Modelling copolymerization kinetics

The composition and rate behavior of free radical copolymerizations is usually described by the Mayo-Lewis (ML) model and the associated reactivity ratios, r₁ and r₂. Particularly with respect to rate, a number of systems have been found to be poorly described by the simple ML model and the penultimate unit effect (PUE) model has been suggested as an explanation. A small but significant amount of work has been done with small model analogues of polymer chains and with ESR which has established the chemical feasibility of a PUE. This paper reviews recent work with pulsed laser polymerization kinetic measurements which are successfully described in terms of a modified PUE. It is concluded that the strength of the PUE correlates inversely with the monomer reactivity ratio product, r₁r₂. The effect is important for rate, but not for composition.     

Simulation and analysis of free radical branching copolymerization kinetics

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Molecular weight distribution in composition controlled emulsion copolymerization

The effect of different strategies for copolymer composition control on the molecular weight distribution (MWD) and gel fraction in the emulsion copolymerization of methyl methacrylate and butyl acrylate was investigated. Starved and semistarved processes for copolymer composition control were both considered. For gel‐forming systems it was found that the starved process gave more gel and lower molecular weights than the semistarved process. The feasibility of simultaneous control of the copolymer composition and the MWD was assessed. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1100–1109, 2000     

Diffusion controlled formation of husk-like microcapsules

 Solid microspheres consisting of thermal heterocomplex molecules made from heating a mixture of aspartic acid and proline were transformed into husk-like microcapsules in their aqueous suspensions when pH value increased. The thickness of the outer shell of the husk-like microcapsule decreased as pH increased. Formation of the husk-like microcapsules is discussed to be due to both diffusion of the constituent molecules from the inside of the microspheres and conformational changes of those molecules in the process. Received: 16 October 1996 Accepted: 16 January 1997     

Diffusion kinetics for methanol in polycrystalline ice

Quantitative analyses of the isothermal desorption kinetics from methanol-doped H2O films on Pt(111) reveal that transport kinetics for CH3OH in polycrystalline ice are much slower than previously reported. They also indicate that MeOH displays first-order desorption kinetics with respect to its instantaneous surface concentration below 0.1 mole fraction in ice. These observations allow isothermal desorption rate measurements to be interpreted in terms of a depth profiling analysis providing one-dimensional concentration depth profiles from methanol-doped polycrystalline ice films. Using a straightforward approach to inhibit ice sublimation, transport properties are extracted from the evolution of concentration depth profiles obtained after thermal annealing of binary ice films at high temperature. Heterodiffusion coefficients for methanol in polycrystalline (cubic) ice Ic films are reported for temperatures between 145 and 195 K and for concentrations below 10(-3) mole fraction. Finally, diffusion kinetics for methanol in ice are shown to display a very strong concentration dependence that may contribute, in addition to variations in laboratory samples microstructure, to the disagreements reported in the literature regarding the transport properties of ice.     

Living/controlled copolymerization of acrylates with nonactivated alkenes

The living/controlled copolymerization of methyl acrylate with 1‐alkenes and norbornene derivatives through several radical polymerization techniques has been achieved. These techniques include atom transfer radical polymerization, reversible addition–fragmentation transfer polymerization, nitroxide‐mediated polymerization, and degenerative transfer polymerization. These systems display many of the characteristics of a living polymerization process: the molecular weight increases linearly with the overall conversion, but the polydispersity remains low. Novel block copolymers have been synthesized through the sequential addition of monomers or chain extension. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6175–6192, 2004     

On kinetics of microemulsion copolymerization of butyl acrylate and acrylonitrile

The oil-in-water microemulsion copolymerizations of butyl acrylate and acrylonitrile initiated by water (ammonium peroxodisulfate, AP)—and oil (dibenzoyl peroxide, DBP)—soluble radical initiators were investigated. Copolymerizations show two distinct nonstationary rate regions. The maximum rate of polymerization is found to be proportional to the 0.48th and 0.65th power of the AP and DBP concentration, respectively. The rate per particle is found to be proportional to the 0.05th and 0.2nd power of the AP and DBP concentration, respectively. The rate of polymerization decreases with increasing the acrylonitrile concentration. The number of particle increases with increasing conversion up to 50–70%. The number-average molecular weight increases with conversion up to ca. 20% and then decreases. The number-average molecular weights were found to decrease with increasing the concentration of both initiator and acrylonitrile. The experimental results were discussed in terms of the water-phase polymerization, the chain-transfer and radical desorption events, the particle nucleation during the whole polymerization, and recruiting monomer and emulsifier from the free monomer-swollen emulsifier micelles. © 1996 John Wiley & Sons, Inc.     

