Journal of Molecular Structure xxx (2011) xxx–xxx
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: www.elsevier.com/locate/molstruc
Probing structure and phase-transitions in molecular crystals by terahertz
time-domain spectroscopy
Morten Franz a,c, Bernd M. Fischer d, Markus Walther a,b,⇑
a
Department of Molecular and Optical Physics, University of Freiburg, Stefan-Meier-Strasse 19, 79104 Freiburg, Germany
Freiburg Materials Research Center (FMF), University of Freiburg, Stefan-Meier-Strasse 21, 79104 Freiburg, Germany
c
Kiepenheuer Institute for Solar Physics, University of Freiburg, Schöneckstr.6, 79104 Freiburg, Germany
d
French-German Research Institute of Saint Louis, 5 rue du Général Cassagnou, BP 70034, 68301 Saint Louis Cedex, France
b
a r t i c l e
i n f o
Article history:
Available online xxxx
Keywords:
Far-infrared
Terahertz time-domain spectroscopy
Enantiomers
Racemic crystal
Phase transition
a b s t r a c t
Since the introduction of ultra-fast laser techniques for the generation and detection of broadband terahertz pulses, terahertz time-domain spectroscopy has become a versatile tool for vibrational spectroscopy of molecular systems in the far-infrared. Due to their highly collective and delocalized character
vibrational modes in this part of the spectrum are highly sensitive to molecular structure and arrangement within a molecular crystal. Here we utilize this sensitivity to differentiate between the enantiopure
amino acid L-cysteine and its racemic crystalline DL-form. Using terahertz time-domain spectroscopy we
are able to observe temperature induced solid-state phase transitions in polycrystalline DL-cysteine, as
well as in polycrystalline benzoic acid. The dynamics of the transitions is studied by tracing the temperature dependency of spectral features that are assigned to certain conformational phases.
! 2011 Elsevier B.V. All rights reserved.
1. Introduction
Far-infrared spectroscopic studies on molecular crystals based
on classical fourier-transform techniques have been performed
extensively since the late sixties of the last century. However, most
of these studies only included spectroscopic data above
!200 cm"1. Accessing the lower frequency part of the electromagnetic spectrum was hindered for a long time mainly by experimental difficulties associated with weak incoherent sources as well as
complex solid-state detectors, requiring cryogenic cooling. The
introduction of novel spectroscopic techniques based on the use
of pulsed laser sources for the generation and detection of short
and broadband terahertz pulses triggered new interest in this
neglected part of the electromagnetic spectrum. The number of
publications on far-infrared spectroscopy – or ‘‘terahertz (THz)
spectroscopy’’, as it was newly termed–increased significantly,
and many molecular structures including biomolecules, pharmaceutical substances, and hazardous substances were investigated
[1–10].
One of the most prevalent techniques is terahertz time-domain
spectroscopy (THz-TDS) [11,12]. It allows to record the full dielec-
⇑ Corresponding author at: Department of Molecular and Optical Physics,
University of Freiburg, Stefan-Meier-Strasse 19, 79104 Freiburg, Germany.
E-mail address: walther@physik.uni-freiburg.de (M. Walther).
URL: http://frhewww.physik.uni-freiburg.de/terahertz/ (M. Walther).
tric function of a sample in the frequency range from approximately 3–200 cm"1 (100 GHz–6 THz). At these low frequencies,
collective molecular vibrations, such as lattice modes of mixed intra- and intermolecular nature, predominate in molecular solids.
Therefore, the corresponding spectral signatures are very sensitive
to the intermolecular arrangement and crystalline structure, which
allows to distinguish and identify different polymorphic forms of a
molecular sample. As a striking example the THz spectra of racemic
crystals and their enantiopure counterparts have been recently
demonstrated to be clearly differentiable [13–16]. As molecular
polymorphs often have different physical and chemical properties,
such as for example solubility and melting point, an identification
of the polymorphic configuration is of utmost importance for pharmaceutical research and applications. Induced changes in the crystalline structure, for example during production or due to strong
temperature variations during storage, could potentially have an
impact on the dissolution rates and thus the therapeutic activity
of a drug. Therefore, there is a great interest in the detailed investigation of polymorphism and solid state phase transitions in
molecular systems.
