Eugene Polygalov is a senior research fellow.

Eugene Polygalov

Freeze-drying, also known as lyophilization, is a process that removes water from a frozen material by sublimation to preserve heat-sensitive materials or to make them more convenient for transportation and handling (1, 2). It is a three-step process, which starts with the pre-freezing of the material, followed by primary drying (i.e., sublimation of ice at reduced pressure) and finally, secondary drying (i.e., removal of adsorbed water at elevated temperature).

The most important objectives for the rational design of freeze-drying processes is to characterize the freezing process (i.e., the nucleation and growth of ice crystals), determine the rate of primary drying (and the dry-layer cake resistance), and assess the end point of primary drying. To achieve these objectives for individual vials within a batch requires the development and implementation of new analytical technology that can provide product and process understanding in the complex environment of low temperature and low pressure that exists within the freeze-drying chamber.

All technologies developed to date for freeze-drying process control are based on physical measurements, such as weight (freeze-drying microbalance), pressure (manometric temperature measurement [MTM]), and temperature (thermocouple), or based on the interaction of light with a material (such as in the case of near infrared spectroscopy [NIRS] and Raman). Despite that, each process analytical technology (PAT) method has inherent limitations in its application to understanding and/or control of the freeze-drying cycle (3). 

There are few examples whereby the measurement of electrical properties is used to provide information about a material during processing (4-6). This approach is in contrast to off-line electrical impedance measurements that are being used routinely to identify critical process events, such as phase transitions (i.e., freezing points and eutectics), against process set points (i.e., shelf temperature, and hence, product temperature during the pre-freezing stage) (7). By investigating the interrelations between the electrical properties and the structural characteristics of the solution, it might be possible to develop this technique towards a more comprehensive monitoring of the freeze-drying process. The development of an in-line technology based on impedance analysis, however, requires:

The close proximity of a least one electrode to the freeze-drying vial to have a chance of sensing any changes in the physical state of the material contained within 
  
  •  The integration of the cabling within the freeze-dryer, which necessitates the creation of a pass-through to the freeze-drying chamber without compromising the vacuum seal
  •  The development of a high-precision, high-impedance dielectric analyzer with a high-phase angle resolution (~ 0.001°) to detect small changes in the dielectric loss (i.e., real part impedance) of the material under test
  •  Careful control over material properties other than those of interest, such as variations in the vial wall thickness, the reproducibility of the electrode design, and the proximity of any attachment mechanisms to the vial. 
  
Through-vial impedance measurements were developed specifically to address these issues. The primary aim for the implementation of this new PAT was to demonstrate the use of impedance spectroscopy in the determination of the rate of primary drying, the end point, and the identification of product collapse. The example of a 3% lactose solution is given.


Aliquots (3 mL) of a lactose solution (3% w/v) were added to the impedance measurement vials and placed on the freeze-dryer shelf among a hexagonal array of plain vials and then connected to the data-acquisition system. For collapse measurements, the impedance measurement vials were arranged on the shelf in a straight line. Photographic images were taken every 3 minutes using a Cannon EOS 550D SLR camera. The impedance measurements were performed over a frequency range of 10-10

. The freeze-drying cycle details are shown in 

Table I: Freeze-drying cycle for collapse measurements.


The impedance technology measures the electrical impedance of the product, contained within a standard freeze-drying vial that has been modified with electrodes placed on the outside of the glass wall (8). The impedance measurement vials connect to a high impedance current to voltage converter (I-to-V converter) by a junction box within the freeze-dryer chamber, mounted close to the shelf on which the vials are located. The signals from the stimulating voltage and the signals from the resultant current from the I-to-V converter are compared to determine the impedance of the measurement vial and its contents (see 

Physical basis for through-vial impedance measurement 


The electrical impedance of a material determines how easily the material will conduct a current when an alternating voltage is applied to it. Electrical impedance is a function of both the dielectric and conductive properties of the material, which are in turn defined by the temperature, composition, and physical state of the material contained within the vial. Changes in these electrical parameters, therefore, directly mirror the condition of the sample and progression of the freeze-drying cycle. The electrical parameter that has the most significant effect on the output from the impedance measurement system is the resistance (or conversely, the conductivity) of the product contained within the glass vial. Conductivity is widely used for the determination of the physical properties of materials in a wide spectrum of applications due to the fact that the measurement technology is relatively inexpensive.

To explain the observed impedance spectrum of the object under test and relate it to the physical properties or changes that may happen during the freeze-drying process, it is necessary to create an appropriate equivalent circuit model. The circuit model (see 

) was found to provide an approximate fit to the measured impedance spectrum, where CPE denotes a contant phase element and models the interfacial capacitance formed between the glass walls of a vial and the solution, which is charged through the resistance (R) representing the conductivity of the sample, and C represents the electrical capacitance of the material within the internal volume of a vial. This interfacial polarization imparts a frequency-dependence to the measured dielectric properties, such that the interfacial capacitance  will have sufficient time to charge completely at low frequency, but at high frequency, it will not have time to begin to accumulate any of the electrical charge that could otherwise be accommodated. 

The overall result is that the capacitance spectrum of the material under test (i.e., the glass vial, its contents, and the electrical connections to the vial) will display a step-like decrease in capacitance as the frequency is increased through that critical frequency that corresponds to the time constant for the sample (f = 1/2πτ, where τ = RC) (see 

). There is a corresponding peak in the associated imaginary capacitance spectrum as the material under test starts to conduct electricity through the phase lag between the response of the sample and the applied electric field (see 

). The step in the real part capacitance and the peak in the imaginary capacitance is known as a pseudo-relaxation process because it has the appearance of a real relaxation process within a material (i.e., one that has a frequency dependent to its dielectric properties owing to some molecular relaxation or some form of interfacial charging within the material). In reality, the dielectric properties of the material within the vial may be static (i.e., invariant with frequency), and one is simply measuring the accumulation of charge at the glass surface as ions migrate through the liquid or solid contained within the glass vial. 

