3.1 Phase diagram
The phase diagram of the pyrene (1) + 9,10-dibromoanthracene (2) system determined by thaw-melt method is given in . The phase diagram shows the non-ideality of the pyrene + 9,10-dibromoanthracene system, which is attributed to the difference in size and shape of the two components, see . The surface area and volume of 9,10-dibromoanthracene is larger than that of pyrene. The phase diagram can be crudely divided into 5 regions. The mixtures with relatively low mole fraction of 9,10-dibromoanthracene (< 0.30), in region A, form a pyrene like phase. When the mole fraction of 9,10-dibromoanthracene is between 0.30 – 0.41, in region B, the mixtures transition from a pyrene-like phase to two phases that both have low melting temperatures. The divergence of the liquidus and thaw curve is 2 – 9 K. In region C, mixtures containing about x2 = 0.41 – 0.50 also show two-phase character and start to transition to 9,10-dibromoanthracene behavior. Mixtures with x2 = 0.50 – 0.75, in region D, also have two phases with 9,10-dibromoanthracene like behavior and high melting temperature. Only one of the phases evolves while the other gives a constant low melting temperature (corresponding to the thaw point). In region E, a 9,10-dibromoanthracene like phase is defined based upon the thermal behavior, shown below.
Phase diagram of pyrene (1) + 9,10-dibromoanthracene (2) mixtures, x2 is the mole fraction of 9,10-dibromoanthracene in the mixture: —●—, liquidus curve, T; —▲—thaw curve, T.
Molecular surface area, volume calculated by space filling model (CPK)
3.2 Temperature of crystallization and enthalpy of fusion and crystallization
The full heating, cooling and reheating scan of a pyrene + 9,10-dibromoanthracene mixture at x2 = 0.48 (in region C) is shown in where Φ is heat flow of the DSC. During the heating scan, two peaks appear at 428 K and 440 K, which indicates the two-phase character of the mixture. Two peaks are also observed in the cooling scan, in which the 9,10-dibromoanthracene like phase crystallizes first at 418 K, and then the pyrene like phase crystallizes at 410 K. The cooling scan also suggested two-phase behavior of the mixture just as did the melting behavior. When reheated, the phase transition enthalpies and associated temperatures matched those of the initial heating scan.
Full DSC scan of a pyrene (1) + 9,10-dibromoanthracene (2) mixture at x2 = 0.48.
The temperature and enthalpy of crystallization (subcooled), shown in , correspond to the results obtained from the phase diagram. Mixtures with a mole fraction of 9,10-dibromoanthraene 0.30 – 0.75, in regions B, C and D, have two-phase character, which is observed as two distinct phase-transition peaks during the cooling procedure. Region E showed two-phase melting behavior, but in the DSC experiments of , the low temperature crystallization peak was absent. Likewise, region B showed two distinct melting peaks, whereas in the DSC experiment only a single peak was observed.
Fig. 3 Crystallization temperature and Hcry of pyrene (1) + 9,10-dibromoanthracene (2) mixtures, x2 is the mole fraction of 9,10-dibromoanthracene in the mixture: —•—, Hcry; — -▲— -, low crystallization (more ...)
Since the enthalpies of crystallization of the mixtures with 9,10-dibromoanthracene mole fractions of 0.55 and 0.75 are significantly lower than that of other mixtures, these are at higher energy state and are less stable than other mixtures with nearby compositions. Moreover, the mixture with 0.65 mole fraction of 9,10-dibromoanthracene is in a more stable state than those mixtures with 0.55 and 0.75 mole fraction of 9,10-dibromoanthracene meaning that around a 2:1 molar ratio of 9,10-dibromoanthracene to pyrene, there exists a particular lower energy configuration.
3.3 Interaction energy
The data of may be used to calculate the interaction energy for the system. The results are shown in .
Interaction energy of pyrene (1) and 9,10-dibromoanthracene (2) mixtures, x2 is the mole fraction of 9,10-dibromoanthracene in the mixture: —▲—, interaction energy, Einter.
