Observation of quantum paraelectricity in an intermolecular ionic hydrogen-bonded crystal of a squaric acid derivative

Article abstract of DOI:10.1021/jp030961a

Proton transfer in a hydrated crystal of a squaric acid derivative, p-phenylenebis(squaric acid) (PBSQ), was investigated by means of ac dielectric measurements. The crystal consisted of PBSQ monoanions and protonated water dimer (H₅O₂⁺) counter cations, and a highly symmetric, one-dimensional hydrogen-bonded chain was formed through strong OH?O^- ionic hydrogen bonding between deprotonated PBSQ moieties. The permittivity of the hydrated crystal was nearly temperature independent (ε′ ～ 9), but the deuterated crystal exhibited a Curie-Weiss type temperature dependence and underwent depression of the permittivity at 28 K, which is the characteristic of an (anti)ferroelectric phase transition. Thus, we conclude that the dielectric response of the hydrated PBSQ crystal originates from proton transfer along the intermolecular hydrogen bond and that the temperature-independent dielectric behavior can be interpreted in terms of quantum paraelectricity.

Full text of DOI:10.1021/jp030961a

J. Phys. Chem. B 2004, 108, 5527-5531
5527
Observation of Quantum Paraelectricity in an Intermolecular Ionic Hydrogen-Bonded
Crystal of a Squaric Acid Derivative
Isao Takasu, Akira Izuoka,† and Tadashi Sugawara*
Department of Basic Science, Graduate School of Arts and Sciences, The UniVersity of Tokyo,
Komaba, Meguro-ku, Tokyo 153-8902, Japan
Tomoyuki Mochida
Department of Chemistry, Faculty of Science, Toho UniVersity, Miyama, Funabashi, Chiba 274-8510, Japan
ReceiVed: August 7, 2003; In Final Form: January 12, 2004
Proton transfer in a hydrated crystal of a squaric acid derivative, p-phenylenebis(squaric acid) (PBSQ), was
investigated by means of ac dielectric measurements. The crystal consisted of PBSQ monoanions and protonated
+
water dimer (H5O2 ) counter cations, and a highly symmetric, one-dimensional hydrogen-bonded chain was
formed through strong OH‚ ‚ ‚O- ionic hydrogen bonding between deprotonated PBSQ moieties. The
permittivity of the hydrated crystal was nearly temperature independent (ꢀ′ ∼ 9), but the deuterated crystal
exhibited a Curie-Weiss type temperature dependence and underwent depression of the permittivity at 28 K,
which is the characteristic of an (anti)ferroelectric phase transition. Thus, we conclude that the dielectric
response of the hydrated PBSQ crystal originates from proton transfer along the intermolecular hydrogen
bond and that the temperature-independent dielectric behavior can be interpreted in terms of quantum
paraelectricity.
I. Introduction
transition).4,5 In addition to the mentioned organic systems, some
inorganic zero-dimensional hydrogen-bonded systems, for ex-
Proton tunneling in the double-well potential of gas-phase
malonaldehyde and its analogues has been investigated theoreti-
cally1 and experimentally.2,3 We have found that quantum-
mechanical tunneling also occurs in the intramolecular hydrogen-
bonded crystal of 5-bromo-9-hydroxyphenalenone (BHP),4,5
which exhibits a symmetrical double-well type proton potential
with a low barrier. In our study of the BHP crystal, we evaluated
the degree of tunneling by heat capacity measurements6 and
far-infrared spectroscopy.7 Squaric acid forms an organic two-
dimensional hydrogen-bonded system in the crystalline state.8
Crystalline squaric acid shows an (anti)ferroelectric-paraelectric
phase transition at about 375 K, associated with the order-
disorder transition of the proton sites.9 In the two-dimensional
hydrogen-bonded crystal of squaric acid, protons are considered
to have a heavy effective mass, since they must migrate in
accord with the relocation of the adjacent protons in the
hydrogen-bonded network and also with the change of the
π-conjugated structure of the squaryl groups. Under high
pressure, however, the transition temperature is lowered in
accord with the shortening of the hydrogen-bond length. Above
3 GPa, the transition is entirely suppressed, and a pronounced
dielectric response is observed even at cryogenic temperatures.
