Solubility of cyclohexyl-phosphoramidic acid diphenyl ester in selected solvents

Article abstract of DOI:10.1016/j.molliq.2015.05.024

Cyclohexyl-phosphoramidic acid diphenyl ester (CPADE) was synthesized and characterized by elemental analysis (EA), mass spectrum (MS), infrared spectroscopy (IR) and nuclear magnetic resonance (NMR). The thermostability of CPADE was measured by thermogra

Full text of DOI:10.1016/j.molliq.2015.05.024

Journal of Molecular Liquids 211 (2015) 527–533
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Solubility of cyclohexyl-phosphoramidic acid diphenyl ester in
selected solvents
⁎
Qun-an Zhang, Chao-jun Du
School of Biochemical and Chemical Engineering, Nanyang Institute of Technology, Nanyang 473000, People's Republic of China
a r t i c l e i n f o
a b s t r a c t
Article history:
Cyclohexyl-phosphoramidic acid diphenyl ester (CPADE) was synthesized and characterized by elemental
analysis (EA), mass spectrum (MS), infrared spectroscopy (IR) and nuclear magnetic resonance (NMR). The
thermostability of CPADE was measured by thermogravimetric analysis (TGA) and the melting temperature
and the fusion enthalpy of CPADE were evaluated by using differential scanning calorimeter (DSC). The
solubilities of CPADE in selected solvents were obtained by a gravimetric method. The experimental data were
well correlated by the Wilson, nonrandom two liquid (NRTL), and universal quasichemical (UNIQUAC) equations.
And the dissolution enthalpy, entropy, and the molar Gibbs energy of CPADE in the selected solvents are also
calculated by the van't Hoff equation.
Received 12 February 2015
Received in revised form 8 May 2015
Accepted 13 May 2015
Available online xxxx
Keywords:
CPADE
Solubility
© 2015 Elsevier B.V. All rights reserved.
Flame retardant
Phase equilibrium
1. Introduction
potential candidates, because these materials, working as the modes
of condensed phase action and gas phase action during the flame
Organic polymer materials that greatly improve the quality of mod-
ern life are used in many fields because of their good heat endurance,
chemical corrosion resistance, desired mechanical properties and so on.
Unfortunately, most of the polymers are flammable, which limited their
applications [1]. So the polymer materials with high heat-resistant and
flame-retardant properties are urgently required. The well-known meth-
od to enhance the flame retardancy is to blend the flame retardant addi-
tives into the polymer materials. The flame retardants mainly work as
two modes of actions, condensed phase and/or gas phase activities [2].
The condensed phase effects of flame retardants are relevant to a char
layer which can obstruct the polymer surface from heat and air [3–5],
while the gas phase effects are related to the mechanism of hydrogen
and hydroxyl radical scavengers [6,7].
In general, the halogenated compounds with the antimonous oxide
are often applied to give the polymers flame retardancy because of
their good flame-resistant characteristics. However, this material causes
environmental problems as toxic combustion products are released
during combustion [8]. Hence, non-halogenated based flame retardants
become increasingly popular alternatives in replacing the halogenated
flame retardants. Among the available non-halogenated based flame
retardants, phosphorus containing compounds are often regarded as
retardancy process, typically do not generate any toxic gas [9]. In recent
years, nitrogen–phosphorus flame-retardant synergism is recognized
by the researchers [10]. The compounds containing phosphorus and
nitrogen are usually named intumescent flame retardants owing to a
foam char layer in the condensed phase [11]. The incombustible gases
without toxic smoke and fog generated from these materials can dilute
the concentration of the oxygen near the flame and foam superior
protective barriers to the main materials against flame and heat while
heating [12,13]. Now, most of the literatures on the halogen-free retar-
dants are deeply relevant to the phosphorus–nitrogen-based products.
Furthermore, they are believed to be the biggest growing share of the
flame retardant market in the future [8].
Cyclohexyl-phosphoramidic acid diphenyl ester (CPADE)
(C18H22O3PN, CAS Registry No. 6372-21-0) is one of versatile intumes-
cent flame retardants; its chemical structure is shown in Fig. 1.
