Mathematical modeling of diffusion‐controlled free‐radical terpolymerization reactions

A comprehensive mathematical model is developed to describe the kinetics and molecular and compositional developments in a free‐radical terpolymerization batch reactor. This model is based on a fairly general kinetic mechanism, including chain‐transfer and terminal double‐bond reactions. We take into account the effects of diffusion‐controlled phenomena (i.e., gel, glass, and cage effects) on polymerization kinetics by extending our previous model on diffusion‐controlled reactions to terpolymerization systems. Triple moments for the live and dead trivariate chain‐length terpolymer composition distributions are introduced to describe the molecular and compositional developments in the terpolymerization system. The predictive capabilities of this model are demonstrated by simulation of the free‐radical, bulk terpolymerization of butyl acrylate/methyl methacrylate/vinyl acetate under different experimental conditions. It is shown that the model predictions are in good agreement with experimental data on monomer conversion, average molecular weights, and terpolymer composition, as reported by Dube and Penlidis. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 161–176, 2003     

Mechanochemical polymerization in mixtures of diallyl terephthalate and distilled water by ultrasonic irradiation

Summary Mechanochemical polymerization in systems of diallyl terephthalate-distilled water has been studied by ultrasonic irradiation at 90°C. An additional effect of distilled water on mechanochemical polymerization of diallyl terephthalate was investigated. When a 1.2 wt % distilled water solution, the conversion of poly(diallyl terephthalate) was the greatest and the initial rate of the polymerization R _p was 1.3x10^-5 mol/l sec. This polymerization proceeded by a radical mechanism and the primary radicals produced from water molecules by ultrasonic waves. In addition, changes in the iodine value and the weight-average molecular weight of the resulting polymers were proved.     

Kinetics of dispersion polymerization of dimethyl diallyl ammonium chloride and acrylamide

Dispersion copolymerization of dimethyl diallyl ammonium chloride with acrylamide has been investigated by the dilatometer technique using the mixture of poly(vinylpyrrolidone) and poly(dimethyl diallyl ammonium chloride) as the composite stabilizer and 2,2′-azobis(2-methylpropionconidine)dihydro chloride as the initiator. Monomer reactivity ratios of AM and DMDAAC were determined by the application of Fineman-Ross methods. The analysis of reactivity ratios revealed that DMDAAC is less reactive than AM, and copolymers formed are statistically in nature. The influences of the molar ratio of AM to DMDAAC, concentrations of monomers, stabilizer and initiator, etc. on polymerization rate and intrinsic viscosity of polymer have been examined. The rate of polymerization (R_p) can be represented by R_p μ [M]^1.44,R_p μ [S]^0.39,R_p μ [I]^0.60 {R_{\rm{p}}} \propto {[M]^{1.44}},{R_{\rm{p}}} \propto {[S]^{0.39}},{R_{\rm{p}}} \propto {[I]^{0.60}} . The overall activation energy for the rate of polymerization is 37.38 kJ/mol over the temperature range 35–55°C.Based on the experimental results, the polymerization mechanisms were discussed.     

Modeling of diffusion‐controlled reactions in free radical solution and bulk polymerization: Model validation by DSC experiments

In this work, a detailed experimental study of diffusion‐controlled reactions in free radical polymerization by using differential scanning calorimetry (DSC) was carried out. The systems studied include the methyl methacrylate bulk polymerization as well as the solution and the bulk polymerization of vinyl acetate at a wide range of experimental conditions including initial initiator concentration, reaction temperature, and type and amount of solvent. The conversion data obtained by DSC was successfully simulated by using a mathematical model based on sound principles such as the free volume theory. The estimated parameters, by fitting predictions of this model to conversion data obtained by DSC were found to be in close agreement with the reported parameters in the literature, thus validating both the experimental and theoretical methods used in this work. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Kinetics of the solid‐state polymerization of nylon‐6