This phenomenon is interpreted in terms of quantum paraelec-
tricity, derived from the quantum motion of a proton along the
hydrogen bond.10 In our study, the BHP crystal, a zero-
dimensional hydrogen-bonded system, also shows quantum
paraelectricity under ambient pressure, and its deuterated crystal
shows an (anti)ferroelectric transition (deuteron-induced phase
ample, K3H(SO4)2,11,12 exhibit similar quantum dielectric be-
havior in the solid state.
Under such a circumstance, it would be intriguing to observe
a quantum dielectric phenomenon in an organic one-dimensional
hydrogen-bonded crystalline system under ambient pressure.
Thus, we prepared a one-dimensional hydrogen-bonded crystal
of phenylsquaric acid, in which one of the hydroxy groups of
squaric acid is replaced with a phenyl group. Crystalline
phenylsquaric acid (PSQ), however, does not exhibit any proton
dynamics along the hydrogen-bonded chain. This is partially
due to the relatively long distance (O‚ ‚ ‚O, 2.618(2) Å) and
the low symmetry of the hydrogen bond in the crystal.
Taking the above cases into consideration, two strategies
emerge for observing proton tunneling along a hydrogen-bonded
chain: first, formation of strong hydrogen bonds of high
symmetries between hydrogen-bonding building blocks and,
second, weakening of the intramolecular electronic correlation
between a proton-donating site and a proton-accepting site
* Corresponding author. Fax: +81-3-5454-6997. E-mail: suga@
pentacle.c.u-tokyo.ac.jp.
† Present address: Department of Materials and Biological Sciences,
Faculty of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-
8512, Japan.
10.1021/jp030961a CCC: $27.50 © 2004 American Chemical Society
Published on Web 04/14/2004

5528 J. Phys. Chem. B, Vol. 108, No. 18, 2004
Takasu et al.
TABLE 1: Crystallographic Parameters for PSQ and PBSQ
within a tautomeric molecule. p-Phenylenebis(squaric acid)
(PBSQ) was prepared as a model compound for observing the
proton dynamics along a one-dimensional intermolecular hy-
drogen-bonded chain for the following reasons: (1) The
molecular symmetry of PBSQ is reasonably high (C2h), provided
that the molecular structure is planar. (2) The squaric acid
moieties are nearly independent electronically because they are
separated by a p-phenylene unit; protonation or deprotonation
at one of the squaric moieties does not significantly affect the
acidity of the other. Here we report the proton dynamics of
crystalline hydrated PBSQ.
PSQ
C10H6O3
174.15
PBSQ
C14H10O8
306.23
empirical formula
formula weight
crystal dimensions/mm 0.50 × 0.22 × 0.10 0.60 × 0.50 × 0.08
crystal system
space group
a/Å
triclinic
P1h (No. 2)
7.177(2)
9.343(2)
6.494(2)
101.67(2)
102.47(3)
105.71(2)
393.2(2)
2
triclinic
P1h (No. 2)
8.113(1)
8.119(2)
5.3235(7)
96.55(1)
96.02(1)
112.90(1)
316.6(1)
1
b/Å
c/Å
R/deg
â/deg
γ/deg
V/Å3
II. Experimental Section
Z
D
calc/(g cm-3
)
1.471
1.606
A. Preparation of Squaric Acid Derivatives. Phenylsquaric
acid (PSQ) was synthesized by the coupling of iodobenzene
and 3-(tri-n-butylstannyl)-4-isopropoxy-3-cyclobutene-1,2-di-
one,13 followed by deprotection with hydrochloric acid (yield
92%). Single crystals were obtained by slow evaporation from
aqueous solution at room temperature. The crystal was a
colorless prism (the largest crystal was ∼0.5 × 0.2 × 0.1 mm3).
p-Phenylenebis(squaric acid) (PBSQ) was synthesized by the
coupling of diiodobenzene and 3-(tri-n-butylstannyl)-4-isopro-
poxy-3-cyclobutene-1,2-dione, followed by deprotection with
hydrochloric acid (yield 89%). Single crystals were obtained
by slow evaporation from a 5% aqueous solution of trifluo-
romethanesulfonic acid at room temperature. The crystal was a
yellow plate (the largest crystal was ∼2.0 × 0.8 × 0.08 mm3).
