Experimental determination and model correlation for the solubilities of trialkyl phosphates in supercritical carbon dioxide

Article abstract of DOI:10.1039/c6ra10897k

The solubilities of a series of trialkyl phosphates in supercritical carbon dioxide have been investigated. The solubility measurement was carried out using a dynamic flow method. The measurements were performed at 313, 323 and 333 K and in the pressure range of 10 to 25 MPa. The trialkyl phosphates were found to be highly soluble in supercritical carbon dioxide and the solubilities were in the range of 0.01 to 0.1 mol fraction. The solubility of trialkyl phosphates increases with an increase in pressure at constant temperature. A reverse behavior was observed, wherein the solubilities decreased with increase in temperature in the investigated pressure region. At constant temperature and pressure, the solubilities of the trialkyl phosphates decrease with the alkyl chain length. The solubility data was found to be consistent with the Mendez-Teja model. The solubilities were correlated by the Chrastil model and an association model based on the van Laar activity coefficient model with absolute deviations of less than 10%. A key result is that the model parameters based on the association model varied linearly with the carbon number.

Full text of DOI:10.1039/c6ra10897k

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PAPER
Experimental determination and model correlation
for the solubilities of trialkyl phosphates in
supercritical carbon dioxide
Cite this: RSC Adv., 2016, 6, 51286
a
a
b
b
K. C. Pitchaiah, N. Sivaraman,* Neha Lamba and Giridhar Madras
The solubilities of a series of trialkyl phosphates in supercritical carbon dioxide have been investigated. The
solubility measurement was carried out using a dynamic flow method. The measurements were performed
at 313, 323 and 333 K and in the pressure range of 10 to 25 MPa. The trialkyl phosphates were found to be
highly soluble in supercritical carbon dioxide and the solubilities were in the range of 0.01 to 0.1 mol
fraction. The solubility of trialkyl phosphates increases with an increase in pressure at constant
temperature. A reverse behavior was observed, wherein the solubilities decreased with increase in
temperature in the investigated pressure region. At constant temperature and pressure, the solubilities of
the trialkyl phosphates decrease with the alkyl chain length. The solubility data was found to be
consistent with the Mendez–Teja model. The solubilities were correlated by the Chrastil model and an
association model based on the van Laar activity coefficient model with absolute deviations of less than
Received 27th April 2016
Accepted 19th May 2016
DOI: 10.1039/c6ra10897k
10%. A key result is that the model parameters based on the association model varied linearly with the
www.rsc.org/advances
carbon number.
criterion for the use of a ligand in SFE is that it should have
1
. Introduction
appreciable solubility in SCCO . Therefore, the solubility of
2
Supercritical Fluid Extraction (SFE) of metal ions from diverse ligand as well as that of metal complex plays a crucial role in
matrices is considered as an environmentally friendly alterna- designing and optimization of a SFE process.
tive to conventional solvent extraction. SFE is an attractive
The organophosphorus compounds contain the phosphoryl
technique for nuclear applications because it can minimize the group that is used in the extraction and purication of various
amount of liquid waste generation. Supercritical uids have metal ions in chemical and hydrometallurgical industries.
many interesting properties such as liquid-like densities, high Extraction of actinides from acidic waste solutions is an
1,2
diffusivity, low viscosity and low surface tension. CO
2
is important task in nuclear waste management that can reduce
a widely used supercritical uid and is considered as a green the radiological burden of the waste. Neutral organophos-
solvent. It has moderate critical constants and it is also inex- phorus compounds such as phosphates, phosphonates, phos-
pensive, non-ammable, non-toxic and easily recyclable. phinates and phosphine oxides have been used for solvent
Supercritical carbon dioxide (SCCO
2
) has several applications in extraction of metal ions for the extraction and recovery of acti-
material synthesis and processing and it is also used as nides from liquid and solid matrices. These compounds have
a solvent for the extraction of non-polar and moderately polar wide range of applications in nuclear industry from mining of
3
8–10
2
compounds. Extraction of metal ions using neat CO is not nuclear materials to reprocessing of the spent nuclear fuel. The
2
possible because of its weak solute–solvent interactions and extraction power of these molecules was found to be increasing
4,5
charge neutralization. However, metal ion extraction can be in the order: phosphates < phosphonates < phosphinates <
11
achieved by complexing them with suitable ligands and the phosphine oxides. Among these, trialkyl phosphate based
1
2
resultant metal complex could become quite soluble in molecules have been used for the metal ion extraction.
