17 сентября, 2015 
Pokraskin The physical background of optical interference effects has been the subject of many publications [3-8, 43, 44]. The optical principles of pearlescent (interference) pigments are shown in Figure 7.2 for a simplified case of nearly normal incidence without multiple reflection and absorption. At the interface P1 between
Figure 7.2 Simplified diagram showing nearly normal incidence of a beam of light (L/) from an optical medium with refractive index n, through a thin solid film of thickness d with refractive index n2. L,’ and L2′ are regular reflections from phase boundaries P, and P2. L3 represents diffuse scattered reflections from the transmitted light.
two materials with refractive indices n, and n2, part of the beam light Lj is reflected (Lj’) and part is transmitted (i. e., refracted) (L2). The intensity ratios depend on nj and n2. In a multilayer arrangement as found in pearl or pearlescent and iridescent materials (Figure 7.1d), each interface produces partial reflection. After penetration through several layers, depending on the size and difference between nj and n2, virtually complete reflection is obtained, provided that the materials are sufficiently transparent.
In pigments that simulate natural pearl effects, the simplest case is a plateletshaped particle with two phase boundaries Pj and P2 at the upper and lower surfaces of the particles, i. e., a single, thin, transparent layer of a material with a higher refractive index than its surroundings. For small flakes with a thickness of ca. 100 nm, the physical laws of thin, solid, optical films apply.
Multiple reflection of light on a thin solid film with a high refractive index causes interference effects in the reflected light and in the complementary transmitted light. For the simple case of nearly perpendicular incidence, the intensity ofthe reflectance (f depends on the refractive indices (n1, n2), the layer thickness (d), and the wavelength (k):
A2 + B2 + 2AB cos © 1 + A2B2 + 2AB cos ©
With given n, and n2 the maximum and minimum intensities of the reflected light — seen as interference colors — can be calculated and agree well with experimental results. Values for the refractive index of the most important materials for pearlescent pigments are shown in Table 7.2.
In practice, platelet crystals are synthesized with a layer thickness d calculated to produce the desired interference colors (iridescence). Most pearlescent pigments now consist of at least three layers of two materials with different refractive indices. Thin flakes (thickness ca. 500 nm) of a material with a low refractive index (mica, silica, alumina, glass) are coated with a highly refractive metal oxide (TiO2, Fe2O3, layer thickness ca. 50-150 nm). This results in particles with four
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Table 7.2 Refractive indices of materials.
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interfaces that constitute a more complicated but still predictable thin film system. The behavior of more complex multilayer pigments containing additional, thin, light-absorbing films can also be calculated if appropriate optical parameters are known.
Color effects depend on the viewing angle. Pearlescent pigment platelets split white light into two complementary colors that depend on the platelet thickness. The reflected (interference) color dominates under regular (maximum) reflection, i. e., when the object is observed at the angle of regular reflection. The transmitted part dominates at other viewing angles under diffuse viewing conditions, provided there is a nonabsorbing (white) or reflecting background. Variation of the viewing angle therefore produces a sharp gloss (reflectance) peak, and the color changes between two extreme complementary colors. The resulting complex interplay of luster and color is measured goniophotometrically in reflection and at different angles. A pearlescent pigment is characterized by a minimum of three L*a*b* data sets (CIE L*a*b*-system) measured under different conditions (e. g., 0°/45° black background, 22.5°/22.5° black background, 0°/45° white background). An analysis of these data specifies a pigment on the basis of its hiding power, luster, and hue [7, 9, 10].
Against a black background or in a blend with carbon black, the transmitted light is absorbed and the reflected interference color is seen as the mass tone (i. e., overall color) of the material. In blends of nacreous pigments with absorbing colorants, the particle size of the latter must be well below the scattering limit, i. e., they must be transparent. The nacreous effect or iridescent reflection is otherwise
quenched by the hiding pigments. This also applies to blends with strongly reflecting metal effect pigments (e. g., aluminum). Blends of pigments with different interference colors obey an additive mixing law, (e. g., blue + yellow = green).
7.2.2
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