The ∼100% deuterated PBSQ crystal was prepared by recrys-
tallization from 99.8% deuterium oxide at room temperature in
the first run, followed by recrystallization from a 5% solution
of trifluoromethanesulfonic acid-d (98%) in deuterium oxide
(99.8%) at room temperature in the second run. The ∼50%
deuterated PBSQ crystal was prepared by recrystallization from
50% deuterated water in the first run, followed by recrystalli-
zation from a 5% aqueous solution of trifluoromethanesulfonic
acid at room temperature in the second run. The deuterium
contents of the crystals were estimated to be the same as the
deuterium contents of the solutions used for the recrystalliza-
tions.
B. X-ray Structure Analyses. The X-ray structure analyses
were performed with Rigaku AFC-5 and Rigaku AFC-7R
diffractometers for PSQ and PBSQ, respectively, using Mo KR
radiation. The data were collected at 298 K using the ω-2θ
scan technique to a maximum 2θ value of 55.0°. Crystal data
and data collection parameters for PSQ and PBSQ are listed in
Table 1. Selected bond lengths and angles are listed in Table 2.
All calculations were performed with the teXsan crystallographic
software package (Molecular Structure Corp.). Calculations were
carried out on a Silicon Graphics INDY system.
Crystallographic data (excluding structure factors) for the
structures in this paper have been deposited with the Cambridge
Crystallographic Data Centre as supplementary publication nos.
CCDC 189458 (PSQ) and 207519 (PBSQ). Copies of the data
can be obtained, free of charge, upon application to CCDC, 12
Union Road, Cambridge CB2 1EZ, U.K. (fax, +44 1223
336033; e-mail, deposit@ccdc.cam.ac.uk).
µ/cm-1
1.10
2793
1.35
measured reflections
1552
independent reflections 1391
1249
(I > 3σ)
a
R1
0.0426
0.0412
1.8
0.038
0.138
1.1
b
Rw
GOF
a R1 ) ||Fo| - |Fc||/|Fo|. b Rw ) [w(Fo - Fc2)2/w(Fo )2]1/2
.
2
2
TABLE 2: Selected Bond Distances (in Angstroms) and
Bond Angles (in Degrees) for PSQ and PBSQ
PSQ
O(1)-C(1)
1.218(2)
1.201(2)
1.302(2)
1.531(2)
0.95(2)
85.3(1)
88.9(1)
94.2(1)
91.5(1)
C(1)-C(4)
C(2)-C(3)
C(3)-C(4)
C(4)-C(5)
1.469(2)
1.485(2)
1.383(2)
1.455(2)
O(2)-C(2)
O(3)-C(3)
C(1)-C(2)
O(3)-H(O(3))
C(1)-C(2)-C(3)
C(2)-C(1)-C(4)
C(2)-C(3)-C(4)
C(1)-C(4)-C(3)
O(2)-C(2)-C(1)
O(3)-C(3)-C(2)
C(1)-C(4)-C(5)
137.7(2)
135.3(2)
136.3(1)
PBSQ
O(1)-C(1)
1.229(2)
1.209(2)
1.263(2)
1.515(2)
1.239(1)
86.7(1)
92.8(1)
91.1(1)
89.4(1)
C(1)-C(4)
C(2)-C(3)
C(3)-C(4)
C(4)-C(5)
1.444(2)
1.501(2)
1.414(2)
1.448(2)
O(2)-C(2)
O(3)-C(3)
C(1)-C(2)
O(1)-H(O(1))
C(1)-C(2)-C(3)
C(1)-C(4)-C(3)
C(2)-C(3)-C(4)
C(2)-C(1)-C(4)
O(1)-C(1)-C(4)
O(2)-C(2)-C(3)
O(3)-C(3)-C(4)
C(3)-C(4)-C(5)
136.9(2)
137.2(2)
134.1(2)
133.9(2)
D. Measurement of ac Dielectric Permittivity. The tem-
perature dependence of the dielectric permittivity was measured
with a Hewlett-Packard 4274A LCR meter in the frequency
range 1 × 103 to 100 × 103 Hz for alternating electric fields of
∼10 V/cm. Both sides of the sample (a very thin plate-shaped
crystal of PBSQ (thickness ∼0.08 mm)) were painted with
conductive gold paste to allow electrical measurement. The
temperature of the sample was measured with a Au/Fe chromel
thermocouple. The anisotropy of the permittivity was not
measured, owing to the thinness of the crystal.
