Lyophilization of Pharmaceuticals and Biologicals pp 241-290 | Cite as

# Through Vial Impedance Spectroscopy (TVIS): A Novel Approach to Process Understanding for Freeze-Drying Cycle Development

## Abstract

Through vial impedance spectroscopy (TVIS) provides a new process analytical technology for monitoring a development scale lyophilization process, which exploits the changes in the bulk electrical properties that occur on freezing and subsequent drying of a drug solution. Unlike the majority of uses of impedance spectroscopy, for freeze-drying process development, the electrodes do not contact the product but are attached to the outside of the glass vial which is used to contain the product to provide a non-sample-invasive monitoring technology. Impedance spectra (in frequency range 10 Hz to 1 MHz) are generated throughout the drying cycle by a specially designed impedance spectrometer based on a 1 GΩ trans-impedance amplifier and then displayed in terms of complex capacitance. Typical capacitance spectra have one or two peaks in the imaginary capacitance (i.e., the dielectric loss) and the same number of steps in the real part capacitance (i.e., the dielectric permittivity). This chapter explores the underlying mechanisms that are responsible for these dielectric processes, i.e., the Maxwell-Wagner (space charge) polarization of the glass wall of the vial through the contents of the vial when in the liquid state, and the dielectric relaxation of ice when in the frozen state. In future work, it will be demonstrated how to measure product temperature and drying rates within single vials and multiple (clusters) of vials, from which other critical process parameters, such as heat transfer coefficient and dry layer resistance, may be determined.

## Key words

Impedance spectroscopy Process-analytical-technology PAT Freeze-drying Lyophilization Maxwell-Wagner Polarization Dielectric relaxation Ice## Abbreviations

- ADC
Analog digital converter

- AWG
American wire gauge

- BDS
Broadband dielectric spectroscopy

- DAQ
Data acquisition card

- DSC
Differential scanning calorimetry

- DTA
Differential thermal analysis

- ER
Electrical resistivity measurements

- ETA
Electrical thermal analysis

- FDM
Freeze drying microscope

- IS
Impedance spectroscopy

- IVC
Current to voltage converter

- MW
Maxwell-Wagner polarization process

- OUT
Object under test

- TSC
Thermally stimulated current spectroscopy

- TVIS
Through vial impedance spectroscopy

## Symbols

- −
Series arrangement of two elements in an electrical circuit

*C*′Real part capacitance or dielectric storage of complex capacitance

*C*″Imaginary part capacitance or dielectric loss of complex capacitance

*C*′(∞)Real part capacitance at high frequency

- \( {C}_{\mathrm{PEAK}}^{{\prime\prime} } \)
Peak amplitude of the imaginary capacitance

- \( {C}_{\mathrm{fit}}^{\prime } \)
Real part capacitance from equivalent circuit modelling

- \( {C}_{\mathrm{fit}}^{{\prime\prime} } \)
Imaginary part capacitance from equivalent circuit modelling

*C*_{a}Capacitance of adhesive layer

*C*_{a−g}Capacitance of the composite glass wall and adhesive layer in series

*C*_{a−G}Total capacitance of the composite glass wall and adhesive layer in series

*C*_{g}Capacitance of glass-sample interface

*C*_{G}Total glass-sample interface capacitance

*C*_{i}Capacitance of the interfacial layer between glass and sample

*C*_{o}Capacitance of empty cell

*C*_{s}Capacitance of sample

*C*_{s}(∞)Capacitance of sample in the limit of high frequency

*C*_{s}(0)Capacitance of sample in the limit of low frequency

*C*_{s}(*f*)Capacitance of sample as a function of frequency

- CPE
_{G} Constant phase element of glass wall

- \( {C}_{\mathrm{fit}}^{\prime}\left(\infty \right) \)
Real part capacitance from modelling at high frequency

- \( {C}_{\mathrm{fit}}^{\prime }(f) \)
Real part capacitance from modelling as the function of frequency

- \( {C}_{\mathrm{fit}}^{\prime }(o) \)
Real part capacitance from modelling at low frequency