Branching kinetics in copolymerization of styrene with a chain-transfer monomer

In an earlier work it was shown that a random long-chain branching structure can be incorporated in polystyrene by copolymerizing styrene with a small amount of monomer that contains a chain transfer group. The use of vinylbenzylthiol as the chain transfer monomer produced a polystyrene with low number-average molecular weight and a degree of branching lower than expected. In this study polymerization kinetics were used to compute the theoretical molecular weight and degree of branching. The results show that if the chain-transfer constant of the chain transfer monomer is as high as that for vinylbenzylthiol the expected molecular weight and degree of branching will indeed be as low as those found experimentally. The theory also predicts that if the chain transfer constant is near one a highly branched bushy structure will result.     

Reaction kinetics in anionic copolymerization: A revisit on Mayo-Lewis equation

Reactivity ratio is a traditional parameter quantifying the reaction kinetics in copolymerization, which is important for potentially controlling microstructures of polymers and guiding the copolymerization process. Our recent experiments using tube-NMR technique enable us to in situ monitor the concentration profiles of the co-monomers during the anionic copolymerization process. This motivates us to revisit the Mayo-Lewis(ML) equation, which is the basis for derivation of reactivity ratio and has been extensively utilized in addition copolymerization. We found that although an explicit ML expression is desirable for ease of calculation and correlation with experimental data, it fails in our anionic copolymerization experiment as well as some data available in the literature. The origin is ascribed to the validity of the steady state assumption which is essential in the ML equation. This assumption can be released in anionic copolymerization and replaced by the fact that the overall concentration of the living chain ends keeps constant throughout the copolymerization. Alternative numerical method has been utilized to obtain the rate constants and consequently the reactivity ratios. Our work suggests that the ML equation should be applied with caution.     

Influence of intrachain interactions on the kinetics of styrene polymerization and copolymerization

In the free-radical polymerization of styrene, it has been observed that the onset of an acceleration of the polymerization due to increased solution viscosity can be quantitatively measured as occurring at a critical point. The product of the degree of polymerization of the polymer in solution at the critical point times its volume fraction can be represented by a temperature-dependent constant (P?_n, V_c, = K ). The value of the constant passes through a maximum between 60 and 90°C. The value of the constant is somewhat lower than that for the phenomenon called chain entanglement. It is postulated that the temperature-dependent behavior of K is due to a previously reported solution phase transition which is believed to be caused by interaction between phenylgroups on the polystyrene chain. Observations on the ultraviolet absorbance of styrene copolymers and calculations on the absolute rate of copolymerization of styrene with methyl methacrylate are presented to support the postulated intrachain interactions.     

Homopolymerization and copolymerization kinetics of trimethylene carbonate bearing a methoxyethoxy side group

The polymerization kinetics of 5‐[2‐{2‐(2‐methoxyethoxy)ethyoxy}‐ethoxymethyl]‐5‐methyl‐trimethylene carbonate (TMCM‐MOE3OM) synthesized using the organocatalyst 1,8‐diazabicyclo[5.4.0]undec‐7‐ene (DBU) were studied and compared to those with the commonly used catalyst/initiator for ring‐opening polymerization of cyclic carbonates and esters, stannous 2‐ethylhexanoate. Further, the utility of each of these catalysts in the copolymerization of TMCM‐MOE3OM with trimethylene carbonate (TMC) and l ‐lactide (LLA) was examined. Regardless of conditions with either catalyst, homopolymerization of TMCM‐MOE3OM yielded oligomers, having number average molecular weight less than 4000 Da. The resultant molecular weight was limited by ring‐chain equilibrium as well as through monomer autopolymerization. Interestingly, autopolymerization of TMC was also achieved with DBU as the catalyst. Copolymerization with TMC using stannous 2‐ethylhexanoate as the catalyst yielded random copolymers, while diblock copolymers were formed by copolymerization with LLA. With DBU as the catalyst, copolymers with LLA could not be formed, while blocky copolymers were formed with TMC. These findings should be useful in the incorporation of this monomer in the design of polymer biomaterials. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 544–552     

Asymmetric stochastic localization in geometry controlled kinetics

We consider the motion of Brownian particles confined in a two-dimensional symmetric bilobal enclosure with uneven cross section. Varying cross section of the confinement results in an effective entropic potential in reduced dimension. By employing two external noise forces, one additive and another multiplicative along x direction, we demonstrate that a correlation between them causes a symmetry breaking of entropic stability, i.e., a difference in relative stability of two lobes. This leads to an asymmetric localization of population in the stationary state. A two-state model is proposed to explain the asymmetric localization of population due to entropic diffusion.     

