Termination Rate Coefficient Research Articles

Termination Kinetics of N‐Vinyl Formamide Radical Polymerization in Aqueous Solution

AbstractTermination kinetics of radical polymerization of N‐vinyl formamide (NVF) in aqueous solution has been measured via SP–PLP–NIR, i.e., single pulse (SP) initiation of pulsed laser polymerization (PLP) in conjunction with microsecond time‐resolved near‐infrared (NIR) detection of monomer concentration. Experiments are performed at initial NVF weight fractions from 0.20 up to bulk NVF, at monomer conversions up to 40%, and at temperatures from 40 to 70 °C as well as pressures from 500 to 2500 bar. Applying high pressure improves signal‐to‐noise quality. Data obtained upon pressure variation allow for extrapolation toward ambient pressure. The primary quantity from SP–PLP–NIR is kp/<kt>, i.e., the ratio of propagation rate coefficient, kp, to apparent chain‐length‐averaged termination rate coefficient, <kt>. With kp being available from literature, kp/<kt> yields <kt>. This quantity is relevant for modeling polymerization rate and polymer properties. Termination in the initial polymerization period turns out to be controlled by segmental diffusion and, at higher degrees of monomer conversion up to 40%, by translational diffusion.

The hidden secrets of the average number of radicals per particle ([formula omitted]) and their implications in control of emulsion polymerization reactors

Emulsion polymerization is the method of choice to produce waterborne polymers but is susceptible to run-to-run variations. This variability is hard to avoid because on-line measurement of many of the characteristics of interest, in particular the molar mass distribution (MMD) of non-linear polymers, is not possible. This work offers a way to solve this problem. First, it is shown that the average number of radicals per particle (n¯), a value that can easily be obtained from kinetic measurements, contains sufficient information to directly determine the distribution of particles with n radicals. It is then demonstrated that for a given measured MMD, knowledge of the distribution of radicals per particle allows solving the long standing problem of the accurate estimation of the effective termination rate coefficient in emulsion polymerization. Combining this knowledge, it is shown the value of n¯ alone (a value that can be obtained experimentally by calorimetric measurements) can be used to develop a soft sensor able to estimate on-line the molar mass distribution of highly non-linear polymers. This, for the first time, offers the possibility of on-line control of the MMD of non-linear emulsion polymers.

Detailed analysis of termination kinetics in radical polymerization

AbstractStudies into the termination step of radical polymerization have mostly been carried out via chain‐length‐averaged properties. With the advent of pulsed laser polymerization (PLP) induced by single pulses (SPs), the analysis of termination rate coefficients kt has significantly improved. In conjunction with highly time‐resolved near‐infrared (NIR) detection of monomer consumption, SP‐PLP‐NIR allows for the measurement of chain‐length‐averaged termination rate coefficients as a function of temperature, pressure and degree of monomer conversion. With the addition of a suitable reversible addition−fragmentation chain−transfer agent, this technique even allows for the determination of chain‐length‐dependent termination rate coefficients kti,i, where i refers to the chain length of two terminating radicals of identical size. The decay of kti,i with chain length is more pronounced at small radical size below a crossover chain length ic. At larger chain lengths, kti,i decreases to a weaker extent. Thus, the so‐called composite model is perfectly suited for representing kti,i behaviour across the entire chain‐length range. A further clear improvement of kti,i determination is provided by the SP‐PLP‐EPR method, which directly measures the type and concentration of radicals via microsecond time‐resolved electron paramagnetic resonance (EPR) spectroscopy. This EPR‐assisted technique is particularly valuable for polymerizations where secondary radicals undergo backbiting and thus two types of radicals, secondary and tertiary, are simultaneously present, as is the case with acrylic monomers. © 2023 The Authors. Polymer International published by John Wiley & Sons Ltd on behalf of Society of Industrial Chemistry.

