The document discusses the application of terahertz spectroscopy for the characterization of amorphous materials, emphasizing the techniques of dielectric spectroscopy and terahertz radiation. It highlights the capabilities of terahertz spectroscopy to measure molecular dynamics and structural changes in disordered systems, particularly polysaccharides. Additionally, the study delves into crystallization processes and phase transitions using terahertz time-domain spectroscopy, showing its potential for in situ monitoring of these phenomena.

1. Terahertz Spectroscopy for the Solid State
Characterisation of Amorphous Systems
Juraj Sibik and Axel Zeitler
Department of Chemical Engineering and Biotechnology, University of Cambridge,
Pembroke Street, Cambridge CB2 3RA, UK
jaz22@cam.ac.uk
http://thz.ceb.cam.ac.uk – www.pssrc.org
19 June 2015

2. Outline
Introduction
Dielectric Spectroscopy
Terahertz Radiation
Amorphous Materials
What Can be Measured at THz Frequencies?
Model System: Polyalcohols
Crystallisation
Stability Prediction
Summary

3. Outline
Introduction
Dielectric Spectroscopy
Terahertz Radiation
Amorphous Materials
Summary

4. Introduction Dielectric Spectroscopy
Dielectric Spectroscopy
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
10
13
10
14
10
15
10
16
10
17
10
18
10
19
10
20
10
21
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
-10
10
-11
10
-12
10
-13
Visible Light
Infrared UltravioletRadiowaves Microwaves X-rays Gamma
1 MHz 1 ZHz1 EHz1 PHz1 THz1 GHz
Frequency / Hz
THz
1 nm1 m1 mm1 m1 km
Wavelength / m
Complementary technique to terahertz spectroscopy at lower
frequencies
2 of 31

5. Introduction Dielectric Spectroscopy
Absorption Mechanisms
This technique spans
the frequency range
over 102 to 1012 Hz
Dipoles and charges
respond to the
excitation by an
external electric field
and move as a whole
during relaxation
ˆε = ε + iε = (n + iκ)2
where α = 4πκ/λ0
Image source: https://commons.wikimedia.org/wiki/file:
Dielectric_responses.svg 3 of 31

6. Introduction Dielectric Spectroscopy
Dielectric Relaxation – Molecular Mobility
α-relaxation
Structural relaxation
process
Relaxation time changes
from 10−12 to 102 s upon
glass transition
Concept of cooperatively
rearranging regions
(CRR)
β-relaxations
Local motions involving
the entire molecule or
intra-molecular
reorientations
Much faster than α
relaxations
Commonly observed
either as a separate peak
or as a high frequency
wing of the α-relaxation.
G. Adam, J.H. Gibbs, The Journal of Chemical Physics. 43, 139 (1965). 4 of 31

7. Introduction Dielectric Spectroscopy
Dielectric Relaxation in Amorphous Solids
α and β relaxation process are
separated in frequency (but are
very broad and often overlap)
The secondary β-relaxation
processes are typically related to
local mobility
It is possible to directly measure the
relaxation times using dielectric
spectroscopy
H. Wagner, R. Richert, J. Non-Cryst. Sol. 242, 19 (1998).
S. Bhattacharya, R. Suryanarayanan, 98, 2935 (2009). 5 of 31

8. Outline
Introduction
Dielectric Spectroscopy
Terahertz Radiation
Amorphous Materials
Summary

9. Introduction Terahertz Radiation
What does Terahertz Radiation Refer to?
1 0
5
1 0
6
1 0
7
1 0
8
1 0
9
1 0
1 0
1 0
1 1
1 0
1 2
1 0
1 3
1 0
1 4
1 0
1 5
1 0
1 6
1 0
1 7
1 0
1 8
1 0
1 9
1 0
2 0
1 0
2 1
1 0
3
1 0
2
1 0
1
1 0
0
1 0
- 1
1 0
- 2
1 0
- 3
1 0
- 4
1 0
- 5
1 0
- 6
1 0
- 7
1 0
- 8
1 0
- 9
1 0
- 1 0
1 0
- 1 1
1 0
- 1 2
1 0
- 1 3
V i s i b l e L i g h t
I o n i s i n g
T r a n s p a r e n c y
I n f r a r e d U l t r a v i o l e t
T r a n s p a r e n c y
S p e c t r o s c o p i c I n f o r m a t i o n
T H zR a d i o w a v e s M i c r o w a v e s X - r a y s G a m m a
1 M H z 1 Z H z1 E H z1 P H z1 T H z1 G H z
F r e q u e n c y / H z
1 n m1 µm1 m m1 m1 k m
W a v e l e n g t h / m
0 . 0 1 0 . 1 1 1 0 1 0 0
F r e q u e n c y / T H z
1 . 0 1 0 . 0 1 0 0 . 0 1 0 0 0 . 0
H y d r o g e n - b o n d i n g s t r e t c h e s a n d t o r s i o n s ( l i q u i d s )
S e c o n d a r y d i e l e c t r i c r e l a x a t i o n s ( s o l i d )
I n t r a m o l e c u l a r v i b r a t i o n a l m o d e s
C r y s t a l l i n e p h o n o n v i b r a t i o n s ( s o l i d )
W a v e n u m b e r / c m
- 1
M o l e c u l a r r o t a t i o n s ( g a s )
6 of 31

