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Dielectric properties of alternative refrigerants

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 1070-9878/06/$20.00 © 2006 IEEE 503
Dielectric properties of alternative refrigerants
F. J. V. Santos, R. S. Pai-Panandiker, C. A. Nieto de Castro
Departamento de Química e Bioquímica and Centro de Ciências Moleculares e Materiais Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
and
U. V. Mardolcar
Instituto Superior Técnico, Departamento de Física e Núcleo de Termofísica, Av. Rovisco Pais, 1049-001 Lisboa, Portugal and Centro de Ciências Moleculares e Materiais Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
ABSTRACT
This paper gives an overview of our research, from experimental measurements of the relative permittivity on new and alternative refrigerants, to theoretical interpretation of the data and density functional and density functional self-consistent reaction field calculations for a series of HFC molecules. Experimental measurements were obtained as a function of temperature and pressure for Class B refrigerants – HCFC-123, HCFC-142b, HCFC-141b, Class A refrigerants – HFC-32, HFC-134a, HFC-152a, HFC-143a, HFC-227ea, HFC-245fa, HFC-365mfc and some mixtures of them: HFC-125/143a/134a (R-404A), HFC-32/125/134a (R-407C), HFC-125/143a (R-507), HFC-32/125 (R-410A). Density functional and density functional self-consistent reaction field calculations were performed for CHF2CF3 (HFC-125), CH2FCF3 (HFC-134a), CH3CF3 (HFC-143a), CH2F2 (HFC-32), and CHF2CH3 (HFC-152a). A particular emphasis has been given to the calculation of dimerisation energies, rotational potentials, polarisabilities and dipole moments.
Index Terms
—
Cooling, dielectric liquids, dielectric measurements.
1 INTRODUCTION
THE
measurement of the relative permittivity allows the study of fluid molecular behavior when subjected to an electric field, related to chemical structure and molecular interactions. In industry, measurements of relative permittivity of these fluids give operational values for design parameters of machinery used in the air conditioning and refrigeration industry. This property also affects the electric properties of compressor lubricants, where the refrigerants are soluble. The search for the replacement of harmful halocarbons used in the refrigeration, air conditioning and foam blowing industries lead the international community to the establishment of a concerted effort to determine the thermophysical properties of the alternative compounds, chosen to have a small or zero ozone depletion potential and small global warming potential. Since 1990, our research group has done a considerable work on dielectric properties environmentally acceptable refrigerants. The current international agreements addressing global environmental issues (the Montreal and Kyoto Protocols) provide the guidelines needed to ensure that all refrigerant and blowing agent solutions are environmentally safe. The Montreal Protocol has provided a phase-out of all ozone depleting substances, inducing the utilization of substances with zero ozone depletion potential. Our work started with the study of Class B compounds, evolving to Class A compounds, those with zero ozone depletion potential
1
.An instrument for the determination of absolute values of relative permittivity was designed and constructed to operate in an extended thermodynamic range, from 170 K up to 370 K, at pressures up to 30 MPa. The measurements use the direct capacitance method. The description of the cell has been presented before by Mardolcar
et al
. [1] and the sample handling, vacuum and pressure system by Gurova
et al
. [2]. The measuring process uses a fully automated instrumentation, operated from a computer graphics user interface, described elsewhere [3]. Vacuum capacitance was measured as a function of temperature before filling the cell with the fluid.
1
Ozone Depletion Potential – capacity of destruction of a given number of ozone molecules by chlorine atoms, calculated through a chemical model for the stratospheric ozone, assuming the stationary state of emission and destruction. Relative to CFC-11 (trichlorofluoromethane).
Manuscript received on 15 July 2005, in final form 26 December 2005.
