Measurement and prediction of solubility of four arylamine molecules in benzene, hexane, and methanol

Article abstract of DOI:10.1021/je0495785

In this paper, the solubility of selected arylamine molecules in methanol, hexane, and benzene has been investigated. Solubility of mmmTTA in hexane and benzene is the highest while mTTA has the lowest solubility in benzene and hexane. The UNIFAC and the UNIQUAC binary adjustable parameters have been determined. On the basis of these parameters, the solubility of these molecules has been predicted and compared with the experimental data. The effect of meta or para substitutions in arylamine molecules on their solubility in organic solvents was experimentally determined and theoretically established. The adjustable parameters of the UNIFAC equation obtained in this study will help estimate the solubility of macromolecules with the same constitutional groups or estimate the solubility of mixture of arylamine molecules. Thermal properties such as specific heat, melting point, boiling point, and heat of vaporization of the selected arylamine molecules have been determined.

Full text of DOI:10.1021/je0495785

1794
J. Chem. Eng. Data 2005, 50, 1794-1800
Measurement and Prediction of Solubility of Four Arylamine
Molecules in Benzene, Hexane, and Methanol
Touraj Manifar and Sohrab Rohani*
Department of Chemical and Biochemical Engineering, The University of Western Ontario,
London, Ontario, N6A 5B9 Canada
In this paper, the solubility of selected arylamine molecules in methanol, hexane, and benzene has been
investigated. Solubility of mmmTTA in hexane and benzene is the highest while mTTA has the lowest
solubility in benzene and hexane. The UNIFAC and the UNIQUAC binary adjustable parameters have
been determined. On the basis of these parameters, the solubility of these molecules has been predicted
and compared with the experimental data. The effect of meta or para substitutions in arylamine molecules
on their solubility in organic solvents was experimentally determined and theoretically established. The
adjustable parameters of the UNIFAC equation obtained in this study will help estimate the solubility
of macromolecules with the same constitutional groups or estimate the solubility of mixture of arylamine
molecules. Thermal properties such as specific heat, melting point, boiling point, and heat of vaporization
of the selected arylamine molecules have been determined.
Introduction
(N,N-bis-(4-methylphenyl)-N-(3-methylphenyl)amine, Beil-
stein Registry No. 9202276), mmTTA (N,N-bis-(3-meth-
ylphenyl)-N-(4-methylphenyl)amine, CAS Registry No.
97413-60-0); mmmTTA (N,N,N-tris-(3-methylphenyl)amine;
CAS Registry No. 20676-79-3)] in hexane, methanol, and
benzene. Figure 1 shows the structure of these molecules.
We want to show the effect of the substitution of a methyl
group on the solubility of these molecules in polar-protic
and nonpolar-aprotic solvents. Since these solvents cover
a wide range of polarity index, the results can be extended
to other solvents with a similar polarity index. For solubil-
ity estimation, the UNIQAC binary adjustable parameters
of these molecules are obtained in the selected solvents.
In addition, binary parameters of the constitutional group
for the UNIFAC method are obtained. The estimated
solubility by the ideal mixture and by UNIFAC and
UNIQUAC are compared with the experimental data.
Arylamine compounds are extensively used for many
industrial applications. The pharmaceutical,1 polymer,2 and
xerographic industries3 are among the well-known com-
munities that have interests in these compounds. High drift
mobilities4-6 make these molecules a good choice for the
OLED (organic light-emitting diodes) or organic photore-
ceptors as a hole transport material.
In the OLED, the arylamine molecules form a thin solid
film whereas in an organic photoreceptor they present a
solid-state solution in a polymeric binder. In either case,
the continuously increasing need on the improvement of
these devices (durability, thermodynamic stability, and
higher efficiency) necessitates stricter control over the
properties and characteristics of the arylamine molecules.
Progress on the area of synthesis has been achieved, and
still much work is being carried out in this area.7-15 In the
area of application, many researchers use arylamine
molecules in optoelectronic diodes (both OLEDs16-18 and
organic photoreceptors19-21). However, to our knowledge,
there is no published data on the solubility, purification,
and crystallization of these molecules. In the area of
synthesis, the solubility data for arylamine molecules in
different solvents is important since many hydrocarbon
solvents are usually utilized as the reaction medium.3,22-24
On the basis of our study,25 the success of the synthesis
method necessitates that the catalyst, reactant, and prod-
uct be soluble in one phase under homogeneous condition
to reduce mass transfer limitations.
