Carbonic acid: From polyamorphism to polymorphism

Article abstract of DOI:10.1021/ja073594f

Layers of glassy methanolic (aqueous) solutions of KHCO₃ and HCl were deposited sequentially at 78 K on a CsI window, and their reaction on heating in vacuo in steps from 78 to 230 K was followed by Fourier transform infrared (FTIR) spectroscopy. After removal of solvent and excess HCl, IR spectra revealed formation of two distinct states of amorphous carbonic acid (H₂CO₃), depending on whether KHCO₃ and HCl had been dissolved in methanol or in water, and of their phase transition to either crystalline α-or β-H₂CO₃. The main spectral features in the IR spectra of α- and β-H₂CO₃ are observable already in those of the two amorphous H₂CO₃ forms. This indicates that H-bond connectivity or conformational state in the two crystalline phases is on the whole already developed in the two amorphous forms. The amorphous nature of the precursors to the two crystalline polymorphs is confirmed using powder X-ray diffraction. These diffractograms also show that α- and β-amorphous H₂CO₃ are two distinct structural states. The variety of structural motifs found within a few kJ/mol in a computational search for possible crystal structures provides a plausible rationalization for (a) the observation of more than one amorphous form and (b) the retention of the motif observed in the amorphous form in the corresponding crystalline form. The polyamorphism inferred for carbonic acid from our FTIR spectroscopic and powder X-ray diffraction studies is special since two different crystalline states are linked to two distinct amorphous states. We surmise that the two amorphous states of H₂CO₃ are connected by a first-order-like phase transition.

Full text of DOI:10.1021/ja073594f

Published on Web 10/18/2007
Carbonic Acid: From Polyamorphism to Polymorphism
Katrin Winkel,† Wolfgang Hage,† Thomas Loerting,*,†,‡ Sarah L. Price,§ and
Erwin Mayer†
Contribution from the Institute of General, Inorganic, and Theoretical Chemistry and the
Institute of Physical Chemistry, UniVersity of Innsbruck, A-6020 Innsbruck, Austria, and from
the Department of Chemistry, UniVersity College London, 20 Gordon Street,
London WC1H 0AJ, U.K.
Received May 18, 2007; E-mail: Thomas.Loerting@uibk.ac.at
Abstract: Layers of glassy methanolic (aqueous) solutions of KHCO3 and HCl were deposited sequentially
at 78 K on a CsI window, and their reaction on heating in vacuo in steps from 78 to 230 K was followed
by Fourier transform infrared (FTIR) spectroscopy. After removal of solvent and excess HCl, IR spectra
revealed formation of two distinct states of amorphous carbonic acid (H2CO3), depending on whether KHCO3
and HCl had been dissolved in methanol or in water, and of their phase transition to either crystalline R-
or â-H2CO3. The main spectral features in the IR spectra of R- and â-H2CO3 are observable already in
those of the two amorphous H2CO3 forms. This indicates that H-bond connectivity or conformational state
in the two crystalline phases is on the whole already developed in the two amorphous forms. The amorphous
nature of the precursors to the two crystalline polymorphs is confirmed using powder X-ray diffraction.
These diffractograms also show that R- and â-amorphous H2CO3 are two distinct structural states. The
variety of structural motifs found within a few kJ/mol in a computational search for possible crystal structures
provides a plausible rationalization for (a) the observation of more than one amorphous form and (b) the
retention of the motif observed in the amorphous form in the corresponding crystalline form. The
polyamorphism inferred for carbonic acid from our FTIR spectroscopic and powder X-ray diffraction studies
is special since two different crystalline states are linked to two distinct amorphous states. We surmise
that the two amorphous states of H2CO3 are connected by a first-order-like phase transition.
Introduction
temperatures by two basically different routes: (1) high-energy
irradiation of cryogenic CO2/H2O mixtures11-18 and proton
Carbonic acid (H2CO3), the short-lived intermediate in CO2-
HCO3-/CO32- proton-transfer reactions, is a key compound in
biological and geochemical carbonate-containing systems.1-9 At
ambient temperature, H2CO3 dissolved in water dissociates
rapidly into CO2 and H2O, with a rate constant of ∼20 s-1 and
an activation enthalpy of ∼70 kJ mol-1; the reaction is highly
exergonic.1 Carbonic acid was long believed to be an unstable
molecule decomposing rapidly into its constituents CO2 and
H2O. However, in 1987, it had been detected in the gas-phase
decomposition products of (NH4)HCO3(s) by observation of a
irradiation of pure solid CO214 and (2) protonation of bicarbonate
or carbonate in a new cryogenic technique developed by our
group.19-24 Fourier-transform infrared (FTIR) spectroscopic
studies led to characterization of two polymorphs. One (â-
H2CO3) is formed by high-energy irradiation11-18 or by pro-
tonation in freeze-concentrated aqueous solution.20,21,23 The other
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† General, Inorganic, and Theoretical Chemistry, University of Innsbruck.
‡ Institute of Physical Chemistry, University of Innsbruck.
§ University College London.
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A R T I C L E S
Winkel et al.
(R-H2CO3) is formed by protonation in methanolic solu-
tion,19,20,22-24 with â-H2CO3 transforming into R-H2CO3 on
treatment with methanol/HCl.20 We have shown experimentally
that R-H2CO3 can be sublimated and recondensed without
decomposition.24 For the gas phase of H2CO3, our high-level
molecular quantum mechanical calculations show that hydrogen
bonding stabilizes the dimer,25 that water-free H2CO3 is kineti-
cally very stable, with a half-life of about 180.000 years at
ambient temperature,26 and that it requires up to three water
molecules to approach the experimental decomposition rate.27
Since H2O and CO2 coexist in various astrophysical environ-
ments such as in icy grain mantles in the interstellar medium,
the formation of solid or gaseous carbonic acid by high-energy
irradiation and its astrophysical significance is being dis-
cussed.8,13,14,17,18,20,21,24,28-32 Recently, detection of carbonic acid
adsorbed on calcium carbonate indicated that under ambient
conditions, “carbonic acid may be an important albeit short-
lived intermediate in the surface chemistry of calcium carbonate”
on earth.33,34
Here, we show by FTIR spectroscopy and X-ray diffraction
that the two crystal polymorphs R-H2CO3 and â-H2CO3 are
formed from two distinctly different amorphous states, indicating
polyamorphism for H2CO3. Polyamorphism is the term for
having multiple distinct glassy states,35 and it was observed for
the first time in amorphous ice.36,37 Since then, many one-
component types of systems showing multiple amorphous solids
have been discovered (reviewed in refs 38-40). The polyamor-
phism inferred for carbonic acid from our FTIR spectroscopic
and X-ray diffraction studies is special since two different
crystalline states are linked to two distinct amorphous states.