F. J. V. Santos et al.: Dielectric properties of alternative refrigerants504
An impedance gain-phase analyzer (Schlumberger, model SI 1260) has been used with an uncertainty of 5x10
-4
pF. This equipment was calibrated by Laboratório de Metrologia Eléctrica da Companhia Portuguesa Radio Marconi, Lisbon, using the standards of capacitance of 1 pF, 10 pF, 100 pF, 1000 pF, 0.01 mF, 0.1 mF and 1 mF, with an uncertainty of 0.01%. The technique employed a four terminal connection to the cell in order to compensate for parasitic impedances. The mean value of a 10-dimensional sample taken at a 10 kHz frequency provides the experimental value of relative permittivity, which proved to be properly suited to the working accuracy. As referred above the measuring process is now completely automatic and operated from a computer graphics user interface, making the data analysis faster and statistically more significant. Relative permittivity
ε
of the fluid is determined from the ratio between
C
(
p,T
) - the geometric capacitance at pressure p and temperature
T
- and
C
0
(
T
) - the capacitance under vacuum at a temperature
T
, equation (1):
)(),(
0
T C T pC
=
ε
(1)The cell temperature was measured with a calibrated platinum resistance thermometer (100
Ω
at 0 ºC) located near the sample, and which resistance was determined with a four-wire measurement, by a digital multimeter (Keithley, model 199 DMM), calibrated with three standard resistors, giving an uncertainty for the temperature measurement of 0.01 K. The pressure vessel is immersed in a cylindrical copper vessel cooled by a cryostat (Julabo Model FPW90-SC), filled with ethanol and operative in the range from 183 to 373 K with an uncertainty of 0.1 K. A high-pressure system composed of a HIP manual liquid-pressure generator and an air-operated, diaphragm-type compressor (Newport Scientific) was used. The pressure was measured with a pressure transducer (Setra Systems) with an uncertainty of 0.01 MPa. Vacuum points were stable at the level of 10
-4
pF over the duration of this study. The presence of impurities causes an extra source of uncertainty, can amount to a maximum of 0.5 mass %, with a maximum contribution to the uncertainty budget of the order of 1 part in 10
3
. The uncertainty of the experimental measurements of the relative permittivity with the present apparatus was found to be better than 0.16%, for a confidence interval of 95%
2
.The schematic diagram of the apparatus set-up for the measurements of the relative permittivity in the liquid phase is presented in Figure 1. All the experimental points measured at a given temperature
T
, were adjusted to nominal temperatures
T
n
, close to
T
, by using: (2)
2
ISO definition of uncertainty, with
k
= 2 (95% confidence) was used. Using current calculations for uncertainty (accuracy), the values reported here must be divided by two.
Density was obtained from the best available equations of state or reference databases, like REFPROP
[4]. The results were expressed as functions of temperature, and pressure or density. Figure 2 shows the results obtained for 1,1,1,3,3- pentafluoropropane (HFC-245fa). The behavior is qualitatively identical for all the pure fluids and mixtures studied, as
T
P
∂∂
ε
is positive and
P
T
∂∂
ε
is negative. However,
T
∂∂
ρ ε
is always positive.
Figure 1.
Schematic diagram of the apparatus. The figure is self contained.
Figure 2.
The relative permittivity of 1,1,1,3,3- pentafluoropropane,
ε
, as a function of density,
ρ
, for the different isotherms.
+
303.84 K;
- 293.23 K;
- 283.19 K;
- 273.12 K;
×
- 263.00 K;
−
- 253.01 K;
- 243.02 K;
- 233.12 K;
- 224.16 K;
- 218.53 K
( ) ( ) ( )
T T T p ,T p ,T
n pn
−
∂∂+=
ε ε ε
678910111300135014001450150015501600
ρ
/ kg.m
-3
ε εε ε
IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 505
2 DATA ANALYSIS
An analysis of the experimental data of relative permittivity as a function of density is also presented in this paper. The Vedam formalism was applied based on the work of Vedam
et al
. [5,6] and Diguet [7]. According to this theory, the variation of the relative permittivity with pressure is a function of the deformation of the volume, showing a non-linear behavior in the case of liquids. This non-linearity can be reduced when the variation of
ε
,
∆
, defined by equation (3) is analyzed as a function of the Eulerian deformation,
Σ
, also named the Eulerian strain, defined by equation (4). It is possible to verify that
Σ
provides a linear relation for
∆
independently of the type of molecules that compose the fluid. (3) (4)In these equations,
ρ
0
is the reference density, taken in this case as the saturation value for each isotherm. The calculations made show that the function
∆
indeed represents a linear variation with the Eulerian Strain
Σ
, as can be seen in Figure 3, for liquid pentafluoropentane (HFC-125)[8]. The same result has been obtained for all pure fluids, and mixtures of fixed composition. This behavior is really remarkable and can be used as a predictive tool, as the intercept B of equation (3) is nearly zero, with a decrease in the accuracy of the data predicted. See, p.e., [8].