III. Results and Discussion
A. Characteristics of the Hydrogen-Bonded Crystal of
Phenylsquaric Acid (PSQ). In the PSQ crystal, the PSQ
molecules form a chain structure along the c-axis through
intermolecular hydrogen bonding between a hydroxy group and
a carbonyl group of the adjacent molecule (Figure 1 and Tables
1 and 2). The hydrogen-bond O‚ ‚ ‚O distance in the PSQ crystal
is 2.618(2) Å (the bond lengh of O-H, 0.95 Å; the bond angle
of O-H‚ ‚ ‚O, 163(1)°), which is longer than that in the squaric
acid crystal (2.55 Å). The phenyl group of PSQ is twisted 6.8-
(4)° from the plane of the squaric acid moiety. The two planar
groups in the unit cell are stacked alternately in a head-to-tail
C. Solid-State 13C NMR (CP/MAS) Spectra. High-resolu-
tion solid-state 13C NMR (CP/MAS) spectra were recorded on
a Chemagnetics CMX300-NMR spectrometer at 75.6 MHz with
a spinning rate of 4700 Hz. The data acquisition conditions were
as follows: spectral width, 40 kHz; proton 90° pulse, 5 ms;
cross polarization time, 5 ms; spectral width, 40 kHz; recycle
delay, 10 s; number of acquisitions, 1000. Chemical shifts were
externally referenced to the methyl carbons of hexamethylben-
zene (δ ) 17.35 ppm).

Quantum Paraelectricity in a PBSQ Crystal
J. Phys. Chem. B, Vol. 108, No. 18, 2004 5529
Figure 1. ORTEP-3 [27] diagram of the crystal structure of PSQ
molecules forming one-dimensional hydrogen-bonded chains. The
molecules are stacked along the a-axis. Thermal ellipsoids are drawn
at 30% probability. The hydrogen bonds are shown by the dashed lines.
Figure 3. ORTEP-3 [27] diagram of the sheet structure of the PBSQ
crystal. Thermal ellipsoids are drawn at 30% probability. The hydrogen
bonds between the PBSQ molecules are shown by the dashed lines.
The major factor for the proton dynamics is the height of the
potential barrier in the hydrogen bond. The potential barrier
becomes low when the hydrogen-bond length is short and the
intermolecular electrostatic or electronic interaction between the
surrounding molecules is small. Furthermore, a symmetric
hydrogen bond may induce the tunneling effect of the protons.
In the PSQ crystal, however, the hydrogen-bond length is longer
and the shape of the hydrogen bond is less symmetric compared
with the case of the squaric acid crystal. These results are
consistent with the fact that the hydrogen-bonded chain of the
PSQ crystal does not exhibit a dynamic property.
Figure 2. Definition of (a) the configuration of the hydrogen-bonding
pattern of the squaric acid moiety, (b) the configuration of the hydrogen-
bonding pattern of the PSQ crystal, and (c) the configuration of the
hydrogen-bonding pattern of the PSQ crystal after hypothetical proton
transfer.
B. Crystal Structure of Hydrated p-Phenylenebis(squaric
acid) (PBSQ). Crystallization of PBSQ from a 5% aqueous
solution of trifluoromethanesulfonic acid afforded one-dimen-
sional hydrogen-bonded PBSQ crystals composed of PBSQ-
manner along the a-axis. The C-O bond lengths corresponding
to the enol and carbonyl groups are 1.302(2) and 1.218(2) Å,
respectively. The C(1)-C(4) and -C(4)-C(3) bond lengths are
1.469(2) Å and 1.383 Å, respectively. The O-H bond length
of PSQ is 0.95(2) Å. In general, the bond alternation in the
π-conjugated system and the O-H bond length are closely
correlated to the degree of localization of a proton in a hydrogen
bond. On the other hand, in the X-ray analysis of the paraelectric
phase of the squaric acid, the bond alternation in the π-conju-
gated system is diminished and the molecular skeleton shows
+
(monoanionic PBSQ) and H5O2+. The PBSQ-‚H5O2 crystal
is characterized by a layered structure (space group P1h) (Figure
3 and Tables 1 and 2). In the unit cell of PBSQ-‚H5O2+, one
PBSQ molecule and two water molecules are incorporated and
each PBSQ molecule has only one hydrogen atom per two
hydroxy groups, indicating that PBSQ exists as a monoanion.
