An evaporation study for phthalic acids - A rapid method for pharmaceutical characterization

Article abstract of DOI:10.1002/jps.10044

The objective of this study was to develop and analyze an analytical method in order to evaluate preformulation candidates by their thermodynamic parameters and evaporation characteristics. Ortho, meta and tere-phthalic acids were chosen as model compounds. The relative advantages and disadvantages of a rapid thermogravimetric method have been studied in detail, which would aid in the preformulation characterization for pharmaceuticals. Methyl paraben was taken as the model compound for calibration, as its evaporation characteristics are well known. Using the Antoine and the Langmuir equation for evaporation conjointly, the parameter k, known as the coefficient of evaporation was determined. The value for this constant was validated by three methods simultaneously. Previously the use of such methods for compounds having uninhibited zero order evaporation has been documented. In the present study, phthalic acid was chosen as the model compound since its evaporation is a two-step overlapping phenomenon. In this study we have shown the use of Pressure Differential Scanning Calorimetry in separating such simultaneous endothermic processes. The Clausius-Clapeyron equation seemingly has anomalous behavior for vapor pressure over high temperature ranges. In this study a modification of the equation has been suggested to take into account the changes in the heat capacities that result due to high temperature effects. This study aims at documenting a concise method for rapid pharmaceutical characterization and suggests modifications for some basic thermodynamic parameters over higher temperature ranges.

Full text of DOI:10.1002/jps.10044

An Evaporation Study for Phthalic AcidsÐA Rapid Method
for Pharmaceutical Characterization
KOUSTUVCHATTERJEE, ANASUYA HAZRA, DAVID DOLLIMORE,* KENNETH S. ALEXANDER
College of Pharmacy, Department of Pharmacy Practice, The University of Toledo, 2801 West Bancroft Street,
Toledo, Ohio 43606
Received 7 February 2001; revised 5 October 2001; accepted 11 October 2001
ABSTRACT: The objective of this study was to develop and analyze an analytical
method in order to evaluate preformulation candidates by their thermodynamic
parameters and evaporation characteristics. Ortho, meta and tere-phthalic acids were
chosen as model compounds. The relative advantages and disadvantages of a rapid
thermogravimetric method have been studied in detail, which would aid in the
preformulation characterization for pharmaceuticals. Methyl paraben was taken as the
model compound for calibration, as its evaporation characteristics are well known.
Using the Antoine and the Langmuir equation for evaporation conjointly, the parameter
k, known as the coef®cient of evaporation was determined. The value for this constant
was validated by three methods simultaneously. Previously the use of such methods for
compounds having uninhibited zero order evaporation has been documented. In the
present study, phthalic acid was chosen as the model compound since its evaporation is
a two-step overlapping phenomenon. In this study we have shown the use of Pressure
Differential Scanning Calorimetry in separating such simultaneous endothermic
processes. The Clausius±Clapeyron equation seemingly has anomalous behavior for
vapor pressure over high temperature ranges. In this study a modi®cation of the
equation has been suggested to take into account the changes in the heat capacities that
result due to high temperature effects. This study aims at documenting a concise
method for rapid pharmaceutical characterization and suggests modi®cations for some
basic thermodynamic parameters over higher temperature ranges. ß 2002 Wiley-Liss,
Inc. and the American Pharmaceutical Association J Pharm Sci 91:1156±1168, 2002
Keywords: preformulation; vapor pressure curves; evaporation kinetics; Antoine
equation; Langmuir equation; Clausius±Clapeyron equation
INTRODUCTION
studies attempt to de®ne the basic physicochem-
ical parameters, which later determine the ®nal
formulation characteristics of the product. One
such basic area includes the thermodynamic
parameters for the compound, which are related
to the vaporization 5and/or sublimation) charac-
teristics of the compound. Some common methods
used to determine the thermodynamic para-
meters to date are the reduced boiling point
method,1 the Knudsen cell diffusion apparatus,2
isothermal thermogravimetry 5TG),3 etc. We have
already reported the detailed description of the
novel and rapid 5rising temperature) TG method
that can be employed to obtain the accurate
During the advent of any new pharmaceutically
active compound, the solid-state characteriza-
tion studies are mandatory. Such preformulation
*Posthumously.
Koustuv Chatterjee's present address is The University of
Minnesota, College of Pharmacy, Minneapolis, MN 55455.
Anasuya Hazra's present address is College of Pharmacy,
State University of New York at Buffalo, Buffalo, NY 14223.
Correspondence to: Kenneth S. Alexander 5Telephone: 419-
530-1988; Fax: 419-530-1950;
E-mail: kalexan@utnet.utoledo.edu)
Journal of Pharmaceutical Sciences, Vol. 91, 1156±1168 52002)
ß 2002 Wiley-Liss, Inc. and the American Pharmaceutical Association
1156
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1157
evaporation characteristics of single-component
THEORETICAL SECTION
The Antoine Equation
systems.4,5 In this paper we report the results
of using this method for characterizing ortho-,
meta-, and para-phthalic acids and address some
of the basic questions in physical chemistry that
arose during the implementation of this method.
We also investigate some modi®cations of the
main methodology that have been proposed,
making comparisons of the modi®cations and
the original main method.
We have explained in detail the possible novel use
of the Antoine equation in pharmaceutical for-
mulations.4 Brie¯y, in moderate pressure ranges,
the Antoine equation is an excellent empirical tool
for the determination of vapor pressure curves
and is primarily empirical in nature.11 It can be
written as
We have already reported the utility of the
rapid TG method for compounds that either do or
do not evaporate rapidly. It remained to be seen
whether the method is applicable for compounds
that exhibit unusual evaporation behavior.
