is the heat of sublimation of ice (670 cal/g used as constant), P
is the vapor pressure of ice (Torr, known from the first experiment), P
is the chamber pressure (Torr), R
and Rs are the product and stopper resistance, respectively (cm2 ×Torr ×h/g, known from the first experiment), A
is the vial outer cross-sectional area (6.83 cm2), K
is the vial heat transfer coefficient (104 ×cal/sec ×cm2 ×K, cf.) (see Table I), T
is the shelf-inlet temperature (°C) and Tb the temperature at the bottom of the vial (°C).
Table I illustrates the theoretical values obtained from the steady-state model for the maximum product temperature (T
) when using a ± 5 °C shelf temperature variation at constant pressure (62 mTorr) or an increase in chamber pressure from
62 to 200 mTorr at constant T
Table I: Summary of process conditions for 50–200 mg/mL sucrose solutions and corresponding maximum product temperature data
(Tp-max) during primary drying.
The modeled results obtained for T
p-max were found in fairly good agreement to the experimental data. Note that this observation has been reported in the literature
(11). However, the effect of T
s and P
on product temperature was lower in the experiments performed relative to the theoretical calculations, in particular for
applied pressure changes. Although such simulation is useful for scale-up, rational design of the freeze-drying process and
troubleshooting, simulations cannot eliminate the need for careful experimentation (12).
Rp data determined for products dried by the optimized cycle increased almost linearly over Ldry, indicating an absence of shrinkage and microcollapse (see Figure 4) (4, 5). The variation of T
by ± 5°C showed no clear impact on R
p. However, the pressure increase up to 200 mTorr resulted in a significant decrease in R
dry. Microcollapse as well as shrinkage in these products could be detected visually and by SEM (see Figure 5b).
Note that an increase in solute concentration led to a similar R
curve shape relative to the samples at high P
c, but the product matrix revealed much greater robustness to elevated temperature (see Figures 4 and 5c). This observation
was in excellent agreement with the T
difference measured by FDM between 50 mg/mL (T
c= –34° C) and 200 mg/mL (T
= –32 °C) sucrose solutions. Note that the dependency of sucrose concentration on T
was recently investigated but is in contrast to data obtained in early studies on a different amorphous system (8, 13).