Measurement and Correlation of Saturated Vapor Pressure of Ethylphenyldimethoxysilane and Ethylphenyldiethoxysilane

Article abstract of DOI:10.1021/acs.jced.5b00255

The saturated temperatures of ethylphenyldimethoxysilane (EPDMOS) and ethylphenyldiethoxysilane (EPDEOS) were determined using an inclined ebulliometer from 2.035 to 64.0 kPa. The experimental data were fitted with the Antoine and Clarke-Glew equations by a weighted least-squares regression method, which yielded Antoine parameters (A = 9.1280, B = 1590.18, C = minus100.39 K and A = 9.1049, B = 1678.64, C = minus102.84 K) and standard vaporization enthalpies (δlgHm0(298.15 K) = 62.52 kJ·mol^-1 and δlgHm0(298.15 K) = 65.19 kJ·mol^-1) for EPDMOS and EPDEOS, respectively. The critical properties of EPDMOS and EPDEOS, such as critical temperature, pressure, and volume, were estimated by the group contribution method introduced by Nannoolal et al. The acentric factors of EPDMOS and EPDEOS were estimated from these critical parameters and the reduced saturated vapor pressures calculated from either the Clarke-Glew equation or the Antoine equation.

Full text of DOI:10.1021/acs.jced.5b00255

Article
pubs.acs.org/jced
Measurement and Correlation of Saturated Vapor Pressure of
Ethylphenyldimethoxysilane and Ethylphenyldiethoxysilane
Xia Wu, Hong Dong, Xinliang Wang, Zhenghao Zeng, and Chuan Wu*
Key Laboratory of Organosilicon Chemistry and Material Technology, Ministry of Education, Hangzhou Normal University,
Hangzhou 311121, China
S
* Supporting Information
ABSTRACT: The saturated temperatures of ethylphenyldimethoxysilane
(EPDMOS) and ethylphenyldiethoxysilane (EPDEOS) were determined using
an inclined ebulliometer from 2.035 to 64.0 kPa. The experimental data were
fitted with the Antoine and Clarke−Glew equations by a weighted least-squares
regression method, which yielded Antoine parameters (A = 9.1280, B = 1590.18,
C = −100.39 K and A = 9.1049, B = 1678.64, C = −102.84 K) and standard
vaporization enthalpies (Δgl Hm0 (298.15 K) = 62.52 kJ·mol−1 and ΔlgH0m(298.15
K) = 65.19 kJ·mol−1) for EPDMOS and EPDEOS, respectively. The critical
properties of EPDMOS and EPDEOS, such as critical temperature, pressure,
and volume, were estimated by the group contribution method introduced by
Nannoolal et al. The acentric factors of EPDMOS and EPDEOS were estimated
from these critical parameters and the reduced saturated vapor pressures
calculated from either the Clarke−Glew equation or the Antoine equation.
introduced into the polysiloxane molecules, the rigidity of the
polysiloxane molecule increases with a decrease in flexibility.
The Tg value of the copolymer increases proportionally with
content of modified units.3−6 The Tg of polydiethylsiloxane is
as low as −145 °C.7,8 Its cold resistance is the most prominent
among polysiloxanes, and thus, they show broad application
prospects.9,10 The function of the phenyl group attached to the
side chain of polysiloxane is not only to inhibit low-temperature
crystallization but also to improve the thermal and UV
resistance of silicone materials, together with a significant
increase in their refractive index. Consequently, phenyl-
modified silicone materials are used extensively to encapsulate
high-brightness light-emitting diode chips. In short, ethyl
group-modified silicone polymers exhibit a cold resistance,
whereas phenyl-containing silicone polymers possess excellent
thermal and UV resistance. Because of the enormous structure
and ring-opening polymerization rate differences between
diethylsiloxane, diphenylsiloxane, and methylphenylsiloxane
units, poly(diethyl-methylphenyl)siloxane or poly(diethyl-
diphenyl)siloxane copolymers with uniform structure and
excellent performance are difficult to prepare.