The kinetics of the thermally induced solid‐state polymerization (SSP) of nylon‐6 were examined in both a fixed‐bed reactor and a rotary reactor. Factors such as the regulator content, the reaction temperature and time, the particle size, the type and geometry of the nylon‐6 prepolymer, the nitrogen gas flow rate, the water content of the nitrogen gas flow, and the polymerization process were studied. The results showed that the regulator content, the reaction temperature and time, and the particle size were the primary factors, and that the others were negligible. Moreover, the SSP rate and number‐average molecular weight (M_n) increased with increasing reaction temperature and time and decreasing particle size. The SSP rate and M_n had maximum values with increasing regulator content in an experimental range of 0.03–0.07 wt %. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 616–621, 2002; DOI 10.1002/app.10341     

Initiator‐fragment incorporation radical polymerization of diallyl phthalate: Kinetics,formation of hyperbranched polymer,and iridescent porous film thereof

Diallyl phthalate (DAP) was polymerized in toluene using dimethyl 2,2′‐azobisisobutyrate (MAIB) of high concentrations (0.1–0.9 mol/L) as initiator. The polymerization of DAP of 1.50 mol/L with MAIB of 0.50 mol/L proceeded homogeneously at 80°C without gelation to give soluble polymers in a high yield of 93%. Kinetic results of the homogeneous polymerization at 80°C suggest significant contributions of the degradative chain transfer and the primary radical termination as shown by the rate equation, R_p = k [MAIB]^0.8[DAP]^1.0 (R_p = polymerization rate). The polymer formed in the polymerization of DAP (1.30 mol/L) with MAIB (0.50 mol/L) at 80°C for 8 h consisted of the DAP units with (17 mol %) and without (47 mol %) double bond and the methoxycarbonylpropyl group (36 mol %) as MAIB‐fragment. The large fraction of the incorporated initiator‐fragment as terminal group indicates that the polymer has a hyperbranched structure. The film cast from a solution of the hyperbranched poly(DAP) in tetrahydrofuran showed an iridescent color. The confocal scanning laser microscope image of the film revealed that the iridescent film contained the pores of about 1 μm arranged in an ordered array. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 408–415, 2006     

Solid‐state polymerization of poly(trimethylene terephthalate)

The solid‐state polymerization (SSP) of poly(trimethylene terephthalate) (PTT) has been studied and compared with that of poly(ethylene terephthalate) (PET). Because PTT and PET share the same SSP mechanism, the modified second‐order kinetic model, which has successfully been used to describe the SSP behaviors of PET, also fits the SSP data of PTT prepolymers with intrinsic viscosities (IVs) ranging from 0.445 to 0.660 dL/g. According to this model, the overall SSP rate is ?dC/dt = 2k_a(C ? C_ai)², where C is the total end group concentration, t is the SSP time, k_a is the apparent reaction rate constant, and C_ai is the apparent inactive end group concentration. With this equation, the effects of all factors that influence the SSP rate are implicitly and conveniently incorporated into two parameters, k_a and C_ai. k_a increases, whereas C_ai decreases, with increasing SSP temperature, increasing prepolymer IV, and decreasing pellet size, just as for the SSP of PET. Therefore, the SSP rate increases with increasing prepolymer IV and increasing SSP temperature. The apparent activation energy is about 26 kcal/mol, and the average SSP rate about doubles with each 10°C increase in temperature within the temperature range of 200–225°C. The SSP rate increases by about 30% when the pellet size is decreased from 0.025 to 0.015 g/pellet. Compared with PET, PTT has a much lower sticking tendency and a much higher SSP rate (more than twice as high). Therefore, the SSP process for PTT can be made much simpler and more efficient than that for PET. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3188–3200, 2003     

Entropically‐driven ring‐opening polymerization of cyclic butylene terephthalate: Rheology and kinetics

