Quantum Chemical Investigation of Secondary Reactions in Poly(vinyl chloride) Free‐Radical Polymerization

Free‐radical polymerization of vinyl chloride is investigated computationally with special attention to the secondary reactions involving mid‐chain radicals (MCRs). Namely, the rate constants of backbiting, chain scission, chain transfer, and propagation reactions are evaluated using a density functional theory method. The rate coefficients of such reactions are estimated taking into account the position of the radical along the chain as well as its distance from the chain‐end. In particular 1:5, 5:1, and 5:9 backbiting are the most relevant secondary reactions, followed by the slower propagation of MCRs. Finally, a kinetic model of suspension polymerization including the investigated reactions is developed, in order to determine their impact on the quality of the final polymer.

     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.     

Ab Initio Calculation of the Propagation Kinetics in Free Radical Polymerization: Chain Length and Penultimate Effects

Summary: In this work, Quantum Chemistry is applied to investigate the propagation kinetics in free radical polymerization. Energies, structures and transition state geometries are determined using density functional theory, which combines good accuracy with reasonable computational demand. In particular, B3LYP functional is used to evaluate the exchange and correlation energy with the 6-311+G(d,p) basis sets. The capabilities of the approach with respect to the prediction of the kinetic constants of elementary processes relevant to polymeric systems (propagation reactions) is first tested using literature experimental data as reference values. 1 Namely, two different monomers of industrial relevance have been selected, acrylonitrile and styrene. For such systems, the effect of chain-length on the propagation rate coefficient is examined. Finally, for the selected monomer pair, the relative reactivity (so-called reactivity ratios) is also analyzed, in particular considering the penultimate effect.     

Thioketone‐Mediated Polymerization of Butyl Acrylate: Controlling Free‐Radical Polymerization via a Dormant Radical Species

It is demonstrated by experiment and simulation that the commercially available thioketone 4,4‐bis(dimethylamino)thiobenzophenone is capable of controlling AIBN‐initiated bulk butyl acrylate polymerization at 80 °C. On the basis of molecular weight data and from monomer conversion versus time curves, the associated rate parameters are estimated. The addition rate coefficient, k_ad, for the reaction of a propagating chain with the thioketone is close to 10⁶ L · mol⁻¹ · s⁻¹ and the fragmentation rate coefficient, k_frag, is around 10⁻² s⁻¹ giving rise to large equilibrium constants in the order of 10⁸ L · mol⁻¹. Furthermore, cross‐ and self‐termination of the dormant radical species are identified to be operational.

     

A Comprehensive Kinetic Model of Free‐Radical‐Mediated Interfacial Polymerization

A mathematical model describing interfacial radical polymerization‐based film formation on hydrogels is elucidated. A glucose oxidase‐mediated multistage initiation reaction is used to accomplish interfacial film formation. A polymer concentration‐dependent diffusion coefficient is used to reflect the changing mass transport conditions as the film develops. Model predictions of the film thickness as a function of the species concentrations agree well with experiments. The model predicts that the degree of initiation reaction delocalization with the enzyme‐mediated initiation system is significantly higher than an enzyme‐independent system, thus affecting the film growth rate and structure. The mass transport properties of the film and its adhesion to the underlying substrate are also investigated.

     

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.     

Termination in Dilute‐Solution Free‐Radical Polymerization: A Composite Model

Literature data are summarized for the chain‐length‐dependence of the termination rate coefficient in dilute solution free‐radical polymerizations. In essence such experiments have yielded two parameter values: the rate coefficient for termination between monomeric free radicals, kequation/tex2gif-stack-1.gif, and a power‐law exponent e quantifying how k_t values decrease with increasing chain length. All indications are that the value e ≈ 0.16 in good solvent is accurate, however the values of kequation/tex2gif-stack-2.gif which have been deduced are considerably lower than well‐established values for small molecule radicals. This seeming impasse is resolved by putting forward a ‘composite’ model of termination: it is proposed that the value e ≈ 0.16 holds only for long chains, with e being higher for small chains – the value 0.5 is used in this paper, although it is not held to dogmatically. It is then investigated whether this model is consistent with experimental data. This is a non‐trivial task, because although the experiments themselves and the ways in which they are analyzed are elegant and not too complicated, the underlying theory is sophisticated, as is outlined. Simulations of steady‐state polymerization experiments are first of all carried out, and it is shown that the composite model of termination both recovers the e values which have been found and beautifully explains why these experiments considerably underestimate the true value of kequation/tex2gif-stack-3.gif. Simulations of pulsed‐laser polymerizations find the same, although not quite so strikingly. It is therefore concluded that our new termination model, which retains the virtue of simplicity and in which all parameter values are physically reasonable, is consistent with experimental data. Taking a wider view, it seems likely that the situation of the exponent e varying with chain length will not just be the case in dilute solution, but will be the norm for all conditions, which would give our model and our work a general relevance.