1. INTRODUCTION
With rapid developments in space technology, an increasing
number of requirements have been raised for rubber products
and components for use in outer space. In such environments,
rubber products need to maintain their flexibility and sealing
performance at ultralow temperatures, and withstand frequent
impact resistance at high and low temperatures, ultraviolet
(UV) irradiation, and the impact of vacuum particles. Only
special silicone rubber can meet these requirements under such
stringent conditions. Rubber products can exhibit high
flexibility at room temperature; however, they lose elasticity
at lower temperature because of decreases in rubber molecular
thermal motion and freezing of molecular chains. Two
significant characteristics that affect the cold resistance of
rubber are the glass phase and crystal transitions. The glass
phase transition temperature (Tg) of silicone rubber is
determined mainly by properties of the side organic groups
attached to Si atoms in polysiloxane molecules, especially their
amount, volume, and cohesive energy.1 When the phenyl group
is introduced into the side group of the Si atom in the
polysiloxane backbone, the regularity of the polysiloxane
backbone is destroyed and crystallization conducted at
approximately −50 °C is inhibited extensively. Therefore,
phenyl-group-modified silicone rubber exhibits better cold
resistance. The regularity of the polysiloxane backbone could
also be destroyed when the side methyl group is substituted
partially by an ethyl group. With the introduction of an ethyl
group, the crystallization process occurring at lower temper-
ature is inhibited significantly, and thus, ethyl-modified silicone
rubber manifests much better cold resistance than phenyl
silicone rubber.2 When aryl or polar-substituted groups are
Polysiloxane copolymers contain phenyl and ethyl groups in
the side chains of repeating Si−O−Si segments could be
prepared by ring-opening copolymerization with difunctional
silane compounds containing diethyl and diphenyl or the
methylphenyl group. When a difunctional silane compound
that contains an ethyl and phenyl group is used as the
Received: March 18, 2015
Accepted: October 15, 2015
Published: October 22, 2015
© 2015 American Chemical Society
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Scheme 1. Schematic Diagram for EPDMOS Synthesis
Scheme 2. Schematic Diagram for EPDEOS Synthesis
Table 1. Sample Description
chemical name
CAS registry number
112123-25-8
source
initial mass fraction purity
0.568
purification method
final mass fraction purity
analysis method
b
a
EPDMOS
synthesis
synthesis
distillation
distillation
0.9967
0.9985
GC
c
a
EPDEOS
16522-50-2
0.557
GC
a
b
c
Gas−liquid chromatography. EPDMOS = ethylphenyldimethoxysilane. EPDEOS = ethylphenyldiethoxysilane.
polymeric monomer, the copolymers mentioned above can also
be prepared. Compared with the former, the latter exhibit more
advantages because the irregularity of the copolymer structure
that arises from differences in the polymeric rate of two or
more kinds of monomers can be avoided substantially. On the
basis of such considerations, high purity ethyltrialkoxysilane
compounds were synthesized and separated by Ru-catalyzed
hydrosilylation initiated from trialkoxysilane and gaseous
ethylene in our previous work.11,12 Ethylphenyldialkoxysilanes
can be prepared by the Wurtz−Fittig reaction that occurs
between ethyltrialkoxysilane and chlorobenzene.13
Although ethylphenyldimethoxysilane (EPDMOS, CAS RN:
112123-25-8, EPDMOS) and ethylphenyldiethoxysilane (EP-
DEOS, CAS RN: 16522-50-2, EPDEOS) have been synthe-
sized, some important experimental data, such as their density,
normal boiling point, enthalpy of evaporation, and flash point,
have never been reported in the literature. In the Chemical
Abstracts Service database, only predicted results of parameters
calculated from Advanced Chemistry Development (ACD)
software have been provided.14 A comparison of experimental
data and predicted results given by ACD software indicates that
significant differences exist for other high boiling point
chemicals. For example, the experimental normal boiling
point of dimethylphenylethoxysilane (CAS RN: 1825-58-7) is
in the range (195 to 196) °C,15 whereas the predicted result
given by ACD software is 209.0 9.0 °C.14 The accuracy of
predicted results for high boiling point chemicals therefore is
difficult to guarantee.
