Total cohesive energy

While the solubility parameter can be used to conduct solubility studies, it is more informative, in dealing with charged polymers such as SPSF, to employ the three dimensional solubility parameter (A7,A8). The solubility parameter of a liquid is related to the total cohesive energy (E) by the equation 6 = (E/V) 2, where V is the molar volume. The total cohesive energy can be broken down into three additive components E = E j + Ep + Ejj, where the three components represent the contributions to E due to dispersion or London forces, permanent dipole-dipole or polar forces, and hydrogen bonding forces, respectively. This relationship is used... 

The division of total cohesive energy into multicomponents has been successfully studied by Hansen (1967) and has been extended for solubility prediction for different compounds in separate cases (Martin etal., 1981 Bustamante etal., 1991 Richardson etal., 1992). 

At the basis of such a refinement should be the different interactions which together constitute the total cohesive energy. These can be classified as follows ... 

We may now write the total cohesive energy density as the sum of a series of contributions, each due to one of the interactions described above ... 

In the derivation of Eq. (7.3) by Hildebrand only dispersion forces between structural units have been taken into account. For many liquids and amorphous polymers, however, the cohesive energy is also dependent on the interaction between polar groups and on hydrogen bonding. In these cases the solubility parameter as defined corresponds with the total cohesive energy. 

In general, the total interatomic potential between any pair of atoms is the sum of the pair-wise interaction and the interactions between three atoms (triplets), four atoms (quartets), etc. The problem is pair potentials are by far the easiest to compute, however, their exclusive use gives results that are only semiquantitative (even with ionic solids), accounting for only up to 90 percent of the total cohesive energy in a solid. The three-body term simply cannot be neglected, although the higher-order terms often can be. 

SOURCES of data Values of V d) were chosen to bring the total cohesive energy into agreement wiih experiment for the homopolar solid, and held fixed in the compounds isoelcctronic with them. The theoretical is predicted by using Eq. (7-3) and the values from the first three columns. Experimental values were obtained by adding the heal of formation (the energy required to separate the compound into elements in the standard state), from Wagman ct al. (1968), to the heat of atomization of the elements, from Kittcl (1967, p. 98). A correction of about 0.01 cV/bond should be made to compensate for the different temperatures at which the heat was measured. 

The total cohesion energy itself, E, can be divided into parts. The three parts used by Hansen are those attributable to nonpolar interactions, Ejy, permanent dipole-permanent dipole interactions, Ep,... 

The Hoftyser-van Krevelen method These researchers proposed group values for the cohesive energy, i.e., for the ratio A W. The total cohesive energy is estimated from the group values via Equation 16.1. Then the solubility parameter is estimated from the definition. Equation 16.8. 

The most comprehensive approach to resin solubilities has been that of Hansen [19] in which the solubility parameter is divided into three components. The basis of this three-dimensional solubility parameter system is the assumption that the energy of evaporation, i.e., the total cohesive energy AjEJt which holds a liquid together, can be divided into contribution from dispersion (London) forces ABd, polar forces AEp, and hydrogenbonding forces AEh- Thus,... 

The total cohesive energy Ecoh can therefore be divided formally into three parts [1,2], Ed, Ep and Eh, representing contributions from dispersion, polar and hydrogen bonding interactions. 

The solubility parameter system used here assumes that the energy of evaporation—i.e., the total cohesive energy which holds a liquid together, E—can be divided into contributions from three forces (1) dispersion (London) forces, ED, (2) permanent dipole-permanent dipole forces, EP, and (3) hydrogen-bonding forces, EH. Thus,... 

According to the liquid-drop model, the total cohesive energy (E, ) of a nanoparticle with N atoms is equal to the volumetric or bulk energy a N minus the surface energy, the latter term arising from the presence of atoms on the surface. Hence, the cohesive energy per atom, i.e., E /N = flv,Rp, is given by... 

More detailed approaches have made use of Hansen solubility parameters (HSP), based on the realization that the heat of vaporization consists of several components arising from van der Waals dispersion forces (D), dipole-dipole interaction (P), and hydrogen bonding (H). The total cohesive energy density is then the sum of the three contributions, and so the overall solubility parameter is... 

Parameters involved in this equation may be estimated using the concept of the homomorph. The homomorph of a polar molecule is a non-polar molecule with nearly the same size and shape as its polar counterpart. The cohesion energy of the homomorph is assumed to be the measure of the effect of the dispersion forces. The polar contribution to the cohesion energy is the difference between the total cohesion energy and the cohesion energy of the homomorph. 

What are lattice energies useful for In principle, a larger lattice energy means a more stable material. In practice, mechanical stability often depends more on the directional properties of the cohesive energy, such as planes of easy cleavage. Besides, crystals made of organic molecules are mechanically weak anyway, so that minor differences in total cohesive energy may be quite irrelevant. 

Perhaps even more important than a consideration of the total cohesive energies -that is, the strength of the bond as represented by the depths of the bonding wells - is the consideration of the force constants for the stretching of the intermolecular liaisons, - that is, the flexibility of these bonds as represented by the widths of the corresponding potential energy wells. Table 12.11 is a pictorial view of the overall landscape of intermolecular bonding. 

Figure 10.4 Periodic trends as observed by reporting the HDS activity results (a) of Pecoraro and Chianelli [121] and (b) ofLedouxet al. [137] versus metal-sulfur bond strength (determined as the total cohesive energy divided by the number of bonds per unit cell, as defined in Refs [138,139]). Adapted from Ref [140], Copyright 2002 with permission from Elsevier.

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