High chroma pearlescent pigments designed by optical simulation.
Keywords Optical simulation, High chroma, Iron oxide
Pearlescent pigments, which consist of a plate substrate coated with metal oxides, e.g., titanium dioxide and/or iron oxide, have been widely used in paints, plastics, and printing inks. The optical effect comes from interference between a light ray reflected from the top and bottom surfaces of the metal-oxide layer. The interference color depends on the coating thickness. The interference effect that is different from that or absorption pigment and metal pigment gives pearlescent pigments higher chroma, brightness, and color travel effect (changing with viewing angle). Also, pearlescent pigments have become an essential material for cosmetics makers. The applications range from lipstick to powder foundation. In particular, the pearlescent pigments with high chroma are in high demand.
Recently, we have tried to develop a foundation powder that can reproduce beautiful skin properties. The optical Properties have been extracted from the BRDF (Bidirectional Reflectance Distribution Function) measurement of bare skin. As a result, we found the following: the chroma of aged skin decreases repidly in the specular region, while beautiful skin maintains high chroma even in the specular region. Thus, we have attempted to develop a yellowish chroma pearlescent pigment which gives higher chroma in the specular region. (1)
Furthermore, a mica substrate coated with colorless metal oxide (e.g., titanium dioxide) gives a powdery finish to made-up skin due to the white mass tone. However, the finishing often leads to bad feedback from users.
In high chroma pearlescent pigments, multilayer pigments containing additional layers of metal oxides with different refractive indices are well known. In addition to that, to avoid the powdery finish, we have adopted multilayer pigments with light-absorbing metal oxide.
The features of this paper are twofold.
(1) Design of layer structure of a pearlescent pigment using computer simulation.
It is difficult to predict multilayer pigments experimentally with a light-absorbing metal oxide, e.g., the thicknesses and combination of layers. Also, the simple evaluation used in the mica substrate coated with titanium dioxide is not good enough. Hence. we have designed the layer structure of a pealescent pigment using computer simulation. In the simulation we have considered its layer structure. the complex refractive indices of the layers, and the thickness distribution of mica substrate that was measured with Atomic Force Microscopy (AFM).
(2) Development of a manufacturing method to achieve low roughness iron-oxide surface.
there are several attempts to produce high chroma pearlescent pigments using a light-absorbing metal oxide in multilayer systems. (2-4) In these references a thin layer of [Fe.sub.2] [O.sub.3] is deposited between the mica substrate and the colorless metal oxide to enhance the reddish interference color. As the interference and the mass tone color are the same reddish hue. not only high chroma color but also deep rich color with the change of luster at all angles come out.
However, they could only produce pearlecent pigments where the interference color was the same hue as the mass tone color because of the strong diffuse color originating from a rought surface of [Fe.sub.2] [O.sub.3] layer. When light strikes the rough surface., the light scattered in the backward direction increases and the light penetrating into the coated layer decreases. The indicates that the rough surface decreases the interference effect and increases diffuse color.
To reduce the roughness of surface, we have developed a new manufacturing method.
Design of layer structure of pearlescent pigment using computer simulation
The features of high chroma
To design a high chroma pearlescent pigment, we have to know the features of high chroma from the view point of the spectral reflectance curve.
Figure 1 shows the relationship between chroma and spectral reflectance curve. The figure indicates that high reflectance and sharp falloff of spectrum give high chroma. The spectume. The spectral spreads out over the whole spectrum. The spectral curve of high chromas is concentrated within a narrower span of the spectrum where the same quantity of energy emits. which is the same brightness. Monospectral lights are always maximal chroma.
[FIGURE 1 OMITTED]
In other words, enhancing a spectrum at a specific wavelength and sharpening the curvature of the spectrum are necessary for high chroma.
To enhance a spectrum at a specific wavelength, we have applied multilayer structure used in enhanced mirror and anti-reflection coating. And selective absorption of certain wavelengths has been utilized to make the curvature of the spectrum shape.
Hence, we adopted a multilayer structure with light absorbing metal oxide for the light chroma pearlescent pigment.