Theory
In a binary system, the relationship between fugacities
of the solute in solid and subcooled liquid forms is given:30
f2L
f2S
∆
fusH T
∆Cp T
∆C
Ttp
T
ln
)
tp - 1 -
tp - 1 +
p ln
(
)
(
)
(
)
RTtp
T
R
T
R
(1)
where fS2 is the fugacity of pure solid, fL2 is the fugacity of
pure subcooled solute, ∆fusH is the enthalpy of fusion, and
∆Cp is the difference in heat capacities of the solute
between liquid state and solid state at temperature T. Ttp
is the triple point of solute, which can be assumed as
the melting point. This assumption creates only minor
error.15,30 This equation is true for all cases regardless of
ideality or nonideality of the solution. To solve this equation
one needs thermal properties of the pure solid. However,
certain assumptions have to be made. First, ∆Cp is constant
over the temperature range T to Ttp. Second, the effect of
pressure on the properties of solid and subcooled liquid is
negligible. This is true unless the pressure is high. Finally,
In the xerographic industry, a minor impurity in aryl-
amine materials would result in poor quality and resolu-
tion. Besides, unwanted crystallization of these molecules
as a result of aging has a serious consequence on the
lifespan and functionality of the OLEDs.26-29
In this study, we present the solubility of selected
arylamine molecules [tritolylamine or TTA (N,N,N-tris-(4-
methylphenyl)amine, CAS Registry No. 1159-53-1); mTTA
* Corresponding author e-mail: rohani@eng.uwo.ca.
10.1021/je0495785 CCC: $30.25 © 2005 American Chemical Society
Published on Web 10/04/2005

Journal of Chemical and Engineering Data, Vol. 50, No. 6, 2005 1795
Figure 1. (a) TTA, (b) mTTA, (c) mmTTA, and (d) mmmTTA molecule.
Table 1. Group Description, Volume, and Specific Area
Parameters30,36-39
there is no solid-solid-phase transition and no solid
solution formed. It should be noted that the first term on
the right-hand side of eq 1 is the dominant term. The
second and third terms are of comparable magnitude and
tend to cancel each other.30
main group
subgroup
Rk
Qk
CH2
CH2
0.674
0.901
0.531
1.039
1.266
1.266
1
0.540
0.848
0.400
0.660
0.968
0.968
1.200
1.432
1.204
CH3
ACH
ACH
Fugacities are related through the activity coefficient by
ACCH2 (para position)
ACCH2
ACCH3
ACCH3
OH
f2S
f2L
ACCH2 (meta position)
OH
CH3OH
AC2NH (arylamines with two
substitutions)
AC3N (arylamine with three
substitutions)
x2γ2 )
(2)
CH3OH
AC2NH
1.431
1.463
where x2 is the molar solubility of solute in solvent and γ2
is the activity coefficient of solute in the solvent. Therefore,
calculation of this ratio by eq 1 renders the mole fraction
of the solute in the solvent presuming that the activity
coefficient is known.
AC3N
1.866
1.592
General Synthetic Method. All reactions for the syn-
thesis of TTA, mTTA, mmTTA, and mmmTTA were carried
out in glassware under an inert atmosphere created by
argon. For synthesis, we used the copper-ligated synthesis
method, first proposed by Goodbrand and Hu3 and modified
by our team.25 The progress of each reaction was monitored
by HPLC (Varian, Inc., R-18, acetonitrile:methanol 1.0
mL/min:0.2 mL/min) until the reaction came to completion.
Samples were smaller than 1 mL, and their withdrawal
did not disturb the process.
Typical Synthetic Method for Tritolylamine (TTA).
A 500 mL round-bottom three-necked flask was used as
the reactor. The reactor was equipped with a paddle-like
mechanical stirrer, an argon gas purge, a Dean-Stark trap
under reflux condenser, and a heating mantle. At the outset
of the reaction, 100 g of 4-iodotoluene, 17.43 g of p-tolui-
dine, 110 g of KOH pellets, 1.16 g of CuBr, and 1.265 g of
2,2′-dipyridyl (ligand) were weighed and added to the
100 g of hydrocarbon solvent as the reaction medium. Using
a reflux condenser, as well as the choice of hydrocar-
bons, enabled us to control the temperature and maintain
isothermal condition during the course of the reaction.
