Kinetics and modeling of the diffusion‐controlled diallyl terephthalate polymerization

Free radical polymerization kinetics of diallyl terephthalate in bulk was investigated in a wide temperature range from 50°C to 150°C with four different peroxide initiators. Conversion points were measured using Fourier Transform Infrared (FTIR) measurements. The initiator efficiencies and the initiator decomposition rate constants were evaluated from special experiments, applying the theory of dead end polymerization. In addition, the ratios between the degradative and the effective kinetic rate constants to propagation rate constants were obtained from molecular weight measurements at various initiator concentrations. The ratio of chemically controlled termination and propagation rate constant k/k_tc of the polymerization system was obtained using the initial rates of polymerization and the number average molecular weight data between 0.25 · 10^?3 and 15.7 · 10^?3 L mol^?1 s^?1. The glass transition temperature of the polymer, 191°C, was measured by the Alternating Differential Scanning Calorimetry (ADSC) technique. Computed conversions from the developed kinetic model were in good agreement with the conversion and molecular weight measured data. The values of diffusion controlled propagation and termination rate constants k_td0 and k_pd0 with clear and physical meaning were the only two parameters obtained from the developed kinetic model fitting. Polym. Eng. Sci. 44:2005–2018, 2004. © 2004 Society of Plastics Engineers.     

Specific hydroxide ion catalysis of the endwise depolymerization of cellulose

The endwise depolymerization (unzipping reaction) of hydrolyzed cotton cellulose (x = 200) in water under a nitrogen atmosphere was followed at 98°C at several alkalinities in the pH range of 8.0–10.5. The observed apparent first-order rate constant k₁ was invariable at low alkalinity (k₁ = k₀), while above pH 8.5, k₁ increased with pH. The data conform with the expression where [SH] denotes substrate concentration. The specific hydroxide ion catalysis is considered to involve ionization of the anomeric hydroxyl group at the reducing chain end that leads to elimination of the glucosidic oxygen atom bearing the polymer chain from C4 of the terminal D-glucose residue. In this initiation process, the glucosidic oxygen is eliminated as an anion so that rapid propagation of the unzipping along the polymer chain may occur. Thus, entire chains will depolymerize. The kinetic chain length v is defined as the ratio k₁:k_t, where k_t is the pseudofirst-order rate constant for chain terminations, and a value of v ～ 100 D-glucose residues was found at all the alkalinities investigated.     

Radiation-induced polymerization of ethylene in pilot plant. IV. Kinetic analysis

The kinetics of the radiation-induced polymerization of ethylene in a flow system using tert-butyl alcohol aqueous solution as a medium were studied. The polymerization was carried out in a large-scale pilot plant with a 50-liter central source-type reactor at various mean residence times and does rates under constant pressure of 300 kg/cm², temperature of 30°C, and ethylene molar fraction of ca. 0.4. The reaction mixture in the reactor was back-mixed flow from the residual polymer concentration in the reactor. The results of the polymerization were analyzed by kinetic treatment based on a reaction mechanism with both first-and second-order terminations for the propagating radical. The apparent rate constants, except for that of second-order termination (k_t2), were consistent with those determined by small-scale batch experiments. The k_t2 is 20 to 40 times larger than that in the batch experiments. The k_t2 increases with decrease in mean residence time and with agitation, probably because of mobility of the propagating radical.     