Recently, it has been reported that the amorphous calcium
carbonate phase in larval snail shells has the short-range order
of aragonite before it crystallizes,41 whereas the amorphous
calcium carbonate phase transforming in sea urchin embryos
into calcite has already the short-range order of calcite.42,43 It
shows that organisms build their calcium carbonate skeletons
starting with amorphous phases, with short-range order of the
crystalline calcite or aragonite phases into which they are
transforming. Thus, the concept of polyamorphism to polymor-
phism seems to be important in the biomineralization of calcium
carbonate, suggesting that the process that we have observed
Figure 1. The amorphousfâ-H2CO3 phase transition as seen by the
temperature dependence of a film made by reaction of aqueous solutions
of KHCO3 and HCl recorded on heating in vacuo at 200, 220, and 230 K
(curves 1-3). Curve 4 shows for comparison the IR spectrum of a fully
crystalline â-H2CO3 film made by reaction of KHCO3 with HBr and
recorded in vacuo at 200 K. Vertical dashed lines mark the peak positions
of amorphous H2CO3. The spectral region at ∼1020/1035 cm-1 is also
shown fourfold enhanced. In curves 1-3, the band at ∼1363 cm-1 is from
a nonvolatile impurity on the window. Curves 1-3 are shown on the same
scale; curve 4 is reduced by a factor of 0.5. The sharp band at 2344 cm-1
in curves 2 and 3 is from enclosed CO2.
Figure 2. The amorphousfR-H2CO3 phase transition as seen by the
temperature dependence of a film made by reaction of methanolic solutions
of KHCO3 and HCl recorded on heating in vacuo at 190, 200, and 210 K
(curves 1-3). Curve 4 shows for comparison the IR spectrum of a nearly
fully crystalline R-H2CO3 film made also by reaction of methanolic solutions
of KHCO3 and HCl and recorded in vacuo at 200 K. Vertical dashed lines
mark the peak positions of amorphous H2CO3. The two-band region at
∼561/584 cm-1 is also shown enhanced after smoothing of the spectra of
curves 1-3. In curve 4, the weak band at 1032 cm-1 is from a trace of
CH3OH. Curves 1-4 are shown on the same scale. (Curve 4 is from Figure
1 in ref 24.)
(25) Liedl, K. R.; Sekusak, S.; Mayer, E. J. Am. Chem. Soc. 1997, 119, 3782.
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for carbonic acid may help understand the formation of
polymorphs in a wide range of systems.
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Experimental Section
H2CO3 films were prepared on a CsI window by depositing
sequentially at 78 K layers of glassy aqueous solutions of 0.1 M KHCO3
and ∼1 M HCl in the form of droplets for Figure 1 (∼1 M HBr for
curve 4) or of glassy methanolic solutions of 0.1 M KHCO3 and ∼1
M HCl for Figure 2. The deposits were then heated in vacuo from 78
to 200 K (190 K for curve 1 of Figure 2) to induce protonation of
-
HCO3 and removal of solvent (H2O or CH3OH) and excess HCl.
Removal of solvent, protonation of HCO3-, and phase transition to
either R- or â-H2CO3 was followed by FTIR spectroscopy on further
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Carbonic Acid: From Polyamorphism to Polymorphism
A R T I C L E S
heating of the films in steps. IR spectra were recorded in transmission
on Biorad’s FTS 45 at 2 cm-1 resolution (UDR1) by coadding 256
scans. The spectrum of water vapor was subtracted from the spectra,
but no other spectral manipulations were carried out. For further
experimental details see ref 44.
X-ray diffractograms were recorded on a diffractometer in θ-θ
geometry (Siemens, model D 5000, Cu-KR), equipped with a low-
temperature camera from Paar. The sample plate was in horizontal
position during the whole measurement. Installation of a “Goebel
mirror” allowed to record small amounts of sample without distortion
of the Bragg peaks. To obtain sufficient intensity, the procedure had
to be modified: samples were prepared by freezing of droplets (about
1 mm in diameter) of the solutions in liquid nitrogen, which were then
pestled in a glass mortar at 77 K and were transferred to the X-ray
sample holder. For preparation of R-H2CO3, methanolic solutions of
0.1 M KHCO3 and ∼1 M HBr were quenched separately in liquid
nitrogen; for â-H2CO3, aqueous solutions of 1 M KHCO3 and ∼4 M
HBr were quenched. The pestled starting materials were slowly heated
in vacuo (5‚10-4 mbar) for inducing protonation of KHCO3 and
pumping off the solvents methanol and water and excess HBr.
MOLPAK48 was used to search for the low-energy, Z′ ) 1, crystal
structures of the MP2 6-31G** optimized rigid conformers of carbonic
acid. The lattice energy, calculated from the distributed multipole
analysis of this ab initio charge density and an empirical atom-atom
repulsion model,49 was minimized using DMAREL.50 The crystal
symmetry was reduced until a stable minimum was found, generating
some structures with Z′ > 1. More extensive searches using the expected
hydrogen-bonded dimers (i.e., two monomers starting in this geometry)
as the crystal building unit were also performed. Unfortunately, more
accurate calculations of the relative crystal energies are not currently
possible as the adjustment of the molecular conformations in response
to the packing forces is too demanding of correctly modeling the balance
between the various inter- and intramolecular hydrogen bonding and
dispersion forces.