Figure 3.
Variation of
∆
with the Eulerian strain,
Σ
(equations (3) and 4)) for liquid pentafluoropentane (HFC-125) [8].
The molecular theories developed to interpret the relation between the dipole moment of a liquid of polar molecules and the electric permittivity are based on the definition of Onsager`s local field [9]. The most important are those based on the statistical theories of polarizability, namely the theories of Kirkwood [10] and of Frölich [11]. Unfortunately, in the absence of information about the refractive index of the liquids studied, and of its dependence on density and frequency, the only molecular theory that can be applied to the data of all refrigerants measured, is the theory of molecular polarizability developed by Kirkwood [10]. In this theory, the apparent dipole moment of the liquid
µ
* is calculated from the following relation:
( )( )
( )
+=
+−
T k N M
B* A
02
339121
ε µ α ρ ε ε ε
(5)where M is the relative molar mass of the fluid,
N
A
is the Avogadro constant,
α
is the molecular polarizability of the molecule,
ε
0
is the electric permittivity in vacuum,
T
is the absolute temperature,
k
B
is the Boltzmann constant and
ρ
is the density, evaluated for each thermodynamic state of the liquid. The apparent dipole moment is
µ
*=
g
1/2
µ
, where
µ
is the dipole moment in the ideal gas state and
g
is the Kirkwood correlation parameter, which represents the restriction to rotation imposed by a cage of molecules surrounding a given molecule (the model assumes a spherical cavity, see Figure 7). Kirkwood, on the basis of a quasi-crystalline model, defined this parameter
g
as: (6)where
z
i
is the number of neighbors to the central molecule under consideration in the i-th coordination shell, and
i
cos
γ
is the average cosine angle
γ
formed by the dipole moments of molecules in the i-th shell with the dipole of the central molecule, exemplified in Figure 4, with schematic dipoles.
Figure 4.
Schematic representation of the first coordination shell, for
z
i
= 5.
For non-polar or non-associated liquids
g
≈
1, but for polar liquids it considerably differs from unity (for water a value of 2.6, for
z
i
= 4 was found
)
. The greater the value of
g
, the bigger the orientational order imposed by the neighbors. Equation (5) shows that, if the theory is correct, the value of
µ
* can be calculated by a linear regression of the left-hand side of equation (7) as a function of 1/
T
. Figure 5 shows the variation of the Kirkwood function, equation (5), with the reciprocal temperature, for 1,1,1,3,3-penta-fluoropropane
( ) ( )
02121
ρ ε ρ ε
−=∆
−=Σ
320
121
ρ ρ
0.000.020.040.060.080.100.120.140.16
0.0000.0050.0100.0150.0200.0250.0300.0350.0400.045
−Σ −Σ −Σ −Σ ∆∆∆∆
303.74 K294.08 K283.21 K273.19 K263.32 K 253.29 K243.31 K233.19 K223.20 K214.32 K
∞=
+==
12
1
2
iii*
cos z g
γ µ µ
γ
i
First coordination shell
F. J. V. Santos et al.: Dielectric properties of alternative refrigerants506
(HFC-245fa) [12]. A value of
µ
* = 2.688 D is obtained. Using the value of the dipole moment (
µ
=1.549 D) in the gas phase [13], the value of the Kirkwood parameter
g
was found to be equal to 3.01, a value which demonstrates a complete hindered rotation of these molecules in the liquid state. Looking to the values obtained for the apparent dipole moments in the liquid phase, the corresponding values for the dipole moments in the gaseous phase and the Kirkwood factors, it was found that the HFC’s and the HCFC’s exhibit gas phase dipole moments (
µ
g
) in the following order [14,15]: (1) 123 < 125 < 134a < 32 < 141b < 142 b < 152a < 143a
Figure 5.
