Diagnostic Checks and Measures of Information in the Bayesian Design of Experiments with Complex Polymerizations

Summary: A case study is presented from the bimolecular nitroxide-mediated radical polymerization of styrene. A Bayesian approach is implemented in order to design two optimal sequences of 2-trials each, and compared with a standard fractional factorial design. The improved effectiveness of the Bayesian design is demonstrated through a discussion of diagnostic criteria (on the quality of prior knowledge and the significance of estimated effects) and enhanced information content measures.     

NMP与ROP相结合制备PCL-b-PSt共聚物及其性能研究

以4-羟基-2,2,6,6-四甲基哌啶氮氧自由基（HTEMPO）为引发剂,通过ε-己内酯（ε-CL）的开环聚合,合成末端基为氮氧自由基的聚己内酯（PCL-T）。在其调控下,进行过氧化苯甲酰（BPO）引发苯乙烯（St）的自由基聚合,合成结构规整的聚己内酯-b-聚苯乙烯（PCL-b-PSt）共聚物。用氢核磁共振（1H-NM...     

Modeling of Network Formation in Nitroxide‐Mediated Radical Copolymerization of Vinyl/Divinyl Monomers Using a Multifunctional Polymer Molecule Approach

A mathematical model for the kinetics of copolymerization with crosslinking of vinyl/divinyl monomers in the presence of stable nitroxyl radicals is presented. A reaction scheme considering multifunctional polymer molecules is proposed. The Flory‐Stockmayer theory is used for the post‐gelation period. Average crosslink and cyclization densities are calculated using two different approaches. Good agreement between predicted profiles and experimental data from our and other groups is observed in all cases. Overall monomer concentration, controller/initiator ratio, and crosslinker initial concentration are found to be the governing factors for the development of average crosslink and cyclization densities and therefore for the homogeneity of the resulting polymer network.

     

Recent Advances in the Study of High‐Temperature Free Radical Acrylic Solution Copolymerization

Semibatch starved‐feed solution copolymerization is used to produce acrylic resins for coatings formulations. Mechanisms and rate coefficients for polymerization of methacrylates, acrylates, and styrene (ST) under these high‐temperature conditions are reviewed. An extended set of experimental results at 138 °C is used to refine a model describing the solution copolymerization of ST and methacrylates. The data suggest that both changing initiator efficiency and transfer reactions of oxygen‐centered radicals to polymer affect the development of polymer molecular weight. A penultimate model is used to describe the variation in termination rate coefficient with copolymer composition. Significant progress has been made to develop an extended model capable of representing multicomponent high‐temperature acrylic polymerizations.

     

Parameter Selection and Estimation Techniques in a Styrene Polymerization Model

Styrene polymerization literature is reviewed and a model with dicumyl peroxide and benzoyl peroxide initiators is developed. Nine parameters are selected for estimation using statistical methods that account for the influence of parameters on model predictions, correlated effects of parameters and uncertainties of initial literature values. Updated parameters result in improved fits to conversion and molecular weight data from three research groups, reducing the least‐squares objective function by 73%. Use of industrial data from 19 batch reactor runs increases the number of estimable parameters to 16. Good predictions are obtained for validation runs with temperature ramps using both initiators.

     

Studying the Fundamentals of Radical Polymerization Using ESR in Combination with Controlled Radical Polymerization Methods

Electron spin resonance (ESR) spectroscopy can contribute to understanding both the kinetics and mechanism of radical polymerizations. A series of oligo/poly(meth)acrylates were prepared by atom transfer radical polymerization (ATRP) and purified to provide well defined radical precursors. Model radicals, with given chain lengths, were generated by reaction of the terminal halogens with an organotin compound and the radicals were observed by ESR spectroscopy. This combination of ESR with ATRPs ability to prepare well defined radical precursors provided significant new information on the properties of radicals in radical polymerizations. ESR spectra of the model radicals generated from tert-butyl methacrylate precursors, with various chain lengths, showed clear chain length dependent changes and a possibility of differentiating between the chain lengths of observed propagating radicals by ESR. The ESR spectrum of each dimeric, trimeric, tetrameric, and pentameric tert-butyl acrylate model radicals, observed at various temperatures, provided clear experimental evidence of a 1,5-hydrogen shift.     

Nitroxide‐Mediated Controlled/Living Free Radical Copolymerization of Styrene and Divinylbenzene in Aqueous Miniemulsion

Summary: The nitroxide‐mediated controlled/living free radical copolymerization of styrene and divinylbenzene using a polystyrene‐TEMPO macroinitiator in aqueous miniemulsion and in bulk have been investigated. The crosslink densities were estimated based on the content of pendant vinyl groups as determined by ¹H NMR. Considerably lower crosslink densities were revealed in the miniemulsion than in the corresponding bulk system. The rate of polymerization in the miniemulsion increased with decreasing particle size, and was significantly higher than in bulk.

Crosslink density for the TEMPO‐mediated free radical copolymerization of S(1) and DVB(2) (f = 0.99, f = 0.01) at 125 °C in bulk (□) and in miniemulsions with d_n = 585 nm (○) and 53.3 nm (•).     

Semibatch Atom Transfer Radical Copolymerization of Styrene and Butyl Acrylate

Summary: Batch and semibatch butyl acrylate (BA) polymerizations are carried out using a heterogeneous atom transfer radical polymerization (ATRP) catalyst system, with excellent molecular weight (MW) control maintained at temperatures below 80 °C. A kinetic model, using rate coefficients from literature and catalyst solubility data from this study, provides a good representation of the experimental results, after modifying the model to account for the decrease in rate caused by intramolecular chain transfer. It is also demonstrated experimentally that well-defined random, gradient, and block styrene/BA copolymers can be synthesized by manipulating monomer feed profiles in the ATRP semibatch process.     