To supplement fundamental data in silicone chemistry and to
provide detailed parameters for industrial applications, values of
saturation temperature at different pressures for EPDMOS and
EPDEOS were measured using an inclined ebulliometer. The
Antoine and Clarke−Glew equations were fitted to the
experimental data and gave the Antoine parameters A, B, and
C, standard vaporization enthalpy Δgl Hm0 (θ), standard Gibbs
energy Δgl G0m(θ), and difference between the heat capacities of
the ideal gas and liquid phase Δgl Cp0,m(θ). The critical properties
of EPDMOS and EPDEOS, including the critical temperature,
pressure, and volume, were estimated using the group
contribution method introduced by Nannoolal et al.21 The
acentric factors of EPDMOS and EPDEOS were estimated
using their respective critical parameters and their saturated
vapor pressures calculated using either the Clarke−Glew
equation or the Antoine equation.
2. EXPERIMENTAL SECTION
2.1. Chemicals. EPDMOS and EPDEOS were synthesized
by the Wurtz−Fittig method as shown in Schemes 1 and 2.13
Synthetic crude products were separated and purified by
vacuum distillation in a 1 m column of 30 mm inner diameter
filled with Dixon θ packings (3 mm outer diameter, 3 mm
length). The temperature at the top of the vacuum distillation
tower was measured with a standard platinum resistance
thermometer Pt-100 connected to an artificial intelligence
industrial controller (AI-708 model, China Xiamen Yudian
Automation Technology Co., Ltd.), and the absolute pressure
in this distillation system was monitored by an Anschutz
vacuum gauge (AM-1 type, China Shanghai Xingzhi Instrument
Factory) with measurement range ranging from 0.027 kPa to
26.664 kPa. After removal of the low boiling point impurities
and the front cut fractions, EPDMOS and EPDEOS were
collected from the top of the distillation tower at 59.1 °C/0.23
kPa and 84 °C/0.23 kPa, respectively. The standard uncertainty
in temperature is u(T) = 0.2 K and the relative standard
uncertainty in pressure is ur(p) = 10 %.
The purity of the EPDMOS and EPDEOS was determined
using a Rainbow gas chromatograph (GC) SP-6890 equipped
with a flame ionization detector (Rainbow Chemical Instru-
ment Co. Ltd., Shandong Lunan). A capillary column HP-5
(stationary phase cross-linked 5 % phenyl methyl silicone) was
used with a column length of 25 m, inner diameter of 0.32 mm,
and film thickness of 0.25 mm. The GC vaporizer and detector
temperatures were set to T = 533 K. The standard GC column
temperature program was started from T = 333 K followed by a
heating rate of 0.167 K·s−1 to T = 533 K. Samples used for
vapor pressure measurements were detected with a mass
fraction of 0.9967 and 0.9985 for EPDMOS and EPDEOS,
respectively, and the results are listed in Table 1.
2.2. Vapor Pressure Measurement for EPDMOS and
EPDEOS. The apparatus used in this work has been described
previously16 and includes a high-accuracy pressure controller
and measurement system, an inclined ebulliometer, and a
vacuum pump (ILMVAC, Model P6Z). The system pressures
were controlled by a DPI 515 precision pressure controller. The
measurement stability of the pressure controller was 0.02 kPa
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up to 200 kPa with a control stability of 0.002 kPa. The relative
standard uncertainty in pressure measurement was ur(p) = 2
%.The temperature was measured with a standard platinum
resistance thermometer Pt-100 connected to an artificial
intelligence industrial controller (AI-526P model, China
Xiamen Yudian Automation Technology Co., Ltd.). Temper-
ature data were collected every 0.1 s by a computer through an
RS-485/RS-232 converter and the uncertainty of the temper-
ature measurement was 0.02 K.
The reliability and accuracy of the apparatus setup was
verified during our previous work by measuring and comparing
the saturation temperatures of N-methyl-2-pyrrolidone from
4.742 kPa to 99.402 kPa with those reported in the literature.17
The maximum absolute error of the apparatus was 0.13 K and
the maximum relative difference was 0.034 %.
Samples of EPDMOS or EPDEOS with an approximate
volume of 100 cm3 were loaded into the inclined ebulliometer.