On the other hand, the water molecules in the crystal exist as
protonated water dimers (H5O2+), where the two water mol-
ecules are strongly linked by an excess bridging proton
(H2O‚ ‚ ‚H+‚ ‚ ‚OH2).
D
4h symmetry.8 These results indicate that, in the PSQ crystal,
Such deprotonation of acids and generation of oxonium ions
(such as H3O+ and H5O2+) in crystals has been reported for
the hydrated crystals of strong acids.16,17 Squaric acid is known
as a strong oxoacid (pKa1 ) 0.54 and pKa2 ) 3.48), and strong
acidity of PSQ is also reported (pKa ) -0.22).18 Therefore,
the protons in the hydrogen bonds are localized.
The high-resolution solid-state 13C NMR (CP/MAS) spectrum
of PSQ recorded at room temperature was consistent with the
foregoing results. The enol and carbonyl carbons, especially,
resonated at different positions (190 and 197 ppm, respectively),
and the line shape did not change even when the temperature
was increased to 373 K. The experimental data confirmed the
the PBSQ molecule is estimated to have strong acidity (pKa1
<
1) and the hydroxy group is deprotonated to form an oxonium
ion in a hydrated crystal. In the case of squaric acid, various
crystal structures of monohydrogen squarates have been re-
ported.19,20
Since PBSQ- is located at the center of the inversion
symmetry, a symmetrical, one-dimensional, ionic hydrogen-
bonded chain consisting of PBSQ- is constructed on the layer
(Figure 4a). Ionic hydrogen bonds such as O-‚ ‚ ‚H-O and
O‚ ‚ ‚H-O+ are known to be very strong with a short hydrogen-
bond length,17 owing to the strong electrostatic interaction. The
hydrogen-bond O‚ ‚ ‚O distance in the one-dimensional chain
composed of PBSQ- is 2.478(1) Å (the bond lengths of C-O
and O-H are 1.263(2) and 1.239(1) Å, respectively), even
absence of a rapid exchange process (faster than 2 × 103 s-1
)
between intermolecular proton sites. Because proton transfer
along the intermolecular hydrogen-bonded network of the PSQ
crystal is strongly coupled with the π-bond switching in the
squaryl group, the protons in the one-dimensional hydrogen-
bonded chain in the PSQ crystal have a heavy effective mass.
It should be noted that the hydrogen-bonding pattern of the PSQ
crystal is of the syn-anti type14,15 (Figure 2b). If the correlated
proton transfer occurs along the hydrogen bond, the hydrogen-
bonding pattern changes to the anti-syn type (Figure 2c).
Therefore, the hydrogen-bond structure of the PSQ crystal is
asymmetric.

5530 J. Phys. Chem. B, Vol. 108, No. 18, 2004
Takasu et al.
Figure 5. Deuteration effect on the temperature dependence of the
permittivities (10 kHz) of the PBSQ crystal: (a) nondeuterated crystal;
(b) ∼50% deuterated crystal; (c) ∼100% deuterated crystal; (d) Curie-
Weiss behavior of the ∼100% deuterated crystal.
has been investigated both theoretically and experimentally as
the simplest model for proton transfer in water.21-24 Accord-
ingly, the protons in the PBSQ crystal are expected to be
dynamically disordered with respect to the location of the proton
in the symmetric, strong hydrogen bond.