The very weak band centered at 1032 cm-1 in curve 4 of Figure 2
is from a trace of CH3OH. On request of reviewers, we used this band
to estimate the minimum amount of CH3OH which can be detected by
FTIR spectroscopy and the relative amounts of H2CO3 to CH3OH. This
band assigned to the C-O stretching vibration is very intense in the
IR spectrum of CH3OH,45 and it is in a spectral region free of H2CO3
IR bands. This band was reported to be insensitive to the presence of
water46 or electrolytes.47 For the following, it is important that this
CH3OH band shows little change in peak position and band shape in
going from liquid CH3OH at ∼300 K to CH3OH in R-H2CO3
preparations below 200 K. First, the IR spectrum of liquid CH3OH
(Aldrich, HPLC quality) was recorded in a calibrated liquid cell with
15.6 µm path length. Thereafter, fractional amounts of this spectrum
were coadded to spectra of R-H2CO3 free of the band at 1032 cm-1
(using Origin 7.5), for example, curve 1 in Figure 2, to determine the
minimal amount of CH3OH which is detectable. Addition of a fraction
of 0.0002 to the latter R-H2CO3 spectrum is clearly observable by
intensity increase. This corresponds to an average CH3OH thickness
of ∼3 nm. The weak CH3OH band in curve 4 of Figure 2 then is
estimated to have an average thickness of ∼6 nm. Second, the amount
of H2CO3 formed on protonation of HCO3- was determined, as outlined
in footnote 17 of ref 24, by comparison of band areas. Deuterated
solvents were chosen because then the KDCO3 band at 1632 cm-1 does
not contain contributions from other bands (for example, the OH
deformation mode). For this comparison, spectra depicted in Figure
1b of ref 19 as curves 1 and 5 were selected because the 1:1
Results
-
correspondence between D2CO3 and DCO3 was established by
Phase Transitions Followed by FTIR Spectroscopy. We
first show how the IR spectrum of â-H2CO3 develops on heating
an amorphous H2CO3 film in vacuo (Figure 1). The film was
obtained by reaction of aqueous solutions of ∼0.1 M KHCO3
and ∼1 M HCl. Curve 1 recorded at 200 K is attributed to
mainly amorphous H2CO3, and curves 2 and 3 recorded at 220
and 230 K show how the spectrum of â-H2CO3 develops from
that of amorphous H2CO3. For assignment of the IR bands of
â-H2CO3 in terms of a qualitative description of the modes,
see Tables 1 in refs 21 and 13. Vertical dashed lines mark the
peak positions of amorphous H2CO3. The sloping background
between 4000 and ∼3500 cm-1 in this and the following figures
is caused by the Christiansen effect.51
The spectral changes are characteristic for an amorphous-to-
crystalline phase transition (reviewed in ref 52). These are in
particular shift of peak maxima, narrowing and splitting of bands
in a narrow temperature region, and several examples are
discussed as follows. First, the intense band centered in curve
1 at 2555 cm-1 shifts on crystallization to 2614 cm-1 (curve
3). The latter band had been assigned to the overtone of the
in-plane (COH) bending mode centered at 1302 cm-1 (Table 1
in ref 21). The appearance of a broad band at ∼1265 cm-1 in
curve 1 is consistent with the assignment; its intensity decreases
and develops to a shoulder on heating and phase transition.
Second, the broad band centered in curve 1 at 1476 cm-1 shifts
to 1503 cm-1 in curve 3 (assigned to the antisymmetric C(OH)2
stretching mode). Third, sharp bands centered at 683 and 657
quantitative conversion and the absence of CO2. Band area ratio was
0.33 for νCdO (in D2CO3)/νCdO (in DCO3-). Thereafter, absorbance
of the KHCO3 band was determined in a calibrated liquid cell (15.0
µm path length) for 0.10 M KHCO3 dissolved in CH3OH. From KHCO3
concentration and path length, an average thickness of ∼0.10 µm is
calculated for solid KHCO3 of density 1.5 g cm-3. Band area of the
KDCO3 band, curve 1 in Figure 1b,19 is slightly smaller which results
in an average thickness of ∼0.085 µm. By comparison with formic
acid’s density of 1.22 g cm-3, we assume for H2CO3 a slightly higher
density of 1.3 g cm-3. This then gives for curve 5 of Figure 1b in ref
19 an average thickness of ∼0.10 µm. This estimate can be used for
estimations of the average thickness of R-H2CO3 in other experiments
by considering the relative heights of the CdO stretching vibrations
(assuming similar band shapes). The height of the R-D2CO3 band used
for the estimation (curve 5 in Figure 1b of ref 19) is similar to that
shown as curve 4 in Figure 2, about 0.03 absorbance units. These are
typical values in most of our experiments; only in a few experiments
were we able to obtain an about fivefold intensity by multilayer deposits.
In a third step, for curve 4 of our Figure 2, this average thickness of
R-H2CO3 of ∼0.10 µm, or 100 nm, can be compared with the average
CH3OH thickness of ∼6 nm obtained as described above. Considering
the differences in densities (and assuming a density of 0.80 for CH3OH
and of 1.3 for H2CO3), the H2CO3/CH3OH molar ratio is ∼14. For
curve 1 of Figure 2, where no CH3OH band can be detected at 1032
cm-1, the H2CO3/CH3OH molar ratio must be higher: from the CH3OH
detection limit of ∼3 nm (see above), we estimate it to be at least
∼28. â-H2CO3 solvent impurity could not be estimated in this manner
because the solvent water does not have a suitable sharp IR band.
(44) Hage, W.; Hallbrucker, A.; Mayer, E. J. Chem. Soc., Faraday Trans. 1996,
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Spectra of Polyatomic Molecules; van Nostrand: New York, 1945.
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A R T I C L E S
Winkel et al.
cm-1 (curve 3, in-plane (CO3) bending mode) develop from
the broad band at ∼649 cm-1 (curve 1). Fourth, the weak broad
band centered in curve 1 at ∼1020 cm-1 shifts in curve 3 on
crystallization to a sharp band centered at 1035 cm-1. The latter
band had been assigned to the symmetric C(OH)2 stretching
mode. This band system seems to consist of two bands only, a
broad one at ∼1020 cm-1 from the amorphous phase and a sharp
one at 1035 cm-1 from â-H2CO3, and therefore it is very useful
in estimating relative amounts of amorphous and crystalline
phase. Curve 3 contains a minor broad feature at ∼1020 cm-1
which indicates that even on heating to 230 K crystallization is
not complete.
