Temperature stability and photodimerization kinetics of β-cinnamic acid and comparison to its α-polymorph as studied by solid-state NMR spectroscopy techniques and DFT calculations

Article abstract of DOI:10.1039/b806861e

Photoreactions of the α- and β-polymorphs of trans-cinnamic acid were studied by ¹³C CPMAS solid-state nuclear magnetic resonance spectroscopy, and the reactants and products were spectroscopically characterized in detail. Chemical shifts and c

Full text of DOI:10.1039/b806861e

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Temperature stability and photodimerization kinetics of b-cinnamic acid
and comparison to its a-polymorph as studied by solid-state NMR
spectroscopy techniques and DFT calculations
I. Fonseca,a S. E. Hayes,b B. Blumicha and M. Bertmer*ac
¨
Received 23rd April 2008, Accepted 12th June 2008
First published as an Advance Article on the web 24th July 2008
DOI: 10.1039/b806861e
Photoreactions of the a- and b-polymorphs of trans-cinnamic acid were studied by 13C CPMAS
solid-state nuclear magnetic resonance spectroscopy, and the reactants and products were
spectroscopically characterized in detail. Chemical shifts and chemical shift anisotropy tensors
calculated using density functional theory (DFT) were found to be in good agreement with the
experimental results and helped to identify the polymorphs and the individual assignments of
reactant and photoproduct carbon atoms. The b-polymorph is metastable. Its transformation into
the a-cinnamic acid polymorph is monitored by temperature-dependent 13C NMR spectroscopy.
The transformation occurs at a very slow rate at room temperature but is highly accelerated at
elevated temperatures. Analysis of the kinetics of the photoreaction shows that the b-polymorph
progresses at a slower rate compared to that of a-cinnamic acid. Based on chemical shift tensor
values of reactants and products as obtained from 2D PASS spectra, the difference in reaction
rates is suggested to be due to the higher amount of molecular reorientation of functional groups
upon photoreaction and the larger distance between the reacting double bonds.
the first two follow the topochemical principle11 and undergo
Introduction
photodimerization under UV irradiation, while the third is
photo-inactive. The topochemical principle states that two
molecules with parallel double bonds should have an inter-
molecular double bond distance of less than 4.2 A in order for
a photoreaction to occur. This photoreaction should involve a
minimum amount of molecular displacement, and stereoselec-
tive photoproducts are obtained according to the orientation
of the reacting molecules in the crystal. As a result, the
photoproduct of the head-to-tail a-cinnamic acid polymorph
is the centrosymmetric a-truxillic acid dimer, whereas the
Solid-state reactions are interesting to the field of (green)
organic chemistry because highly stereospecific products are
directly obtained as a consequence of the molecular arrange-
ment in the crystal packing as well as the fact that no solvent is
required.1–3 In addition to the interest of the synthetic che-
mists, such reactions, especially those that are reversible and
driven by light, have gained attention because of a potential
application in optical memory storage systems.4,5 This field of
research is motivated by the pursuit of miniaturization of high
capacity data storage systems, with conventional techniques
soon reaching physical limits. Here, the design of materials for
molecular switches is an essential step. Necessary requirements
for these materials are—among others—two stable conforma-
tions of a molecule. Several reaction types are currently
investigated for this purpose (see, for example, ref. 4 and
references therein). The great advantage of organic molecules
is the fact that small changes to the structure enable an
adjustment of the physical properties (e.g. absorption wave-
length) for a desired application.
One of the most widely investigated solid-state reactions is
the [2+2] photodimerization.6–10 A classical example is that of
trans-cinnamic acid, which is investigated in the current work.
Cohen and co-workers8 observed that trans-cinnamic acid
crystallizes in three different polymorphs a, b, and g, where
a Macromolecular Chemistry, RWTH Aachen University, 52056
Aachen, Germany
b Department of Chemistry and Center for Materials Innovation,
Washington University, St. Louis, Missouri, 63130, USA
c Faculty of Physics and Geosciences, University Leipzig, 04103
Leipzig, Germany. E-mail: bertmer@physik.uni-leipzig.de
Scheme 1 Photodimerization reaction of a- and b-cinnamic acid
(double bonds not shown) forming a-truxillic and b-truxinic acid,
respectively. The 3D display also indicates the necessary movement of
the functional groups next to the reaction centers.
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photoproduct of the head-to-head b-cinnamic acid polymorph
is the mirror-symmetric b-truxinic acid dimer (Scheme 1).
Please note: in the trans-cinnamic acid parent, solid state pack-
ing in a head-to-tail arrangement is termed the a-polymorph,
while the head-to-head packing is the b-polymorph. These
a- and b-labels should not be confused with those of the
photodimer products, shown in Scheme 1 as a-truxillic
acid and b-truxinic acid. The latter labels refer to the
specific stereochemistry for the substituents surrounding the
cyclobutane ring moiety.
systems. For verification, NMR chemical shifts and chemical
shift tensors were calculated by density functional theory
(DFT) using the available X-ray crystal structures of the
polymorphs. These calculations together with the calculated
chemical shift tensor values aid in the assignment of the NMR
spectra.
Experimental details
The a- and b-polymorphs of cinnamic acid were crystallized
from commercial 99% trans-cinnamic acid (Aldrich). The
a-polymorph was recrystallized from a hot toluene solution
by slow cooling.15 The b-polymorph was prepared following
the procedure of ref. 29. A solution of 1.5 g of cinnamic acid in
25 mL of ether was prepared and divided among 5 test tubes.