Hence, we chose phthalic acids to be model com-
pounds. To the best of our knowledge, the exact
vaporization behavior for ortho-phthalic acid has
not been documented. There is also much dis-
agreement among the thermodynamic para-
meters that have been reported in the literature
for phthalic acid. We have attempted to give an
explanation for such varying results, which will
be elucidated later in this paper.
As a substance undergoes the phase transition
from liquid to vapor, determining the rate of mass
loss can monitor the evaporation process.6 This
monitoring is achieved by TG, using a linear
rising temperature program. The advantages of
TG methods can be summarized as follows: ®rst,
minute amounts of the sample 55±10 mg) are
required; second, the effective experiment time is
relatively short; and third, the validation with the
actual experimental results, calculated by tradi-
tional methods, is quite precise. However, TG
alone might not be enough, and, if the evaporation
behavior is extremely complex, then one might
need to resort to other thermoanalytical techni-
ques, as we have in this study 5vide infra). On the
other hand, one important advantage of TG is that
precise estimations of the order of reaction,
activation energies, and pre-exponential factor
terms 5from the Arrhenius equation) can be
arrived at quite rapidly. There is a plethora of
information in this regard,7±10 and we will not go
into the mathematical details in this paper. We
will, however, attempt to explain the anomaly in
Clausius±Clapeyron plots when we calculate the
latent heat of evaporation. We will also give a
brief account of the main theory involved in using
this TG process. Though this method has been
reported in much more detail elsewhere,4,5 a brief
account here will help in better understanding of
the mathematical treatment.
b
ln P ˆ a À
ꢀ1†
T ‡ c
where P is the vapor pressure, T is the absolute
temperature, a ˆ 2.303A, b ˆ 2.303B, and c ˆ C.
Here A, B, and C are the Antoine constants at a
given temperature range, obtained from the book
by Stephenson and Malamowski,12 which are
mainly used to evaluate the temperature depen-
dence of vapor pressure. In this study, methyl
paraben was taken as the reference standard. The
Antoine constants that have been recorded for
methyl paraben are A ˆ 5.23662, B ˆ 1159.34, and
C ˆ À220.03 for a given temperature range of
446±517 K. It is, however, necessary not to over-
estimate the utility of this equation and keep in
mind that the Antoine constants would be useful
in predicting vapor pressure curves only within
the temperature range speci®ed for a particular
compound. In this study, the basic idea is to keep
the evaporation of methyl paraben 5as described
by its Antoine constants) as a standard and
compare the evaporation of the phthalic acids
with this standard 5the details will be elucidated
in the Results and Discussion section).
The Langmuir Equation
The Langmuir equation13 can be represented as
follows:
r
dm
dt
M
ˆ P a
ꢀ2†
2p RT
where dm/dt is the rate of mass loss per unit area,
P is the pressure, a is the vaporization constant, T
is the absolute temperature, R is the universal gas
constant, and M is the molecular weight of the
evaporating vapor. The objective is to determine
the vaporization constant in the presence of a
purge gas.
In his 1913 paper,13 Langmuir derived eq. 2
from the principles of kinetic theory of gases,
though his work involved quantifying the eva-
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1158
CHATTERJEE ET AL.
poration phenomena for metallic tungsten. Lang-
muir spent considerable time discussing the value
of the vaporization constant and was of the
opinion that it is unity if the initial conditions
are those of a vacuum, but did not exclude the fact
that it may have different values from unity. One
important change in the experimental design
adopted in this study, compared with that of
Langmuir, is that we used an atmosphere of dry
nitrogen and did not maintain vacuum conditions.
To use the Langmuir equation for TG data, one
must assume the fact that a is a constant that is
not unity in the presence of a purge gas. The
Langmuir equation holds true for a certain rate of
mass loss in volatilization from a given container
exposing a constant area of interface. It depends
considerably on the experimental set up and is
independent of the vapor being examined, pro-
vided it is not associated.
where p2 and p1 are the corresponding vapor
pressures at temperatures T2 and T1, respec-
tively, and R is the universal gas constant. When
implementing this equation, it was observed that
®tting a straight line through the data points was
providing anomalous results, indicating that the
DHvap value was not constant over higher tem-
perature ranges. Often we do not consider the
change in heat capacity of a substance in higher
temperature ranges, which leads us to obtaining
anomalous value for DHvap. We came to the
conclusion15 that heat capacity effects have to be
taken into consideration, and we proposed a
treatment that is very analogous to the tempera-
ture dependence on solubility of polar organic
compounds.16 We start with the differential form
of the Clausius±Clapeyron equation,
d ln p ÁHvap
ˆ
RT2
ꢀ5†
To suit TG data, eq. 2 can be rewritten as
dT
r
p
and take into account that DHvap is a function of
change in heat capacity at constant pressure and
the absolute temperature. In other words,
2pR
a
T
dm
dt
P ˆ
Â
Â
ꢀ3†
M
ˆ kn
ÁHvap ˆ a ‡ bT
ꢀ6†
where k ˆ HpR/a and n ˆ 5HT/M)  5dm/dt).