After reaction completion, the mixture was cooled and
partitioned between dichloromethane and water for puri-
fication.
For the ideal case γ2 is assumed to be one. For the
nonideal solutions, γ2 has to be calculated. There are
many different methods such as the Scatchard-Hilde-
brand, NRTL, Van Laar, Wilson,31,32 UNIQUAC,33,34 and
UNIFAC30,35 methods that can be use for the calculation
of the activity coefficient of a solute in a solvent. The theory
behind the UNIQUAC model33-36 and its application to
arylamines has been discussed.15 However, the application
of the UNIFAC method for arylamine molecules will be
addressed in this paper. The UNIFAC method of estimation
for activity coefficient is suitable for creating a group
contribution correlation. Table 1 presents the group de-
scription and dimensionless r and q associated to each
individual group.30,37-39
Experimental Section
Materials. Hexane was purchased from Avocado Re-
search Chemicals Ltd. (Lancaster, PA). All other materials
were from Sigma-Aldrich Chemical Co. Inc. (Milwaukee,
WI) and used as received. The selected arylamine molecules
in this study were synthesized in our laboratory by the
method that is described in the General Synthetic Method
section. They were purified using the method described in
the Typical Synthetic Method for Tritolylamine section. All
solvents were HPLC grade.
Typical Purification Method for Tritolylamine
(TTA). The organic portion obtained from the synthesis

1796 Journal of Chemical and Engineering Data, Vol. 50, No. 6, 2005
Table 2. Melting Point, Boiling Point, Enthalpy of
Vaporization, and Enthalpy of Fusion of TTA, mTTA,
mmTTA, and mmmTTA
was diluted in toluene and then treated with a mixture of
acidic alumina and acid-leached bentonite at 80 °C for
about 2 h. The solution was filtered while hot, and then
the resulting mixture was further treated by a Rotavapor
system to remove all the liquid (dichloromethane and
toluene). The resulting viscous liquid was dissolved in
methanol and crystallized, except for mTTA and mmmTTA,
where a yellowish oil as a stable second-phase liquid was
formed. To overcome the oiling-out problem for mTTA and
mmmTTA, large quantities of methanol were used, reduc-
ing the concentration of mTTA and mmmTTA. After cooling
the mixture, crystals formed and were separated by filtra-
tion. The HPLC results confirmed the high purity of the
compound, close to 100%.
molecule
Tfus/°C
fusH/J‚g-1
TTA
mTTA
mmTTA
mmmTTA
115.59
69.43
300.89
252.5
15.36
56.70
75.53
315.94
264.2
15.78
89.5
91.83
274.15
241.1
15.01
39.81
45.48
294.84
130.8
10.91
∆
Tb/°C
∆
vapH/J‚g-1
0.5 a
δ/(J‚cm-3
)
a These results are calculated based on [(∆vapH - RT)/ν]0.5 where
vapH is the molar heat of vaporization, T is the melting point,
∆
and ν is the molar liquid volume in cm3‚mol-1
.
The optimization procedure was based on the minimiza-
tion of the errors between the calculated and experimental
values of the activity coefficients. Therefore, we have
Solubility Measurement. Several methods can be
utilized for the measurement of solubility: refractive
index,40,41 an online density meter,42-45 turbidity,46 spec-
trophotometer,47,48 NMR,47 HPLC,48 GC,48 gravimetric,34
and FTIR. We used the gravimetric method.
n
min J )
(γe2x,kp - γcalc 2
)
2,k
(3)
∑
amn,anm
Solubility Measurement Using Gravimetric Method.
A number of 5 mL screw-capped vials were prepared. Each
vial was weighed and marked. Different amounts of
crystals were added to the vials and then weighed. An
approximately identical volume of the solvent (under
investigation) was added to each vial and weighed. Vials
were immersed in a constant-temperature bath while
shaking. The temperature was gradually increased by 0.1
°C every (30 to 45) min to find the saturation temperature
by visual observation. At the saturation point, no crystals
were observed in the solution. A focused light (Leica CLS
150) was applied for visual monitoring and reducing the
errors associated in this step. It was found that (30 to 45)
min of shaking provided sufficient time for dissolution of
the samples at each temperature increment.
