TA 003; Reprinted from American Laboratory August 2004
A DSC Method to Determine
the Relative Stability of
Pharmaceutical Polymorphs
by R. Bruce Cassel and Robert Behme
When developing a substance as a candidate pharmaceutical product, tests are performed to identify and characterize possible polymorphic forms. Depending on how
the material was produced or treated, it may exist as several crystalline structures, which may have different solubilities, reactivities, and thermal behaviors. The information characterizing the polymorphic forms is required for
legal protection, processing, shelf life, and solubility considerations. Differential scanning calorimetry (DSC) can
be used not only to determine the melting point, which is
unique to a given crystalline state, but also to better characterize a polymorphic system.
Thermal behavior, as observed by DSC, can be quite complex, showing both endothermic and exothermic transitions on heating. This reflects the fact that a material in a
less stable form will convert with time to a more stable form
as it is heated. The relative stabilities of the forms also
change with temperature, and DSC can quantify the relative Gibbs free energy as a function of temperature for each
form. The change in Gibbs free energy (∆G) quantifies the
driving force for any process, and in terms of measured thermodynamic properties, can be calculated from changes in
enthalpy (∆H) and entropy (∆S), both of which can be calculated from DSC heat capacity (Cp) data.
∆G = ∆H–T∆S
(1)
The main contributor to the enthalpy and entropy
changes going from below each polymorph’s melting point
to a point above the melting point is crystalline melting.
By ignoring differences in the contribution to the relative
free energy from changes in heat capacity between transitions, an estimation can be made of the free energy from
the melting points and heats of fusion alone.1
A Q1000 DSC (TA Instruments, New Castle, DE),
(Figure 1) was used to obtain heat flow data on the
crystalline forms of drug A, a proprietary, candidate
pharmaceutical material. The calibration inherent in
the instrument’s Tzero technology provides internal
compensation for the effects of DSC cell asymmetry.2
The result is a straight instrumental baseline close to
Figure 1
Q1000 DSC with Tzero™ technology.
zero milliwatts, and a displacement from that baseline
that is due almost entirely to the specific heat of the
sample specimen itself. This allows accurate analysis of
the compound melting/crystallization melting peaks
commonly observed in polymorph melting analysis.
Also, the compensation for thermal lags within the
DSC/sample pan system results in sharp melting transitions and correction of melting temperatures for the
effects of thermal lag. This permits rapid heating rates
to be conveniently used without the usual problems of
correcting data after analysis. The DSC was calibrated
for temperature and energy using indium as the reference material. Because the data were to be analyzed at
100 °C/min, the temperature calibration was checked
at this rate. The results from a 1.6-mg sample showed a
peak width at half height of only 1°, a peak return to
baseline of less than 3 sec, and a thermal lag for the
indium onset of 0.2 °C, all at 100 °C/min.
PHARMACEUTICAL POLYMORPHS continued
The analyses of the
forms of drug A were
carried out using small
sample sizes (~1 mg)
and 100 °C/min heating rates to minimize
crystallization after
melting of metastable
polymorphic forms.
The melting characteristics were complex and
very thermal history
dependent. When run
in the DSC under standard conditions of 10
°C/min in the “as
received” form, the
heat flow trace appears
as in Figure 2.
Thermal treatment of drug A:
Ostwald’s Law of
Stages
Hess’s Law of
Heat Summation
Figure 2
DSC of drug A at 10 °C/min (endothermic down).
Generating the relative
free energy curves for
polymorphic forms
requires the melting
points and heats of
melting of each of
these forms. However,
when an unstable polymorph is heated, there
is often an overlap of
melting and crystallization such that much of
the melting energy is
not observed. However,
according to Hess’s Law
of Heat Summation,
the enthalpy difference
between two defined
states of a system is
independent of the
path taken between the
states. Therefore, once
the specimen has been
placed into a given
polymorphic form,
integrating the DSC
curve from a point
below the initial melting to a point above the
final melting event
quantifies the energy
that is the latent heat of
melting of the firstmelting polymorph,
regardless of any crystallization and melting
effects in between.
A key to successfully
characterizing the various polymorphs of drug
A requires that it be
obtained in each of its
available forms. While
this can be accomplished by dissolving the
drug and precipitating
metastable forms from
different solvent mixtures, DSC can be a conDSC of drug A at 100 ºC/min starting in each of its polymorphic
venient alternative. 3 . Figure 3
forms,
showing
Tm and ∆Hm calculations.