Explicit stochastic modeling of termination chain length dependencies for all disparate radical pairs in single phase free radical induced grafting

In radical (co)polymerization and polymer recycling processes with branch and crosslinking formation easily more than two macroradical types exist, defining a variety of termination reaction possibilities. However, in many kinetic modeling studies the termination of each distinct radical pair is described by the same average (apparent) rate coefficient formula, only acknowledging polymer mass fraction variations but ignoring chain length dependencies. In the present work, it is demonstrated that coupled matrix-based Monte Carlo (CMMC) simulations can reliably predict the termination behavior of distinct radical pairs. This is illustrated for free-radical induced grafting (FRIG) of polybutadiene with styrene, distinguishing six termination (by recombination) reaction channels as defined by (conventional) polystyrene radicals, polybutadiene mid-chain radicals, and grafted end-chain radicals. Model validation is uniquely performed under both free radical polymerization (FRP) and FRIG conditions, highlighting that the CMMC simulations should be applied with the so-called shooting method, in which each average apparent termination rate coefficient is updated per reaction event to capture to dynamic changes of all chain length distributions in the FRIG process. These updates should be done based on the composite kt (diffusion) model while considering better-tuned chain transfer kinetic parameters, as recommended based on recent developments in the polymer reaction engineering field. It is showcased that the FRIG reaction conditions have a clear impact on the kinetic importance of all radical types and their termination pattern determining the evolution of the bimodal log-molar mass distribution. The current work further enhances the stochastic modeling field to accurately represent (de)polymerization kinetics with several macroradical types and topological variations.

Roadmap for Monomer Conversion and Chain Length-Dependent Termination Reactivity Algorithms in Kinetic Monte Carlo Modeling of Bulk Radical Polymerization

Radical polymerization is prone to diffusional limitations on termination, leading to a rate acceleration by the gel-effect and molecular changes, with strong increases in average chain length in free radical polymerization (FRP) and improvement of the end-group functionality in reversible deactivation radical polymerization. What complicates the correct implementation of the termination rates in kinetic modeling studies is (i) the chain length and monomer conversion dependence of the individual (apparent) termination rate coefficients (k(t,app,ij) values; i,j: chain length) and (ii) the wide variations in macroradical chain length distribution (CLD) types and shapes along the polymerization and upon altering the reaction conditions, including variations in CLD modality and broadness. In this work, we compare four major kinetic Monte Carlo modeling algorithms to sample termination reaction events in bulk radical polymerization, using literature k(t,app,ij) values. We present a roadmap allowing one to select the most suited algorithm depending on the radical polymerization technique and reaction conditions, therefore opening the pathway to more correct representations of chain length and monomer conversion dependencies in radical polymerization. Case studies are related to bulk nitroxide-mediated polymerization, FRP, and pulsed laser polymerization, following an increasing complexity in the active macroradical CLD type and shape.

Kinetic modelling of the reversible addition–fragmentation chain transfer polymerisation of N-isopropylacrylamide

Reversible addition–fragmentation chain transfer (RAFT) polymerisation is a complex process involving multiple fundamental reaction steps that makes estimation of rate coefficients and exact kinetic simulation problematical. In this paper, we show that the homopolymerisation of N-isopropylacrylamide (NIPAM) can be kinetically modelled using a much-simplified method involving only a few kinetic parameters. The experimental polymerisation of NIPAM was performed with 4-cyano-4-(phenylcarbonothioylthio)pentanoic acid as the RAFT agent and 4,4′-azobis(4-cyanopentanoic acid) as the initiator in dioxane at three different temperatures (60, 70 and 80 °C) with the initial [RAFT]:[initiator] ratio kept at 5:1 and different initial [monomer]:[RAFT] ranging from 100:0.2 to 100:1. Our method for the kinetic simulation makes use of a pseudo-concentration of polymer, in which all chains are assumed to have the same molar mass equal to the average molar mass Mn. With these approximations, the apparent rate coefficients for propagation, termination and initiator decomposition (kp,app, kt,app and kd,app respectively) and three fitting parameters, αp (ratio of propagating radicals to macroRAFT agent), αkp (ratio krein,app/kp,app), and αkt (exponent describing the chain length dependence of kt) were optimised. Our modelling results adequately simulated the experimental polymerization kinetics. Values of kt,app, kd,app, αp, αkp, αkt appeared essentially independent of [monomer]:[RAFT] and the values kt,app, kd,app and αkt were consistent in magnitude with literature values of the corresponding kt, α and kdf. Retardation associated with the RAFT process is encompassed in the value of kp,app, which was strongly dependent on [monomer]:[RAFT], with higher kp,app and Rp being observed for higher [monomer]:[RAFT].