10. Introduction Terahertz Radiation
Vibrational Spectroscopy
Mid-infrared
Intramolecular Modes
Information about the structure of a single
molecule, identification of molecules
Terahertz
Intermolecular Modes
Information about the structure and
dynamics of molecular interaction
7 of 31

11. Introduction Terahertz Radiation
Terahertz Time-Domain Spectroscopy
0 1 0 2 0 3 0 4 0 5 0
- 8
- 6
- 4
- 2
0
2
4
6
8
1 0
1 2
THzelectricfield/a.u.
t i m e / p s
1 2 3 4 5
0 . 1
1
1 0
1 0 0
power/a.u.
f r e q u e n c y / T H z
Typical terahertz pulse in time-domain (left) and frequency components of the pulse (right).
Coherent sub-picosecond pulses, bandwidth of 0.1 to 4.0 THz, excellent signal-to-noise
detection
8 of 31

12. Introduction Terahertz Radiation
Terahertz Time-Domain Technology
In THz-TDS both amplitude and phase of the electric field
is measured and not just its intensity
This means that the complex refractive index can be
extracted directly without resorting to Kramer-Kronig
relations:
ˆEsam(ω)
ˆEref(ω)
= T(ω)eiφ(ω)
In terms of absorption coefficient and refractive index:
α(ω) = −
2
d
ln
(nm + n)2
4nmn
T(ω)
n(ω) = 1 +
φ(ω)c
ωd
This can also directly be expressed in terms of dielectric
losses:
ˆn = n + iκ =
√
ˆε =
√
ε + iε
9 of 31

13. Outline
Introduction
Amorphous Materials
What Can be Measured at THz Frequencies?
Model System: Polyalcohols
Crystallisation
Stability Prediction
Summary

14. Amorphous Materials What Can be Measured at THz Frequencies?
Amorphous Materials
http://www.ndt-ed.org/EducationResources/CommunityCollege/
Materials/Structure/solidstate.htm
J. Bicerano, D. Adler, Pure & Appl. Chem., 59, 101 (1987) 10 of 31

15. Amorphous Materials What Can be Measured at THz Frequencies?
Disordered Materials – Losses at THz Frequencies
Amorphous Solids and Supercooled Liquids
Mid-IR: Bond vibrations, slight shift and
broadening compared to crystalline
materials
THz: No phonon vibrations occur as there
is no long range order
At lower frequencies molecular rotations
and translations take place
These molecular motions can be described
by the first order decay of macroscopic
polarisation as proposed by Debye in his
dielectric relaxation theory
11 of 31

16. Outline
Introduction
Amorphous Materials
What Can be Measured at THz Frequencies?
Model System: Polyalcohols
Crystallisation
Stability Prediction
Summary

17. Amorphous Materials Model System: Polyalcohols
Dielectric Response of Amorphous Materials
S. Kastner et al., J. Non-Cryst. Sol. 357, 510 (2011). 12 of 31

18. Amorphous Materials Model System: Polyalcohols
Dielectric Response of Amorphous Materials
S. Kastner et al., J. Non-Cryst. Sol. 357, 510 (2011). 12 of 31

19. Amorphous Materials Model System: Polyalcohols
Amorphous Sorbitol
100 150 200 250 300
0
50
100
150
200
1.5 THz
1.0 THz
0.5 THz
α[cm
-1
]
100wt% sorbitol
T [K]
Tg
Glass
transition
Structural relaxation at Tg leads to increase in absorption
J. Sibik et al., Phys. Chem. Chem. Phys. 15, 11931 (2013). 13 of 31