Cyclic butylene terephthalate oligomers (CBT) with ultra‐low melt viscosity can be polymerized into poly (butylene terephthalate) (pCBT) via entropically‐driven ring‐opening polymerization (ED‐ROP) in a short time (ranging from several seconds to 10 min) with no chemical emission and no heat generation during the polymerization process. Due to no heat generation, dynamic rheological measurements were used to monitor the polymerization of CBT from 220 to 250°C. The polymerization was accompanied by a steep increase of the melt viscosity and modulus in isothermal rheological tests, and much faster at higher temperature. With rheological results, reptation theory and Double reptation model were adopted to determine the variation of the molecular weight and concentration with time for pCBT. According to the ED‐ROP mechanism of CBT, kinetics equations were also established to simulate the polymerization process. Furthermore, using the results of variation of molecular weight with time for pCBT and kinetics equations, the polymerization rate constants for initiation and propagation steps were evaluated, and the activation energy was also obtained. It was proved that rheological method is a convenient and reliable way to investigate the kinetics of ED‐ROP of CBT. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Benzotriazinyl‐mediated controlled radical polymerization of styrene

The stable free radical polymerization (SFRP) process based on (1,3‐diphenyl‐1,4‐dihydro‐1,2,4‐benzotriazin‐4‐yl), the so‐called ‘Blatter radical’, and several C‐7 substituted derivatives is introduced for the first time for the polymerization of styrene. Polystyrenes characterized by polydispersity indices in the 1.05 ? 1.27 range were obtained in the presence of the Blatter radical and its derivatives containing CF₃, Ph, Fur‐2‐yl and 4‐PhC₆H₄ substituents, while polymerization proceeded either in a non‐controlled manner or in very low polymerization yields in the presence of derivatives containing halogen (Cl, Br, I) substituents. This preliminary investigation, demonstrating the potential use of the Blatter radical and its derivatives in mediated SFRP, creates new opportunities to design and develop radicals to optimize performance in such polymerization processes. © 2013 Society of Chemical Industry     

Kinetics of polycondensation and copolycondensation of Bis(3‐hydroxypropyl terephthalate) and Bis(2‐hydroxyethyl terephthalate)

The kinetics of polycondensation and copolycondensation reactions of bis(3‐hydroxypropyl) terephthalate (BHPT) and bis(2‐hydroxyethyl) terephthalate (BHET) as monomers were investigated at 270°C, in the presence of titanium tetrabutoxide (TBT) as a catalyst. BHPT was prepared by ester interchange reaction of dimethyl terephthalate (DMT) and 1,3‐propanediol (PD). Applying second‐order kinetics for polycondensation, the rate constants of polycondensation of BHPT and BHET, k₁₁ and k₂₂, were calculated as 3.975 and 2.055 min⁻¹, respectively. The rate constants of cross‐reactions in the copolycondensation of BHPT and BHET, k₁₂ and k₂₁, were obtained by using the results obtained from a proton nuclear magnetic resonance spectroscopy. The rate constants during the copolycondensation of BHPT and BHET at 270°C decreased in the order k₁₁ > k₁₂ > k₂₂ > k₂₁, indicating the block nature of the copolycondensation. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 693–698, 2000     

Kinetics and modeling of diethylene glycol bisallyl carbonate bulk polymerization

The free‐radical polymerization kinetics of diethylene glycol bisallyl carbonate in bulk were investigated with Fourier transform infrared and Fourier transform Raman techniques in a wide temperature range of 50–140°C with four different peroxide initiators. In addition, the ratios of the degradative kinetic rate constant to the propagation rate constant under different reaction conditions were obtained from molecular weight measurements under various reaction conditions. The ratio of the chemically controlled termination and propagation rate constants of the polymerization system were obtained with the initial rates of polymerization and the number‐average molecular weight data, which were between 8.22 × 10^?5 and 1.47 × 10^?3 L mol^?1 s^?1. The initiator efficiencies were evaluated with special experiments at low initiator concentrations with the theory of dead‐end polymerization. The computed conversions from the developed kinetic model were in good agreement with the conversion and molecular weight measured data. The values of the diffusion‐controlled propagation and termination rate constants, with clear and physical meaning, were the only two parameters obtained from the developed kinetic model fitting the measured conversion points. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 345–357, 2005     