Here, we demonstrate the sensitivity of THz-TDS to molecular
structure and arrangement in molecular crystals on the example
of two prototypical systems, the amino acid cysteine and benzoic
acid, the simplest aromatic carboxylic acid. Apart from distinguishing a pure enantiomer from its racemic compound we also report
the observation and characterization of temperature induced solid-state phase transitions in molecular crystals.
0022-2860/$ - see front matter ! 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2011.05.061
Please cite this article in press as: M. Franz et al., J. Mol. Struct. (2011), doi:10.1016/j.molstruc.2011.05.061
2
M. Franz et al. / Journal of Molecular Structure xxx (2011) xxx–xxx
2. Experiment
A conventional THz-TDS system as shown in Fig. 1 is used for
this study. It is based on the generation and detection of THz pulses
by semiconductor-based photoconductive antennas. The output of
a mode-locked Ti:sapphire laser (20 fs pulses, 800 nm, 80 MHz repetition rate) is split into an excitation beam driving a THz emitter
antenna and a detection beam gating a THz detector. Collimating
silicon lenses and off-axis parabolic mirrors generate a THz-focus
at the position of the sample (!8 mm diameter) and re-focus the
transmitted THz pulses onto the detector antenna, where the signal is measured by lock-in amplification. By scanning a variable delay-line in the path of the laser beam gating the detector the
temporal profile of the THz electric field is directly measured. In
contrast to most other spectroscopic techniques, which measure
only intensities and not the electric field, this coherent technique
also provides information on the phase accumulated by the electromagnetic wave upon transmission through the sample. As a result the full complex dielectric function ^eðmÞ ¼ e0 ðmÞ þ ie00 ðmÞ, or
^ ðmÞ ¼ nðmÞ þ ijðmÞ
equivalently the complex index of refraction n
of the investigated sample is determined without the need to invoke Kramers–Kronig calculus. The entire spectrometer is purged
with dry nitrogen in order to avoid absorption by residual water
vapor in the THz beam path. For a typical THz-TDS measurement
THz pulses are recorded with and without the sample in the spectrometer. Fourier transformation of the measured sample and reference waveforms yields their complex-valued spectra. From their
amplitude ratio A and phase difference / the dielectric properties
of the sample can be extracted. For a particular sample the frequency-dependent index of refraction n and absorption coefficient
a = 4pjm/c is calculated as [5]
c
' /ðmÞ;
2p"md
#
2
ðnðmÞ þ 1Þ2
;
aðmÞ ¼ " ln AðmÞ
d
4nðmÞ
nðmÞ ¼ 1 þ
ð1Þ
ð2Þ
where m is the frequency, c the speed of light and d the sample
thickness. Our setup allows to record the absorption coefficient
and index of refraction in the frequency range 6–140 cm"1 (0.1–
4.2 THz) with a spectral resolution of 0.5 cm"1 (15 GHz).
For this study L- and DL-cysteine, as well as benzoic acid were
purchased from Sigma–Aldrich. Samples were prepared by gently
grinding 20–40 mg of each substance, mixing the powder with
!150 mg polyethylene (PE) and pressing the mixture to free-
standing pellets by a hydraulic press. As a result we obtain diluted
polycrystalline samples of 13 mm diameter with an approximate
thickness of 1 mm. In order to perform temperature dependent
spectroscopy, the sample pellets were mounted in a closed cycle
He-cryostat equipped with Teflon windows. The temperature was
measured near the sample by a calibrated Si-diode with an accuracy of !1 K. The entire cryostat can be moved so that the THz
beam passes through either the sample or through an empty aperture as reference.
