(432d) Modeling of Atom-Transfer Radical Polymerization of Butyl Acrylate Using a Novel Tool for Multiple-Parameter Variation

Modeling of Atom-Transfer Radical Polymerization of Butyl Acrylate Using a Novel Tool for Multiple-Parameter Variation

Hendrik Schroeder, Johannes Buback, Jens Schrooten, Michael Buback,* Krzysztof Matyjaszewski

Abstract

Atom-transfer radical polymerization (ATRP) of butyl acrylate (BA) is modeled for pressures up to 5000 bar. Kinetics of acrylate polymerization is particularly challenging due to intramolecular chain transfer and termination via Cu-organometallic intermediates. These side reactions have been quantitatively studied at ambient pressure. Absolute rate coefficients are, however, not available for higher pressures. We have checked for the effect of backbiting and Cu-catalyzed radical termination (CRT) on polymerization kinetics within the extended pressure range by means of PREDICI^® simulations and stepwise adjustment of the associated rate coefficients. We present novel software that may be used for systematic variation of rate coefficients and initial concentrations in order to simulate experimental data. Each set of parameters is automatically processed by PREDICI^®. In conjunction with the well-established PREDICI^® program, the software enormously improves the efficiency of multiple-parameter variation in modeling of chemical processes and engineering.

With respect to experimental monomer and catalyst concentration-vs.-time traces for ATRP, PREDICI^® simulations indicate a significant preference for intramolecular chain transfer, the so-called backbiting reaction, towards higher pressure. Such insight into chain transfer reactions is also relevant for conventional radical polymerization.

Reversible-deactivation radical polymerization (RDRP) methods such as ATRP allow for the synthesis of polymeric materials with precisely tailored topology, architecture, chain length, functionality and narrow molar-mass distribution.^[1] Termination in ATRP is largely reduced by reversible activation and deactivation of radicals mediated by a metal catalyst. Polymerization rate and dispersity depend on the size of the equilibrium constant, K_ATRP, defined as the ratio of the activation rate coefficient, k_act, and the deactivation rate coefficient, k_deact. The latter coefficient describes the rate of formation of the “dormant” alkyl halide, R–X. Cu-mediated ATRP has been most extensively studied. Absolute K_ATRP as well as the individual rate coefficients k_act and k_deact have been determined for various Cu/ligand and initiator systems from both monomer-free model systems as well as from styrene and methyl methacrylate (MMA) ATRP.^[2−6] Applying pressure primarily aims at detailed mechanistic insight into the kinetics of ATRP. Pressurization resulted in significant rate enhancement due to the increase in both the propagation rate coefficient, k_p, and in K_ATRP.

The decrease in termination rate due to diffusion control further contributes to the pressure-induced acceleration of polymerization and also allows for ATRP at very low levels of Cu catalyst as has been shown for BA polymerization.^[7] The rate enhancement towards higher pressure was, however, much less pronounced as compared to expectations based on the reported studies into the Cu catalyst. The associated reaction volume of K_ATRP essentially depends on the type of ligand but is almost independent of the type of radical or initiator fragment. Thus it appeared reasonable to check for additional effects on polymerization rate other than those induced by the ATRP catalyst. Intramolecular chain transfer during acrylate polymerization has been of major interest in conventional radical polymerization. In particular, the 1,5‑hydrogen shift (backbiting) reaction transforms highly reactive secondary propagating radicals into weakly reactive mid-chain radicals. The ratio of secondary and mid-chain radicals has been directly monitored via electron paramagnetic resonance (EPR) spectroscopy at ambient pressure^[8] which allowed for estimation of the associated rate coefficients for backbiting, k_bb, and propagation of mid-chain (tertiary) radicals, k_p^t. Such EPR measurements have, however, not been carried out towards higher pressure so far. Via near-infrared (NIR) spectroscopic measurements, which are applicable towards monitoring monomer conversion in a wide pressure and temperature range, it is not possible to monitor or distinguish between secondary and mid-chain radicals. The corresponding concentrations which affect experimental monomer and catalyst concentration-vs.-time traces in high-pressure ATRP of BA may, however, be estimated via PREDICI^® simulations. These simulations include the known pressure dependence of the ATRP-related rate coefficients. It was checked whether intramolecular chain transfer might be responsible for lowering the expected rate enhancement during high-pressure ATRP. Polymerization rate is associated with the absolute concentration of reactive secondary radicals, since propagation of mid-chain radicals is slower by about three orders of magnitude as known from conventional radical polymerization. The effect of different k_bb-to-k_p^s ratios on polymerization rate in the entire pressure range between 1 and 5000 bar was systematically examined.

The simulations in conjunction with NIR spectroscopic measurements of BA polymerization indicate a preference for backbiting at high pressure, i.e. the associated negative activation volume, Δ^‡V°(k_bb), is higher in absolute value than absolute Δ^‡V°(k_p^s). The essential effect of higher pressure appears to be that a larger proportion of growing radicals are rapidly transformed into mid-chain radials at the expense of highly reactive secondary radicals. Pulsed-laser polymerization in conjunction with size-exclusion chromatography (PLP–SEC) has emerged as an effective method to determine backbiting rate coefficients.^[9] Preliminary investigations into PLP of butyl acrylate at 2000 bar indicated an increased k_bb-to-k_p^s ratio compared to the reported ambient pressure value. Such insight is also of interest for conventional radical polymerization, as the deduced rate coefficients apply irrespective of the polymerization technique.

Our PREDICI^® model also includes Cu-catalyzed radical termination which has recently been discovered and quantified for Cu-mediated ATRP of acrylates.^[10] The proposed mechanism involves the formation of a highly active organometallic Cu^II intermediate which reacts with poly(BA) radicals to form dead polymer chains. Experimental results indicate no significant preference for CRT under high pressure as deduced from the Cu^II concentration-vs.-time traces monitored via online NIR spectroscopy.^[7] It is a specific feature of ATRP that each termination event results in accumulation of Cu^II and, due to K_ATRP being constant, is accompanied by a decrease in radical concentration and thus in propagation rate. The influence of CRT may thus easily be deconvoluted from online NIR spectroscopy of Cu^II. Due to the complexity of the kinetics during acrylate polymerization, it may not be ruled out that additional effects such as different types of chain-transfer reactions contribute to the observed pressure dependence. However, modeling in conjunction with experimental results suggests that chain transfer via backbiting induces the major pressure effect. Thus, detailed studies by means of PLP–SEC appear particularly rewarding.

The rate coefficients which have been used for PREDICI^® simulation are mostly known from independent experiments. Coefficients such as k_bb,^[8,9]k_p^t,^[8,9] and k_CRT^[10]  were estimated for high-pressure conditions based on reported ambient-pressure values. These coefficients were systematically varied within a pre-defined range which resulted in a multi-dimensional parameter set of polymerization models to be simulated with PREDICI^®. In order to reduce the enormous workload of manually processing each PREDICI^® simulation, the novel software was developed which allows for simulation with extended parameter variation. In general, this tool allows for processing of PREDICI^® models with automatic variation of the input parameters. For example, variation of k_bb, k_p^t, and k_CRTwith ten systematically chosen values each results in a total of 10 × 10 × 10 = 1000 simulations. Additionally, refinement of further coefficients and parameters may be considered, since the accessible number of scans and parameter dimensions, in principle, is unlimited. The software may also be used for overall analysis of a multiple set of polymerization models including mathematical operations and generation of data plots. The demonstrated software is of general applicability within the entire field of modeling chemical processes.

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