Extracting kinetic parameters of aniline polymerization from thermal data of a batch reactor. simulation of the thermal behavior of a reactor

A simulation model of the thermal behavior of a reactor during aniline polymerization is proposed. The model takes into account the polymerization mechanism together with heat production and dissipation. The temperature–time profiles can be simulated with different kinetic parameters. The model is used for two purposes: to extract kinetic parameters by fitting experimental temperature–time profiles of a cooled agitated batch reactor; and to estimate the temperatures changes occurring in a reactor under different experimental conditions to find the best conditions for industrial production of polyaniline. The rate equation used includes two rate constants: one in the absence of polymer (k₁) and another in the presence of polymer (k₂). The thermal factors, such as the heat transfer coefficient and the reaction enthalpy, are experimentally measured. A computer program is written that fits the experimental data using different kinetic parameters. The data analysis shows a temperature peak (T_max) whose magnitude decreases when k₂ decreases, whereas it is not affected by k₁. The time to reach the T_max is inversely proportional to k₁ and k₂. The model allows obtaining the kinetic parameters in different reaction media, e.g. varying the concentration of acid. The model is used to simulate the thermal behavior, to polymerize 1M of aniline: in one step the temperature of the reactor will increase till 82ºC, such thermal runaway will cause polymer degradation, successive additions of portions of the total oxidant amount, paced at defined time intervals, is devised to maintain low temperatures while producing the same amount of polymer. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39409.     

Solvent effects in butyl acrylate and vinyl acetate homopolymerizations in toluene

A series of butyl acrylate (BA) and vinyl acetate (VAc) homopolymerizations in toluene was conducted to investigate the effect of solvent at different solvent and chain transfer agent (CTA) concentrations. Because the experimental determination of the individual propagation and termination rate constants for these systems is challenging, experimental observations were limited to the lumped rate constant (k_p/k). Differences in the lumped rate constant, at different solvent and CTA concentrations, were assumed to be attributed to the effect of solvent on the termination rate constant. Our hypothesis was that the termination rate constant k_t was affected by the presence of solvent. At higher solvent concentrations, chain transfer to solvent occurs more frequently and leads to the formation of shorter chains, which move more easily and are able to terminate more quickly compared to longer chains. Thus, k_t will increase, leading to a decrease in the lumped rate constant. The experimental results confirmed the presence of a solvent effect on the lumped rate constant. This effect was more pronounced in the case of VAc compared to BA solution homopolymerizations. Under the investigated conditions, increased CTA concentrations did not substantially affect the rate of BA homopolymerizations, whereas a slight synergistic effect between the CTA and solvent at higher CTA and solvent concentrations was apparent for VAc homopolymerizations. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 871–876, 2004     

Monomolecular chain termination in the kinetics of dimethacrylate postpolymerization

The kinetics of postpolymerization (after ultraviolet illumination was stopped) for a number of dimethacrylates that differed by nature and molecular mass was experimentally studied over a wide range of temperatures. A series of kinetic curves that differed by the starting conversion of the dark period of time was obtained for every temperature. The proposed kinetic model of the process is based on the following main principles: (1) the process at an interface on the liquid monomer–solid polymer (micrograins) boundary takes a main share of the kinetics of postpolymerization; (2) chain termination at an interface is monomolecular, is controlled by the chain propagation rate, and represents by itself the self‐burial act of active radicals in the conformation trap; and (3) monomolecular chain termination is characterized by a wide spectrum of characteristic times and that is why the function of the relaxation is described by Kohlrausch's stretched exponential law. The obtained kinetic equation was in good agreement with all of the sets of experimental data. This permitted us to estimate the rate constant of chain termination (k_t) and to determine the scaling dependence of k_t on the molar‐volumetric concentration of the monomer in bulk [M₀]. We assumed that the stretched exponential law and scaling dependence k_t from [M₀] were characterized by common peculiarities, namely, a wide range of characteristic times of relaxation possessed by a property of the fractal set. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2376–2382, 2004     

New approach for the estimation of kinetic parameters in emulsion polymerization systems. II. Homopolymerization under conditions where n̄ > 0.5

A new approach for the estimation of kinetic parameters in emulsion polymerization systems in which the average number of radicals per particle exceeds 0.5 is presented. The approach uses the time evolution of the conversion in chemically initiated systems and is based on a model that includes fundamental parameters such as the propagation rate constant, k_p, the termination rate constant in the polymer particles, k_t, the rate coefficient for initiator decomposition, k_I, and the entry, k_a, and exit, k_d, rate coefficients. It was found that k_p, k_t, k_I, k_a, and, under some circumstances, k_d can be accurately estimated provided that termination in the aqueous phase is significant. When the extent of the aqueous phase termination is negligible, only k_p, k_t, and k_I can be estimated. The effect of both the experimental noise level and the run-to-run irreproducibility on the accuracy of the estimates was studied. In addition, it was found that significant inaccuracies resulted from the poor determination of the exact time when polymerization begins. A method to circumvent this problem was proposed.     