Variation of the Kirkwood function (equation (8)) with the reciprocal temperature for 1,1,1,3,3-pentafluoropropane (HFC-245fa).
Experimental values; line – (equation (5)).
The values obtained for the liquid phase (
µ
*), based on the Kirkwood theory have a slightly different trend given by: (2) 123 < 125 < 141b < 142b < 143a < 134a < 32 < 152a As a consequence of these differences, the Kirkwood correlation factor
g
, has an interesting behavior: (3) 143a < 141b < 142b < 125 < 123 < 152a < 32 < 134a Since
g
is indicative of the restriction to rotation imposed by a cage of surrounding molecules on a given molecule, the results may suggest that the HFC
143a has the greatest rotational mobility in the liquid state, whereas HFC
134a has the greatest rotational hindrance. The values obtained are displayed in Table I, along with values obtained with the Kirkwood-Frölich theory [11], using only refractive index data for the gas phase. Although this is a simplification, it might suggest that the apparent dipole moments obtained with the Kirkwood theory are overestimated. In fact and as previously mentioned, the relationship between the apparent dipole moments and the effective dipole moment in the liquid is not direct and involves statistical-mechanical theories of relative permittivity. In this sense, some of the more recent studies on liquid water [16-18] have contributed to a better definition of the meaning and value of the dipole moment in the liquid state. As an example, Silvestrelli and Parrinello [16] estimated the dipole moment of liquid water to be 2.95 D, using classical molecular dynamics calculations, Gregory
et al
. [17] using
abinitio
cluster calculations estimated it to be 2.7 D and Baydal
et al
. [18] from the x-ray structure measured with synchrotron radiation to be 2.9 ± 0.6 D. The value obtained for water using Kirkwood theory is 2.98, in excellent agreement with these calculations, a strong indication that Kirkwood model is a simple and reliable calculation procedure. There is a strong correlation between the apparent dipole moment in Kirkwood theory and the dipole moment of the same compound in the gas phase, given by equation (6). If we represent
µ
* as a function of
µ
g
, we can obtain the plot of Figure 6. A line is sketched in the plot, just dividing the zones for free rotation and restricted rotation of the molecules in the liquid phase, the number of fluorine atoms being significant in this decision (the more fluorine atoms, or the bigger the ratio between fluorine and hydrogen atoms in the molecule, the more restricted the rotation in the liquid phase).
Figure 6.
Plot of
µ
* as a function of
µ
g
for the liquids studied.
All these facts suggested the development of a density functional theory approach and self-consistent-reaction field calculations for these five molecules and HFC-32, the methane fluorinated compound [19], to try to understand better this behavior. The SCRF calculations were based in the polarized continuum model (PCM) and on the self-consistent isodensity polarized continuum model (SCIPCM). The “solvent” is modeled as a continuum of uniform dielectric constant. The main difference between these two models is the cavity shape definition, or the cage that surrounds a test or “solvent” molecule, as illustrated in Figure 7. Dimerisation energies, rotational potentials, polarisabilities and dipole moments were calculated. Hydrogen bonding in hydrofluorocarbon dimmers was also studied and the relationship between the structure and charge distribution of the dimers and the dipole moment in the liquid predicted by dielectric constant measurements. Details of the DFT geometrical optimizations and basis sets used can
1.21.41.61.8233.544.55
10
3
/T / K
-1
1 0
4
. (
ε εε ε
- 1 ) * ( 2
ε εε ε
+ 1 ) / 9
ε εε ε
* (
M
/
ρ ) ρ ) ρ ) ρ ) / // /
m
3 .
m o l
- 1
012340123
µ µµ µ µ∗ µ∗ µ∗ µ∗
12332143a134a152a141b142b125245fa
Free RotationRestricted Rotation
IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 507
be found in Cabral
et al.