Errors originate from different sources related to the
measurement of solubility and thermal parameters. In
solubility measurement, errors associated with weighing
were minimized by using a precise balance (Metller Toledo,
AX205) with a resolution of ( 0.01 mg. The precision of
the thermometer was ( 0.1 °C. Error associated with
evaporation of solvents was minimized by employing tightly
closed screw-cap vials. The largest experimental error was
attributed to the exact determination of the saturation
temperature by visual inspection. This error was minimized
using a small temperature increment (0.1 °C) and allowing
enough time, (30 to 45 min) for the dissolution of solids to
take place.
k)1
where γe2x,kp is the experimental activity coefficient of solute
calc
2,k
based on the solubility data and γ
is the calculated
activity coefficient. Minimization was carried out by using
the function “fmincon” in Matlab (Mathwork, Massachu-
setts).
Results and Discussion
The solubility of TTA in 12 solvents was reported
previously by our group.15 The solvents were chosen to
cover a wide range of polarity index. From those solvents,
methanol, hexane, and benzene were selected for further
solubility studies. Some of the data are repeated here for
comparison with the solubility of structurally similar
arylamine molecules.
Solubility depends on the molecular attractive forces
between the solute and the solvent molecules. The energy
of vaporization is related to the molecular forces between
solute molecules. According to the results of the differ-
ential scanning calorimeter (DSC) (Table 2), the order of
enthalpy of vaporization (∆vapH) of these arylamine mol-
ecules is
∆vapH (mTTA) > ∆vapH (TTA) > ∆vapH (mmTTA) >
∆
vapH (mmmTTA)
In DSC analysis, although the crucible of sample was
not thermally isolated, using a reference crucible mini-
mized the error. The calibration of the DSC instrument
(Mettler Toledo, Switzerland) was performed using pure
indium. The acceptable deviation in enthalpy of fusion was
27.85 J/g to 29.05 J/g, and deviation in temperature of
melting was 156.3 °C to 159.9 °C. Precise weighing of
samples ensured minimizing the errors associated with the
differential calorimetry (DSC).
This shows that mTTA has the strongest intermolecular
forces, while mmmTTA has the weakest. Since there is no
hydrogen bonding sites in the solute molecules, the van
der Waals or dipole-dipole interactions must affect the
solubility. Therefore, the tendency of these molecules
dissolving in polar protic solvents is minimal. This suggests
that the expected solubility in nonpolar solvents such as
hexane or benzene must be high and follow
w*mmmTTA > w*mmTTA > w*TTA > w*mTTA
Optimization of the Adjustable Parameters of
Activity Coefficient Model
Using the experimental thermal properties of pure solids
as well as the experimental solubility data, the activity
coefficients of selected arylamine molecules in different
solvents were calculated. The activity coefficients were then
used to find the adjustable parameters of the UNIQUAC
and the UNIFAC models by minimization procedure. These
parameters can be used for further equilibrium calculation
(e.g., vapor-liquid equilibrium) for highly nonideal solu-
tions.
, which was confirmed by our experimental data. w*,
saturation concentration, represents mass in grams of
solutes per 100 grams of the solvent. In some references
C* is used instead. In crystallization, usually, the unit of
solubility is expressed in terms of grams of solute per 100
grams of solvents is used. However, in thermodynamic
equations, mole fraction or mole per volume is the common
unit. These units are interchangeable. The following equa-
tions can be used to calculate the solubility (w) in terms of

Journal of Chemical and Engineering Data, Vol. 50, No. 6, 2005 1797
Figure 2. Experimental solubility of selected arylamines in
Figure 3. Experimental solubility of selected arylamines in
hexane: 0, w TTA/(g of TTA/100 g of hexane); ], w mTTA/(g of
mTTA/100 g of hexane); 4, w mmTTA/(g of mmTTA/100 g of
hexane); ×, w mmmTTA/(g of mmmTTA/100 g of hexane).
benzene: ], w TTA/(g of TTA/100 g of benzene); [, w mTTA/(g of
mTTA/100 g of benzene); 0, w mmTTA/(g of mmTTA/100 g of
benzene); *, w mmmTTA/(g of mmmTTA/100 g of benzene).