Because n would be a constant for a given set of
experiments, the plot of P versus n would give the
value of k. Alternatively, if we take the logarithm
of eq. 3, then a plot of log P versus log n would give
the value of log k.14 From eq. 3 it is apparent that
the value of k, a constant, will change with the
changing temperature. There might be various
methods with which one could calculate the value
for k. First, an arithmetic average could be taken
for all the values for k. Second, the vapor pressure
values could be individually computed with
different values for k. Third, this problem of
choosing the correct value for k could be overcome
by eliminating this factor totally from the vapor
pressure calculations. All these methods will be
analyzed in considerable detail in the Results and
Discussion section.
where a and b are constants and T is the absolute
temperature. The factor b is de®ned by the
relation
b ˆ ÁCp ˆ Cp ꢀvapor† À Cp ꢀliquid†
ꢀ7†
where DCp is the change in heat capacity at
constant pressure; hence,
d ln p ÁHvap
ˆ
ꢀ8†
ꢀ9†
dT
RT2
or,
or,
d ln p
dT
a
b
ˆ
‡
RT2 RT
ꢀ
ꢁ
a
b
d ln p ˆ
‡
dT
ꢀ10†
RT2 RT
Integrating both sides results in eq. 11:
The Clausius±Clapeyron Equation
a
b
ln p ˆ À
‡
ln T ‡ c
ꢀ11†
Often referred to as the classical and most widely
used relationship for evaluating vapor pressure
characteristics, the Clausius±Clapeyron equation
is used to obtain the latent heat of evaporation
value. The equation can be written as follows:
RT
R
where c is a constant of integration.
Equation 11 would be the corrected form of the
Clausius±Clapeyron equation, which takes into
account the change in heat capacity over higher
temperature ranges. Thus, a simple plot of ln p
versus 1/T might not give an accurate result, as
p2
ÁHvap T2 À T1
log
ˆ
Â
ꢀ4†
p1 2:303R
T2T1
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1159
the DHvap cannot remain constant over all tem-
perature ranges. Aplot of ln p versus ln T would
also not be exclusive, as is obvious from eq. 11. We
have plotted these conventional ®gures sepa-
rately, and the exact picture is probably some-
where in between. In other words, a proper
nonlinear ®t for eq. 11 would perhaps be ideal in
nature. The plots and the discussions are dealt
with detail in the Results and Discussion section.
Pressure Differential Scanning
Calorimetry 2PDSC)
Differential scanning calorimetry 5DSC) is routi-
nely used for the characterization of pharmaceu-
ticals.17 PDSC would be a modi®cation of the
normal DSC in which the normal DSC cell is
replaced with a cell that is specially designed to
withstand elevated pressures of nitrogen gas. To
understand the relevance of this technique in the
present study, one has to ®rst inspect the
evaporation pattern for phthalic acid.
The thermal decomposition of phthalic acid is a
complex process,18 and for evaporation studies
exclusively with the TG balance, it is mandatory
that the evaporation pattern is simple. The
Figure 2. TG±DTG plots for isophthalic acid 5---) and
terephthalic 5Ð) acids.
phthalic acid eventually produces 1 mol of
phthalic anhydride and 1 mol of water.18,19 The
problem with this type of a reaction is that the
exact temperature at which this decomposition
occurs is not known.20 There have been con¯icting
reports for the thermal properties of phthalic acid
mainly because the melting of phthalic acid and
subsequent formation of phthalic anhydride
depend heavily on the rate of heating.18,19 From
the TG plot, it is observed that the process of
melting starts at ꢁ1808C, and the loss of weight
from ꢁ1978C becomes very pronounced. This
result can be explained by the fact that although
the actual melting point for phthalic acid is
ꢁ180±1908C, minute quantities of the anhydride
formed actually depress the melting point and
the process starts at a lower temperature than
expected. The amount of anhydride formed, as
explained earlier, would again depend on the
heating rate; for the purpose of this study, a
relatively high heating rate 5108C/min) was used.
The water molecules would immediately vaporize
at these high temperatures. Also, the melting
point for phthalic anhydride is 1308C. Thus, the
process of anhydride formation and its evapora-
tion is almost simultaneous.
thermogravimetric±differential
thermogravi-
metric 5TG±DTG) plot for phthalic acid 5Figure 1)
does not show a simple evaporation pattern,
and the DTG plot suggests a complex pattern
of decomposition. The DTG plot 5Figure 2) shows
one single endotherm, which suggests that
the other energy changes might be hidden
due to the broad melting endotherm for phthalic
acid.
To explain the unusual nature of decomposi-
tion, one must consider the decomposition pro-
ducts for phthalic acid. When heated, 1 mol of
Thus, the thermal treatment of phthalic acid is
not a single-component evaporation process. After
ꢁ1808C, there are a total of three different
contributors to the overall pressure on the system;
they are, the presence of the purge gas, nitrogen,
the partial pressure exerted by the phthalic
anhydride vapor, and the water vapor in the
system. At ꢁ2308C, the melting of phthalic acid is
complete and so is the complete vaporization of all
the gases in the system. Hence, using TG alone, it
is impossible to ®nd the exact temperature range
Figure 1. TG±DTG plot for phthalic acid.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1160
CHATTERJEE ET AL.
for the evaporation phenomenon. The objective
was to separate the overlapping endotherms and
obtain the temperature range for the evaporation
process. It might be worthwhile mentioning here,
that although PDSC has existed for a long time, it
has found very limited application in the study of
pharmaceuticals.21 It has been well documen-
ted22,23 that PDSC is an effective tool in separat-
ing the dehydration and evaporation processes for
pharmaceutical hydrates. The difference in this
case is that the water molecule for phthalic acid is
structural water rather than water of crystal-
lization, although the basic principles of separa-
tion of endotherms at elevated pressures remain
the same. At ꢁ200 psi, complete separation of the
overlapping endotherms was observed and the
temperature for the evaporation range was deter-
mined. Isophthalic and terephthalic acids, how-
ever, did not have to go through such measures.