vacuo (Figure 2). The film was obtained by reaction of
methanolic solutions of ∼0.1 M KHCO3 and ∼1 M HCl. Curve
1 recorded at 190 K is attributed to mainly amorphous H2CO3
with the broad peak in the O-H stretching band region
originating from traces of included ice. Curves 2 and 3 recorded
at 200 and 210 K show how the spectrum of R-H2CO3 develops
from that of amorphous H2CO3. For assignment of the IR bands
of R-H2CO3, see Table 1 in ref 22. Vertical dashed lines mark
the peak positions of amorphous H2CO3, and the spectral
changes on phase transition to R-H2CO3 are pointed out as
follows. First, the IR band centered in curve 1 at 1457 cm-1
shifts on crystallization to 1476 cm-1 (curve 3, assigned to
antisymmetric C(OH)2 stretching vibration). Second, the bands
at 1372 and ∼1253 cm-1 (curve 1) decrease in intensity (curves
2 and 3), and the band centered in curve 1 at 1717 cm-1 (CdO
stretching vibration) narrows considerably in particular at lower
wavenumbers in curves 2 and 3. Third, the two weak bands at
2693 and 2586 cm-1 in curve 3 (at 2702 and 2586 cm-1 in
curve 2) had been assigned to O-H stretching vibrations, in
accordance with the spectral positions in the R-H213CO3 and
R-D2CO3 isotopomers (see Table 1 in ref 22). These peaks are
not observable in curve 1, apparently because of band broaden-
ing. Fourth, a very weak two-band system consisting of a broad
band at ∼561 cm-1 and a sharp one at 584 cm-1 (shown
enhanced) allows to follow the phase transition from amorphous
These results are consistent with our previous findings that
on protonation of KHCO3 with HCl, amorphous H2CO3 is first
formed which slowly converts with increasing temperature to
â-H2CO3.21 However, this conversion is not complete, even at
the highest temperatures. On the other hand, on protonation of
KHCO3 with HBr, a fully crystalline film is immediately
obtained. Therefore, we show as curve 4 the IR spectrum of a
film of â-H2CO3 made by protonation of KHCO3 with HBr:
in this spectrum, the features of amorphous H2CO3, as defined
above, are now absent. In particular, the broad band at ∼1020
cm-1 attributed to amorphous H2CO3 is now absent and the
sharp band at 1035 cm-1 from â-H2CO3 is very intense.
While most of the band systems show gradual changes in
going from the amorphous to the fully crystalline state (curve
1 to 4), the broad shoulder at ∼3310 cm-1 in curve 1 and at
∼3210 cm-1 in curve 4 is an exception because it is not
observable in curves 2 and 3. This shoulder had been assigned
to an overtone of the CdO stretching vibration (ν CdO).21 In
carboxylic acids generally, the occurrence of subpeaks super-
imposed on the broad and intense O-H stretching band region
(ν O-H) has been ascribed to Fermi resonance effects where
the intensity of combination bands or overtones is enhanced by
interaction with νO-H.53-56 Thus, it seems reasonable to
attribute also in curves 1 and 4 the intensity of the shoulders to
Fermi resonance. On phase transition from amorphous to
â-H2CO3, νO-H narrows and the shoulder shifts from ∼3310
cm-1 in curve 1 to ∼3210 cm-1 in curve 4. This decrease is
consistent with decreasing νCdO peak frequency in going from
the amorphous state (curve 1, 1721 cm-1) to the crystalline state
(curve 4, 1700 cm-1). Band narrowing by second-derivative
curves further shows that the two shoulders are caused by
different subbands (not shown). The question remains why the
shoulder is not observable anymore in curves 2 and 3. These
spectra contain varying amounts of amorphous/crystalline
H2CO3, and superposition of the two broad shoulders is expected
to lead to further broadening and so the shoulders could become
unobservable. In addition, changes of the νO-H peak shape
on crystallization can lead to decrease in intensity enhancement
by Fermi resonance.45
H2CO3 (band at ∼561 cm-1) to R-H2CO3 (band at 584 cm-1
,
assigned to in-plane (CO3) bending mode) by the changes in
relative intensity from curves 1-3. This two-band system also
shows that curve 1 contains already a minor amount of R-H2CO3
and that crystallization is not complete on heating to 210 K
(curve 3).
According to the criteria for the presence of amorphous
H2CO3 listed above, the crystallinity of R-H2CO3 varies
considerably depending on experimental details. This is indicated
by the IR spectra reported in refs 19, 22, and 24. Therefore, we
show as curve 4 the IR spectrum of a film of R-H2CO3 made
in the same manner by reaction of methanolic solutions of
KHCO3 and HCl and recorded in vacuo at 200 K. The high
crystallinity of the film is indicated by further sharpening of
bands and band splitting in comparison to curve 3, for example,
the band centered in curve 3 at 1306 cm-1 with a shoulder at
higher frequency (in the second derivative) splits in curve 4
into two bands at 1308 and 1328 cm-1. According to the criteria
for amorphous H2CO3 listed above, only a minor amount of
amorphous H2CO3 is indicated in curve 4 by some residual
intensity at ∼1250 cm-1 and some tailing of the band centered
at 1713 cm-1. This spectrum further shows a trace of CH3OH
by the weak band at 1032 cm-1. This film had been used in
our sublimation and recondensation experiment of R-H2CO3,
and its IR spectrum is depicted in Figure 1 of ref 24 as curve
1. The IR spectrum of sublimated and recondensed R-H2CO3
shown in the same reference as curve 2 is nearly identical with
that of the film before sublimation and recondensation except
that now the two features from a minor amount of amorphous
H2CO3 and the weak peak from CH3OH had disappeared.
In the same manner, we show how the IR spectrum of
R-H2CO3 develops on heating an amorphous H2CO3 film in
(52) Bulkin, B. J. Vibrational Spectroscopy for the Study of Order-Disorder
Phenomena in Organic Materials. In Chemical, Biological and Industrial
Applications of Infrared Spectroscopy; Durig, J. R., Ed.; Wiley: New York,
1986; p 139.
We next compare the IR spectra of the two amorphous forms
with those of R- and â-H2CO3 (Figure 3). Curves 1 and 2 are
the IR spectra of the amorphous forms of H2CO3 obtained on
reaction of methanolic solutions (curve 1) or aqueous solutions
(curve 2) of KHCO3 with HCl. Curve 3 is the IR spectrum of
(53) Bratoz, S.; Hadzi, D.; Sheppard, N. Spectrochim. Acta 1956, 8, 249.
(54) Bellamy, L. J.; Pace, R. J. Spectrochim. Acta 1963, 19, 435.