All measurements were conducted in sequence with increasing
pressure which was controlled at the desired value for each
experimental point. Samples were heated and stirred using a
magnetic stirrer to provide isothermal conditions and to
prevent superheating. When thermal equilibrium was reached,
the temperature and pressure were recorded. Experimental
temperatures were measured in triplicate at each pressure. The
recorded saturation temperatures and corresponding vapor
pressures are listed in Table 2.
Table 2. Experimental and Calculated Saturation
Temperatures T and Calculated Vaporization Enthalpies,
a
Δgl H0m
b
ps
Texptl
Tcalc
Δgl H0m
AD
K
kPa
K
K
kJ·mol−1
EPDMOS
373.64
382.04
388.35
393.46
397.77
401.52
407.84
413.09
417.61
423.40
428.37
432.72
436.62
440.15
443.38
449.16
451.77
454.22
456.54
458.74
460.83
462.83
464.75
466.59
EPDEOS
401.12
407.89
413.36
445.37
450.66
455.31
459.47
463.24
466.69
480.73
483.08
485.32
487.45
489.49
491.45
493.34
2.035
3.035
373.53
382.10
388.41
393.45
397.78
401.60
407.85
413.14
417.63
423.35
428.51
432.86
436.68
439.99
442.88
449.11
451.67
454.20
456.35
458.80
460.83
462.89
465.00
466.79
56.45
55.76
55.25
54.85
54.50
54.19
53.68
53.26
52.90
52.44
52.02
51.67
51.36
51.10
50.86
50.36
50.15
49.95
49.78
49.58
49.42
49.25
49.08
48.94
0.11
0.06
0.06
0.01
0.01
0.08
0.01
0.05
0.02
0.05
0.14
0.14
0.06
0.16
0.50
0.05
0.10
0.02
0.19
0.06
0.00
0.06
0.25
0.20
4.035
5.035
6.035
7.035
9.035
11.035
13.035
16.035
19.035
22.035
25.035
28.035
31.035
37.035
40.035
43.035
46.035
49.035
52.035
55.035
58.035
61.035
3. RESULTS AND DISCUSSION
3.1. Regression of the Antoine Equation. The Antoine
equation (eq 1) was used to correlate the relationship between
the saturation temperature and vapor pressure for EPDMOS
and EPDEOS and was solved using a weighted least-squares
regression method with Eviews software (Version 5.0).16 The
parameters A, B, and C of eq 1 determined with different
weighted factors are listed in Tables S1a and S2a (in the
Supporting Information), together with each standard errors.
Their corresponding coefficient covariance matrixes were
provided in Tables S1b and S2b (in the Supporting
Information). Values of the standard deviations of the fit
(σF), as defined in eq 2, are also provided in Tables S1a and
S2a. The regression results are evaluated on the basis of the
lowest value of σF. Values of the sum squared residuals (SSR)
between the experimental saturation temperature and the fitted
ones are also used as an auxiliary criterion to determine which
is the most proper weighted factor because values of σF with 2
significant figures reported in Tables 1a and 2a could yield
almost the same results for different weighted factors and thus
the best regression is hard to be distinguished. For those
regressions with the same lowest σF value and the same SSR
value, values of the standard errors for parameters A, B, and C
are compared and the proper weighted factor that yields the
lowest standard errors for parameters could be determined. The
best regression results are listed in Table 3, together with the
values of the standard deviations of the fit (σF). As an
illustration, the regressed curves are shown in Figure 1.
3.000
4.000
400.94
408.11
413.43
444.87
450.61
455.77
459.73
463.28
466.73
479.98
482.71
485.65
487.6
57.70
57.18
56.79
54.50
54.08
53.71
53.42
53.16
52.91
51.95
51.75
51.53
51.39
51.24
51.10
50.97
0.18
0.22
0.07
0.50
0.05
0.46
0.26
0.04
0.04
0.75
0.37
0.33
0.15
0.18
0.10
0.02
5.000
16.000
19.000
22.000
25.000
28.000
31.000
46.000
49.000
52.000
55.000
58.000
61.000
64.000
489.67
491.55
493.36
a
The standard uncertainty in temperature is u(T) = 0.02 K and the
b
relative standard uncertainty in pressure is ur(p) = 2 %. Absolute
deviations (AD) = |Texptl − Tcalc|, where Texptl is the experimental value
and Tcalc is calculated from the Antoine equation.
where Texptl is the experimental data, Tcalc is the fitted data
calculated using the Antoine eq (eq 1), n is the number of
experimental points used in the fit, and m is the number of
adjustable parameters in the Antoine equation.
