1. Higher chamber pressure decreases the driving force for water vapor transport from the ice interface within the product
to the chamber. This driving force is defined as the difference between the pressure at the ice interface within the product
and the chamber pressure (Pi-Pc). This effect can be seen by following the lines of constant product temperature in Figure
1, noting the linear increase in sublimation rate with decreasing chamber pressure, as long as product temperature remains
2. Higher chamber pressure increases the rate of heat transfer to support sublimation rate by increasing the thermal conductance
of the gas in the narrow gap between the shelf surface and the bottom of the product vial.4 This effect increases the product temperature, which in turn increases the vapor pressure of ice in the product, thereby
increasing the pressure of water vapor at the ice interface. This condition increases the driving force for flow of this water
vapor from the product into the chamber.
Within the range of chamber pressures used for pharmaceuticals and vaccines, the net effect of a higher chamber pressure is
to increase the product temperature and sublimation rate of the product. This occurs because the improved heat transfer provided
by higher pressure outweighs the negative effect on the sublimation rate of decreasing the driving force for flow of water
vapor from the product to the chamber.
Therefore, for the most efficient processing, it is desirable to operate at the highest possible shelf temperature and the
lowest chamber pressure that still maintains the target product temperature during primary drying.
Table 1. Current paradigm compared to the Quality by Design paradigm
HOW IS SUBLIMATION RATE MEASURED?
Traditionally, sublimation rates are measured gravimetrically. A representative number of vials are weighed before beginning
the cycle, and the cycle is terminated before the end of primary drying. The average sublimation rate is calculated by re-weighing
the pre-weighed vials after partial drying, and by knowing the time interval during which drying took place. Of course, this
method is destructive, and weighing the vials can be tedious, but the process information is generally worth the loss of material
and the work involved.
There is a new process analytical technology in freeze-drying, however, that provides instantaneous, nondestructive measurement
of sublimation rate. Tunable diode laser absorption spectroscopy is a technique in which sensing hardware is placed in the
connecting duct between a chamber and a condenser. TDLAS is not applicable to freeze-dryers designed with an internal condenser.
A near-infra-red beam is directed at an angle to the axis of the duct, and the Doppler shift of the water absorption band
is measured by comparison with a sealed reference cell containing water vapor at a known partial pressure. The frequency shift
between the two absorption maxima is proportional to the velocity of water vapor in the duct. By measuring the concentration
of water vapor by traditional absorption spectroscopy, and by knowing the cross-sectional area of the duct, the instantaneous
mass flow rate is determined.
In the laboratories at Baxter Pharmaceutical Solutions, scientists have compared gravimetric measurement of the sublimation
rate with the integrated area under the mass flow rate versus time curve, and have generally found agreement within about
3%, which they consider satisfactory.
A photograph of the sensing hardware mounted on an FTS Systems Lyostar II freeze-dryer is shown in Figure 2, and a graph showing
sublimation rate during the time course of freeze-drying is shown in Figure 3.