Formation enthalpies and polymorphs of nicotinamide-r-mandelic acid co-crystals

Article abstract of DOI:10.1021/cg3005757

Co-crystals provide an opportunity to improve the properties of pharmaceuticals and other materials. We report a method for determining the formation enthalpies of co-crystals in which enthalpies of melting are measured for a co-crystal and the physical mixture of its component crystals. Because the two melting processes arrive at the same liquid, the difference of their enthalpy changes is the co-crystal's formation enthalpy. For the system of nicotinamide (NIC) and R-mandelic acid (RMA), the formation enthalpy at 30 °C is -23 (3) J/g for polymorph 1 and -18 (3) J/g for polymorph 2. These values are comparable with the enthalpy of mixing for NIC and RMA liquids [-49 (4) J/g at 160 °C], indicating the need for correcting for nonideal mixing in calculating formation enthalpies of co-crystals via thermodynamic cycles. This correction is made automatically in our method by performing measurements with physical mixtures of component crystals, as opposed to pure component crystals. One of the NIC-RMA polymorphs (2) was discovered in this work, and its structure and thermodynamic relation to polymorph 1 are reported.

Full text of DOI:10.1021/cg3005757

Article
pubs.acs.org/crystal
Formation Enthalpies and Polymorphs of Nicotinamide−R‑Mandelic
Acid Co-Crystals
Si-Wei Zhang,† Ilia A. Guzei,† Melgardt M. de Villiers,† Lian Yu,†,* and Joseph F. Krzyzaniak‡
†School of Pharmacy and Department of Chemistry, University of WisconsinMadison, Madison, Wisconsin 53705, United States
‡Pfizer Global Research & Development, Groton, Connecticut 06340, United States
S
* Supporting Information
ABSTRACT: Co-crystals provide an opportunity to improve the properties of pharmaceuticals and other materials. We report a
method for determining the formation enthalpies of co-crystals in which enthalpies of melting are measured for a co-crystal and
the physical mixture of its component crystals. Because the two melting processes arrive at the same liquid, the difference of their
enthalpy changes is the co-crystal’s formation enthalpy. For the system of nicotinamide (NIC) and R-mandelic acid (RMA), the
formation enthalpy at 30 °C is −23 (3) J/g for polymorph 1 and −18 (3) J/g for polymorph 2. These values are comparable with
the enthalpy of mixing for NIC and RMA liquids [−49 (4) J/g at 160 °C], indicating the need for correcting for nonideal mixing
in calculating formation enthalpies of co-crystals via thermodynamic cycles. This correction is made automatically in our method
by performing measurements with physical mixtures of component crystals, as opposed to pure component crystals. One of the
NIC-RMA polymorphs (2) was discovered in this work, and its structure and thermodynamic relation to polymorph 1 are
reported.
where CA, CB, and CAB are the crystal of component A, the
crystal of component B, and the co-crystal of A and B,
respectively. The enthalpy of formation ΔHf is the enthalpy (or
effectively energy at ambient pressure) of the co-crystal relative
to its component crystals; the free energy of formation ΔGf
measures the thermodynamic stability of the co-crystal relative
to the component crystals, with the entropy effect included.
ΔHf and ΔGf are valuable data for understanding co-
crystallization. For example, the formation properties for a
series of co-crystals in which components are systematically
varied help understand the molecular factors that influence the
stability of co-crystals. One aim of this study was to test a
general method for measuring formation enthalpies of co-
crystals.
INTRODUCTION
■
A co-crystal is a solid phase that contains multiple chemical
components.1 The existence of co-crystals has been known for
a long time, under the name “compound” for fixed
stoichiometry and “solid solution” for variable stoichiometry.
A racemic compound is a co-crystal of two opposite
enantiomers (resolvable chiral molecules).2 Interest in co-
crystals has increased in recent years, driven in part by their
applications in improving the properties of pharmaceutical
solids,3−8 including solubility,5 bioavailability,6 and mechanical
properties.8
Many studies have examined the discovery, structure, and
formation of co-crystals, while the work has been limited on the
thermodynamics of co-crystals. Little data exist, for example, on
the enthalpy and free energy of formation of co-crystals,9,10
which are fundamental measures of their stability. The
formation properties are defined in reference to the following
reaction:
A question concerning co-crystallization is whether multi-
component crystals are less likely polymorphic than single-
component crystals.11 Besides a fundamental interest in
Received: April 27, 2012
Revised: July 3, 2012
Published: July 6, 2012
CA + CB → CAB
(1)
© 2012 American Chemical Society
4090
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
answering this question, the fact that many co-crystals are
polymorphic12−16 requires that the study of co-crystals takes
into account the discovery and control of co-crystal
polymorphs.
can be imagined that complete eq 1; for example, paths that
involve evaporation or combustion. In practice, temperature-
scanning calorimeters can yield the enthalpies of melting
needed in eq 2, as we demonstrate in this work, and isothermal
calorimeters the enthalpies of solution in eq 3.
