Enthalpies of relaxation

Figure 9. Diagram showing the relationship of the enthalpy difference between relaxed ground and excited states when the enthalpies of relaxation are similar.

Microcalorimetry is an extremely sensitive technique that determines the heat emitted or adsorbed by a sample in a variety of processes. Microcalorimetry can be used to characterize pharmaceutical solids to obtain heats of solution, heats of crystallization, heats of reaction, heats of dilution, and heats of adsorption. Isothermal microcalorimetry has been used to investigate drug-excipient compatibility [82]. Pikal and co-workers have used isothermal microcalorimetry to investigate the enthalpy of relaxation in amorphous material [83]. Isothermal microcalorimetry is useful in determining even small amounts of amorphous content in a sample [84]. Solution calorimetry has also been used to quantitate the crystallinity of a sample [85]. Other aspects of isothermal microcalorimetry may be obtained from a review by Buckton [86]. 

Fig. 19.20. Relationship between the nucleation rate and the enthalpy of relaxation aging at below the glass transition temperatures for PESff...

Data are sparse. Let us thus relax the earlier phase restriction to the gas phase. We therefore briefly discuss some conjugated dienes for which we have enthalpy of formation data solely in the condensed phase. The first pair of species are the isomeric (Z,Z)-and... 

Poisoning is caused by chemisorption of compounds in the process stream these compounds block or modify active sites on the catalyst. The poison may cause changes in the surface morphology of the catalyst, either by surface reconstruction or surface relaxation, or may modify the bond between the metal catalyst and the support. The toxicity of a poison (P) depends upon the enthalpy of adsorption for the poison, and the free energy for the adsorption process, which controls the equilibrium constant for chemisorption of the poison (KP). The fraction of sites blocked by a reversibly adsorbed poison (0P) can be calculated using a Langmuir isotherm (equation 8.4-23a) ... 

Considerable attention has also been paid to modelling the thermodynamics of defects. This includes, for example, studies of the enthalpies of formation of vacancies or interstitial atoms and the association energies associated with the clustering of such defects. It is usually crucial to allow for the relaxation of the... 

To be useful from a CALPHAD point of view, it is mandatory to have a characterisation of the liquid phase, and the insistence on working totally from FP has to be relaxed. The simplest solution is to add data for the melting points and enthalpies of fusion for the elements from conventional CALPHAD sources. As for heat of mixing for the liquid phase, one approximation is to assume it will follow a suitably weighted behaviour of the f.c.c. and b.c.c. phases. This kind of treatment... 

Adsorption and desorption reactions of protons on iron oxides have been measured by the pressure jump relaxation method using conductimetric titration and found to be fast (Tab. 10.3). The desorption rate constant appears to be related to the acidity of the surface hydroxyl groups (Astumian et al., 1981). Proton adsorption on iron oxides is exothermic potentiometric calorimetric titration measurements indicated that the enthalpy of proton adsorption is -25 to -38 kj mol (Tab. 10.3). For hematite, the enthalpy of proton adsorption is -36.6 kJ mol and the free energy of adsorption, -48.8 kJ mol (Lyklema, 1987). 

The pretreatment temperature is an important factor that influences the acidic/ basic properties of solids. For Brpnsted sites, the differential heat is the difference between the enthalpy of dissociation of the acidic hydroxyl and the enthalpy of protonation of the probe molecule. For Lewis sites, the differential heat of adsorption represents the energy associated with the transfer of electron density toward an electron-deficient, coordinatively unsaturated site, and probably an energy term related to the relaxation of the strained surface [147,182]. Increasing the pretreatment temperature modifies the surface acidity of the solids. The influence of the pretreatment temperature, between 300 and 800°C, on the surface acidity of a transition alumina has been studied by ammonia adsorption microcalorimetry [62]. The number and strength of the strong sites, which should be mainly Lewis sites, have been found to increase when the temperature increases. This behavior can be explained by the fact that the Lewis sites are not completely free and that their electron pair attracting capacity can be partially modified by different OH group environments. The different pretreatment temperatures used affected the whole spectrum of adsorption heats... 

The ionization potentials of some of the bipyridines have been investigated. Solubility data for 2,2 -bipyridine in aqueous solution, in aqueous solvent mixtures, and in various aqueous salt solutions have been obtained, whereas the heat of solution, heat capacities, and related data for 2,2 - and 4,4 -bipyridines in water have been measured. The enthalpies of solution of 2,2 -bipyridine in water and aqueous solvent mixtures have also been obtained. Dielectric relaxation studies of 2,2 -bipyri-dine in carbon tetrachloride have been reported in connection with hindered internal rotation. Partition coefficients for 2,2 -bipyridine between water and various organic solvents have been measured. ... 

The available evidence thus suggests that relaxation times for planar-tetrahedral equilibria in nickel(II) complexes in solution at room temperature fall in the range 0.1-10 /isec, corresponding to rate constants of the order 105-107 sec-1. These relaxation times are several orders of magnitude longer than those observed for octahedral spin equilibria. The reaction coordinate for the planar-tetrahedral equilibria is characterized by large enthalpies of activation for the reaction in both directions, in contrast with a relatively low enthalpy of activation for the high-spin to low-spin process in octahedral iron complexes. 

The measurement of relaxation times 7j and T2 and the subsequent application of the theory formulated by Bloembergen et al. (236), and extended by Kubo and Tomita (272) and Torrey (288), leads to the determination of motional and thermodynamic parameters such as mean times between molecular jumps, diffusion coefficients, and activation enthalpies for translation. For example, Resing and Thompson (289, 290) used this... 

An Arrhenius-type analysis of temperature dependence can be used to calculate the enthalpy and entropy of activation for the relaxation process. For liquid water, the enthalpy of activation is 19 kjmol-1, which corresponds approximately to the energy required to break one hydrogen bond. For ice, the equivalent enthalpy is 54 kj mol-1,... 

Were we to relax our restriction to consider solely hydrocarbyl substituents and accept both benzenoid and non-benzenoid aromatic imines, we would find other relevant compounds. For example, there is ALf-butyl-p-nitrobenzaldi mi ne with a gas-phase enthalpy of formation of 49.4 3.6 kJmol-1 from W. E. Acree, Jr., J. J. Kirchner, S. A. Tucker, G. Pilcher and M. D. M. C. R. Ribeiro da Silva, J. Chem. Thermodyn., 21, 443 (1989) and A-methyl-7-(methylamino)-troponimine (misnamed in our principal archive, Reference 16) with a gas-phase enthalpy of formation of 211.2 4.2 kJmol-1. Another relevant species is ammonium murexide with its 100-year-old enthalpy of formation of — 1212 kJ mol-1 as chronicled by Domalski. These three compounds are interesting, but it is precisely the non-hydrocarbyl part of these species that confounds simple comparison with other interesting species in this chapter. 

One theory that describes the temperature dependence of relaxation time and structural recovery is the Tool-Narayanaswamy-Moynihan (TNM) model developed to describe the often nonlinear relationship between heating rate and Tg. In this model, the structural relaxation time, x, is referenced as a function of temperature (T), activation enthalpy (Ah ), universal gas constant (R), hctive temperature (7)), and nonlinearity factor (x) (Tool, 1946 Narayanaswamy, 1971 Moynihan et al., 1976) ... 

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