Compared with phthalic acid, the carboxylic
groups for isophthalic and para-phthalic acids
are not ``close enough'' for the elimination of one
molecule of structural water, even after the appli-
cation of heat.
differ by a very large extent compared with the
one in its homologous series. For the present
study, the starting values stipulated in ASTM
methods E1719 and E1782 were used.24
EXPERIMENTAL SECTION
Materials
Methyl paraben 5Fischer Scienti®c Company, lot£
762258), phthalic acid 5Aldrich Chemical, lot£
02431AX), metaphthalic acid 5Aldrich Chemical,
lot£ 01630HZ), and terephthalic acid 5Aldrich
Chemical, lot£ 02109MZ) were obtained and used
as received.
Equipment
The SDT 2960, simultaneous thermogravimetric
analysis±differential thermogravimetric analysis
5TGA±DTA) TA instrument, with the thermal
analyst 2000 TAoperating system version 1.0B,
was employed to investigate the evaporation
behavior of methyl paraben and the phthalic
acids. An electronic ¯ow meter, model ADM
1000 from J&W Scienti®c, was used to regulate
the ¯ow of nitrogen 5purge gas) through the
samples. Aconventional DSC 5model 910, TA
Instruments) was ®tted with a specially designed
pressure chamber 5model 910 cell, TAInstru-
ments) in which the PDSC experiments were
carried out. For the statistical calculations of
Antoine constants, the SPSS 10.0 for Windows
software, 2000, was used.
Curve Fitting for Antoine Constants
Nonlinear regression analysis is a useful tool for
curve-®tting purposes. The empirical Antoine
constants for each compound can be effectively
determined by the ``least-square curve-®t'' method
where the vapor pressure plot for each compound
is ®tted to the Antoine equation. The parameters
A, B, and C would be susceptible to changes
depending on the algorithm used. For practical
purposes, the Levenberg±Marquardt algorithm
was used, and the ``global'' least-square ®t was
found to be consistently accurate in predicting the
Antoine parameters. It must be kept in mind that
the method of statistical iterations can be easily
subjected to change according to the stipulations
5or constraints) applied by the experimenter.
Thus, after meeting the convergence criteria in
nonlinear regression iterations, it is mandatory to
use the values for A, B, and C and corroborate the
fact that these parameters indeed describe the
vapor pressure curve. All statistical software used
for nonlinear regression purposes require a start-
ing value for each parameter before it proceeds
with the iterations. This task might be simpli®ed
if the Antoine values for one of the compounds in
the homologous series being evaluated are known.
It can be expected that the unknown Antoine
parameters for the compounds in study will not
Method
The methods are elucidated step-by-step for
clarity.
1. Areference material has to be chosen that
has known Antoine constants. For the pur-
pose of this study, methyl paraben, the
most commonly used pharmaceutical pre-
servative, was used.
2. Methyl paraben was subjected to TG runs
under a variety of experimental conditions.
The objective here was to ®nd the optimum
condition that would result in the best
possible DTAplot 5®gure not shown). In
other words, the melting and sublimation
processes would be distinguished clearly
from one another. Nitrogen was the obvious
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1161
choice as the purge gas because oxygen and
carbon dioxide might trigger oxidation and
other chemical processes within the com-
pound. The ¯ow rates studied were 25, 50,
80, 100, and 125 mL/min. The rates of
temperature rise in the rising temperature
program chosen were 2, 5, 10, and 158C/
min. It was experimentally veri®ed that the
best ¯ow rate would be 100 mL/min, with
the temperature rising at 108C/min. The
runs were conducted in a temperature
range from ambient to 4008C. An open,
110-mL platinum crucible with a cross-
sectional area of 0.34 cm2 was used to
contain the sample, and an empty platinum
crucible of equivalent area was used as the
reference. The sample size was 9.6 mg. The
DTAcurve showed two distinct endother-
mic processes of melting and sublimation,
and the temperature range for evaporation
was chosen.
at which the phthalic acid was run 5200 psi).
The entire calibration was carried out with
same Indium samples to minimize the
errors associated with sample weighing. A
detailed description of the PDSC cell can
found in the paper by Levy et al.25 The
overlapping endotherms for phthalic acid
were separated, and the exact temperature
range was determined.
6. Using the k value of 124 525 Æ 0.8 obtained
from methyl paraben, the vapor pressure
curves for the phthalic acids were con-
structed. From the Langmuir equation, the
value for a was determined to be 5.8 Â 10À5
.
This unusually small value for a was intri-
guing, keeping in mind that Langmuir had
theorized that the value should be unity for
vacuum. So, we tried out other mathema-
tical operations to calculate the k, and
hence a, by two other methods. Expectedly,
the variation was small and each method
had its share of advantages and disadvan-
tages 5details in Results and Discussion
section).
3. The rate of loss of methyl paraben due to
heat, along with the ®rst derivative of
weight loss data, were obtained from the
instrument. Using the Arrhenius equation,
the activation energy and pre-exponential
factors were calculated. With the Antoine
equation reported, the theoretical vapor
pressure calculations were made. and the
vapor pressure curve was obtained. The k
value, in SI units, from the Langmuir
equation was 124 525 [Pa Kg0.5 mol0.5 sÀ1
7. The Antoine constants over a speci®c tem-
perature range had to be evaluated for the
three compounds. It was obvious that the
vapor pressure curve was not linear for all
the compounds studied. Also, the Antoine
equation could not be transformed into a
linear form. Nonlinear regression was
deemed to be the best possible measure for
curve ®tting purposes and statistically, the
Antoine constants were obtained. The
Levenberg±Marquardt algorithm was used
to obtain the ``global least square ®t.''
