The Dried Product - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 149

directly in Equation (12) or (13), to evaluate the parameter m:

DE T g
2 : 303 RT g

m ¼ ð 17 Þ

11.4.3 Glass Transition Width

An undercooled liquid has a distribution of relaxation times and hence
the observed glass transition occurs over a range of temperatures.
''Strong'' glass formers do not show rapid changes in t with temperature
and therefore give rise to broad glass transitions. Fragile behaviour
leads to a narrower glass transition temperature range.
Moynihan et al. 143 proposed the useful relations:

! ¼ constant

1
T on

DE Z
R

1
T off

ð 18 Þ

g g

or

, ! ¼ CRT o g T of g = DT g

1
T on

1
T off

DE Z ¼ CR ð 19 Þ

g g

as a means for the estimation of fragility. The superscripts ''on'' and
''off'' refer to the start and completion of the glass transition range as
observed by DSC. In Equation (19), C is a constant and DT g is the width
of the glass transition. Experimentally, the proportionality constant
C ¼ 5 0.5.
Assuming an equivalence of DE Z and DE T g , then both m (pragmati-
cally) and D (more rigorously) can be calculated, as discussed in Section
11.4.2.
In summary, all the three methods give similar results, but the calcu-
lation of m or D from the temperature dependence of the glass transition
width is the most practical first-choice method, especially as the method
that is based on the temperature dependence of T g requires rather
careful calibration of the instrument. Generally for pharmaceutical
materials, T g /T m falls within the range 0.71-0.86 and D in the range
7-13, i.e. they are moderately fragile materials. There appears to be no
simple relationship between T g /T m and fragility.
Finally, the question of relaxation below T g and its relation to fragility
requires comment. Experimental data suggest that pharmaceuticals are
moderately fragile above T g , but there seems to be no a priori reason