Molecular weight/branching distribution modeling of low-density-polyethylene accounting for topological scission and combination termination in continuous stirred tank reactor

Three-dimensional chain-length-branching-combination points distribution modeling of low density polyethylene in a continuous stirred tank reactor allowing for gelation

“…In contrast, since the pseudo distributions method will be employed for the combination points dimension, only the implementation of combination moment expression arising from the hypergeometric combination points redistribution assumption is required. This proceeds in the same manner exactly as for branching in the pseudo distribution approach discussed in Yaghini and Iedema (2014a) …”

“…In the 3D formulation, the additional concern is with redistribution of combination points over scission fragments. In Yaghini and Iedema (2014a) it is argued that for branch points redistribution, a hypergeometric distribution is the best model, thus the number of branch points on a scission fragments is proportional to its length. The same reasoning is valid for combination points.…”

“…Here, ) , ( 1 j i w is the weight belonging to the node )) , ( ( 1 1 j i z s of the summation grid and it is calculated in an identical way as the regular weights of the Galerkin approach (Yaghini and Iedema, 2014a). The number of rows in convolution matrices 1 Z and 2 Z always equals to the total number of nodes, …”

“…The 2D Regarding the convolution operation required to address combination termination we have extended the convolution procedure described in Yaghini and Iedema (2014a) using two convolution matrices. Note that a distribution ) (s P , could be convoluted with itself or with another distribution ) (s Q , where the second distribution may or may not be equal to the first one.…”

“…The 2D combination points pseudo distribution problem is solved for the case of random scission, either linear or topological scission, which determines the shape of the fragment length distribution ) , ( m n f (Yaghini and Iedema, 2014a). In the previous paper (Yaghini and Iedema, 2015d) the issues of redistribution of ) , ( m n f in the 2D context and the redistribution of branch points on scission fragments has been extensively discussed.…”