8. The Antoine parameters needed to be
validated, and the experimental and theo-
retical vapor pressure data were compared
with each other. They showed very close
proximity, con®rming the validity of the
calculated Antoine constants over a speci-
®ed temperature range for each compound.
It should be mentioned here that the
method of iterations is an arbitrary proce-
dure. If different algorithms were used,
there would be a different set of iterations
generated. Irrespective of the algorithm
used, after determining the Antoine con-
stants, the validation step, where the
degree of ``goodness of ®t'' is validated, is
absolutely necessary. As long as ``goodness
of ®t'' is achieved, any method should be
valid.
m
À2 KÀ0.5]. The run for methyl paraben was
repeated three times, and the average
calculated k value was taken.
4. The phthalic acids were subjected to TG
runs under the same experimental condi-
tions; it is important that the identical
experimental parameters be maintained to
make conclusions about any scienti®c out-
come common to the entire class of com-
pounds. The sample sizes for all the
compounds were maintained at ꢁ10 mg.
Apart from phthalic acid, evaporation of the
other two compounds exhibit perfect zero-
order kinetics.
5. For phthalic acid, the TG data showed two
overlapping endotherms and it was very
dif®cult to conclude about the exact tem-
perature range for evaporation. Hence, the
PDSC was used for this purpose. The DSC
was calibrated with Indium 5TAInstru-
ments). The pressure cell was calibrated at
ambient pressure and also at the pressure
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1162
CHATTERJEE ET AL.
Table 1. Summary of the Values for Eact and DHvap
for the Compounds Studied
curves for the isophthalic and terephthalic acids
are shown in Figure 2 from inspection it can be
concluded that they follow perfect zero-order
evaporation processes. Nevertheless, detailed
calculations were carried out to be absolute
certain. It might be worth mentioning that unless
the compounds follow perfect zero-order kinetics,
the method for vapor pressure calculations as
described in this paper will not be suitable. Hence,
it is mandatory that the determination for order of
reaction be carried out initially. The parameters
for methyl paraben are also shown in Table 1.
Methyl paraben is our model compound, and the
shape of its DTG curve 5Figure 3) simulates a
perfect zero-order rate process. Another attribute
of a zero-order process is that the energy of
activation should be very close 5equal, in ideal
situations) to the enthalpy of vaporization. This
phenomenon will be alluded to later.
Compound
Eact 5kJ molÀ1
)
DHvap 5kJ molÀ1
)
Methyl paraben
Phthalic acid
Isophthalic acid
Terephthalic acid
75.1
418.9
122.3
129.6
77.1
407.8
124.7
132.7
RESULTS AND DISCUSSION
Determination of Kinetic Parameters
Determination for order of reaction has been
studied in great detail and references are avail-
able: Wilburn26 has studied various methods for
determining the order of reaction in rising
temperature thermal analysis; Dollimore et al.
have studied the kinetic mechanisms of reactions
from the shape of the TG curve;27 Dollimore,
Tong, and Alexander have studied the thermal
decomposition of calcium carbonate by rising
temperature TG.28 The details of such methods
are not the objectives of this report. The Arrhe-
nius parameters of activation energy and pre-
exponential factors for the three phthalic acids
are shown in Table 1. The TG±DTG curve for
phthalic acid is shown in Figure 1 it is clear that
separation of two endothermic processes 5melting
and evaporation) is not possible with TGAalone.
This problem was overcome by PDSC, as would be
described in the next section. The TG±DTG
Separation of Overlapping Endotherms
for Phthalic Acid
As mentioned earlier, to obtain the accurate
temperature range for evaporation, the endo-
therms for phthalic acid evaporation had to be
separated. Because the objective was to obtain the
best separation, multiple pressures were not
employed. It has been reported22,23 that pressures
of ꢁ200 psi can cause resolution of overlapping
endotherms that involve loss of water. Thus,
using ꢁ200 psi of pressure in the pressure cell,
Figure 3. DTG plot for methyl paraben, showing zero-order evaporation process.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1163
the two endotherms were well separated and the
exact evaporation temperature range was deter-
mined. It should be mentioned here that the
variables of heating rate 5108C/min) and ¯ow rate
for purge gas 5ꢁ100 mL/min) were maintained
constant. One possible disadvantage of this design
is that even if we maintain the same experimental
parameters for uniformity, the change of instru-
ment 5TGAand PDSC) will always cause some
variations. However, for the purposes of this
study, we assume that such differences are negli-
gible. The calibration steps are more stringent for
PDSC compared with normal DSC; that is, calib-
ration has to be repeated for every single pressure
value that is being tested. The well-separated
PDSC endotherms for phthalic acid are shown in
Figure 4 the evaporation endotherm falls in the
range 469±486 K. The determination of the vapor
pressure curve for phthalic acid was also carried
out over this particular temperature range.
Figure 5. Plot of pressure versus n; obtaining the
value for k.
paraben only hold true in the temperature range
446±517 K. We obtain the value for k from methyl
paraben data by plotting pressure versus n
5Figure 5). Thus, when we are plotting the vapor
pressure curve for methyl paraben 5Figure 6) from
these data, the curve should only be considered
valid in that speci®c temperature range. The
vapor pressure curves for the three phthalic acids
are shown in Figure 7.
Determination of Vapor Pressure Curves
As referred to earlier 5in the Methods section),
methyl paraben is our model compound for
primarily two reasons; one, it exhibits perfect
zero-order evaporation kinetics, as determined by
actual calculations, and two, its Antoine con-
stants have been well reported. Before the actual
vapor pressure calculations are carried out, it
must be noted that the Antoine constants for each
compound are valid only in the speci®c tempera-
ture range that is reported. No effort should be
made to stretch that temperature range, though
this might ease out a lot of technical dif®culties.