4,6
SCCO
2
.
The extraction behavior mainly depends on the (a) Further, among trialkyl phosphates, tributyl phosphate (TBP) is
solubility of ligand/complexing agent and (b) solubility and widely used as an extractant in various steps of nuclear fuel
7
13,14
stability of the resultant metal-complex in SCCO . The primary reprocessing.
A wide range of other trialkyl phosphates such
2
as triisobutyl phosphate (TiBP), triisoamyl phosphate (TiAP),
triamyl phosphate (TAP) and trihexyl phosphate (THP) have also
a
Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam-603102,
India. E-mail: sivaram@igcar.gov.in; Fax: +91-044-27480065; Tel: +91-044-
15–17
examined for the extraction of actinides.
SFE of metal ions
such as heavy metals, lanthanides and actinides from different
2
7480500-24166
b
matrices using organophosphorus compounds was carried
Department of Chemical Engineering, Indian Institute of Science, Bangalore-560012,
India
4,5,7,18,19
out.
SFE based methods were developed for the
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16
extraction of actinides from various matrices with organo- with n-heptane as the reaction medium. TAP and THP were
20–24
phosphorus compounds.
puried by vacuum distillation followed by washing with
The determination of solubility of organophosphorus concentrated sodium hydroxide and water. The characteriza-
ligands in SCCO is crucial towards designing a SFE method for tion of TAP and THP was carried out using infrared (IR) spec-
2
3
1
recovery of a metal ion. The solubility of a variety of complexing troscopy, elemental analysis and P NMR. The purity of these
agents and metal complexes in SCCO
25–30
2
has been reviewed.
compounds was determined by gas chromatography (GC) with
However, the literature on the solubilities of organophosphorus ame ionization detector (FID) and the purity was found to be
2
7,31
compounds in SCCO
2
is scarce. The solubilities of TBP,
tri- ꢀ99%. All other chemicals used were of analytical grade.
phenyl phosphate (TPP), triphenyl phosphine (TPPh), triphenyl
phosphine oxide (TOPO) and other paraffinic hydrocarbon have
already been determined. But the solubility behavior of other
trialkyl phosphates has not been studied.
2
.2. Procedure
30
The schematic of continuous ow apparatus used in this study
for measuring the solubility in supercritical carbon dioxide is
shown in Fig. 1. The experimental setup consisted of a carbon
The experimental determination of solubilities of
compounds in supercritical uid (SCF) is difficult and time
consuming. Mathematical models have been used to correlate
dioxide cylinder (1), a high pressure reciprocating CO
(JASCO-PU-2080-CO ) (3), 10 mL CO tank (6), 50 mL twin high
pressure equilibrium cells (7 & 8), thermostat (JASCO-CO-156)
10), and a back pressure regulator (JASCO-880-81-BP) (11).
2
pump
32
2
2
the solubility data. There are certain types of models such as
33–35
equation of state based models, neural network models
and
(
semi-empirical models that can be used to correlate and predict
the solubilities of compounds in SCF. The equation of state
based models require the knowledge of pure component prop-
erties that are not readily available and require group contri-
The uncertainties in the temperature and pressure measure-
ments are ꢁ0.1 K and ꢁ0.1 MPa, respectively.
An appropriate amount of trialkyl phosphate was loaded into
the equilibrium cells (7 & 8). The outlet of the rst vessel (7) was
connected as inlet for the second vessel (8). The saturated
carbon dioxide stream from the second vessel (8) ows through
an entrainer column (9) that traps the entrained liquid. Two
equilibrium cells and entrainer column were placed in a ther-
mostat (10) to maintain a constant temperature. The system
pressure was regulated and controlled by a back pressure
regulator.
3
2,36
bution theory methods.
Similarly, neural network models
37
has a disadvantage of time requirement to train the nets.
Thus, empirical or semi-empirical models are preferably used
for solubility determination. Several empirical models are
38–47
available in the literature.
Density based models are the
most commonly used semi-empirical equations. Many of these
models correlate the solubilities of solids. However, the models
that correlate the solubility of liquid solutes in supercritical
Carbon dioxide from the gas cylinder (1) was passed through
a silica gel column (2) to remove traces of water and then fed
into a CO pump (3) where it was liqueed by using a Peltier
2
element. Liquid carbon dioxide was pressurized and sent to the
CO tank (6) placed inside the thermostat to reach the super-
critical state prior to its entry into the equilibrium cells (7 & 8).
