Vapor-liquid critical properties of some tetraalkoxysilanes

Article abstract of DOI:10.1021/je800086s

The critical pressures and the critical temperatures of ten tetraalkoxysilanes (tetraalkyl esters of silicic acid) Si[O(CH₂) _nH]₄ with n = 1 to 10 have been measured. All the substances studied begin to decompose at temper

Full text of DOI:10.1021/je800086s

J. Chem. Eng. Data 2008, 53, 1371–1374
1371
Vapor-Liquid Critical Properties of Some Tetraalkoxysilanes
Eugene D. Nikitin* and Alexander P. Popov
Institute of Thermal Physics, Ural Branch of Russian Academy of Sciences, Amundsena Street,
106, 620016 Ekaterinburg, Russia
Viktoria A. Simakina
Institute of Organic Synthesis, Ural Branch of Russian Academy of Sciences, Sof’i Kovalevskoi Street,
20, 620219 Ekaterinburg, Russia
The critical pressures and the critical temperatures of ten tetraalkoxysilanes (tetraalkyl esters of silicic acid)
Si[O(CH2)nH]4 with n ) 1 to 10 have been measured. All the substances studied begin to decompose at
temperatures below their critical points. The method of pulse-heating applicable to thermally unstable
compounds has been used. Residence times were from (0.03 to 1) ms, which resulted in little decomposition
of the substances during measuring. The experimental critical properties of tetraalkoxysilanes have been
compared with the values estimated by the group-contribution methods of Lydersen and Nannoolal et al.
Table 1. Purities of Compounds Used in Critical Point
Measurement
Introduction
Tetraalkoxysilanes (tetraalkyl esters of silicic acid)
Si[O(CH2)nH]4 are widely used in many applications as liquid
purity/%
before measuring after measuring
critical constants critical constants
polymers, as glues, as lacquers, as start materials for forming
mesaporous silica oxide structures, for stabilizing thermoplastic
polycarbonates, etc. This paper presents the critical temperatures
and pressures of tetraalkoxysilanes with straight alkyl chains
from tetramethoxy- (n ) 1) to tetradecoxysilane (n ) 10).
Previously, the critical constants were measured only for
tetramethoxy-, tetraethoxy-, and tetrapropoxysilanes.1 Alkox-
ysilanes that contain SiOCH3 or SiOC2H5 groups are known to
decompose at temperatures higher than 475 K, and the thermal
stability of alkoxysilanes decreases with increasing length of
the alkyl chain.2 The critical temperatures of tetraalkoxysilanes
measured are from (558 to 849) K. Therefore, it is reasonable
to assume that all the tetraalkoxysilanes studied are thermally
unstable at their critical points. The pulse-heating method with
ultralow residence times applicable to unstable compounds was
used for the measurements.
compound
tetramethoxysilane 681-84-5
tetraethoxysilane 78-10-4
tetrapropoxysilane 682-01-9
tetrabutoxysilane 4766-57-8
tetrapentoxysilane 6382-12-3
tetrahexoxysilane 7425-86-7
tetraheptoxysilane 18759-42-7
CASRNa
99.9
99.9
99.9
99.9
99.9
99.8
99.9
99.9
99.9
99.9
99.9
99.9
99.8
99.9
99.9
99.7
99.9
99.9
99.8
99.9
tetraoctoxysilane
tetranonoxysilane
tetradecoxysilane
78-14-8
18817-76-0
18845-54-0
a Chemical Abstracts Service Registry Number.
the samples is not significantly changed in the course of
measuring the critical properties.
Method. The technique used here for measuring the critical
constants has previously been extensively used by our group.
It has proven to be reliable and useful for compounds that
decompose significantly near their critical temperatures. The
pulse-heating apparatus and procedure have been described in
detail in previous publications.3–5 A liquid under study filled a
thin-walled Teflon cup, and the pressure outside the cup was created
by a press and measured by a dial gauge. A platinum wire probe,
2·10-3 cm in diameter and (1 to 3) cm in length, was placed in
the liquid. The probe was heated by pulses of electric current in
such a way that by the end of a pulse the probe and the thin
liquid layer near it were heated to the temperature of spontane-
ous boil-up (attainable superheat). The time from the start of a
pulse to the moment of boil-up was from (0.03 to 1.0) ms. At
the moment of boil-up, a probe temperature perturbation arises
from an abrupt change of the conditions of heat transfer from
the probe to the liquid. The probe temperature was determined
from its resistance at that moment. The probe temperature
perturbation may be both positive and negative. The pressure
in the liquid increased until the negative temperature perturbation
Experimental Section
Materials. Samples of tetraalkoxysilanes were synthesized,
purified, and analyzed at the Institute of Organic Synthesis of
RAS (Ekaterinburg) under the leadership of Dr. Yuri Yatluk.
The alkoxysilanes were prepared by transesterification of
tetramethoxysilane or tetraethoxysilane with 1-alkanols. For
example, Si[OCH3)4 (1 mol) was transesterified with 1-decanol
containing sodium decylate (0.017 mol) as a catalyst. The
mixture was refluxed for 2 h. The methanol was distillated, and
the residue was fractioned at vacuum. The yield was from (60
to 70) %. Before and after the critical properties measurements,
the purities of the samples were determined by proton magnetic
spectroscopy (Bruker DRX 400). Table 1 gives the Chemical
Abstract Service Registry Numbers (CASRN) of the tetraalkox-
ysilanes studied and the purities of the samples. The purity of
* Corresponding author. E-mail: e-nikitin@mail.ru. Fax: +7-343-2678800.
10.1021/je800086s CCC: $40.75
2008 American Chemical Society
Published on Web 05/07/2008

