Revisiting Chain Transfer to Polymer and Branching in Controlled Radical Polymerization of Butyl Acrylate

Acrylic monomers undergo chain transfer to polymer during polymerization leading to branched and even gelled polymers. It has been experimentally demonstrated that the extent of branching is higher for conventional free radical polymerization than for controlled radical polymerization (ATRP, RAFT, NMP) and this has been qualitatively explained in terms of the differences in the concentrations of highly reactive short‐chain radicals between controlled and conventional radical polymerizations. Contrary to this explanation, in this work, it is quantitatively demonstrated that the short transient lifetime of the radicals, i.e., the time between activation and deactivation of the radical in controlled radical polymerization, is the cause for the low level of branching in these polymerizations.

     

Predicting MWD and Branching Distribution of Terminally Branched Polymers Undergoing Random Scission

A new semi‐analytical approach to model simultaneous chain scission and branching is described that assumes the separation of the scission and the branching problem. The required properties of the linear segments or primary polymers forming the branched architectures are found by a kinetic model. The general rules for the construction of branched architectures from populations of linear segments then lead to an analytical expression for the branching distribution and a semi‐analytical expression for the bivariate length/branching distribution. The method is applied to the scission of an initially branched polymer and subsequent terminal branching on scission points and activated terminal double bonds. Exact agreement is found with Monte Carlo sampling results.

     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

Free‐Radical Polymerization with Long‐Chain Branching and Scission in a Continuous Stirred‐Tank Reactor

Free‐radical polymerization that involves the polymer transfer reactions leading to both long‐chain branching and scission, as in the cases of high‐pressure olefin polymerization, is considered. In CSTR, the residence time distribution is broad and the primary polymer chain, whose residence time is large, is subjected to polymer transfer reaction for a longer time, leading to a larger number of branching and scission points. The distributions of both branching and scission density are much broader in a CSTR than in a batch, or equivalently, a PFR. The radius of gyration for larger sized polymers formed in a CSTR tends to be much smaller than that for randomly branched polymers.

     

Monte Carlo Simulation of Controlled/Living Radical Polymerization in Emulsified Systems

A new MC simulation method is proposed for the controlled/living radical polymerization in a dispersed medium, assuming an ideal miniemulsion system. This tool is used to consider the effects of particle size on the polymerization rates and the molecular weight distributions. For NMP, the polymerization kinetics are basically governed by two conflicting factors, (i) the confined space effect that promotes the coupling reaction between a radical and a trapping agent and (ii) the isolation effect of radicals into different particles that suppresses the overall frequency of bimolecular termination. For RAFT polymerization, a significant rate enhancement by reducing the particle size could be observed only for the systems with fast fragmentation of adduct radicals.

     

Bimodal molecular weight distribution formed in the emulsion polymerization of ethylene

It is known that the molecular weight distribution (MWD) formed in an emulsion polymerization of ethylene can be bimodal. However, the origin of the bimodality has not been elucidated. In this article, a Monte Carlo simulation is conducted, mostly with parameters reported in the literature. The simulated MWDs are bimodal because of the limited volume effect; that is, the high molecular weight profiles are distorted by the small particle size, which is comparable to the size of the largest branched polymer molecule in a particle. The simulated MWDs agree reasonably well with the experimentally obtained MWDs. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3426–3433, 2002     

Molecular Weight Development during Simultaneous Chain Scission,Long‐Chain Branching and Crosslinking, 1

A general matrix formula is proposed for the weight‐average molecular weights of the polymer systems formed through simultaneous scission, branching and crosslinking of N types of chains, assuming the chain connection statistics are Markovian. For the polymerization systems in which chains are generated consecutively, such as for free‐radical polymerization, the present theory can be applied by increasing the number of chain types N to infinity, by considering the chains formed at different times as different types of chains. The gel point determination reduces to the eigenvalue problem and the present theory extends the classical gelation theory to non‐random, history‐dependent reaction systems. From the mathematical point of view, this theory is capable of describing complex molecular build‐up processes through end‐linking, T‐ and H‐shaped chain connections, irrespective of reaction/reactor types used.

Schematic representation of the 0^th generation segment and the connection to the 1^st generation segments.     

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

Full chain‐length distribution (CLD) modelling applying the Galerkin finite‐element method^[1] (FEM) to polymerization reactors featuring a certain degree of gel formation is confronted with extremely long computation times. The paper describes a new method to predict CLDs for systems where gel formation may occur. The new concept is to model a part of the CLD up to a cut‐off length L, while satisfying the full set of population balances. With transfer to polymer as the mechanism responsible for gelation, this gives rise to a closure problem, which has been solved by assuming the dead CLD beyond L to be represented by a part of a Flory distribution. The method could be proved to work by performing simulations and comparing cut‐off CLDs to full CLDs for non‐gelling systems and comparing results for different L for systems with gelation. The model is demonstrated for polymerization reactors, the batch reactor and the continuous stirred‐tank reactor (CSTR), with either disproportionation or recombination termination. Reliable results are obtained for systems with moderate gel formation. Comparing these results to those from moment models including balance equations up to the fourth moment, a number of interesting differences have been found.     