In each tube, 5 mL petroleum ether pre-cooled at B0 1C was
poured very slowly along the wall to obtain two separate
layers, with the ether solution at the bottom of the tube and
the petroleum ether on top. The tubes were filled inside the
freezer at ꢁ20 1C to ensure minimal displacement of the tubes
and avoid mixture of the two liquids. Initiated by diffusion,
crystallization of b-cinnamic acid started between the two
layers. After one day the b-cinnamic acid needles were care-
fully removed from the tube. Crystals of a-cinnamic acid
(square plates) also formed and deposited at the bottom of
the tube. The amount of a-crystals increased significantly with
time after approximately 24 h, similar to prior reports.29 The
b-cinnamic acid crystallites are fairly small, on the order of
100 mm in the largest dimension. In comparison, a-cinnamic
acid crystallites on the other hand can easily be prepared with
millimetre dimensions.
While many systems are investigated currently, several
issues regarding this type of [2+2] reaction are not fully
understood. trans-Cinnamic acid, being a small and relatively
simple molecule, is therefore a good model system to get a
better understanding of solid-state reactions in general.
Applications of cinnamic acid are manifold, for example,
those involving photodimerization use cinnamic acid side-
chains in polymers as crack-healing agents,12 as well as
reversible cross-linkers in shape-memory polymers.13
Several techniques have been used in the past to study the
[2+2] photodimerization of trans-cinnamic acid such as X-ray
diffraction,14 atomic force microscopy (AFM),15 and vibra-
tional spectroscopy.16 We think that solid-state nuclear mag-
netic resonance (NMR) is the most suitable to study these
systems owing to its ability to resolve element-selective atomic
arrangements in the bulk with access to short- and medium-
range ordering effects. NMR can be applied to powders and
single crystals, as well as partially or fully amorphous materi-
als, and the flexibility of this technique allows for a tailoring of
the experiment to the desired question of interest. In particu-
lar, NMR has been confirmed to be an efficient method for the
differentiation of polymorphs17–20 as well as reactants and
products in solid-state reactions,21,22 and prior studies on
cinnamic acid have demonstrated the applicability of NMR
for this material.22–25
As we have previously demonstrated,26 13C CPMAS spec-
troscopy is especially suited to study [2+2] photodimeriza-
tions because the change from a carbon–carbon double bond
to a single-bonded four-member ring (changing hybridization
from sp2 to sp3) is accompanied by a drastic change of 13C
isotropic chemical shift. The chemical shifts therefore allow
for a clear indication of the progress of the reaction. In the
current work, this study is extended from the a- to the
b-polymorph of trans-cinnamic acid, and the comparison of
the two is done in terms of reaction rate and differentiation of
polymorphs and reaction products using 13C solid-state NMR
spectroscopic techniques. The kinetics of the reaction is mon-
itored in a straightforward way by means of 13C cross-
polarization, magic-angle-spinning (CPMAS) spectra and in-
terpreted in terms of a model that relates the reaction con-
stants to the dimensionality of the growth. Moreover, 13C
chemical shift anisotropy (CSA) tensors have been measured
with the 2D PASS sequence27,28 to obtain information on the
relative orientations of functional groups, which are sensitive
to molecular conformational changes during the reaction.18,19
A detailed study of the changes to the CSA tensors of both
polymorphs during photodimerization can elucidate differ-
ences in the photoreaction kinetics and provide important
information to gain a comprehensive understanding of these
The reaction products of a- and b-cinnamic acids, i.e.,
a-truxillic and b-truxinic acid, respectively, were prepared as
follows. The parent acids were irradiated by UV light with an
OSRAM Ultravitalux lamp under water-cooling (filtering
wavelengths less than 280 nm) for consecutive irradiation
periods of 10 min, and agitated between periods until (almost)
full conversion was reached. Each respective reaction product
was separated from residual cinnamic acid by extraction with
ether, where the reaction product is the insoluble fraction.30
For the photoreaction kinetics studies an amount of ap-
proximately 50 mg of b-cinnamic acid crystals was evenly
distributed in a thin layer and placed in the focus of a 150 W
xenon arc lamp (Thermo Oriel). The lamp was equipped with a
dichroic mirror to transmit wavelengths between 280 and
400 nm. Since the longer (infrared) wavelengths were blocked,
the sample temperature could be maintained at room tem-
perature (21 ꢂ 2 1C). The samples were irradiated for con-
secutive periods of 10 min of broadband light, with agitation
of the powders between each period.
The photoreaction kinetics of the UV irradiated samples
was studied with a 4 mm triple resonance MAS probe from
Varian, and the data were recorded using a Tecmag Apollo
spectrometer. Resonance frequencies were 294.35 and
1
1
74.028 MHz for H and 13C, respectively. The H p/2 pulse
length was 2.5 ms and the contact time 1 ms. The MAS
rotation frequency of 4.8 kHz was chosen to avoid overlap
of centerbands with spinning sidebands. The spectra were
acquired with a recycle delay of 1200 s, 5 times the longitudinal
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relaxation time (T1) of the reactant, in order to quantitatively
compare the relative ratios of the reactant and photoproduct
signals. Furthermore, the contact time was chosen based on
variable contact time experiments (data not shown) to obtain
correct relative ratios between vinylic and cyclobutane signals,
for quantitative analysis of the CPMAS spectra.
optimization was successful for the cinnamic acids, for
a-truxillic acid this procedure could not be adopted, because
it yielded a conformation that is not representative of the
solid-state 13C spectra. The full geometry optimization of the
non-centrosymmetric photodimer yielded a centrosymmetric
photodimer, which is the most stable conformation (poly-
morph) when no neighbor molecules are present. In fact, the
centrosymmetric photodimer is observed in the solution state
spectrum of a-truxillic acid.