(55) Marechal, Y. Infrared Spectra of Cyclic Dimers of Carboxylic Acids: The
Mechanics of H-Bonds and Related Problems. In Vibrational Spectra and
Structure, 1987; Vol. 16, p 311.
(56) Wolfs, I.; Desseyn, H. O. Appl. Spectrosc. 1996, 8, 1000.
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Carbonic Acid: From Polyamorphism to Polymorphism
A R T I C L E S
sublimation) is compared with that of the film of R-H2CO3
without KCl (curves 2, after sublimation and recondensation).
X-ray Diffractograms of the Two Amorphous Forms of
H2CO3. We further show X-ray diffractograms of R-amorphous
and â-amorphous H2CO3 (Figure 4). The samples were made
by reaction of KHCO3 with HBr in methanolic solution for
R-amorphous H2CO3 (a) and in aqueous solution for â-amor-
phous H2CO3 (c). In both cases, KBr is one of the reaction
products on heating to 200 K (a) or 210 K (c), and the reflections
of crystalline KBr are marked by open circles.57 The other
reaction product on protonation of HCO3-, H2CO3, is attributed
to broad peaks centered at 2θ ∼26° in a and at 2θ ∼27° in c,
and the broadness of these peaks indicates that H2CO3 is
amorphous. These broad peaks are superimposed by sharp peaks
from hexagonal ice (marked by asterisks) and the substrate (full
triangles). The broad peak attributed to â-amorphous H2CO3
(c) is clearly broader than that of R-amorphous H2CO3 (a), and
its peak maximum is shifted slightly to higher 2θ values. Both
broad peaks disappear on heating to 300 K in vacuo as expected
for both forms of H2CO3 (Figure 4, b and d),11,19,21,22 and only
the reflections of crystalline KBr and the substrate remain. We
emphasize that reflections of the starting material KHCO3 were
not observable at 200 or 300 K, indicating that its protonation
must have gone to completion. We further note that we did
observe onset of crystallization of R-amorphous H2CO3 (â-
amorphous H2CO3) by the appearance of sharp Bragg peaks
when the sample was kept over hours at 200 K (210 K) (not
shown) or slightly above these temperatures. These ongoing
studies of X-ray diffraction patterns of R- and â-H2CO3 will be
reported separately.
Figure 3. Comparison of IR spectra of the two amorphous states (curves
1 and 2) with those of R- and â-H2CO3 (curves 3 and 4). Curves 1 and 2
are curves 1 in Figures 1 and 2, and curves 3 and 4 are curves 4 in Figures
1 and 2.
R-H2CO3, and curve 4 is that of â-H2CO3. It is obvious that
the IR spectra of the two amorphous forms (curves 1 and 2)
differ in the same manner as those of the two crystalline forms
(curves 3 and 4). Furthermore, the spectral pattern observable
in the IR spectra of the crystalline forms is apparent already in
those of the amorphous forms. This is particularly clear for
amorphous and crystalline â-H2CO3 in curves 2 and 4. Phase
transition from amorphous H2CO3 to â-H2CO3 further involves
shift of several IR bands to higher wavenumbers, for example,
2555f2616 cm-1, 1476f1501 cm-1, 1265f1297 cm-1
,
1020f1035 cm-1, and 649f661/683 cm-1. For the phase
transition from amorphous H2CO3 to R-H2CO3 (curves 1 and
3), the IR spectra also show similar patterns, with shift of
IR bands to higher wavenumbers on crystallization, for
Discussion
Vibrational spectroscopy is an established technique for
following phase transitions and for studies of polymorphism
(reviewed in refs 58 and 59). Studies of polyamorphism by
vibrational spectroscopy are more recent, and they concentrated
on the high- and low-density forms of amorphous water.60-63
The polyamorphism shown in Figures 1-3 for H2CO3 is special
since two different crystalline states are linked to the two
different amorphous states. These FTIR spectroscopic studies
are corroborated by X-ray diffractograms (Figure 4). It shows,
therefore, that in carbonic acid polyamorphism leads directly
to polymorphism. It indicates that the two amorphous states are
separated by potential energy barriers which are higher than
those to their crystalline states. It is conceivable that this type
of behavior is much more general and that it occurs in many
other systems (e.g., in calcium carbonate, see Introduction).
However, it will often only be observable if the amorphous
forms are made by a low-temperature technique, such as that
used for H2CO3, so that on heating structural changes caused
by the amorphousfcrystalline phase transition can be followed.
example, 1457f1477/1486 cm-1, ∼1253f1308/1328 cm-1
,
and ∼561f584 cm-1. These distinct amorphous states of
H2CO3 are called in the following R-amorphous H2CO3 (curve
1) and â-amorphous H2CO3 (curve 2).
We summarize that demonstration of the amorphous-to-
crystalline H2CO3 phase transition is tricky for both R- and
â-H2CO3. First, the extent of crystallization depends on several
factors. For example, the reaction of aqueous solutions of
KHCO3 and HBr proceeds quickly and directly to â-H2CO3,
and amorphous H2CO3 cannot be identified. However, with HCl
the reaction occurs much more slowly; amorphous H2CO3 can
be characterized, but crystallization stops before conversion of
amorphous H2CO3 to â-H2CO3 is complete (see Figure 1). This
has been discussed, but not understood, in ref 21. Second, it is
difficult to pump off the solvent in vacuo and to obtain IR
spectra of amorphous H2CO3 without significant crystallization.
This turned out to be a problem for reaction of methanolic
solutions. CH3OH has a very intense peak at ∼1030 cm-1, and
the absence of this peak in curves 1-3 of Figure 2 indicates
that the film does not contain CH3OH anymore. We have
obtained additional IR spectral evidence for the two amorphous-
to-crystalline H2CO3 phase transitions of the isotopomers
H213CO3 and D2CO3 which are not shown here. We note that
KCl, which is the second reaction product in the protonation of
KHCO3 with HCl, seems to have only a very minor influence
on the extent of crystallization from methanolic solutions. This
is demonstrated by Figure 1 in ref 24, where the IR spectrum
of a film of R-H2CO3 containing KCl (curves 1, before
(57) Meisalo, V.; Inkinen, O. Acta Crystallogr. 1967, 22, 58.
(58) Sherman, W. F.; Wilkinson, G. R. Raman and Infrared Studies of Crystals
at Variable Pressure and Temperature. In AdVances in Infrared and Raman
Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Heyden: London, 1980;
Vol. 6, p 158.
