Crystal Engineering of Organic Pigments

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

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