Kinetic Simulations of Atom Transfer Radical Polymerization (ATRP) in Light of Chain Length Dependent Termination

Kinetic simulations using the composite k_t model allows a better understanding of the effects of the persistent radical affecting ATRP or for that matter any activation–deactivation system. It also provides a better fit to experimental data in either bulk or solution conditions for ATRP polymerizations carried out at 110 °C. The results suggest that the composite model has broad utility over a wide range of experimental conditions and temperatures. The advantage of incorporating an accurate k_t model is that one can then use simulations as predictive tool to obtain polymers with higher chain‐end fidelity or polymers with low PDI values. This becomes important when attempting to use the chain‐ends for further functionalization to make complex polymer architectures. This model can also be used in simulations of miniemulsion or seeded emulsions to determine the effect of compartmentalization with particle size.

     

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.

     

Experimental Validation of Intermediate Termination in RAFT Polymerization with Dithiobenzoate via Comparison of Miniemulsion and Bulk Polymerization Rates

To understand if either of two controversial models for the retardation by RAFT agents is applicable, styrene polymerization using dithiobenzoate as the RAFT agent is carried out in both bulk and miniemulsion systems with the same rates of radical generation and the same RAFT agent concentrations. Miniemulsion polymerization with average diameters of the miniemulsion droplets of ≈107 nm is by far faster than in bulk, and the obtained rate of polymerization agrees well with the calculated results assuming a bimolecular termination between propagating radical and intermediate radical, generated by the addition reaction of propagating radical to the RAFT agent, which shows that the intermediate termination is the major reason for rate retardation by the RAFT agent.

     

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.

     

Improving the control of styrene polymerization at 60 °C using a dialkylated α‐hydrogenated nitroxide

A new dialkylated α‐hydrogenated linear nitroxide and the corresponding 1‐phenylethyl alkoxyamine were synthesized in two and three steps, respectively. The alkoxyamine was involved in the polymerization of styrene at 60 °C, and the in situ concentration of nitroxide was monitored by electron spin resonance spectroscopy. The enhanced characteristics of these new alkylated alkoxyamine and nitroxide (k = 1.5 × 10^?4 s^?1 and k = 5.7 × 10⁴ L mol^?1 s^?1) yielded a monomer consumption one order of magnitude higher than styrene thermal polymerization. This resulted in well‐defined polystyrenes up to 70,000 g mol^?1 and the observation of a control occurring through the establishment of the radical persistent effect, that is, ln([M]₀/[M]) = t^2/3. Experimentally determined kinetic constants were involved in PREDICI modelings to investigate the influence of temperature and initial alkoxyamine concentration on the kinetics as well as on the livingness and the controlled character of the polymerization. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Mechanism and kinetics of the imidazolidinone nitroxide‐mediated free‐radical polymerization of styrene

Styrene radical polymerizations mediated by the imidazolidinone nitroxides 2,5‐bis(spirocyclohexyl)‐3‐methylimidazolidin‐4‐one‐1‐oxyl (NO88Me) and 2,5‐bis(spirocyclohexyl)‐3‐benzylimidazolidin‐4‐one‐1‐oxyl (NO88Bn) were investigated. Polymeric alkoxyamine (PS‐NO88Bn)‐initiated systems exhibited controlled/living characteristics at 100–120 °C but not at 80 °C. All systems exhibited rates of polymerization similar to those of thermal polymerization, with the exception of the PS‐NO88Bn system at 80 °C, which polymerized twice as quickly. The dissociation rate constants (k_d) for the PS‐NO88Me and PS‐NO88Bn coupling products were determined by electron spin resonance at 50–100 °C. The equilibrium constants were estimated to be 9.01 × 10^?11 and 6.47 × 10^?11 mol L^?1 at 120 °C for NO88Me and NO88Bn, respectively, resulting in the combination rate constants (k_c) 2.77 × 10⁶ (NO88Me) and 2.07 × 10⁶ L mol^?1 s^?1 (NO88Bn). The similar polymerization results and kinetic parameters for NO88Me and NO88Bn indicated the absence of any 3‐N‐transannular effect by the benzyl substituent relative to the methyl substituent. The values of k_d and k_c were 4–8 and 25–33 times lower, respectively, than the reported values for PS‐TEMPO at 120 °C, indicating that the 2,5‐spirodicyclohexyl rings have a more profound effect on the combination reaction rather than the dissociation reaction. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 327–334, 2003     

Simulation of Styrene Polymerization by Monomolecular and Bimolecular Nitroxide‐Mediated Radical Processes over a Range of Reaction Conditions

Simulations of polymerization rate, molecular weight development and evolution of the concentrations of species participating in the reaction mechanism over a range of operating conditions, and a parameter sensitivity analysis showing the effects of temperature, activation/deactivation equilibrium constant and initial concentrations of controller and initiator (if present) on these variables are presented for the nitroxide‐mediated radical polymerization of styrene. The simulations were performed with a computer program based on a detailed reaction mechanism. The simulated profiles of conversion, number average molecular weight ( ), and polydispersity agree well with experimental data. Previously unknown activation energies for reactions involved in the mechanism are estimated. The temperature dependence of the kinetic rate constants obtained in this study will be useful for future modeling and optimization studies.

     

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.

     

On the Incorrectness of the Factor 2 in the Radical Termination Equation

The IUPAC recommended factor 2 preceding rate coefficients in the radical termination kinetic equations is claimed to be incorrect and confusing. This recommendation can lead to incorrect analysis of experimental data, especially while applying kinetic Monte Carlo simulations. The statement is based on the derivation of the corresponding relationships.

     

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.