For example, the Antoine constants for methyl
Signi®cance of k
The coef®cient of vaporization 5k) is perhaps the
most important parameter in the Langmuir
equation that is being utilized in such studies.
Figure 4. Separation of endotherms for phthalic acid
Figure 6. Vapor pressure plot for methyl paraben.
by PDSC.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1164
CHATTERJEE ET AL.
is the impurity of the sample that in¯uences the
vaporization constant. The purity grades of the
samples studies were according to USP speci®ca-
tions, but the effect of an extremely small per-
centage of impurity can be magni®ed many-fold
when the evaporation interface is in fact a
capillary-like thin ®lm of solid. Moreover, in the
melt, it is the impurity that would migrate to the
surface, which might lead to considerable differ-
ences in the value for a. This possibility will
require resolution in the future.
Modi®cations for the Calculation of k
Figure 7. Vapor pressure plots for phthalic 5~),
isophthalic 5^), and terephthalic 5&) acids by the
constant k method.
To investigate the accuracy of the procedure, a
few alternative methods have been suggested.
Two such methods, the comparative method and
the constant k method, will be discussed here.
This parameter is a constant, and is independent
of the material being studied. In this study, it was
deemed best to use SI units in a uniform manner,
and the value for k was found to be 124 525 Æ
The Comparative Method
Using feasible experimental conditions, it is not
possible to improve on the results obtained so far
and, hence, the objective was to determine
whether any change in mathematical treatment
of the data can result in a better value for k and a.
Recalling eq. 3, we have
0.8 Pa Kg0.5 mol0.5 À1 mÀ2 KÀ0.5. This value is in
s
good correlation with the value of k reported in
the literature.29 The units of k can also be ex-
pressed in units other than SI, though nonunifor-
mity might lead to confusion in certain cases. We
have recently seen the units of k being reported in
parameters different from ours.30 There also
might exist experimental factors that may alter
the k value, such as the ¯ow rate of nitrogen and
the heating rate, but these factors were not
investigated in this study. In the ASTM method
referred to in this study,24 it has also been spe-
ci®ed that all terms be reported in the SI system of
units.
r
p
2pR
a
T
dm
dt
P ˆ
Â
Â
ꢀ3†
M
ˆ kn
where k ˆ HpR/a and n ˆ 5HT/M)  5dm/dt). Here,
k would be independent of the material being used
and is inversely proportional to a
Modifying eq. 3, we can write
s
ꢀ
ꢁ
dm
dt
T
Psam
ˆ
Â
 k
ꢀ12†
ꢀ13†
Signi®cance of a
Msam
sam
From the Langmuir equation, it can be observed
that the k value is inversely proportional to a.
Langmuir had suggested that the value of a is
unity under vacuum conditions, though he did not
categorically state that it couldn't change under
the in¯uence of a purge gas. It is important to note
that the experimental design utilized in this study
would have a multicomponent atmosphere. First,
there is nitrogen as the purge gas and second, the
compound being investigated is itself vaporizing
and continuously adding to the partial pressure of
the material. This situation would be expected to
alter the value for a. However, the value of a is
obtained as 5.8 Â 10À5. This extremely small
quantity is very dif®cult to explain with the
resources available. However, we believe that it
s
ꢀ
ꢁ
dm
dt
T
Pref
ˆ
Â
Â
Mref
ref
Pressure of the reference would be the pressure
for the known calibration compound and pressure
for the sample would be of the compound for
which Antoine constants are unknown. Combin-
ing eqs. 12 and 13, we have
s
Â
Ã
dm
dt
dm
dt
Psam
Pref
Mref
sam
Â
Ã
ˆ
Â
ꢀ14†
Msam
ref
Thus, from eq. 14, we can directly calculate the
vapor pressure for the unknown substance,
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1165
provided we have the complete vapor pressure
pro®le for the reference. Anoticeable fact about
this equation is that the unusual values for k and
hence a, has been eliminated. In other words,
though we are not tackling the problem directly,
this method might serve as a means to get
around the problem by eliminating those values
in the vapor pressure calculations altogether.
Though this method has the advantage of ignor-
ing the k value, it would ®nd limited use compared
with the original method. In eq. 14 the tempera-
ture term is cancelled out after assuming the fact
that the temperature range for evaporation would
be approximately equal for both the sample and
the reference compounds. This problem arises
particularly when we proceed to construct the
vapor pressure curves for isophthalic and ter-
ephthalic acids. The temperature pro®le for
vaporization for the calibration compound
5methyl paraben) is entirely different from that
of isophthalic and terephthalic acids. Thus, such a
method can only be carried out for phthalic acid.
Calculations would be severely limited by this
constraint, and very few compounds can be
obtained that satisfy these criteria.
calculation, averaging that value might lead to
errors. It would also be interesting to note changes
5if any) that might occur in the ®nal vapor
pressure curves if we do not take the mean value
for k. Moreover, this method has the same dis-
advantage as that of the comparative k method.
The temperature in which the value is being
compared has to be exactly the same as that of the
reference compound for the method to have any
realistic meaning. Again, vapor pressure curves
for isophthalic and terephthalic acids could not be
constructed by this method because of such
restraints. Such limitations would restrict the
number of compounds suitable for this study
because there would be very few systems for
which the reference compound and the unknown
have the same temperature range for evapora-
tion. Thus, such speculations with different
calculative approaches are practically not com-
parable to the constant k method. Finally, it is
worthwhile to note that there are negligible
variations among the vapor pressure curves of
phthalic acid alone determined by three different
methods 5Figure 8).