One-layer system for designing pearlescent pigment
We will explain a simple evaluation method to design pearlescent pigments using a mica substrate coated with titanium dioxide (see Fig. 2).
[FIGURE 2 OMITTED]
In conventional colorants such as absorption pigment. the color is obtained through selective absorption of white light. The color of pearlescent pigment. however, originates from the interference effect in which light is reflected selectively depending on the wavelengths and the angle of incidence and observation.
Figure 3 shows the schematic illustration of the interference effect of mica substrate coated with titanium dioxide.
[FIGURE 3 OMITTED]
Light is partially reflected from the top interface (between [TiO.sub.2] and air) and penetrates partially reflected from the lower interface (between [TiO.sub.2] and mica substrate) and penetrates into the [TiO.sub.2] layer again. The refractive indices of mica and [TiO.sub.2] are 1.5 and 2.5 respectively. As the light of a particular wave-length passes through the layer, its phase changes in direct proportion to the wavelength. The two path reflections reinforce one another when exactly in phrase and cancel each other when out of phase.
The path length (the difference between path AD and path ABC) depends on the layer thickness d, the angle of incident light, and refractive index of [TiO.sub.2]. Furthermore, the phase of reflected light will change 180 degrees when the light is reflected from a medium of higher refractive index.
The thickness of [TiO.sub.2] layer to enhance the reflection at a particular wavelength are written as follows.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where d is the thickness of [TiO.sub.2] [theta] is incident angel, [lambda] is wavelength, and L is an integer, which means that the difference of phase must be an odd half-number of wavelengths.
This is called the one-layer system. (5)
In general, as the mica substrate coated with titanium dioxide consists of three layers ([TiO.sub.2]/Mica/ [TiO.sub.2]), it is necessary to consider the three-layer structure. But some papers mention that the mica substrate thickness does not affect the interference color in many particles' system. (5-8) This is because the thickness of the mica substrate varies with a statistical distribution and the thickness within a mica substrate is not uniform. The reference (8) gives the following numerical proof. After calculating the reflectance of the three-layers ([TiO.sub.2]/ Mica/ [TiO.sub.2]) structure with different mica thickness, they have averaged those reflectance curves and showed that the obtained curve approaches a curve calculated by neglecting its mica thickness.
Our approach for designing pearlescent pigments
As mentioned above, the one-layer system is useful in designing a mica substrate coated with titanium dioxide. It is, however, difficult to deal with the multilayer pigment a with light-absorbing metal oxide in the system. Furthermore, since spatial orientation of the pearlescent pigments on bare skin has a strong effect on the appearance of made-up skin, it is important to relate the orientation to optical properties.
To tackle these problems, we have applied the thin film theory (9) and the Torrance-Sparrow model. (10) The features of this method are as follows.
(1) Calculation of interference effect by the thin film theory.
(2) Adoption of the complex refractive index for the light-absorbing material.
(3) Measurement of thickness distribution of synthetic mica substrate.
(4) Spatial orientation of pearlescent pigments on rough surface.
(1) Calculation of interference effect by the thin film theory.
As the pearlescent pigment has a platelet shape with about 20-micrometer in diameter, edge effect, i.e., diffuse scattering from the finite size of the pigments, must be considered. The size of the pigments is, however, large compared to that of the visible wavelength. Using transfer-matrix method we have calculated a multilaver pigment containing layers. With the size of the width and the depth being infinite (See Fig.4).
[FIGURE 4 OMITTED]
This transfer-matrix method has been used to analyze reflectance, transmittance, and absorptance of optical multilayer accurately.
In theory each layer is represented by a 2x2 transfer matrix which satisfies the boundary conditions of the electric and magnetic fields.
For s-polarization, the transfer matrix is written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [N.sub.i] and [d.sub.i] are reflractive index and thickness of ith layer, respectively, and [[lambda].sub.o] is wavelength in vaccum.
The whole transfer matrix M of multilayer structure is given by the each layer.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
We get the following reflectance equation.