The co-crystallization of nicotinamide (NIC) and R-mandelic
acid (RMA) (Scheme 1) has been studied by Frisc
̌
i
̌
c
́
and
The key point of our proposed method is not the possibility
to measure the formation enthalpies of co-crystals in different
ways, but the advantage of performing measurements on the
physical mixture (CA + CB), as opposed to the pure component
crystals CA and CB, in achieving this goal, which we now
explain. If the enthalpy of mixing for components A and B in
the liquid state is negligible, ΔHm(A+B) and ΔHs(A+B) in eqs 2
and 3 are the sums of the corresponding enthalpies for the pure
component crystals (properly weighted to ensure mass
balance), yielding
Scheme 1. Structures of Nicotinamide (NIC) and R-
a
Mandelic Acid (RMA)
ΔHf = ΔHmA(T → T ) + ΔHmB(T → T ) − ΔHmAB(T → T )
(4)
S
L
S
L
S
L
a
θ1, θ2, and θ3 indicate angles of torsion.
ΔHf = ΔHsA(T ) + ΔHsB(T ) − ΔHsAB(T )
(5)
S
S
S
Jones.17 NIC (Vitamin B3) is a generally recognized as safe
(GRAS) substance useful as solubility enhancer18 and co-crystal
former.13,17,19−21 Besides RMA, NIC can co-crystallize with
many other carboxylic acids.17,19,20
We report here a new polymorph of the NIC-RMA co-
crystal, which is thermodynamically less stable than the known
structure.17 We also report the formation enthalpies for the two
polymorphs measured with a method implemented in this
work. For the NIC-RMA system, the enthalpy of mixing in the
liquid state is substantial and correction for this effect is needed
in calculating the co-crystals’ formation enthalpies via
thermodynamic cycles. Our method automatically makes this
correction, by making measurements with a physical mixture of
component crystals, as opposed to the pure component
crystals.
Here ΔHmA, ΔHmB, and ΔHmAB are the enthalpies of melting
of CA, CB, and CAB; ΔHsA, ΔHsB, and ΔHsAB are the
corresponding heats of solution. Thus, instead of measuring
the physical mixture (CA + CB), one can measure the pure
component crystals CA and CB separately and calculate ΔHf via
eqs 4 and 5. This method has been used to calculate the
formation enthalpies of racemic compounds (special co-crystals
in which A and B are the opposite enantiomers)2,22 and some
other co-crystals,10 but it is important to note the assumption
of ideal mixing that leads to eqs 4 and 5.
For racemic compounds, the assumption of ideal mixing has
been justified on the ground that except for different
handedness, opposite enantiomers are chemically identical (if
one is an acid, for example, so is the other), such that their
mixing in the liquid state is similar to “mixing” the same
molecules with ΔHmix ≈ 0.2 In contrast, ideal mixing is not
justified for two arbitrary components that co-crystallize. It is
common that acid-like and base-like components combine to
form co-crystals, for which the heat of component mixing is
likely significant, and found to be so for the system
carbamazepine-saccharin.9
To account for nonideal mixing, Oliveira et al. measured the
dissolution of component crystals not in a pure solvent but one
containing the second component9 such that the final solution
is the same as that formed by dissolving the co-crystal CAB.
Their procedure is thermodynamically equivalent to ours. In
their procedure, two measurements were performed to yield
the enthalpy of dissolving CA in a solvent that contains B,
ΔHsA(B), and the enthalpy of dissolving CB in the solvent that
contains A, ΔHsB(A), and the sum [ΔHsA(B) + ΔHsB(A)] was
calculated. It is evident that the latter sum is the same as
ΔHs(A+B) in eq 3, which in our proposal, would be measured in
a single dissolution experiment of the physical mixture (CA +
CB) in the pure solvent. Thus, as long as the physical mixture is
stable against conversion to the co-crystal before testing, our
method would require one fewer measurement.
DETERMINATION OF FORMATION ENTHALPIES
OF CO-CRYSTALS
■
In this section, we describe a method for determining the
formation enthalpies of co-crystals and compare it with other
procedures for this purpose. This method relies on the fact that
the co-crystal CAB and the physical mixture of component
crystals (CA + CB) (the two sides of eq 1) have the same liquid
upon melting or the same solution upon dissolution. Thus, the
formation enthalpy of CAB can be calculated from the relevant
enthalpies of melting or dissolution as follows:
ΔHf = ΔHm(A+B)(T → T ) − ΔHmAB(T → T )
(2)
(3)
S
L
S
L
ΔHf = ΔHs(A+B)(T ) − ΔHsAB(T )
S
S
In eq 2, TS is a temperature at which CAB and (CA + CB) are
solid and at which ΔHf is to be evaluated, TL is a temperature at
which CAB and (CA + CB) are both melted, and ΔHm(A+B)
(TS→TL) and ΔHmAB (TS→TL) are the corresponding changes
in enthalpy, with (TS→TL) signifying that ΔHm is measured
cumulatively from TS to TL. In eq 3, ΔHsAB (TS) and ΔHs(A+B)
(TS) are the enthalpies of solution for CAB and (CA + CB) in the
same solvent to the same concentration at TS.