3. Results
3.1. Temperature dependent low-frequency vibrational spectra of
L-cysteine
Cysteine is a naturally occurring, sulfur-containing amino acid
that is found in most proteins. It is unique amongst the twenty natural amino acids as it contains a thiol group which can undergo redox reactions. When oxidized, cysteine can form cystine, a dimer
which is formed by linking two cysteine residues via a disulfide
bond. This disulfide bond is crucial in defining the structures of
many proteins as it functions as a cross-link between different
groups of the protein molecule. Insulin is an example of a protein
with cystine cross-linking, where two separate peptide chains are
connected by a disulfide bond pair [17].
Being a chiral amino acid, cysteine can occur in both enantiomeric forms, as either L- or D-cysteine. Fig. 3 (top) shows THz
absorption and refractive index spectra of polycrystalline L-cysteine measured at various temperatures. At low temperature three
distinct absorption peaks are observed in the spectral region
6–80 cm"1 due to the excitation of vibrational modes in the molecular crystal. These sharp spectral features are superimposed onto a
rising background originating from frequency dependent light
scattering on the sample grains embedded in the PE host medium
[18]. All absorption peaks are associated with a characteristic
phase shift in the refractive index. Upon cooling the initially broad
absorption bands become narrower and slightly shift towards
higher frequencies. This behavior is widely observed in THz spectra
of molecular systems as the result of the anharmonicity of the shallow vibrational potentials associated with these low-frequency
modes. Note that in some cases anomalous resonance behavior
(shifts to lower frequencies with decreasing temperature) has been
observed and interpreted as the result of the interplay between
Fig. 1. The THz time-domain spectrometer based on THz pulse emission and detection by a photoconductive emitter (E) and a detector antenna (D). Both are driven by a
Ti:sapphire short-pulse laser system.
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M. Franz et al. / Journal of Molecular Structure xxx (2011) xxx–xxx
3
Fig. 2. Molecular structure of L-cysteine (a) and of a benzoic acid dimer (b).
Fig. 3. Temperature dependent absorption and refractive index spectra of L- and
different weak bonding forces [19,14]. In the case of L-cysteine,
however, all observed features show normal behavior, i.e. a slight
continuous blue-shift and significant narrowing of the bands when
the sample is cooled to cryogenic temperatures.
Since the corresponding D-enantiomer is the exact mirror
image, also the structure and arrangement in the crystal lattice is
simply mirrored. Consequently THz spectra of enantiopure D- or
L-cysteine crystals, as well as their physical mixtures, cannot be
distinguished. However, when both enantiomers have been crystallized to form a corporate crystal lattice, the situation is changed.
3.2. Distinguishing between enantiopure cysteine and its racemic
compound
Owing to their collective nature and the significant mixing of
intra- with intermolecular vibrations, a precise assignment of
DL-cysteine
(curves are shifted vertically for better representation).
the low-frequency modes observed in our spectra is extremely
difficult and typically requires extensive solid-state density functional theory [20]. Nevertheless, the strong structure dependency
of these modes allows to distinguish even structurally closely related compounds. A striking example is the capability of THzTDS to probe the composition and crystalline configuration in
crystals of chiral molecules. Whereas in a racemic mixture pure
crystals of a given enantiomer and its racemic counterpart are
physically mixed together, in the case of the racemic compound,
the crystal consists of a pure crystalline phase of both enantiomers arranged in a well-ordered structure. So while both samples, the racemic mixture and the racemic crystal, contain the
same types of molecules in the same ratio, they differ in the order of the enantiomers in the crystal, i.e. whether they are
bound to molecules of the same enantiomer or to their oppositely handed counterpart. This different arrangement can
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M. Franz et al. / Journal of Molecular Structure xxx (2011) xxx–xxx
(b)
(a)
B
A
Fig. 4. (a) THz absorption spectra of DL-cysteine around the phase-transition temperature. Upon cooling the absorption band B disappears while band A appears below 200 K.
A double Lorentz profile has been fitted to the spectra (red line). (b) Temperature dependence of the corresponding normalized absorption strengths as extracted from the fits.
change the intermolecular modes and therefore alter the far-IR
spectra dramatically [13–16].