[absolute value of ([r.sup.2])] = [[absolute value of (([c.sub.11] + [c.sub.12][p.sub.air])[p.sub.air] - ([c.sub.21] + [c.sub.22][p.sub.air])/[c.sub.11] + [c.sub.12][p.sub.air])[p.sub.air] + ([c.sub.21] + [c.sub.22][p.sub.air]))].sup.2] (4)
where [p.sub.air] = [N.sub.air] cos [[theta].sub.i]
For p-polarization, pi=[N.sub.i] cos [[theta].sub.i] is replaced with [q.sub.i] =cos [[theta].sub.i]/[N.sub.i]] in the above equations.
(2) Adoption of the complex refractive index for thee light-absorbing material.
To take into account the light-absorbing effect of the material, we need to replace the refractive index of the material, we need to replace the refractive matrix method.
The complex refractive index is defined as
[N.sub.i] = [n.sub.r] + [in.sub.k], (5)
where [n.sub.r] is the refractive index and [n.sub.k] is the exitinction coefficient. In a dielectric material such as glass, none of the light is absorbed and therefore [n.sub.k] =0.
Through the measurement data of the complex refractive index are not many, the values of [Fe.sub.2] [O.sub.3] (Hematite) (11-13) and phthalocyanine Blue (14) are known. The complex refractive index of F[e.sub.2] [O.sub.3] is higher in short wavelength regions. The absorption of blue color makes [Fe.sub.2] [O.sub.3] masstone (diffuse color) red.
(3) Measurement of thickness distribution of synthetic mica substrate.
We have used synthetic mica as a substrate of the pearlescent pigments and measured its thickness distribution to calculate interference color.
Recently, new substrates have been explored to acquire new optical effects. For example, silica flake (15) and alumina flake (16) having a very and smooth surface have been produced. The resulting pigments suppress diffuse scattering and cause high chroma, color purity, and color travel effect. It is, however, difficult to produce or obtain new substrates.
On the other hand, it is rather easy to obtain a mica substrate since natural mica is the most widely used substrate pearlescent pigments. Also the mica substrate has good skin feel. which is an important feature for cosmetics application. But natural mica has a yellowish hue due to the presence of a small amount of colored impurities. Hence, we have chosen synthetic mica as a substrate of the pearlescent pigments.
[FIGURE 5 OMITTED]
Though we use synthetic mica, we have to take into account its thickness distribution. This is because the effect of light absorption materials depends on the path that light-absorbing metal oxide has at least two absorptive layers (top and back of the substrate), neglecting the mica substrate effect is not good enough to evaluate reflectance of the thickness distribution to calculate the interference color (Fig.6).
[FIGURE 6 OMITTED]
The thickness of the substrate was measured with Atomic Force Microscopy (AFM).
The procedure is as follows.
(i) Synthetic micas dispersed into a solvent (e.g., ethnol) are adhered on a flat substrate.
(ii) After the solvent vaporize, synthetic micas are attached firmly on the flat substrate.
(iii) The gap between the top of the synthetic mica and the flat substrate is measured with AFM (Fig. 7).
[FIGURE 7 OMITTED]
Figure 6 shows the distribution of mica substrate thickness. Using the distribution. we calculate the average reflectance F:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where f(x) is mica substrate thickness distribution, [x.sub.min] is minimum thickness, [x.sub.max] is maximum thickness, and [[absolute value of ([r(x).sup.2])] is reflectance of the pearlescent pigment with the substrate thickness x.
(4) Spatial orientation of pearlescent pigments on rough surface.
To develop products for cosmetics application, it is important to understand not only the optical properties of the pearlescent pigment itself but also the reflection from its spatial orientation on bare skin having wrinkless and skin texture. Using a gonio-spectrophotometric colorimeter we often measure artifical black skin samples on which pigments have been applied using a sponge. As the artificial skin has a rough surface similar to the wrinkles and the skin texture, the pearlescent pigments on the artificial skin show not only specular reflection but also diffuse reflection coming from the roughness of surface.