20. Amorphous Materials Model System: Polyalcohols
Amorphous Sorbitol
100 150 200 250 300
0
50
100
150
200
1.5 THz
1.0 THz
0.5 THz
α[cm
-1
]
100wt% sorbitol
T [K]
Tg
Glass
transition
Subtle but noticeable change in absorption below Tg – origin?
J. Sibik et al., Phys. Chem. Chem. Phys. 15, 11931 (2013). 13 of 31

21. Amorphous Materials Model System: Polyalcohols
Secondary Relaxation in Polyalcohols
A. Döss et al., Phys. Rev. Lett. 88 (2002), doi:10.1103/PhysRevLett.88.095701. 14 of 31

22. Amorphous Materials Model System: Polyalcohols
Terahertz Spectroscopy of Polyalcohols
10
0
10
-1
10
0
300 K
80 K
120 K
190 K
''()
(THz)
(a) glycerol
10
0
150 K
230 K
240 K
90 K
(THz)
(b) threitol
10
0
310 K
80 K
180 K
250 K
(THz)
(c) xylitol
10
0
310 K
(THz)
180 K
260 K
(d) sorbitol
90 K
10
1
10
2
(cm
-1
)
10
1
10
2
(cm
-1
)
10
1
10
2
(cm
-1
)
10
1
10
2
(cm
-1
)
The blue and red circles highlight the losses in the proximity of 0.65 Tg and Tg
respectively.
The sample of threitol recrystallised above 250 K – no data above this temperature
are shown.
J. Sibik et al., J. Phys. Chem. Lett. 5, 1968 (2014). 15 of 31

23. Amorphous Materials Model System: Polyalcohols
Terahertz Spectroscopy of Polyalcohols
0.5 1.0 1.5
0.1
0.3
0.5
0.7
T
T
(iii)(ii)
1.00 T
g
sorbitol(+0.1)
xylitol
threitol(+0.1)
glycerol(-0.1)
''(=1THz)
T/Tg
0.65 T
g
(i)
The sample of threitol recrystallised above 250 K – no data above this temperature
are shown.
J. Sibik et al., J. Phys. Chem. Lett. 5, 1968 (2014). 15 of 31

24. Amorphous Materials Model System: Polyalcohols
Terahertz Spectroscopy of Polyalcohols
At temperatures well below Tg, a
temperature-independent microscopic peak is
observed, which persists into the liquid phase
and which is identified as being due to
librational/torsional modes.
For 0.65 Tg < T < Tg, additional thermally
dependent contributions are observed, and we
found strong evidence for its relation to the
Johari-Goldstein secondary relaxation process.
Clear spectroscopic evidence is found for a
secondary glass transition at 0.65 Tg, which is not
related to the fragility of the glasses.
At temperatures above Tg, the losses become
dominated by primary α-relaxation processes.
Our results show that the thermal changes in the
losses seem to be underpinned by a universal
change in the hydrogen bonding structure of the
samples.
0.5 1.0
Molecular relaxations
0.67 T
g
''
THz
T/T
g
T
g
VDOS
JG-
Libration-vibration motions
Decoupling
(independent of m)
J. Sibik et al., J. Phys. Chem. Lett. 5, 1968 (2014). 16 of 31

25. Outline
Introduction
Amorphous Materials
What Can be Measured at THz Frequencies?
Model System: Polyalcohols
Crystallisation
Stability Prediction
Summary

26. Amorphous Materials Crystallisation
Phase Transitions – in situ Spectroscopy
0 . 7 5 0 . 9 0 1 . 0 5 1 . 2 0 1 . 3 5 1 . 5 0 1 . 6 5 1 . 8 0
0 . 5
1 . 0
1 . 5
2 . 0
2 . 5
2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0
w a v e n u m b e r / c m
- 1
absorbance/a.u.
f r e q u e n c y / T H z
f o r m I I I
f o r m I
Conversion of carbamazepine form III to I at 433 K
Terahertz spectroscopy is very sensitive to changes in supramolecular structure
J.A. Zeitler et al., Thermochimica Acta. 436, 71 (2005). 17 of 31

27. Amorphous Materials Crystallisation
Phase Transitions – Kinetics
Kinetics of the solid state transition. Mechanism occurs as
solid-gas-solid transition and can be resolved using THz-TDS.
J.A. Zeitler et al., ChemPhysChem. 8, 1924 (2007). 18 of 31