C. Temperature Dependence of the Dielectric Permittivi-
ties of PBSQ‚2H2O and the Deuterated Crystals. The
temperature dependence of the ac dielectric permittivity of the
hydrated PBSQ crystal was measured on an LCR meter over
the temperature range 4-300 K (Figure 5a). The permittivity
of the hydrated PBSQ crystal remained almost constant (ꢀ′ ∼
9) over the temperature range 4-300 K, with no frequency
dependence (1-100 kHz). Because the crystals are very thin
plates (thickness ∼0.08 mm), the alternating electric field was
applied only along the [110] direction. Thus, the anisotropy of
the permittivity could not be measured.
The effect of deuteration on the temperature dependence of
the ac permittivity was examined. The permittivity of the
∼100% deuterated sample increased with decreasing temper-
ature, obeying the Curie-Weiss law over 60 K (Figure 5c,d).
At temperatures lower than 28 K, the permittivity decreased
slightly (Figure 5c). The Curie-Weiss behavior and the decrease
in the permittivity are characteristic of the (anti)ferroelectric
phase transition. The results can be rationalized by the fact that
the deuterons in the strong hydrogen bonds are ordered at 28 K
by the antiferroelectric interaction between the hydrogen-bonded
sites. Such a deuteron-induced (anti)ferroelectric transition has
been reported in zero-dimensional hydrogen-bonded crystals,
such as BHP4,5 and K3H(SO4)2.11,12 It should be noted that, for
detecting a structural phase transition more precisely, further
experiments such as heat capacitance measurements, X-ray
analyses, and vibration spectra (IR and Raman) analyses in the
low-temperature region are desirable. Incidentally, the magnitude
of the decrease in the permittivity of the deuterated PBSQ crystal
at temperatures below 28 K is less than that expected for a
typical (anti)ferroelectric phase transition. This may be due to
the residual quantum fluctuation of deuterons in the (anti)-
ferroelectric phase. A similar temperature dependence of the
permittivity is found in the dielectric phase transitions of the
squaric acid crystal under high pressure12 and the partially
deuterated BHP crystal.5
Figure 4. (a) Schematic structure of the one-dimensional hydrogen-
bonded chain in the PBSQ crystal. The configuration of the hydrogen-
bonding pattern of the PBSQ crystal is indicated. (b) Schematic structure
of H5O2 in the PBSQ crystal. The hydrogen bond within H5O2 is
directed perpendicular to the sheet. The hydrogen bonds between
PBSQ- and H5O2+ are shown by the dashed lines. (c) Hydrogen bonds
between the water molecules and the PBSQ molecules. The O‚ ‚ ‚O
distances are indicated.
+
+
shorter than that in the squaric acid crystal (O‚ ‚ ‚O, 2.55 Å).
As for the counter ion, the axis of the hydrogen bond connecting
+
the two water molecules in H5O2 is located perpendicular to
the layer (Figure 4b), and the bridging proton is situated between
the layers, although the proton is not shown in Figure 4b. The
+
O‚ ‚ ‚O distance in H5O2 is only 2.443(2) Å (the O-H bond
length is 1.222(1) Å). The hydrogen atoms of two water
+
molecules in H5O2 form hydrogen bonds also with two
carbonyl groups of the PBSQ molecules (O‚ ‚ ‚O, 2.633(2) and
2.761(2) Å) on layers above and below, connecting them to
the PBSQ- chains within the layer, respectively (Figure 4c).
As described in the preceding paragraph, there are two strong
hydrogen bonds: one is formed between PBSQ- ions, and the
other is within H5O2+. In the crystal, half of the PBSQ molecule
is crystallographically independent, and the symmetrical center
is at the center of the phenylene ring. Moreover, symmetrical
centers are located at the middle of the hydrogen bond between
the squaric acid moieties and at the middle of the hydrogen
bond between the water molecules (H5O2+). The hydrogen
atoms in the hydrogen bonds above-mentioned are refined as a
single hydrogen located at the center of the hydrogen bond,
because both of them were not able to separate by the difference
Fourier syntheses. Therefore, whether or not the hydrogen is in
a double-well potential or in a single-well potential cannot be
judged from the X-ray analyses. These results, however, indicate
that the hydrogen-bond potential in this crystal is symmetrical
and the barrier to proton transfer should be relatively low.