The validity of eqs 2 and 3 is clear from the thermodynamic
principle that the enthalpy change of a given reaction can be
obtained by summing the enthalpy changes along different
paths that connect the initial to the final state. Equations 2 and
3 correspond to two different paths from (CA + CB) to CAB,
involving melting and dissolution, respectively. Still other paths
METHODS
■
R-Mandelic acids (RMA) and nicotinamide (NIC, the stable
polymorph23) were purchased from Sigma-Aldrich (St. Louis, MO,
USA) and used as received. Anhydrous acetonitrile (Fisher Scientific,
Pittsburgh, PA, USA) was of the HPLC grade.
Powder X-ray diffraction was performed with a Bruker D8 Advance
diffractometer (Cu Kα radiation, voltage 40 kV, and current 40 mA).
Approximately 5 mg of powder was sprinkled on the surface of a zero-
4091
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
background silicon (510) sample holder and scanned from 2° to 40°
2θ at a speed of 1.2°/min and a step size of 0.02°. Hot-stage
microscopy was performed with a Linkam THMS 600 hot-stage and
an Olympus BH2-UMA light microscope equipped with a digital
camera. Raman microscopy was performed with a Thermo Scientific
DXR Raman microscope and a 10 mW 532 nm laser and was used to
distinguish crystal polymorphs.
Differential scanning calorimetry (DSC) was conducted in Tzero
aluminum pans using a TA Instruments Q2000 unit under 50 mL/min
N2 purge. In a typical measurement, 5−10 mg of sample was heated at
20 °C/min to 160 °C to measure the temperature and heat of melting,
cooled at 20 °C/min, and heated again at 10 °C/min to record the
glass transition temperature of the melt.
̌ ̌ ́
Friscic and Jones prepared a co-crystal of NIC and RMA (hereafter
polymorph 1) by liquid-assisted grinding.17 In this study, polymorph 1
was also obtained by crystallizing a supercooled liquid of NIC and
RMA in 1:1 molar ratio. In this preparation, a liquid film (3 mg) was
formed between two coverslips by melting at 100 °C and cooling to 25
°C. The liquid crystallized spontaneously at 25 °C in 4 days, and the
product was found to be polymorph 1 by X-ray diffraction. Polymorph
1 was also obtained by solution crystallization with seeding. For this
purpose, a 2 mL acetonitrile (ACN) solution of NIC and RMA (both
at 1 M) was prepared at 60 °C, filtered through a 5 μm syringe filter,
and seeded at room temperature. The resulting crystals were filtered,
washed with ACN, and dried in vacuum.
Figure 1. XRD patterns of NIC-RMA co-crystals. Bottom: Polymorph
1 (CSD: JILZOU).17 Top: Polymorph 2 (this work). Middle:
Simulated pattern from the crystal structure of polymorph 2 (Table 1).
a
Table 1. Crystal Structures of NIC-RMA Co-Crystals
polymorph
1 (JILZOU)17
2
A second polymorph (polymorph 2) of the NIC-RMA co-crystal
was discovered by crystallizing an ACN solution of NIC and RMA at a
1:1 molar ratio. The solution was evaporated at 25 °C to form a thick
transparent liquid and evacuated to dryness. The resulting crystals
showed a different X-ray diffraction pattern from polymorph 1. Later,
higher-quality crystals of polymorph 2 were precipitated from solution
by seeding. For this purpose, the same procedure described above for
the seeded crystallization of polymorph 1 was employed, except with
seeds of polymorph 2.
To prepare a physical mixture of NIC and RMA crystals, each
material was passed through a sieve with 250 μm openings. The sieved
powders were mixed in 1:1 molar ratio with a vortex mixer (Vortex
Genie K-550-G Mixer) at the maximum speed for 1 min. The final
mixture was analyzed by X-ray diffraction to ensure that it contained
only component crystals and no co-crystals and used immediately for
subsequent DSC analysis.
T, K
150(2)
100(1)
wavelength, Å
0.71073
monoclinic
C2
1.54178
crystal system
monoclinic
P21
space group
description
crystal size, mm3
needle
plate
0.46 × 0.07 × 0.07
32.6557(9)
5.475(1)
14.9264(5)
99.400(1)
2632.9(5)
8
0.28 × 0.18 × 0.16
5.2406(3)
10.0477(6)
12.6006(7)
95.678(4)
660.24(7)
2
a, Å
b, Å
c, Å
β, deg
volume, Å3
Z
ρ, g cm−3
1.384
1.380
μ, mm−1
0.103
0.857
F(000)
1152
288
Single-crystal X-ray diffraction evaluation and data collection were
performed at 100 K on a Bruker SMART APEXII diffractometer with
Cu Kα (λ = 1.54178 Å) radiation, and the crystal structure was solved
using a standard procedure (see Supporting Information for details).
