion et al.
[see Bibliography].)