Table 3. Cp Equation of Arylamines in Solid and Liquid
Phasea
stitution in the para position increases the electron cloud
over the nitrogen atom and therefore increases the dipole
moment of the molecule. On the other hand, substitution
in the meta position does not affect the electron cloud over
nitrogen. Therefore, it can be speculated that TTA has a
stronger dipole moment as compared to mmmTTA and,
consequently, a stronger bond energy than the van der
Waals forces operating in mmmTTA. In addition, placing
all methyl groups in the meta position reduces the volume
of the molecule, and they may act like a shield for the
nitrogen atom. Therefore, intermolecular forces between
molecules of solutes decrease and lead to an increase in
the solubility. In mTTA, there is both asymmetry and the
effect of two para substitutions that make the molecular
dipole-dipole strong, leading to the least solubility in
nonpolar solvents. For mmTTA asymmetry exists, and it
affects the polarity of the molecules. On the other hand, it
has only one para substitution. From the results for
mmTTA and mTTA, it may be concluded that the effect of
asymmetry is less than the effect of the dipole moment
caused by the substitution of an electron donor compound
in the para position. Figures 2 and 3 demonstrate the effect
of the polarity of the solvent. Increasing the polarity of the
solvent from polarity index 0.4 (solubility parameter 14.9
(J/cm3)0.5) for hexane to polarity index 2.7 (solubility
parameter 18.2 (J/cm3)0.5) for benzene, a large difference
between the solubility of mmTTA and TTA molecules is
noticed. Table 4 presents the solubility correlations for
different arylamines and their validity range.
temp
validity
range
component phase A*10+6
B*10+3
C
R2
K
TTAb
solid
liquid
solid
liquid
solid -1559.4
liquid -203.13
19.08
97.81
2087.8 -1288.00
-4.96 1.83
-12.96
-26.05
3.58 0.92 298 to 373
3.35 0.80 393 to 413
199.87 0.92 298 to 325
1.49 0.99 339 to 393
mTTA
mmTTA
1039.20 -172.72 0.99 330 to 340
146.80 -26.02 0.85 365 to 372
mmmTTA solid
liquid
844.16 -459.79
59.33 -40.94
66.79 0.94 240 to 306
11.41 0.99 336 to 381
a Equation is in the form: Cp/J‚g-1‚K-1 ) A(T2/K2) + B(T/K) +
C. b These results are from ref 15.
g of solute/100 g of solvent using the saturation mole
fraction of the solute, x2:
x2
x × Msolute
x )
and w )
× 100
1 - x2
Msolvent
where M is the molar mass (g/mol).
Figures 2 and 3 present the experimental solubilities of
the studied arylamines in benzene and hexane, respec-
tively. The raw solubility data of all the arylamine mol-
ecules studies are listed in Table 4.
There is a huge difference between the enthalpy of
vaporization of mmmTTA and TTA although both have
symmetrical structures, suggesting that the intermolecular
forces in mmmTTA are much weaker than in TTA. Sub-
Although we could measure the solubility of TTA and
mmTTA in methanol (see Figure 4), the attempts to find
Table 4. Experimental Solubility Data for Hexane (1), Methanol (2), and Benzene (3)a
system
t/°C
w
system
t/°C
w
system
t/°C
w
mTTA + 1
23.5
29.0
46.5
0.04
0.08
0.33
mTTA + 2
na
na
mTTA+3
5.0
16.44
19.23
30.36
34.05
56.17
60.55
66.75
86.97
89.66
123.18
185.09
238.25
333.12
16.0
43.0
54.5
5.0
mmTTA + 1
19.0
19.5
22.5
27.0
30.0
20.5
21.7
25.5
29.3
33.0
8.70
mmTTA + 2
15.5
19.0
26.0
30.7
40.5
na
0.43
0.49
0.63
0.84
1.18
na
mmTTA + 3
9.31
6.9
9.0
9.37
12.25
12.96
23.81
28.28
44.39
71.08
94.28
15.9
17.0
12.0
16.5
19.0
24.0
mmmTTA + 1
mmmTTA + 2
mmmTTA + 3
a w is g of solute/100 g of solvent. na is not available.

