Modeling methyl methacrylate free radical polymerization: Reaction in hydrophobic nanopores

Free radical polymerization of methyl methacrylate in nanopores has been shown to result in a decrease in the time for the onset of autoacceleration. In this work, we simplify our previous kinetic model of nanoconfined methyl methacrylate polymerization, which was based on the work of Verros and coworkers, and incorporate diffusion effects into the model using the Doolittle free volume theory. The simplified model well describes the experimental calorimetric conversion versus time data for isothermal bulk methyl methacrylate polymerization, capturing autoacceleration and the dependence of the limiting conversion on temperature. In order to model the reaction in nanopores, we assume that the diffusion coefficient scales with molecular size to the ?3 power and with nanopore diameter to the 1.3 power. Experimental calorimetric conversion versus time data for polymerization in hydrophobic nanopores are well captured by the model, including the decrease in the time to reach autoacceleration with decreasing pore size. The scaling assumed is consistent with that predicted using molecular simulations for good solvent conditions by Avramova and Milchev and by Cui, Ding, and Chen. According to the fit of the experimental data, chain diffusivity is 20–50% of the bulk value in 13 nm-diameter pores.     

Experimental and theoretical study of the use of multifunctional initiators in the high impact polystyrene bulk process

The performance of three multifunctional peroxide initiators in a bulk high impact polystyrene (HIPS) process was experimentally and theoretically investigated. For the experimental work, a series of batch reactions was carried out, comprising the main stages of an industrial HIPS bulk process using multifunctional initiators with varying functionality and structure: DEKTP (cyclic trifunctional), PDP (cyclic bifunctional) and L331 (linear bifunctional). The theoretical work consisted of the development of a comprehensive, generic yet detailed mathematical model for bulk HIPS polymerization using multifunctional initiators. The model predicts the evolution of the main polymerization variables (including conversion, molecular weights, grafting efficiency) as well as the detailed molecular structure of the polymeric species (free polystyrene, residual polybutadiene and graft copolymer), and the melt flow index of the obtained HIPS. The model was adjusted and validated using experimental results, obtaining a good agreement between measured and predicted values. The model was used to theoretically evaluate the effect of the operating conditions on the molecular and physical characteristics of the obtained polymer. It was found that the use of multifunctional initiators leads to high polymerization rates and high molecular weights simultaneously, while promoting the grafting of styrene onto butadiene, generating a microstructure with salami‐type morphologies. POLYM. ENG. SCI., 58:198–212, 2018. © 2017 Society of Plastics Engineers     

Free volume-based modelling of free radical crosslinking polymerisation of unsaturated polyesters

A new mechanistic kinetic model is presented for the cure behaviour of unsaturated polyester (UP) resins. The model is based on free radical polymerisation mechanism and the free volume concept. The quasi steady-state assumption for the free radical concentration is not used, and the decrease in initiator efficiency with conversion and radical trapping are modelled separately. The glass transition temperature of partially cured samples was measured employing differential scanning calorimetry (DSC) in conjunction with dynamic mechanical analysis (DMA), and the values obtained were incorporated into the model. DSC obtained conversion-time data for a standard commercially available UP resin under isothermal conditions. The kinetic parameters of the model were estimated using parameter optimisation procedures resulting in good agreement between model predictions and experimental data. Modelling in combination with experimental cure data showed that at higher isothermal cure temperatures a greater extent of physical trapping of radicals occurs rendering them inactive.     

Comparative study by DSC and FTIR techniques of an unsaturated polyester resin cured at different temperatures

The polymerization of a commercial polyester resin was investigated by differential scanning calorimetry (DSC). The conversion profiles were obtained in the temperature range 60–80°C. The autocatalytic model satisfactorily describes the experimental data. Fourier transform infrared spectroscopy (FTIR) measurements were also made in order to obtain both the styrene and polyester unsaturations conversions, which were compared to the overall conversion obtained by DSC. Overall conversion measured by DSC lies between styrene and polyester C=C bond conversion obtained by FTIR. © 1998 SCI.     

Modeling of the bulk free radical polymerization up to high conversion—three stage polymerization model I. Model examination and apparent reaction rate constants

In this paper, a simple and useful model, the three stage polymerization model (TSPM) is proposed on the basis of recent experimental evidence and our preliminary treatment of the experimental kinetic results found in the literature. The model accounts for gel effect and glass effect in bulk free-radical polymerization. Equations for calculating the conversion of the polymerization reaction are derived based on TSPM. Using experimental kinetic data available in the literature, general expressions for apparent reaction rate constants in three stages for methylmethacrylate (MMA) and styrene (St) are obtained. In general, the experimental kinetic data can be treated very well with the TSPM from the low conversion stage to high conversion, except for some experimental data near the transition points. However, the deviation for this data may be reasonably explained by the non-isothermal effects that occur in this regime of experiments. This deviation is smaller for a smaller ampoule reactor used in polymerization experiments because of its better heat transfer ability. In order to establish that there is no glass effect stage when the reaction temperature is greater than the glass transition temperature for a polymerization process, some experimental data for ethylmethacrylate (EMA) bulk polymerization at a reaction temperature higher than its glass transition temperature were checked with TSPM. The plots show that the model is also suitable for EMA bulk polymerization.     