Values of the saturation temperature for EPDMOS and
EPDEOS at each experimental pressure were calculated from
the Antoine equation with parameters A, B, and C listed in
Table 3 and compared with the respective experimental values
as shown in Table 2. The maximum absolute deviation between
the calculated value and the experimental data was 0.50 K and
B
log ps = A −
C + (T/K)
(1)
n
σ = [ (T
− Tcalc,i)2/(n − m)]1/2
∑
F
exptl,i
(2)
i=1
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Table 3. Regressed Parameters of Antoine Equation, Equation 1, for EPDMOS and EPDEOS
chemical name
A
B
C
pmin − pmax
σF
K
kPa
K
EPDMOS
EPDEOS
9.1280 0.0633
9.1049 0.1744
1590.18 40.49
1678.64 119.53
−100.39 4.04
−102.84 12.11
2.035−61.035
3.0−64.0
0.16
0.34
As stated by Fulem et al.,19 use of the Clarke−Glew equation
(eq 3) with three parameters is adequate for a given
temperature range. Therefore, the experimental data listed in
Table 2 were also fitted with the Clarke−Glew equation by a
weighted least-squares regression method with different
weighted factors and the results are shown in Tables S3a and
S4a (in the Supporting Information), and their corresponding
coefficient covariance matrixes are provided in Tables S3b and
S4b (in the Supporting Information). The regression results are
evaluated with the same method as introduced in former
section. The regressions of the fit obtained with the Clarke−
Glew equation are graphically shown in Figure 1. The proper
parameters in eq 3 together with the standard deviation of the
fit (σF) as defined in eq 2 (with the exception that Tcalc is the
smoothed data calculated using the Clarke−Glew equation, eq
3) are presented in Table 4.
As shown in Figure 1, the Clarke−Glew and Antoine
equations exhibit good correlations between the model and
experimental data when they were used within the experimental
pressure or temperature range. The curves almost overlapped,
and they matched the experimental data well. However, when
the Clarke−Glew and Antoine equations were compared in the
fractional deviation plot (Figure 2), it was found that the
maximum absolute deviations and relative differences between
the experimental and smoothed data calculated using the
Antoine equation were slightly larger than those obtained using
the Clarke−Glew equation.
As shown in Tables 3 and 4, the Clarke−Glew gave standard
deviations (σF) in evaluation of the overall dispersion of the
residuals between the model and experimental data for both
EPDMOS and EPDEOS with values of 0.14 K and 0.33 K,
respectively, which were close to those obtained using the
Antoine equation for both EPDMOS (σF = 0.16 K) and
EPDEOS (σF = 0.34 K). Because these differences are not
significant, both the Clarke−Glew equation and the Antoine
equation were used to calculate the saturated pressures of
ethylphenyldialkoxysilane at the reduced temperature (T = 0.7·
Tc) for the estimation of acentric factors.
3.3. Extrapolated Normal Boiling Points. Because
EPDMOS and EPDEOS belong to high boiling point
chemicals, they react readily with atmospheric moisture
through hydrolyzable diethoxy groups under higher temper-
ature. Therefore, accurate measurements of the normal point
for such substances are difficult to obtain. Apart from
experimental measurements, the normal boiling point of a
chemical can be extrapolated from the empirical equations with
determined parameters.
▲
▽
Figure 1. Vapor pressure curves: , EPDMOS; , EPDEOS; solid
lines, the fitted Clark−Glew equation and Antoine equation.
0.75 K for EPDMOS and EPDEOS, respectively. These high
dispersions might be related to the unbalanced gas−liquid
equilibrium resulted from the heat loss at higher temperatures
or the possible hydrolysis, condensation, and polymerization
reactions conducted between EPDMOS or EPDEOS and the
accumulated moisture in the air inhaled through the pressure
regulating valve of DPI 515 precision pressure controller.