Modification of poly-HEMA with nonreactive POSS derivatives by in situ photopolymerization

Photo-induced polymerization of 2-hydroxyethyl methacrylate (HEMA) in the presence of various amounts of nonreactive polyhedral oligomeric silsesquioxanes (POSS) functionalized with glycidyl, fluoroalkyl or hydroxyl groups was investigated. HEMA/POSS systems were characterized before, during and after the photocuring, with the special emphasis on the photopolymerization kinetics (measured by isothermal differential scanning calorimetry). It was found that the introduction of tested POSS derivatives into HEMA strongly affects the photopolymerization kinetics (enhancement of the gel effect, increase in the polymerization rate and conversion), mainly due to the increase in the viscosity of the initial formulation which leads to a reduction in the termination rate coefficient. However, interactions HEMA–POSS cause also a slight increase in the propagation rate coefficient. The behavior of the polymerization rate coefficients during the reaction suggests that POSS cages may mitigate the inhibitory effect of viscosity on the diffusion of macroradicals by exerting a slip effect. The materials produced are microcomposites due to the partial phase separation occurring during the curing process. Small amounts of added POSS modifiers cause plasticization of the material; at higher loads, POSS domains behave like nanofiller aggregates that increase the glass temperature. The nonreactive POSS have very little effect on thermal decomposition of the poly-HEMA matrix, which can result in a degree from the phase separation; the latter is also the main cause of the deterioration of the mechanical properties of composites compared to a pure polymer matrix.

RAFT Polymerization of Tert-Butyldimethylsilyl Methacrylate: Kinetic Study and Determination of Rate Coefficients.

Well-defined poly(tert-butyldimethylsilyl methacrylate)s (TBDMSMA) were prepared by the reversible addition-fragmentation chain transfer (RAFT) process using cyanoisopropyl dithiobenzoate (CPDB) as chain-transfer agents (CTA). The experimentally obtained molecular weight distributions are narrow and shift linearly with monomer conversion. Propagation rate coefficients (kp) and termination rate coefficients (kt) for free radical polymerization of TBDMSMA have been determined for a range of temperature between 50 and 80 °C using the pulsed laser polymerization-size-exclusion chromatography (PLP-SEC) method and the kinetic method via steady-state rate measurement, respectively. The CPDB-mediated RAFT polymerization of TBDMSMA has been subjected to a combined experimental and PREDICI modeling study at 70 °C. The rate coefficient for the addition reaction to RAFT agent (kβ1, kβ2) and to polymeric RAFT agent (kβ) is estimated to be approximately 1.8 × 104 L·mol−1·s−1 and for the fragmentation reaction of intermediate RAFT radicals in the pre-equilibrium (k-β1, k-β2) and main equilibrium (k-β) is close to 2.0 × 10−2 s−1. The transfer rate coefficient (ktr) to cyanoisopropyl dithiobenzoate is found to be close to 9.0 × 103 L·mol−1·s−1 and the chain-transfer constant (Ctr) for CPDB-mediated RAFT polymerization of TBDMSMA is about 9.3.