Predicting the Change of MWD Caused by Interchange Reactions During Melt‐Mixing of Linear and Branched Polycondensates (AB2)

During mix melting of hyperbranched AB₂‐ and linear CD‐polycondensates distributive properties are changing by interchange reactions. Two mathematical modeling approaches are presented: (i) Simplified approach of monodisperse population of three‐arm stars undergoing interchange reactions, both analytical and by Monte Carlo simulations, assuming interchange as subsequent scission and recombination of fragments. (ii) Full system of interchange and polycondensation/hydrolysis reactions with Monte Carlo simulations and kinetic model describing reactions of free groups (A, B, C, D) and bonds (AB, CD, BC, AD). MC simulations show that the final molecular weight and branching distribution is attained after 10% of reaction time. The change of structure, from few large fragments to more, smaller ones, is slower.

     

Reconstruction of the Chain Length Distribution for Vinyl‐Divinyl Copolymerization Using the Numerical Fractionation Technique

A proposed theory for evaluating the chain length distribution (CLD) using the numerical fractionation (NF) technique was extended to the vinyl‐divinyl (VDV) copolymerization. The CLD is reconstructed for this system, in which pendant double bond propagation leads to crosslinking and gel formation. The method was earlier developed for a non‐linear free‐radical polymerization scheme where chain transfer to polymer and termination by combination resulted in gel formation. The VDV study presented indicates that the proposed method of weighted summation (WS) accurately predicts the resulting CLDs evaluated using NF.

Comparison of the overall polymer NF and the direct solution CLDs near the gel point.     

Evaluation of the Chain Length Distribution in Free‐Radical Polymerization, 1. Bulk Polymerization

A method for the direct computation of the chain length distribution in a bulk polymerization is developed, based on the discretization procedure introduced by Kumar and Ramkrishna (Chem. Eng. Sci. 1996 , 51, 1311) in the context of particle size distribution. The overall distribution of chain lengths is partitioned into a finite number of classes which are supposed to be concentrated at some appropriate pivotal chain lengths. Several of the involved reactions lead to the formation of chain whose length differs from the pivotal values. Rules have been introduced in order to share chains between two contiguous classes, which have been designed so as to preserve two well‐defined properties of the distribution, such as, for example, two of its moments. The method has been applied to a polymerization system including propagation, bimolecular terminations and two different chain branching mechanisms: chain transfer to polymer and crosslinking. In addition, complex systems such as one with chain length‐dependent kinetic constants or a two‐dimensional distribution of chain length and number of branches have been considered.     

Simulation of Molecular Weight Distributions Obtained by Pulsed Laser Polymerization (PLP): New Analytical Expressions Including Intramolecular Chain Transfer to the Polymer

A new approach for the simulation of PLP (pulsed laser polymerization) is presented. This approach allows one to obtain new analytical solutions for different polymerization schemes, including either chain transfer to the monomer or intramolecular chain transfer to the polymer. The first results of the simulation of PLP experiments on n‐butyl acrylate at 20 °C and ambient pressure are presented.

MWDs simulated for PLP of n‐butyl acrylate, in bulk at 20 °C and ambient pressure using three models: the model with intramolecular chain transfer to the polymer (solid line), the model with chain transfer to monomer (dashed line), and the classical model (dotted line).     

Pulsed Laser Polymerization at Low Conversions: Broadening and Chain Transfer Effects

Pulsed laser polymerization (PLP) is widely employed to measure propagation rate coefficients k_p in free radical polymerization. Various properties of PLP have been established in previous works, mainly using numerical methods. The objective of this paper is to obtain analytical results. We obtain the most general analytical solution for the dead chain molecular weight distribution (MWD) under low conversion conditions which has been hitherto obtained. Simultaneous disproportionation and combination termination processes are treated. The hallmarks of PLP are the dead MWD discontinuities located at integer multiples of n₀ = k_pt₀C_M, where t₀ is the laser period and C_M is the monomer concentration. We show that chain transfer reduces their amplitude by factors , consistent with numerical results obtained by other workers. Here c_tr is the chain transfer coefficient and Ln₀ (L = integer) are the discontinuity locations. Additionally, transfer generates a small amplitude continuous contribution to the MWD. These results generalize earlier analytical results which were obtained for the case of disproportionation only. We also considered two classes of broadening: (i) Poisson broadening of growing living chains and (ii) intrinsic broadening by the MWD measuring equipment (typically gel permeation chromatography, GPC). Broadening smoothes the MWD discontinuities. Under typical PLP experimental conditions, the associated inflection points are very close to the discontinuities of the unbroadened MWD. Previous numerical works have indicated that the optimal procedure is to use the inflection point to infer k_p. We prove that this is a correct procedure provided the GPC resolution σ is better than nequation/tex2gif-stack-1.gif. Otherwise this underestimates Ln₀ by an amount of order σ²/n₀.

