Monte Carlo calculations of UV protective properties of emulsions containing TiO 2 , Si and SiO 2 nanoparticles

Abstract

In this paper, we investigate the effect of nanoparticles made of different materials, such as titanium dioxide (TiO 2 ), silicon (Si), and silica (SiO 2 ) on UV protective properties of transparent emulsion used for sunscreens within the range of diameters d = 10 -200 nm by means of Monte Carlo simulations. As a result, silicon nanoparticles of appropriate sizes are the most protective-efficient within the whole UV spectral range among all kinds of investigated particles. Within one kind of particles, specific sizes are the following. For shorter wavelengths of the considered range (λ = 290 nm) 20-100-nm TiO 2 and 30-100-nm Si particles are the most effective protectors. For longer wavelengths (350 and 400 nm) the most pronounced attenuation is obtained with: a) for Si: d = 40 -120 nm (λ = 350 nm) and d = 60 -140 nm-sized (λ = 400 nm) particles, b) for TiO 2 : d = 80 -160 nm (λ = 350 nm) and d = 120 -180 nm-sized (λ = 400 nm) particles. Silica particles are much less protective than those mentioned above due to small refractive index mismatch between them and the surrounding emulsion.

Inorganic UV filters

“…The UV protection spectral range provided by TiO 2 is broad, extending from UVA II to UVB region (Serpone, Dondi, Albini, 2007), while the ZnO protection range peaks in the UVA spectrum (Popov et al, 2008). Thus, ZnO is used as a complement to UVB attenuators, thereby, affording preparations that provide broad spectrum protection all day long.…”

“…The equations describing this scattering are very complex, involving a combination of Legendre polynomials and Ricatti-Bessel and Hankel functions, but software can be employed to facilitate these calculations (Sorensen, Fischbach, 2000). The Mie theory has been used to determine the TiO 2 particle size that protects best at specific wavelengths using calculations: particles between 20 and 100 nm attenuate radiation best at wavelength 290 nm (UVB), particles between 80 and 160 nm attenuate the wavelength 350 nm (UVA) and particles between 120 and 180 nm attenuate at wavelength 400 nm (UVA) (Popov et al, 2008). Mie Law gives a general solution for diffusion radiation, while Rayleigh scattering relates the particle radius to the scattering intensity at a given wavelength, for very small particles.…”