Non-steady-state model for kinetics of free radical polymerization, 2. Redox initiation

This work deals with the non-steady-state kinetics of free radical polymerization with redox initiation. Rigorous expressions for the radical concentration, monomer conversion, molecular size distribution function, and number-average and weight-average molecular weights, etc., were derived. The molecular parameters of the resulting polymer were evaluated in relation to the polymerization conditions.     

Non-steady-state model for kinetics of free radical polymerization, 3. Direct photo-initiation

The non-steady-state kinetics of directly photo-initiated polymerization were studied theoretically. Taking account of the facts that the amount of monomer consumed in propagation is much more than that in initiation for a process producing high polymer and that the rate constant of chain termination is much larger than that of chain propagation or transfer, a few very close approximations were adopted to solve the set of kinetic differential equations of the polymerization under consideration. The inexplicit function method developed in a previous paper of this series for the derivation of the molecular weight distribution function is still valid in this work. Some numerical computation was implemented to show the tendency of free radical concentration decay and the plots of molecular size distribution.     

Atom transfer radical polymerization of lauryl methacrylate

The atom transfer radical polymerization (ATRP) of lauryl methacrylate (LMA) with an ethyl 2‐bromobutyrate/CuCl/N,N,N′,N″,N″‐pentamethyldiethylenetriamine initiation system was successfully carried out in toluene, and poly(lauryl methacrylate) with a low polydispersity (1.2 < weight‐average molecular weight/number‐average molecular weight < 1.5) was obtained. Plots of ln ([M])₀/([M]) versus time and plots of the molecular weight versus conversion showed a linear dependence, indicating a constant number of propagating species throughout the polymerization. The rate of polymerization was 0.56‐order with respect to the concentration of the initiator and 1.30‐order with respect to the concentration of the Cu(I) catalyst. In addition, the effect of the solvent on the polymerization was investigated, and the thermodynamic data and activation parameters for the solution ATRP of LMA were reported. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1117–1125, 2003     

Probing the reaction kinetics of vinyl acetate free radical polymerization via living free radical polymerization (MADIX)

Living free radical polymerization technology (macromolecular design via the interchange of xanthates (MADIX)) was applied to give accesses to chain length and conversion dependent termination rate coefficients of vinyl acetate (VAc) at 80 °C using the MADIX agent 2-ethoxythiocarbonylsulfanyl-propionic acid methyl ester (EPAME). The kinetic data were verified and probed by simulations using the PREDICI^® modelling package. The reversible addition-fragmentation transfer (RAFT) chain length dependent termination (CLD-T) methodology can be applied using a monomer reaction order of unity, since VAc displays significantly lower monomer reaction orders than those observed in acrylate systems (ω(VAc, 80 °C)=1.17±0.05). The observed monomer reaction order for VAc is assigned to chain length dependent termination and a low presence of transfer reactions. The α value for the chain length regime of log(i)=1.25−3.25 (in the often employed expression ) reads 0.09±0.05 at low monomer to polymer conversion (10%) and increases significantly towards larger conversions (α=0.55±0.05 at 80%). Concomitantly with a lesser amount of midchain radicals, the chain length dependence of k_t is significantly less pronounced in the VAc system than in the corresponding acrylate systems under identical reaction conditions. The RAFT(MADIX)-CLD-T technique also allows for mapping of k_t as a function of conversion at constant chain lengths. Similar to observations made earlier with methyl acrylate, the decrease of k_t with conversion is more pronounced at increased chain lengths, with a strong decrease in k_t exceeding two logarithmic units from 10 to 80% conversion at chain lengths exceeding 1800.     

Surfactant-enhanced free radical polymerization of styrene in emulsion gels

The presence of a surfactant (such as hexadecyltrimethylammonium bromide, CTAB) enhanced the rate of polymerization of styrene in emulsion gels with and without silica. The emulsion gels consisted of styrene, azobisisobutyronitrile (AIBN), surfactant, water, and, in some cases, fumed silica. Polymerization of the emulsions was carried out at room temperature in one or several days depending on the composition of the emulsion. The conversion of monomer to polymer could exceed 90% in a couple of days. In contrast, very little polymerization occurred in the absence of surfactant. A simple model, incorporating a surfactant-initiator complex and standard free radical polymerization, successfully fits the experimental kinetics data. This analysis suggests that the initiator is complexed with approximately three surfactant molecules.     