All other NMR experiments were performed on a Bruker
Avance DSX 500 spectrometer with frequencies of 500.46 and
1
125.84 MHz for H and 13C, respectively. The MAS experi-
ments were carried out using a 4 mm MAS probe. A rotation
frequency of 8 kHz was chosen in this case to avoid overlap of
centerbands with spinning sidebands. The 1H p/2 pulse length
was 2.5 ms, and the contact time was set to 1 ms. Temperature-
dependent spectra were acquired from room temperature
(B298.5 K) up to 350 K in 101 intervals with a 20 min
temperature stabilization period. Each spectrum was acquired
with 64 scans. The 2D PASS sequence for the determination of
the chemical shift anisotropy (CSA) tensors, originally devel-
oped by Dixon,27 was used with the modification of Levitt and
coworkers28 containing 5 p-pulses together with cogwheel
phase cycling,31 where a 2D Fourier transformation directly
leads to a separation of spinning sidebands by order in the
indirect dimension. Because of the long recycle delays, cog-
wheel phase cycling is ultimately important for these systems
since it reduces the phase cycle from 243 to just 11 individual
phases. The sideband intensities were analyzed with the
Herzfeld–Berger method32 using the HBA software pro-
gram.33 In order to have several spinning sidebands for a
more accurate analysis, the experiments were performed at a
rotation frequency of 1.5 kHz. The recycle delays for the
different samples were 400 s for a-cinnamic acid, 200 s for
a-truxillic acid, 160 s for b-cinnamic acid, and 30 s for
b-truxinic acid. All spectra were referenced to tetramethylsi-
lane (TMS) using glycine as a secondary reference. With the
given recycle delays, the experimental time for the 2D PASS
experiments varied for the four samples between 55 and 85 h
depending on the number of scans for the different samples.
NMR chemical shift calculations were performed using the
commercial program Gaussian03.34 In all the simulations, the
atomic coordinates were taken from the available X-ray
crystal structures. The geometry optimizations were per-
formed using density functional theory with the B3LYP func-
tional35,36 and a 6-311G(2df, 2p) basis set.37 The chemical
shifts were calculated using the GIAO method38,39 with the
B3LYP functional and a cc-PVDZ basis set,40 which is well-
suited for the calculation of NMR parameters. The spectra
were referenced to tetramethylsilane calculated at the same
level of theory.
Results and discussion
Spectroscopic assignment of a- and b-cinnamic acid polymorphs
Fig. 1 shows a comparison of the 13C CPMAS spectra of the
two cinnamic acid polymorphs, a and b. It can be seen that the
two polymorphs can be clearly differentiated by their 13C
spectra. Assignments (Table 1) for the a-polymorph were
already carried out in a previous contribution26 and confirmed
by theoretical chemical shift calculations done in this work
(Table 1). The resonances of the b-polymorph were assigned
through comparison with those of the a-polymorph and
documented by the corresponding DFT calculations. The
results are included in Table 1. In comparing the spectra of
the two polymorphs, the observed vinylic and aromatic signals
of the b-polymorph are shifted to slightly lower frequencies,
with the exception of the ipso carbon (C4, non-protonated, cf.
Scheme 2). The carboxylic carbon is observed at a lower
chemical shift value in the a-polymorph. Differences observed
in the spectra originate from the different solid-state structure
of the polymorphs, where intramolecular distances are slightly
different in each of the crystal structures.14,29 In addition, the
fact that the a-cinnamic acid polymorph adopts an antiplanar
conformation, whereas the b-polymorph adopts a synplanar
conformation (see Scheme 2) contributes to some of these
chemical shift differences. These observations are confirmed
At first, geometry optimizations were done only for the
protons, that is, keeping all other atom positions fixed, since
the position of light atoms such as hydrogen is not accurately
determined by X-ray techniques. In some cases, after relaxing
the proton positions, the forces on the carbon backbone were
still large so that a relaxation of the whole structure, a further
optimization of all the atom positions, yielded better results.
The full optimization will yield the minimum energy confor-
mation of a free molecule, as in the gas phase, which can be
different from the structure in a solid, since packing effects and
hydrogen bonding are not accounted for. While this full
Fig. 1 13C CPMAS spectra of a-(bottom) and b-cinnamic acid (top).
Spinning sidebands are indicated by asterisks. The arrows in the
top spectrum indicate signals from additional a-cinnamic acid
(see text). The dashed vertical lines represent the results of the
Gaussian simulations.
