Percolating network development

This behavior can be understood if a superimposed kinetic aggregation process of primary carbon black aggregates in the rubber matrix is considered that alters the local structure of the percolation network. A corresponding model for the percolation behavior of carbon black filled rubbers that includes kinetic aggregation effects is developed in [22], where the filler concentrations and c are replaced by effective concentrations. In a simplified approach, not considering dispersion effects, the effective filler concentration is given by ... 

Internal protein motion (H exchange) increases from 1/1000 at 0.04 A to full solution rate at 0.15 A At 0.1-0.15 A chymotrypsin and some other enzymes develop activity At 0.15 A long-range proton movements along percolative networks, seen in dielectric measurements... 

Statistical network models were first developed by Flory (Flory and Rehner, 1943, Flory, 1953) and Stockmayer (1943, 1944), who developed a gelation theory (sometimes referred to as mean-field theory of network formation) that is used to determine the gel-point conversions in systems with relatively low crosslink densities, by the use of probability to determine network parameters. They developed their classical theory of network development by considering the build-up of thermoset networks following this random, percolation theory. 

Using field-based models, it is more difficult to provide information about the chain conformation on the surface however, attempts have been made to understand phase separation and mechanical properties of composites. Shou et al. combined SCF/DFT techniques with lattice spring model (LSM) to study the effects of the spatial distribution and aspect ratio of particles (rods and spheres) on the mechanical properties of the composite. Buxton and Balazs combined TDGL theory for polymer blends with BD for nanorods in the simulations of nanocomposites. i A percolating network of nanorods was identified in the minority phase of a bicontinuous structure. Clancy and Gates developed a hybrid model for CNTs in a bulk poly(ethylene vinyl acetate) matrix. Molecular structures of... 

In Section 9.1 the concept of percolation was developed to examine the spatial continuity of polymer networks. The concept can be extended to clusters of molecules or particles in space. Percolation clusters are fractal objects which do not fill space in a dense manner, but fill only a fraction of space. Thus the mass, M, versus distance, R, is given by... 

For the polymers containing filler that touch each other, the percolation theory has been developed. This assumes a sharp increase in the effective conductivity of the disordered media, polymer matrix composite, at a critical volume fraction of the reinforcement known as the percolation threshold (( )percoi) which long-range connectivity of the system appears. The model that best expresses these aspects is the one created by Vysotsky (Vysotsky and Roldughin 1999), which presumes a percolation network of nanofiller particles inside the polymer matrix as shown in equation (11.10) ... 

Monte Carlo simulations. Wescott et also applied DPD approaches to investigate the self-assembly of CNT percolating networks in thin films of block copolymer melts. Similarly, Tozzi et al. used particle-level simulations to investigate the stmctural evolution and electrical conductivity of CNT suspensions in shear flow. These approaches can be extended in future work to study the effects of complex interparticle and matrix-induced interactions, as well as the effects of external fields on the network stmcture and electrical properties of composite materials. The synthesis of chemically heterogeneous or Janus particles further motivate these developing techniques. 

---