θ range, deg
3.77−27.43
5773/1/361
1.12
3.52−67.60
1235/1/183
1.011
data/restraints/parameters
S
R1
0.055
0.0430
wR2 for [I > 2σ(I)]
R1
0.128
0.1138
RESULTS AND DISCUSSION
0.070
0.0472
■
wR2 for all data
Δ, e Å−3, min, max
0.138
0.1174
Polymorphs of NIC-RMA Co-Crystals. Our crystallization
experiments reproduced the co-crystal of Frisc
̌
i
̌
c
́
and Jones17
−0.295, 0.293
−0.248, 0.306
a
and found a new polymorph. The XRD pattern of the new
polymorph differs from that of the known polymorph (Figure
1) and those of the component crystals (not shown). Single
crystals of the new polymorph were grown from a seeded ACN
solution and used for structural solution by X-ray diffraction
(Table 1). The XRD pattern simulated from the single-crystal
structure matches well with the powder XRD pattern of the
new polymorph (Figure 1). Hereafter we refer to the new
polymorph as “polymorph 2” and the previous polymorph
“polymorph 1”.
Table 1 compares the structures of the two polymorphs of
NIC-RMA co-crystals. Polymorph 1 is monoclinic (space group
C2) with two symmetry-independent RMA molecules and two
symmetry-independent NIC molecules.17 Polymorph 2 is
monoclinic (space group P21) with one each symmetry-
independent molecule of NIC and RMA. Polymorph 1 is
slightly denser than polymorph 2, even at a higher temperature.
Molecular formula: C14H14N2O4. Molecular weight: 274.27 g/mol.
To evaluate their structural difference, we calculated the
radial distribution functions (RDF) of molecular centers of
mass for both polymorphs (Figure 2). The RDF is one
descriptor of the local molecular environment in a crystal. The
RDF is to be calculated for each symmetry-independent
molecule and each chemical component in a co-crystal. Thus,
NIC-RMA polymorph 2 has three distinct RDFs (Figure 2):
NIC-NIC, which reports the distribution of NIC molecules
around an NIC molecule; RMA-RMA, the distribution of RMA
molecules around an RMA molecule; and NIC-RMA, the
distribution of RMA molecules around an NIC molecule (or
equivalently, NIC molecules around an RMA molecule). For
polymorph 1, there are more unique RDFs owing to its
symmetry-independent molecules. For simplicity, Figure 2
displays only the average RDFs for the NIC and RMA
4092
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
Table 2. Torsional Angles of NIC-RMA Co-Crystals
a
NIC
polymorph 1
polymorph 2
151.6
pure NIC
23.1
θ1, deg
−143.0 (mol 1)
−167.5 (mol 2)
polymorph 1
b
RMA
polymorph 2
pure RMA
θ2, deg
−103.3 (mol 1)
−129.5 (mol 2)
138.0 (mol 1)
135.1 (mol 2)
−106.0
−120.8 (mol 1)
−122.5 (mol 2)
149.2 (mol 1)
98.2 (mol 2)
θ3, deg
104.8
a
Retrieved from CSD (NICOAM02). θ1 is defined in Scheme 1.
Calculated from the crystal structure of S-mandelic acid (FEGHAA)
b
in CSD.24 θ2 and θ3 are defined in Scheme 1.
NIC crystal is close to the global minimum of the conforma-
tional energy curve relative to amide torsion, and those in the
NIC-RMA co-crystals are near a local minimum ca. 1 kcal/mol
higher in energy. Lemmerer et al. surveyed the changes of NIC
conformation as a result of co-crystallization with carboxylic
acids.19
Conformational differences are also seen in the RMA
molecule between the NIC-RMA polymorphs. Table 2 shows
the relevant torsional angles θ2 and θ3 that define the RMA
conformations (see Scheme 1). The change of torsional angle is
especially pronounced in θ3. Note, however, that similar
changes exist between the two symmetry-independent
molecules in the crystal of pure RMA. (We drew the last
conclusion from the structure of S-mandelic acid,24 for the CSD
has no entry for RMA.)
The two polymorphs have different networks of hydrogen
bonds (Figure 3). In polymorph 1, two NIC molecules form an
Figure 2. Radial distribution functions (RDF) of molecular centers of
mass in polymorphs 1 and 2 of NIC-RMA co-crystals.
molecules in polymorph 1; the individual RDFs are reasonably
similar for the symmetry-independent molecules of NIC and
RMA.
The RDF analysis shows that for every molecule in an NIC-
RMA co-crystal, the nearest molecular neighbor is approx-
imately 5 Å away. The spatial distributions of molecules in the
two polymorphs are significantly different. Within the first 10 Å,
the NIC−NIC and RMA−RMA distances are more clustered in
polymorph 2 than in polymorph 1.
Another way to assess the structural difference between these
polymorphs is to compare their morphologies predicted by the
BFDH model. This model predicts the anisotropic growth of
crystals on the basis of the spacing between lattice planes.
According to this model, the crystals of polymorph 1 grow
more elongated than those of polymorph 2. This predicted
difference is consistent with our limited observations that
polymorph 1 forms needle-like crystals and polymorph 2 plate-
like ones. By this comparison, the structure of polymorph 1 is
more anisotropic than that of polymorph 2.
We next consider the differences in molecular conformation
between the co-crystal polymorphs. For NIC, conformational
flexibility is associated mainly with the torsion of the amide
group relative to the pyridine ring (θ1 in Scheme 1). In both
polymorphs, the amide group is rotated out of the pyridine
plane (θ1 ≠ 0 or 180°) but in different directions (the signs of
θ1 are different; see Table 2). It is noteworthy that the NIC
conformations in NIC-RMA co-crystals differ from that in the
crystal of pure NIC, whose amide group is rotated nearly 180°
relative to the molecules in the NIC-RMA co-crystals.