To estimate the reflectance of the coated pigments, we applied the Torrance-Sparrow model to the pigments on the rough surface and got total reflectance R:
R = F.G.D/4cos[[theta].sub.i]cos[[theta].sub.r]
F = Reflection from multilayer pigment
G = Geometrical Attenuation Factor
D = Distribution Function of Microfacets
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Where [[pi]/2.[integral] (0)]d[beta] D([[right arrow].L], [[right arrow].V], m) cos[beta] = 1, [[theta].sub.i] is incident angle and [[theta].sub.r] is reflection angle. (7)
Here the parameter s is the root-means-square (RMS) of the slope of the microfacets, and a large s indicates that the reflection spreads out over the surface. We have evaluated the parameter s so as to reproduce the reflectance of commercial pearlescent pigments applied to artificial black skin (Fig. 8).
[FIGURE 8 OMITTED]
(6) The Torrance-Sparrow model assumes that the surface is made up of microscopic perfect Lambertian reflectors called microfacets. The model consists of Fresnel reflection term, the distribution of the microfacet orientation, and geometric attenuation, which deals with how individual microfacets shadow and mask each other. Our improvement is to replace the microfacets with pearlescent pigments whose shape is almost plate like.
The procedure of design
Using the above optical model, we have designed a yellowish chroma pearlescent pigment as follows.
(1) Yellow is a color with a dominant wavelength of 565-590 nm. The spectrum of high chroma yellow is characterized by strong absorption in the blue region and a steep sloping curve in the green region, thus reflecting almost all light above about 565 nm. To reduce the spectral reflection in the short wavelength region, [Fe.sub.2][O.sub.3], which almost absorbs the visible light below 500 nm, has been selected.
(2) As, multilayer structure, we compared Mica/[Fe.sub.2][O.sub.3]/[TiO.sub.2] structure with Mica/[TiO.sub.2]/[Fe.sub.2][O.sub.3] structure by numerical simulation.
The simulation condition is:
(I) Incident angle is set at 45[degrees]; reflection angles range from 0[degrees] to 75[degrees] at 15[degrees] increments; wavelengths are 390-730 nm at 10-nm increments.
(II) The refractive indices of [TiO.sub.2] are uniformly 2.5 from 390 to 730 nm; the complex refractive indices of [Fe.sub.2][O.sub.3] are shown in Fig. 5.
(III) The thickness of [Fe.sub.2][O.sub.3] is fixed at 20 nm; the thicknesses of [TiO.sub.2] range from 140 to 180 nm at 10-nm increments.
First of all, we made an a* - b* graph of two structures where Illuminant and Observer are C and 2[degrees], respectively (Fig. 9).
[FIGURE 9 OMITTED]
Figure 9 shows that the structure of [TiO.sub.2], being the outermost layer, gives a higher chroma than that of [Fe.sub.2][O.sub.3], being the outermost layer. Even in the off-specular region, interference color is visible due to the spatial orientation of the pigments on the rough surface.
To understand the difference of the chroma from the viewpoint of spectral curve, we have compared the reflection curve between Mica/[Fe.sub.2][O.sub.3]/[TiO.sub.2] and Mica/[TiO.sub.2]/[Fe.sub.2][O.sub.3] where the thicknesses of [Fe.sub.2][O.sub.3] and [TiO.sub.2]are 20 and 150 nm, respectively, at 45[degrees] incident angle and 45[degrees] reflection angle in Fig. 10. The figure indicates that the structure of [TiO.sub.2], being the outermost layer, has a steep slope reflection curve in the short wavelength region. That is the main reason for the high chroma yellowish pearlescent pigment.
[FIGURE 10 OMITTED]
Development of a manufacturing method to achieve low roughness iron-oxide surface
A rough surface masks the interference effect, causing the absorption color to be more dominant. As a result, the produced pigments have strong diffuse color and weak interference color. To develop a yellowish chroma pearlescent pigment, we have decreased the surface roughness of the [Fe.sub.2][O.sub.3] layer and achieved the smooth [Fe.sub.2][O.sub.3] surface using neutralizing titration.
The manufacturing process is the following.
(1) Mica substrates are dispersed in water and fully stirred to prepare an aqueous dispersion. After heating this dispersion to 80[degrees]C. hydrochloric acid is added to adjust the pH to 3.