This compound has a bright future, owing to its powerful flame
retardancy to the polymers. It was widely used in Ethylene-
Propylene-Diene Monomer (EPDM) [14], thermoplastic polyolefin
[15], poly(styrene–ethylene/butene–styrene) (SEBS) [16], polyethylene
[17,18], epoxy resins [19], polycarbonate (PC) [20] etc. However, some
impurities have greatly affected its thermal property and applications.
Thus, the purification process employed to obtain CPADE with high
purity is very significant.
In the industry, the pure production of CPADE is always obtained by
crystallization which is an important separation and purification process
[21]. The (solid + liquid) equilibrium (SLE) measurements of CPADE in
⁎
Corresponding author.
E-mail address: chaojundu@126.com (C. Du).
http://dx.doi.org/10.1016/j.molliq.2015.05.024
0167-7322/© 2015 Elsevier B.V. All rights reserved.

528
Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
N
P
O
O
O
Fig. 1. Structures of the cyclohexyl-phosphoramidic acid diphenyl ester (CPADE).
Fig. 2. Schematic diagram of the experimental apparatus: 1, thermostatic water-circulator
bath; 2, sample gauge; 3, jacketed glass vessel; 4, magnetic stirrer; 5, magnetic agitator
drive; 6, thermometer; 7, condenser.
organic solvents are helpful to determine and estimate some crystalliza-
tion parameters and reaction kinetics or thermodynamics study. Howev-
er, there has no report as to the solubilities of CPADE in selected solvents.
In this work, CPADE was synthesized and characterized. To achieve more
thermodynamic data on the crystallization of CPADE from some organic
solvents, the solubilities of CPADE in the ten selected organic solvents
were measured. The Wilson [22], nonrandom two-liquid (NRTL) [23],
and UNIQUAC [24] models were employed to fit the solubility data
based on the pure component thermophysical properties. Comparison
and discussion of the solubility were also presented in this study. And
the dissolution behaviors of CPADE in the selected solvents were also
estimated by van't Hoff equation [25].
2.2. Apparatus and procedure
The experimental apparatus for the solubility measurements was
the same as it was described in our previous work [26]. The diagram-
matic sketch of the experimental apparatus was shown in Fig. 2.
A jacketed equilibrium cell was applied for the solubility measure-
ments with a working volume of 120 mL and a magnetic stirrer, and a
circulating water bath was used with a thermostat (type 50 L, made
from Shanghai Laboratory Instrument Works Co., Ltd.) with an uncer-
tainty of 0.01 K so that the system could reach and keep the required
temperature. To prevent the evaporation of the solvent, a condenser
was introduced. An analytical balance (type TG328B, Shanghai Balance
Instrument Works Co., Ltd.) with an uncertainty of 0.1 mg was used
during the mass measurements.
2. Experimental
2.1. Materials
Fourier transform infrared (FTIR) spectrum was performed on a
Perkin Elmer 400 spectrometer (Connecticut, USA). The melting point
and enthalpy of fusion were measured with a DSC Q100 (TA Instru-
ments) differential scanning calorimeter (DSC) in flowing nitrogen at
a heating rate of 10 K·min−1. The uncertainty of DSC measurement
was the same as it was described in the literature [26]. The elemental
Diphenyl chlorophosphate was purchased from Zhangjiagang Xinyi
Chemical Co., Ltd. and purified by distillation before used. Triethylamine
and cyclohexylamine were kindly supplied by Weisi Chemical Reagents
Co., Ltd. All of the organic solvents used for the experiments were analyt-
ical grade reagents, which were purchased from Beijing Chemical Factory.
Purities and sources of all the materials used in this study are shown in
Table 1.
Table 1
0.035
0.030
0.025
0.020
0.015
0.010
0.005
0.000
The source, mass purity and purification method of the sample used in this paper.