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Table 1 13C NMR assignments for a- and b-cinnamic acid together
with chemical shifts obtained from Gaussian calculations. Numbering
of carbon atoms as shown in Scheme 2. For most of the aromatic
carbon signals a clear comparison to the theoretical values is not
possible due to the small shift differences. The accuracy of both the
experimental and theoretical values is smaller than 1 ppm, hence
omitted for clarity
Stability of the b-polymorph of cinnamic acid
It is known that the b-polymorph of cinnamic acid is meta-
stable and converts to the a-polymorph at temperatures above
45 1C,9 a situation which originally led to confusion regarding
the origin of different photoproducts (see ref. 9 and references
therein). Interestingly, a sample of b-cinnamic acid stored at
room temperature in the dark was measured 6 months after its
preparation and showed full conversion into a-cinnamic acid,
as confirmed by its 13C CPMAS spectrum (cf. Fig. 1). This
indicates that the b-to-a conversion also proceeds at tempera-
tures below 45 1C. Temperature-dependent 13C CPMAS mea-
surements were performed in order to follow this conversion
experimentally. The temperature dependent spectra are shown
in Fig. 2 where the relative intensities of the carboxylic signals
of a- and b-cinnamic acid are used to deduce the degree of
conversion. The shifting of the b-polymorph signals towards
that of the a-polymorph can be clearly followed with increas-
ing temperature. The amount of the a-polymorph slowly
increases until 330 K (at room temperature there is already
some amount of the a-polymorph present, as discussed above),
Sample
Assignment
d/ppm
dtheoretical/ppm
a-Cinnamic acid
C1
C2
C3
C4
C5
C6, C7, C8
C9
173
147
119
134
131
129
127
161
145
117
136
133
128, 129, 130
125
b-Cinnamic acid
C1
C2
174
146
162
147
C3
C4
118
134
114
135
C5–C6
C7, C8, C9
127
129, 128, 130
125, 128
130, 129, 134
by the chemical shift simulations, which only took into
account one molecule, such that there are no influences of
neighboring molecules or solid-state packing effects, resulting
in simulated spectra that differ for both polymorphs. The
results of the Gaussian calculations are in very good agree-
ment with the experimental observations, deviations being on
the order of 2 ppm. An exception is the carboxyl carbon with
differences between experiment and simulation of 12 and
8 ppm for the a- and b-polymorph, respectively. This relatively
large deviation originates from the fact that the carboxylic
group participates in a hydrogen bond to a neighbor molecule,
which is not taken into account in the simulation.
The b-cinnamic acid spectrum contains small peaks that
correspond to contributions of a-cinnamic acid (indicated by
arrows in Fig. 1) contaminating the b-polymorph sample. This
small contribution of the a-polymorph arises from the synth-
esis procedure of the b-cinnamic acid, because of the difficulty
differentiating between small a-crystal plates or cubes from
b-crystal needles. Additionally, the a modification is the
thermodynamically more stable polymorph which will be
discussed in the following section.
Fig. 2 (a) 13C CPMAS spectra of b-cinnamic acid as a function of
temperature. The dashed line indicates the shifting of the carboxyl
peak as conversion from b- to a-cinnamic acid takes places.
(b) Amount of a-cinnamic acid signal as a function of temperature
calculated from the intensity ratios of the carboxyl signals of a- and
b-cinnamic acid.
Scheme 2 Numbering scheme of a- and b-cinnamic acid (double
bonds not shown) used in the theoretical simulations and also for the
numbering of carbon atoms in Table 1.
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where it starts to increase rapidly with full conversion at
350 K. Additionally, a slight broadening of the peaks is
observed (even at temperatures below 340 K), probably be-
cause of loss of crystallinity. The observation that the b-form
transforms into the a-form even below 340 K may have
consequences for the spectra measured under MAS, since the
rapid spinning will induce some heating of the samples, and it
might be difficult to obtain pure b-cinnamic acid spectra. This
effect could be aggravated both at higher spinning speed-
s—leading to larger temperature increases—and long
measurement times, where there is more time for the conver-
sion to take place.
Assignment of photodimerization products
Fig. 3 13C CPMAS spectra of a-truxillic (bottom) and b-truxinic acid
(top), spinning sidebands are marked by asterisks. The dashed vertical
lines represent the results of the Gaussian calculations for a-truxillic
acid only.
Stereoselective photodimerization of a- and b-cinnamic acid
leads to different structural isomers, a-truxillic and b-truxinic
acid, that have a different arrangement of substituents at the
newly generated cyclobutane ring. The corresponding 13C
CPMAS spectra of the photoproducts are shown in Fig. 3.
Distinct differences between a-truxillic and b-truxinic acid are
visible for the aromatic region as well as for the resolved peaks
of the four-member ring of the photoproduct.
Table 2 Resonance assignments for a-truxillic and b-truxinic acid
together with chemical shifts obtained from Gaussian calculations.
Numbering of carbon atoms as shown in Scheme 3
Sample
Assignment
d/ppm
dtheoretical/ppm
Based on Scheme 1, the photoproduct of the head-to-tail
a-cinnamic acid is expected to exhibit inversion symmetry while
that of the head-to-head b-cinnamic acid should have mirror
symmetry. In both cases, two signals would result for the carbons
of the four-member ring since two carbons each are magnetically
equivalent. Additionally, one signal each for the adjacent
carboxyl and ipso-carbon is expected. However, the truxinic
and truxillic acid 13C spectra in Fig. 3 exhibit three and four
cyclobutane signals for b-truxinic and a-truxillic acid, respec-
tively, as well as two carboxyl and two ipso-carbon signals each
(for a-truxillic acid the second ipso-carbon signal is visible as a
shoulder only), thereby indicating loss of the magnetic equiva-
lence of these carbons ostensibly due to a loss of symmetry. The
three observed cyclobutane signals for b-truxinic acid actually
account for four signals that partially overlap, as evidenced
by the 1 : 2 : 1 signal ratio, in contrast to the four truxillic acid
cyclobutane signals for the a-polymorph that are of almost equal
intensity. Although symmetric photoproducts are expected, the
number of signals in the 13C CPMAS NMR spectra indicates that
the symmetry is broken for both photoproducts. For a-truxillic
acid this is additionally verified by crystal structure data.29
The assignment of the photoproducts spectra is summarized
in Table 2 with the numbering of carbon atoms from Scheme 3.