(2) A pre-prepared ferric nitrate aqueous solution is added slowly to the mica dispersion. The pH of the dispersion is kept at 3 by adding an aqueous solution of sodium hydroxide.
(3) After completing the addition, the pH of the mixed solution is adjusted to 5 using the aqueous solution of sodium hydroxide. The pH-adjusted solution is subsequently isolated, washed, dried, and calcined at 700[degrees]C for 60 min. Thus, iron-oxide coated mica is obtained.
The important feature in the process is that an aqueous solution of [Fe.sub.2][O.sub.3] precursor is added into the aqueous dispersion of mica substrates from 5 x [10.sup.-4] to 12 x [10.sup.-4] mol/min per 100 g of the mica substrates.
Figure 11 shows SEM images of the [Fe.sub.2][O.sub.3] surface after neutralizing titration (Advanced Method) and the conventional method. Comparing the SEM image of the neutralizing titration with that of the conventional method, we found the smoothness of the surface significantly improves.
(4) The iron-oxide-coated mica is added to and fully dispersed in water. After heating this dispersion to 75 [degrees] C, hydrochloric acid is added to adjust the pH to 1.6.
(5) 40% by weight titanium tetrachloride aqueous solution is added at the rate of 1.4 g/min to the dispersion. The pH of the dispersion is kept at 3 by adding 20% by weight aqueous solution of sodium hydroxide. After that, the pH of the dispersion is adjusted to 7 using 20% by weight aqueous solution of sodium hydroxide.
(6) The dispersion is subsequently isolated, washed, dried, and calcined at 700 [degrees] C for 90 min. Finally, a mica substrate, homogeneously coated with iron oxide and further coated with colorless titanium dioxide is obtained.
[FIGURE 11 OMITTED]
The evaluation of the developed pigment
We discuss the evaluation of the developed pigment against current commercial products on the market, which is often used as yellowish pigment in cosmetic products.
First, we compared the chroma difference between the developed pigment and the commercial product using our simulation where the thickness of the commercial product is set to 80 nm so as to reproduce yellowish interference color.
The L* value as a function of the reflection angle and a*-b* value with reflection angles ranging from 0 [degrees] to 75 [degrees] at incident angle of 45 [degrees] are shown in Fig. 12.
Figure 12 shows that both pigments have the almost same lightness; however, the chroma value at specular angle is quite different. The result proves that the structure of Mica/[Fe.sub.2][O.sub.3]/[TiO.sub.2] gives two times more chroma than the commercial product.
[FIGURE 12 OMITTED]
Since a standard for the measurement of pearlescent pigments is under development by an ASTM committee, ASTM-E2194, which recommends 15 [degrees], 45 [degrees], and 110 [degrees] from specular angle at incident angle 45 [degrees] for metal flake, (17) is one of the candidates fro the multiangle measurement. But we adopted the reflection angle at 15 [degrees] intervals because we measured the bare skin at 15 [degrees] increments. (1). Also, we have evaluated the chroma difference between the developed pigment and the commercial product at an incident angle of 15 [degrees]. This is because more than one angle of incident is needed to evaluate the pearlescent pigments properly.
Next, optical microscope images of the developed pearlescent pigment and the commercial product are shown in Fig. 13. These images suggest that the developed pigment has much more golden chroma than the commercial pigment.
[FIGURE 13 OMITTED]
To confirm the validity of our simulation method and the enhancement of chroma, we measured the inplane bydirectional reflectance of artificial black skin samples on which those pigments have been applied using a gonio-spectrophotometric colorimeter (GCMS-4 manufactured by Murakami Color Research Laboratory Co., Ltd.). The incident angle is set at 45 [degrees] or 15 [degrees] and the reflection angles range from 0 [degrees] to 75 [degrees] and 15 [degrees] increments. The incident angle is from the normal to the artificial black skin (See Fig. 14).
[FIGURE 14 OMITTED]
Here we mention that the diffuse plate made of ceramic was used to calibrate the reflection data, and the reflectance of the sample is divided by that of the diffuse plate at each incident and reflection angle. The calibration method leads to specular reflection beyond 100%.
Since the chroma has to be compared under the same lightness level, we measured the color difference with approximately the same lightness (see L* graph of Fig. 15).