Chemical name
Source
Mass
purity method
Purification
Diphenyl
chlorophosphate
Triethylamine
Zhangjiagang Xinyi Chemical
Co., Ltd
Weisi Chemical Reagents Co.,
Ltd
Beijing Chemical Factory
Weisi Chemical Reagents Co.,
Ltd
Beijing Chemical Reagents Co.,
Ltd
Beijing Chemical Factory
Beijing Chemical Factory
Beijing Chemical Factory
Beijing Chemical Factory
Beijing Chemical Factory
Beijing Chemical Factory
Sigma-Aldrich
Beijing Chemical Factory
Beijing Chemical Factory
As prepared
N 0.990 Distillation
N0.990 None
Chloroform
Cyclohexylamine
N0.995 None
N0.990 None
Ethyl acetate
N0.995 None
Acetone
Ethanol
N0.995 None
N0.995 None
N0.995 None
N0.998 None
N0.995 None
N0.995 None
N0.990 None
N0.995 None
N0.995 None
N0.990 Recrystallization
Methanol
Tetrahydrofuran
Dichloromethane
Benzene
Adipic acid
Toluene
300
310
320
330
T / K
340
350
360
Acetonitrile
CPADE
Fig. 3. Comparison of the literature and experimental mole fraction of adipic acid solubility
(x) against temperature in water: ■, literature; △, this work.

Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
529
analysis was performed on an Elementar Vario EL element analyzer, 1H
0
-1
-2
-3
-4
-5
-6
-7
NMR and 13C NMR spectra were obtained with a Bruker ARX-400.
Thermogravimetric analysis (TGA) was obtained with an SDT Q600
(TA Instruments) thermogravimetric analyzer at a heating rate of
10 K·min−1 under nitrogen atmosphere.
2.3. Synthesis and characterization of CPADE
CPADE was prepared by the method similar to our previous work [27].
To a dry chloroformic solution of (C6H5O)2P(O)Cl, a dry chloroformic
solution of cyclohexylamine and triethylamine (1:1:1.1 molar ratio) was
added dropwise over a period of 1 h at 273 K. After 6 h of stirring, the
solvent was removed at reduced pressure and recrystallization of
the residual material after being washed with cold distilled water from
acetone afforded CPADE as a white crystalline solid. The mass fraction
purity of PAETE was about 0.99.
300
320
340
360
380
400
T
/ K
EI mass spectrum of CPADE can be seen in Fig. S1. The intensity (%)
m/z of CPADE is 332.3 (M+). Elemental analysis (%, calcd): C, 65.25%
(65.37%); H, 6.69% (6.72%); N, 4.23% (4.28%). In Fig. S2, the infrared
spectrum of CPADE contains characteristic absorptions at 3216 cm−1
for N–H stretching, 3072 cm−1 for aromatic –C_C–H stretching, 2933
and 2854 cm−1 for –HC–H stretching, ring carbon–carbon stretching
vibrations occur in 1589, 1489 and 1455 cm−1, 1194 cm−1 for the
P_O stretching, 1024 cm−1 for the P–N stretching, 1236 cm−1 for the
C–N stretching and 904–955 cm−1 for the P–O–Aryl stretching. The
1H NMR spectrum of CPADE is shown in Fig. S3 of the Supporting infor-
mation. 1H NMR (400 MHz, CDCl3) δ 7.92–7.00 (m, 10H), 3.35 (d, J =
11.9 Hz, 1H), 2.03 (d, J = 13.2 Hz, 1H), 1.80–1.22 (m, 10H). Fig. S4
presents 13C NMR (400 Hz, CDCl3) spectrum of CPADE. The chemical
shifts of carbons with different chemical environments in CPADE struc-
ture are 25.03, 25.35, 35.50, 51.30, 120.25, 124.83, 129.67, and 151.06,
respectively.
Fig. 4. Experimental heat Q flow from DSC measurement of CPADE.
3. Results and discussion
3.1. Evaluation of pure component properties
From the results achieved by DSC and TGA analysis, as shown in
Fig. 4 and Fig. 5, the melting point was 381.69 K 0.05 K; the enthalpy
of fusion of CPADE was 27.57 kJ·mol−1. TGA results illustrate that there
is one single step decomposition, and about 1% char residue for CPADE
which shows that the CPADE should be used as intumescent flame
retardant together with the char-forming agent. The entropy of fusion
of CPADE ΔfusS was 72.24 J/(mol·K), which was calculated by Eq. (1).
