Page 399 - Book Hosokawa Nanoparticle Technology Handbook

6.7 OPTICAL PROPERTIES FUNDAMENTALS
(photoluminescence). Scattering takes place based on I 46 2 1⎞
d ⎛
the inhomogeneity of a substance. 24 ⎜ m ⎟ ( 1 cos 2 ) (6.7.1)
2
The pattern of scattering depends on the light wave- I 0 8 R ⎝ m 1⎠
length and the particle size to be measured. A large where I is the intensity of the incident light, R the dis-
0
particle, with micrometer to millimeter order diameter, tance, m the refractive index, the wavelength of inci-
scatters light forward at a comparatively narrow angle. dent light, and d the particle diameter. This equation
Mie scattering prevails in particulates with a particle indicates that light with a shorter wavelength is scat-
size that is comparable to the wavelength of visible tered more vigorously. Moreover, as Rayleigh scatter-
light [1]. In the Mie scattering region, as shown in ing decreases in proportion to the sixth power of
Fig. 6.7.1, light is also backscattered. The smaller the particle size, nanoparticles scatter light less vigorously
particle size becomes, the higher is the ratio of backscat- and become transparent. That is, if an isolated nanopar-
tering to forward scattering. For particulates of 200 nm ticle exists, it will appear almost transparent to visible
or less, the intensity distribution of forward scattered light. However in fact, it is not common to use a sole
light changes only slightly, but a great change appears nanoparticle in a perfectly isolated state as an optical
in the intensity distribution of backscattered light. Mie material. One practically important embodiment is to
addressed the diffraction of a plane monochromatic disperse nanoparticles in a transparent matrix. Its
wave with a uniform sphere with an arbitrary diameter examples include sunscreens and foundations with dis-
in a homogeneous medium, using electromagnetics to persed nanoscale titanium oxide pigment, and LEDs
obtain an exact solution for the scattering pattern in with nanoscale phopshor materials dispersed in resins
1908. Numerical solutions calculated by many [4]. Future work will enhance the functionality of
researchers are described in the work of Van de Hulst nanoparticles, such as absorption and luminescence,
[2]. This principle has been applied also to the laser while retaining transparency to visible light.
diffraction particle-size measurement technique of Such transparent films containing nanoparticles can
particulates that are commonly used today. be evaluated using the total light transmission and haze
Rayleigh scattering prevails for even smaller parti- value. Total light transmission is the transmittance of
cles of nanometer range [3]. Because incident light light in a transparent matrix, and the experimental pro-
penetrates almost uniformly throughout the entire cedure on visible light and UV rays are regulated. For
particle, light is scattered symmetrically to form a a highly transparent material, an integrating sphere
pattern like a cocoon, as shown in Fig. 6.7.2. The light transmissometer is used. The incident light quantity
intensity of Rayleigh scattering I is expressed by the and the total light quantity that pass through a speci-

following equation:
men are measured, and the ratio is computed and
expressed as a percentage, for visible radiation and UV
rays, respectively. The haze value represents the degree
of opacity, and is given as the scattered light transmit-
tance divided by total light transmission in percentage.
Empirically speaking, one would notice misting under
conditions such as backlighting when the haze value is
greater than about 2%. Therefore, to maintain the trans-
Incident light parency of a material, particles to be dispersed therein
must be nanoparticles that scatter light only slightly.
The particle size should be about 100 nm or less when
ceramic particles of a refractive index of about 2 are
dispersed. On the other hand, too much particle size
reduction increases the particle amount required to
assure a desired shielding property, in spite of high
Figure 6.7.1 transparency. Some numerical computation results
Mie scattering of fine particles. have been reported for shielding of UV rays, a practi-
cally important issue [5–7]. The result of Stamatakis et
al., which is most commonly used, demonstrates that
the optimal particle diameters of titanium oxide for the
protection of UV irradiation are 50 nm for 300 nm UV
Incident light rays and 120 nm for 400 nm UV rays, respectively.
However, because it is difficult to exclude the effect of
Particle dispersion of nanoparticles completely, only a few
studies have actually addressed particle size depend-
ence on the shielding of UV rays. Sakamoto et al. con-
ducted experiments using titanium oxide particles with
Figure 6.7.2 various primary particle diameters. They reported the
Rayleigh scattering of nanoparticles.
effect of the diameter on the shielding ability against
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