[19]. The values obtained for the dipole moments in the gas-phase agree very well with the experimental values, for different theoretical levels, reproducing the experimental order (1). Results obtained using the SCIPCM model, with B3PW91/D95V(d,p) level, are also displayed in Table 1. The effective dipole moments obtained confirm that the Kirkwood theory overestimates the dipole moments in the liquid phase, by inducing less mobility of the molecules. The order (2) of the dipoles in the liquid agrees with the experimental ones, except for HFC-143a, where the calculated value is the greater one. Kirkwood-Onsager Model Polarized Continuum Model (PCM) Self-consistent isodensity polarizedcontinuum model (SCIPCM)
Figure 7.
Schematic of the models referred in this work, illustrating the cavity shape. All the models assume the “solvent” as a continuous media (no local structure).
Table 1.
Experimental dipole moments and Kirkwood factors for several refrigerants Refrigerant
µ
K
*
g
K
µ
KF
*
µ
T
*
µ
g
Class
HCFC-141b 2.96 2.17 - - 2.01 B HCFC-123 2.13 2.48 - - 1.36 B HCFC-142b 3.17 2.20 - - 2.14 B HFC-32 3.60 3.31 2.61 2.35 1.98 A HFC-125 2.48 2.46 1.84 1.94 1.56 A HFC-134a 3.54 3.44 2.67 2.61 2.06 A HFC-143a 3.34 2.04 2.63 2.75 2.34 A HFC-152a 3.69 2.67 2.55 2.77 2.26 A HFC-245fa 2.69 3.01 - - 1.55 A
µ
T
* for the liquid phase was obtained using the SCIPCM model, with B3PW91/D95V(d,p) level [19]It is noteworthy to refer here the calculations with difluoromethane (HFC-32). HFC
32 clusters (n=2
10), where n is the number of molecules have been generated by Monte Carlo simulations at a temperature T=50K. For some clusters (n=2
6) full geometry optimizations at the B3LYP/D95V(d,p) level have been carried out. Figure 8 shows the DFT optimized structures for n=3
6. These calculations indicate a small reduction of some F...H distances from the trimer (2.43 Å) to the hexamer (2.39 Å) indicating some cooperative polarization effects typical of hydrogen bonding systems [20]. Comparison between the results for the HFC
32 and water clusters shows a much stronger polarization effect in water [19]. Moreover, the procedure used provides a reliable estimation of the average dipole moment in water clusters that is similar, in the case of the water hexamer, to the measured dipole moment of bulk water. Thus, our DFT results show that the large dipole moments of HFC’s based on dielectric constant measurements and Kirkwood theory cannot be fully explained by polarization effects induced by hydrogen bonding. Reasons for this discrepancy are probably related to limitations of the Kirkwood theory and to the eventual formation in the liquid phase of dimers and small clusters in all the liquids studied, carrying large dipoles
3
.
Figure 8.
Difluoromethane (HFC
32) clusters optimized structures from B3LYP/D95V(d,p) calculations: (a) n=3; (b) n=4; (c) n=5; (d) n=6. F...H distances in Å.
In addition, the occurrence of hydrogen bonding in HFC-134a and HFC-143a can be easily seen in Figure 9, were electronic densities are shown around the different atoms. For HFC-134a, the distances between the active fluor and hydrogen atoms in the different dimmers vary between 2.53 and 2.95
Å.
For HFC-143a, the same distances vary between 2.51 and 2.94 Å, exactly the same type of interaction. The experimental studies were extended to mixtures of fixed composition. Two binary systems (HFC-32/HFC-125 (R410A) [3] and HFC-125/HFC-143a (R-507)) and two ternary systems HFC125/143a/134a (R-404A), HFC32/125/134a (R-407C) [21] in the liquid phase was measured at temperatures from 217 to 303K and pressures up to 16 MPa. Kirkwood theory was applied to these systems and the value of the apparent dipole moment in the liquid state was obtained for the first time for these mixtures, considering the mixture as a single fluid, with a molar fraction dependent dipole moment. The relation between the dipole moment of a binary mixture in the liquid state with the dipole moments of its components is
3
A complete discussion of this problem is found in section 4.3 of reference [19], namely in its Figure 6.

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