Δ
Tm
f usH
Δ
f usS ¼
:
ð1Þ
2.4. Solubility measurement
A gravimetric method [26] was used to measure the solubilities of
the CPADE in methanol, acetone, acetonitrile, tetrahydrofuran, ethyl
acetate, chloroform, ethanol, benzene, toluene and dichloromethane.
For each measurement, an excess mass of CPADE was introduced into
a known mass of solvent. Then the equilibrium cell was heated and
stirred at a constant temperature. After at least 3 h (different dissolution
times were tested to determine the suitable equilibrium time. It was
found that 3 h was enough to reach equilibrium), the stirring was
stopped, and the solution was kept still until it was clear. Then, samples
of the clear saturated solution were withdrawn by a preheated injector
with a cotton filter. The mass of the saturated clear solution sample was
determined with the analytical balance. Each solution sample was dried
in a vacuum oven for at least 3 days to evaporate all solvents. The mass
of the samples was weighed repeatedly throughout the drying process
to make sure that no solvent remained. The weights were recorded
after the solvents have been completely evaporated. During our experi-
ments, three parallel measurements were performed at the same compo-
sition of solvent for each temperature, and an average value is given. FTIR
was used to analyze the sample to ensure that no thermal decomposition
effect had occurred on PNBE and no solvate material was generated
during the experiments. Finally the sample was characterized by DSC to
ensure that the solute maintained the crystalline form under all the
experimental conditions. Based on error analysis and repeated observa-
tions, the estimated relative uncertainty of the solubility values was
ur(x) = 0.02.
3.2. Solubility data and correlation
The measured solubility data of CPADE in acetonitrile, methanol,
acetone, tetrahydrofuran, chloroform, ethyl acetate, toluene, ethanol,
benzene and dichloromethane are shown in Table 2. The mole-fraction
solubility data of CPADE in the selected solvents are plotted in Fig. 6.
100
80
60
40
20
0
250 300 350 400 450 500 550 600 650 700
The solubility of adipic acid in water was obtained by using
experimental apparatus and illustrated in Fig. 3. Fig. 3 showed that
T/K
the experimental data agreed well with the data in the literature28
,
thus the reliability of our experimental setup was verified.
Fig. 5. TGA thermograms of CPADE under N2.

530
Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
Table 2 (continued)
Table 2
Mole fraction solubilities (x) and activity coefficients (γ) of CPADE in the selected solvents
at temperature T and pressure p = 0.1 MPa.a
Solvent
T/K
γ
102x
338.15
343.15
293.15
298.15
303.15
313.15
323.15
333.15
343.15
278.15
283.15
288.15
293.15
298.15
303.15
308.15
0.65709
0.65599
1.4871
1.4091
1.2787
55.03
63.59
5.395
6.883
9.112
15.43
25.87
40.86
61.13
8.840
10.22
12.91
15.53
18.02
21.56
26.04
Solvent
T/K
γ
102x
4.110
Methanol
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
343.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
343.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
1.9518
1.8203
1.6606
1.4566
1.3676
1.2122
1.0838
0.95454
0.87751
1.8259
1.5882
1.4629
1.2808
1.2369
1.0438
1.0013
0.98926
6.9513
5.6787
4.7060
3.7544
3.1731
2.5720
2.1602
1.8069
1.6352
1.3736
1.1650
0.47651
0.50460
0.50880
0.51754
0.51964
0.52415
0.54749
0.53219
0.55079
2.6308
2.4579
2.1216
1.9294
1.7473
1.5249
1.3814
1.2710
1.1842
1.0599
0.98010
0.38795
0.41548
0.43873
0.44499
0.46890
0.48727
0.50015
0.51719
2.2387
1.9802
1.8268
1.6053
1.4303
1.2748
1.1678
1.0600
0.9856
0.8911
1.0420
0.97824
0.92121
0.87495
0.84909
0.78048
0.78423
0.71749
0.68310
Toluene
5.328
7.017
9.553
12.08
16.10
21.16
28.09
35.56
4.394
6.107
7.965
10.86
13.36
18.70
22.90
27.11
1.154
1.708
2.476
3.706
5.208
7.588
10.62
14.84
19.09
26.32
35.81
16.84
19.22
22.90
26.89
31.80
37.24
41.89
50.39
56.66
3.049
3.946
5.492
7.212
9.457
12.80
16.60
21.10
26.35
34.11
42.56
20.68
23.34
26.56
31.27
35.24
40.05
45.85
51.85
3.585
4.898
6.378
8.669
11.55
15.31
19.64
25.30
31.67
40.58
7.699
9.915
12.65
15.90
19.46
25.01
29.24
37.37
45.69
1.0708
0.88656
0.76373
0.68232
0.49305
0.52642
0.51063
0.51669
0.53811
0.54057
0.53439
Dichloromethane
Acetone
a
The standard uncertainties u is u(x) = 0.0002.
