0 foreword

 

Mica pearlescent pigment is in order to meet the human pursuit of beauty, simulation of a pearl is natural and develop compound paint products. For the first time since 1970, when the scientists since synthetic mica titanium pearl pigment, pearl pigment made rapid progress, develop with all kinds of special color effects of pearl pigment. Pearl pigment also occupy a more and more important position in the decoration industry.

 

In the field of pearl pigment production preparation, the United States, Germany and other developed countries has been the world's leading position. Form late pearl pigment industry in China, the lack of systematic study, compared with the developed countries, not only of the insufficiency of the existing production, the main difference lies in the quality of paint and paint color, the design of structure [1]. Mica titanium pearl pigment mainly divided into silver series, iridescence series and shading products [2]. In this paper, using the optical principle, this paper studies the silver beads light the chromogenic mechanism of pigment and illusion, and deepened the understanding of mica titanium pearl pigment special optical effect, is helpful to develop more different color effect of pearl pigment.

 

1 the spread of the light inside the mica pearlescent pigment

 

Mica titanium pearl pigment with low refractive index of the flake mica powder as the base material, evenly on the surface covered with a high refractive index of TiO2 thin film. Transparent TiO2 film layer's thickness may change within a certain range.

 

Mica titanium pearl pigment various special color effects, mainly because of the incident light in paint different refractive index of reflection and refraction on the interface between the layers, assuming that interface between 1 and 2 for the coating on the surface of the mica sheet, TiO2 thin film is light in pearl pigment on the surface of the optical propagation process is shown in figure 1. Where d is the geometry of TiO2 thin film thickness. N0 as the light source in the phase of the refractive index, n1 for titanium dioxide thin film refractive index, n2 as substrate mica phase refractive index (n0 < n1, and n2 (n1). Light source the light irradiation in L membrane reflection in the interface 1 first, reflected light for r1, part through high refractive index of TiO2 after reflection in the interface 2 [3], the reflected light to r2, r1 and r2 in parallel to the interface 1 and 2 are parallel, impossible to interfere, but when two beams of light focused on the retina interference happens [4]. According to the coherence of light, interference of two beams of light to meet the same frequency (a); (b) a constant phase difference; (c) the same direction of vibration; (d) the strength of the two coherent beams [5]. The reflected beams, first of all meet the top three conditions. Under a certain incident Angle analysis of the energy of the reflected beam, r1, r2 were similar between energy, starting from the third bunch of r3, energy fell sharply, negligible, the reflected beams r1, r2 (d) of interference conditions. So the pearl pigment with Angle different color effect, can be thought of by the reflected beams r1, r2 between interference effect.

The interference between r1 and r2 strength depends on the optical path difference, as shown in figure, a CD is perpendicular to the r1, optical path difference can be expressed as:

Δ = n1 + BC (AB) - n0AD (1)

From the geometry, it can be concluded:

AB = BC = d/sin gamma (2)

AD = DTG gamma sini ACsini = 2 (3)

According to the law of refraction and geometrical optics has the following relationship:

N0sini = n1sin gamma (4)

Will type (2) (3) (4) into (1) available:

Δ = 2 n1dcos gamma (5)

When the incident light is incident to the interface 1, the phase for high refractive index, TiO2 incident light from a low refractive index with high refractive index phase incident would have a PI on the interface phase mutation. According to the theory of optical thin film interference, produce the largest constructive interference with maximum destructive interference conditions are:

2 n1dcos gamma = lambda (2 k + 1) / 2

2 n1dcos gamma = k lambda.

Which is suitable for the TiO2 n1d optical thickness; K for interference series (positive integer k is less than 5); Gamma for the Angle of refraction.

Optical path difference depends on two beams reflected light of the incident Angle I and d thin film thickness. Under a certain incident Angle, when the incident light is complex colored light (the sun), some of the wavelengths of light is enhanced by the constructive interference occurs, some wavelengths of light destructive interference and abate, so the interference of pearl pigment can present a particular color. Also, when the thickness changes interference color also changed accordingly.

 

2 coated on the surface of TiO2 thin film thickness and the relationship between the interference color

 

Part of the theory is that super class magic color of pearl pigment mainly by two beams in the process of the reflected light interference, a certain frequency of monochromatic light interference is caused by long [3, 6], but the theory and the preparation of pearl pigment color changes exist in the process of access. In the process of preparation of mica titanium pearl pigment, with the increase of the mica sheet thickness of TiO2 thin film surface, observed by the naked eye of magic bead light interference color pigment change order from yellow to red, purple, blue, green. As yellow as a starting point along the color ring (see figure 2) counterclockwise. If the interference is happened long terms and conditions:

Δ = n1dcos gamma = 2 (k + 1/2) lambda

 

When the incident light Angle must be constructive interference of monochromatic light wavelength lambda and pearl pigment coating on the surface of TiO2 thin film thickness d proportional relationship. That with the increase of TiO2 thin film thickness, interference color should change according to the incident light wavelength of monochromatic light constructive interference occurred in the increasing order of change, from purple to blue, green, yellow, red. And the preparation process of pearl pigment interference color change a different order.