Development of a unified framework for calculating molecular weight distribution in diffusion controlled free radical bulk homo-polymerization

In the present work, two different approaches to model diffusion controlled free radical polymerization, namely the free volume model and the entanglement theory are compared. These approaches are applied to methyl methacrylate bulk polymerization in a batch reactor to calculate the conversion, total radical concentration, the number and weight average molecular weights as well as the entire molecular weight distribution as a function of the polymerization time and the process conditions. All the diffusion-controlled phenomena were taken into account, including gel, glass and cage effects as well as residual termination. The molecular weight distribution is calculated by direct numerical integration of a large system of non-linear ordinary differential equations describing the conservation of the mass of macromolecular species in the batch reactor. Model predictions are in good agreement with available experimental data for conversion, number and weight average molecular weights as well as the entire molecular weight distribution, thus justifying the ability of these models to describe the main issues of the diffusion-controlled free radical polymerization.     

Modeling methyl methacrylate free radical polymerization: Reaction in hydrophilic nanopores

In previous work, we developed a simplified model for the diffusion controlled bulk polymerization of methyl methacrylate and extended the model to capture the reaction under nanoconfinement. The calorimetric conversion versus time data in bulk and in silanized hydrophobic nanopores was well captured by the model. Here we further extend the model to capture the reaction in native hydrophilic controlled pore glass (CPG) nanopores accounting for catalysis by surface silanol groups. The ability of the model to describe experimental data is tested. In order to fit the data, the parameters describing monomer and active chain diffusion differ from that in hydrophobic pores.     

Kinetic analysis of two DSC peaks in the curing of an unsaturated polyester resin catalyzed with methylethylketone peroxide and cobalt octoate

The curing of an unsaturated polyester resin catalyzed with methylethylketone peroxide and cobalt octoate as promoter is studied by DSC at different heating rates. A high promoter/peroxide ratio is used. The DSC curves show two exothermic peaks. It has been assumed that they represent two independent cure reactions. A set of kinetic parameters for each DSC peak has been obtained. They describe the overall cure process using an empirical kinetic model. Nth order and autocatalytic kinetic functions have been employed. A computer program was developed to calculate the degrees of conversion associated with each peak, and to evaluate the kinetic parameters. The calculation algorithm uses the Runge–Kutta numerical integration and the “downhill simplex method.” This methodology permits to find all kinetic parameters simultaneously. DSC experimental data are very well fitted. The simulated first peak occurs always before the second one, and the fraction of reaction heat associated with the first peak over the overall reaction heat decreases with heating rate. Moreover, activation energies are in good agreement with the tabulated values for typical free radical polymerization induced by thermal and redox decomposition of the peroxides. POLYM. ENG. SCI., 47:62–70, 2007. © 2006 Society of Plastics Engineers     

Modeling methyl methacrylate free radical polymerization in nanoporous confinement

Nanoconfinement of methyl methacrylate free radical polymerization is known to impact the molecular weight and molecular weight distribution of the polymer produced, with results in the literature generally indicating an increase in molecular weight and a concomitant decrease in polydispersity index. In the present work, the mathematical model described by Verros et al. (2005) for free radical bulk polymerization of methyl methacrylate is extended to account for polymerization in nanopores. The model of Verros et al. (2005) incorporates diffusion effects and is capable of describing the conversion and the number- and weight-average molecular weights of the resulting poly(methyl methacrylate) as a function of polymerization time and process conditions. The model is extended by incorporating the effect of nanoconfinement on diffusivity using the scaling reported in the literature. The calculations indicate that nanoconfinement will lead to higher molecular weights and lower polydispersity, and the gel effect will occur earlier. The results are compared to experimental work and implications discussed.     

甲基丙烯酸甲酯本体聚合中物性参数的测定及关联

甲基丙烯酸甲酯(MMA)本体聚合过程中比热容、黏度和导热系数等物性参数是影响聚合动力学和体系传热的重要因素.研究了聚合转化率和温度对MMA本体聚合体系密度、比热容、黏度和导热系数的变化,发现随着转化率增大,体系比热容减小,密度、黏度和导热系数增大,并存在黏度发生突变的临界转化率;随着体系温度增大,密度和导热系数减小,比热容和黏度突变对应的临界转化率增大.建立了能描述各物性参数随转化率(聚合物浓度)和温度变化的数学关联式,计算值和实验值吻合较好,建立的各关联式能较好地预测MMA本体聚合中的物性的变化,可为聚合配方及传热的设计提供基础.     

