Cohesive energy calculation results

The solubility parameter (SP) of a polymer is a concept based on cohesive energy calculated from group molar attraction data and the difference in SP between two polymers is a measure of their compatibility. Experimental results suggest that dry-mix grafting will occur only if the SP difference between the polymer and NR is not greater than 1.3 units (Table 1). 

During the 1980 s a major controversy arose when ab initio cohesive energy calculations for transition metals were confronted with semiempirical data obtained from a so called CALPHAD approach, in which Gibbs energies are constructed to reproduce and predict alloy phase diagrams. The issue is often illustrated with reference to a plot such as in Fig. 3, where the results for the enthalpy difference at 0 K from ab initio calculations (solid line) are shown together with semiempirical data (points). 

Said more rigorously, our earlier calculations make a prediction for the crystal structure of Cu at zero pressure. It is certainly important to consider how we can extend our results to more practically relevant conditions In Section 2.5, we described how the relative stability of several possible structures of a material can be compared at nonzero pressures by calculating the cohesive energy of the material as a function of volume. This concept is very important for applications such as geophysics that deal with extremely high pressures. The vignette in Section 1.2 about planetary formation is one example of this situation. 

The electrostatic energy of a molecular crystal can be evaluated with summation over the structure factors in Eq. (9.15). But to obtain the cohesive energy of a molecular crystal with such a summation, we would have to subtract the molecular electrostatic energies, which are implicitly included in the result. An alternative is to perform the calculation in direct space. 

The first part of the chapter is devoted to an analysis of these correlations, as well as to the presentation of the most important experimental results. In a second part the following stage of development is reviewed, i.e. the introduction of more quantitative theories mostly based on bond structure calculations. These theories are given a thermodynamic form (equation of states at zero temperature), and explain the typical behaviour of such ground state properties as cohesive energies, atomic volumes, and bulk moduli across the series. They employ in their simplest form the Friedel model extended from the d- to the 5f-itinerant state. The Mott transition (between plutonium and americium metals) finds a good justification within this frame. 

In Fig. 7 the results of the model for the cohesive energy are given, and compared with the experimental values and with the results of band calculations. The agreement is satisfactory (at least of the same order as for similar models for d-transition metals). For americium, the simple model yields too low a value, and one needs spin-polarized full band calculations (dashed curve in Fig. 7) to have agreement with the experimental value. 

Calculations. In theory, p can be obtained by minimizing the part of the cohesive energy that depends on it. In practice, for large structures, the various contributions cannot be calculated with enough accuracy to give reliable results, and thus such a calculation is far beyond what is presently feasible. 

The atom-atom potential fitted to the ab initio data gives fairly re stic results for the equilibrium structure (unit cell parameters and molecular oriratations in the cell), the cohesion energy and the phonon frequencies of the molecular crystal. The latter have been obtained via both a harmonic and a self-consistent phonon lattice dynamics calculation and they were compared with and Raman spectra. About some of the aninncal hydrocarbon atom-atom potentials which are fitted to the crystal data, we can say that they correspond reasonably well with the ab initio results (see figs. 6, 7, 8), their main defect being an underestimate of the electrostatic multipole-multipolc interactions. 

---