The measured melting points and enthalpies of fusion (Δ

_{fus}*H*) for BDE15 and BDE 209 are given in . The melting temperatures are generally in good agreement with literature data, 330.15 K to 333.5 K for BDE15, and 575.6 K to 578.2 K for BDE209 [

13,

27]. No enthalpy of fusion data could be found in the literature for these two PBDEs. The enthalpy of fusion data are needed to correct the subcooled state vapor pressures to real solid state vapor pressures (see below).

| **Table 1**Melting points and enthalpies of fusion of polybrominated diphenyl ethers (PBDEs) examined in the present study. |

presents the raw data obtained in the present experiment using the Knudsen effusion method. These data were used to calculate the enthalpy (Δ

_{sub}*H*) and entropy (Δ

_{sub}*S*) of sublimation, and vapor pressure at 298.15 K using the Clausius-Clapeyron equation, integrated assuming a constant enthalpy of sublimation,

where

*R* is the universal gas constant,

*T* is the absolute temperature of the sample (

*T* <

*T*_{m}), and

*P*_{0} and

*T*_{0} refer to a reference state.

| **Table 2**Summary of vapor pressure data obtained using the Knudsen effusion method. |

details the quantities calculated from the data in . The enthalpy of sublimation of BDE209 is about 55 kJ/mol higher than that of BDE15 and the difference in entropy of sublimation of these compounds at 298.15 K is about 185 J/mol/K. Moreover, the vapor pressure at 298.15 K for BDE15 is about 9 to 10 orders of magnitude higher than that of BDE209, which shows the strong decrease of vapor pressure with the increasing number of bromine atoms on the aromatic rings of PBDEs.

| **Table 3**Enthalpies of sublimation derived from data in using the Clausius-Clapeyron equation. Also shown are entropies of sublimation and vapor pressures extrapolated to *T* = 298.15 K |

The vapor pressure of BDE15 is shown in . It should be noted that the highest temperature point from the present study was attained for a liquid sample at 333.5 K, about 2 degrees higher than its melting temperature, 331.9 K. This point is seen to approach the estimates of subcooled liquid vapor pressure from GC-retention time studies, log(

*P*_{L}/Pa) = −4074/(T/K) + 11.65 [

15], and log(

*P*_{L}/Pa) = −3528/(T/K) + 10.08 [

17], which report virtual subcooled liquid state vapor pressure.

The subcooled liquid vapor pressure (

*P*_{L}) of BDE15 was converted to solid vapor pressure (

*P*_{S}) at any given temperature by

where

*T*_{m} is the melting temperature and Δ

_{fus}*S* is the entropy of fusion, and where Δ

_{fus}*S* = Δ

_{fus}*H*/

*T*_{m}.

The enthalpies of vaporization for subcooled BDE15 liquid estimated by Wong et al. [

15] and Tittlemier et al. [

17] were 78.0 and 67.6 kJ/mol, respectively. After the adjustment by

equation 4, enthalpies of sublimation estimated by

equation 3 are 95.4 and 85.9 kJ/mol, respectively, which are still lower than the measured solid enthalpy of sublimation from the present study, 102.0 kJ/mol. Additionally, the estimated solid vapor pressure calculated from the subcooled vapor pressure data of Wong et al. is still 15% to 50% higher than the data obtained from the present study, while the difference from the values based on the data of Tittlemier et al. are even greater. It should be emphasized that correction from the virtual subcooled liquid state is essential, as near ambient temperatures vapor pressures predicted based on that state, 1.73×10

^{−2} Pa [

17], can be almost an order of magnitude too high in comparison to actual solid state values, 3.12×10

^{−3} Pa.

shows the vapor pressures of BDE209 compared to those of BDE15. No published vapor pressure data have been found for the former compound. The vapor pressures of BDE15 are about 9 orders of magnitude higher than those of BDE209. With an increase of the number of bromine substitutions, the vapor pressure obviously drops sharply and the enthalpies of fusion and sublimation both increase significantly. Extrapolating to near ambient temperatures, the vapor pressures of BDE209 is negligible (< 10^{−12} Pa).