A walk around the color sphere

14 September 2015
Rajath Mudalamane, Philipp Niedenzu, Sandra Davis, Austin Reid, and Jill McLaughlin
The size distribution of titanium dioxide pigment particles affects the whiteness they impart to a plastic article.

Color plays a critical role in plastics: brand recognition in packaging, color matching in automotive interiors, and so forth. A common consequence of plastics processing is a certain amount of thermal degradation, which tends to shift the color of the end article toward brownish or yellowish tones. White pigments such as rutile titanium dioxide (TiO2) are commonly used to whiten and color plastics. However, it is not broadly known that scattering is the primary mechanism by which TiO2 imparts whiteness and opacity by scattering (see Figure 1). ‘White’ pigments have the ability to scatter all visible wavelengths of light. They might more accurately be called ‘achromatic.’ We have considered how the particle size distribution of the TiO2 can significantly impact the color and brightness of a plastic article.1


Diffraction of light around a particle of rutile titanium dioxide (TiO2).

The relationship of particle diameter and light scattering was first described by Walter Rayleigh2 and further refined by Gustav Mie,3 Horvath,4 and Van de Hulst.5 This is fascinating reading with the main punchline being that the maximum scattering of a given wavelength of light occurs at a particle size close to half the wavelength.6For example, to scatter blue light (wavelength 450nm), a particle near 225nm in diameter would be optimum. Most commercial TiO2 materials have a distribution of particle diameters and therefore will scatter a distribution of wavelengths. Shifting the particle size distribution will enhance light scattering of certain wavelengths. For example, by shifting the median particle diameter to a smaller value, a larger amount of scattering will occur for shorter wavelengths (see Figure 2).


Relative scattering power vs. rutile particle size.

To illustrate this, we blended three TiO2 pigments, which differ in their particle sizes and size distributions, with carbon black in a polyvinylchloride (PVC) matrix, in concentrations ranging from 0.3 to 6.1% by weight. Pigment type A has median diameter typically 0.28–0.32μm and attenuates the longer wavelengths of visible light. The median diameter of pigment type B is typically 0.25–0.28μm, and that of pigment type C is typically 0.22–0.25μm. (These measurements were made by x-ray centrifuge techniques).7 The three pigments are commonly referred to by the color or wavelength that is attenuated to the highest degree. Type A is often referred to as ‘yellow’ in undertone. In contrast, the undertones of types B and C are described as ‘neutral’ and ‘blue,’ respectively.

The impact of different TiO2 particles on the final color of a plastic part can be charted by noting the relationship between the CIE (International Commission on Illumination) L*, a*, and b* color axes.8 The CIE L*a*b* axes describe a color space in three coordinates. The L* values describe the diffuse white (i.e., L* = 0 is black, L* = 100 pure white). The a* axis represents the red to green scale (a* negative indicates green), and b* is the position between the blue and yellow (b* negative indicates blue). The ideal CIE L*a*b* graph would have all possible colors located within a sphere where the black to white scale represents the poles of the sphere and the equator represents the perfect gray with the highest amount of color mixtures between red/green/blue/yellow/white/black. The diameter of the circle along the a* and b* axes at a particular L* value is referred to as the ‘chroma,’ and the circumference of the circle at a particular L* value is referred to as the ‘hue.’ Hence, as the amount of TiO2 increases, the color space moves from the south pole of the CIE L*a*b* sphere to the equator. As the L* values rise, the chroma possibilities increase and the hue grows. Once the equator color coordinates have been achieved, adding more TiO2 continues to increase L* but decreases chroma and hue.

Figure 3 highlights several features of walking along the surface of the color sphere. For example, each additional amount of TiO2 added to the PVC formulation creates a step up in L*, a step outward or inward toward zero in b*, and forward or backward toward zero in a*. The differences along the b* axis highlight the nomenclature assigned to each pigment type analyzed. For example, the yellow TiO2 has the most positive b* value at a given constant concentration of TiO2. An a* difference among the three types of pigments is also present but at a smaller scale than with b*. To increase the L* value, more TiO2 is added. By adding more TiO2, the expectation is that L* increases and the a* and b* axes move accordingly. The key point of Figure 3 is that each pigment has a unique color surface that cannot be matched at the same concentration. At no point will the yellow pigment A be able to provide the same b* value as the blue pigment C. Additionally, the blue pigment will achieve the closest ‘ideal white’ color at a given concentration.


Scatter plot of CIE (International Commission on Illumination) L*a*b* color values for different TiO2materials.

The ‘whiteness index’ (WI) is a measure of the degree to which a surface resembles an ideal white. The ASTM313 whiteness index is used for measuring near-white, opaque materials.9, 10 Figure 4 shows the WI achieved with the different TiO2 grades, at different loading levels. As expected, the WI increases with increasing TiO2 content. It is interesting to note the significant differences between WI achieved by the different TiO2 grades.11


Whiteness index (WI) of the compounded polyvinylchloride as TiO2content increases.

In summary, we have shown that each TiO2 material results in a unique color space, primarily in the b*. As the amount of each pigment increased, we compared the tri-stimulus values to the ideal white material of L* = 100, a* = 0, and b* = 0. At a given concentration of TiO2, the smaller particle diameter pigment approached the ideal white the most among the three pigments. Hence, a plastics processor should take care in selecting TiO2 grades for coloring. Rutile TiO2 grades with tight and accurate control of particle size are best suited for consistent color matching. For white articles, a grade of TiO2 with the bluest undertone or the finest average particle size will provide the highest WI to the part.


Authors

Rajath Mudalamane
The Chemours Company

Philipp Niedenzu
The Chemours Company

Sandra Davis
The Chemours Company

Austin Reid
The Chemours Company

Jill McLaughlin
The Chemours Company


References

  1. P. Niedenzu, A walk around the color sphere: effect of titanium dioxide particle size distribution on color of plastics, SPE ANTEC, 2015.

  2. P. Lilienfeld, A blue sky history, Opt. Photon. News 15 (6), pp. 32-39, 2004.

  3. G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Annal. Phys. 330, pp. 377-445, 1908.

  4. H. Horvath, Gustav Mie and the scattering and absorption of light by particles: historic developments and basics, J. Quantit. Spectrosc. Radiat. Trans. 110, pp. 787-799, 2009.

  5. H. C. Van de Hulst, Light Scattering by Small Particles, Dover, New York, 1981.

  6. A. R. Robertson, Historical development of CIE recommended color difference equations, Color Res. Applic. 15 (3), pp. 167-170, 1990. http://onlinelibrary.wiley.com/doi/10.1002/col.5080150308/pdf

  7. N. Stanley-Wood and R. W. Lines, Particle Size Analysis, Royal Soc. Chem., Cambridge, UK, 1992.

  8. R. Berns, Billmeyer and Saltzman's Principles of Color Technology 3rd ed. ed., Wiley, 2000.

  9. ASTM313-10: Standard Practice for Calculating Yellowness and Whiteness Indices from Instrumentally Measured Color Coordinates, ASTM Int'l, 2010. http://www.astm.org/DATABASE.CART/HISTORICAL/E313-10.htm Accessed 30 April 2015

  10. A Guide to Understanding Color Communication, X-rite Inc., 2007. http://www.xrite.com/documents/literature/en/L10-001_Understand_Color_en.pdf Accessed 30 April, 2015

  11. D. Pascale, A Review of RGB Color Spaces, BabelColor Company, 2003. http://www.babelcolor.com/download/A review of RGB color spaces.pdf Accessed 30 April 2015

DOI:  10.2417/spepro.005924



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