As an example Fig. 3 shows the absorption and refractive index
spectra of enantiopure polycrystalline L-cysteine and the racemic
crystal DL-cysteine. As the result of the different crystalline structure the characteristic features occur at different spectral positions
and with different amplitudes. Hence, THz-TDS enables a spectroscopic discrimination between either pure or mixed enantiomers
and the corresponding racemic compound, which may have useful
applications in the chemical and pharmaceutical industry.
the disappearance of one feature and the appearance of another
upon heating. This is the direct signature for the transition from
a crystalline phase A into a different phase B.
To a first approximation, the respective absorption strengths,
which correspond to the area under each absorption band, can be
assumed to be a measure for the amount of crystalline domains
being in either phase A or phase B. For a better quantification, a
double Lorentz profile has been fitted to our data (red1 curves in
Fig. 4a) according to
3.3. Structural phase transition in
aðmÞ ¼
DL-cysteine
In a protein subtle changes of a molecular fragment, e.g. a particular amino acid, may trigger instabilities resulting in a conformational transition of the entire biomolecule. Similar instabilities
can occur in crystalline amino acids. Slight changes of the intramolecular structure result in lattice instabilities which may trigger
phase transitions that change the crystal’s H-bond network. Therefore, amino acid crystals may serve as model systems for investigating and understanding conformational changes in biosystems
[21]. As we will show in the following, such a structural change
can be tracked in the temperature dependent THz spectra of DLcysteine.
Whereas most spectral features of DL-cysteine in Fig. 3 show a
continuous behavior with changing temperature, the absorption
peak around 49 cm"1 exhibits a strikingly different characteristic.
The feature disappears above 200 K associated with the appearance of a different band at 44 cm"1. Such an abrupt spectral change
is typically interpreted as the signature of a phase transition
[22–24]. Indeed, a reversible solid state phase-transition in the
crystalline amino acid DL-cysteine has been previously observed,
either induced by changes in temperature [25–29] or pressure
[30,31]. In order to study this transition in more detail we have
performed several measurements with increased temperature resolution (DT = 10 K) around the transition point (150–270 K). For
this purpose the sample was initially cooled from ambient temperature down to 20 K and heated in steps from cryogenic temperatures back to 295 K. A measurement was performed after each
heating step. Fig. 4a shows the corresponding absorption spectra
for selected temperatures in a spectral window around the characteristic feature. Note, that all spectra were baseline corrected by
subtracting a power law dependent background to compensate
for increased scattering at high frequencies [18]. Clearly visible is
2
1 X
Si ci
;
2p i¼1 ðm " m0i Þ þ c2i =4
ð3Þ
where Si is the strength, m0i the central frequency and ci the width of
the ith absorption peak. Plotting the absorption strengths Si for both
bands A and B versus temperature allows to follow the temperature
dynamics of the transition as shown in Fig. 4b. The absorption
strengths have been normalized to unity, at 20 K for absorption
band A, and at 295 K for band B. We note, that such a quantitative
analysis based on spectral features assumes that (i) each absorption
band correlates solely to one crystalline phase and (ii) that the dipole moments associated with each resonance, i.e. its IR-activity, remains constant over the entire temperature range. Both are
reasonable assumptions in the present example. Simple Boltzmann
fits are superimposed on the data (solid curves in Fig. 4b) to model
temperature activated interconversion between the two phases. We
find an average transition temperature of slightly below 200 K with
the entire sample being converted into phase B for temperatures
above 210 K. This observation is in reasonable agreement with previous studies that reported the phase-transition at comparable temperatures [26,28,31], in particular considering the fact that the
transition has been shown to exhibit a large hysteresis (over
100 K) and is strongly dependent on the size and structure of the
particles in the sample [28]. The latter could be one reason for
our observation of an extended temperature range of the phase
transition: Due to the inhomogeneous size distribution of the grains
in the sample pellet the transition occurs at slightly different temperatures in different grains leading to a broad distribution of transition temperatures.
1
For interpretation of color in Figs. 1, 2, and 4–6, the reader is referred to the web
version of this article.