Per Ostwald’s Law of
Stages, a process (here
Results
crystallization from the melt) with multiple possible prodFigure 3 shows the results of running four samples of drug
ucts (here the different polymorphic forms) will yield the
A, each ushered into a different polymorphic form by
product closest in free energy.4 By starting with the least staannealing just below its melting point. The material was
ble form (e.g., the amorphous form, which is higher in free
received in form I, the lowest-melting form. The top
energy than the crystalline forms) and heating slowly, the
curve is the result of heating the specimen as received at
material will tend with time to crystallize into the lowest100 °C/min from –50 to +200 °C. Per Hess’s law, the
stability, highest-free-energy polymorph. When this polyintegration is carried out from just below the melt to
morph melts as it is heated in the DSC, it will tend to crysabove the final melt. The second curve is that of form III
tallize with time into the next least stable polymorphic
heated at 100 °C/min after initially being generated by
form, and so on. A slow DSC scan will often reveal all the
heating form I to 158 °C and annealing at that temperapolymorphic forms in succession. By stopping and annealture. The third curve is that of form II heated at 100
ing at a crystallization point, one can place the sample
°C/min after initially being generated by heating form I
specimen into the next higher-melting polymorphic state
to 150 °C with subsequent annealing at that temperafor analysis.
ture. The fourth curve is that of form IV
heated at 100 °C/min after initially being
generated by heating form I to 168 °C and
annealing at that temperature. Peak calculations were determined using either a
linear or sigmoidal-tangent peak baseline.
The criterion for baseline selection
should be that the peak pretransition and
posttransition baselines form a smooth
curve under the peak, reflecting the small
change in heat capacity attending melting or crystallization.
Calculations
Calorimetry data is useful to estimate the
relative physical stabilities of crystalline
polymorphs.1 At the melting point, the
change in free energy from solid to liquid is
zero; hence,
∆Hm
∆Sm = 
Tm
(2)
Figure 4
Eq. (4).
Relative stability plot in J/g (relative to form IV) generated in a spreadsheet from
From the Tm and ∆Hm data collected, ∆Sm can be calculated for each polymorph. Assuming that these
parameters are approximately independent of temperature, for each polymorph the relationship among ∆Gm,
∆Hm, and ∆Sm can be expressed as a function of temperature. Thus, for the melting of form I and form II:
∆GI>m = ∆HI>m –T∆SI>m
∆GII>m = ∆HII>m –T∆SII>m
(3)
Subtraction of these relationships allows expression of
the relative free energy of one polymorphic form to
another.5 Thus, for the transition from form I to form II:
∆∆GI>II = ∆∆HI>II –T∆∆SI>II
(4)
In this way, for drug A the free energy of three of the
polymorphic forms can be expressed in terms of the
fourth, and these data can be plotted in a spreadsheet
program to make a relative stability plot. For example,
Figure 4 displays these data for forms I, II, and III relative to form IV, the most stable polymorph.
polymorphs is unstable with respect to conversion to a
lower-energy form and Form IV is the most stable form
above 0°. Forms III and IV are enantiotropic, however,
their transition temperature is well below zero at about
–70 °C where their free energy curves intersect. The fact
that the other free energy curves do not cross one
another indicates the other polymorphic pairs of drug A
are monotropic with respect to each other. That is, there
are no reversible solid–solid transitions, which would
appear at temperature cross-over points.
References
1. Behme RJ. Differential scanning calorimetry to crystallize
metastable polymorphs to construct free-energy temperature diagrams. Proceedings of the NATAS Conference, 2003, Albuquerque, NM.
2. Danley RL. A new technology to improve DSC performance. Thermochim Acta 2003; 395:201–8.
3. Stowell GW, Behme RJ, Denton SM, et al. Thermally-prepared polymorphic forms of cilostazol. J Pharm Sci 2002; 91(12).
4. Ostwald W. Grudriss der Allgemeinen Chemie. Leipzig, Germany:
Whilhelm Engelman, 1899.
5. Yu. L. Inferring thermodyanmic stability relationship of polymorphs
from melting data. J Pharma Sci 1995; 84(8).
Discussion
The data in Figure 3 indicate the relative stability of the
four polymorphic forms. The upper temperature limit of
each curve is its melting point. A sample in form IV is
stable at all temperatures up to its melting point. The
order of the melting temperatures is the order of the polymorphs in increasing stability over the temperature range
of 0–200 °C. A sample in any of the higher-free-energy
Dr. Cassel is Marketing Specialist, TA Instruments, 109 Lukens Dr.,
New Castle, DE 19720, U.S.A..; tel.: 302-427-4000; fax: 302-4274001; e-mail: bcassel@tainst.com. Mr. Behme was Director, Science
Resources, Newburgh, IN, U.S.A., when this paper was written. He
currently is Senior Analytical Chemist, Eli Lilly & Company, Indianapolis, IN, U.S.A.