The Continuous k Method
Clausius±Clapeyron Plots
One of the disadvantages of the original method
that we used was taking the average for k over the
temperature range for evaporation. Understand-
ably, for a long temperature range, the k value
will differ and for suiting the purposes of easier
The classical Clausius±Clapeyron plots, in which
natural logarithm of pressure is plotted against
the reciprocal of absolute temperature, are shown
in Figure 9. If we assume the latent heat of
vaporization 5DHvap) to be constant, then the slope
Figure 8. Comparing methods to obtain k; vapor pressure plots for phthalic acid
using all three methods.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1166
CHATTERJEE ET AL.
considerable difference between the two. Thus,
the DHvap value is not accurate. Probably, when
we have cases where the DHvap value has to be
obtained over high temperature ranges, some
average value has to be computed to approxi-
mately obtain the overall DHvap value.
Curve Fitting for Antoine Constants
The method of nonlinear regression was used for
the determination of the unknown Antoine con-
stants. The Antoine equation cannot be linearized
without making some bold assumptions, and such
assumptions might not be valid over a large
temperature range. Therefore, nonlinear regres-
sion was deemed to be the best method to use in
this instance. The SPSS 10.0 software was used
and the Levenberg±Marquardt algorithm for the
global least square ®t was applied. To compute
iterations for nonlinear regression, one has to
specify the starting parameters for the Antoine
constants. This might not be always an easy task.
ASTM methods E1719 and E1782 specify the
starting values for A, B, and C to be 9.3, 2000, and
À37, respectively, when the pressure is in Pascal
and temperature is in Kelvin.24 For the list of
compounds studied, these values proved to be use-
ful because they generated acceptable curve ®ts
5Table 2). If these values did not prove to be
useful, one might have to take into consideration
a different algorithm to arrive at acceptable curve
®ts. Operating with the same parameter con-
straints would be valid only if the compounds
under study are chemically similar in nature. Two
compounds with totally different chemical enti-
ties might not follow the same analogies when
their vapor pressure curves are being veri®ed for
suitable curve ®ts.
Figure 9. Classic Clausius±Clapeyron plots for
phthalic 5&), isophthalic 5^), and terephthalic 5~)
acids.
of this straight line would give us the value
directly. However, even from general inspection of
the data it can be seen that the straight line ®t is
inaccurate because considerable curvature is pre-
sent at higher temperatures. This curvature, as
already explained in the Introduction section, is
due to the change in value for DHvap due to the
change in heat capacity at higher temperatures.
As observed from eq. 11, ln P versus ln T was
plotted 5Figure 10) and the correct picture for the
DHvap value would lie somewhere in between the
values obtained from Figures 9 and 10. Aproper
nonlinear curve ®t would also give the same
result. We have mentioned earlier that for perfect
zero-order evaporation processes, the energy of
activation should be almost equal to the DHvap
value. In other words, evaporation processes are
non-activated processes. If we compare the acti-
vation energy values with the DHvap values
obtained from Figure 11, we see that there is
CONCLUSIONS
The initial physical characterization of a pharma-
ceutically active compound involves the calcula-
tion of the thermodynamic parameters, such as
enthalpy of fusion, sublimation, etc., and the
melting and subsequent evaporation characteris-
tics of the compound have to be determined. In
pre-formulation and formulation development,
calculating vapor pressures for the compounds
being studied is undertaken to generates the
vapor pressure curve needed to de®ne and quan-
tify the vaporization characteristics. The process
of actually measuring the vapor pressures has not
Figure 10. Plots of ln P versus ln T for phthalic 5&),
isophthalic 5^), and terephthalic 5~) acids.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

EVAPORATION CHARACTERISTICS OF PHTHALIC ACIDS
1167
Table 2. List of Antoine Constants for Compounds Undergoing Evaporation
Antoine Constant
Compound
A
B
C
Temp. Range 5K)
Methyl paraben**
Isophthalic acid
Phthalic acid
5.23
6.48
8.93
8.96
1159.34
382.87
61.49
À220.03
À430.47
À450.90
À343.01
446±499
553±585
469±486
595±631
Terephthalic acid
1338.60
**Antoine constants available in Ref. 12.
only been time consuming but also cumbersome,
keeping in mind the classical manometric mea-
surements. The method described in this study
attempts to shorten the time span of such
processes and offer comparable results. This work
also demonstrates the use of various calculation
methods in determining the vapor pressure of
single components, with their relative advantages
and disadvantages. We also have tried to forward
the modi®cation of methods used to calculate
the latent heat of vaporization by the classical
Clausius±Clapeyron method. Although there
might be other methods as well, there is no doubt
that the latent heat of vaporization value does not
remain constant over large temperature ranges
due to changes in heat capacities. One drawback
of this method is that to date, only single-
component systems can be studied; therefore,
future methods have to be devised to solve the
complexities of the procedure when multicompo-
nent systems are to be investigated. There also
remains a possibility that the melting point of a
pure component might be depressed in the
presence of other formulation additives. Once
the vaporization 5and sublimation, if any) char-
acteristics of multicomponent systems are vali-
dated by the method described in this study, it
would be more relevant to ``real world'' formula-
tion scenario.
help with the PDSC. Finally, we thank Dr. David
Grant 5University of Minnesota, Department of
Pharmaceutics) for his insight and comments on
the modi®cation of the Clausius±Clapeyron equa-
tion, to accommodate changes in heat capacity
over high temperature ranges.