Simulations could be performed only for the a-truxillic acid,29
a-Truxillic acid
C1
182
178
40
44
45
175
172
46
48
53
51
139
141
C01
C2
C02
C03
C3
51
C4
C04
C5-6, C7-9,
C07, C09
C06, C08
C05
137
138
125, 126
123, 124, 126
129
130
128
129
b-Truxinic acid
C1
175
179
41
45
47
136
138
125, 128,
131
C01
C2
C02, C3
C03
C4
C04
C5–C9,
C05–C09
since the crystal structure of the b-truxinic acid is not yet solved.
Again, the results of the simulation are in good agreement with
the experimental data, yielding four cyclobutane ring signals
and two carboxyl and ipso carbon signals. As seen for the
Scheme 3 Numbering scheme of a-truxillic (left) and b-truxinic acid (right).
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cinnamic acids, the chemical shifts of the carboxyl carbons are
the ones that show the biggest differences with respect to the
experimental data, because the hydrogen bonding to a neighbor
molecule is not taken into account in the simulation. However,
the successful simulation of the non-centrosymmetric structure
allows the assignment of all resonances, as well as the simula-
tion of the corresponding chemical shift anisotropy tensors
(see below). It should be noted that our assignments of the
four cyclobutane carbons were made in combination with the
theoretical calculations of a-truxillic acid, which suggest that
the carbon atoms next to the carboxylic carbon resonate at
lower frequencies than those bound to the phenyl ring.
‘‘seeds’’, of the new phase appear randomly in a given volume)
with a constant rate from t = 0, and the growth of seeds
terminates at their points of mutual contact, but otherwise
continues normally elsewhere. In this case the Avrami expo-
nent is n = 4. In the case of a 2-D linear growth, that is, for a
disk of fixed thickness, growing radially, n = 3. Finally, for
1-D linear growth in the shape of a rod, n = 2. The model can
also be used in cases where nucleation is heterogeneous (nuclei
form at preferred sites) with a specific rate throughout the
reaction or where a fixed number of nuclei are present initially
(e.g., prior to irradiation in our case). Using 3-D growth as an
illustrative example, n ranges between 3 and 4, covering all
cases for which the nucleation rate is a decreasing function of
time, up to the limit at longer times when it becomes constant.
At one extreme, when there is initially a fixed number of
nuclei, n = 3. At the other extreme, when not all nuclei are
present at t = 0 but are formed at a constant rate throughout
the reaction, n = 4. Therefore, non-integer Avrami exponents
are representative of the continuum of possible starting points
for the nucleation and growth. In an analogous way, for 2-D
growth, 2 r n r 3 and for 1-D growth, 1 r n r 2. Only an
Avrami exponent of n = 1 gives a non-sigmoidal shape,
whereas all other Avrami exponents give sigmoidal curves
when the transformed fractional volume X(t) is plotted
against t.
The kinetics curve of a-cinnamic acid26 showed the typical
sigmoidal behaviour with an Avrami exponent of n = 1.66
indicative of a heterogeneous 1-D linear growth with a de-
creasing nucleation rate (see Fig. 4). The fit parameters for the
b-polymorph (k = 0.007 ꢂ 0.001 minꢁ1, n = 0.87 ꢂ 0.07) are
considerably smaller than those for the a-polymorph (k =
0.019 minꢁ1, n = 1.66).26 An Avrami exponent of n E 1 is
indicative of a heterogenous 1-D linear growth with an initially
fixed number of nuclei (therefore, the initial sigmoidal beha-
viour is not observed). The nuclei already present before
irradiation may have been induced by exposure to UV radia-
tion from natural light during crystallization of b-cinnamic
acid. Different kinetic model functions were tested for fitting
these data, but the JMAK model was found to be the best
fitting.
Kinetics of photoreaction
During the [2+2] photoreaction of cinnamic acid, the vinylic
bond is broken by UV radiation to form the cyclobutane ring
between two cinnamic acid molecules (Scheme 1). To study the
photoreaction kinetics, samples of b-cinnamic acid were irra-
diated with UV light and their 13C spectra analyzed individu-
ally. The decrease of vinylic signal intensity and build-up of
cyclobutane signal intensity can be easily followed as the
reaction takes place, evident from the spectra in Fig. 1 (top)
and 3 (top). The degree of conversion was calculated from the
ratio between the integrated areas of vinylic and cyclobutane
carbon signals as a function of irradiation time. The resulting
kinetics curve is shown in Fig. 4. As we have previously
presented for the a-polymorph,26 the phase transformation
kinetics can be described by the Johnson–Mehl–Avrami–
Kolmogorov (JMAK)41–45 equation
n
XðtÞ ¼ 1 ꢁ eꢁkt
;
ð1Þ
where X(t) is the transformed fraction as a function of time, k
is the rate of the reaction, and the Avrami exponent n describes
the reaction order and with that the dimensionality of the
growth of the new phase. The model was initially developed
for the case of a 3-D linear growth (sphere), using simplifying
assumptions, where the nucleation is homogenous (nuclei, i.e.,
The questions arise as to why the photoreaction kinetics of
the two polymorphs are so different. The a-polymorph seems
to be more favorable for photoreaction based on the rapid rate
of reaction. From the several possible factors influencing the
rate of reaction, one could be the size of the crystals used for
irradiation. The a-cinnamic acid crystals consisted of laths
varying between 1–2 mm in their largest dimension (high
aspect ratio), whereas the crystals of b-cinnamic acid were
much smaller, consisting of needles of less than 500 mm.