At a xed experimental temperature, the equilibrium cells were
pressurized with SCCO
The system was kept at the desired temperature and pressure
for an hour to reach the equilibrium. Aer equilibration, SCCO
was allowed continuously to ow through the system at

uids are scarce. A semi-empirical equation for correlating the
liquid solubilities in supercritical uids based on solution
theory coupled with Wilson activity coefficient model was
48
developed.
Recently, several correlations based on
2
association/solution theories using different activity coeffi-
49
cients have been developed.
The solubilities of various trialkyl phosphates in SCCO were
2
2
until the desired pressure was reached.
experimentally determined at different temperatures and pres-
sures. These solubilities were correlated with various semi-
38
2
empirical correlations such as the Chrastil, M ´e ndez-Santiago
43
and Teja models. The solubilities were also correlated by
a recently developed association model based on van Laar
50
activity coefficient. A key result found in this study was that the
model parameters of the association model based on van Laar
activity coefficient varied linearly with the carbon number of the
trialkyl phosphates.
2. Experimental
2.1. Materials
Carbon dioxide with a purity of 99.9% was used for the solu-
bility measurements. Trimethyl phosphate (TMP) (Koch Light
Laboratories Ltd.), triethyl phosphate (TEP) (99%, Sigma
Aldrich) and tributyl phosphate (TBP) (99%, Alfa), were used as
such without any purication. The compounds, triamyl phos-
phate (TAP) and trihexyl phosphate (THP) were synthesized by
Fig. 1 Schematic of the experimental set-up used for the solubility
measurements. (1) CO cylinder, (2) silica column, (3) high pressure
CO pump, (4) valve, (5) six way valve, (6) CO tank/heat exchanger, (7
8) twin equilibrium cells (9) entrainment column, (10) thermostat, (11)
equivalent of corresponding alcohol in the presence of pyridine back pressure regulator, (12) collection vessel.
2
2
2
3
the condensation reaction between POCl and stoichiometric
&
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Fig. 2 Solubility of (a) trimethyl phosphate, (b) triethyl phosphate, (c) tributyl phosphate, (d) triamyl phosphate, (e) trihexyl phosphate at different
temperatures, -, 313 K; C, 323 K; :, 333 K. Solid line represents the MT model fit (eqn (3)).
ꢂ1
a constant ow rate and the concentration of solute in the min , to ensure saturation of solute in SCCO
2
medium. It was
SCCO
2
stream was monitored continuously. The exiting CO
2
found that the solubilities did not vary with ow rates up to 0.3
ꢂ1
stream from equilibrium cells was introduced into a collection mL min . When the ow rate was increased beyond 0.4 mL
vessel (12), where the pressure was reduced to atmospheric min , the concentration of solute in the exiting stream
ꢂ1
pressure. Saturation solubility was achieved and it was observed decreased with the ow rate, indicating that the exiting stream
by periodically collecting the solute and quantifying the same. It has not been saturated with the solute. Hence, a CO ow rate
2
ꢂ1
was found that the solubility did not vary with the time and of 0.1 mL min was employed to ensure that the exiting CO2
outlet CO
the equilibrium.
The primary criterion for the accurate measurement of hexane, at regular intervals of time. Subsequently, n-hexane
solubilities in SCCO is that the exiting stream has to be was evaporated and the amount of solute collected was
2
stream was saturated with the solute, which ensures was saturated with the trialkyl phosphate. The exiting stream
was trapped and collected in collection vessel containing n-
2
saturated with the solute. Repeated measurements were determined gravimetrically using an analytical balance (ꢁ0.1
carried out at different ow rates of CO between 0.1 and 1 mL mg). However, quartz wool was also used as a trap to collect the
2
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Table 1 Experimental solubilities of trialkyl phosphates in SCCO
a function of temperature and pressure
2
as
n
2
y
2
¼
(1)
(2)
f ꢃ t ꢃ r þ n
2
1
ꢂ1
ꢀ
ꢁ
Solubility y
2
(mol mol
)
W
ꢃ 1000
ðf ꢃ t ꢃ r Þ þ ðW ꢃ r2ꢂ1Þ
a
ꢂ3
M
w
T (K) P (MPa) Density (kg m
)
TMP TEP TBP TAP THP
S ¼
1
3
13 8.3
320.54
651.49
727.57
781.32
840.61
880.15
423.74
604.62
701.08
785.16
834.89
309.89
458.89
563.09
638.84
688.34
724.63
787.28
0.188 0.160 0.105 0.097 0.075
0.191 0.162 0.110 0.099 0.081
0.191 0.163 0.113 0.099 0.082
0.192 0.163 0.116 0.101 0.083
0.193 0.163 0.117 0.102 0.084
0.194 0.163 0.115 0.103 0.085
0.180 0.145 0.092 0.091 0.065
1
1
1
2
2
0.3
2.3
5
0
5
In eqn (1) and (2), n
2
is number of moles of compound
ꢂ1
collected, f is the ow rate in mL min of the CO
2
at CO
gives the molar
at pump head, W is the amount of compound
is the molecular weight of the compound and
2
pump,
t represents the collection time in min and r
density of CO
1
2
3
3
23 10.3
1
1
2
2
2.3
5
0
0.189 0.152 0.103 0.098 0.074 collected in g, M
w
0.190 0.156 0.108 0.098 0.079 r2 is the density of the compound at experimental temperature.