(59) Iqbal, Z.; Owens, F. J. Vibrational Spectroscopy of Phase Transitions;
Academic Press: London, 1984.
(60) Klug, D. D.; Mishima, O.; Whalley, E. J. Chem. Phys. 1987, 86, 5323.
(61) Mishima, O.; Suzuki, Y. Nature 2002, 419, 599.
(62) Tse, J. S.; Klug, D. D.; Tulk, C. A.; Svensson, E. C.; Swainson, I.; Shpakov,
V. P.; Belosludov, V. R. Phys. ReV. Lett. 2000, 85, 3185.
(63) Loerting, T.; Salzmann, C.; Kohl, I.; Mayer, E.; Hallbrucker, A. Phys. Chem.
Chem. Phys. 2001, 3, 5355.
9
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A R T I C L E S
Winkel et al.
Figure 4. X-ray diffractograms (Cu-KR) (a) of the reaction products of 0.1 M KHCO3 with ∼1 M HBr in methanolic solution recorded after heating in
vacuo from 77 to 200 K, the broad peak centered at ∼26° is attributed to R-amorphous H2CO3, and (b) recorded on subsequent heating to 300 K, which
causes H2CO3 to be pumped off, (c) of the reaction products of 1 M KHCO3 with ∼4 M HBr in aqueous solution recorded after heating in vacuo to 210 K,
the broad peak centered at ∼27° is attributed to â-amorphous H2CO3, and (d) recorded on subsequent heating to 300 K which causes H2CO3 to be pumped
off. Bragg peaks in a-d from crystalline KBr are marked by open circles;57 Bragg peaks from hexagonal ice in c are marked by asterisks and from the
substrate in a, b, and d by full triangles.
We expect to find it in substances where molecules form a
variety of hydrogen-bonded structures of varying energies.
H2CO3 is a dicarboxylic acid. For small carboxylic acids, the
dimer and the catemer are the preferred hydrogen-bonding
motifs.64 The structures of R- and â-H2CO3 are not known, and
it will be very difficult to obtain sufficient sample for deter-
mination of their structures by diffraction. However, it is obvious
that in addition to crystal field and packing effects, the
conformational flexibility of H2CO3 has to be considered
because, as pointed out by Bernstein and Hagler, “in most cases
energy differences between polymorphs do not exceed 2-3 kcal
mol-1, which is also the energy domain for torsional conforma-
tion parameters in many organic molecules. This suggests the
possibility that molecules with torsional degrees of freedom may
adopt different conformations in different polymorphs, a
phenomenon known as conformational polymorphism”.65,66
Thus, the monomer conformation of H2CO3 is an important
factor for crystal packing. Numerous calculations for the
formation of the H2CO3 monomer from gaseous H2O and CO2
have been performed at various levels, and they agree that the
anti-anti conformer (i.e., both hydrogens point toward the
carbonyl oxygen) is the most stable conformation and that the
syn-anti conformer is only slightly less stable.6,7,9,67-69 High-
level molecular quantum calculations of the H2CO3 dimer made
from two anti-anti monomers indicated that this dimer is
remarkably stable and that the energy difference between the
dimer and the constituents H2O and CO2 is, after correction for
zero-point energy differences, “astonishingly close to zero”.24,25
Thus, the dimer and higher H2CO3 clusters68,69 have to be
considered as building blocks in the crystal structures of R- and
â-H2CO3.
We emphasize that the main spectral features in the IR spectra
of R- and â-H2CO3 are observable already in those of the two
amorphous H2CO3 forms (see Figure 3). This indicates that
H-bond connectivity or conformational state in the two crystal-
line phases is on the whole already developed in the two
amorphous forms. Thus, the determination of the possible crystal
structures will show the possible short-range/intermediate-range
motifs of the two H2CO3 amorphs.
Search for Hydrogen-Bonding Motifs in Amorphous
H2CO3. The existence of amorphous phases of carbonic acid is
not surprising given that there are a vast number of ways of
packing this molecule in the solid state within a small energy
range. Our simple search for crystal structures of the anti-anti
conformer had four different stackings of the hydrogen-bonded
sheet shown in Figure 5a within 1 kJ mol-1 of the global
minimum in the lattice energy plus an alternative motif with
three-dimensional hydrogen bonding (Figure 5b). Thus, stacking
errors in growth with some regions of 3D hydrogen bonding
seem highly likely70 with the small energy differences between
interchangeable motifs promoting the amorphous phase. A
similar search with the syn-anti conformer also had many low-
energy structures, including two different stackings of a sheet
containing the doubly hydrogen-bonded motif (Figure 5c) and
an alternative layer structure (Figure 5d) within a kJ mol-1 of
(64) Beyer, T.; Price, S. L. J. Phys. Chem. B 2000, 104, 2647.
(65) Bernstein, J.; Hagler, A. T. J. Am. Chem. Soc. 1978, 100, 673.
(66) Bernstein, J.; Hagler, A. T. Mol. Cryst. Liq. Cryst. 1979, 50, 223.
(67) Janoschek, R.; Csizmadia, I. G. J. Mol. Struct. 1993, 300, 637.
(68) Ballone, P.; Montanari, B.; Jones, R. O. J. Chem. Phys. 2000, 112, 6571.
(69) Tossell, J. A. Inorg. Chem. 2006, 45, 5961.