REFERENCES
1. Goodrum JW, Siesel EM. 1996. Thermogravimetric
analysis for boiling points and vapor pressure.
J Thermal Anal 44:1251±1258.
2. Riberio da Silva MAV, Monte MJS. 1990. The
construction, testing and use of a new Knudsen
effusion apparatus. Thermochim Acta 171:169±
183.
3. Gueckel W, Synnatschke G, Ritting R. 1973.
Method for determining the volatility of active
ingredients used in plant protection. Pestic Sci
4:137±147.
4. Chatterjee K, Dollimore D, Alexander KS. 2001. A
new application for the Antoine equation in
formulation development. Int J Pharm 213:31±44.
5. Chatterjee K, Dollimore D, Alexander KS. 2001. A
thermal analysis study of hydroxy benzoic acid
derivatives using rising temperature thermogravi-
metry. J Therm Anal 63:629±639.
6. Dollimore D, O'Connell C. 1998. Acomparison of
the thermal decomposition of preservatives, using
thermogravimetry and rising temperature kinetics.
Thermochim Acta 324:33±48.
7. Wilburn FW, Dollimore D. 2000. Non-isothermal
kinetics: Adifferent approach. Thermochim Acta
357±358:141±145.
8. Dollimore D. 1999. Abreath of fresh air. Thermo-
chim Acta 340±341:19±29.
9. Foo Lee Y, Dollimore D. 1998. The identi®cation of
the reaction mechanism in rising temperature
kinetic studies based on the shape of the DTG
curve. Thermochim Acta 323:75±81.
10. Wilburn FW. 1999. The determination of kinetics
parameters from DTG curves- fact or ®ction?
Thermochim Acta 340±341:77±87.
ACKNOWLEDGMENTS
We thank Dr. Jim Olson, Union Carbide, Phila-
delphia, for his helpful suggestions. We are
grateful to Dr. Raj Suryanarayanan 5University
of Minnesota, Department of Pharmaceutics) for
his help and advice in general and for the
suggestion regarding the utilization of the PDSC
in particular. We also acknowledge the help from
Mr. Cletus Nunes 5University of Minnesota,
Department of Pharmaceutics) for his practical
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002

1168
CHATTERJEE ET AL.
11. Majer V, Svoboda V, Pick J. 1989. Heats of
Vaporization of Fluids. Amsterdam: Elsevier, p. 27.
12. Stephenson RM, Malamowski S. 1987. Handbook of
the Thermodynamics of Organic Compounds. New
York: Elsevier, p. 263.
13. Langmuir I. 1913. The vapor pressure of metallic
tungsten. Phys Rev 2:329.
14. Shen L, Alexander KS. 1999. A thermal analysis
study of long chain fatty acids. Thermochim Acta
340±341:271±278.
22. Han J, Suryanarayanan R. 1997. Applications of
pressure differential scanning calorimetry in the
study of pharmaceutical hydrates I. Carbamaze-
pine dihydrate. Int J Pharm 157:209.
23. Han J, Gupte S, Suryanarayanan R. 1998.
Applications of pressure differential scanning
calorimetry in the study of pharmaceutical
hydrates II. Ampicillin trihydrate. Int J Pharm
170:63.
24. Annual Book of ASTM Standards, Designation: E
1719±97. 1997. Standard Test Method for Vapor
pressure of Liquids by Ebulliometry, 11.01, Con-
shockton, Pennsylvania.
15. Grant DJW. 2000. University of Minnesota,
Department of Pharmaceutics, Minneapolis, MN.
Personal communication.
16. Grant DJW, Higuchi T. 1990. Solubility Behavior of
Organic Compounds. New York: Wiley-Inter-
science, p. 30.
25. Levy PF, Nieuweboer G, Ludwig S. 1970. Pressure
differential scanning calorimetry. Thermochim
Acta 1:429.
17. Brittain HG. 1999. Methods for the characteriza-
tion of polymorphs and solvates. In: Brittain HG,
editor. Polymorphism in Pharmaceutical Solids.
New York: Marcel Dekker, p. 251.
18. Allen I. 1914. Commercial Organic Analysis,
Volume III, Fourth Edition, Philadelphia: P. Bla-
kiston's Son & Company, p. 43.
19. Finar IL. 1989. Organic Chemistry, Volume 1.
London: Longman, p. 1967.
20. Alekseev VG, Kizaev VD, Fedyainov NV, Bushinski
VI. 1989. Standard enthalpies of anhydrization of
phthalic and pyrometallic acids. Zhurnal Fiziches-
koi Khimii 63:2327±2331.
26. Wilburn FW. 2000. Kinetics of overlapping reac-
tions. Thermochim Acta 354:99.
27. Dollimore D, Evans TA, Lee YF, Wilburn FW. 1992.
Correlation between the shape of a TG/DTG curve
and the form of the kinetic mechanism which is
applying. Thermochim Acta 198:289.
28. Dollimore D, Tong P, Alexander KS. 1996. The
kinetic interpretation of the decomposition of
calcium carbonate by use of relationships other
than the Arrhenius equation. Thermochim Acta
282:13.
29. Shen L, Alexander KS. 1999. A thermal analysis
study of long chain fatty acids. Thermochim Acta
340:271.
21. Dwivedi SK, Suryanarayanan R, Mitchell AG.
1990. Anomerization of lactose during differential
scanning calorimetry at atmospheric and elevated
pressures. Pharm Res 7:107.
30. Price D, Hawkins M. 1998. Calorimetry of two
disperse dyes using thermogravimetry. Thermo-
chim Acta 315:19.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 4, APRIL 2002