Acetonitrile
For each solvent researched, the solubility of CPADE increases as
the temperature rises, but the systems behave differently. At a given
temperature, the order of solubility of CPADE is as follows:
chloroform
N tetrahydrofuran N dichloromethane N benzene N
toluene N acetone N methanol N ethanol N ethyl acetate N acetonitrile.
The solubility of CPADE in acetonitrile shows the lowest value, and
in chloroform gives the highest value. The higher solubility value in
chloroform and dichloromethane than other solvents but tetrahy-
drofuran might be owing to the strong electronegativity of elemental
chlorine. As there coexist both NH group and P_O group in CPADE, it
can be the proton donor or acceptor. The fact that the solubility value
in tetrahydrofuran is higher than that in the alcohols shows the
property of the proton donor of NH group in CPADE. Accordingly, it
might be the hydrogen bond between tetrahydrofuran and CPADE
molecules that play an important role in contributing to the higher
solubility of CPADE in tetrahydrofuran in the ten solvents. From the
solubility data, tetrahydrofuran, chloroform and dichloromethane ap-
pear to be more appropriate solvents for the crystallization of CPADE.
The three solvents are also suggested as the appropriate reaction
solvents.
Tetrahydrofuran
Ethyl acetate
From the thermodynamic principles, solid–liquid phase equilibrium
can be described as follows [29]:
Chloroform
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
Δ
RTm
f usH
1
x1γ1
T
T
ΔtrH
RTtr
T
T
ΔCp
R
T
Tm
T
ln
¼
m −1
þ
tr −1
−
ln
þ
T
m −1
ð1Þ
where, Tm is the melting temperature of the solute, respectively; ΔfusH,
and ΔHtr stand for enthalpy of fusion of the solute at melting tempera-
ture and enthalpy of solid–solid phase transition of the solute, respec-
tively; Ttr denotes temperature of phase transition and ΔCp denotes
heat capacity of the solute at melting temperature. Here, ΔHtr and ΔCp
can be neglected because no transition in CPADE solid phase occurs,
which is determined by the DSC throughout the whole experiments
[30]. And thus a simplified form of the solid–liquid phase equilibrium
equation can be written in the following form [31]:
Ethanol
Benzene
ꢀ
ꢁ
Δ
RTm
f usH
1
x1γ1
Tm
T
ln
¼
−1
:
ð2Þ
Based on the values of x1, Tm and ΔfusH, the activity coefficients of
CPADE in solid–liquid equilibrium can be calculated via Eq. (2) and are
also presented in Table 2.

Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
531
Table 3
The solubility of CPADE varying with temperature can be correlated
by the Wilson equation. In the binary system, Wilson model can be
shown in the following form:
Molar volume (V), UNIQUAC volume parameter (r), and surface parameter (q) values for
selected solvents.a
Solvent
106Vi/m3·mol−1
r
q
ꢀ
ꢁ
Λ12
Λ21
Methanol
Ethanol
40.70
58.52
64.43
52.68
98.59
81.94
80.66
89.48
106.6
73.93
275.9
1.4311
2.1055
2.2564
1.8701
3.4786
2.9415
2.8700
3.1878
3.9228
2.5735
1.432
1.972
1.988
1.724
3.116
2.720
2.410
2.400
2.968
2.336
lnγ1 ¼ − lnðx1 þ Λ12x2Þ þ x2
−
ð3Þ
ð4Þ
ð5Þ
x1 þ Λ12x2 x2 þ Λ21x1
Dichloromethane
Acetonitrile
Ethyl acetate
Tetrahydrofuran
Chloroform
Benzene
Toluene
Acetone
CPADE
ꢀ
ꢀ
ꢁ
ꢁ
ꢀ
ꢀ
ꢁ
ꢁ
v2
v1
λ
λ
12−λ11
RT
v2
v1
Δλ12
RT
Λ12
Λ21
¼
¼
exp
exp
−
−
¼
¼
exp
exp
−
−
v1
v2
21−λ22
RT
v1
v2
Δλ21
RT
:
12.326
13.09
Here, v1 and v2 denote the molar volumes of solute and solvent
a
Data from Prausnitz.26
respectively. Δλ11, and Δλ12 represent the cross interaction energy
parameters, (J·mol−1), which can be regressed from the experimental
data.
