Enthalpies of phase transition

This method is used to locate phase transitions via measurements of the endothennic enthalpy of phase transition. Details of the teclmique are provided elsewhere [25, 58]. Typically, the enthalpy change associated with transitions between liquid crystal phases or from a liquid crystal phase to the isotropic phase is much smaller than the melting enthalpy. Nevertheless, it is possible to locate such transitions with a commercial DSC, since typical enthalpies are... 

The word energetics, rather than thermochemistry, was adopted in figure 1.2 and in the book title to emphasize that most of the methods displayed do not involve the experimental determination of heat. Furthermore, the use of energetics avoids the traditional link between thermochemistry and calorimetry (which is semantically correct because thermo is the Greek designation for heat ). The word molecular, on the other hand, stresses that this book will be mainly concerned with single molecules. Properties like enthalpies of phase transition, which depend on intermolecular interactions, are very important data in their own right, but the methods used to derive them will not be comprehensively covered. 

The enthalpies of phase transition, such as fusion (Aa,s/f), vaporization (AvapH), sublimation (Asut,//), and solution (As n//), are usually regarded as thermophysical properties, because they referto processes where no intramolecular bonds are cleaved or formed. As such, a detailed discussion of the experimental methods (or the estimation procedures) to determine them is outside the scope of the present book. Nevertheless, some of the techniques addressed in part II can be used for that purpose. For instance, differential scanning calorimetry is often applied to measure A us// and, less frequently, AmpH and AsubH. Many of the reported Asu, // data have been determined with Calvet microcalorimeters (see chapter 9) and from vapor pressure against temperature data obtained with Knudsen cells [35-38]. Reaction-solution calorimetry is the main source of AsinH values. All these auxiliary values are very important because they are frequently required to calculate gas-phase reaction enthalpies and to derive information on the strengths of chemical bonds (see chapter 5)—one of the main goals of molecular energetics. It is thus appropriate to make a brief review of the subject in this introduction. 

The heat flux and energy calibrations are usually performed using electrically generated heat or reference substances with well-established heat capacities (in the case of k ) or enthalpies of phase transition (in the case of kg). Because kd, and kg are complex and generally unknown functions of various parameters, such as the heating rate, the calibration experiment should be as similar as possible to the main experiment. Very detailed recommendations for a correct calibration of differential scanning calorimeters in terms of heat flow and energy have been published in the literature [254,258-260,269]. 

The types of values reported in the database standard enthalpies of formation at 298.15 K and 0 K, bond dissociation energies or enthalpies (D) at any temperature, standard enthalpy of phase transition—fusion, vaporization, or sublimation—at 298.15 K, standard entropy at 298.15 K, standard heat capacity at 298.15 K, standard enthalpy differences between T and 298.15 K, proton affinity, ionization energy, appearance energy, and electron affinity. The absence of a check mark indicates that the data are not provided. However, that does not necessarily mean that they cannot be calculated from other quantities tabulated in the database. 

Enthalpies of phase transitions are reported in kilojoules per mole. The enthalpy change for a reverse reaction is the negative of the enthalpy change for the forward reaction. Enthalpy changes can be added to obtain the value for an overall process. 

The minimum information covers chemical formula, molecular weight, normal boiling point, freezing point, liquid density, water solubility and critical properties. Additional properties are enthalpies of phase transitions, heat capacity of ideal gas, heat capacity of liquid, viscosity and thermal conductivity of liquid. Computer simulation can estimate missing values. The use of graphs and tables of properties offers a wider view and is strongly recommended. 

The temperatures, enthalpies of phase transitions, and heat capacities of pure lanthanide chlorides (LaCb, CeCls, PrCb, NdCb, GdCb, DyCb, ErCls, and TmCls) and of the MsLnCle compounds (Ln = La, Ce, Pr, Nd M = K, Rb, Cs) were determined by Gaune-Escard et al. (1994a). 

Where and LH are the corresponding activation energy and enthalpy of phase transition and the coefficient defines the maximum probability that molecules will cross the interface between the liquid and SCF (vapor) phases. This simple relationship can explain the behavior of the mass transfer coefficient in Figure 15 when it is dominated by the interfacial resistance. Indeed, increases with temperature T according to Eq. (49) also, both parameters E and A// should decrease with increase of pressure, since the structure and composition of the liquid and vapor phases become very similar to each other around the mixture critical point. The decrease of A/f with pressure for the ethanol-C02 system has been confirmed by interferometric studies of jet mixing described in Section 3.2 and also by calorimetric measurements described by Cordray et al. (68). According to Eq. (43) the diffusion mass transfer coefficient may also increase in parallel with ki as a result of more intensive convection within the diffusion boundary layer. 

Enthalpies of phase transitions (fusion, solid-solid transformation, sublimation, and solution)... 

Differential scanning calorimetry (DSC) has been employed to obtain enthalpies of thermal decomposition of organometallic substances. Details of the data treatment to extract A,// from the obtained results have been discussed. Sometimes information on the reaction kinetics can simultaneously be derived from the same data used to compute In addition, the method can also be used to obtain enthalpies of phase transitions (fusion,... 

After Thiesen (1923), it seems favorable to plot the enthalpy of vaporization vs. the difference of the critical temperature and the temperature 7 in a double logarithmic diagram (see Fig. 2.1-4). A straight line results as long as the critical point is not very close. This diagram also shows that the enthalpy of phase transition changes at the triple point. At the triple point the enthalpy of vaporization and the enthalpy of melting add up to the enthalpy of sublimation ... 

Differential scanning calorimetry (DSC) instruments can be used to determine both the temperatures and the enthalpies of phase transitions and chemical reactions. With conventional instruments these two types of measurements have to be carried out individually, i.e., using different runs. The reason is that the temperature difference AT = Tg-Tj between the sample (S) and the... 

From DSC thermogram, optical anisotropy under polarizing optical microscope (p.o.m.) and wide-angle X-ray diffraction (w.a.x.d.) data it can be deduced that the endothermic peak at 77 °C is due to the mesomorphic-isotropic phase transition. The enthalpy of phase transition is 20.35 J/g. Hence, according to Brandon and Marmur (1996), the structure of PAC8 below 77 °C is ordered in smectic crystalline, which can be classified as smectic B (Sb) type. 

From the latent enthalpy of phase transition from I II follows... 

In addition to the enthalpies of phase transitions just discussed, enthalpy changes also occur when two substances are mixed, such as when a solute is dissolved in a solvent (the enthalpy of solution) or when a solution is diluted (the enthalpy of dilution). 

The basic methods for the determination of phase transition temperatures (7 ) are DSC (differential scanning calorimetry), DTA (differential thermal analysis), and polarization microscopy. Every method has its advantages and restrictions. DSC allows one to determine the enthalpies of phase transitions (A// ). Microscopy allows one both to determine the phase transition temperatures and to identify the t)fpe of mesophase. DTA gives reliable results for melting temperatures of LCs that show solid-state polymorphism, and of LC mixtures. The differences in that can be found in publications by different authors arise from different measurement techniques and the presence of impurities. We have selected the data with the higher 7 values in such cases. 

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