0.191 0.158 0.113 0.099 0.080
0.192 0.160 0.113 0.100 0.081
0.122 0.090 0.062 0.014 0.005
0.153 0.116 0.087 0.054 0.024
0.165 0.144 0.102 0.092 0.046
0.177 0.150 0.104 0.096 0.064
0.182 0.153 0.107 0.096 0.070
0.185 0.154 0.110 0.097 0.074
The solubilities were measured three times at each experi-
mental conditions. The uncertainty of experimental measure-
ments was found to be ꢁ5%. The density data used in this study
5
33 10.3
1
1
1
1
2
2
2.3
4
6
8
0
was from NIST Web Book.
5
0.186 0.155 0.111 0.098 0.077 3. Models and correlations
a
Density values taken from http://www.webbook.nist.gov/chemistry/ 3.1. M ´e ndez–Teja (MT) model
uid/

43
M ´e ndez-Santiago and Teja derived an expression that can be
used for checking the consistency of the experimental data of
solubility of solutes in supercritical carbon dioxide. This model
represents the solubility in terms of temperature, pressure and
density as
solute in the collection vessel and the collection efficiency was
found to be similar to that of n-hexane. The precision of the
gravimetric determination was 0.5%. The reliability of the
experimental set-up and procedures were tested by measuring
the solubility of tributyl phosphate and trioctyl amine in
T ln(Py
2
) ¼ A
1
+ B r + C
1
1
T
(3)
ꢂ1
In eqn (3), y
2
is the solubility in mol mol , P is the pressure
in MPa, T is the temperature in K and A , B and C are the
SCCO
literature data.
2
medium. The results were in good agreement with the
1
1
1
2
5,27
temperature independent constants. Thus a plot of T ln(Py ) ꢂ
2
ꢂ1
2
The mole fraction solubility (y ) and solubility in g L (S) is
C T and r would be linear with all the isotherms collapsing on
1
calculated using the expressions
to a single straight line.
Table 2 Regression analysis and model parameters for the correlation of solubilities of trialkyl phosphates by Chrastil model (eqn (3)), MT model
eqn (4)) and the association model based on van Laar activity coefficient model (eqn (7))
(
Model
Model Parameters
TMP
TEP
TBP
TAP
THP
MT model
A
B
C
R
1
ꢂ2313 ꢁ 36
0.85 ꢁ 0.05
6.4 ꢁ 0.5
0.942
ꢂ2358 ꢁ 35
0.92 ꢁ 0.05
6.26 ꢁ 0.5
0.954
ꢂ2593 ꢁ 30
0.96 ꢁ 0.04
6.54 ꢁ 0.54
0.967
ꢂ2363 ꢁ 60
0.97 ꢁ 0.08
5.7 ꢁ 0.5
0.885
ꢂ2052 ꢁ 60
0.94 ꢁ 0.08
4.54 ꢁ 0.4
0.913
1
1
2
AARD (%)
7
7
6
9
10
Chrastil model
A
B
k
2
ꢂ1.56 ꢁ 0.01
514 ꢁ 4
0.890 ꢁ 0.03
0.937
ꢂ1.75 ꢁ 0.02
433 ꢁ 4
0.957 ꢁ 0.04
0.954
ꢂ1.50 ꢁ 0.01
392 ꢁ 4
0.929 ꢁ 0.01
0.968
0.53 ꢁ 0.02
106 ꢁ 1
0.758 ꢁ 0.01
0.997
ꢂ1.84 ꢁ 0.01
546 ꢁ 3
0.896 ꢁ 0.01
0.973
2
2
R
AARD (%)
6
7
5
3
4
Association model based on van Laar
k
VL
1
1
1
1
1
activity coefficient model
A
C
D
VL
2369 ꢁ 27
ꢂ3295 ꢁ 18
ꢂ118 ꢁ 5
10.9 ꢁ 0.4
ꢂ9.3 ꢁ 0.1
0.90
3169 ꢁ 40
ꢂ3885 ꢁ 23
ꢂ176 ꢁ 5
13 ꢁ 0.1
ꢂ12.1 ꢁ 0.12
0.87
4400 ꢁ 150
ꢂ5192 ꢁ 27
ꢂ289 ꢁ 6
17.8 ꢁ 0.6
ꢂ16.6 ꢁ 0.13
0.92
5520 ꢁ 105
ꢂ6110 ꢁ 61
ꢂ376 ꢁ 12
21 ꢁ 1.2
ꢂ20.3 ꢁ 0.4
0.70
6250 ꢁ 150
ꢂ6980 ꢁ 48
ꢂ390 ꢁ 20
24 ꢁ 0.8
ꢂ23 ꢁ 0.5
0.84
VL
VL
E
VL
F
VL
2
R
AARD (%)
3
3
3
7
5
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.2. Chrastil model
Paper
3
333 K in the pressure range of 10 to 25 MPa. The consistency of
