9.2 Adjustment of the Index of Refraction and Visually Transparent UV Absorbers 183
should be smaller than one tenth of the shortest wavelength under consideration.
For a transparent composite in the visual range, which is for human beings the
range from 400 to 800 nm, the maximum particle size in such a composite must
be less than 40 nm.
Furthermore, as the next step, one has to look at the production process of such
a composite. Assuming the particles of equal size and individualized are put into
the precursor of the polymer. After the process of blending, there is a concentration c of particles in the mixture. Even when the concentration of particles is small,
there is a probability of forming clusters. The probability c i that there is a cluster
of i particles is estimated by
c c
i
i
= .
(9.3)
This equation proposes to keep the concentration of particles in the composite as
low as possible to avoid the formation of clusters. Low concentration of particles
results in the use of particles with high index of refraction, as there are for
example, ZrO 2 and TiO 2 . On the other hand, these oxides, like all oxides from
transition metals, are photocatalysts. When, besides visible or infrared, IR, light,
there is also ultraviolet, UV, present, composites containing these oxides have a
propensity to self-destruction. In such cases, the application of silica, SiO 2 , or
alumina, Al 2 O 3 , is recommended. The other possibility is to coat the highly
UV-absorbing oxides with alumina or silica.
Looking at Eqs. (9.1) and (9.2), both are linear in concentration and the difference in the indices of refraction, it makes no difference for the power of the scattered light, if the modification of the index of refraction is obtained by high
concentration and a small difference of the indices of refraction or vice versa.
Therefore, particle size and clustering are the criteria for decisions. When one
applies particles coated with the matrix polymer, the risk of particle clustering is
avoided. Lastly, if possible, one should seek this choice (see Chapters 2 and 4).
Additions of ceramic nanoparticles to a polymer not only alters the index of
refraction. By proper selection of particle composition and size, one can produce
composites that are transparent in the wavelength range of the visible light but
nontransparent for UV in the wavelength range below 400 nm. When designing
such composites, it is necessary to select the particle size in a way to obtain optimal
absorption in the intended range of wavelength. Figure 9.2 displays the wavelengthdependent absorption of titania with different particle sizes. This figure demonstrates two important phenomena: It is very well visible, that with decreasing
particle size, the maximum of the absorption is found at shorter wavelength; one
observes a blueshift with decreasing wavelength. Furthermore, it is important to
realize that the particle-diameter distributions with mean values of 45 and 145 nm
were very broad, whereas that for particles with 4.5 nm diameter was narrow. A
broad size distribution results in a broad absorption maximum, and vice versa.
For 145-nm particles, this is an intended effect, as this is a white pigment.
Therefore, any preferred wavelength in the absorption spectrum is detrimental.
Other oxides used for UV absorption, which are, as small particles, colorless to
should be smaller than one tenth of the shortest wavelength under consideration.
For a transparent composite in the visual range, which is for human beings the
range from 400 to 800 nm, the maximum particle size in such a composite must
be less than 40 nm.
Furthermore, as the next step, one has to look at the production process of such
a composite. Assuming the particles of equal size and individualized are put into
the precursor of the polymer. After the process of blending, there is a concentration c of particles in the mixture. Even when the concentration of particles is small,
there is a probability of forming clusters. The probability c i that there is a cluster
of i particles is estimated by
c c
i
i
= .
(9.3)
This equation proposes to keep the concentration of particles in the composite as
low as possible to avoid the formation of clusters. Low concentration of particles
results in the use of particles with high index of refraction, as there are for
example, ZrO 2 and TiO 2 . On the other hand, these oxides, like all oxides from
transition metals, are photocatalysts. When, besides visible or infrared, IR, light,
there is also ultraviolet, UV, present, composites containing these oxides have a
propensity to self-destruction. In such cases, the application of silica, SiO 2 , or
alumina, Al 2 O 3 , is recommended. The other possibility is to coat the highly
UV-absorbing oxides with alumina or silica.
Looking at Eqs. (9.1) and (9.2), both are linear in concentration and the difference in the indices of refraction, it makes no difference for the power of the scattered light, if the modification of the index of refraction is obtained by high
concentration and a small difference of the indices of refraction or vice versa.
Therefore, particle size and clustering are the criteria for decisions. When one
applies particles coated with the matrix polymer, the risk of particle clustering is
avoided. Lastly, if possible, one should seek this choice (see Chapters 2 and 4).
Additions of ceramic nanoparticles to a polymer not only alters the index of
refraction. By proper selection of particle composition and size, one can produce
composites that are transparent in the wavelength range of the visible light but
nontransparent for UV in the wavelength range below 400 nm. When designing
such composites, it is necessary to select the particle size in a way to obtain optimal
absorption in the intended range of wavelength. Figure 9.2 displays the wavelengthdependent absorption of titania with different particle sizes. This figure demonstrates two important phenomena: It is very well visible, that with decreasing
particle size, the maximum of the absorption is found at shorter wavelength; one
observes a blueshift with decreasing wavelength. Furthermore, it is important to
realize that the particle-diameter distributions with mean values of 45 and 145 nm
were very broad, whereas that for particles with 4.5 nm diameter was narrow. A
broad size distribution results in a broad absorption maximum, and vice versa.
For 145-nm particles, this is an intended effect, as this is a white pigment.
Therefore, any preferred wavelength in the absorption spectrum is detrimental.
Other oxides used for UV absorption, which are, as small particles, colorless to