1372 Journal of Chemical & Engineering Data, Vol. 53, No. 6, 2008
dropped to the level of the apparatus sensitivity (1·10-3 K).
This pressure was taken to be equal to the measured value of
the critical pressure pmc , and the temperature of the attainable
superheat at this pressure was taken to be equal to the measured
value of the critical temperature Tmc . The values of pcm and Tmc
are always lesser than the true critical properties and require
correction. It is an inherent feature of the pulse-heating method
that cannot be removed by modification of the apparatus. The
true critical constants of a stable compound were calculated from
the following equations
Table 2. Normal Boiling Points and Critical Temperatures of
Tetraalkoxysilanes: Experimental Values and Comparison with
Predictive Methods
Tb/K
Tc/K
ref 9 ref 16
compound
exptl calcd, ref 17
exptl
tetramethoxysilane 394.5a
442a
tetrapropoxysilane 502b
394.3
450.0
519.7
558 ( 6d
562.8 ( 0.2e
587 ( 6d
547.2 580.0
578.5 600.0
631.8 653.7
tetraethoxysilane
592.2 ( 0.2e
649 ( 6d
647.7 ( 0.4e
682 ( 7d
tetrabutoxysilane
tetrapentoxysilane
tetrahexoxysilane
tetraheptoxysilane
tetraoctoxysilane
tetranonoxysilane
tetradecoxysilane
AAPE/%f
548c
578.2
628.9
673.9
714.5
751.6
785.9
817.8
674.8 688.1
765.0
pc ) pmc ⁄ πo, Tc ) Tcm ⁄ τ0
(1)
714 ( 7d
757 ( 8d
797.0
824.1
847.8
868.7
where 1/π0 and 1/τ0 are correction factors.3 To calculate the
correction factors, the thermophysical properties of the liquid
and the vapor phase near the critical point are required. These
properties are calculated by the principle of corresponding states
using the formulas given in a previous paper.6 The formulas
contain a similarity parameter of the compound under study:
the acentric factor or the analogous parameter suggested by
Filippov7
778 ( 8d
812 ( 8d
830 ( 8d
849 ( 8d
887.6
1.8
2.7
4.0
7.1
MAPE/%g
a Ref 8. b Ref 9. c Ref 10. d This work. e Ref 1. f AAPE ) (1/
N)(Σ|Yecxptl - Yccalcd|Yecxptl), where N is the number of experimental data
points, Ycexptl is the experimental value of the critical property, and Yccalcd
is the calculated value of the critical property. g MAPE ) (|Ycexptl
-
pvp T ⁄ T ) 0.625
Yccalcd max/Yecxptl).
|
(
)
c
A ) 100
pc
Table 3. Critical Pressures pc/MPa of Tetraalkoxysilanes:
Experimental Values and Comparison with Predictive Methods
where pvp is the vapor pressure at a reduced temperature equal
to 0.625.
compound
exptl
ref 9
ref 16
2.975
The Filippov parameters and the critical properties of
alkoxysilanes were calculated by an iteration method. For the
first iteration, pmc and Tcm were used as the critical constants.
The vapor pressure of the tetraalkoxysilanes with n ) 1 to 4
was estimated by the following equation
tetramethoxysilane
2.89 ( 0.09a
2.873 ( 0.007b
2.04 ( 0.06a
2.045 ( 0.007b
1.37 ( 0.04a
1.696 ( 0.007b
1.10 ( 0.03a
0.89 ( 0.03a
0.79 ( 0.02a
0.74 ( 0.02a
0.66 ( 0.02a
0.61 ( 0.02a
0.60 ( 0.02a
2.779
tetraethoxysilane
tetrapropoxysilane
1.981
1.539
2.017
1.508
tetrabutoxysilane
tetrapentoxysilane
tetrahexoxysilane
tetraheptoxysilane
tetraoctoxysilane
tetranonoxysilane
tetradecoxysilane
AAPE
1.259
1.064
0.922
0.813
0.728
0.658
0.601
8.7
1.168