The NRTL activity coefficient model is used in this work to correlate
the experimental solubility data, which has been successfully used to
correlate the solid–liquid equilibrium for many nonideal solutions in
wide temperature ranges [32–34]. The NRTL model which is applied
to determine the activity coefficient of a solute in pure solvents can be
expressed as following:
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ϕ1
x1
z
2
θ
ϕ1
r
r2
C
lnγ1 ¼ ln
þ
q1 ln
þ ϕ2 l1− 1 l2
ð10Þ
ꢀ
ꢁ
τ21
τ12
R
lnγ1 ¼ −q1 lnðθ1 þ θ2τ21Þ þ θ2q1
−
ð11Þ
ð12Þ
θ1 þ θ2τ21 θ2 þ θ1τ12
"
#
ꢀ
ꢁ
G21
x1 þ x2G21
τ
12G12
2
lnγ1 ¼ x2 τ21
2 þ
ð6Þ
z
2
l1
l2
¼
¼
ðr1−q1Þ−ðr1−1Þ
ðr2−q2Þ−ðr2−1Þ
ðx2 þ x1G12
Þ
2
z
where G12, G21, τ12 and τ21 represent NRTL model parameters that
2
demand to be experimentally determined by
ꢀ
ꢀ
ꢁ
ꢁ
ꢄ
ꢅ
ꢅ
u12−u22
Δu12
RT
ꢂ
ꢃ
τ12 ¼ exp −
¼ exp
¼ exp
−
−
ð13Þ
ð14Þ
RT
Gij ¼ exp −aijτi
ð7Þ
ð8Þ
j
ꢄ
u21−u11
Δu21
RT
gij−gjj Δgij
τ21 ¼ exp −
:
τij
¼
¼
:
RT
RT
RT
In which, Δg12 and Δg21 refer to the two cross interaction energy
In which, Δu12(Δu21), z, Φ and θ denote two adjustable energy
parameters; the coordination number usually taken as 10; the volume
fraction and molecular surface fraction of solute or solvent, respectively.
Parameters r and q refer to the UNIQUAC volume parameter and surface
parameter of solvent and solute, which are listed in Table 3. The values
of r and q of solute can be obtained from the group volume parameters
(R) and surface parameters (Q) of the UNIFAC model, which are listed in
Table 4.
parameters (J·mol−1); a reflects the parameter related to the nonran-
domness in the mixture. a is chosen to be 0.3 as usual.
The mole fraction solubility data in the selected solvents were also
described by the UNIQUAC model in the following form:
C
R
lnγ1 ¼ lnγ1 þ lnγ1
ð9Þ
The cross-interaction parameters of the Wilson equation (Δλ12 and
Δλ21), the NRTL equation (Δg12 and Δg21), and the UNIQUAC equation
(Δu12 and Δu21) are written as the following Eq. (15):
70
65
60
55
50
45
40
35
30
25
20
15
10
5
kij ¼ αij þ βijT
ð15Þ
where k stands for any interaction parameter mentioned above. α and β
denote the parameters to be fitting the solubility data.
The parameters of the Wilson, nonrandom two-liquid (NRTL), and
UNIQUAC model which were obtained by fitting the experimental
solubility data and the relative standard deviations (RSDs) defined by
Table 4
Van der Waals group volume and surface area parameters for the UNIQUAC model.