The L* graph and A*-b* graph of Fig. 15 show that the developed pigment gives about the same lightness and 1.5 times as much chroma as the commercial pigment. For example, at reflection angle of 45 [degrees] the chroma values of the developed and the commercial pigments are 45.03 and 30, respectively. The difference between the simulation and the measurement comes from the roughness of [TiO.sub.2] or [Fe.sub.2][O.sub.3]. The more the thickness of the layer is, the worse the roughness is.
[FIGURE 15 OMITTED]
Figure 16 shows spectral reflectance at incident angle 45 [degrees] and reflection angle 45[degrees]. This figure shows that the developed pigment has a sharp peak between 565 and 590 nm. As explained in section "Design of layer structure of a pearlescent pigment using computer simulation," the sharp peak gives higher chroma.
[FIGURE 16 OMITTED]
Finally, we show results at the incident angle of 15[degrees] in Fig. 17. In the specular region the difference of chroma between the developed pigment and the commercial pigment becomes small compared to that of the incident angle of 45[degrees], which is consistent with our simulation. On the contrary in the off-specular region, the difference of chroma becomes apparent due to [Fe.sub.2][O.sub.3] masstone color. But this effect is not included in our simulation.
[FIGURE 17 OMITTED]
As a result, we obtained the desired pearlescent pigment, which is free from the red color of iron oxide, and confirmed in field tests that this multilayer pigment could be used in blended foundation to reproduce the characteristics of what is considered a beautiful skin (for some information, see reference (1)).
We also show an automobile-shaped object coated with the developed pearlescent pigment in Fig. 18, which gives an impressive golden color. Some of the authors have tried to supply these pigments to the coating industry. (18)
[FIGURE 18 OMITTED]
We have designed a highly yellowish chroma peariescent pigment It is a mica substrate homogeneously coated with iron oxide which is further coated with colorless titanium dioxide. We have determined the layer structure of the peariescent pigment using computer simulation. In the simulation we have considered its layer structure, the complex refractive indices of the layers, and the thickness distribution of mica substrate that was measured with Atomic Force Microscopy (AFM). Also we have taken into account the spatial orientation of peariescent pigments on rough surface.
The feature of this design is that iron oxide having selective light absorption has been adopted as the layer material to enhance certain wavelengths of the reflected light. Also the peariescent pigment has been produced with neutralizing titration.
We have already applied the developed peariescent pigment to blended foundation and confirm that the pigment is useful in reproducing the characteristics of beautiful skin.
We hope our simulation will be widely used in developing new pearlescent pigments.
(1.) Misaki E, Shiomi H, et al., "Reproducing Beautiful Complexion with the Makeup Foundation Designed by Multi-Angle Image-Capture and Optical Simlulation." 24th IFSCC Congress Proceedings, 2006
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(15.) Gerd, B, et al., Merck Patent GmbH. WO Patent 93/08237. 1993
(16.) Nitta. K, et al., Merck Patent GmbH. EP Patent 0763573, 1997
(17.) ASTM E2194-03. "Standard Practice for Multiangle Color Measurement of Metal Flake Pigmented Materials." Volume 06.01
(18.) Adachi, M. Suzuki, F, et al., "Adjustment of a High Chroma Pearl Pigment by Interference Colors of a Laminate which Have a Different Film of a Retractive Index." 80th JSCM Anniversary Conference, 2007
Processing Development Research Lab., kao Corporation, 2606 Akabane, Ichikai-Machi, Haga-Gun, Tochigi 321-3497, Japan
e-mail: shiomi. firstname.lastname@example.org
Beauty Cosmetics Research Lab., Kao Corporation, 2-1-3
Bunka, Sumida-ku, Tokyo 131-8501, Japan
M. Adachi, F. Suzuki
Nihon Koken Kogyo Co., Ltd., Ichiban-cho. Tachikawa-shi, Tokyo 190-0033. Japan
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|Author:||Shiomi, Hiroyuki; Misaki, Eiichirou; Adachi, Maoya; Suzuki, Fukuji|
|Date:||Dec 1, 2008|
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