Modeling of branched crosslinked composites, using the statistical polymer method

Summary form only given. The problem of modeling of branched cross-linked structures is one of most complicated in composite science. Most existing composite materials have branched cross-linked structure, and their theoretical study is indispensable for their optimal application in practical needs. Conventional methods of description of branched cross-linked structures are numerical and do not allow solution in the general case. Their application needs complicated and long computing and the physical sense of the obtained results is not always clear. Some researchers try application of classical chain models to branched systems, although such approximation is incorrect and may cause serious errors. The problem of modeling of branched cross-linked structures was recently solved by statistical polymer method. This method is based on the consideration of averaged structures (statistical polymers). In such approximation, all reactions in equilibrium are considered as reactions between statistical polymers. The statistical polymer method was tested directly and indirectly. The direct test comprised the exact reproduction of Trommsdorf effect for non-equilibrium polymers, whereas the indirect test allowed the theoretical interpretation of adsorption isotherms for silica and alumina gels. In all cases, the correlation of experimental and theoretical results was very good. The statistical polymer method allows modeling of composites, e.g. materials based on quaternary ammonium silicates. Silica globulaes in solution or solid are successfully modeled. Such modeling allows serious reduction (for hundreds-thousands times) of the number of numerical experiments. The proposed statistical polymer method is commendable for description of all kinds of composites with complex structure.