Interestingly, vibrational studies in o-methoxy cinnamic acid
have revealed that larger crystals seem to react more slowly
than smaller ones.16 However, this is not reflected in the
case of a- and b-cinnamic acid described here, since the
b-polymorph is the one reacting more slowly even with much
smaller crystal sizes.
Fig. 4 Photodimerization kinetics of b-cinnamic acid converting
into b-truxinic acid. The solid curve is the fit with the Johnson–
Mehl–Avrami–Kolmogorov model with k = 0.007 ꢂ 0.001 minꢁ1
and n = 0.87 ꢂ 0.11. The dashed curve displays the result for the
a-polymorph with k = 0.019 ꢂ 0.004 minꢁ1 and n = 1.66 ꢂ 0.1.26
Another factor that could influence the kinetics of the
photoreaction is the distance between the vinylic carbons of
the two reacting cinnamic acid molecules, which is clearly
larger in the case of b-cinnamic acid (4.015 A29 compared to
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was analyzed with the HBA software.33 As an example, the 2D
PASS spectrum of a-cinnamic acid is shown in Fig. 5 along
with the projection of the isotropic spectrum. The resulting
principal values of the chemical shift tensor as well as the
reduced anisotropy dCS and asymmetry
Z parameters
(Haeberlen convention46) are given in Tables 3–6 for the four
samples, along with the corresponding theoretical CSA values.
For a better illustration of the changes between reactants and
photoproducts, the principal values of the chemical shift
tensor for the aromatic and carboxylic carbons are plotted
for comparison in Fig. 6 for the a-system and in Fig. 7 for the
b-system.
Due to the reaction of the two carbon–carbon double bonds,
the participating carbons change their hybridization from sp2 to
sp3. The CSA tensors of the vinylic and cyclobutane carbons
are therefore considerably different, as expected. Thus, their
changes will not be discussed any further.
The carbon atoms next to the reaction center, the carboxyl
carbon (C1) and the non-protonated (ipso) carbon (C4), both
have larger isotropic chemical shift values for the photoproduct,
since the neighbouring nucleus changes its hybridization from
sp2 to sp3 which directly affects the next covalently bonded
carbon.47 For the a-polymorph this is due to a change of the d11
principal tensor element, which is more pronounced for the
carboxyl carbon (C1). The other tensor values remain more or
less constant. For the b-polymorph, the situation is more
complex. For the carboxyl carbon (C1) the biggest changes
are again observed for the d11 component, but also rather big
variations are present for the d22 component and happen in a
direction opposite to that of the d11 component. For the ipso
carbon (C4) all principal tensor values show changes in different
directions. Furthermore, for both C1 and C4 carbons, two
signals are present for both photoproducts, which are attributed
to the fact that the cyclobutane ring is not planar (as already
mentioned above). Nevertheless, the principal tensor elements
are quite similar for both C1 and C4 sites.
Fig. 5 (Bottom) 13C 2D PASS spectrum of a-cinnamic acid at a
spinning speed of 1.5 kHz; (top) slice representing only the isotropic
signals.
that of 3.591 A14 for a-cinnamic acid). Therefore, larger
movements of atoms adjacent to the reaction centre are
required for the photoreaction to take place, potentially lead-
ing to a slower rate. For example, if these movements were
more severe in one of the cases this could lead to a slower
reaction rate.
Determination of the chemical shift anisotropy tensor values
Reorientational changes of functional groups during the
photoreaction could be reflected by changes to the chemical
shift anisotropy (CSA) tensors between reactant and product.
In this study, these tensors have been measured with the 2D
PASS sequence28 that separates spinning sidebands by order in
the second dimension, overcoming the problem of overlapping
signals and sidebands for slow spinning. Slow spinning is
necessary to obtain several spinning sideband manifolds for
accurate simulation of the spinning sideband pattern, which
For the remaining aromatic carbon signals of the a-system
(C5–C9), the situation is more distinct (Fig. 6). The differences
between reactant and product for the principal tensor values
Table 3 CSA values [in ppm except for Z] of a-cinnamic acid. Numbering of carbon atoms as used in Scheme 2 and Table 1. The values from the