According to Lemmerer et al.,19 the conformer in the pure
Figure 3. Hydrogen bonds in NIC-RMA co-crystal polymorph 1 (top)
and polymorph 2 (bottom).
amide−amide R22(8) “homo-dimer”, and RMA molecules are
hydrogen-bonded to the NIC dimer through the carboxylic acid
group of RMA and the pyridine N of NIC. In polymorph 2,
NIC and RMA molecules hydrogen-bond to form R22(9)
“hetero-dimers” through the amide group of NIC and the α-
hydroxyl carbonyl group of RMA. These “hetero-dimers” are
further joined by hydrogen bonds (carboxylic acid H···pyridine
4093
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
N and hydroxyl O···amide anti-H; Figure 3, bottom) to form
infinite ribbons along b.
Table 3. Thermal Properties of NIC-RMA Polymorphs
phase
Tm, °C
ΔHm, J/g
ΔHf, J/g
Tg, °C
The hydrogen-bonded R22(9) “hetero-dimer” in polymorph 2
(Figure 3, bottom) is noteworthy in reference to the known
structures of the co-crystals containing NIC and carboxylic
acids. Of the 12 co-crystals formed by NIC and a
monocarboxylic acid in the CSD, 9 have the NIC-NIC R22(8)
“homo-dimer” (including polymorph 117), two have the R22(8)
“hetero-dimer” formed between the NIC amide group and the
carboxylic acid group, and one does not have any dimer
motif.19 To our knowledge, the R22(9) “hetero-dimer” in NIC-
RMA polymorph 2 is not present in other co-crystals
containing mandelic acid and an amide; for example, iso-
nicotinamide,25 piracetam,26 (1R,3S)-camphoramic acid,27 and
NIC-RMA polymorph 1.
a
polymorph 1
polymorph 2
CA (NIC)
CB (RMA)
CA + CB
89.1 (0.2)
85.2 (0.2)
140.8 (0.4)
128.4 (1.9)
197.0 (0.6)
176.9 (0.6)
−23 (3)
−18 (3)
0
0
0
−3.1 (0.1)
−4.2 (0.2)
128.3 (0.1)
131.7 (0.1)
b
b
−2.7 (0.1)
a
b
Reference 17 reports 89 °C. Tg could not be measured due to
crystallization.
data are uncorrupted by thermal decomposition. The Tg values
in Table 3 are the glass transition temperatures observed during
the second heating of the liquids produced by melting crystals.
The similar Tg values indicate similar chemical compositions of
the crystalline samples before melting.
Relative Stability of the Polymorphs of NIC-RMA Co-
Crystals. Figure 4a shows the typical DSC traces of the two
polymorphs of NIC-RMA co-crystals (CAB1 and CAB2). Table 3
summarizes the relevant data from DSC measurements.
Thermogravimetric analysis shows no significant weight loss
for either polymorph up to 140 °C, indicating that the melting
Polymorph 1 is higher melting and has higher enthalpy of
fusion than polymorph 2 (Table 3). The lower enthalpy of
polymorph 1 is consistent with its higher density, a correlation
observed for many polymorphic pairs.28 According to the heat
of fusion rule28 and thermodynamic calculations,29 the two
polymorphs are monotropic, with polymorph 1 being more
stable than polymorph 2 at any temperature. We tested this
conclusion via polymorphic conversions. In the first experi-
ment, a liquid of NIC and RMA at 1:1 molar ratio was formed
between two coverslips and seeded with polymorphs 1 and 2 at
opposite sides by contact with seed crystals. Both polymorphs
grew into the liquid over time at room temperature. Viewed
between crossed polarizers, crystals of polymorph 1 were gray
and those of polymorph 2 were brighter and more colorful. The
polymorphs were also distinguishable by X-ray diffraction and
Raman microscopy. Polymorph 2 grew faster than polymorph
1; in some samples, polymorph 2 could be observed to grow
along the interface between the melt and polymorph 1 (Figure
5a−c). This peculiar mode of crystal growth yielded samples
useful for determining the relative stability of polymorphs 1 and
2. It is significant that after polymorph 2 covered the growth
front of polymorph 1, the latter continued to grow in a different
fiber-like morphology (Figure 5d). The fibers were confirmed
to be polymorph 1 by Raman microscopy, and the surrounding
crystals polymorph 2. Although the faster-growing polymorph 2
consumed most of the liquid, the subsequent conversion
eventually transformed the sample to polymorph 1 in two
months at 23 °C. This conversion indicates that polymorph 1 is
more stable than polymorph 2.
In a second experiment to test the relative stability of
polymorphs 1 and 2, solvent-mediated conversion was
performed. Seeds of polymorph 1 (<1 mg) were added to a
suspension of polymorph 2 (40 mg) in 0.2 mL of ACN. At 23
°C, polymorph 2 converted to polymorph 1 over time. Thus,
observations of polymorphic conversion in both the solid state
and in liquid suspension indicate that polymorph 1 is more
stable than polymorph 2 near the ambient temperature. This
finding and the higher melting point and higher heat of fusion
of polymorph 1 are consistent with the prediction that the two
polymorphs are monotropic.
