Molecular-Weight-Distribution Modelling of Radical Polymerization in Batch and Continuous Reactors with Transfer to Polymer Leading to Gel Formation

2005

Polymer

A theoretical analysis is presented on the use of semibatch reactors for producing non-linear copolymers through the homogeneous freeradical polymerization of mono-and divinyl-monomers. The kinetic scheme distinguishes two kinds of pendant double bonds and five kinds of polymer radicals, as it also takes into account the primary cyclization of terminal divinyl units. In spite of the fairly large number of groups and reactions, the generating function of vector chain length distribution of polymer species can still be accurately computed by a numerical implementation of the method of characteristics and thus average molecular weights before and after gelation can be reliably obtained. The influence of feed policies of the monomers, initiator and transfer agent on gelation, average chain lengths and weight fraction of sol is discussed, as well as their sensitivity to some kinetic parameters.

Section: Modeling Of Non-linear Free-radical Polymerization: a Summarmentioning

confidence: 99%

Semibatch operation and primary cyclization effects in homogeneous free-radical crosslinking copolymerizations

2005

Polymer

“…This is a completely different (and much simpler) system and a comparison with this work is not relevant. Other methods were applied for the simulation of long-chain branching or vinyl/divinyl copolymerization in continuous free radical polymerizations: Monte Carlo simulation, [25] but retaining the steady state, ''numerical fractionation'' technique [23,47] without transient behavior analysis and Galerkin finite-element method [26] but without quantifying the amount of gel. This has been more recently taken into account by excluding from sol the polymer molecules with some high enough degree of polymerization.…”

Section: When a New Methods For Simulation Is Presented The Natural Qumentioning

confidence: 99%

“…Such is the case of simulations of free radical polymerizations using ''numerical fractionation'', [22,23] Mote Carlo method, [24,25] and Galerkin finite-elements method. [26,27] The problems to be faced in the modeling of this kind of systems become much tougher if gel is present and if the transient behavior of the reactor is to be described. Therefore some further limitations in the application of these modeling techniques can also be identified: L1) Analysis restricted to the steady state operation of the reactor L2) Analysis restricted to the pre-gel region.…”

Section: Introductionmentioning

confidence: 99%

Transient Behavior and Gelation of Free Radical Polymerizations in Continuous Stirred Tank Reactors

Macro Theory & Simulations

2005

Summary: Using the authors' previously developed method for the general kinetic analysis of non‐linear irreversible polymerizations, the simulation of free radical homogeneous polymerization systems with terminal branching and chain transfer to polymer has been carried out for continuous stirred tank reactors. Its improved accuracy on the numerical evaluation of generating functions has been exploited in order to perform their numerical inversion and chain length distributions could also be estimated with or without the presence of gel. A comparison with alternative techniques emphasizing the effect of their simplifying assumptions on the accuracy of calculations is also presented.Predicted CLD before gelation (t = 1 h), after gelation (t = 15 h, steady state), and close to gel point for a free radical polymerization with transfer to polymer in a CSTR with τ = 60 min.magnified imagePredicted CLD before gelation (t = 1 h), after gelation (t = 15 h, steady state), and close to gel point for a free radical polymerization with transfer to polymer in a CSTR with τ = 60 min.

“…Recent simulations of non-linear free radical polymerisations using Galerkin finite-elements method (Iedema and Hoefsloot, 2002) have once again neglected the presence of multiple radical centres together with some simplifications in the kinetic schemes. In addition, the properties of the gel cannot be obtained by this method.…”

Section: Modelling Of Free Radical Polymerisation With Transfer To Pomentioning

confidence: 99%

An improved general kinetic analysis of non-linear irreversible polymerisations

Chemical Engineering Science

2005

A method to predict average molecular weights before and after gelation for general irreversible non-linear polymerisations forming tree-like molecules is described. Recently developed numerical methods for solving two point boundary value problems are essential for the success of these calculations after gelation and open the way to eventually be able to efficiently predicting chain length distributions. Anionic and free-radical polymerisation of vinyl monomers in the presence of divinyl monomers or with transfer to polymer are taken as case studies. Comparison to experimental data and with simulation results obtained through "numerical fractionation" confirms the usefulness of current approach.