- DE
_{s} Distribution element of sample

*F*_{PEAK}Peak frequency of the imaginary capacitance

*I*_{o}Current amplitude

*Q*_{o}Admittance of a constant phase element at an angular frequency of

*ω*= 1 rad s^{−1}*R*_{s}Resistance of sample

*T*_{c}Collapse temperature

*T*_{eu}Eutectic temperature

*T*_{g}Glass transition temperature

- \( {T}_{\mathrm{g}}^{\prime } \)
Glass transition of the maximally freeze concentrated solution

*T*_{m}Melting temperature

*T*_{b}Ice temperature at the base of a vial

*T*_{i}Ice temperature at the sublimation interface

*V*_{o}Voltage amplitude

- |
*Y*| Admittance magnitude

*Y*_{C}Admittance of a capacitor

*Y*_{CPE}Admittance of a constant phase element

*Y*_{R}Admittance of a resistor

*Z*′Real part impedance

*Z*″Imaginary part impedance

*Z*^{∗}Complex impedance

*Z*_{C}Impedance of capacitance

*Z*_{CPE}Impedance of constant phase element

*Z*_{R}Impedance of resistance

*d*_{g}Glass wall thickness

*k*_{g}Cell constant of glass

*k*_{s}Cell constant of sample

*ε*_{∞}Permittivity in the limit of high frequency

*ε*_{a}Permittivity of adhesive

*ε*_{g}Permittivity of glass

*ε*_{o}Permittivity of free space

*ε*_{r}Relative permittivity

*ε*_{s}Static permittivity

*ρ*_{s}Sample resistivity

*ω*_{c}Angular frequency at cross over between the dominance of two circuit elements

- |
*Z*| sin*φ* Imaginary part of the complex impedance or reactance

- |
*Z*| Impedance magnitude

- =
Parallel arrangement of two elements in an electrical circuit

- Δ
*C*′ Increment in the real part capacitance

*C*Capacitance

*h*Electrode height

- I/O
Input/output

*N*A number of sine wave periods

- Ø
Fill factor in relation to the electrode height

*R*Resistance

*α*Exponent parameter describing the broadening of a dispersion process

*ρ*Density

*A*Electrode area

- CPE
Constant phase element

*I*Current

*V*Voltage

*Y*Admittance

*Z*Impedance

*d*Separation of two electrodes

*f*Frequency

*i*Notation for an imaginary number

*k*Cell constant

*p*Frequency independent parameter (CPE exponent) which corresponds to the phase angle

*t*Time

*w*Electrode width

*τ*Time constant or relaxation time

*φ*Phase difference between the voltage and current

*ω*Angular frequency

*ϑ*Phase angle

## Units

- °
Degree

- °C
Degree Celsius

- dB
Decibel

- F m
^{−1} Farad per meter

- fF
Femtofarad

- g
Gram

- g cm
^{−3} Gram per cubic centimeters

- GΩ
Gigaohm or 10

^{9}ohm- Hz
Hertz

- K
Kelvin

- kg m
^{−3} Kilogram per cubic meters

- kHz
Kilohertz or 10

^{3}hertz- MHz
Megahertz or 10

^{6}Hertz- min
Minute

- mL
Milliliter

- mm
Millimeter

- mm
^{2} Square millimeter

- ms
Millisecond

- pF
picoFarad

- rad s
^{−1} radians per second

- s
Second

- V
Volt

- μs
Microsecond

- Ω
Ohm

## Notes

### Acknowledgments

The original TVIS system used to generate the spectra within this book chapter was developed by Evgeny Polygalov and Geoff Smith (from De Montfort University) in a collaboration with GEA Pharma Systems (Eastleigh, UK) and was part-funded by a UK government, Innovate UK Collaborative R&D project called LyoDEA (Project Reference: 100527).

Special thanks go to Yowwares Jeeraruangrattana (from the Government Pharmaceutical Organization, in Thailand and one of De Montfort University’s PhD students from 2015 to 2018) for creating the majority of the images, drawings and figures, and assisting in formatting of the text and bibliography.

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