the solubility data was checked by the MT model (eqn (3)) as
shown in Fig. 2. The constants A , B , and C in the eqn (3) were
obtained by the multiple linear regression of the experimental
data and given in Table 2. The plot of T ln(Py T and r was
38
The Chrastil model relates the solubility of solute and density
1
1
1
of the pure supercritical uid (SCF) as follows
A
2
lnðSÞ ¼ k lnðrÞ þ
þ B
2
(4)
2
) ꢂ C
1
T
linear with all experimental data tting onto single straight line
and this indicates that the data is self-consistent.
ꢂ1
In eqn (4), S is the solubility of solute in SCF in g L ; r is the
In general, the solubilities of trialkyl phosphates were found
ꢂ1
density of the SCF in g L ; k is the association number that to be high in the investigated region and are shown in Table 1.
describes the number of solvent molecules associated with the The variation of solubilities with temperature and pressure is
complex; A2 is a function of enthalpy of vaporization and shown in Fig. 3 for different trialkyl phosphates. Across all the
enthalpy of solvation; T is the temperature in K; B depends on isotherms (313, 323 and 333 K) the solubilities of trialkyl
2
the association number and molecular weight of solute and phosphates increases with the pressure. We have included the
27
supercritical uid. Thus a plot of ln(S) with ln(r) will be linear at solubility data for TBP from existing literature and compared
a constant temperature.
it with the present data in Fig. 3 and the agreement is reason-
able. Increasing the pressure at isothermal conditions increases
3.3. Association model with van Laar activity coefficient
the density of SCCO
2
that improves the specic interactions
model
between CO and solute molecules, enhancing the solvating
2
power and leading to higher solubility. The reverse behavior was
observed with temperature and the solubilities of trialkyl
phosphates decreases with temperature in the entire pressure
region. The effect of temperature on the solubility is not straight
forward and there are two competing factors that can inuence
the solubility. The vapor pressure of the solute generally
An association model, such that a molecule of solute A (liquid)
associates with k molecules of solvent B (SCCO
2
) to form
50
a solvate complex, AB
k
was developed with the assumption of
formation of solvato complex which is in equilibrium with the
supercritical phase. An expression in terms of densities of both
phases, fugacities, activity coefficients, pressure and tempera-
ture was obtained as
increases with the temperature whereas density of SCCO
2
49
decreases with increase in temperature. However, the vapor
pressure of the trialkyl phosphates in the investigated temper-
ature region of 313 to 333 K is low and hence making density as
ꢀ
ꢁ
P
DH
s
ꢂ ꢃ
ꢄ
ln y
2
¼ ðk ꢂ 1Þln
þ
ꢂ q
s
ꢂ 2 BAB B ꢂ kBBB
k
P*
RT
!
*
k
*
*
ꢅ
f
f
P
2
the dominating factor. The decrease of SCCO density with
temperature results in reduced solubility at 333 K compared to
that obtained at 313 K, as depicted by Fig. 3.