Kinetics and flow of diallyl phthalate resins

The analysis of molding operations for thermosetting polymers requires knowledge of the rheology and reaction rates of the materials. The purpose of this research was to measure kinetic and rheological data on diallyl phthalate resins and to integrate these results into models describing the flow behavior. The chemical kinetics of the curing reactions were derived from calorimetric measurements taken with a differential scanning calorimeter. The rheological data were measured with a mechanical spectrometer equipped with eccentric rotating discs. A model based on the theory of ideal rubber elasticity was used to correlate the elastic storage modulus with reaction time and temperature. For the region below the gel point, the dynamic viscosity exhibited a power law dependence on angular frequency and an Arrhenius dependence on temperature.     

Micromechanical modeling of roll‐to‐roll processing of oriented polyethylene terephthalate films

In this article, the thermo‐mechanical time‐dependent behavior of oriented polyethylene terephthalate (PET) films, which are used as a substrate material for flexible Organic Light‐Emitting Diode (OLED)s, is analyzed. These films are subjected to conditions that are representative for the industrial manufacturing process. Effects of creep and thermal shrinkage are experimentally observed simultaneously. The aim of the article is to demonstrate the ability of the micromechanically‐based model, which was previously used to separately describe both creep and thermal shrinkage of the polyethylene terephthalate film, to simulate experimentally observed anisotropic behavior of the film under complex loading conditions. This anisotropic behavior results from the microstructure, the internal stress state, and differences in constitutive behavior of the phases. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43384.     

Kinetics of UV‐initiated RAFT crosslinking polymerization of dimethacrylates

The UV‐initiated RAFT polymerizations of a series of poly(ethylene glycol) dimethacrylates (PEGDMA) were investigated using differential scanning photocalorimetry (DPC) at room temperature. The rate of the RAFT system was much lower than that of a conventional free radical polymerization. A mild autoacceleration occurred as the addition reaction became diffusion controlled. The influence of the spacer length (CH₂CH₂O)_x between the vinyl moieties of the dimethacrylates on the polymerization kinetics was examined. The polymerization rate of PEGDMA decreased with an increased x value from 4 to 9, but it increased with a further increased x value from 9 to 14. Mechanical properties of the resulting polymers were also examined by dynamic mechanical analysis (DMA). It was concluded that the presence of the RAFT agent during polymerization of multifunctional monomers did not have an effect on the heterogeneity of the polymer network. In comparison with three different PEGDMAs, the PEGDMA with the longest spacer formed the most homogeneous networks with a lower crosslinking density. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Minimum time heating cycles for diffusion‐ versus permeability‐controlled binder removal from ceramic green bodies

A comparison of minimum time heating cycles (MTHCs) was conducted for binder removal from ceramic green bodies for two mass transfer mechanisms: diffusion and gas permeability. The MTHCs were determined by combining approximate analytic solutions to the governing reaction‐diffusion and reaction‐gas permeability equations with a variational calculus algorithm containing a constraint on pressure buildup within the green body. Both the temperature‐time profile and duration of the MTHCs were sensitive to the operative transport process as well as to a number of model parameters including the pressure constraint, the total furnace pressure, the reaction kinetics, the gas permeability, and the diffusivity as described by the free volume theory. Strategies were identified which are most effective for decreasing the cycle time for each mass transfer mechanism.     