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M. Franz et al. / Journal of Molecular Structure xxx (2011) xxx–xxx
3.4. Continuous phase transition in benzoic acid crystals
Benzoic acid and its derivatives are important molecules in biology as well as for pharmaceutical applications. From a scientific
point-of-view they represent prototype systems for studying
hydrogen bonding in organic molecules which plays an important
role in many chemical and biological processes. In solution and in
the condensed phase benzoic acid forms centrosymmetric dimers
linked by two strong hydrogen bonds between their carboxyl
groups, as illustrated in Fig. 2b. In the crystal the dimers are held
together by van-der-Waals forces to maintain the rigid crystal
structure. Owing to the weak potential forces and the large moving
masses involved, translational and torsional motions of the molecules within the dimers fall into the far-IR part of the spectrum.
Fig. 5 shows the measured absorption coefficient and index of
refraction of polycrystalline benzoic acid at various temperatures,
exhibiting a number of characteristic spectral features. Again, we
observe that the broad absorption bands present at room temperature resolve into narrow peaks at 10 K as the result of the anharmonicity of vibrational potentials. Based on previous studies
[32,33] and density functional calculations [34–36] the modes at
5
lowest frequencies (<50 cm"1) can be unambiguously assigned to
the inter-dimer (lattice) vibrations, while the bands in the region
above 60 cm"1 originate from internal dimer modes (rotations
and translations of the monomer units with respect to each other)
partially mixed with the lowest intra-molecular mode, the carboxyl-torsion.
In addition to its ability to form very characteristic H-bonded
systems, benzoic acid represents a prototype system for molecules
undergoing proton transfer along hydrogen bonds, a process which
plays an important role in many chemical and biological processes.
The cyclic structure of the benzoic acid dimer allows a simultaneous proton transfer along the two hydrogen bonds [37]. In this
process the net charge of the dimer is conserved and the structure
of the centrosymmetric dimer is unchanged. The displacement of
the two protons occurs in concert. It can be described by a single
proton transfer coordinate in a double minimum potential with a
barrier height determined by the activation energy. Whereas at
low temperatures the proton transfer process is dominated by tunneling, at room temperature the interconversion dynamics is compatible with an Arrhenius law [38]. This is widely recognized as a
prototypical case of a transition from the quantum regime at low
Fig. 5. Absorption and refractive index spectra of benzoic acid at various temperatures (curves are shifted vertically for better representation). The dashed red lines indicate
the temperature dependent frequency shifts of prominent spectral features. The peak at highest frequency shows a discontinuous behavior (red arrows) indicative for a
temperature induced phase transition.
(a)
(b)
B
A
Fig. 6. (a) In the temperature dependent spectra of benzoic acid the band above !110 cm"1 is assigned to two superimposed modes, which correspond to structural
configurations A and B, respectively. The fit of a double Lorentz profile is used to quantify both species during the phase-transition. (b) Temperature dependence of the
respective normalized absorption strengths. Inset: interconversion between the A- and B-configuration of benzoic acid dimers takes place via double proton transfer along the
hydrogen bonds. In the crystal, configuration A is energetically favored by DE, resulting in a slightly asymmetric double well potential with an activation energy Ea.
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M. Franz et al. / Journal of Molecular Structure xxx (2011) xxx–xxx
temperature, to the semiclassical regime at sufficiently high
temperatures.
In the isolated benzoic acid dimer the two minima of the potential energy surface, which correspond to the two symmetric
tautomers, are equivalent and a symmetric double well potential
is anticipated for the simultaneous transfer of the protons. In the
crystalline state however, the symmetry with respect to the
crystal axis is broken resulting in two inequivalent configurations A and B. Configuration A is energetically favored leading
to an asymmetric double-well potential, as schematically illustrated in the inset of Fig. 6b. For benzoic acid the estimated energy difference between configurations A and B is
DE = (58 ± 1) cm"1 [39] and estimates for the activation energy
range from 400 to 500 cm"1 [38].
The proton-transfer dynamics in benzoic acid has been studied
by various methods, including quasi-elastic neutron scattering
[37], ultraviolet [40], or infrared and Raman spectroscopy [38].
Especially the OH stretching band at around 2500 cm"1 has been
observed to be influenced significantly by the proton transfer.