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13868 J. AM. CHEM. SOC. VOL. 129, NO. 45, 2007

Carbonic Acid: From Polyamorphism to Polymorphism
A R T I C L E S
Figure 5. Hydrogen-bonding motifs from low-energy structures found for (top) anti-anti and (bottom) anti-syn carbonic acid. (a) The hydrogen-bonded
sheet structure found in four low-energy structures (ak11, P21/c Z′ ) 1 at -81.80 kJ/mol; av11 Pc Z′ ) 2 at -81.56 kJ/mol; ai10, P21/c at -81.28 kJ/mol;
cc46 Pbca at -81.27 kJ/mol; and fc48 P21/c at -80.99 kJ/mol). (b) A 3D hydrogen-bonded structure, bi8 P1Z ) 4 at -81.24 kJ/mol. (c) The hydrogen-
bonded sheet containing the anti-syn doubly hydrogen-bonded dimer, found, for example, in b22, P21 Z′ ) 2 at -84.10 kJ/mol and in al35 Pc Z′ ) 2 at
-83.19 kJ/mol. (d) An alternative sheet without the dimer, ak35 P21/c at -83.15 kJ/mol. Blue-dashed lines indicate hydrogen bonds as defined by the
default lengths in Mercury.84
its global minimum. This also suggests that crystallization into
an ordered structure would be prone to growth errors. Since
the syn-anti conformer gave slightly lower lattice energies than
the anti-anti conformer, this would partially compensate for
the higher conformational energy, making polymorphs of either
conformer energetically feasible. Thus, a plausible rationalization
of our observations is that the two sets of reaction conditions
generate different conformations of the molecule as the growth
units of the solid phase, possibly through the different solvation
clusters formed in water or methanol. Either growth unit would
readily form an amorphous phase because of the variety of
locally ordered hydrogen-bonded sheets and 3D networks that
can be formed. Since the barriers to changing an anti to syn
conformation within the amorphous solid state would be greater
than those involved in correcting growth mistakes such as mis-
stackings of layers, the conformers would be maintained in the
transformation to the ordered polymorph.
aqueous solution leads to formation of first â-amorphous H2CO3
which then crystallizes to â-H2CO3, whereas protonation of
HCO3 in methanolic solution (Figure 2) gives first R-amor-
-
phous H2CO3 which crystallizes to R-H2CO3. Protonation of
-
HCO3 in methanol-water solution made by mixing equal
volumes (56 wt % water) leads to formation of R-amorphous
H2CO3 which does not crystallize anymore (see Figure 5, curve
1, in ref 22). â-H2CO3 can be transformed into R-amorphous
H2CO3 on treatment with methanol/HCl (Figure 3 in ref 20).
Thus, we obviously have a directing effect of the solvent,
methanol or water, on the formation of the two amorphous and
crystalline forms. A special case is the sublimation and
recondensation experiment of R-H2CO3 where a trace of CH3OH
is observable by the very weak peak centered at 1032 cm-1
(Figure 1, curve 1, in ref 24) which is absent after condensation
(curve 2). The H2CO3/CH3OH molar ratio of this trace amount
is estimated as ∼14 (see Experimental Section). Whether or
not this CH3OH impurity has a directing effect on the crystal
form obtained after sublimation and recondensation, we cannot
say.
Solvent Effect on Carbonic Acid’s Polyamorphism and
Polymorphism. We next discuss the effect of solvent on
carbonic acid’s polyamorphism and polymorphism. As shown
above (Figure 1), protonation of HCO3- in freeze-concentrated
It is well-known that solvents can have a dramatic effect on
crystal polymorphism, and glycine is a good example where
“addition of methanol or ethanol to aqueous solutions induces
the precipitation of the least stable â form of glycine”, whereas
the thermodynamically more stable R- and γ-glycine forms
crystallize from aqueous solution.71,72 Weissbuch et al. suggest
(70) The prediction that aspirin has two possible almost equi-energetic stackings
of its sheet structure (Ouvrard, C.; Price, S. L. Cryst. Growth Des. 2004,
4, 1119) correlates with the observation of intergrowth of domains of both
polymorphs (Bond, A. D.; Boese, R.; Desiraju, G. R. Angew. Chem., Int.
Ed. 2006), and a disordered crystal polymorph of chlorothalonil can be
rationalized (Tremayne, M.; Grice, L.; Pyatt, J. C.; Seaton, C. C.; Kariuki,
B. M.; Tsui, H. H. Y.; Price, S. L.; Cherryman, J. C. J. Am. Chem. Soc.
2004, 126, 7071) as arising from two low-energy layers structures with
different stackings. There are many more low-energy interchangeable crystal
structures for carbonic acid, and it is crystallized at significantly lower
temperatures, so it is more likely to form an amorphous rather than a simple
disordered state.
(71) Weissbuch, I.; Torbeev, V. Y.; Leiserowitz, L.; Lahav, M. Angew. Chem.,
Int. Ed. 2005, 44, 3226.
(72) Torbeev, V. Y.; Shavit, E.; Weissbuch, I.; Leiserowitz, L.; Lahav, M. Cryst.
Growth Des. 2005, 5, 2190.
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A R T I C L E S
Winkel et al.
Scheme 1. First-Order-Like Phase Transition between
R-Amorphous and â-Amorphous H2CO3 Deduced from Phase
Transitions between Amorphous and Crystalline Forms of H2CO3
that various factors should be considered to understand the effect
of solvent on crystal polymorphism, “for example the formation
of structured clusters in solution prior to crystallization, the
structure of growing surfaces that delineate emerging nuclei,
the interaction between these surfaces and the solvent, as well
as solvent-solute and solute-solute interactions.”71 and they
conclude that “removal of the solvent molecules is an important
rate-determining step in the growth of a given face.” FTIR
spectroscopic studies by Davey et al. recently have shown for
the first time a direct relationship between the assembly of
molecules in solution and the solid form which crystallizes:
treatment with CH3OH/HCl and that R-H2CO3 forms only from
the methanolic solution after pumping off CH3OH/HCl. At 200
K, the rate of sublimation of R-H2CO3 was determined as 1.10-8
g cm-2 s-1 (see ref 24 and footnote 17 therein). At this
temperature, â-H2CO3 does not show measurable sublimation,
and thus, it is much lower than that of R-H2CO3. An estimate
for the saturation vapor pressure can be obtained from the
sublimation rate by using the Knudsen formula.24,80 According
to this estimate, R-H2CO3 has a higher vapor pressure at 200 K
than â-H2CO3 and, thus, would be less stable than â-H2CO3.