Normalized chain length distributions from PLP simulations.     

Free‐Radical Propagation Rate Coefficients via n‐Pulse Periodic Polymerization

Aspects of applying n‐pulse periodic initiation in pulsed laser polymerization/size‐exclusion chromatography (PLP/SEC) experiments are studied via simulation of molecular weight distributions (MWDs). In n‐pulse periodic PLP/SEC, sequences of n laser pulses at successive time intervals Δt₁ up to Δt_n are periodically applied. With the dark time intervals being suitably chosen, n‐modal MWDs with n well separated peaks occur. The n‐pulse periodic PLP/SEC method has the potential for providing accurate propagation rate coefficients, k_p. Among several measures for k_p, the differences in molecular weights at the MWD peak positions yield the best estimate of k_p under conditions of medium and high pulse laser‐induced free‐radical concentration. Deducing k_p from n dark time intervals (corresponding to n regions of free‐radical chain length) within one experiment at otherwise identical PLP/SEC conditions allows addressing in more detail a potential chain‐length dependence of k_p. Simulations are compared with experimental data for 2‐pulse periodic polymerization of methyl methacrylate.

Measured MWD (solid line) and associated first derivative curve (dotted line) for a 2‐pulse periodic bulk polymerization experiment of MMA at 20 °C.     

Kinetics and Molecular Weight Development of Dithiolactone‐Mediated Radical Polymerization of Styrene

Calculations of polymerization kinetics and molecular weight development in the dithiolactone‐mediated polymerization of styrene at 60 °C, using 2,2′‐azobisisobutyronitrile (AIBN) as initiator and γ‐phenyl‐γ‐butirodithiolactone (DTL1) as controller, are presented. The calculations were based on a polymerization mechanism based on the persistent radical effect, considering reverse addition only, implemented in the PREDICI® commercial software. Kinetic rate constants for the reverse addition step were estimated. The equilibrium constant (K = k_add/k_‐add) fell into the range of 10⁵–10⁶ L · mol^?1. Fairly good agreement between model calculations and experimental data was obtained.

     

Free‐Radical Termination Kinetics Studied Using a Novel SP‐PLP‐ESR Technique

Summary: A novel method for measuring termination rate coefficients, k_t, in free‐radical polymerization is presented. A single laser pulse is used to instantaneously produce photoinitiator‐derived radicals. During subsequent polymerization, radical concentration is monitored by time‐resolved electron spin resonance (ESR) spectroscopy. The size of the free radicals, which exhibits a narrow distribution increases linearly with time t, which allows the chain‐length dependence of k_t to be deduced. The method will be illustrated using dodecyl methacrylate polymerization as an example.

Two straight lines provide a very satisfactory representation of the chain‐length dependence of k_t over the entire chain‐length region (c_R = radical concentration).     

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

A novel technique is developed to predict the evolving topology of a diacrylate polymer network under photocuring conditions, covering the low‐viscous initial state to full transition into polymer gel. The model is based on a new graph theoretical concept being introduced in the framework of population balance equations (PBEs) for monomer states (mPBEs). A trivariate degree distribution that describes the topology of the network locally is obtained from the mPBE, which serves as an input for a directional random graph model. Thus, access is granted to global properties of the acrylate network which include molecular size distribution, distributions of molecules with a specific number of crosslinks/radicals, gelation time/conversion, and gel/sol weight fraction. Furthermore, an analytic criterion for gelation is derived. This criterion connects weight fractions of converted monomers and the transition into the gel regime. Valid results in both sol and gel regimes are obtained by the new model, which is confirmed by a comparison with a “classical” macromolecular PBE model. The model predicts full transition of polymer into gel at very low vinyl conversion (<2%). Typically, this low‐conversion network is very sparse, as becomes apparent from the predicted crosslink distribution.     