Autoacceleration in Bulk Free‐Radical Polymerization: Effect of Chain Transfer

AbstractThe model and methodology for estimating diffusion‐controlled rate coefficients for the methyl methacrylate polymerization system reported in Parts I and II of this series is extended to include the chain transfer reaction to an agent (CTA). Theoretical and experimental results exhibit minima in the rate of polymerization curves at low conversions as it is observed in the absence of CTA. Such minima are proposed to be the onset of the autoacceleration effect where the termination reaction undergoes a transition from chemically controlled to diffusion controlled where the segmental mobility of the chain ends plays a key role. As the CTA concentration increases, the conversion at which the minimum is presented is higher and the autoacceleration is less pronounced. This behavior is explained in terms of the effect of polymer chain entanglements and segmental mobility of the chain ends on the termination rate coefficient k t.

Kinetics of Bulk Free‐Radical Polymerization of Butyl Methacrylate Isomers Studied by Reaction Calorimetry

AbstractThe kinetics of bulk free‐radical polymerizations of n‐butyl methacrylate (n‐BMA), iso‐butyl methacrylate (i‐BMA), and tert‐butyl methacrylate (t‐BMA) are studied by differential scanning calorimetry and with the aid of a mathematical model previously reported by the authors. In all the cases, the rate of polymerization (Rp) evolution curve exhibits a minimum at low conversions and the characteristic maximum of the autoacceleration effect. It is found that the monomer conversion xmin at which the minimum is observed, follows the order n‐BMA > i‐BMA > t‐BMA and that for monomer conversions (x) smaller than xmin, the termination rate coefficient (kt) shows a plateau. According to the model results it is obtained that for x > xmin, the termination reaction is chemically controlled whereas for x > xmin, it is diffusion‐controlled and that the xmin values are related to the value of the termination rate coefficient of the chemical step (kt0) of every isomer, which is highly influenced by the steric hindrance of the alkyl substituent group.

Radical Copolymerization Kinetics of Bio-Renewable Butyrolactone Monomer in Aqueous Solution

The radical copolymerization kinetics of acrylamide (AM) and the water-soluble monomer sodium 4-hydroxy-4-methyl-2-methylene butanoate (SHMeMB), formed by saponification of the bio-sourced monomer γ-methyl-α-methylene-γ-butyrolactone (MeMBL), are investigated to explain the previously reported slow rates of reaction during synthesis of superabsorbent hydrogels. Limiting conversions were observed to decrease with increased temperature during SHMeMB homopolymerization, suggesting that polymerization rate is limited by depropagation. Comonomer composition drift also increased with temperature, with more AM incorporated into the copolymer due to SHMeMB depropagation. Using previous estimates for the SHMeMB propagation rate coefficient, the conversion profiles were used to estimate rate coefficients for depropagation and termination (kt). The estimate for kt,SHMeMB was found to be of the same order of magnitude as that recently reported for sodium methacrylate, with the averaged copolymerization termination rate coefficient dominated by the presence of SHMeMB in the system. In addition, it was found that depropagation still controlled the SHMeMB polymerization rate at elevated temperatures in the presence of added salt.

Chain-Length-Dependent Termination of Styrene Bulk Polymerization up to High Degrees of Monomer Conversion

Single pulse–pulsed laser polymerization in conjunction with the highly time-resolved detection of radical concentration by electron paramagnetic resonance (SP-PLP-EPR) was applied for the first time toward measuring termination kinetics up to high degrees of monomer conversion with styrene bulk polymerization up to 80% conversion taken as an example. Monomer conversion was mimicked by the addition of polystyrene. The composite model turns out to provide an adequate representation of the termination kinetics. A constant value of the power-law exponent for small-chain radicals, αs, holds up to about 50% conversion, in which region the model parameter kt(1,1), the rate coefficient for termination of two radicals of size unity, exhibits a minor decay. Above 50% polymer content, both αs and kt(1,1) decrease significantly. Above 80% polymer, the chain-length dependence almost disappears, and termination runs under reaction-diffusion control. As the region of large radicals is not accessible at higher monomer c...

