Лако-красочные материалы — производство

In general, the low solubility and high thermal stability of pigments are indicative of large packing energies due to the strong intermolecular attractive forces within crystals. These intermolecular forces may be evaluated using various molecular modeling methods. For practical reasons, lattice or packing energies of molecular crystals are calculated by force field methods.

The packing or lattice energy PE of a molecular crystal is defined as the sum of all intermolecular potentials, i. e., van der Waals plus Coulomb energy (Eq. (8-1)). In this chapter the van der Waals energies have been calculated using the 6-12 potential Lennard-Jones type function and the common and universal Dreiding 2.21 parameter set [15]. Atomic point charges were derived from charge equilibration with­in the packing [16]. The Coulomb energy has been calculated by the Ewald summa­tion method. All calculations have been performed using the modeling package Cerius2© [17].

(8-1)

with PE: packing energy

interatomic distance empirical forcefield parameters q: atomic charges

For a series of high-performance pigments, packing energies have been found to be in the range of-56.8 > PE > -86.4 kcal/mol (Table 8.2). In the case of P. B.16 the calculated value of the packing energy of -57.5 kcal/mol corresponds reason­ably to the experimentally determined sublimation enthalpy of 50 ± 2 kcal/mol [18]. Experimentally determined sublimation enthalpies for pigments are rare,

but, as a rule, for calculated packing energies, an error of ca. 10-15% (roughly the same as for experimental data) must be considered.

Analyses of large sets of structures have shown that the packing energy corre­lates reasonably with the molecular volume and also with the number of valence electrons in the molecule [19]. In another approach, neural network techniques have been used to identify a correlation between molecular composition and sub­limation enthalpy based on 60 compounds [20]. The correlation is based on a 3-parameter model involving the number of carbon atoms C, the number of hydrogen bond donors HBD and hydrogen bond acceptors HBA (Eq. (8-2)).

AHsub= 3.47 + 1.41 x C + 4.55 x HBD + 2.27 x HBA (8-2)

According to Eq. (8-2), atoms which induce polarity and which are capable of hydrogen bonding contribute considerably more to the packing energy than car­bon atoms. The specific packing energies, SPE2 (per mol. surface), which are based on the force field derived packing energies in Table 8.2 clearly confirm this trend. They increase with the ratio of hetero to carbon atoms in the molecule.

The empirical correlations do not differentiate between configurational isomers or polymorphs, but they are useful in order to estimate the overall expected values of PE. As can be seen from Table 8.2, the values derived from the multilinear regres­sion analysis (MLRA) are at average 28% (!) lower than the PEs calculated by the force field, which indicates a likely overestimation of polar forces by the chosen charge model. In contrast, the values for the least polar molecule listed in Table 8.2, P. B.16, are almost identical.

From the statistical regression analyses of homologous sets of crystal structures (e. g., hydrocarbons, oxo, and aza hydrocarbons), the SPE2 may roughly be esti­mated to range from 0.10 to 0.16 [19]. Regardless of the method for calculating the packing energy, specific packing energies (SPE2) of most pigments in Table

8.2 exceed these average values significantly, pointing to outstanding thermody­namic properties of these solids. For the moment, the limited number of high — performance pigment crystal structures and the diversity of their chemical consti­tution do not allow for a more detailed and comprehensive analysis of the thermo­dynamic data of the structures.

8.2.3