A Density Functional Theory Study of Secondary Reactions in n‐Butyl Acrylate Free Radical Polymerization

In this work, secondary reactions involved in the free radical polymerization of butyl acrylate are investigated using quantum chemistry. First, various backbiting reactions are studied by adopting a simplified molecular model suitable for treating long polymer chains. The predicted reaction kinetics suggest the possibility of a radical migration along the poly(butyl acrylate) (PBA) chain as a consequence of subsequent j:j + 4 hydrogen abstractions, which are characterized by a low activation energy. Moreover, branching propagation and β‐scission reactions originating from mid‐chain radicals are investigated using a complete PBA model composed of five monomer units. The reaction kinetics involving short‐branch radicals are also examined, and a novel backbiting step leading to the formation of short branches is proposed.

     

Modeling of Nitroxide‐Mediated Semibatch Radical Polymerization

A mechanistic model is developed for high‐temperature (138 °C) styrene semibatch thermally and conventionally initiated FRP, as well as NMP with a two‐component initiating system (tert‐butyl peroxyacetate, 4‐hydroxy‐TEMPO). The model, using kinetic coefficients from literature, provides a good representation of the FRP experimental results. Implementation of a gel effect correlation to represent the change in the diffusion‐controlled termination rate coefficient with conversion improves the fit to the thermally initiated system, but is not required to represent the production of low molecular weight material ( Dalton) by conventionally initiated FRP or NMP. The low initiator efficiency found in NMP is well explained by a reaction network involving combination of free nitroxide with methyl radicals formed from initiator decomposition.

     

Nitroxide‐Mediated Radical Polymerization in Miniemulsion at Stationary State: Rationale for Independence of Polymerization Rate on Nitroxide Partitioning Using Oil‐Phase Initiation

Summary: Simulations based on the kinetics and mechanism of nitroxide‐mediated free radical polymerization (NMP) have been carried out in order to understand the hitherto largely unexplained effects (or lack thereof) of nitroxide partitioning in aqueous miniemulsion NMP. The focus has been on the miniemulsion NMP of styrene mediated by TEMPO and 4‐hydroxy‐TEMPO, two nitroxides with very similar activation‐deactivation equilibria, but very different organic phase‐aqueous phase partition coefficients. The general conclusion is that the organic phase propagating radical and nitroxide concentrations are unaffected by the partition coefficient in the stationary state, but the rate of polymerization and the extent of bimolecular termination increase with increasing nitroxide water solubility in the pre‐stationary state region. Specific NMP systems are, therefore, affected differently by nitroxide partitioning depending on whether polymerization predominantly occurs in the stationary state or not, which in turn is governed mainly by the activation‐deactivation equilibrium constant and the rate of thermal initiation.

Simulated organic‐phase propagating radical concentrations in the presence of thermal initiation for TEMPO‐mediated miniemulsion free radical polymerization of styrene for different nitroxide partitioning coefficients at 125 °C.     

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.

     

Atom Transfer Radical Polymerization in the Solid‐State

Poly(2‐vinylnaphthalene) was synthesized in the solid‐state by ball milling a mixture of the corresponding monomer, a Cu‐based catalyst, and an activated haloalkane as the polymerization initiator. Various reaction conditions, including milling time, milling frequency and added reductant to accelerate the polymerization were optimized. Monomer conversion and the evolution of polymer molecular weight were monitored over time using ¹H NMR spectroscopy and size exclusion chromatography, respectively, and linear correlations were observed. While the polymer molecular weight was effectively tuned by changing the initial monomer‐to‐initiator ratio, the experimentally measured values were found to be lower than their theoretical values. The difference was attributed to premature mechanical decomposition and modeled to accurately account for the decrement. Random copolymers of two monomers with orthogonal solubilities, sodium styrene sulfonate and 2‐vinylnaphthalene, were also synthesized in the solid‐state. Inspection of the data revealed that the solid‐state polymerization reaction was controlled, followed a mechanism similar to that described for solution‐state atom transfer radical polymerizations, and may be used to prepare polymers that are inaccessible via solution‐state methods.     

Atom‐Transfer Radical Batch and Semibatch Polymerization of Styrene

Batch and semibatch styrene polymerizations are carried out using a heterogeneous ATRP catalyst system that provides excellent molecular‐weight control. The observed initiator efficiency is lower for semibatch operation due to the high initiator concentrations required to make a low‐MW polymer. Experiments verified that the insoluble metal complex does not participate in the polymerization and that Cu(I) solubility is an order of magnitude higher than that of Cu(II). A mechanistic model, using kinetic coefficients from literature and the solubility data from this study, provides a good representation of the experimental results.