Termination, Transfer, and Propagation Kinetics of Trimethylaminoethyl Acrylate Chloride Radical Polymerization in Aqueous Solution

The SP–PLP–EPR (single pulse–pulsed laser polymerization–electron paramagnetic resonance) method has been used to measure the rate coefficients of termination, intramolecular transfer, and propagation for the radical polymerization of 20 wt % trimethylaminoethyl acrylate chloride (TMAEA) in the temperature range 0–90 °C. The high complexity of this acrylate system is due to water being the solvent, to the monomer being a strong electrolyte, and to both secondary chain-end radicals and tertiary midchain radicals being simultaneously present. The termination kinetics, which was analyzed by a chain-length-dependent scheme, largely differs from the situation met with nonionized radicals. The reliability of the rate coefficients obtained from the SP–PLP–EPR experiments has been demonstrated by the almost perfect agreement of TMAEA conversion vs time data from simulation, on the basis of these coefficients, and from the chemically initiated TMAEA polymerization experiment at 70 °C.

Kinetic Monte Carlo Modeling Extracts Information on Chain Initiation and Termination from Complete PLP-SEC Traces

Complete pulsed laser polymerization (PLP) log-molar mass distributions (log-MMDs) are accurately simulated using kinetic Monte Carlo (kMC) modeling to gain not only knowledge on the propagation but also on the chain initiation and termination reactivity. The isothermal kMC model (306–325 K) accounts for diffusional limitations and all relevant elementary reactions, considering n-butyl acrylate, 2,2-dimethoxy-2-phenylacetophenone (DMPA), and a frequency of 500 s–1. The disparate reactivities toward vinylic bonds of the DMPA fragments are essential to ensure the well-defined multimodality of the log-MMDs necessary to identify consecutive inflection points. It is also illustrated that PLP log-MMD data can be used to test the validity of models for apparent termination rate coefficients at low monomer conversions and that kMC simulations are a powerful tool to track the chain growth of the different radical types between laser pulses and to identify dominant elementary reactions.

Chain-Length-Dependent Termination of Sodium Methacrylate Polymerization in Aqueous Solution Studied by SP-PLP-EPR

Via the single pulse–pulsed laser polymerization–electron paramagnetic resonance (SP-PLP-EPR) technique, the chain-length-dependent termination of 5 and 10 wt % sodium methacrylate (NaMAA) in aqueous solution was measured from 5 to 60 °C. The rate coefficients kt(i,i) for termination of two ionized radicals of identical size i were analyzed by the composite model. Three out of the four composite-model parameters behave similarly to nonionized monomers, whereas the fourth parameter, the rate coefficient for termination of two radicals of chain length unity, kt(1,1), exhibits a distinctly different behavior. The temperature dependence of kt(1,1) is significantly below the one of fluidity (inverse solution viscosity). Moreover, absolute kt(1,1) increases with NaMAA concentration, i.e., toward higher viscosity. Both observations indicate that the termination kinetics of ionized radicals largely differs from the Smoluchowski-type behavior.

Kinetics and Modeling of the Radical Polymerization of Trimethylaminoethyl methacrylate chloride in Aqueous Solution

For the radical polymerization of ionized trimethylaminoethyl methacrylate chloride (TMAEMA) in aqueous solution, two strategies to determine the propagation rate coefficient (kp) are proposed for systems where the pulsed‐laser polymerization–size‐exclusion chromatography (PLP–SEC) method fails. This problem occurs with some fully ionized or sterically highly hindered monomers, where termination may become too slow. As TMAEMA is a borderline case with kp being accessible by PLP–SEC and from single‐pulse–pulsed‐laser polymerization with electron paramagnetic resonance (SP–PLP–EPR) spectroscopy, studies into this monomer allow for judging the quality of the suggested alternative approaches of kp measurement and serve for consistency checks of the previously published kp and termination rate coefficient (kt) data. Within both approaches, kp/〈kt〉0.5 is measured via chemically initiated polymerization, with 〈kt〉 referring to chain‐length‐averaged termination. The kp/〈kt〉0.5 data are combined either with kp/〈kt〉 values from highly time‐resolved near‐infrared detection of monomer conversion induced by a single laser pulse (SP–PLP–NIR) or with Predici modeling on the basis of known chain‐length‐dependent termination kinetics. As coupled rate coefficients are measured, the obtained kp data also provide 〈kt〉 for a particular chain‐length distribution. The differences between propagation and termination rates of nonionized and fully ionized monomers are discussed. image