 

The author thinks that, pearl pigment iridescence phenomena occurred in part of monochromatic light is a result of reflection caused by destructive interference. When white natural light source (parallel light) at a fixed Angle irradiation on the thickness of TiO2 thin films, at this point, the thickness d and incident Angle is fixed, I each frequency of colored light in the medium phase refractive index n only slightly along with the change of wavelength is small, negligible, variable is wavelength lambda and interference series k, satisfy the destructive interference level interference (small) wavelength of light conditions disappear in the reflected light, interference effect occurs, such as color, uniform color in a film, it is the wavelength of incident it removed meet the destructive interference of other wavelengths of light interference blending effect. So open hole observed in pearl pigment color for incident light destructive interference of monochromatic light complementary color.

 

According to the conditions of the destructive interference, lambda n1dcos gamma = 2 k, also the thickness of TiO2 thin film and was positively proportional relationship between the reflected light wavelength, can get along with the increase of TiO2 thin film thickness, destructive interference of monochromatic light from purple to blue, green, yellow, red, pearl pigment observed interference color for its complementary color, according to the color ring, the complementary color chromaticity ring diameter on the two corresponding point [8], so the observed interference color pigment from yellow to red, purple, blue, green, and the preparation process of pearl pigment interference color change order.

 

With incident Angle is 45 °, calculated along with the increase of the thickness of TiO2 thin film on the surface of mica titanium pearl pigment interference color changes. According to the reflected beams r1, r2 optical path difference and destructive interference conditions available:

Lambda n1dcos gamma = 2 k? Qian Bridges d = s (6)

 

Visible light wavelength changes between 380 ~ 780 nm, k = 1, calculation can get corresponding TiO2 thin film thickness changes between 78 ~ 138 nm. When the thickness is less than 78 nm by Yu Guangcheng bad enough to cause any interference of monochromatic light, all monochromatic light paint surface reflection, and according to the principle of negative film, make the pigment presents silvery white flash effect. When the film thickness between 78 ~ 78 nm increases, the destructive interference of light wavelength increases, change from purple to red. Light source is located for air, take its refractive index was 1.0; Due to paint after heat treatment on the surface of TiO2 thin film is more than 90% for the rutile type, take the TiO2 thin film's refractive index was 2.71. According to the type (6), into the center of each monochromatic visible light wavelength, TiO2 coating layer thickness and pigment unreal colour corresponding relationship between the following table:

 

Similarly, when k? Barbary 2, you can get another round of interference color from yellow to green phantom beads light to paint, but because of increased the thickness of TiO2 thin film, light color in pigment dispersion strengthening, the reflected light energy is lost, so when k? When she 2 of magic bead light interference color pigment color not enough brightness, the effect is not obvious.

 

3 conclusion

 

The paper calculated when the natural light of the incident Angle is 45 °, pearl pigment interference color and the relationship between the TiO2 surface coating thickness. When the mica titanium pearl pigment on the surface of TiO2 thin film thickness is less than 78 nm, cannot cause the two beams emitted light enough, which is generated by the optical path difference, all incident light is reflected and presents the silvery white, when in 78 ~ 138 nm TiO2 thin film thickness, incident occurred in part of monochromatic light natural light destructive interference and make the pearl pigment presents its tone. At the same time using the geometrical optics principle combined with the Munsell color ring can reasonable explanation in the process of preparing mica titanium pearl pigment, pigment interference color change order from yellow to green (changes along the chromaticity ring counterclockwise), rather than change the order of the wavelength of monochromatic light interference increases.

 

reference

[1] Xu Yang group. The manufacturing process and application of pearl pigment. Beijing: chemical industry press, 2005:10-20;

[2] Tan Junru. Fu Xiansong. Hou Wenxiang, Chen Xiuzeng. Wang Li. The Preparation and characteristics of a multi - cover - layer type, blue mica titania, pearlescent pigment, Dyes and pigments, 2003, when 3 ~ 98;

[3] Werner Rudolf Cramer. Examples of Interference and the Color Pigment Mixtures, Green with Red and Red with Green, the Color research and application, 2002, 27 (4) : 276 ~ 281.

[4] Tang Jinfa Zheng Quan. Application of thin film optics. Shanghai: Shanghai science and technology press, 1984:4 to 6;

[5] and deal. Optical. Beijing: higher education press, 1999:56-156;

[6] Maria e. Nadal, Edward a. Early. The Color Measruements for Pearlescent Coatings. The Color research and application, 2002, 29 (1) : 38 to 42;

[7] Ma Dengjun Hao Gang. Pearl iridescent mica titanium conform to the optical properties of the material and color characterization. Journal of hebei construction engineering college, 2002, 9:77-80;

[8] JingJiCheng JiaoShuLan, YuBaiLin etc. Colorimetry. Beijing: science press, 1979:46 ~ 47.