Elasticity of DLCA model gels with loops

Aggregation is a common natural phenomenon, but the structure-property relationship of the resulting porous, fractal gels is not well understood. An earlier study using the diffusion-limited cluster-cluster aggregation model revealed that loop structure is lacking in the model gels to account for their mechanical properties. The dangling bond deflection model was then developed to address loop formation during the aggregation process. This article describes the finite element method implemented to measure the various moduli of the resulting gel structure, which was modeled as a network of linearly elastic beams. The well-known empirical correlation in gels-the power-law scaling of Young's modulus with relative densities-was reproduced, and the scaling exponent of about 3.6, which is consistent with the experimental results, was captured in the analysis. About 70% of the total strain energy in the network came from bending of the beams. The contrast in the scaling exponent as compared to the open-cell foam model is attributed to the change of connectivity in the gel network when the density of the aggregate is adjusted.