Study on the synthesis,characterization, and kinetic of bulk polymerization of disproportionated rosin (β‐acryloxyl ethyl) ester

Disproportionated rosin ((β‐acryloxyl ethyl) ester (DR‐2‐HEA) was synthesized by esterification of dispoportionated rosin (DR) with 2‐hydroxyethyl acrylate (2‐HEA) and evaluated by FTIR spectroscopy, GC/MS, ¹³C‐NMR spectroscopy. Kinetics parameters of bulk polymerization of DR‐2‐HEA in the presence of initiator AIBN was studied by using DSC. It has been assumed that the process of polymerization obey nth order empirical kinetic model to evaluate the kinetic parameters. The relative molecular weight and glass transition temperature of polymer of DR‐2‐HEA at different temperature was measured by GPC and DSC, respectively. The results showed that the temperature had no significant effect on the enthalpy of polymerization and the velocity of polymerization increased by the increase of temperature. DSC experimental data fit the simulation well while the reacted fraction (α) in the interval of 0.4<α<1. The polymer of DR‐2‐HEA is oligomer. The molecular weight and T_g did not affect by polymerization temperature. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Ring opening polymerization of ε‐caprolactone initiated by decamolybdate anion: Determination of kinetic and thermodynamic parameters by DSC and 1H‐NMR

The aim of this work is the kinetic and thermodynamic study (by differential scanning calorimetry (DSC) and proton nuclear magnetic resonance (¹H‐NMR)) of the polymerization of ε‐caprolactone initiated by ammonium decamolybdate. By means of isothermal kinetics, enthalpies of reaction in the range 150–160°C, as well as constant rates of polymerization (using an nth‐order kinetics function model), were determined. From an Arrhenius plot, activation energy (E_a = 85.3 kJ/mol) and preexponential factor (A = 1.78 × 10⁸ min^?1) were estimated. Using dynamic methods, crystallization and melting temperatures for the polymer obtained in situ were derived. Kinetic data for polymerization (obtained by ¹H‐NMR) were fitted to 13 different model reaction functions. It was found that power law equations represent better the conversion versus time plots for this system. On the basis of experimental facts, a coordination‐insertion mechanism involving molybdenum(V) species is proposed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Kinetics of heterogeneous polymerization of vinylidene chloride. II. Discussion of model

In the present article, the kinetic model for vinylidene chloride polymerization obtained in the previous article was analyzed and simplified. A series of kinetic experiments was carried out in stainless‐steel batch reactors to evaluate the model. The kinetic parameters were estimated by using these experimental data. The theoretical model prediction was compared with the experimental data. The result shows that the present model is in good agreement with experimental data over nearly the entire conversion range. © 2003 Wiley Periodicals, Inc. J Apply Polym Sci 91: 2582‐2587, 2004     

Development of a comprehensive mathematical model for free radical suspension polymerization of methyl methacrylate

In this work a detailed mathematical model for free radical suspension polymerization of methyl methacrylate (MMA) in water is developed. This model is based on sound principles such as the free volume theory to account for the diffusion limited reactions in suspension polymerization. Additionally, the complex polymerization kinetics process of the aqueous suspension polymerization of MMA is studied as a one‐dimensional numerical experiment. For this purpose, the polymerization process is modeled as a moving boundary mass transfer problem coupled with polymerization reactions. The Galerkin finite element method is used to simultaneously solve the nonlinear governing equations. The model predictions for conversion and average molecular weights vs. time were found to be in close agreement with laboratory data. It is believed that this work, as it provides fundamental understanding of the process, it might contribute to a more rational design of polymerization reactors. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

Kinetic studies of a composite thermoset cure reaction—application in pultrusion simulations

A mechanistic kinetic model based on the concept of free radical polymerization and corrected for diffusion controlled reactions was used to describe the curing behavior of an unsaturated polyester resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry (DSC) scans using a multiple regression technique. The presence of kaolinite or fiber glass in the system does not affect the progression of the reaction. The results obtained from the kinetic studies were used to simulate the influence of system composition on temperature and conversion profiles inside a pultrusion die. The results of the simulations show that kaolinite and fiber glass act as heat sinks for the composite system reducing the peak exotherm and delaying curing progression.     