0.930
0.758
0.628
0.529
0.451
0.389
12.6
C
ln pvp ) B -
T
The parameters B and C were calculated from the values of
pmc and Tmc and the normal boiling points. The normal boiling
temperatures were taken for tetramethoxy- and tetraethoxysilanes
from the NIST Chemistry WebBook,8 for tetrapropoxysilane
from the paper by Myers and Danner,9 and for tetrabutoxysilane
according to the Sigma-Aldrich recommendations.10 We failed
to find any information about the vapor pressure of heavier
tetraalkoxysilanes. The Filippov parameters of tetraalkoxysilanes
with n ) 5 to 10 were estimated using the equation suggested
in our previous paper11
MAPE
16.5
35.2
a This work. b Ref 1.
study in the course of heating. The critical properties of
tetraalkoxysilanes were measured with the help of probes (1,
2, and 3) cm in length at heating times t* ) (0.03, 0.06, 0.11,
0.22, 0.45, and 1.00) ms. Two to four samples of each compound
were used in the experiments. The tetraalkoxysilanes studied
are unstable at their critical points. However, in our experiments,
the tetraalkoxysilanes showed no evidence of decomposition,
and no dependence of the apparent critical properties on the
heating time t* was found; therefore, the experimental data were
averaged over all the probe lengths, heating times, and samples.
Uncertainties. The uncertainties of the critical constants
measured by the pulse-heating method were discussed in detail
in our previous papers.13,14 We estimate the uncertainties for
tetraalkoxysilanes investigated at 0.03pc and 0.01Tc, where Tc
is the absolute temperature. It corresponds to an uncertainty from
(( 0.09 to ( 0.02) MPa for the critical pressure and from ((
6 to ( 8) K for the critical temperature.
ln A ) a + bn2⁄3
Then, from the values of π0 and τ0 and using eq 1, pc and Tc
were calculated. For the second iteration, the Filippov parameter
and the critical temperature and pressure were calculated using
the values obtained after the first iteration. Two iterations were
enough because the values of π0 and τ0 are little affected by
the variations of Filippov’s parameter.
For calculating the correction factors, two additional quantities
are needed: the factor GT ≡ ∂ ln J/∂T, where J is the rate of
bubble nucleation in a superheated liquid, and the ideal gas heat
capacity of a compound under investigation. The factor GT was
measured in one experiment with the critical constants as
described previously3 and estimated at 1.5 K-1. The ideal gas
heat capacity was estimated using the atomic contribution
method by Harrison and Seaton12 with the contribution for
silicon recommended by Myers and Danner.9
Results and Discussion
The apparent critical temperature and pressure of a thermally
unstable compound determined as described above may depend
on the time from the beginning of a heating pulse to the moment
of boiling-up, t*, due to the decomposition of a compound under
The critical temperatures and pressures of tetraalkoxysilanes
included in this study are given in Tables 2 and 3 and Figure 1.
These tables and the figure also contain the critical constants
of tetramethoxy-, tetraethoxy-, and tetrapropoxysilanes measured