1798 Journal of Chemical and Engineering Data, Vol. 50, No. 6, 2005
Figure 6. Comparison of ideal solubility of mmTTA with experi-
Figure 4. Experimental solubility of selected arylamines in
methanol: [, w TTA/(g of TTA/100 g of methanol); ], w mmTTA/
(g of mmTTA/100 g of methanol).
mental results in methanol, hexane, and benzene: *, x mmTTA/
(mol of mmTTA/mol of solution of methanol); 9, x mmTTA/(mol of
mmTTA/mol of solution of benzene); 2, x mmTTA/(mol of mmTTA/
mol of solution of hexane); s, UNIQUAC; -, the ideal law.
Table 5. Pure Component Volume Constant (r) and Pure
Component Area Parameter (q) Used in Calculation of
the UNIQUAC Parameters
molecule
r
q
molecule
r
q
hexane
benzene
methanol
TTA
4.499 3.852
3.190 2.400
1.432 1.432
12.041 9.296
mTTA
12.041 9.296
12.041 9.296
mmTTA
mmmTTA 12.041 9.296
Table 6. UNIQUAC Method Adjustable Parameters,
Minimized Value J ) ∑nk)1 (γexp - γcalc
)
and Average Error
2
2,k
2,k
) (∑nk)1 (Cexp - Ccalc)2)/na
solution
J minimized average
mixtureb
a12/K
a21/K
value
error
Figure 5. Oiling-out problem: oily mTTA in methanol.
TTA + 1c
420.31 -241.71
0.12
540.43
0.01
1.73
TTA + 2c
204.89
653.86
-90.83
0.01
the solubility of mTTA and mmmTTA in methanol was not
successful since they formed an oily phase that was stable
in the solvent (liquid phase). Figure 5 shows this phenom-
enon.
Ideal Solubility. As it was stated earlier, in order to
use eq 1, thermal properties of the solute are needed. The
differential scanning calorimeter was used to measure
these properties. Specific heats calculated from DSC stud-
ies are reported in Table 3. The DSC results also confirmed
that there is no solid-solid enantiotropic transition over
the temperature range studied for TTA, mTTA, mmTTA,
and mmmTTA.15,49
TTA + 3c
23.09
1387.72 -193.41
36.94
mTTA+ 1
0.25
0
mTTA + 2
-20.77
-8.20
284.82
12.41
5.69E5
0.01
0.16
177.16
0.49
0.38
0
mmTTA + 1
mmTTA + 2
mmTTA + 3
mmmTTA + 1
mmmTTA + 2
0
304.29 -124.91
0
997.57
127.15
207.68
0.53
125.60
-43.20
0
0
0.01
a γe2x,kp is the experimental activity coefficient of solute based on
the solubility data; γ2ca,klc is the calculated activity coefficient; Cexp
(g of solute/100 g of solvent) is the experimental concentration;
and Cest/(g of solute/100 g of solvent) is the estimated concentra-
tion. b 1, benzene; 2, hexane; 3, methanol. c Data from ref 15.
/
Using the thermal properties in eqs 1 and 2 and
assuming the activity coefficient is equal to 1 renders the
ideal solubility. Figure 6 compares the experimental and
theoretical solubilities of mmTTA in methanol, hexane, and
benzene, expressed in mole fraction. Methanol and hexane
show lower solubility than the predicted ideal behavior.
However, the prediction for benzene is different. For
solution of mmTTA in benzene γ2 is less than one, and
corresponding solubility is more than the ideal solubility.
In solutions where only dispersion forces are important,
γ2 is generally larger than unity; therefore, solubility is
lower than that corresponding to the ideal behavior.
Methanol and hexane show the same behavior, but benzene
has the activity coefficient less than unity. Benzene has
partially a similar structure with mmTTA; therefore, the
solution of mmTTA in benzene shows less deviation from
the ideal behavior.
using eq 3 were calculated. The calculation was based on
the procedure described in our previous contribution15 and
using pure component van der Waals volume (r) and pure
component area parameters (q) in Table 5. Results shown
in Table 6 include minimized function values and average
errors. The estimated solubility of mmTTA in methanol,
hexane, and benzene by the UNIQUAC method is shown
in Figure 6.