3.2. Regression of the Clarke−Glew Equation. In
addition to the Antoine equation, the experimental saturated
vapor pressure data could be correlated using the Clarke−Glew
equation (eq 3).18 The advantage of the Clarke−Glew equation
is that important thermodynamic parameters such as the
standard vaporization Gibbs energy [Δgl Gm0 (θ)] (the difference
in molar Gibbs energy between the gaseous phase, considered
as an ideal gas and the liquid phase at the selected reference
pressure and temperature), the standard vaporization enthalpy
[Δgl H0m(θ)], and the difference between the heat capacity of the
ideal gas and the liquid phase [Δgl Cp0,m(θ)] can be determined
using a regression of the Clarke−Glew equation19
ΔlgGm0(θ)
s
⎛
⎞
p
⎛
⎜
⎞
⎟
1
θ
1
T
g
0
Rln⎜ ⎟ = −
+ Δl Hm(θ)
−
p0
⎝
⎠
⎤
θ
⎝
⎠
⎡
⎛
⎜
⎞
⎟
⎛
⎜
⎞
θ
T
T
θ
+ ΔgCp0,m(θ)
− 1 + ln
⎟
⎠
⎢
⎣
⎥
⎦
l
⎝
⎝
⎠
(3)
where ps is the vapor pressure, p0 is the selected reference
pressure (p0 = 105 Pa), θ is the selected reference temperature
(θ = 298.15 K), and R is the molar gas constant (R = 8.314462
J·K−1·mol−1).
Table 4. Parameters of Clarke−Glew Equation, Equation 3, at Reference Temperatures θ = 298.15 K and Pressure p0 = 105 Pa
chemical name
Δgl G0m
Δgl H0m
Δgl C0p,m
(pmin − pmax
)
σF
J·mol−1
J·mol−1
J·K−1·mol−1
kPa
K
EPDMOS
EPDEOS
21713.00 44.81
24556.29 299.13
62522.38 276.25
65188.54 1625.34
−80.56 2.18
−72.83 10.98
2.035−61.035
3.0−64.0
0.14
0.33
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Because the Clarke−Glew equation (eq 3) was used with three
parameters, the temperature dependence of Δgl Hm0 (T) in the
studied temperature interval results in a linear equation.19 The
molar enthalpies of vaporization for EPDMOS and EPDEOS at
each saturation temperature were calculated using eq 4 and the
results are shown in Table 1
ΔlgHm0(T) = ΔlgHm0(298.15 K) + ΔlgCp0,m(298.15 K)
(T − 298.15 K)
(4)
where Δgl Cp0,m(298.15 K) is the difference between C (298.15
g,0
p,m
K) and Clp,m(298.15 K) as presented in eq 5
ΔlgCp0,m(298.15 K) = Cpg,,m0(298.15 K) − Cpl ,m(298.15 K)
(5)
The value of Δgl Cp0,m(298.15 K) for EPDMOS and EPDEOS
result from the vapor pressure data are −80.56 J·mol−1·K−1 and
−72.83 J·mol−1·K−1, respectively.
To estimate the uncertainty of the vaporization enthalpy,
experimental data were correlated with the linear equation, ln
(ps) = f(T−1) and fitted using the least-squares method. If
uncertainties in ΔlgCp0,m are not taken into account, the
uncertainty in the enthalpy of vaporization is assumed to be
identical with an average deviation of experimental ln(ps) from
this linear correlation.20
3.5. Acentric Factor ω. The acentric factor (ω, eq 9),
which is also known as the eccentricity, is defined as the ratio of
the distance between two focal points to the length of the major
axis of an elliptical molecule. The acentric factor is a specific
constant to measure the flat or nonspherical degree of the
molecules and it reflects the molecular shape and substance
polarity. Larger eccentricity factors imply greater molecular
polarity. The acentric factor was first introduced in 1955 by
Pitzer, has been proven to be a useful parameter for the
description of matter, and has become a standard for the phase
characterization of single and pure components. In addition to
molecular weight, critical parameters such as critical temper-
ature, pressure, and volume are also important state description
parameters. However, critical parameters are still difficult to
measure directly and no critical parameters for EPDMOS and
EPDEOS have been reported in the literature. Therefore,
critical parameters are estimated mainly by a group
contribution method with known thermodynamic data.16
Nannoolal and co-workers21 proposed a new group
contribution method to estimate critical property data for
pure organic chemicals including some silicone compounds. In
comparison with traditional Lydersen22 and Joback23 methods,
this new method can be used to investigate the influence of
complex structures, especially the type and number of groups
attached to the central Si atom, on the estimation of critical
parameters and gave more accurate results for Si-containing
compounds. Therefore, the critical parameters, which include
Figure 2. Relative deviation of the experimental saturation temper-
atures Texptl of (a) EPDMOS and (b) EMDEOS from 2035 Pa to
○
▲
64 000 Pa from Tcalc obtained in this work: , Antoine equation;
,
Clarke−Glew equation.