28. Amorphous Materials Crystallisation
Amorphous vs. Crystalline Organic Solids
1 0 2 0 3 0 4 0 5 0 6 0 7 0
0 . 0
0 . 5
1 . 0
1 . 5
2 . 0
2 . 5
a m o r p h o u s
c r y s t a l l i n e
Absorbance(decadic)
W a v e n u m b e r [ c m
- 1
]
Crystalline vs. amorphous indomethacine.
C.J. Strachan et al., Chem. Phys. Lett. 390, 20 (2004). 19 of 31

29. Amorphous Materials Crystallisation
Relaxation and Crystallisation
1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
0
2
4
6
8
1 0
1 2
1 4
Absorbance(decadic)
W a v e n u m b e r [ c m
- 1
]
654321
330-340 K
1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
0
2
4
6
8
1 0
1 2
1 4 65432
Absorbance(decadic)
W a v e n u m b e r [ c m
- 1
]
1
340-356 K
1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
0
2
4
6
8
1 0
1 2
1 4 65432
Absorbance(decadic)
W a v e n u m b e r [ c m
- 1
]
1
357-368 K
1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
0
2
4
6
8
1 0
1 2
1 4
Absorbance(decadic)
W a v e n u m b e r [ c m
- 1
]
654321
410-440 K
J.A. Zeitler et al., J. Pharm. Sci. 96, 2703 (2007). 20 of 31

30. Amorphous Materials Crystallisation
Change in Absorbance
2 9 0 3 0 0 3 1 0 3 2 0 3 3 0 3 4 0 3 5 0 3 6 0 3 7 0 3 8 0 3 9 0 4 0 0 4 1 0 4 2 0 4 3 0 4 4 0 4 5 0
0 . 5
1 . 0
1 . 5
2 . 0
3 0 0 3 1 0 3 2 0 3 3 0 3 4 0 3 5 0
0 . 9 0
0 . 9 5
1 . 0 0
1 . 0 5
f o r m IT g
f o r m I I Ig l a s s y
s t a t e
Normalisedabsorbance(decadic)
T e m p e r a t u r e [ K ]
f e a t u r e 1 f e a t u r e 2
f e a t u r e 3 f e a t u r e 4
f e a t u r e 5 f e a t u r e 6
r u b b e r y
s t a t e
c r y s t a l l -
i s a t i o n
p h a s e t r a n s i t i o n
At Tg sample relaxes and crystallises subsequently at higher temperature.
J.A. Zeitler et al., J. Pharm. Sci. 96, 2703 (2007). 21 of 31

31. Amorphous Materials Crystallisation
Crystallisation Kinetics
0 1 2
0
40
80
120
160
200
240
a )
α(cm
-1
)
Frequency (THz)
320 325 330 335 340 345
0.0
0.2
0.4
0.6
0.8
1.0
r a
, amorphous fraction
r c
, crystalline fraction
Avrami-Erofeev fit
Temperature (K)
ra
,rc
b )
a) Terahertz spectra of paracetamol crystallising form the amorphous phase. As
the crystallisation progresses distinct vibrational modes emerge from the VDOS.
b) Kinetics of the crystallisation process and corresponding fit using the
Avrami-Erofeev model.
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 22 of 31

32. Amorphous Materials Crystallisation
Crystallisation of Amorphous Paracetamol
Spectra of the three observed polymorphs
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 23 of 31

33. Amorphous Materials Crystallisation
Crystallisation of Amorphous Paracetamol
0 1 2 3
0
100
200
300
400
300
350
400
450
T
e
m
p
e
ra
tu
re
(K
)
Frequency (THz)
(cm
-1
)
Crystallisation and subsequent phase transitions
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 23 of 31

34. Amorphous Materials Crystallisation
Crystallisation of Amorphous Paracetamol
10
30
50
300 350 400 450
10
30
50
70
50
70
90
110
300 350 400 450
180
240
300
360
T (K)
(cm
-1
)
(a)
0.7 THz
1.0 THz
LIIIIII
(b)
(cm
-1
)
A
1.5 THz
(c)
(cm
-1
)
2.5 THz
(d)
T (K)
(cm
-1
)
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 23 of 31