In-situ polymerization of styrene in AAO nanocavities

One of the most promising aspects of the anodic aluminium oxide (AAO) template is the ability to generate a variety of different hierarchical one-dimensional (1D) polymer morphologies with structural definition on the nanometric scale. In-situ polymerization of monomers in reduced space of porous AAO template nanocavities can give rise to the direct production of versatile polymer nanostructures. In this work, porous AAO devices of 35 nm of diameter have been obtained by a two-step electrochemical anodization process and used as a nanoreactor to study the radical polymerization kinetics of styrene (St) in confinement and the results compared to those of polymerization in bulk. SEM morphological study has been conducted to establish the final structure of obtained polymer nanostructures. Confocal Raman microscopy has been performed to study the formation of the polymer through the AAO cavities as a function of time and with this methodology it has been possible to establish the monomer conversion for styrenic polymerization in AAO devices. Polystyrene obtained in the nanoreactor was characterized by SEC, NMR, TGA and DSC and the properties compared with those of bulk polymer. It was found that both the average molecular weights and polydispersity index of nanostructured polymer are lower than those obtained for bulk polymer. NMR studies have shown that the use of a reactor with nanometric size dimensions gave the obtained polystyrene greater stereospecificity than that obtained in bulk. Thermal stability and glass transition temperature (T_g) values are higher for nanostructured than bulk polymers. Moreover, the methodology proposed in this work, using AAO nanocavities as nanoreactors for polymerization reaction, can be generalized and applied to obtain polymer nanostructures of very different chemical nature and morphology by choosing the appropriate monomer or monomer reactants and by tailoring the dimension of AAO cylindrical nanocavities, that is, diameter from 20 to 400 nm and length from a few to hundreds of microns.     

Algorithms for Using Some Models of Gel and Glass Effects in Free-Radical Polymerization of Methyl Methacrylate

The aim of this article is the modeling and simulation of the batch bulk polymerization of methyl methacrylate (MMA). Simple dependencies between the propagation and termination rate constants and monomer conversion for the gel and glass effects are proposed. The empirical parameters in these relations are determined from conversion and molecular-weight experimental data obtained under various reaction conditions (initiator concentration and temperature). Sometimes, different relations were necessary to express the variation of the kinetic constants on conversion subintervals. Thus, these models have been used continuously or discontinuously, as a function of their results. An algorithm for using this model was also established.

The analysis of this model has two aims: (1) to get a good agreement between simulation and experiment; (2) to provide a simple model to be used under different reactor conditions (batch, semibatch, or continuous) or which can be easily handled in polymer engineering studies, such as sensitivity analysis, optimal control, and so forth.     

Modeling the kinetics of anionic polymerization in cyclohexane as a non-complexing solvent

In this work it is presented a model of alkyllithium initiated anionic polymerization. The model was developed from the balance of living polymer chains of each chain length, taking into account the participation of molecular aggregates of lithium compounds in initiation and propagation reactions. The model was applied to styrene polymerization in cyclohexane, where the known but not explained acceleration of initiation reaction takes place. The well established reaction order respect to polystyryllithium in propagation reaction allowed some simplification of the model. A more simplified model of three parameters was also developed by using apparent kinetic constants. As part of the work, the apparent propagation constants were determined experimentally and are reported in the Arrhenius equation form. The remainder kinetic parameters used in the model were assumed or fitted to experimental data and are described into the work. The model allows explaining acceleration of the initiation reaction and experimental data of molecular weight averages (M_n, M_w and M_z) during the polymerization. The three-parameter model was only able to explain the acceleration of initiation reaction and monomer conversion data.     

高抗冲聚苯乙烯(HIPS)连续生产的模拟

根据热引发连续本体聚合生产高抗冲聚苯乙烯 (HIPS)的动力学机理 ,建立了苯乙烯 /顺丁二烯橡胶本体聚合过程的多釜串联 (CSTR)数学模型 ,并由两个不同品牌的实际工业生产数据对模型进行了验证。得到了各釜出口苯乙烯单体的转化率、HIPS的接枝效率、接枝率以及自由PS的重均分子量及其分布     

苯乙烯热引发本体聚合的动力学研究 1 转化率与时间的关系

基于三段聚合模型 (TSPM) ,研究了 10 0— 2 0 0℃苯乙烯 (St)热引发本体聚合。结果表明 ,TSPM同样适用于描述 St热引发本体聚合。用文献中发表的大量实验数据进行 TSPM标绘表明 ,由低转化阶段向凝胶效应阶段转变时的临界转化率 x1与聚合温度无关 ,为一定值 ,大致等于 0 .5。同时 ,聚合各阶段的表观速率常数可用阿累尼乌斯 (Arrhenius)方程关联。用得到的表观速率常数计算方程和 x1,对转化率与时间关系进行了计算 ,并与文献中发表的大量实验数据作了比较。结果表明 ,二者较为吻合