The interaction energy is defined by,
is interaction energy, (ΔHfus
are enthalpies of fusion of pyrene and 9,10-dibromoanthracene, respectively, (ΔHfus
is the calculated enthalpy of fusion of the mixtures, (ΔHfus
is enthalpy of fusion of the mixtures determined from the DSC measurements, x1
are the mole fractions of pyrene and 9,10-dibromoanthracene, respectively.
Since the enthalpy of crystallization agrees with the total enthalpy of fusion, the equations (3)
) can be written as
are enthalpies of crystallization of pyrene and 9,10-dibromoanthracene, respectively, (ΔHcry
is the calculated enthalpy of crystallization of the mixtures, (ΔHcry
is enthalpy of crystallization of the mixtures determined from the DSC measurements.
This suggests that pyrene and 9,10-dibromoanthracene form mixtures with a higher energy state than that of the pure components, and that different kinds of interaction exist in the mixtures than in the pure compounds. There is weaker interaction between molecules in the mixtures with 0.55 and 0.75 mole fraction of 9,10-dibromoanthracene than that in the mixture with 0.65 mole fraction of 9,10-dibromoanthracene, which suggests that the latter mixture is in a lower energy state than others, as already noted above. The energy state of this 2:1 mixture is close to that of pure materials.
3.4 Powder XRD analysis
The powder X-ray diffraction method was used to study the crystal structures of pure pyrene, 9,10-dibromoanthracene and their mixtures (see ). The results are qualitative. For the 9,10-dibromoanthracene rich mixture at the region D–E boundary, at x2 = 0.75 (curve E), the XRD data show a 9,10-dibromoanthracene like microstructure though there are distinct differences from 9,10-dibromoanthracene. The pyrene rich mixture in region A at x2 = 0.25 (curve A) has the pyrene like microstructure. However, the mixture at x2 = 0.65 (curve D) reflects neither pyrene nor 9,10-dibromoanthracene like microstructure, and in fact is amorphous.
Fig. 5 X-ray diffraction patters of pure components and mixtures, x2 is the mole fraction of 9,10-dibromoanthracene in the mixture: 1, pure pyrene (1); 2, pure 9,10-dibromoanthracene (2); E, mixture at edge of region E at x2 = 0.75; D, mixture in region D at (more ...)
3.5 Vapor pressure
The Knudsen effusion technique was used to measure the vapor pressure of pyrene and 9,10-dibromoanthracene mixtures in two different types of experiments. The experimentally measured vapor pressures are compared to those calculated by Raoult's law, an ideal weighted average of pure component vapor pressures.
shows the vapor pressure and the change in concentration of pyrene with sample mass loss in an experiment that begins with a mixture at x1 = 0.75 and 333.3 K. The temperature was changed to 358.7 K, after about 20 % of the original mass was lost. Compositions were determined by interruption of the experiment, and removal of some of the sample for analysis. At the beginning, the vapor pressure of mixture with x1 = 0.75 closely follows a Raoult's law prediction corresponding to roughly 0.70 mole fraction of pyrene. After the mixture in the cell loses about 35% mass, the vapor pressure of the mixture falls to another stable state which is at Raoult's law prediction for a 0.35 mole fraction of pyrene. This further suggests that the pyrene and 9,10-dibromoanthracene prefer to form a mixture at x1 = 0.35, even though the initial mole fraction of pyrene before melting is different. These results strongly indicate that the system has a preferred composition.
Fig. 6 Vapor pressure and composition change of a mixture initially at x1 = 0.75 versus sample mass loss, x1 is the mole fraction of pyrene in the mixture: _____, Pmeasured; —•—•—, measured x1 of solid mixture; - - - - (more ...)
shows the vapor pressures of pure pyrene, consistent with [2
], and 9,10-dibromoanthracene, consistent with [4
]. The vapor pressure of pyrene is about 2 orders of magnitude higher than that of 9,10-dibromoanthracene. From linear regression of the data, the enthalpy of sublimation can be obtained. The enthalpies of sublimation of pyrene and 9,10-dibromoanthracene are 93.1 kJ·mole−1
in a temperature range of 324 – 359 Kand 110.1kJ·mole−1
in a temperature range of 359 – 392 K, respectively. Roux et al.[1
] remark that most sublimation enthalpy of pyrene published over the past 50 years range from 93 to 101 kJ·mole−1
in a temperature range of 322 – 423 K. Our value fits well within this range.
