Molecular Weight Distribution of Branched Polymers: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory

Abstract

It is challenging to predict the molecular weight distribution (MWD) for a polymer with a branched architecture, though such information will significantly benefit the design and development of branched polymers with desired properties and functions. A Monte Carlo (MC) simulation method based on the Gillespie algorithm is developed to quickly compute the MWD of branched polymers formed through step-growth polymerization, with a branched polyetherimide from two backbone monomers (4,4′-bisphenol A dianhydride and m-phenylenediamine), a chain terminator (phthalic anhydride), and a branching agent (tris[4-(4-aminophenoxy)phenyl] ethane) as an example. This polymerization involves four reactions that can be all reduced to a condensation reaction between an amine group and a carboxylic anhydride group. A comparison between the MC simulation results and the predictions of the Flory-Stockmayer theory on MWD shows that the rates of the reactions are determined by the concentrations of the functional groups on the monomers involved in each reaction. It further shows that the Flory-Stockmayer theory predicts MWD well for systems below the gel point but starts to fail for systems around or above the gel point. However, for all the systems, the MC method can be used to reliably predict MWD no matter if they are below or above the gel point. Even for a macroscopic system, a converging distribution can be quickly obtained through MC simulations on a system of only a few hundred to a few thousand monomers that have the same molar ratios as in the macroscopic system.

Educational series: turning monomers into crosslinked polymer networks

“…Further, as the reaction progresses the number average molecular weight ( x n ) increases and can be approximated under ideal conditions using Flory theory as shown below for step polymerization. 22,24,25 where x n is the number average molecular weight, p is the conversion of functional groups, p A is the extent of reaction of the A functional groups, r is the ratio between initial A and B functional groups present and f is the average functionality of monomers.where α A and α B are the conversion of A and B functional groups respectively and f A and f A are the functionality of A and B functional groups respectively.…”

Rotary Friction Welding of Dissimilar Polymer Rods Containing Metal Powder

“…Thus, PLA plastic is suitable for making consumer products that need to withstand heavy use [21]. Generally, the reliability and validity [22] of the frictionally welded components are significantly related to the ambient temperatures [23,24]. Additive manufacturing is widely used for manufacturing a variety of functional components.…”

Fatigue Behavior of Rotary Friction Welding of Acrylonitrile Butadiene Styrene and Polycarbonate Dissimilar Materials

“…However, few studies focus on the fatigue life of ABS/PC polymer rods jointed via RFW. According to practical experience, the welded parts’ reliability [ 21 , 22 ] is related to the fatigue life [ 23 ]. The main objective of this study was to investigate the fatigue life [ 24 ] of the polymer rods with five different cyclic loads.…”