Journal of Chemical & Engineering Data, Vol. 53, No. 6, 2008 1373
Figure 2. Correlation of the critical pressure of tetraalkoxysilanes
Si[O(CH2)nH]4 as a function of the number of CH2 groups n in the alkyl
radical and molar mass M. 9, this work; O, ref 1. The solid line corresponds
to eq 2.
methods require the normal boiling points to calculate the critical
temperatures. We know experimental normal boiling tempera-
tures only for four tetraalkoxysilanes from tetramethoxy- to
tetrabutoxysilane. For these alkoxysilanes, the critical temper-
atures were calculated using experimental normal boiling points.
For the rest of the alkoxysilanes the normal boiling temperatures
were estimated by the method suggested by Nannoolal et al.17
Table 2 shows that the discrepancy between experimental and
calculated values of the normal boiling temperature increases
progressively with increasing number of CH2 groups in a
molecule of tetraalkoxysilane and achieves about 30 K for
tetrabutoxysilane. One may suggest that this discrepancy will
hardly be lesser for heavier tetraalkoxysilanes. For the reason
of unsatisfactory estimates of the normal boiling points, we
calculated the critical temperatures of tetrapentoxy- to tetrade-
coxysilane using only the method by Nannoolal et al.16 The
idea was as follows. The methods of the estimation of the normal
boiling temperature and the critical temperature suggested by
Nannoolal et al. are the two parts of one approach and use the
same set of structural groups, whereas in the Lydersen method,
another set of groups is used.
The critical properties of tetraalkoxysilanes calculated in such
a way are given in Tables 2 and 3. Percent deviations of the
calculated values from the experimental critical constants are
shown in Figure 3. If the experimental normal boiling temper-
atures are used, both estimation methods give reasonable critical
temperature estimates that compare favorably with experimental
critical temperature data. The average absolute percent deviation
(AAPE) is equal to 1.8 % and 1.9 % for the estimation methods
by Lydersen and Nannoolal et al., respectively. For tetraalkox-
ysilanes from tetrapentoxy- to tetradecoxysilane when the
estimated normal boiling points are used, AAPE is considerably
greater and exceeds 5.3 %. The critical pressure is predicted by
the Lydersen method to be better than the method of Nannoolal
et al. AAPE is equal to 8.7 % for the method by Lydersen
against 12.6 % for that by Nannoolal et al.
Figure 1. Critical temperatures (a) and pressures (b) of tetraalkoxysilanes
Si[O(CH2)nH]4 vs the number of CH2 groups n in the alkyl radical. 9, this
work; O, ref 1.
by Waterson and Young.1 In Tables 2 and 3, the experimental
values of the critical properties are shown together with their
uncertainties. The difference between our values of the critical
temperatures and those by Waterson and Young does not exceed
the combined uncertainties. The situation with the critical
pressure is more complex. The critical pressures of tet-
ramethoxy- and tetraethoxysilanes obtained by us and Waterson
and Young are very close to each other, but the critical pressure
of tetrapropoxysilane determined by Waterson and Young is
considerably higher than ours. A possible reason for this may
be greater thermal decomposition of tetrapropoxysilane in the
experiments of Waterson and Young. They write nothing about
decomposition of tetraalkoxysilanes in the course of their
experiments. However, against this explanation is the fact that
the critical temperatures of this compound obtained by us and
Waterson and Young practically coincide.
According to the well-known correlation by Lydersen,15 the
quantity (M/pc)1/2 should be a linear function of the number of
CH2 groups in a molecule for a given homologous series. Here
M is the molar mass. However, for tetraalkoxysilanes, a
quadratic equation works better
{[M/(kg · mol-1)]/[pc/MPa]}1/2
0.0998 + 0.1217n - 0.0026n2 (2)
The solid line in Figure 2 corresponds to eq 2.
)
Conclusion
The critical temperatures and pressures of tetraalkoxysilanes
Si[O(CH2)nH]4 with n ) 1 to 10 have been measured.
Previously, the experimental critical constants were available
only for tetramethoxy-, tetraethoxy-, and tetrabutoxysilanes. The
critical properties of tetraalkoxysilanes have also been estimated
by the group-contribution methods of Lydersen and Nannoolal
et al. For tetraalkoxysilanes from tetramethoxy- to tetra-
Most of the well-known group-contribution methods do not
apply to tetraalkoxysilanes because they do not have contribu-
tions for silicon atoms and groups containing silicon. In fact,
we found in the literature only two methods: the method by
Lydersen15 with group and atomic contributions determined by
Myers and Danner9 and that by Nannoolal et al.16 Both of the

1374 Journal of Chemical & Engineering Data, Vol. 53, No. 6, 2008
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Figure 3. Percent deviations of the experimental critical temperatures (a)
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calculated by group contribution methods as a function of the number of
CH2 groups in the alkyl radical n. GC methods: 9, ref 9; O, ref 16.
propoxysilane, when the experimental normal boiling temper-
atures are used, both estimation methods give reasonable critical
temperature estimates. For tetraalkoxysilanes from tetrapentoxy-
to tetradecoxysilane, the normal boiling points and then the
critical temperatures have been estimated using the method of
Nannoolal et al. In this case, the calculated critical temperatures
are considerably higher than the experimental ones. The critical
pressure is predicted by the Lydersen method to be better than
the method of Nannoolal et al.
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Acknowledgment
We are grateful to Dr. Danner and Dr. Nannoolal for sending copies
of their papers.
Literature Cited
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Received for review February 5, 2008. Accepted March 24, 2008.
JE800086S