Direct conversion of the two crystal polymorphs in the absence
of solvent could not be observed at e200 K and 1 bar, that is,
in the low-temperature range accessible without decomposition,
and it seems doubtful for kinetic reasons whether this will ever
be possible. Thus, we do not know whether the relationship
between R- and â-H2CO3 is enantiotropic or monotropic, as
expressed in a free energy versus temperature diagram.81
Organic crystal polymorphs are usually connected via a first-
order phase transition,81 and the evidence above supports this
assumption for R- and â-H2CO3. The phase transition from both
the R-amorphous and the â-amorphous state to R- and â-H2CO3
is expected to be first-order. It then follows that the R- and
â-amorphous states are also connected by a first-order-like phase
transition. An “apparently first-order transition between two
amorphous phases of ice” (that is, high-density and low-density
amorphous ice) was first postulated in 1985 by Mishima et al.37
Since then, many examples for first-order-like phase transitions
between amorphous states with different short-range order/
intermediate-range order structural types and thermodynamic
properties have been reported that are analogous to the crystal-
crystal transitions (reviewed in ref 40). That is, the two
amorphous states are separated by major energy barriers and
can be treated as “phases”. Another scheme similar to Scheme
1 could be drawn for calcium carbonate where the amorphous
calcium carbonate phase in larval snail shells has the short-
range order of aragonite before it crystallizes,41 whereas the
amorphous calcium carbonate phase transforming in sea urchin
embryos into calcite has already the short-range order of calcite
(see Introduction).42,43 The two crystal polymorphs calcite and
aragonite apparently are connected via a first-order phase
transition,82,83 and thus the two distinct amorphous calcium
carbonate states seem also connected by a first-order-like phase
transition.
73,74
solutions of tetrolic acid rich in dimers nucleate the
R-polymorph, whereas solutions in more polar solvents, where
dimer formation is disrupted, nucleate the catemeric â-poly-
morph. These studies also demonstrated the application of IR
spectroscopy in in-situ studies for understanding the relationship
between solution and solid-state interactions on crystallization.
Such detailed studies are not experimentally feasible for carbonic
acid. However, it seems clear that the solvent, methanol or water,
has a directing effect on H-bond connectivity probably via the
conformational state a in the two amorphous states and in the
subsequently formed crystal polymorphs.
A crystalline CH3OH adduct or a hydrate could be a precursor
to formation of R- or â-H2CO3, and because of that we have
searched from the beginning of our studies on H2CO3 for these
but without success.75 A CH3OH adduct as precursor to
R-H2CO3 would be easily recognizable by intense CH3OH bands
in the CH and CO stretching band region,19 whereas a crystalline
hydrate is expected to show OH stretching bands between 3550
and 3200 cm-1 which sharpen at low temperatures.76,77 In
several of our experiments, films obtained by reaction of KHCO3
with HCl or HBr aqueous solution were cooled to 78 K at
various stages of the experiments, that is, for fully amorphous,
partially crystalline, and fully crystalline films.21 In none of these
experiments could sharp OH stretching bands assignable to a
crystalline hydrate of â-H2CO3 be observed. The only sharp
bands observable in this spectral region could be assigned to
the hexahydrate of HCl (HBr),78 to the dihydrate of NaCl (when
using sodium salts), or to a mixed hydrate of CsCl (for Cs
salts).79 This shows that crystalline hydrates can, in principle,
be formed under these experimental conditions.21
First-Order-Like Phase Transition? We next discuss the
relation between the two amorphous states of H2CO3 called
R-amorphous H2CO3 and â-amorphous H2CO3 (Scheme 1). The
relative stability of the two crystalline phases is unclear and
may well depend on thermodynamic variables. We have reported
that â-H2CO3 transforms partly into R-H2CO3 on treatment with
CH3OH/HCl and because of that have tentatively suggested that
R-H2CO3 is the thermodynamically more stable form.20 How-
ever, we cannot rule out that â-H2CO3 simply dissolves on
(73) Parveen, S.; Davey, R. J.; Dent, G.; Pritchard, R. G. Chem. Commun. 2005,
1531.
(74) Davey, R. J.; Dent, G.; Mughal, R. K.; Parveen, S. Cryst. Growth Des.
2006, 6, 1788.
(75) Hage, W. Isolierung von reiner Kohlensa¨ure und deren FTIR-spektrosko-
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Ph.D. Thesis, Universita¨t Innsbruck, 1995.
(76) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination
Compounds, 4th ed.; Wiley: New York, 1986.
(77) Falk, M.; Knop, O. Water in Stoichiometric Hydrates. In Water a
ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1973;
Vol. 2, p 55.
(78) Ritzhaupt, G.; Devlin, J. P. J. Phys. Chem. 1991, 95, 90.
(79) Maki, A. G.; West, R. Inorg. Chem. 1963, 3, 657.
(80) Umrath, W. Mikroskopie 1983, 40, 9.
(81) Bernstein, J. Polymorphism in Organic Crystals; Clarendon: Oxford, 2002.
(82) Zimmermann, H. D. Nature 1971, 231, 203.
(83) Topor, N. D.; Tolokonnikova, L. I.; Kadenatsi, B. M. J. Thermal Analysis
1981, 20, 169.
(84) Mercury, CCDC. http://www.ccdc.cam.ac.uk/products/csd_system/mercury/
(accessed May 14, 2007).
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Carbonic Acid: From Polyamorphism to Polymorphism
A R T I C L E S
Conclusions
acid which are very close in energy. The two sets of reaction
conditions with methanol or water as solvent may generate
different conformations of the molecule as the growth units of
the solid phase, which readily form an amorphous state. These
conformations are likely retained upon crystallization.
We show by FTIR spectroscopy and X-ray diffraction that
the precursors of the two crystal polymorphs of carbonic acid,
R- and â-H2CO3, are two distinct amorphous states. It indicates
that the two amorphous states are separated by potential energy
barriers which are higher than those to their crystalline states.
It is plausible that this type of behavior is much more general
and that it occurs in many other systems. Furthermore, from
comparison of IR spectra of R- and â-H2CO3 with those of their
amorphous forms, we conclude that the two distinct H-bonding
motifs observable in the crystalline phases exist already in the
amorphous forms but without the translational symmetry and
long-range order of the crystalline phases. Our computational
polymorph search provides a plausible rationalization for these
observations: we find a vast number of low-energy structures
showing a variety of locally ordered hydrogen-bonded sheets
and 3D networks for both low-energy conformers of carbonic
Acknowledgment. We gratefully acknowledge financial
support by the Austrian Science Fund (project P18187) and the
British Council Academic Research Collaboration program. The
Basic Technology program of the Research Councils UK funded
“Control and Prediction of the Organic Solid State” (CPOSS,
www.cposs.org.uk) which provided the infrastructure for the
computational work. The computed crystal structures for
carbonic acid are stored on CCLRC e-Science Centre data portal
and are available on request.
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J. AM. CHEM. SOC. VOL. 129, NO. 45, 2007 13871