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

  • Geoff SmithEmail author
  • Evgeny Polygalov
Protocol
Part of the Methods in Pharmacology and Toxicology book series (MIPT)

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

Ca

Capacitance of adhesive layer

Ca−g

Capacitance of the composite glass wall and adhesive layer in series

Ca−G

Total capacitance of the composite glass wall and adhesive layer in series

Cg

Capacitance of glass-sample interface

CG

Total glass-sample interface capacitance

Ci

Capacitance of the interfacial layer between glass and sample

Co

Capacitance of empty cell

Cs

Capacitance of sample

Cs(∞)

Capacitance of sample in the limit of high frequency

Cs(0)

Capacitance of sample in the limit of low frequency

Cs(f)

Capacitance of sample as a function of frequency

CPEG

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

DEs

Distribution element of sample

FPEAK

Peak frequency of the imaginary capacitance

Io

Current amplitude

Qo

Admittance of a constant phase element at an angular frequency of ω = 1 rad s−1

Rs

Resistance of sample

Tc

Collapse temperature

Teu

Eutectic temperature

Tg

Glass transition temperature

\( {T}_{\mathrm{g}}^{\prime } \)

Glass transition of the maximally freeze concentrated solution

Tm

Melting temperature

Tb

Ice temperature at the base of a vial

Ti

Ice temperature at the sublimation interface

Vo

Voltage amplitude

|Y|

Admittance magnitude

YC

Admittance of a capacitor

YCPE

Admittance of a constant phase element

YR

Admittance of a resistor

Z

Real part impedance

Z

Imaginary part impedance

Z

Complex impedance

ZC

Impedance of capacitance

ZCPE

Impedance of constant phase element

ZR

Impedance of resistance

dg

Glass wall thickness

kg

Cell constant of glass

ks

Cell constant of sample

ε

Permittivity in the limit of high frequency

εa

Permittivity of adhesive

εg

Permittivity of glass

εo

Permittivity of free space

εr

Relative permittivity

εs

Static permittivity

ρs

Sample resistivity

ωc

Angular frequency at cross over between the dominance of two circuit elements

|Z| sinφ

Imaginary part of the complex impedance or reactance

|Z|

Impedance magnitude

=

Parallel arrangement of two elements in an electrical circuit

ΔC

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

Gigaohm or 109 ohm

Hz

Hertz

K

Kelvin

kg m−3

Kilogram per cubic meters

kHz

Kilohertz or 103 hertz

MHz

Megahertz or 106 Hertz

min

Minute

mL

Milliliter

mm

Millimeter

mm2

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Pharmaceutical Technologies, Leicester School of PharmacyDe Montfort UniversityLeicesterUK

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