Branching determination from radius of gyration contraction factor in radical polymerization

Simulating Light Scattering Behavior of Branched Molecules

“…This says that a molecule of n monomeric units is considered being cut into two parts of n 1 c and n 2 c , while is obtained by summing over all possible ways, c , of cutting the molecule . Thus, they arrive at their much cited formula for the contraction factor of the radius of gyration of a branched molecule as compared to the radius of a linear molecule of the same number of units .…”

“…With light scattering of polymer in dilute solution both average square radius of gyration and molar mass may be determined, allowing to establish the contraction factor . Besides the radius of gyration also the angular dependence of the scattered light in dilute solution (P(θ) −1 ) is determined.…”

“…Main issue of the present paper is to predict the scattering function, P −1 (θ) versus sin 2 (θ/2) for ldPE based on Benoit's model, now exactly accounting for the branching topologies, i.e., branch‐on‐branch structures and branch lengths. The specific structure arises from the kinetics of radical polymerization under conditions of ldPE manufacturing . The algorithm to perform this task is based on graph theory and analyzes the adjacency matrix describing the branching topology in terms of the path lengths between any two nodes of the graph.…”

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

“…Architectures of large hyper-branched molecules even in low concentrations play a dominant role in determining the physical properties of polymers such as rheology and also in polymer characterization by size exclusion chromatography (Yaghini and Iedema, 2015a). Predicting these architectures by mathematical modeling is therefore highly interesting and many researchers have been engaged in such an activity.…”

Population balance modeling of full two-dimensional molecular weight and branching distributions for ldPE with topological scission in continuous stirred tank reactor

“…In deriving physical properties of polymers usually we deal with discrete variables (chain length, number of branch points, number of combination points, etc.). Among chemical reactions, modeling polymerization reactions by population balances is favorable over many other methods as clarified in Yaghini and Iedema (2014a, 2015a, 2015b, 2015c, although a very hard task even in one dimension. The challenge is in relation to the difficulties in Population Balance Equations (PBEs) formulation, and their numerical solutions (Schutte and Wulkow, 2010).…”