The extrapolated normal boiling points for EPDMOS and
EPDEOS were calculated by the Antoine and Clarke−Glew
equations with parameters listed in Tables 3 and 4, and the
results are presented in Table 5. The Clarke−Glew and Antoine
equations are not recommended for extrapolation once
parameters were out of the applicable pressure or temperature
range. However, when saturation temperatures higher than the
applicable range are necessary in the design or as a guide for
operation, both the Clarke−Glew and Antoine equations
should be used with caution.
3.4. Standard Molar Enthalpy of Vaporization. When
the vapor pressure data are regressed using the Clarke−Glew
equation (eq 3), the standard molar enthalpies of vaporization
for EPDMOS and EPDEOS at T = 298.15 K, Δgl Hm0 (298.15 K)
are 62.52
0.28 and 65.19
1.63 kJ mol−1, respectively.
Table 5. Properties of EPDMOS and EPDEOS
a
b
c
d
e
chemical name
Tb
Tb
Tb
Tc
Pc
Vc
ω
ω
K
K
K
K
kPa
cm3·mol−1
EPDMOS
EPDEOS
487.35 9.0
526.75 9.0
486.14
512.35
486.52
512.59
687.00
698.34
2416.88
1912.22
657.11
791.06
0.4343
0.5255
0.4373
0.5256
a
b
Literature value in ref 14 calculated using ACD/Laboratories Software V11.02. Extrapolated value from Antoine equation with parameters listed in
c
d
Table 3. Extrapolated value from Clarke−Glew equation with parameters listed in Table 4. The acentric factor calculated with the Clarke−Glew
equation. The acentric factor calculated with the Antoine equation.
e
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DOI: 10.1021/acs.jced.5b00255
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Journal of Chemical & Engineering Data
Article
critical EPDMOS and EPDEOS temperature (Tc), pressure
(pc), and volume (Vc) were estimated using this method, as
shown in eqs 6 to 8.
weighted least-squares regression method. Both equations
exhibit a good correlation between the model and experimental
data, and both sets of regressed parameters could satisfy the
estimation requirements for the development and design of the
chemical separation process. The fractional deviations of the
experimental saturation temperatures of EPDMOS and
EPDEOS in the experimental pressure range from values
calculated from the Clarke−Glew equation are lower than those
from values calculated from the Antoine equation since the
Clarke−Glew equation yields a lower standard deviation of fit
(σF) than the Antoine equation.
Regression using the Antoine equation gives Antoine
parameters (A = 9.1280, B = 1590.18, C = −100.39 K and A
= 9.1048, B = 1678.64, C = −102.84 K) for EPDMOS and
EPDEOS, respectively. When using the Clarke−Glew equation,
the standard vaporization enthalpy at 298.15 K, Δgl Hm0 (298.15
K) and the difference between the heat capacities of the ideal
gas and the liquid phase at 298.15 K, Δgl Cp0,m(298.15 K) were
determined. The values of Δgl H0m(298.15 K) for EPDMOS and
EPDEOS are 62.52 0.28 kJ·mol−1 and 65.19 1.63 kJ·mol−1,
respectively, and their Δgl Cp0,m(298.15K) values are −80.56
2.18 J·mol−1·K−1 and −72.83 10.98 J·mol−1·K−1, respectively.
The critical parameters of these two compounds are
estimated from the group contribution and group interaction
method. When the saturated vapor pressures at the reduced
temperatures are calculated using the Clarke−Glew equation,
the acentric factors, ω, of EPDMOS and EPDEOS are
estimated to be 0.4373 and 0.5256, respectively. When the
saturated vapor pressures at the reduced temperatures are
calculated using the Antoine equation, the acentric factors, ω, of
EPDMOS and EPDEOS are estimated to be 0.4343 and
0.5255, respectively.