35. Amorphous Materials Crystallisation
Crystallisation of Amorphous Paracetamol
0 1 2 3
0
100
200
300
0.6 0.9
20
40
(cm
-1
)
Frequency (THz)
325 K
330 K
335 K
0 25 50 75 100
Wavenumber (cm
-1
)
1 2
0
100
200
300
300 K
330 K
335 K
470 K
fit
n(cm
-1
)
Frequency (THz)
20 40 60
Wavenumber (cm
-1
)
Deviation from power law: onset of crystallisation
n (ν) α (ν) = A + C (ν − ν0)q
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 23 of 31

36. Amorphous Materials Crystallisation
Crystallisation of Amorphous Paracetamol
0
10
20
30
40
290 300 310 320 330 460 470
120
130
140
290 300 310 320 330 460 470
1.0
1.1
1.2
1.3
1.4
1.5
T (K)
A(cm
-1
)
(a)
(b)
C(cm
-1
THz
-q
)
(c)
T (K)
q
In paracetamol the crystallisation from the amorphous
phase is observed to form III
Subsequent phase transitions occur to forms II and I
before the sample melts
This observation is in agreement with a previous study
of paracetamol by low frequency Raman scattering
The featureless spectra of the supercooled liquid and
liquid melt can be fitted using a power law model
The melt spectrum is dominated by the dielectric
relaxation as well as the VDOS, while in the
supercooled liquid the contribution due to the dielectric
relaxation vanishes close to Tg (q changes from 2 in the
glassy state to 1 in the liquid melt state)
Using the simple power law model introduced previously,
the onset of crystallisation can be determined precisely
J. Sibik et al., Molecular Pharmaceutics. 11, 1326 (2014). 24 of 31

37. Amorphous Materials Crystallisation
Crystallisation Below Tg
0.5 1.0 1.5 2.0
0
100
200
(b)(a)
310 K
Naproxen
()(cm
-1
)
(THz)
100 K
0.4 0.6 0.8 1.0 1.2
50
100
150
200
250
1.2 THz
1.5 THz
1.8 THz
(T/T
g
)(cm
-1
)
T/T
g
0.67 Tg
~4x faster
Seeded crystallisation: rate increases at ≈ 0.67 Tg!
Role of molecular mobility below Tg
J. Sibik et al., Molecular Pharmaceutics, doi:10.1021/acs.molpharmaceut.5b00330
(2015). 25 of 31

38. Outline
Introduction
Amorphous Materials
What Can be Measured at THz Frequencies?
Model System: Polyalcohols
Crystallisation
Stability Prediction
Summary

39. Amorphous Materials Stability Prediction
Amorphous Drug Stability
J. Sibik et al., Molecular Pharmaceutics, doi:10.1021/acs.molpharmaceut.5b00330
(2015). 26 of 31

40. Amorphous Materials Stability Prediction
Amorphous Drug Stability
0.2 0.4 0.6 0.8 1.0 1.2
20
25
30
35
40
45
50
0.5 1.0 1.5 2.0 2.5
0
50
100
150
320 K
Indomethacin
Paracetamol
(cm
-1
)
Frequency (THz)
80 K
0.67 Tg
Paracetamol
Indomethacin
1.0THz
(cm
-1
)
T/Tg
J. Sibik et al., Molecular Pharmaceutics, doi:10.1021/acs.molpharmaceut.5b00330
(2015). 26 of 31

41. Amorphous Materials Stability Prediction
Amorphous Drug Stability
0.2 0.4 0.6 0.8 1.0 1.2
1.0
1.1
1.2
1.3 paracetamol
indomethacin
flufenamic acid
simvastatin
linear fit
0
T/T
g
J. Sibik et al., Molecular Pharmaceutics, doi:10.1021/acs.molpharmaceut.5b00330
(2015). 26 of 31

42. Amorphous Materials Stability Prediction
Prediction of Amorphous Stability
J. Sibik et al., Molecular Pharmaceutics, doi:10.1021/acs.molpharmaceut.5b00330
(2015). 27 of 31

43. Summary
Terahertz Spectroscopy
The terahertz molecular dynamics is strongly related to the molecular
mobility governing the stability of amorphous drugs.
While molecular relaxations are often extracted by dielectric spectroscopy or
DSC and used to predict the stability of the amorphous drugs, concerns have
been raised about the robustness of these methods.
DSC is useful mainly for measurements of molecular mobility around and
above Tg, but cannot be easily used to measure molecular mobility at lower
temperatures.
Measurements by dielectric spectroscopy are very useful to measure the
local mobility in terms of JG-β relaxation, except for cases where this
relaxation is submerged in the α-relaxation.
In contrast, terahertz spectroscopy does not suffer from this limitation as it
measures fast motions and only indirectly resolves the effect of the JG-β
relaxation, which may in principle be observed even when no clear JG-β
peak is present (such as in the case of indomethacin).
28 of 31

