The modified Mackay (mM), the Grain-Watson (GW), Myrdal and Yalkovsky (MY), Lee and Kesler (LK), and Ambrose-Walton (AW) methods for estimating vapor pressures (
Atmospheric aerosols (AA) have a strong influence on the earth’s energy balance [
Parameters in (
Nomenclature.
Parameters | Names |
---|---|
|
Mass flux for volatile species |
|
The particle wet diameter |
|
Mass of species |
|
Molar diffusivity in the air of species |
|
Gas-phase concentration of species |
|
Fuchs-Sutugin function |
|
Concentration at the surface of species |
|
Gas constant |
|
Temperature in Kelvin |
|
Vaporisation enthalpy |
|
Mole fraction |
|
Activity coefficient |
|
Vapour pressure of each volatile compound |
In (
In this paper, our focus will be on the (i) evaluation of a number of vapor pressure estimation methods against experimental data using all volatile organic compounds present in our database and (ii) assessment of the accuracy of each of these methods on the base of each class of compounds.
The rest of the paper is organized as follows. In Section
The molecules selected in this study have been identified during in situ campaigns [
Using the boiling temperature of Joback [
We have used Joback [
New group contributions have been added by Camredon and Aumont [
The two techniques listed in the previous section have been used to estimate critical pressure
As said earlier, many methods for vapor pressure estimation have been developed and are based on the Antoine or on the extended form of the Clausius-Clapeyron equation. Let us present in what follows each of the five methods used.
The MY method [
In (
Thus, in the MY method, vapor pressure is estimated by the relatively simplified formula
Often called simplified expression of Baum [
In (
Finally, the mM method is reduced to the following equation:
The GW method is based on the following equation [
Like the methods described previously, the LK method required critical temperature, critical pressure, and boiling temperature. Here, the vapor pressure is estimated on the base of Pitzer expansion [
AW method [
In (
We present in this section the results obtained for the Joback and Lydersen techniques described previously. The accuracy of each of the five vapor pressure estimation methods used in this study is assessed taking into account the reliability of pure substance property estimates. The reliability of the two techniques presented in Section
In Figure
Estimated boiling point for a set of 253 species versus experimental values for the Joback technique. The black line is the 1 : 1 diagonal.
The two techniques for the estimation of
Estimated critical temperature for a set of 138 species versus experimental values for the (a) Joback technique and (b) Lydersen technique. The black line is the 1 : 1 diagonal.
Figures
Figure
Estimated critical pressure for a set of 117 species versus experimental values for the (a) Joback technique and (b) Lydersen technique. The black line is the 1 : 1 diagonal.
Some of the five methods described in Section
The accuracy of each method is assessed in terms of the mean absolute error (MAE), the main bias error (MBE), and the root mean square error (RMSE) (Table
In (
The logarithms of vapor pressures estimated at
Logarithm of estimated vapor pressure of all VOCs used in this study versus experimental values for the (a) GW, (b) LK, (c) mM, (d) MY, and (e) AW methods. The black line is the 1 : 1 diagonal.
Logarithm of estimated vapor pressure for a set of 74 hydrocarbons versus experimental values for the (a) GW, (b) LK, (c) mM, (d) MY, and (e) AW methods. The black line is the 1 : 1 diagonal.
Figure
MAE, MBE, and RMSE of vapor pressure computed based on various methods.
GW | LK | mM | MY | AW | |
---|---|---|---|---|---|
MAE | 0.3235 | 0.3240 | 0.3186 | 0.2652 | 0.3013 |
MBE | 0.0736 | −0.1513 | 0.0263 | 0.0270 | −0.0980 |
RMSE | 0.4496 | 0.4909 | 0.4426 | 0.3811 | 0.4525 |
MAE, MBE, and RMSE of vapor pressure computed based on various methods for each class of compounds.
GW | LK | mM | MY | AW | |
---|---|---|---|---|---|
|
|||||
MAE | 0.1455 | 0.1303 | 0.1424 | 0.1251 | 0.1384 |
MBE | 0.0547 | 0.0427 | 0.0486 | 0.0054 | 0.0603 |
RMSE | 0.1983 | 0.1750 | 0.1930 | 0.1711 | 0.1848 |
| |||||
|
|||||
MAE | 0.3692 | 0.3168 | 0.1424 | 0.2699 | 0.2900 |
MBE | 0.0355 | −0.1712 | −0.0189 | −0.0402 | −0.1141 |
RMSE | 0.4992 | 0.4471 | 0.4955 | 0.3891 | 0.4130 |
| |||||
|
|||||
MAE | 0.4494 | 0.5641 | 0.4109 | 0.4291 | 0.5063 |
MBE | 0.2875 | −0.3322 | 0.2084 | 0.2378 | −0.2456 |
RMSE | 0.5506 | 0.6978 | 0.5120 | 0.5398 | 0.6291 |
| |||||
|
|||||
MAE | 0.4407 | 0.5946 | 0.4596 | 0.4261 | 0.5489 |
MBE | 0.0536 | −0.3661 | −0.0339 | 0.1632 | −0.2739 |
RMSE | 0.5494 | 0.8386 | 0.5592 | 0.5065 | 0.7704 |
Figure
Figure
It can be seen in Figure
Except for tri- and more functionalized species (see Figure
Logarithm of estimated vapor pressure for a set of 128 monofunctionalized species versus experimental values for the (a) GW, (b) LK, (c) mM, (d) MY, and (e) AW methods. The black line is the 1 : 1 diagonal.
Logarithm of estimated vapor pressure for a set of 32 difunctionalized species versus experimental values for the (a) GW, (b) LK, (c) mM, (d) MY, and (e) AW methods. The black line is the 1 : 1 diagonal.
Logarithm of estimated vapor pressure for a set of 28 tri- and more functionalized species versus experimental values for the (a) GW, (b) LK, (c) mM, (d) MY, and (e) AW methods. The black line is the 1 : 1 diagonal.
The AW and LK methods are both based on Antoine’s equation. According to all figures plotted, it is clear that these two methods give very similar results. The peculiarity of AW is that, for the monofunctionalized compounds, the predicted and experimental values are strongly correlated with a coefficient
Vapor pressures for a set of 74 hydrocarbons are higher than
We have evaluated in this study five vapor pressure estimation methods useful for simulating the dynamics of atmospheric organic aerosols. These are the Myrdal and Yalkovsky (MY), the Lee and Kesler (LK), the Grain-Watson (GW), the modified Mackay (mM), and the Ambrose-Walton (AW) methods. Some of them are based on the Antoine equation, while others are based on the extended form of the Clausius-Clapeyron equation. But all of them take into account boiling temperature
When using Joback to provide the
This work highlights that the choice of a method to predict vapor pressure of volatile organic compounds depends on the number of functional groups existing in the species.