Formation Enthalpies of NIC-RMA Co-Crystals. To
obtain the formation enthalpies of NIC-RMA co-crystals, we
measured the enthalpy changes for melting the co-crystals and
the physical mixture of the component crystals (eq 2). For this
purpose, the heat-flow data in Figure 4a were integrated from a
common liquid-state temperature (140 °C) down to a common
solid-state temperature (20 °C). The results are shown in
Figure 4. (a) DSC melting endotherms of the NIC-RMA co-crystals
(CAB1 and CAB2, for the two polymorphs) and a physical mixture of the
crystals of NIC and RMA at 1:1 molar ratio (CA + CB). A and B refer
to NIC and RMA, respectively. (b) Relative enthalpies of CAB1, CAB2
,
and (CA + CB) obtained by integrating the heat-flow data in (a) from
the common liquid state of the three materials (starting from 140 °C).
The enthalpy of a co-crystal relative to the physical mixture is its
formation enthalpy ΔHf.
4094
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
purpose of determining ΔHf, a constant shift of heat capacity
only rotates the set of curves in Figure 4b and does not change
the ΔHf values.
For our method to be valid, the physical mixture of
component crystals must not react to form co-crystals before
DSC analysis. Such stability was confirmed for all the physical
mixtures by XRD prior to DSC. The significantly different DSC
traces of the physical mixtures from those of the co-crystals
(Figure 4a) also indicate no substantial transformation to co-
crystals. Finally, consecutive measurements of the same physical
mixture showed no significant changes of melting enthalpies,
again suggesting the mixture was stable.
DSC measurements were performed to measure the enthalpy
of mixing the liquids of NIC and RMA, ΔHmix. We did so to
assess whether it is necessary to correct for nonideal mixing in
calculating formation enthalpies of co-crystals via thermody-
namic cycles and, in particular, whether measurements are
needed with the physical mixture of component crystals as
opposed to the pure component crystals. Figure 6a shows the
Figure 5. (a−c) Simultaneous growth and transformation of NIC-
RMA co-crystal polymorphs 1 (1) and 2 (2). The same scale bar
applies to (a−c). (d) Enlarged view of the box in (c).
Figure 4b. The enthalpies of the co-crystals relative to the
physical mixture are their formation enthalpies. NIC being
polymorphic,23 the physical mixture of NIC and RMA was
prepared to contain the stable NIC polymorph (CSD:
NICOAM02), in accord with the thermodynamic convention
for evaluating formation enthalpies. Both co-crystal polymorphs
have lower enthalpies than the physical mixture of component
crystals: ΔHf = −23 (3) J/g for polymorph 1 and −18 (3) J/g
for polymorph 2. These values are consistent with those
reported for several co-crystals that contain saccharin.9
Figure 4a shows that upon heating, the physical mixture (CA
+ CB) undergoes several thermal events en route to the liquid
state. These events could involve formation of co-crystals,
eutectic melting, and dissolution. It is noteworthy, however,
that the exact sequence of events is immaterial for our purpose
of determining the enthalpy of melting the physical mixture, so
long as the heat flow is integrated from the initial temperature
at which (CA + CB) is solid (TS) to the final temperature at
which the mixture is liquid (TL). This conclusion follows the
path independence in calculating enthalpy changes. While
calorimetric error can increase when integrating over a wide
temperature range, such concerns diminish with the improved
baseline stability and precision of modern DSCs and can be
assessed objectively from the reproducibility of data.
Figure 6. (a) DSC melting endotherms of NIC crystals (CA), RMA
crystals (CB), and their physical mixture at 1:1 molar ratio. (b) Relative
enthalpies of liquid NIC (LA), liquid RMA (LB), and their solution LAB
obtained by integrating the heat-flow data in (a) from 20 °C. The
enthalpy of mixing NIC and RMA liquids is the enthalpy of LAB
relative to the average enthalpy of the component liquids (LA and LB)
weighted according to the 1:1 molar ratio.
melting endotherms of the crystals of NIC, the crystals of
RMA, and their physical mixture at 1:1 molar ratio. Because
physically mixing NIC and RMA crystals is expected to have
negligible change in enthalpy, the enthalpy of mixing for NIC
and RMA liquids can be obtained by integrating the three
endotherms in Figure 6a from a common solid-state temper-
ature (20 °C) to a common liquid-state temperature (160 °C).
The slopes of the liquid and solid portions in Figure 4b are
the respective heat capacities reported by the DSC instrument
(TA Instruments Q2000) operating in the standard mode. The
instrument is capable of more accurate determination of heat
capacities, but we made no effort to do so because for the
4095
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
If ΔHmix = 0, the enthalpy of the NIC-RMA solution (LAB in
Figure 6b) would lie between those of the pure liquids (LA and
LB). In contrast, LAB is substantially below LA and LB. Our data
yield ΔHmix = −49 (4) J/g for mixing liquid NIC and RMA at
160 °C at 1:1 molar ratio.
