(174a) A Monte Carlo and Continuum Study of the Mechanical Properties of Porous Titania Nanoparticle Aggregate Films

In this work, an approach has been developed to study the mechanical properties of porous films composed of titania nanoparticle aggregates. These results are expected to have applications in production of high surface area, mechanically strong films. Control of properties such as surface area and mechanical strength can occur by varying the amount of chemical and van der Waals bonds in the film, through annealing or by changing the process parameters of the synthesis of the films. We simulate the growth of the film deposit using a Monte Carlo approach with diffusion-limited aggregation. Each aggregate in the simulation is fractal-like and random in structure. In the deposit structure, it is assumed that there are only two values for the bond strengths; one representing the strong chemical bond between the particles in an aggregate and the other representing the weak Van der Waals bond between particles from different aggregates. The Van der Waals bond strength is calculated from the theory of Hamaker [Hamaker, 1937]. As a first approximation, the chemical bond strength is assumed to be two orders of magnitude greater than the van der Waals bond strength. This assumption is consistent with what has been reported in literature [Froeschke et al., 2003]. The elastic modulus is estimated using an equivalent-continuum modeling approach [Odegard et al., 2002]. The particles and the bonds between them are represented as an equivalent mechanical pin jointed truss model. The truss model is then converted to an equivalent-continuum model, which is representative of the nanoparticulate structure. The equivalent continuum model is strained and the elastic modulus is calculated from the strain energy. This approach is computationally fast as finite element analysis is applied only on one structure (described by the equivalent continuum model). The elastic modulus is observed to increase with a decrease in primary particle size and is independent of the size of the aggregates deposited.

References:

Hamaker H.C., The London-Van der Waals attraction between spherical particles. Physica 4, 1058 (1937).

Froeschke S., Kohler S., Weber A.P., Kasper G., Impact fragmentation of nanoparticle agglomerates. Journal of Aerosol Science 34, 275 (2003).

Odegard G.M., Gates T.S., Nicholson L.M., Wise K.E., Equivalent-continuum modeling of nano-structured materials. Composites Science and Technology 62, 1869 (2002).