44. Summary Acknowledgments
Acknowledgments
Dr Korbinian Löbmann and Professor Thomas Rades (Copenhagen)
U.K. Engineering and Physical Sciences Research Council (EPSRC,
EP/J007803/1)
29 of 31

45. Summary Acknowledgments
Literature I
G. Adam and J. H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids,
The Journal of Chemical Physics, 43:139, 1965.
S. Bhattacharya and R. Suryanarayanan, Local Mobility in Amorphous Pharmaceuticals-Characterization and
Implications on Stability, 98(9):2935–2953, January 2009, http://dx.doi.org/10.1002/jps.21728.
A. Döß, M. Paluch, H. Sillescu, and G. Hinze, From Strong to Fragile Glass Formers: Secondary Relaxation in
Polyalcohols, Phys. Rev. Lett., 88(9), February 2002, http://dx.doi.org/10.1103/PhysRevLett.88.095701.
S. Kastner, M. Köhler, Y. Goncharov, P. Lunkenheimer, and A. Loidl, High-frequency dynamics of type B glass formers
investigated by broadband dielectric spectroscopy, J. Non-Cryst. Sol., 357(2):510–514, January 2011,
http://dx.doi.org/10.1016/j.jnoncrysol.2010.06.074.
J. Sibik, S. R. Elliott, and J. A. Zeitler, Thermal decoupling of molecular-relaxation processes from the vibrational
density of states at terahertz frequencies in supercooled hydrogen-bonded liquids, J. Phys. Chem. Lett., 5(11):
1968–1972, 2014a, http://dx.doi.org/10.1021/jz5007302.
J. Sibik, E. Y. Shalaev, and J. A. Zeitler, Glassy dynamics of sorbitol solutions at terahertz frequencies., Phys. Chem.
Chem. Phys., 15(28):11931–11942, July 2013, http://dx.doi.org/10.1039/c3cp51936h.
J. Sibik, M. J. Sargent, M. Franklin, and J. A. Zeitler, Crystallization and Phase Changes in Paracetamol from the
Amorphous Solid to the Liquid Phase, Molecular Pharmaceutics, 11(4):1326–1334, March 2014b,
http://dx.doi.org/10.1021/mp400768m.
J. Sibik, K. Loebmann, T. Rades, and J. A. Zeitler, Predicting Crystallisation of Amorphous Drugs With Terahertz
Spectroscopy, Molecular Pharmaceutics, page 150619135054002, June 2015,
http://dx.doi.org/10.1021/acs.molpharmaceut.5b00330.
30 of 31

46. Summary Acknowledgments
Literature II
C. J. Strachan, T. Rades, D. Newnham, K. C. Gordon, M. Pepper, and P. F. Taday, Using terahertz pulsed spectroscopy
to study crystallinity of pharmaceutical materials, Chem. Phys. Lett., 390(1-3):20–24, May 2004,
http://dx.doi.org/10.1016/j.cplett.2004.03.117.
H. Wagner and R. Richert, Spatial uniformity of the β-relaxation in D-sorbitol, J. Non-Cryst. Sol., 242(1):19–24, 1998.
J. A. Zeitler, P. F. Taday, K. C. Gordon, M. Pepper, and T. Rades, Solid-State Transition Mechanism in Carbamazepine
Polymorphs by Time-Resolved Terahertz Spectroscopy, ChemPhysChem, 8(13):1924–1927, 2007a,
http://dx.doi.org/10.1002/cphc.200700261.
J. A. Zeitler, P. F. Taday, M. Pepper, and T. Rades, Relaxation and crystallization of amorphous carbamazepine studied
by terahertz pulsed spectroscopy, J. Pharm. Sci., 96(10):2703–2709, October 2007b, http://dx.doi.org/10.1002/jps.20908.
J. A. Zeitler, D. A. Newnham, P. F. Taday, C. J. Strachan, M. Pepper, K. C. Gordon, and T. Rades, Temperature
dependent terahertz pulsed spectroscopy of carbamazepine, Thermochimica Acta, 436(1-2):71–77, October 2005,
http://dx.doi.org/10.1016/j.tca.2005.07.006.
31 of 31