Percolation in nanocomposites with complex geometries: Experimental and Monte Carlo simulation studies

The development of nanocomposites (a matrix, often polymeric, enhanced by a particle with a nanometer-sized dimension) has expanded dramatically in recent years with a particular focus on materials with complex microstructure and nanostructure. Such composites rely on formation of a connected network of particles throughout the sample volume in order to enhance the polymer's mechanical and electrical properties. From a fundamental perspective, this network formation will be governed by a percolation process within the constrained geometry of the particular microstructure. In this paper, the percolation process within a particular complex nanostructure, namely, a mat of electrospun nanofibers with fiber size of approximate to 100 nm and high porosity, is studied via continuum Monte Carlo simulations, where the sample geometry (fiber and particle sizes, orientation, and sample porosity) is matched to the mats utilized in our previous experimental work. A good agreement between experimental and computational results is observed. Simulations of spherical dopant in uniform samples, with zero, one, or two sample dimensions similar in size to the particle, were completed to explore the effects of confinement, in particular within a single fiber. These results were compared and contrasted with those from porous fibrous mats to determine the influence of porosity on the critical volume fraction. The results indicate that percolation in fibrous mats occurs via pathways that include sections of many fibers rather than being contained within single fibers which span the sample. The detailed dependence of critical volume fraction on porosity and the sensitivity to fiber number and width is discussed.