The significant enthalpy of mixing for liquid NIC and RMA
makes it necessary to account for this effect in calculating their
co-crystals’ formation enthalpies via thermodynamic cycles. In
other words, eqs 2 and 3 are preferred over eqs 4 and 5, unless
the latter are modified as by Oliveira et al. to account for
nonideal mixing.9 Without correction for nonideal mixing, our
data in Figures 5 and 6 would lead to positive formation
enthalpies for the NIC-RMA co-crystals.
It is of interest to compare the enthalpy of formation for a
co-crystal ΔHf and the enthalpy of mixing for the liquid
components ΔHmix. ΔHf is the enthalpy change for the solid-
state reaction CA + CB = CAB (eq 1); ΔHmix is the enthalpy
change for the liquid-state reaction LA + LB = LAB. For the NIC-
RMA system, ΔHf and ΔHmix are both negative (reactions are
exothermic), indicating the mixed state has lower energy than
the separated state. For this system, ΔHf is approximately half
ΔHmix, although we note that the two values were measured at
different temperatures (30 and 160 °C). Work is in progress to
measure liquid heat capacities to obtain ΔHmix at the same
temperature at which ΔHf is measured. It might be instructive
to systematically compare ΔHf and ΔHmix for co-crystallizing
systems to learn the extent to which the stability of a co-crystal
is ascribable to favorable enthalpy of mixing in the liquid state.
To this end, the method described here may prove useful for
energies of co-crystals and to extract empirical structure−
energy relations.
In future studies, it would be of interest to apply the
calorimetry method to series of co-crystals in which the
components are systematically varied. By doing so, one can
probe the molecular factors that influence the formation and
stability of co-crystals. Also valuable would be a systematic
comparison of the enthalpies of co-crystal formation and the
enthalpies of liquid-state mixing, both quantities readily
obtained using our method, to learn whether the thermody-
namics of liquid mixing can help understand the stability of co-
crystals. Finally, it is desirable to determine the free energies of
formation of co-crystals, which requires that the entropy effect
be included: G = H − TS. Such efforts would extend to general
co-crystal systems the methods for measuring free-energy
differences between racemic compounds and conglomerates of
resolvable enantiomers.30,31 The free energies of formation
define the thermodynamic stability of co-crystals relative to
their component crystals and manufacturing conditions under
which co-crystals are favored. In advancing the science of co-
crystals, thermodynamic studies are a valuable complement to
structural and kinetic investigations.
ASSOCIATED CONTENT
■
S
* Supporting Information
The crystallographic data on NIC-RMA polymorph 2 are
included (PDF and CIF). This material is available free of
charge via the Internet at http://pubs.acs.org.
collecting data on both ΔHf and ΔHmix
.
AUTHOR INFORMATION
■
CONCLUSION
■
Corresponding Author
*E-mail: lyu@pharmacy.wisc.edu.
Co-crystals provide an opportunity to improve solid-state
properties for pharmaceuticals and other materials. We have
studied the co-crystallization of nicotinamide (NIC) and R-
mandelic acid (RMA), a member of the class of co-crystals
containing NIC and carboxylic acids. We report a new
polymorph of the NIC-RMA co-crystal and propose a
procedure for determining the formation enthalpies of co-
crystals. In this procedure, enthalpy changes are measured for
the melting (or dissolution) of a co-crystal and the physical
mixture of its component crystals. Because the two processes
arrive at the same liquid, the difference of their enthalpy
changes is the co-crystal’s formation enthalpy. For NIC-RMA
co-crystals, the error in calculated formation enthalpies is
substantial from neglecting nonideal mixing in the liquid state,
and the error is likely significant for other co-crystal systems
and must be taken into account in calculating their formation
enthalpies via thermodynamic cycles.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We thank Pfizer and the National Science Foundation (DMR
0804786) for supporting this work and Paul Meenan and
Brendan Murphy for helpful discussions.
REFERENCES
■
(1) Findlay, A.; Campbell, A. N.; Smith, N. O. Phase Rule and Its
Applications; Dover Publications: Mineola, NY, 1951.
(2) Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates, and
Resolutions; Krieger Publishing Company: Malabar, FL, 1991.
̈
(3) Almarsson, O.; Zaworotko, M. J. Chem. Commun. 2004, 1889−
1896.
In our calorimetric method, the enthalpy changes are
measured for the transformation of a co-crystal and a physical
mixture of component crystals to the same physical state. The
use of a physical mixture of component crystals, as opposed to
the pure component crystals, automatically corrects for
nonideal mixing in the liquid state in calculating the co-crystal’s
formation enthalpy. While we have implemented the method
with a temperature-scanning calorimeter to measure heats of
melting (eq 2), one can do so with an isothermal calorimeter to
acquire heats of solution (eq 3). Regardless of its
implementation, this method has the potential of providing
thermodynamic data for understanding the stability and
prediction of co-crystals. For example, the data can be used
to validate computer models for calculating the formation
(4) Vishweshwar, P.; McMahon, J. A.; Bis, J. A.; Zaworotko, M. J. J.