Alkyl chain length effects on copolymerization kinetics of a monoacrylate with hexanediol diacrylate

Copolymerizations of hexanediol diacrylate with three monoacrylates were analyzed using high-throughput conversion analysis to elucidate the effects of varying alkyl pendant groups at different compositions. Each analyzed copolymerization system contained hexanediol diacrylate (HDDA), and copolymerizations with 30-60 wt % monoacrylate reached nearly complete conversion after 30 s of exposure time. For higher amounts of monoacrylate, the photopolymerization kinetics of the hexyl acrylate (HA) copolymerization were significantly slower than the copolymerization with either ethylhexyl acrylate (EHA) or dodecyl acrylate (DDA). With 20 wt % HDDA, conversion at 30 s with a comonomer of HA was 62+/-3%, as compared to 76+/-3% and 84+/-3% when copolymerized with EHA and DDA, respectively. Model kinetic parameters were estimated for all four monomer systems, with HDDA monomer parameters found to be within the same error when estimated from any of the copolymerizations. With kinetic parameters for each monomer, comparison maps showing the difference in conversion between two copolymerizations were generated. These comparison maps allow for an assessment of two comonomer systems to determine the optimal photopolymerization conditions. Slower photopolymerization kinetics for HA occur at nearly all compositions containing monoacrylate, with the largest reduction occurring between 20 and 40 wt % monoacrylate.     

Organostibine mediated controlled/living random copolymerization of styrene and methyl methacrylate

The first example of organostibine mediated controlled/living random copolymerization of styrene (St) and methyl methacrylate (MMA) was achieved by heating a solution of St/MMA/organostibine mediator at 100 °C or St/MMA/organostibine mediator/AIBN with various monomer feed ratios at 60 °C. The addition of AIBN significantly decreased the reaction temperature and enhanced the rate of copolymerization. The structure of poly(St-co-MMA) was verified by ¹H NMR. The reactivity ratios at 60 °C were determined by the extended Kelen-Tüd?s method to be γ_St = 0.40 and γ_MMA = 0.44. The ln([M]₀/[M]) increased linearly with increasing reaction time. The number-average molecular weights of poly(St-co-MMA) increased linearly with conversion. Poly(St-co-MMA) with expected number-average molecular weight and low polydispersity index was formed. The living characteristic was further confirmed by chain-extension of poly(St-co-MMA) to form poly(St-co-MMA)-b-PMMA.     

Stabilization and kinetics in the emulsion copolymerization of butyl acrylate and methyl methacrylate

We carried out emulsion homopolymerizations and copolymerizations of butyl acrylate (BuA) and methyl methacrylate (MMA) with different types and concentrations of surfactants to determine the influence of these parameters on the particle size and particle size distribution and to elucidate the mechanism of particle formation. As expected, the mechanisms of nucleation above and below the critical micelle concentration were very different; however, it was also found that the presence of partially soluble monomers such as MMA in the water phase had a significant influence on the critical micelle concentration of Triton X‐405 (>50%). In addition, the nucleation mechanism during copolymerization seemed to be dominated by BuA, with the number of particles per liter being very similar to the number nucleated during its homopolymerization. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2832–2846, 2001     

反应性乳化剂存在下半连续苯丙乳液共聚合表观动力学

研究了在反应性乳化剂SE-10N存在下,采用半连续滴加工艺进行苯丙乳液共聚合的表观动力学.首先利用间歇法研究了引发剂、乳化剂用量、单体总量和温度对聚合反应速率的影响,得到了相应的聚合反应速率方程为Rp =k[M]0.30[I]0.18[E]0.97,并计算得到聚合反应的表观活化能为90.8 kJ·mol-1.然后采用半连续滴加法,讨论了不同滴加速率对聚合表观速率Rp的影响,结果表明,随滴加速率Ra 的增加,反应速率Rp也增加,但增加的幅度逐渐减少,且聚合过程的状态不断远离饥饿态.要使该聚合过程的状态保持在稳定的饥饿态,单体滴加时间应控制在140 min 以上.