Termination rate coefficients for acrylamide in the aqueous phase at low conversion

The kinetics of acrylamide (AAm) free radical polymerization at low conversion of monomer to polymer in the aqueous phase was investigated at 50 °C using γ-radiolysis relaxation, which is sensitive to radical-loss processes. The values of the termination rate coefficients for AAm ranged from 8×10⁶ to 3×10⁷ M⁻¹ s⁻¹ as the weight fraction of polymer ranged from 0.002 to 0.0035, which is significantly lower than the low-conversion values for monomers such as styrene (2×10⁸ M⁻¹ s⁻¹) and methyl methacrylate (4×10⁷ M⁻¹ s⁻¹) in organic media. These can be quantitatively explained by applying a chain-length-dependent model of free-radical polymerization kinetics [Russell GT, Gilbert RG, Napper DH. Macromolecules 1992;25:2459. [19]] in which termination kinetics are expressed in terms of a diffusion-controlled encounter of radicals which ultimately yields an expression for the chain-length-averaged termination rate coefficient, 〈k_t〉. The lower 〈k_t〉 for AAm arises due to a combination of the high k_p value, promoting rapid formation of slower terminating long chains, and the slow diffusion of short propagating chains, relative to other common monomers. The chain transfer to monomer constant for AAm in water at 50 °C, C_M, was estimated using the chain-length-distribution method with correction for band-broadening [Castro JV, van Berkel KY, Russell GT, Gilbert RG. Aust J Chem 2005;58:178. [21]] and found to be 1.2×10⁻⁴ (±10%). The diffusion characteristics for AAm were adapted from those obtained for a similar aqueous system (hydroxyethyl methacrylate) together with a 0.5 exponent for the power law dependence on penetrant degree of polymerization at zero weight fraction polymer. This provides an adequate fit to the 〈k_t〉 data. This is the first application of the chain-length-dependent model to describe experimental termination rate coefficients for an aqueous system at low conversion to polymer. The result that the experimental termination rate coefficients can be reproduced with an a priori model with physically reasonable parameters supports the physical assumptions underlying that model.     

Zur physikalisch‐chemischen Charakterisierung von 5‐Amino‐1‐aryl‐1H‐tetrazolen: Kinetik der Verteilung im Zweiphasensystem Octan‐1‐ol/Wasser

The kinetics of distribution of 27 5‐amino‐1‐aryl‐1H‐tetrazoles in the two‐phase system octan‐1‐ol/water were investigated UV/Vis‐spectrophotometrically at various temperatures. Studies on relationships between the obtained firstorder rate constants (logk₁, logk₂) and the hydrophobicity of the tetrazoles described by their partition coefficients (logP) show a nearly constant rate of transport from the aqueous to the organic phase (k₁) above logP = 1,5 while the reverse rate (k₂) strongly depends on hydrophobicity. In the whole logP range investigated the kinetic behaviour can be described by bilinear relationships between logk and logP corresponding to known kinetic models for distribution processes in two‐layer systems.     