Gaussian calculation are indicated in brackets; if not all carbons are resolved individually, also average theoretical values for those carbons are
given. The uncertainty of the experimental principal values is less than 5 ppm
Carbon
C1
diso
d11
d22
d33
dCS
Z
173
(161)
146
(145)
119
(117)
134
(136)
131
221.2
(253.4)
236.7
(246.7)
192.6
(201.7)
227.2
(222.5)
227.5
192.1
(129.0)
144.7
(142.3)
110.6
(103.8)
159.4
(170.6)
139.9
105.7
(100.5)
55.5
(47.1)
54.2
(44.1)
15.9
(13.6)
24.8
ꢁ67.3
0.43
(0.31)
0.98
(0.94)
0.76
(0.70)
0.57
(0.42)
0.83
(92.4)
91.0
C2
C3
C4
C5
(101.4)
73.5
(85.2)
ꢁ118.2
(ꢁ122.0)
ꢁ105.9
(ꢁ105.0)
ꢁ104.8
(115.7)
(ꢁ114.6)
(ꢁ117.6)
(ꢁ115.0)
ꢁ113.2
(ꢁ115.8)
(133)
129
(228.1)
229.2
(142.7)
133.0
(27.9)
23.8
(0.81)
0.92
C6-8
(C6–C8)
(C6)
(C7)
(C8)
(129)
(129)
(130)
(128)
127
(231.3)
(230.9)
(232.2)
(230.8)
213.3
(142.5)
(140.8)
(145.5)
(141.1)
153.5
(13.3)
(14.0)
(12.5)
(13.5)
13.7
(0.77)
(0.79)
(0.74)
(0.78)
0.53
C9
(125)
(224.0)
(141.1)
(8.9)
(0.72)
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Table 4 CSA values [in ppm except for Z] of a-truxillic acid. Numbering of carbon atoms as in Scheme 3 and Table 2. The values from the
Gaussian calculation are indicated in brackets, including average values where applicable. The uncertainty of the experimental principal values is
less than 5 ppm
Carbon
C01
diso
d11
d22
d33
dCS
Z
178
(172)
182
(175)
40
(46)
44
(48)
45
(53)
243.2
(270.9)
246.5
(276.8)
58.9
(63.6)
60.3
(69.1)
69.6
(72.3)
66.7
(65.4)
234.7
(228.9)
(226.3)
204.0
(229.6)
219.6
186.4
(149.9)
189.9
(155.1)
35.6
(44.4)
36.4
(42.7)
33.4
(56.7)
56.5
(54.9)
163.9
(171.4)
(179.8)
159.1
(143.3)
139.6
106.2
(94.6)
110.1
(94.4)
26.9
(30.5)
36.4
(32.6)
33.4
(29.1)
29.3
(32.9)
15.6
(17.4)
(17.6)
28.0
(14.6)
27.4
ꢁ72.4
0.78
(0.56)
0.79
(0.60)
0.47
(0.80)
0.00
(0.48)
0.00
(0.66)
0.47
(0.58)
0.58
(0.47)
(0.38)
0.45
(0.75)
0.79
(99.1)
ꢁ72.0
C1
C2
C02
C03
C3
(101.3)
18.4
(17.5)
15.9
(20.9)
24.1
(ꢁ23.6)
51
(51)
ꢁ21.6
(ꢁ18.2)
ꢁ122.5
(ꢁ121.8)
(ꢁ123.6)
ꢁ101.9
(ꢁ114.6)
ꢁ101.5
(ꢁ115.4)
(ꢁ113.4)
ꢁ97.1
C4, C04
(C4)
(C04)
C05
137, 138a
(139)
(141)
130
(129)
129
C06, C08
(C06)
(128)
(127.7)
125, 126
(124)
(126)
(125.9)
(126.2)
(126.4)
(126)
(123)
(124)
(124)
(231.5)
(228.8)
217.2
(140.3)
(140.0)
132.6
(12.8)
(14.3)
29.3
(0.79)
(0.78)
0.87
(C08)
C5–C6, C7–9, C07,C09
(C7–C9)
(C5-6)
(C5)
(C6)
(C07)
(C09)
(C7)
(C8)
(C9)
a
(222.2)
(228.0)
(227.3)
(228.6)
(227.5)
(223.1)
(220.5)
(226.4)
(219.7)
(135.5)
(138.2)
(140.1)
(136. 3)
(140.4)
(127.4)
(137.8)
(133.4)
(135.2)
(13.1)
(12.1)
(10.5)
(13.7)
(11.3)
(27.4)
(10.7)
(13.1)
(15.6)
(110.5)
(114.0)
(ꢁ115.4)
(ꢁ112.5)
(ꢁ115.1)
(ꢁ98.5)
(ꢁ112.3)
(ꢁ111.2)
(ꢁ107.9)
(0.79)
(0.79)
(0.76)
(0.82)
(0.76)
(0.98)
(0.74)
(0.84)
(0.78)
No separation of peaks in the 2D PASS.
are minor for carbons C6–C8 and more pronounced for
carbons C5 and C9. The latter two are the ones closest to
the reaction center among these five carbons. This observa-
tion gives an indication that the CSA tensor of these two
carbons is sensitive to reorientations taking place during the
photoreaction. In the case of the b-polymorph (Fig. 7), a more
complicated situation is encountered. Although an unambig-
uous assignment of all protonated aromatic carbons in the
photoproduct is not possible, larger variations in comparison
to the a-system are observed. Overall, the changes to the
principal tensor values are clearly more pronounced for the
b-photosystem.
Table 5 CSA values [in ppm except for Z] of b-cinnamic acid. Numbering of carbon atoms as in Scheme 2 and Table 1. The values from the
Gaussian calculation are indicated in brackets, including average values where applicable. The uncertainty of the experimental principal values is
less than 5 ppm
Carbon
C1
diso
d11
d22
d33
dCS
Z
174
(162)
146
(147)
118
(114)
134
(135)
127
(127)
(125)
(128)
129
224.0
(250.5)
231.3
(250.5)
212.4
(203.3)
225.0
(222.3)
213.8
(227.2)
(223.7)
(230.6)
221.9
188.9
(131.2)
129.2
(146.3)
100.6
(102.8)
149.3
(170.6)
139.2
(140.4)
(139.9)
(140.8)
156.5
109.5
(104.9)
76.9
(44.5)
41.9
(37.0)
26.7
(13.2)
27.4
(11.9)
(10.2)
(13.5)
7.1
ꢁ64.6
0.54
(0.30)
0.61
(0.98)
0.62
(0.74)
0.70
(0.42)
0.75
(0.76)
(0.73)
(0.78)
0.54
(88.3)
85.5
C2
C3
C4
(103.4)
94.1
(88.9)
ꢁ107.0
(ꢁ122.2)
ꢁ99.4
C5-6
(C5-6)
(C5)
(C6)
C7a
(114.6)
(ꢁ114.3)
(ꢁ114.8)
ꢁ121.3
ꢁ124.1
(ꢁ117.6)
(ꢁ114.6)
108.7
C8a
(C7)
(C8)
C9
128
235.3
144.2
3.6
0.54
(130)
(129)
130
(232.3)
(230.9)
238.2
(145.8)
(141.0)
111.3
(12.6)
(14.0)
38.9
(0.74)
(0.78)
0.67
(134)
(228.4)
(144.4)
(27.6)
(ꢁ105.9)
(0.79)
a
C7 and C8 assignment based on theoretical calculations.