Pharm. Sci. 2006, 95, 499−516.
(5) Good, D. J.; Rodríguez-Hornedo, N. Cryst. Growth Des. 2009, 9,
2252−2264.
(6) McNamara, D. P.; Childs, S. L.; Giordano, J.; Iarriccio, A.;
Cassidy, J.; Shet, M. S.; Mannion, R.; O’Donnell, E.; Park, A. Pharm.
Res. 2006, 23, 1888−1897.
(7) Li, Z. B.; Yang, B. S.; Jiang, M.; Eriksson, M.; Spinelli, E.; Yee, N.;
Senanayake, C. Org. Process Res. Dev. 2009, 13, 1307−1314.
(8) Chattoraj, S.; Shi, L.; Sun, C. C. CrystEngComm 2010, 12, 2466−
2472.
(9) Oliveira, M. A.; Peterson, M. L.; Davey, R. J. Cryst. Growth Des.
2011, 11, 449−457.
(10) Chadha, R.; Saini, A.; Arora, P.; Jain, D. S.; Dasgupta, A.; Row,
T. N. G. CrystEngComm 2011, 13, 6271−6284.
4096
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097

Crystal Growth & Design
Article
(11) Vishweshwar, P.; McMahon, J. A.; Peterson, M. L.; Hickey, M.
B.; Shattocka, T. R.; Zaworotko, M. J. Chem. Commun. 2005, 4601−
4603.
(12) Ueto, T.; Takata, N.; Muroyama, N.; Nedu, A.; Sasaki, A.;
Tanida, S.; Terada, K. Cryst. Growth Des. 2011, 12, 485−494.
(13) Porter, W. W.; Elie, S. C.; Matzger, A. J. Cryst. Growth Des.
2008, 8, 14−16.
(14) Braga, D.; Palladino, G.; Polito, M.; Rubini, K.; Grepioni, F.;
Chierotti, M. R.; Gobetto, R. Chem.Eur. J. 2008, 14, 10149−10159.
(15) Gryl, M.; Krawczuk, A.; Stadnicka, K. Acta Crystallogr., Sect. B:
Struct. Sci. 2008, 64, 623−632.
(16) Aitipamula, S.; Chow, P. S.; Tan, R. B. H. CrystEngComm 2009,
11, 1823−1827.
̌ ̌ ́
(17) Friscic, T.; Jones, W. Faraday Discuss. 2007, 136, 167−178.
(18) Rasool, A. A.; Hussain, A. A.; Ditter, L. W. J. Pharm. Sci. 1991,
80, 387−393.
(19) Lemmerer, A.; Esterhuysen, C.; Bernstein, J. J. Pharm. Sci. 2010,
99, 4054−4071.
(20) Berry, D. J.; Seaton, C. C.; Clegg, W.; Harrington, R. W.; Coles,
S. J.; Horton, P. N.; Hursthouse, M. B.; Storey, R.; Jones, W.; Frisc
̌ ̌ ́
ic,
T.; Blagden, N. Cryst. Growth Des. 2008, 8, 1697−1712.
(21) Fleischman, S. G.; Kuduva, S. S.; McMahon, J. A.; Moulton, B.;
Walsh, R. D. B.; Rodriguez-Hornedo, N.; Zaworotko, M. J. Cryst.
Growth Des. 2003, 3, 909−919.
(22) Braun, D. E.; Ardid-Candel, M.; D’Oria, E.; Karamertzanis, P.
G.; Arlin, J.-B.; Florence, A. J.; Jones, A. G.; Price, S. L. Cryst. Growth
Des. 2011, 11, 5659−5669.
(23) Li, J.; Bourne, S. A.; Caira, M. R. Chem. Commun. 2011, 47,
1530−1532.
(24) Patil, A. O.; Pennington, W. T.; Paul, I. C.; Curtin, D. Y.;
Dykstra, C. E. J. Am. Chem. Soc. 1987, 109, 1529−1535.
(25) Aakeroy, C. B.; Beatty, A. M.; Helfrich, B. A. J. Am. Chem. Soc.
2002, 124, 14425−14432.
(26) Viertelhaus, M.; Hilfiker, R.; Blatter, F.; Neuburger, M. Cryst.
Growth Des. 2009, 9, 2220−2228.
(27) Hu, Z. Q.; Nie, J. J.; Xu, D. J.; Xu, Y. Z.; Chen, C. L. J. Chem.
Crystallogr. 2001, 31, 109−113.
(28) Burger, A.; Ramberger, R. Mikrochim. Acta 1979, 2, 259−271.
Burger, A.; Ramberger, R. Microchim. Acta 1979, 2, 273−316.
(29) Yu, L. J. Pharm. Sci. 1995, 84, 966−974.
(30) Reutzel-Edens, S. M.; Russell, V. A.; Yu, L. J. Chem. Soc., Perkin
Trans. 2 2000, 5, 913−924.
(31) Yu, L.; Huang, J.; Jones, K. J. J. Phys. Chem. B 2005, 109,
19915−19922.
4097
dx.doi.org/10.1021/cg3005757 | Cryst. Growth Des. 2012, 12, 4090−4097