(495e) Advanced Kinetic Monte Carlo Optimization of the Synthesis of Well-Defined (co)Polymers Via Atom Transfer Radical and Nitroxide Mediated Polymerization

In the last two decades, the kinetic Monte Carlo (kMC) technique has emerged as a powerful tool for the simulation and
optimization of polymerization processes.^1-5 Benefiting from its natural
sampling of reaction events, the polymeric microstructure can be simulated in
molecular detail. Not only the chain length of the different macrospecies can
be predicted but other important characteristics such as their topology,
overall comonomer content and incorporated functionalities can be described too.
Moreover, the recent evolution of advanced computer technologies has further
increased the potential of the kMC technique by opening up the possibility to
track the evolution of the complete polymeric microstructure during the
polymerization.

Based on the work of Szymanski⁵ on
living polymerization and the work of Wang and Broadbelt^3,4 on
nitroxide mediated polymerization (NMP), we have developed a general kMC methodology
allowing to track the history of sampled reaction events for a representative
group of macromolecules. For example, tracking kMC propagation events yields
the monomer sequences of every macromolecule in this group throughout the
polymerization process.^6,7 Such detailed information enables the
calculation of new molecular properties e.g. macromolecular deviations
from ideal targeted monomer sequences. In particular, for copolymers gradient
(<GD>) and block deviation (<BD>) criteria were introduced to
characterize, respectively, their linear gradient en diblock quality using atom
transfer radical polymerization (ATRP) as polymerization technique. The main
merit of the kMC methodology is its objective evaluation of the structural
properties of synthesized microstructures, paving the way to unambiguously rank
different copolymer products according to their quality. The latter is a challenging
task in view of experimental difficulties encountered in the characterization
of the polymeric microstructure in molecular detail.⁸

Scheme 1:  Main reactions in (a) atom
transfer radical polymerization (ATRP) (b) nitroxide mediated polymerization
(NMP); R₀X (i=0): ATRP/NMP initiator (halogenide/alkoxyamine); i:
chain length; M_tL_yX: ATRP catalyst in low oxidation state
(activator); M_t: transition metal; L: ligand; X: halogen
atom/nitroxide: end-group functionality (EGF); P: dead polymer; R_iX
(i>0): dormant polymer molecule; ideally no P formed and all dormant polymer
molecules possess equal chain length.

The main reactions occurring in ATRP and NMP,
two important controlled radical polymerization (CRP) techniques, are depicted
in Scheme 1. Initiator radicals (R₀; i=0) are
generated from ATRP/NMP initiator molecules (R₀X). In ATRP,
this activation requires the presence of an ATRP catalyst (M_tL_yX;
activator) as mediating agent whereas in NMP a sufficiently high polymerization
temperature is used to create the mediating nitroxide (X) by cleavage of the
labile C-ON bond of an alkoxyamine initiator. The formed R₀
species ideally take up only a few monomer units before they are temporarily
deactivated to a dormant form (R_iX) thereby introducing end-group
functionality (EGF; X) in the polymeric species. For high deactivation rates, a
low radical concentration is established ensuring a high livingness, i.e.
the formation of dead polymer molecules with concomitant loss of EGF is reduced.
Also, for fast ATRP/NMP initiation, dormant species with almost uniform chain
length can be obtained at sufficiently high conversion, i.e. tailored
polymer molecules both with respect to livingness and chain length result for
CRPs after careful selection of the polymerization conditions and mediating
agent.

Figure 1 illustrates the added value
of the <GD> calculation in CRP processes. For the batch ATRP of methyl
methacrylate (MMA) and n-butyl acrylate (nBuA), of MMA and
styrene (STY) and of STY and nBuA, it has been shown that the <GD> at
complete monomer consumption correlates with the dispersity (also known as
polydispersity index).⁹ For the three copolymerizations studied, the
<GD>decreases for decreasing dispersity indicating that a good control
over chain length is needed for optimal gradient polymer synthesis. The highest
linear gradient quality is obtained for MMA/nBuA, as can be expected based on
the inherent preference of the secondary ?nBuA radicals? to propagate with MMA
with formation of tertiary ?MMA radicals?. Additionally, a fed-batch approach
allows to improve the linear gradient quality in agreement with earlier
deterministic simulations¹⁰ at the expense of polymerization rate. Hence,
the optimal addition profile can be predicted by means of kMC simulations,
taking into account practical limitations.

Figure 1: Correlation between linear
gradient quality (expressed via <GD>) and dispersity at complete monomer
consumption for the batch ATRP of different comonomer pairs A/B; common
polymerization conditions: [A+B]₀:[R₀X]₀:[C]₀
= 100:1:1 with C the ATRP catalyst (only low oxidation state); [A]₀=[B]₀;
perfect linear gradient for <GD> of 0; homopolymer: maximal <GD> of
1.¹⁰

In the present contribution it will be shown
that the kMC methodology can also be used to identify ATRP/NMP conditions that allow
to achieve a maximal control over chain length and EGF for the synthesis of
well-defined poly(STY-b-acrylate) block copolymers taking into account
constraints with respect to the maximal overall polymerization time and desired
number average chain length (50-1000). For the copolymerization, a distinction
is made between ?one-pot? and ?two-pot? approaches. In the ?two-pot? approach, the
first block is, after purification, used as macro-initiator for the synthesis
of the second block. In the ?one-pot? approach, the second monomer is added at
high conversion of the first monomer and no extra purification step is
performed. Hence, once the second monomer is added, both monomers can be
incorporated in the macrospecies resulting in a block-like copolymer. To
evaluate the effect of diffusional limitations on reaction steps with a high
intrinsic reactivity, the concept of apparent rate coefficients¹¹ is
applied.

For the ATRP process, focus is on the use of
low catalyst amounts starting from the oxygen-stable deactivator in the
presence of conventional radical initiator. It has been  shown that a lower
<BD> can be obtained with a ?two-pot? approach under otherwise similar
conditions and that an optimal polymerization temperature exists for each
block.⁶ For the NMP process, commercially available alkoxyamine
initiators are considered. Arrhenius parameters for nitroxide related reaction
steps are determined from an extensive set of experimental data for NMP of both
the first (poly(STY)) and the second block (poly(nBuA)). In the kMC model, a
detailed reaction scheme including thermal¹² self-initiation of styrene
and backbiting of acrylate^14-16 radicals is implemented to maximize
the application field of the developed kMC model. It is illustrated that the
alkoxyamine MAMA-SG1 (also known as Blockbuilder^TM) allows the production
of well-tailored poly(STY-b-nBuA) block copolymers in case an
appropriate temperature profile is applied for both the ?one-pot? and ?two-pot?
approach.