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Table 6 CSA values [in ppm except for Z] of b-truxinic acid. Numbering of carbon atoms as in Scheme 3 and Table 2. The uncertainty of the
experimental principal values is less than 5 ppm
Carbon
diso
d11
d22
d33
dCS
Z
C1
175
179
41
45
47
136
138
125
128
131
243.7
250.6
48.9
53.2
64.6
233.3
232.8
250.0
228.3
223.9
173.7
176.8
48.9
53.2
48.9
156.3
169.0
114.3
145.1
143.7
107.7
109.0
24.4
29.3
27.8
17.6
12.8
12.0
11.4
26.4
68.6
71.8
0.96
0.94
0.00
0.00
0.83
0.65
0.51
0.83
0.71
0.76
C01
C2
ꢁ16.3
ꢁ15.9
ꢁ19.2
ꢁ118.1
ꢁ125.4
124.4
C02, C3
C03
C4
C04
C5–C9
C05–C09
ꢁ116.9
ꢁ104.9
pronounced in the b-system. More important, however, is the
fact that for the aromatic carbons in the ortho position, the
changes to the principal tensor elements are larger compared
to those of the other aromatic carbons. Although clear site
assignments are not straightforward in the b-system, signifi-
cant changes are present for the principal values of the
protonated aromatic carbons. In light of these results, the
differences between the photoreaction kinetics of both systems
may be explained as follows: there is a larger distance between
two reacting molecules in the case of b-cinnamic acid, which
requires a more pronounced orientational change of func-
tional groups upon photoreaction. Such reorientation requires
a higher (activation) energy such that the photoreaction is
slowed down compared to that of the a-polymorph.
Conclusion
The potential of solid-state NMR to study photochemical
reactions has been demonstrated, where different NMR tech-
niques have been successfully applied yielding important
information and new insights into physical rules of solid-state
[2+2] photodimerization reactions. The two photoactive
trans-cinnamic acid polymorphs, a- and b-cinnamic acid, as
well as their photoproducts, a-truxillic and b-truxinic acid,
respectively, were successfully identified and characterized by
13C solid-state NMR spectroscopy. The combination of solid-
state NMR with theoretical DFT calculations showed very
good agreement between experiment and theory. 13C CPMAS
data also demonstrated that transformation of b-cinnamic
acid into the a-polymorph occurs even at room temperature
in contrast to what is stated in the literature. The progress of
the transformation could be directly followed by temperature-
dependent 13C CPMAS, where above 330 K there is a steep
increase in the speed of transformation. The photoreaction of
b-cinnamic acid was interpreted following the JMAK model as
previously done for the a-polymorph,26 where the growth of
initially-present nuclei proceeded 1-Dly through the crystal.
The photoreaction of b-cinnamic acid proceeds at a rate
slower than that of a-cinnamic acid. From the several possible
explanations for this observation, we found that the photo-
dimerization of b-cinnamic acid requires more substantial
conformational changes near the reaction center based on
the comparative CSA tensor analysis of the two polymorphs
before and after photoreaction. Aromatic carbon atoms C5
and C9 in the ortho position show the most significant changes
to the principal values of the tensor in the a-system; for the
Fig. 6 Comparison of the principal components of the 13C chemical
shift tensor between a-cinnamic acid (solid symbols) and a-truxillic
acid (open symbols). Notation of symbols: d11 squares, d22 circles, and
d33 triangles.
To summarize the observations regarding the changes in the
principal CSA tensor elements between reactant and product:
it is found that there are changes of the isotropic shifts for the
carbons next to the reaction center, which mainly originate
from changes in the d11 principal tensor value being more
Fig. 7 Comparison of the principal components of the 13C chemical
shift tensor between b-cinnamic acid (solid symbols) and b-truxinic
acid (open symbols). Notation of symbols: d11 squares, d22 circles, and
d33 triangles.
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b-system, due to limited resolution of all the carbons, signifi-
cant variations of all principal values are found. This observa-
tion goes along with the experimental finding that the
intermolecular distance between the double bonds of the two
reacting molecules (as taken from the X-ray crystal structures)
is larger for the b-polymorph, thereby slowing down the
reaction rate. Further investigations along this line, especially
the effect of aromatic substitution on the photoreaction ki-
netics, in combination with solid-state NMR spectroscopy, are
in progress.
22 K. D. M. Harris and J. M. Thomas, J. Solid State Chem., 1991, 94,
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Acknowledgements
Valuable discussions with MSc Maria Baias (RWTH Aachen
University) concerning the Gaussian calculations are grate-
fully acknowledged. This work was supported by the Deutsche
Forschungsgemeinschaft under the project BE 2434/2.
33 HBA 1.4, K. Eichele and R. E. Wasylishen, PhD Thesis, Dalhousie
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