The appearance of the deuteron-induced (anti)ferroelectric
phase transition suggests that the deuteron transfer takes place
+
Incidentally, the quantum effect on the proton transfer in H5O2

Quantum Paraelectricity in a PBSQ Crystal
J. Phys. Chem. B, Vol. 108, No. 18, 2004 5531
PBSQ crystal began to gradually decrease at ∼320 K, followed
by an abrupt decrease at 370 K, accompanied by an endothermic
peak in the DTA chart. The decrease in mass corresponded to
the mass of two water molecules. We measured the permittivity
of PBSQ‚2H2O above 300 K (Figure 6) and found that the
permittivity increased abruptly at 380 K, accompanied by an
increase in ꢀ′′, and then dropped sharply (ꢀ′ ∼ 6). The dielectric
behavior at ∼390 K originated from the dehydration process.
During the cooling process, the permittivity remained constant
and did not recover to its original value. This result demonstrates
that the dehydrated neutral PBSQ solid cannot exhibit a
dielectric response, and it is further evidence that the observed
response is not derived merely from an electronic polarization
term but also involves an intrinsic contribution from the ionic
hydrogen bonds and the protonated water dimer to the dielectric
permittivity.
Figure 6. Temperature dependence of the ac permittivities (10 kHz)
of the PBSQ crystal. The process of temperature control is shown by
arrows.
IV. Summary
A squaric acid derivative, PBSQ, was designed to promote
proton mobility in the crystal. The PBSQ‚2H2O crystal,
composed of strong ionic hydrogen bonds, exhibited a nearly
temperature-independent permittivity. This result contrasts with
the dielectric property of the deuterated crystal, in which a
deuteron-induced (anti)ferroelectric phase transition was ob-
served. The nearly temperature-independent dielectric response
of the PBSQ‚2H2O crystal is the first example of quantum
paraelectricity originating from the intermolecular proton transfer
in a one-dimensional hydrogen-bonded system.
along the double-well potential. On the other hand, the tem-
perature-independent dielectric behavior of the hydrated PBSQ
crystal indicates that the rate of the intermolecular proton transfer
is nearly constant over the temperature range 4-300 K. The
proton transfer, which is not affected by thermal energy, may
be due to a tunneling effect in the double-well proton potential.
Temperature-independent permittivity has been observed in
inorganic dielectrics (e.g., KTiO3 and SrTiO3) at low temper-
atures25,26 and in the organic, zero-dimensional hydrogen-bonded
crystal BHP.5 Such dielectric behavior may be interpreted in
terms of quantum paraelectricity, which denotes that the (anti)-
ferroelectric ordering of invertible dipole moments is suppressed
by a certain quantum fluctuation,25 such as proton tunneling.12
The nearly temperature-independent dielectric behavior of the
hydrated PBSQ crystal may be regarded as the first example of
quantum paraelectricity originating from intermolecular proton
tunneling in a one-dimensional hydrogen-bonded system.
It is possible that, in the nondeuterated crystal, the proton
potential is of the single-well type, owing to the shortness of
the hydrogen bond. In that case, the proton in the hydrogen
bond should be broadly located in the single well, and the
permittivity would be generated by a shift in the distribution of
the protons in the hydrogen bonds. The permittivity of the ∼50%
deuterated sample increased slightly with decreasing temperature
in the high-temperature region, but in the low-temperature
region, the permittivity was almost constant and a phase
transition did not occur (Figure 6b). These results can be
rationalized as follows: in the high-temperature region, the
dielectric response of the deuterons increases with decreasing
thermal fluctuation of the deuterons, whereas, in the low-
temperature region, the (anti)ferroelectric interaction is sup-
pressed by the quantum fluctuations of the protons.
References and Notes
(1) de la Vega, J. R. Acc. Chem. Res. 1982, 15, 185.
(2) Bondybey, V. E.; Haddon, R. C.; English, J. H. J. Chem. Phys.
1984, 80, 5432.
(3) Tanaka, K.; Honjyo, H.; Tanaka, T.; Kohguchi, H.; Ohshima, Y.;
Endo, Y. J. Chem. Phys. 1999, 110, 1969.