Schematic of a chain transfer reaction with monomer as the transfer agent.     

Chain Transfer and Efficiency of End‐Group Introduction in Free Radical Polymerization of Methyl Methacrylate in the Presence of Poly(methyl methacrylate) Macromonomer

Summary: Experimental and modeling studies of addition–fragmentation chain transfer (AFCT) during radical polymerization of methyl methacrylate in the presence of poly(methyl methacrylate) macromonomer with 2‐carbomethoxy‐2‐propenyl ω‐ends (PMMA‐CO₂Me) at 60 °C are reported. The results revealed that AFCT involving PMMA‐CO₂Me formed in situ during methyl methacrylate polymerization has a negligible effect on the molecular weight distribution.

     

Change and Convergence of Polymer Distribution During Nonrandom Degradation

The CLD development during nonrandom degradation is investigated, assuming the rate of bond scission depends on the chain length and the position of the bond within the chain. As the degradation proceeds, the polydispersity index usually approaches a fixed value pertinent to the degradation mechanism, independent of the initial distribution. The exact limiting values are presented for several cases. These values may be useful to estimate the degradation mechanisms. For example, if the limiting PDI is smaller than 2, the bonds in larger chains may be easier to break than shorter ones, and if it is smaller than 4/3, the size effect is not enough and the breakage may tend to occur in the middle of the chain.

     

Chain Length Distributions of Polyolefins Made with Coordination Catalysts at Very Short Polymerization Times – Analytical Solution and Monte Carlo Simulation

We developed an analytical solution to describe how the CLD of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerization times before the CLD becomes completely developed. We compared the analytical solution with a dynamic Monte Carlo model for validation, obtaining excellent agreement. Our analytical solution can be used to determine when the steady‐state hypothesis, commonly used in polymerization models, becomes valid as a function of polymer chain length. We also extended our model to describe polymerization with multiple‐site‐type catalysts. Depending on the polymerization kinetic parameters of the different site types on the catalyst, the fully developed CLD is reached through very different intermediate CLDs. This modeling approach, although rather simplified, can be used to interpret results from short polymerization time experiments such as the ones done in stopped‐flow reactors.

     

Ethylene Polymerization over Supported Titanium-Magnesium Catalysts: Heterogeneity of Active Centers and Effect of Catalyst Composition on the Molecular Mass Distribution of Polymer

New experimental approach was used for analysis of molecular weight distribution (MWD) of polymers produced over titanium-magnesium catalysts (TMC). Polymers were fractionated on to fractions with narrow MWD (polydispersity (PD) values Mw/Mn ≤ 2). Then some of these fractions were combined to get the minimal quantity of fractions with PD values close to 2 (Flory components). It was found that three fractions corresponding to three groups of active centers are sufficient for proper fitting experimental MWD curve for PE obtained over TMC with different Ti content and with different hydrogen concentration in polymerization.     

Xanthates as Chain‐Transfer Agents in Controlled Radical Polymerization (MADIX): Structural Effect of the O‐Alkyl Group

The capability of three chain‐transfer agents, O‐alkyl‐S‐(1‐ethoxycarbonyl)ethyl xanthates (CH₃CHCO₂C₂H₅)S(CS)OZ′, to control the free‐radical polymerization of styrene and ethyl acrylate by the MADIX process was examined. The reactivity of the xanthates varied according to the following trend: Z′  CH₂CH₃ < CH₂CF₃ < CH[P(O)(OEt)₂]CF₃. This change in reactivity allowed a lowering of the polydispersity index from 2.0 for Z′  CH₂CH₃ to 1.15 for Z′  CH[P(O)(OEt)₂]CF₃ in the case of the polymerization of styrene.

Evolution of M _w/M _n with conversion during the polymerization of ethyl acrylate in the presence of xanthates X₁ , X₂ and X₃ . Reaction conditions: [EA]₀ = 4.6 M , [X]₀ = 5.75 × 10⁻² M , [AIBN]₀ = 1.72 × 10⁻³ M ; T = 80 °C ; solvent: toluene.