Mathematical modeling of the full molecular weight distribution in ATRP techniques

Abstract

In this work the molecular weight distribution (MWD) of several atom transfer radical polymerization (ATRP) techniques has been derived and solved using the Reduced Stiffness by Quasi Steady State Approximation (RSQSSA) methodology. The Quasi Steady State Approximation has been validated on the living radicals for normal, Simultaneous Reversible and Normal Initiation and Activators Regenerated by Electron Transfer (ARGET), and it is shown that the information lost due to its application is negligible. According to these results, RSQSSA shows the best performance in terms of wall-clock time and required memory in comparison to implicit techniques and Predici. In the case of the ARGET technique, the model predictions show good agreement with experimental data. Finally, an analysis on the impact of the slow and fast activation of the initiator on the MWD using ARGET has been carried out, indicating that the optimal initiator to control the MWD should exhibit activation-deactivation rates very similar to those of the polymeric equilibrium.

An Update on the Pivotal Role of Kinetic Modeling for the Mechanistic Understanding and Design of Bulk and Solution RAFT Polymerization

“…For example, Konkolowicz et al have calculated the change of the RAFT polymerization CLD for a given time step by integrating moment equations and subsequent sampling of the polymeric reaction events to construct the CLD. This calculated CLD was used to update the population weighted rate coefficients for the integration of the moment equations for the next time step, an approach also applied for other controlled radical polymerization (CRP) systems …”

“…This calculated CLD was used to update the population weighted rate coefficients for the integration of the moment equations for the next time step, an approach also applied for other controlled radical polymerization (CRP) systems. [106,107]…”

Acrylate Network Formation by Free‐Radical Polymerization Modeled Using Random Graphs

“…However, the analytic criterion for the existence of the giant component derived in Section 4.3 provides a way to find the gel point directly from the time-dependent trivariate degree distribution defined in Equation (26). The gel point conversion χ gel is estimated by calculating the moments of the degree distribution and inserting them into Equation (41). The main advantage of the criterion is that it avoids the numerical solution of Equations (37) and (38).…”

“…accessible computational power on the other resulted in a gradual shift of the focus to MC simulations, [34,35] population balance equation (PBE), [36][37][38][39][40][41] lattice modeling, [42] and molecular dynamics, [43] methodologies offering more flexibility than analytical models. Leiza and co-workers [44,45] were working on elaborate MC simulations for crosslink polymerization.…”

Mathematical modeling of molecular weight distribution in miniemulsion polymerization with oil‐soluble initiator

“…Hence the solution of the MWD is usually a challenging task and several numerical methods have been proposed for this purpose in the literature over the last four decades, including the method of moments associated with a distribution, for example, Schultz-Flory, 5,6 Pearson-type I, 7 or log-normal 8 distribution; Monte Carlo simulation; [9][10][11] probability generating functions; 12 numerical fractionation; 13,14 orthogonal collocation technique; [15][16][17] and direct numerical integration method. [18][19][20][21][22][23] Besides providing the MWD directly (with no need of function inversion), direct numerical integration method also reduces the loss of information during the solution step. The use of this method for MWD of free-radical polymerization was first proposed by Chaimberg and Cohen in 1990, 19 together with the use of continuous variable approximation (CVA) and quasi-steady state assumption (QSSA) for the radicals.…”