From the solubility data, it was observed that TMP has
highest solubility among its homologous series investigated in
B
A
þ ðk ꢂ 1ÞB r ꢂ ln
B
*
ABk
f
f
x
A
sat
B
v
rB
rA
þ A
v
ꢂ
þ ln g þ
(5)
A
T
the present study. The solubilities of TMP ranged from 0.122 to
ꢂ1
The above expression was simplied and the activity coeffi- 0.194 mol mol . THP has relatively lower solubilities, ranging
ꢂ1
cient was modeled using a van Laar activity coefficient model from 0.005 to 0.085 mol mol . All other trialkyl phosphates
and the following expression was obtained,
show intermediate solubility in comparison to TMP and THP. It
was found that the solubility is inversely related to the number
of carbon atoms present in the trialkyl phosphate. The vapor
pressure is a parameter inuencing the solubility behavior and
is directly dependent on the molecular weight of the compound.
For a homologous series, the solubility of a solute decreases
with increase in carbon number where generally, the vapor
"
(
)
ꢀ
ꢁkVLꢂ1
ꢀ ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
2
P
1
rB
rA
rB
rA
y
2
¼
exp
A
VL þ CVL
þ DVL
P*
T
#
ꢀ
ꢁ
rB
þ EVL
þ FVL
rA
(
6)
51,52
pressure decrease with increase in carbon chain.
experimental solubilities of trialkyl phosphates were plotted
In Fig. 4,
In eqn (6), y is solubility, P is pressure in MPa, P* is reference against their carbon number at 20 MPa with temperature
pressure, T is temperature in K, r , r and x , x are the molar ranging from 313 to 333 K. It was found that, in the homologous
B
A
B
A
ꢂ3
densities in kg m and mole fractions of solvent (B) and solute series of trialkyl phosphates, the solubility decreases with its
A), respectively. kVL represents association number and AVL
molecular weight or carbon number at all isotherms. The
VL, CVL, DVL, EVLand FVL are temperature independent solubility of trialkyl phosphates decreases with increase in the
constants. Eqn (6) was used for correlating the solubilities of temperature as the density of SCCO decreases with the
trialkyl phosphates in SCCO
temperature.
The interaction and solubility of trialkyl phosphates in
SCCO is mainly due to Lewis acid (LA)–Lewis-base (LB)
interactions and weak C–H–O hydrogen bonding. Because of
The solubilities of various trialkyl phosphates: TMP, TEP, TBP, large quadrupole moment of CO , there will be a charge
TAP and THP were measured at temperatures of 313, 323 and separation between carbon and oxygen atoms and electron
(
,
B
2
2
.
2
4
. Results and discussion
5
3
2
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Fig. 3 Variation of solubility of trialkyl phosphates (-, trimethyl phosphate; C, triethyl phosphate; :, tributyl phosphate; ;, triamyl phosphate;
=
, trihexyl phosphate) with pressure at different temperatures of (a) 313 K; (b) 323 K; (c) 333 K. Solid symbols and solid lines represent the present
27
work. Open symbols and dash line represent the tributyl phosphate (TBP) data by Meguro et al.
density moves towards oxygen. Therefore, the carbon atom has
partial positive charge acting as a LA and oxygen atoms having
negative charge act as a LB. The phosphoryl group of the tri-
2
alkyl phosphate acts as LB and interacts with the CO through
5
3
LA–LB interactions. The partial negative charge on oxygen
atom induces the electrostatic interaction with –C–H group
present in the trialkyl phosphate to form a weak H-bonding.
Kim et al. performed the quantum mechanical calculations
2
for the CO –TMP complex and found that the LA–LB interac-
tion energy was much higher than the weak H-bonding and it
could be the main driving force for the higher solubility in
5
3
CO
temperature range may be due to the complete miscibility of
the trialkyl phosphates with SCCO . Meguro et al. reported
high solubility behavior of TBP in SCCO due to the formation
2
.
The high solubilities in the investigated pressure and
2
2
2
7
of single phase TBP–SCCO
2
.
Fig. 4 Variation of solubility of trialkyl phosphates with their carbon
Chrastil equation has been employed in the present study to number at 20 MPa, with temperatures -, 313 K; C, 323 K; :, 333 K.
correlate the solubility data of trialkyl phosphates in SCCO2.