Modelling of free radical polymerization of styrene and methyl methacrylate by a tetrafunctional initiator

A mathematical model for free radical polymerizations initiated by tetrafunctional initiators is described in detail with comparisons to experimental results. Reactions involving the fate/efficiency of functional groups are properly accounted for, while in the past, kinetic models for difunctional initiators found in the literature have ignored this. Free volume theory is used to describe the diffusion-controlled regime. Based on model predictions, multi-radical concentrations were estimated to be several orders of magnitude smaller than mono-radical concentrations. Through various case studies, the model was able to demonstrate that the concentration and chain length of various polymer structures (i.e., linear, star or coupled stars) depend upon monomer type and reaction conditions. The model was found to be useful in explaining experimentally observed differences in the behaviour of a tetrafunctional initiator with styrene compared to methyl methacrylate (MMA). In both cases, higher reaction rates could be obtained when switching from a mono- to a tetrafunctional initiator; however, the influence on molecular weight was found to vary between the two systems. Work with styrene showed similar trends as with difunctional initiators, where the tetrafunctional initiator maintained similar molecular weights compared to a monofunctional initiator. Yet, for MMA, replacing the monofunctional initiator with its tetrafunctional counterpart decreased the molecular weight.     

New chain transfer agents for free radical polymerizations

The palmitoyl ester of N-hydroxypyridine-2-thione displayed useful chain transfer properties in free radical polymerizations of methyl methacrylate and styrene. Retardation, however, accompanied the lowering of molecular weight in methyl acrylate and vinyl acetate polymerizations. 4-Methyl-3-palmitoyloxythiazol-2(3H)-thione had good chain transfer activity with methyl methacrylate, styrene and methyl acrylate. Although benzyl thionobenzoate exhibited virtually ‘ideal’ behaviour (chain transfer constant C_x ～1) in styrene and methyl acrylate polymerizations, it was ineffective in lowering molecular weight of poly(methyl methacrylate). Severe retardation was observed with vinyl acetate. Addition-fragmentation pathways are postulated for chain transfer.     

Control of molecular weight distribution and tensile strength in a free radical styrene polymerization process

A new method is presented for modeling and controlling polymer molecular weight distribution (MWD) and tensile strength in a batch suspension polymerization of styrene. The molecular weight distribution is modeled by computing the weight fraction of the polymer in different chain length intervals. Tensile strength is then related to the modeled molecular weight distribution using a correlation available in the literature and based on the concept of a threshold molecular weight. This method enables the design of operating conditions for a batch suspension polymerization reactor, which will theoretically yield amorphous polystyrene with a desired tensile strength. Two numerical examples are presented to illustrate the feasibility of the proposed method. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1017–1026, 1998     

Surface molecularly imprinted polymer prepared by reverse atom transfer radical polymerization for selective adsorption indole

The preparation of indole molecularly imprinted polymers (indole‐MIPs) using 4‐vinylpyridine as functional monomer, silica gel as matrix were used to adsorb indole from fuel oil specifically. The reverse atom transfer radical polymerization (RATRP) technology was introduced to prepare the surface molecularly imprinted polymers, and the precipitation polymerization was adopted in the preparation process. The obtained indole‐MIPs were characterized by nitrogen adsorption, Fourier transform infrared spectrometry and scanning electron microscopy. The results show that indole‐MIPs were provided with the larger surface areas and more pores. The adsorption capacity of indole‐MIPs was 31.80 mg g^?1 at 298 K, and the adsorption equilibrium was reached in a short time. The adsorption process was spontaneous by thermodynamic analysis, and an appropriate decrease in temperature could enhance the adsorption capacity. The adsorption process obeyed pseudo‐second‐order kinetic model by kinetics analysis. The isotherm analysis results show that both Langmuir and Sips equations were suitable to experimental data. The selective adsorption and reusable performance of indole‐MIPs were favorable. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40473.     

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.     

Atom transfer radical polymerization of acrylonitrile

Iron(II) chloride coordinated by succinic acid was first used as the catalyst in 2‐chloropropionitrile‐initiated atom transfer radical polymerization (ATRP) of acrylonitrile. N,N‐dimethylformamide was used as a solvent to improve the solubility of the ligand. An iron(II) chloride to succinic acid ratio of 0.5 not only gives the best control of molecular weight and its distribution but also provides rather rapid reaction rate. Effects of solvent on polymerization of acrylonitrile were also investigated. The induction period is shorter in N,N‐dimethylformamide than in propylene carbonate and toluene and the rate of the polymerization in N,N‐dimethylformamide is fastest. The molecular weight of polyacrylonitrile agrees reasonably well with the theoretical molecular weight of N,N‐dimethylformamide. The rate of polymerization increases and the induction period becomes shorter with increasing polymerization temperature, and the apparent activation energy was calculated to be 56.5 kJ mol^?1. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1050–1054, 2006     

Twin screw extruders as polymerization reactors for a free radical homo polymerization

The bulk polymerization of n-butylmethacrylate was investigated in a counter-rotating twin screw extruder. It appeared that the gel effect, occurring with bulk polymerizations, affected the polymerization progress very strongly. Due to this effect the conversion of the reaction is independent of the rotation speed of the screws. The reactive extrusion diagram, presented in this paper, indicates how the different phenomena interact with each other and helps to understand the influences of extruder parameters and reaction parameters on the process.     