It is the characteristics of this process that are used to “follow” the progression of the freeze-drying cycle. More specifically, it is the peak frequency and peak value for the imaginary capacitance (which can be considered as the magnitude of the pseudo relaxation process) that is used to monitor the freeze-drying cycle. 

 shows a typical surface plot of the imaginary capacitance as a function of frequency and time during the entire freeze-drying cycle. There are characteristic shifts in the relaxation frequency and change in the peak height as the temperature of the sample changes and when the material undergoes a phase change, for example, from liquid to ice. There is then a dramatic decrease in the magnitude of the pseudo-relaxation peak as ice is removed from the sample.

To track these transitions in greater detail, each impedance spectrum was analyzed with the data-viewing software that runs a peak-finding algorithm and displays the data in a variety of formats including peak frequency (

), and a time slice at a particular frequency. When the sample is in the liquid state (i.e., low electrical resistance/high conductivity), the time constant is relatively short and so the pseudo-relaxation peak occurs at high frequency. Conversely, when the sample is in the solid (i.e., frozen) state, the time constant deceases by a factor of ~100 and the pseudo-relaxation peaks shifts to a lower frequency by approximately two orders of magnitude (see 

 profile (see Figure 3b) effectively describes the freezing stage of lyophilization process because the product resistance is changing, both with the temperature and phase state of the liquid. The frequency position of the pseudo-relaxation peak decreases during cooling, then spikes following the onset of ice nucleation because of the sudden increase in temperature due to exothermic ice formation. It then decreases during the solidification and temperature equilibration phase. On either side of the phase transition, the frequency of the peak is strongly coupled to the temperature of the product at the specific time point suggesting a potential application as a non-invasive surrogate temperature probe.

The sublimation phase is studied by analyzing the peak amplitude of the imaginary capacitance (

with time signifies the progressive removal of ice during the primary drying step (

). The time-derivative profile of capacitance at 1 kHz provides an estimate for the sublimation rate, which peaks at 15 h and subsequently decreases due to higher dry-layer resistance (see 

). The data illustrate how the impact of different parameters on the dry-layer resistance can be studied on a single vial, including solute concentrations, freezing rate, annealing temperatures, and hold time. Compared with gravimetric techniques, development scientists may prefer this technology for determining sublimation rates because it permits the positioning of the vials on the shelf in the hexagonal arrays and does not require the persistent perturbation in the heat flow associated with the lifting and weighing of the vial. 

, there are minimal changes in the peak frequency, and hence, time constant (τ) during primary drying (see 

). These observations can be explained in terms of the height of the ice layer across the sensing zone between the electrodes during primary drying. Both the dry layer and the ice layer are modelled as two separate series RC circuits in parallel with each other (see 

). Given the higher dielectric constant and lower resistivity of the ice layer, the impedance of the two layers can be considered simply in terms of the impedance of the ice layer. In effect, the dry-layer impedance can be ignored. The interfacial capacitance (CPE) of the ice layer/glass interface is proportional to its effective area (A) contacting the electrode (CPE α A), whereas the resistance (R) of the ice layer is inversely proportional to the contact area. It follows that as the height (h) of the ice layer decreases, the resistance of the layer decreases as a function of 1/h, whereas the interfacial capacitance decreases in proportion to h. The time constant (τ = RC), and hence, 

, remains approximately constant over the entire primary drying stage but the magnitude of the peak decreases in proportion to the height of the ice layer (h). 

During the last stage of primary drying, the spectra exhibit a certain degree of low frequency noise. At this point (> 20 h), the data-analysis software begins to “locate” the peak at a progressively lower frequency. These uncertainties preclude the use of the pseudo-relaxation peak in determining the end point of the primary-drying phase. While the peak-versus-time profiles are of value in the measurement of temperature changes and in characterizing the various stages of the freezing step, an alternative approach is required for the determination of the end point of primary drying. This alternative approach is to examine the logarithm of the time slice of the capacitance derivative at 1 kHz, which is the predominant position of the pseudo-relaxation peak during primary drying. It has been shown that the alternative approach provides acceptable information regarding the measurement of the end point of sublimation. This is illustrated in Figure 3d, in which the end point of primary drying can be observed from the sharp decrease at approximately 27 h. 


During sublimation, the time derivative of the capacitance increases to a maximum and then decreases to zero (see

), the increase in shelf temperature at 5 h into the primary-drying cycle results in an increase in product temperature and an increase in drying rate. The increased drying rate is evident from the inflection in the dC”/dt plot (left hand vertical line on 

). However, as the temperature rises further, it reaches critical levels, whereby the viscosity of the glassy matrix has decreased to such an extent that its walls are unable to support its structure. At this point, the product is seen to collapse (see 

), and there is a small spike in dC”/dt as the product at the sublimation front loses its integrity. Photographic evidence of the product collapse were found to correlate well with the occurrence of this small spike. In the later stages, the softened mass at the sublimation front merges to produce wider pores that result in higher sublimation rates, which is reflected in the further increase in dC”/dt.

Articles

A new process analytical technology based on impedance spectroscopy has potential applications for characterizing product attributes during the freeze-drying process.