0
Group
R
Q
280
290
300
310
320
330
340
350
(O–)(−O)P(_O)– a
1.9312
1.762
–CHNH–
ACH
AC
0.97950
0.53130
0.36520
0.67440
0.6240
0.4000
0.1200
0.5400
T
/K
Fig. 6. Mole fraction solubility (x) data of CPADE in selected solvents: □, methanol; ○,
acetone; △, acetonitrile; ▽, tetrahydrofuran; ☆, ethyl acetate; ▼, chloroform; ■, ethanol;
▲, benzene; ★, toluene; ◆,dichloromethane.
–CH2–
a
is taken from literature.27 The other values in this table are from literature. 26

532
Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
Table 6
The overall RSD% of different correlation models.
Wilson model
1.45
NRTL model
1.69
UNIQUAC model
1.95
Overall RSD%
Eq. (16) were used to compare the experiment data and the calculated
data by the models mentioned above.
1
"
#
ꢀ
ꢁ2
2
N
xi−xicacld
X
1
N
RSD ¼
ð16Þ
xi
i¼1
Herein, N, xi and xicacld denote the number of experimental points;
the experimental solubility data and the calculated solubility data by
the models, respectively.
The calculated parameters of all the models mentioned above are
listed in Table 5 together with the RSDs. The overall relative standard
deviations are displayed in Table 6. The results show that all the models
can describe the experimental data well with the optimized parameters.
The overall RSDs of the models are 1.45% (Wilson), 1.69% (NRTL) and
1.95% (UNIQUAC). For the CPADE systems, the Wilson model is better
than the other models in reproducing the temperature dependence of
solubility.
3.3. Calculation of dissolution enthalpy, entropy, and the molar gibbs
energy
The values of standard molar dissolution enthalpy and entropy at
saturation can be determined by the van't Hoff equation. The Gibbs
energy of solution at saturation can be calculated by Gibbs–Helmoholtz
equation,[35]
ΔH0d ΔS0d
lnx1 ¼ −
þ
ð17Þ
ð18Þ
RT
R
ΔG0d ¼ ΔH0d−TΔS0d:
The achieved dissolution enthalpy and entropy are listed in Table 7
and the Gibbs energy is plotted in Fig. S5. From the data in Table 7, the
ΔH0d of CPADE in each solvent is endothermic (ΔH0d N 0), which explains
the increasing solubility of CPADE with increasing temperature [36].
4. Conclusions
The CPADE was synthesized in this work. The solubility data of CPADE
in methanol, chloroform, acetone, ethyl acetate, acetonitrile, tetrahydro-
furan, ethanol, benzene, toluene and dichloromethane were obtained at
different temperatures. The melting temperature and the enthalpy of
fusion were measured by DSC. The order of the solubility of CPADE
is: chloroform N tetrahydrofuran N dichloromethane N benzene N
toluene N acetone N methanol N ethanol N ethyl acetate N acetonitrile.
The experimental data were correlated with the Wilson, nonrandom
two-liquid (NRTL), and UNIQUAC model. The results show that the
Wilson model is more suitable in determining the solubility of CPADE
compared with the other models. Based on the van't Hoff equation,
the dissolution enthalpy, entropy, and molar Gibbs free energy of
CPADE are calculated in different solvents.
Notes
The authors declare no competing financial interest.

Q. Zhang, C. Du / Journal of Molecular Liquids 211 (2015) 527–533
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533
Table 7
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pure solvents.
Solvent
ΔHd (K J/mol)
ΔSd (J/(mol × K))
[11] L.j. Chen, L. Song, P. Lu, G.X. Jie, Q.l. Tai, W.Y. Xing, Y. Hua, Prog. Org. Coat. 70
Methanol
Acetone
44.2
42.2
57.5
25.1
44.5
21.3
44.6
35.6
41.2
25.8
124.1
118.2
159.1
70.7
122.7
59.3
124.3
100.3
116.2
72.4
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Acetonitrile
Tetrahydrofuran
Ethyl acetate
Chloroform
Ethanol
Methyl acetate
Toluene
Dichloromethane
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Appendix A. Supplementary data
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Supplementary data of MS spectra of CPADE, IR spectra of CPADE, 1H
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