Camphorquinone-amines photoinitating systems for the initiation of free radical polymerization

Results of the camphorquinone/hindered piperidines, visible-light photoinduced polymerization of triethyleneglycol dimethacrylate are presented. The effectiveness of piperidines as a coinitiator is compared with a few aliphatic amines and aromatic amines. The main objective in this research was to study the mechanism of photoinitiation of polymerization. Reactive radicals that initiate the polymerization are formed by a mechanism of hydrogen atom abstraction by the triplet state of camphorquinone, mediated by photoinduced electron transfer. The different efficiencies of the aliphatic amines and of the aromatic amines affecting photopolymerization are explained on the basis of the different quenching reactivities of the excited states of camphorquinone.     

Calculation method of molecular weight averages in polymerization with chain-length-dependent termination

A systematic method for calculating the molecular weight distribution moments in free radical polymerization where termination rate depends on the size of the participating radicals, is presented. The central part of the method is the evaluation of the distribution of termination rates in the balance equations. From an adopted functional form of the termination rate constant, the moment equations are derived. For evaluating the moments of the termination rate distribution an approximate reconstruction of the radical chain length distribution using Laguerre polynomials is proposed. The calculation method can handle termination by disproportionation and combination simultaneously and allows easily to take into account diffusioncontrolled initiation, propagation and chain transfer reactions. The usefulness of the method is illustrated by simulating the bulk polymerization of methyl methacrylate and styrene. The calculated results of conversion, molecular weight averages (M _n,M _w,M _z and M _z+1) and polydispersity are in good agreement with the reported experimental data.     

N-(n-Alkyl)-2-pyridinemethanimine mediated atom transfer radical polymerization of lauryl methacrylate: Effect of length of alkyl group

The article describes the polymerization of lauryl methacrylate (LMA) using Cu(I)Br as catalyst for atom transfer radical polymerization in conjunction with N-(n-propyl) [PPMI]/(n-hexyl) [HPMI]/(n-octyl) [OPMI]-2-pyridinemethanimine as complex ligands. The polymerization of LMA was investigated in bulk and solution (toluene as solvent) using Cu(I)Br as catalyst, N-(n-alkyl)-2-pyridinemethanimine as ligands and ethyl-2-bromo isobutyrate (EBiB) as initiator. The ratio of LMA : CuBr : Ligand : EBiB was kept constant in all the polymerizations. In bulk polymerization, the solubility of the catalyst complex increased with increasing the length of alkyl chain on the ligand from propyl to octyl and also gave polymers with narrow molecular weight distribution. The PDI was further narrowed by using OPMI as ligand and toluene was used as solvent. The kinetics of polymerization was also analyzed and it clearly shows that % conversion increased with time. Increase in molecular weight with % conversion without affecting PDI clearly show that the system is living and living nature can be controlled by increasing the length of alkyl group. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Synthesis of 4-arms hydroxy-functionalized PMMA-b-PE through combining free radical polymerization with coordination polymerization

The copolymerization of MMA with ethylene was promoted by metallocene complex in the presence of initiator tetra(2,3-epoxy propoxy)silane (I_s), reducing agent Zn and cocatalyst MAO, combining free radical polymerization with coordination polymerization via sequential monomer addition strategy in one-pot to produce 4-arms hydroxy-functionalized PMMA-b-PE. The effects of polymerization conditions such as temperature, time, ethylene pressure and Al/Ti molar ratio on the polymerization performance were investigated. 4-Arms hydroxy-functionalized PMMA-b-PE was obtained by solvent extraction and determined by GPC, MALLS, DSC, FT-IR, WAXD and ¹H(¹³C) NMR. The DSC result indicated that the 4-arms hydroxy-functionalized PMMA-b-PE had one T_g at 87.0 °C and one T_m at 117.0 °C which attributed to T_g of PMMA segment and T_m of PE segment, respectively. The microstructure of 4-arms hydroxy-functionalized PMMA-b-PE was further confirmed by WAXD, FT-IR, and ¹³C NMR analysis. These results demonstrated that the obtained 4-arms block copolymer consisted of PMMA segment and crystalline PE segment.     