Since the far-infrared spectrum of benzoic acid comprises the
hydrogen bond modes, we also expect variations in the THz spectra
reflecting the inter-conversion between the tautomers. Indeed, closer inspection of the spectra in Fig. 5 reveal that the broad feature
at !110 cm"1 in the room temperature spectrum shows a unique
behavior. This is indicated by the red solid arrows. While most
other peaks shift continuously to slightly higher frequencies upon
cooling, this band gradually decreases and finally vanishes below
50 K. The disappearance of this mode is associated with the
appearance of the strong absorption feature around 127 cm"1. This
discontinuous behavior was first observed by Zelsmann and Mielke
in their far-IR spectra and was interpreted as a manifestation of the
decreasing fraction of the B-configuration with decreasing temperature [32]. Reviewing our THz-data, we can rule out that this band
simply shifts and merges into the strong feature at 127 cm"1, since
such a shift would be strongly non-continuous compared to the
monotonous shifts of the other modes. Therefore, we strongly favor
the above interpretation, which explains our observations in the
following way: at a temperature of 10 K we observe distinct bands,
which are characteristic for only the A configuration of the benzoic
acid dimers. At elevated temperature the entire spectrum broadens
significantly and hardly shows any distinct structure. In addition
the band characteristic for configuration B contributes to the spectrum leading to further broadening.
As in the previous section, we fit a double Lorentz function
according to Eq. (3) to the absorption data between 90 and
140 cm"1. The two individual Lorentz-profiles and their sum
are superimposed to the spectra in Fig. 6a. We observe that
the amplitude of band A gradually grows and shifts upon cooling, in a similar manner as the remaining H-bond modes. In contrast, band B decreases in amplitude and finally vanishes below
50 K. Considering the large uncertainties of our fits, this temperature is in reasonable agreement with the reported energy difference between the two potential wells of DE/k = 84 K [39].
This further supports our assignment of the two modes to the
two tautomers A and B.
Fig. 6b shows a plot of the absorption strengths Si associated
with both modes extracted from the fits. The datasets have been
normalized to unity for absorption band A at 10 K, and to 0.5 for
band B at 250 K in order to account for the equal amount of both
configurations expected at ambient temperatures. We wish to
note, that due to the large uncertainties of the fits our analysis
can capture the temperature dependence over the structural transition only qualitatively. Nevertheless, the general trend of a temperature-activated continuous transition from configuration A to B
is reproduced, with both populations reaching an equilibrium at
ambient temperature.
4. Conclusion
In summary, we apply THz-TDS to measure temperature dependent absorption and refractive index spectra of the amino acid cysteine in its L- and DL-forms, as well as of polycrystalline benzoic
acid in the far-IR. We show that the spectra of the pure enantiomer
L-cysteine and the racemic compound DL-cysteine are significantly
different, even though the crystals consist of the same molecular
substance. Their spectral differences arise solely from the different
intermolecular order in the crystalline lattice, which indicates the
sensitivity of THz spectra to structure and arrangement in molecular crystals. THz spectroscopy therefore enables a clear discrimination between pure enantiomers of a substance and its racemic
compound. Furthermore, we demonstrate THz spectroscopy’s ability to track solid-state phase-transitions in molecular crystals on
the examples of DL-cysteine and of crystalline benzoic acid. By following temperature dependent changes in their spectra, the technique permits to trace the balance between different
configurational species in the samples. Further refinement of the
data (measured at more temperatures with better signal-to-noise)
might even enable quantitative determination of energy differences and conversion ratios. Our results demonstrate that
THz-TDS represents an interesting complementary technique to
conventional methods, such as differential scanning calorimetry
(DSC) or temperature-dependent X-ray crystallography, for studying phase-transitions in molecular crystals.
Acknowledgements
The authors gratefully acknowledge P.U. Jepsen and H. Helm for
their support and for fruitful discussion. M.W. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) through Grant
No. WA 2641.
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Please cite this article in press as: M. Franz et al., J. Mol. Struct. (2011), doi:10.1016/j.molstruc.2011.05.061