The UNIFAC R and Q parameters and a12 and a21 are
listed in Tables 1 and 7, respectively. The group interaction
parameters were calculated using the minimization algo-
rithm (eq 3). It was necessary to calculate activity coeffi-
cients from the experimental solubility data and thermal
properties in order to calculate the group interaction
parameters. The functional groups that were considered
in this work were those given in Table 1. While each group
listed has its own values of R and Q, the subgroups within
the same main group (like CH2 and CH3 in group CH2) are
assumed to have the same group energy interaction
parameters.37
Solubility Prediction by the UNIQUAC and
UNIFAC Method. The two adjustable parameters of the
UNIQUAC, amn and anm (m ) 1 and n ) 2) for TTA, mTTA,
mmTTA, and mmmTTA in hexane, methanol, and benzene

Journal of Chemical and Engineering Data, Vol. 50, No. 6, 2005 1799
Table 7. Adjustable UNIFAC Energy Parameters for Pairs Obtained by Minimization (the unit of the numbers is in K)
AC3N
ACH
p-ACCH2
meta ACCH2
CH2
OH
AC3N
0
-2303.0a
0
-2261.2a
167
-2219.5a
-1338.3a
-167.3a
0
-2343.0a
-11.12
-69.7
-2433.3a
0
2500.0a
636.1
803.2
2468.6a
986.5
0
ACH
-2224.7a
-437.5a
-224.3a
541.3a
p-ACCH2
meta ACCH2
CH2
-146.8
-1662.4a
61.13
0
-1993.5a
76.5
-371.1a
-257.6a
OH
1903.2a
89.6
25.82
156.4
a Calculated in the present study.
Figure 7. 3,3′-Dimethyltriphenylamine (phenyl-di-m-tolylamine)
molecule.
Figure 8. UNIFAC solubility prediction for phenyl-di-m-toly-
laminehexane solution: ], experimental data; s, estimated data
by UNIFAC; x/(mol of solute/mol of solution in hexane).
Based on previous studies by Fredenslund et al.,35
interaction parameters for methyl substitution in the meta
position and para position are the same. An exception to
this rule is noted in the solubility of TTA and mTTA
molecules that have the same group contributions. In both
molecules there are 12 ACH (aromatic carbon), 3 ACCH3
(aromatic methyl substitution), and 1 AC3N that is a core
amine molecule with three aryl substitutions. However,
there is a big difference in their solubility. Therefore,
methyl groups substituted in the meta or para positions
should be differentiated.
The resulting parameters can be used in calculation of
the activity coefficient and consequently the solubilities of
the arylamine molecules that have similar constitutional
groups. To check the predictive capability of the UNIFAC
model using the estimated constitutional group interaction
parameters, we synthesized and purified 3,3′-dimethyl-
triphenylamine (Figure 7) in our lab. This molecule has
similar constitutional groups to TTA and m-TTA. It con-
sists of 13 ACH (aromatic carbon), 2 meta ACCH3 (aromatic
methyl substitution), and 1 AC3N that is a core amine
molecule with three aryl substitutions. Hexane consists of
2 CH3 and 4 CH2 molecules. We measured the solubility
of this arylamine molecule in hexane and also predicted
its solubility by using the UNIFAC method with the data
presented in Tables 1 and 7. As it is shown in Figure 8,
there is a good agreement between the predicted and
experimental solubility results. The R2 value for this
estimation is 0.9926, and the average error for the data
based on the formula given in Table 6 is 0.
by UNIFAC model. Ideal solution theory is not capable of
precisely estimating the solubility of arylamines in polar
solvents. However, it can be used for solubility estimation
of arylamines in nonpolar-aprotic solvents.
Melting point, boiling point, enthalpies of vaporization,
and fusion of these molecules were found and reported. As
a result, it can be concluded that replacing each electron
donor group like a methyl substitution from the para
position to the meta position may render a higher solubility
in nonpolar solvents and reduces the heat of vaporization
with the exception of the first substitution. Also from our
results, it can be concluded that the effect of substitution
on the solubility is more than the effect of asymmetry of
dipole-dipole formation.
Acknowledgment
The authors thank Dr. Carol Jennings, Dr. Marko Saban
and their co-workers at Xerox Research Centre (XRCC) in
Mississauga for generating the data listed in Table 2.
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Received for review November 30, 2004. Accepted August 21, 2005.
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