Modeling and simulation method for nonlinear polymer formation
May 10-15, 2015
The random sampling technique is a powerful Markovian method that can be applied to any types of nonlinear polymer formation, irrespective of the reactor types used. The fundamental concept of the random sampling technique is very simple. One just hypothetically samples a polymer molecule from the sea of polymer molecules in the final product, and then the whole structure of the selected polymer molecule is reconstructed, by following its formation history. By choosing one monomeric unit bound into a polymer molecule randomly, one can choose one polymer molecule on a weight basis. When the sampling is made on a weight basis, the weight-based properties can be determined directly. The weight-average chain length is the expected size of the polymer molecule so selected, whose analytic solution can be obtained in a matrix formula, generally represented by . When the concept of random sampling technique is applied to the Monte Carlo simulation, one can observe the structure of each polymer molecule directly on your computer screen, and very detailed structural information can be obtained in a straightforward manner. The statistical properties of the whole reaction mixture can be determined by sampling a large number of polymer molecules. When such structural information is connected with the application properties, one can establish a fully computer-aided polymer design system. In the lecture, I will use free-radical polymerization that involves simultaneous long-chain branching and scission, such as the case of low-density polyethylene synthesis, as an example. This polymerization system cannot be represented by the differential equation approach, but the Markovian method can describe the structural development strictly. The effect of reactor types used for the synthesis, such as a PFR, a CSTR and CSTRs in series, will be discussed.
H. Tobita, "Modeling and simulation method for nonlinear polymer formation" in "Polymer Reaction Engineering IX", E. Vivaldo-Lima, UNAM; J. Debling, BASF; F. Zaldo-Garcia, CP-COMEX; J. Tsavalas, Univ. of New Hampshire Eds, ECI Symposium Series, (2015). http://dc.engconfintl.org/polymer_rx_eng_IX/21