8.2.1
Close Packing
The molecules in organic crystal structures are usually close packed. The ratio of the volume occupied by the molecules to the cell volume, the Kitaigorodskii packing coefficient CK, ranges from ca. 0.65 to 0.8 [5]. Organic pigments usually can be found in the regime above 0.74, thus packing more efficiently than equally sized spheres (Table 8.2, Figure 8.1).
PY 139 |
PR 255 |
PR 254 |
y-PV 19 |
P-PV19 |
PR 122 |
PB 60 |
PR 179 |
P-PB 16 |
|
Formula |
c16h9n5o6 |
c18h,,n, o. |
c18h10ci, n,o. |
^20^12^2^2 |
^20^12^2^2 |
C„H16N,0, |
c,8hun, o4 |
c,6hun, o4 |
c3,h18n8 |
Mass (a. u.) |
367.3 |
288.3 |
357.2 |
312.3 |
312.3 |
340.4 |
442.4 |
418.4 |
514.6 |
Space group |
С nica |
РІ |
P 2,/n |
P 2i/c |
P 2,/n |
РЇ |
P 2,/a |
p А/с |
P2,/a |
z |
8 |
1 |
2 |
2 |
2 |
1 |
2 |
2 |
2 |
Mol. V (a3) |
275.0 |
250.6 |
283.0 |
267.1 |
267.1 |
301.2 |
362.9 |
344.4 |
440.8 |
Surface (A2) |
310.4 |
280.5 |
316.4 |
295.6 |
295.6 |
335.4 |
385.3 |
365.5 |
472.9 |
Cell V (A3) |
2800.2 |
334.4 |
720.8 |
708.6 |
685.1 |
392.5 |
926.5 |
873.2 |
1181.2 |
P (g/cm3) |
1.742 |
1.432 |
1.646 |
1.464 |
1.514 |
1.440 |
1.586 |
1.591 |
1.447 |
CKf (%) |
80.0 |
77.3 |
80.4 |
77.5 |
80.7 |
79.3 |
80.6 |
82.0 |
77.0 |
PE (kcal/mol) |
-86.4 |
-56.8 |
-77.2 |
-60.0 |
-59.3 |
-62.5 |
-69.2 |
-69.1 |
-57.5 |
MLRAb> |
-62.4 |
-42.5 |
— |
-45.3 |
-45.3 |
-48.1 |
-61.1 |
-53.8 |
-57.7 |
SPE1C> |
0.235 |
0.197 |
0.216 |
0.192 |
0.190 |
0.184 |
0.156 |
0.165 |
0.112 |
SPE2d> |
0.278 |
0.202 |
0.244 |
0.203 |
0.201 |
0.186 |
0.180 |
0.189 |
0.122 |
vdW |
-30.7 |
-28.7 |
-31.5 |
-31.2 |
-35.2 |
-40.8 |
-56.2 |
-49.4 |
-56.0 |
Cbe> |
-42.0 |
-20.9 |
-38.2 |
-21.6 |
-17.9 |
-16.6 |
-13.0 |
-19.7 |
-1.5 |
H-bond |
-13.7 |
-7.2 |
-7.5 |
-7.2 |
-6.2 |
-5.1 |
Table 8.2 Crystallographic data, packing coefficient CK, calculated packing energy PE and specific packing energies SPE1 (РЕ/ molecular mass), SPE2 (PE/molecular volume) of organic pigments. |
a) CK = 1 — free volume in cell/cell volume; free volume has been determined by a probe of 1.0 A diameter. b) Packing energy calculated according to multilinear regression analysis from!20!, see also Eq. (8-1). c) SPE1 = PE/molecular mass. d) SPE2 = PE/molecular surface. e) Coulomb energy based on charge equilibration!16! derived atomic point charges. |
8.2 Crystal Engineering of Organic Pigments I 107 |
The reasons behind close packing are the molecular shapes and the intermolecular forces. In a first approximation, medium-range isotropic forces define close packing. Long-range anisotropic forces of mainly electrostatic nature lead to specific molecular arrangements like centrosymmetry, herring-bone stacking, and polar structures. Molecular shapes must support close packing by forming a space filling pattern if oriented according to the long-range forces.
All crystal structures of high-performance pigments are characterized by an excellent match of their molecular shapes to form close packed solids and to simultaneously maximize their intermolecular interactions. In many cases molecular symmetry supports the formation of close packed solids by coinciding with symmetry elements of the crystal lattice (see Figure 14.11 in Chapter 14). But molecular symmetry is not a stringent necessity for close packing, as examples of benz — imidazolone and isoindoline pigments demonstrate (for good examples see Figures 10.5a and 10.5b in Chapter 10, and Figure 14.10 in Chapter 14).
8.2.2