Vapor pressures of pyrene (1), P10, and 9,10-dibromoanthraene (2), P10, where Ln (P10/Pa)= 30.485 – 11197/T and Ln (P20/Pa) = 32.125 – 13247/T: ●, pyrene; ▲, 9,10-dibromanthracene.
is the maximum vapor pressure that can be achieved in the Knudsen effusion cell containing pyrene + 9,10-dibromoanthracene mixtures. By assuming that these components are present as two separate phases,
are the vapor pressure of pure pyrene and 9,10-dibromoanthracene, respectively.
For the pyrene rich mixtures not allowed to lose significant mass (see ), the vapor pressure follows the Raoult's law prediction at x1 = 0.70, which suggests that a preferred state for pyrene rich mixture systems exists at x1 = 0.70. This state exists at the boundary between region A and B and is the limit of a single phase system.
Fig. 8 Vapor pressure measurements of pyrene (1) + 9,10-dibromoanthracene (2) mixtures with high initial mole fraction of pyrene: ----, Pmax; —, Raoult's law prediction P at x1 = 0.70; , P(1) + (2) at x1 = 0.70; ●, P(1) + (2) at x1 = (more ...)
After mixtures initially at x1 = 0.70, 0.75 and 0.90 lose about 19 %, 35 % and 69 % mass, respectively, the vapor pressure transitions to the Raoult's law prediction curve for x1= 0.35 (see ). The vapor pressure stays at this value for a significant degree of mass loss, which suggests that mixtures of pyrene and 9,10-dibromoanthracene form a stable state at x1 = 0.35 that behaves like an azeotrope. This is consistent with the DSC measurements () showing that this mixture composition is a stable state. Thereafter the vapor pressure falls to the vapor pressure of 9,10-dibromoanthracene, even though there is 14 ± 1 % pyrene still left in the mixture in region E. Hence, the observed behavior is not that of a true azeotrope.
Fig. 9 Vapor pressure measurements of pyrene (1) + 9,10-dibromoanthracene (2) mixtures with high initial mole fraction of pyrene that have reached a stable state: —, Raoult's law prediction P at x1 = 0.35; , P(1) + (2) at x1 = 0.70; ●, (more ...)
The vapor pressure behavior of mixtures with moderate initial mole fraction of pyrene is shown in . Mixtures at x1 = 0.50 and 0.60 are in an unstable state. The vapor pressures of these mixtures transition to the Raoult's law prediction value at x1 = 0.35 after they lose about 3 % and 5 % mass, respectively. This again reflects that the mixture with pyrene mole fraction of 0.35 is a stable mixture, whose behavior dominates the solid-vapor equilibrium.
Fig. 10 Vapor pressure measurements of pyrene (1) + 9,10-dibromoanthracene (2) mixtures with moderate initial mole fraction of pyrene: ----, Raoult's law prediction P at x1 = 0.70; —, Raoult's law prediction P at x1 = 0.35; ●, P(1) + (2) at x (more ...)
further demonstrates that a stable state of pyrene and 9,10-dibromoanthraene mixtures exists at x1 = 0.35. Even if the initial pyrene mole faction in the mixture is lower than 0.35 in region D and E, the stable state 2:1 mixture is formed.
Fig. 11 Vapor pressure measurements of pyrene (1) + 9,10-dibromoanthracene (2) mixtures with low initial mole fraction of pyrene:—, Raoult's law prediction P at x1 = 0.35; ●, P(1) + (2) at x1 = 0.25; , P(1) + (2) at x1 = 0.35.
3.6 Sensitivity to mixture preparation condition
Other methods were used to prepare the pyrene + 9,10-dibromoanthracene mixtures, such as slow cooling the melts and ball milling the components together at room temperature. The vapor pressures of pyrene and 9,10-dibromoanthracene mixtures did not depend on the mixture preparation techniques.