(4) Mochida, T.; Izuoka, A.; Sugawara, T.; Moritomo, Y.; Tokura,
Y. J. Chem. Phys. 1994, 101, 7971.
(5) Moritomo, Y.; Tokura, Y.; Mochida, T.; Izuoka, A.; Sugawara,
T. J. Phys. Soc. Jpn. 1995, 64, 1892.
(6) Matsuo, T.; Kohno, K.; Inaba, A.; Mochida, T.; Izuoka, A.;
Sugawara, T. J. Chem. Phys. 1998, 108, 9809.
(7) Matsuo, T.; Kohno, K.; Ohama, M.; Mochida, T.; Izuoka, A.;
Sugawara, T. Europhys. Lett. 1999, 47, 36.
(8) Semmingsen, D.; Hollander, F. J.; Koetzle, T. F. J. Chem. Phys.
1977, 66, 4405.
(9) Feder, J. Ferroelectrics 1976, 12, 71.
(10) Moritomo, Y.; Tokura, Y.; Takahashi, H.; Mojri, N. Phys. ReV.
Lett. 1991, 67, 2041.
(11) Geshi, K. J. Phys. Soc. Jpn. 1980, 48, 886.
(12) Moritomo, Y.; Tokura, Y.; Nagaosa, N.; Suzuki, T.; Kumagai, K.
Phys. ReV. Lett. 1993, 25, 2833.
(13) Liebeskind, L. S.; Fengel, R. W. J. Org. Chem. 1990, 55, 5359.
(14) Etter, M. C.; Urbanczyk-Lipkowska, Z.; Jahn, D. A.; Frye, J. S. J.
Am. Chem. Soc. 1986, 108, 5871.
(15) Bertolasi, V.; Gilli, P.; Ferretti, V.; Gilli, G. Chem.sEur. J. 1996,
2, 925.
(16) Jeffery, G. A. An Introduction to Hydrogen Bonding; Oxford
University Press: New York, 1997.
(17) Kuz’menko, I. V.; Zhilyaev, A. N.; Formina, T. A.; Porai Koshits,
M. A.; Baranovskii, I. B. Russ. J. Inorg. Chem. (Engl. Transl.) 1989, 34,
1457 and references therein.
(18) Patton, E.; West, R. J. Am. Chem. Soc. 1973, 95, 8703.
(19) Gilli, G.; Bertolasi, V.; Gilli, P.; Ferretti, V. Acta Crystallogr. 2001,
B57, 859.
(20) Mathew, S.; Paul, G.; Shivasankar, K.; Choudhury, A.; Rao, C. N.
R. J. Mol. Struct. 2002, 641, 263.
(21) Cheng, H.-P.; Barnett, R. N.; Landman, U. Chem. Phys. Lett. 1995,
237, 161.
Estimation of the relative contribution of the dynamics of
+
H5O2 to the permittivity is difficult, owing to the lack of
anisotropic data on the permittivity. However, the proton
dynamics in hydrogen-bonded squaric acid moieties and in
H5O2+ may be weakly correlated. It is possible that the ordering
of the two kinds of protons occurs, being coupled with an (anti)-
ferroelectric phase transition, because of the breakdown of the
inversion symmetry.
The hydration waters (H5O2+) in the crystal are stable at room
temperature, but the water molecules could be removed by
heating to afford neutral PBSQ solids. To examine the thermal
dehydration processes, we carried out thermogravimetry and
differential thermal analysis (DTA) measurements on the
hydrated PBSQ crystal. We found that the mass of the hydrated
(22) Cheng, H.-P.; Krause, J. L. J. Chem. Phys. 1997, 107, 8461.
(23) Yeh, L. I.; Lee, Y. T.; Hougen, J. T. J. Mol. Spectrosc. 1994, 164,
473.
(24) Vuilleumier, R.; Borgis, D. J. Chem. Phys. 1999, 111, 4251.
(25) Mu¨ller, K. A.; Burkard, H. Phys. ReV. 1979, B19, 3593.
(26) Vogt, H.; Uwe, H. Phys. ReV. 1984, B29, 1030.
(27) Farrugia, L. J. J. Appl. Crystallogr. 1997, 30, 565.