The experimental solubilities were tted using non-linear curve
tting with eqn (4) to obtain the model parameters k (associa-
tion number), A and B and were given in Table 2. The
ꢂ1
logarithm of solubility (g L ) data was plotted against the

ꢂ1
logarithm of density (g L ) of SCCO
straight lines for different isotherms and are shown in Fig. 5.
2
. These plots represent
2
2
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The slopes of the different isotherms are close; however, the model parameters were obtained by non-linear curve tting and
slope shows a small increase at higher temperature. represented in Table 2. The solubilities correlated by the model
Assuming the association number, kVL, to be unity in eqn (6), are depicted by Fig. 6. The deviation of the experimentally
this equation can be rewritten as,
measured solubilities from the solubilities derived from the
model was estimated by calculating the average absolute rela-
tive deviation (AARD%) and is given by eqn (8),
"
(
ꢁ
)
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
2
1
rB
rB
y ¼ exp
A
VL þ CVL
þ DVL
T
rA
rA
ꢆ
ꢆ!
#
X
N
ꢆ
ꢆ
ꢀ
100
y
2;cal ꢂ y2;exp
rB
AARD% ¼
(8)
þ EVL
þ FVL
(7)
N
y
2;exp
i¼1
rA
y
2,cal is the solubility calculated by the model, y2,exp is the
experimental solubility and N is the number of data points. The
average AARD% obtained from MT, Chrastil and the association
Eqn (7) was used to determine the solubility by the model
and was compared with the experimental solubilities. The
Fig. 5 Correlation plots of ln S vs. ln r (eqn (4)) for trialkyl phosphates in the pressure range of 10 to 25 MPa, and the temperature of -, 313 K; C,
23 K; :, 333 K; (a) trimethyl phosphate, (b) triethyl phosphate, (c) tributyl phosphate, (d) triamyl phosphate, (e) trihexyl phosphate.
3
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model based on van Laar activity coefficient are 8%, 5% and 4%, carbon number of the trialkyl phosphates. The model parame-
respectively. ters of the MT and Chrastil model did not show any particular
While correlating the solubilities of alkanes in supercritical trend with the carbon number, as shown in Fig. 7(a) and (b).
carbon dioxide, it was observed that the adjustable binary However, the ve model parameters of the association model
interaction parameters in the model vary linearly with the chain based on van Laar activity coefficient model successfully
54
length of the n-alkanes. Other studies have indicated that the correlated with the carbon number of the trialkyl phosphates. A
vapor pressure is an important physicochemical parameter linear relationship was observed, as shown in Fig. 7(c). These
inuencing the solubility behavior and gives a direct correlation equations reveal the anticipated trend of solubility with the
51
on the solubilities in supercritical uids. Based on the above molecular weight of the trialkyl phosphates. All the three
55,56
observations, the boiling points of the trialkyl phosphates
models discussed in this study gave average AARD values
were correlated with the carbon number of the trialkyl phos- ranging from 4% to 8%. However, the association model gave
phates. This relationship is linear as observed in the inset of a linear relationship between the model parameters and the
Fig. 7(c). Therefore, the model parameters of the all three carbon number of the trialkyl phosphates. This provides an easy
models used in the present study were correlated with the method to calculate the unknown solubilities of other members
Fig. 6 Variation of solubility of trialkyl phosphates with pressure at different temperatures; -, 313 K; C, 323 K; :, 333 K; in supercritical carbon
dioxide. (a) Trimethyl phosphate, (b) triethyl phosphate, (c) tributyl phosphate, (d) triamyl phosphate, (e) trihexyl phosphate; the solid line
represents the association model based on van Laar activity coefficient model (eqn (7)).
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Fig. 7 Correlation of model parameters with carbon number of trialkyl phosphates; (a) MT model (eqn (3)); model parameters are represented by
the symbols, -, A ; C, B ; :, C ; (b) Chrastil model (eqn (4)); model parameters are represented by the symbols, -, k; C, A ; :, B ; (c)
association model based on van Laar activity coefficient model (eqn (7)); model parameters are represented by the symbols, -, AVL; C, CVL; A,
VL; :, EVL; ;, FVL. The inset of this figure represents the relation between carbon number and normal boiling point of the trialkyl phosphates.
1
1
1
2
2
D
of the trialkyl phosphate series as well as predict the solubilities the department of science and technology (DST), India for the J.
of these compounds at different temperatures and pressures.
C. Bose fellowship.
5. Conclusions
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