On the in‐situ polymerization of cyclic butylene terephthalate oligomers: DSC and rheological studies

The thermal and rheological behaviors of cyclic butylene terephthalate (CBT) were studied with differential scanning calorimetry (DSC) and plate–plate rheometry, respectively. DSC scans were taken at different heating rates. The related first‐heat thermograms indicated crystallization and melting of the resulting poly (butylene terephthalate) (PBT) only at very low heating rate (0.5°C/min). As the crystallization and melting enthalpies were closely matched, one could conclude that the polymerization is essentially athermic. The polymerization was accompanied by a steep increase of the melt viscosity in isothermal rheological tests performed in the temperature range T = 145–210°C. Changes in the viscoelasticity of the polymerizing CBT and crystallizing PBT could be best followed by considering the changes in the phase angle. Viscosity increased with the conversion exponentially in the first approximation. POLYM. ENG. SCI., 46:743–750, 2006. © 2006 Society of Plastics Engineers     

Kinetics and crystallization in pH‐sensitive free‐radical crosslinking polymerization of acrylic acid

Free‐radical crosslinking polymerization and crystallization of acrylic acid (AAc) were investigated by shear storage modulus (G′) measurements in pH 2, as well as in pH 6 and pH 10, by varying the molar ratio of crosslinking agent (N,N′‐methylene bis‐acrylamide; MBAAm) to AAc (0.583 × 10^?3, 1.169 × 10^?3, 1.753 × 10^?3, and 2.338 × 10^?3). Our results showed that the pre‐gelation time was the same at pH 2, regardless of the concentration of MBAAm. The propagation time was determined by the initial feed concentration of AAc, and the length of the linear curve in the propagation was proportional to the concentration of MBAAm. The Avrami exponent (n), as an indicative of growing pattern of an infinite molecule, in the crystallization was increased in proportional to the concentration of MBAAm, and generally low at pH 2. In the deceleration phase, n was observed near 1.0 throughout the all specimens. These results indicated that (1) the length of the pre‐gelation period was determined by the ionization of AAc (or pH), (2) the polymerization rate of AAc was not affected by the concentration of MBAAm, and (3) the inhomogeneity of hydrogel was determined by the growing pattern of infinite molecule in propagation phase. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42195.     

Kinetics of microwave‐assisted polymerization of ϵ‐caprolactone

The kinetics of polymerization of ?‐caprolactone (CL) in bulk was studied by irradiating with microwave of 350 W and frequency of 2.45 GHz with different cycle‐heating periods (30–50 s). The molecular weight distributions were determined as a function of reaction time by gel permeation chromatography. Because the temperature of the system continuously varied with reaction time, a model based on continuous distribution kinetics with time/temperature‐dependent rate coefficients was proposed. To quantify the effect of microwave on polymerization, experiments were conducted under thermal heating. The polymerization was also investigated with thermal and microwave heating in the presence of zinc catalyst. The activation energies determined from temperature‐dependent rate coefficients for pure thermal heating, thermally aided catalytic polymerization, and microwave‐aided catalytic polymerization were 24.3, 13.4, and 5.7 kcal/mol, respectively. This indicates that microwaves increase the polymerization rate by lowering the activation energy. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1450–1456, 2004     

Solid‐state polymerization of melt‐spun poly(ethylene terephthalate) fibers and their tensile properties

The production of high modulus and high strength poly(ethylene terephthalate) fibers was examined by using commercially available melt‐spun fibers with normal molecular weight (intrinsic viscosity = 0.6 dL/g). First, molecular weight of as‐spun fibers was increased up to 2.20 dL/g by a solid‐state polymerization, keeping the original shape of as‐spun fibers. Second, the polymerized as‐spun fibers were drawn by a conventional tensile drawing. The achieved tensile modulus and strength of as‐drawn fibers (without heat setting) were 20.0 and 1.1 GPa, respectively. A heat setting was carried out for the as‐drawn fibers. Tensile properties of the treated fibers were greatly affected by the condition of the heat setting. This was related to the increase of sample crystallinity and molecular degradation during the treatments. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1791–1797, 2007