A Monte Carlo determination of the effectiveness of nanoparticles as spacers for optimizing TiO2 opacity

Abstract

Optimal TiO 2 opacity is achieved when the TiO 2 particles are well spaced. Nanoparticle extenders are claimed to improve TiO 2 spacing by positioning themselves between the larger TiO 2 particles (0.25 lm) and preventing the TiO 2 particles from approaching or touching one another. Claims have been made that this can as much as double the light-scattering efficiency of TiO 2 . This concept was tested by a combination of Monte Carlo simulations and image analysis techniques to determine computationally how the effectiveness of this approach is affected by TiO 2 concentration, nanoparticle concentration, and nanoparticle size. Surprisingly, the results showed that nanoparticles did not, in fact, improve the spacing of TiO 2 particles under any of the conditions examined (specifically, in the absence of any inter-particle interactions). Instead, TiO 2 distributions and spacings were completely indifferent to the presence of smaller particles (however, large extender particles were found to cause TiO 2 crowding, consistent with expectations and experiments). Explanation and implications of these findings are discussed.

Composition Effects on Sheen and Spread Rate of an Interior Flat, One Coat Latex Paint Formulation

“…Additionally, if the air voids are of optimal size (approximately 0.3 µm), they will scatter light as the wave enters and exits the void. 13 This affect is similar to that of TiO 2 , but not as effective because the difference in refractive index between the air and binder is smaller than the difference between the binder and pigment. Nonetheless, air voids are beneficial to hiding power, and can greatly affect a paint's spread rate.…”

“…Physical properties such as washability, stain and scrub resistance, and tensile strength can be compromised. 13 The degree of air void formation increases as the PVC increases above the CPVC. The presence of continuous air networks within the dry paint film are responsible for diminished performance.…”

“…A list of refractive indices for common paint ingredients is shown in Table 2: The magnitude of a film's hiding power is determined by the square of the difference in refractive indices between adjacent materials. 13 For this reason, paint films containing air voids are more efficient at scattering light because the air presence decreases the average refractive index of the binder matrix. The difference in refractive index between the air-containing matrix and TiO 2 particles is larger than the difference between the air-free binder and TiO 2 .…”

“…The shear number of particles within a fixed volume creates a "crowding" effect within the system, which reduces the light scattering efficiency of each particle. 13 For this reason, formulations are engineered to maintain optimal particle separation, as much as possible, in order to maximize light scattering. The affects of pigment particle crowding on light scattering can be seen in TiO 2 PVC effect on hiding can be summarized in five parts.…”

“…The affects of pigment particle crowding on light scattering can be seen in TiO 2 PVC effect on hiding can be summarized in five parts. 13 In the first section, an addition of pigment gives an equal (straight black line) addition of total hiding to the paint system. At low levels of PVC, the pigment particle separation is vast enough that the light scattering efficiency is maximized by all of the particles due to the lack of crowding effects.…”