Propagation and Termination Kinetics of Poly(Ethylene Glycol) Methyl Ether Methacrylate in Aqueous Solution

The propagation rate coefficient, kp, of poly(ethylene glycol) methyl ether methacrylate (Mn ≈500 g mol−1) has been measured via pulsed-laser polymerization (PLP)–size-exclusion-chromatography in aqueous solution between 5 wt% monomer and bulk polymerization at temperatures from 22 to 77 °C. kp increases significantly toward higher water content, as is observed for other water-soluble monomers. This entropy-motivated effect enhances the pre-exponential. The activation energy, EA(kp), is more or less identical to the characteristic value of methacrylates. The chain-length-dependent rate coefficient, kti,i, for termination of two radicals of chain length i has been investigated at low degrees of monomer conversion via the single-pulse–PLP–electron paramagnetic resonance technique. kti,i turned out to be adequately represented by the composite model designed by the Russell group. The power-law exponents for the chain-length dependence of small and long radicals are close to the numbers reported for other monomers. The rate coefficient for termination of two radicals of chain length unity scales with the fluidity of the reaction mixture. Viscosity measurements prior to polymerization thus enable estimates of termination rate.

Bulk Free Radical Polymerization of Methyl Methacrylate and Vinyl Acetate: A Comparative Study

The model and methodology for estimating diffusion‐controlled rate coefficients for the methyl methacrylate (MMA) polymerization system is extended to the vinyl acetate (VAc) case. Comparison of the kinetic behavior and termination rate coefficients (kt) of both monomers suggests that at low conversions the termination reaction is controlled by the chemical step, whereas at moderate and high conversions it is controlled by the diffusive step which in turn is determined by the segmental diffusion of the long radicals and not by the center of mass diffusion of short radicals. It is found that, for most of the conversion range, diffusion coefficient for VAc is lower than the one for MMA notwithstanding that ktVAc > ktMMA. An explanation of this apparent inconsistency on the base of the model results and in terms of segmental mobility is proposed. image

Propagation and Chain-Length-Dependent Termination Rate Coefficients Deduced from a Single SP–PLP–EPR Experiment

The laser single pulse (SP)–pulsed laser polymerization (PLP)–electron paramagnetic resonance (EPR) technique allows for deducing propagation (kp) and termination (kt) rate coefficients, including the chain-length dependence of kt, from a single pulsed-laser experiment. The method, which is particularly well suited for slowly terminating radicals, e.g., sterically hindered and ionic radicals, is illustrated for di(n-butyl) itaconate in bulk at temperatures from 30 to 60 °C. The time evolution of the DBI radical concentration is measured with a high time resolution at constant magnetic field. Propagation is associated with a relatively low pre-exponential A(kp), which is responsible for the small kp value of 6.8 L mol–1 s–1 at 30 °C. The chain-length dependence (CLD) of kt, deduced from the same SP–PLP–EPR signal as is kp, turns out to be adequately represented by the composite model. Whereas typical numbers are found for the power-law exponents for short and long radicals and for the crossover chain lengt...

Modeling the Radical Batch Homopolymerization of Acrylamide in Aqueous Solution

A kinetic model for the radical homopolymerization of acrylamide in aqueous solution is developed, incorporating propagation and termination rate coefficients as functions of monomer concentration and including the formation and reaction of midchain radicals based on the insights and measured rate coefficients from recent pulsed‐laser studies. The model successfully represents the batch conversion profiles measured using an in situ NMR technique between 40 and 70 °C with initial monomer concentrations of 5 to 40 wt%, as well as the associated polymer molar mass distributions. In particular, the model captures the decreased rate that occurs at lowered monomer concentrations as a result of the formation of less‐active midchain radicals by backbiting. Previous literature data are also well represented by the model. image