⎛
⎞
1
⎜
⎟
⎟
⎠
T = T b +
c
b
⎜
⎝
a + (∑iN=1 NCi + GI)c
i
(6)
P
Mb(g/mol)
c
=
(a + ∑iN=1 NCi + GI)2
kPa
(7)
(8)
i
N
i=1
∑
NCi + GI
V
i
c
=
+ b
Na
10−6 m3·mol−1
where Ni is the number of groups of type i; Ci is the group
contribution of group i; M is the molecular weight (g·mol−1); a,
b, and c are adjustable parameters listed in Table 6; N is the
Table 6. Parameter Values for Equations 6 to 8
property
a
b
c
Tc
Pc
Vc
0.9889
0.00939
−0.2266
0.6990
−0.14041
86.1539
0.8607
number of atoms in the molecule (except hydrogen); and GI is
the total group interaction contribution. Detailed procedures
for estimation of the critical properties of EPDMOS and
EPDEOS are shown in Tables S5a to S5f (in the Supporting
Information) and the estimated parameters are listed in Table
5.
The acentric factor ω is defined as
ω = −log10(psat) − 1
at T = 0.7
The Antoine parameters, Clarke−Glew parameters, acentric
factors, and the molar enthalpies of vaporization obtained for
EPDMOS and EPDEOS are useful fundamental data for
industrial separation processes.
r
(9)
r
where Tr is the reduced temperature (Tr = T/Tc) and psrat = ps/
pc is the reduced vapor saturation pressure. When values of ps at
T = 0.7·Tc are calculated using either the Antoine (eq 1) or the
Clarke−Glew equation (eq 3), the acentric factors ω of
EPDMOS and EPDEOS are calculated from the deduced vapor
saturation pressure and the results are given in Table 5. The
saturated vapor pressure of EPDEOS at Tr = 0.7 falls within the
range of the measurements and both the Clarke−Glew
equation and the Antoine equation give almost the same
value of the saturated vapor pressure at Tr = 0.7. Therefore,
these two models yield almost the same acentric factor ω for
EPDEOS. Unfortunately, the saturated vapor pressure of
EPDMOS at Tr = 0.7 is out of the range of the measurements
and these two models give different values of the predicted
saturation vapor pressure at Tr = 0.7 (88.91 kPa from eq 1 and
88.30 kPa from eq 3), which yield different values of the
acentric factor ω for EPDMOS (0.4343 vs 0.4373). Just as
mentioned above, both the Clarke−Glew and Antoine
equations are not recommended for extrapolation once
parameters were out of the applicable pressure or temperature
range.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jced.5b00255.
Results of the weighted least-squares regression and their
coefficient covariance matrixes of the Clarke−Glew
equation and the Antotine equation for EPDMOS and
EPDEOS are listed in Tables S1a to S4b. The estimation
of the critical properties of EPDMOS and EPDEOS are
presented in Tables S5a to S5f. (PDF)
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: chaunwu@yahoo.com. Tel: +86 571 28867861.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
4. CONCLUSION
■
The saturation temperature of EPDMOS and EPDEOS at
various pressures ranging from 2.035 kPa to 64.0 kPa was
determined by means of an inclined ebulliometer. To our
knowledge, this is the first study that reports on the saturation
temperature of these two compounds. The Antoine and
Clarke−Glew equations were fitted to the data using the
This work was supported by the Scientific Research Project in
Social Development Field (Grant No. 20130533B16) spon-
sored by Hangzhou Science and Technology Committee of
China, Zhejiang Province Key Project of Science and
Technology (Grant No. 2014C01039) sponsored by Science
and Technology Department of Zhejiang Province and China
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Journal of Chemical & Engineering Data
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