苯乙烯/丙烯酸丁酯反向原子转移自由基乳液聚合的合成与表征

采用Tween 80为乳化剂,FeCl3.6H2O/EDTA/AIBN为催化引发体系,在乳液体系中对苯乙烯、丙烯酸丁酯进行反向原子转移自由基(RATRP)共聚合。考察了原料加入方式、过渡金属催化剂浓度及反应温度对RATRP乳液聚合影响。结果表明,得到聚合物的分子量与单体转化率呈线性增长,分子量分布较窄(PDI为1.40)的无规共聚物。借助于凝胶渗透色谱(GPC)和红外光谱仪(IR)对RATRP共聚乳液进行表征,表明加入催化体系进行RA-TRP乳液聚合是"活性"可控聚合。     

Mathematical model for the bulk polymerization of styrene using the symmetrical cyclic trifunctional initiator diethyl ketone triperoxide. I. Chemical initiation by sequential decomposition

In this study, we experimentally and theoretically investigated the use of the symmetrical cyclic trifunctional initiator diethyl ketone triperoxide (DEKTP) in the bulk polymerization of styrene. The experimental study consisted of a series of isothermal batch polymerizations at different temperatures (120 and 130°C) with different initiator concentrations (0.005, 0.01, and 0.02 mol/L). A mathematical model was developed to predict the evolution of the reacting chemical species and the produced molecular weight distributions. The kinetic model included chemical and thermal initiation, propagation, transfer to the monomer, termination by combination, and reinitiation reactions. The simulation results predict the concentration of diradicals, monoradicals, and polymeric chains, characterized by the number of undecomposed peroxide groups. The experimental results showed that at reaction temperatures of 120–130°C, initiation by DEKTP produced an increase in the polymerization rates (R_p's) and average molecular weights, depending on the initiator concentration, due to sequential decomposition. The mathematical model was adjusted and validated with the experimental data. The theoretical predictions were in very good agreement with the experimental results. Also, an optimum initiator concentration was observed that achieved high R_p's and high molecular weights simultaneously. For polymerization temperatures of 120–130°C, the optimum concentration was 0.01 mol/L. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

The method of moments used in polymerization reaction engineering for 70 years: An overview,tutorial, and minilibrary

In the last seven decades, the method of moments (MoM) has become an invaluable tool in the field of polymerization reaction engineering, due to the simplicity of translating a complex set of population balance equations (PBE) into a system with a limited number of equations. In this work, we offer an overview of the MoM, describing the derivation of the moment equations in a basic kinetic mechanism. Some tools and strategies for the derivation of the moment equations are reviewed and explained in detail, such as the binomial theorem, the method of series expansion and pattern identification (SEPI), extensively used by the community, and a graphical approach of summation inversion. The treatment for multivariate distributions is also exposed, taking advantage of the complete and partial moment techniques. The derivation of the MoM contribution by kinetic mechanisms beyond the basic ones or involving special difficulties, such as depropagation, long chain branching (LCB), random chain scission, LCB and β-scission, short chain branching (SCB) and scission, internal double bond (IDB) (polymerization), termination by combination, reversible deactivation radical polymerization (RDRP), and intermolecular transesterification reactions (ITRs), are explained in a tutorial way. Additionally, the fundamentals of the MoM in copolymerization and the application of the pseudo-homopolymerization approach are briefly described. An introduction of the MoM to emulsion polymerization is also presented. Finally, some advanced applications of MoM in recent works are exposed: MoM models with chain-length dependent or diffusion-controlled termination, and the extension of the MoM for the prediction of the molecular weight distribution (MWD ) .     

Addition-fragmentation of 5-bromopenta-1,3-diene in free radical polymerization of methyl methacrylate

5-Bromopenta-1,3-diene (BPD) was examined as an addition-fragmentation chain transfer agent (AFCTA) in the free radical polymerization of methyl methacrylate (MMA). Studies of the kinetics of polymerization in the presence of this compound showed it to be a very effective chain transfer agent and that retardation was not significant, implying efficient reinitiation by the expelled Br radical. Analysis of the resulting polymers showed that the intermediate radical formed by the addition of the propagating radical to the C₁ carbon of BPD underwent exclusive fragmentation. However, addition on the C₄ carbon, with a relative probability of 0·6, led to its copolymerization with MMA. Kinetic studies showed BPD to be a better chain-end functionalization agent than its 5-t-butyl thio derivative for deriving pentadiene-functional macromonomer. © 1998 SCI.