MATHEMATICAL MODELING OF BIVARIATE DISTRIBUTIONS OF POLYMER PROPERTIES USING 2-D PROBABILITY GENERATING FUNCTIONS

摘要

The addition of monomer units to form polymer chains in a polymerization process is governed by probabilistic issues which depend on changing process conditions. As a result, the reaction product is composed by a mixture of polymer chains with different size and/or structure. Hence, polymer samples usually present distributions of the different molecular properties (i.e. molecular weight distribution (MWD), copolymer composition distribution (CCD), short (SCBD) and long (LCBD) chain branching distribution, sequence length distribution (SLD), particle size distribution (PSD), etc.). A detailed knowledge of these distributions is very important because most of the processing and end-use properties of polymers depend on them. In many cases, a proper characterization of a polymer sample will require simultaneous information on more than one property distribution. For instance, MWD- CCD is important for copolymer systems; MWD-SCBD and/or LCBD are needed in the case of branched polymers. This requirement must be taken into account in the development of advanced mathematical models of polymer systems. Therefore, it is extremely important to count with a methodology that allows the joint modeling of multiple distributions.