Kinetics of graft copolymerization of methyl methacrylate in wool fibers

The graft copolymerization of methyl methacrylate in wool fibers was investigated in the aqueous LiBr–K₂S₂O₈ system without homopolymer. The rate of grafting and the degree of polymerization of graft polymer were determined on varying the extent of reduction of wool fibers and the concentration of monomer. From the graft copolymerization behavior observed at a given concentration of redox catalysts (LiBr and K₂S₂O₈), the thiol groups in wool fibers were considered to play a role as a sort of catalyst of polymerization, not as the chain transfer agent, and also to give the grafting sites. So, the initiation process of grafting was assumed to be started by d[S·]/dt = k_i[SH]_eff, and the kinetic consideration was found to lead to the following expression in agreement with the experimental results: 1/DP = (k_t/k_p²[M]_fib²)R_p, where d[S·]/dt is the rate of formation of thiol radicals by radicalotropy to ? SH from SO₄^?., OH·, or Br·; k_i, k_p, and k_t are the rate constants of initiation, propagation, and termination, respectively; [SH]_eff and [M]_fib are the concentration of the effective thiol groups and the MMA monomers within the wool fibers, respectively; DP is the average degree of polymerization of graft polymers, and R_p the overall rate of grafting.     

In silico mechanically mediated atom transfer radical polymerization: A detailed kinetic study

Mechanically mediated atom transfer radical polymerization (mechanoATRP) utilizing ultrasound to generate activators and improve the diffusivity of macromolecular chains is introduced as an innovative externally controlled ATRP. Herein, a comprehensive kinetic model with free volume theory based “series” encounter pair model accounting for diffusional limitations on termination, activation, and deactivation is developed for the mechanoATRP of methyl acrylate. Comparative study by using different diffusion models, for example, w_p model and reduced composite k_t model, as well as constant apparent k_j^app model confirms the goodness of the as-developed model. Critically, mechanochemically induced reduction rate coefficient k_r,s as a key kinetic parameter is associated with experimental conditions excluding the sonication effect by a fitting equation for the first time. In silico tracking of polymer dispersity with the help of kinetic model shows a better result compared with that by the classical dispersity equation. By defining an ultrasonic factor γ_j, a qualitative analysis for the effect of ultrasound conditions on the diffusional limitation in mechanoATRP is presented.     

An experimental/computational study of steric hindrance effects on CO2 absorption in (non)aqueous amine solutions

The reaction kinetics and molecular mechanisms of CO₂ absorption using nonaqueous and aqueous monoethanolamine (MEA)/methyldiethanolamine (MDEA)/2-amino-2-methy-1-propanol (AMP) solutions were analyzed by the stopped-flow technique and ab initio molecular dynamics (AIMD) simulations. Pseudo first-order rate constants (k₀) of reactions between CO₂ and amines were measured. A kinetic model was proposed to correlate the k₀ to the amine concentration, and was proved to perform well for predicting the relationship between k₀ and the amine concentration. The experimental results showed that AMP/MDEA only took part in the deprotonation of MEA-zwitterion in nonaqueous MEA + AMP/MEA + MDEA solutions. In aqueous solutions, AMP can also react with CO₂ through base-catalyzed hydration mechanism beside the zwitterion mechanism. Molecular mechanisms of CO₂ absorption were also explored by AIMD simulations coupled with metadynamics sampling. The predicted free-energy barriers of key elementary reactions verified the kinetic model and demonstrated the different molecular mechanisms for the reaction between CO₂ and AMP.     

Competitive primary amine/epoxy and secondary amine/epoxy reactions: Effect on the isothermal time-to-vitrify

The effect of temperature on the ratio of the kinetic rate constants, k₂/k₁, has been investigated using FTIR spectroscopy for the competing reactions of epoxy with secondary amine (k₂) and primary amine groups (k₁) in a trimethylene glycol di-p-aminobenzoate/diglycidyl ether of the bisphenol A system. The ratio of the rate constants increases from 0.16 to 0.33 in the temperature range 100?160°C. The corresponding difference in the activation energies for the competing reactions is about 3.7 kcal/mol. The effect of the ratio on the time-to-vitrify contour of the isothermal time–temperature–transformation (TTT) cure diagram is discussed: The effect is more significant at higher curing temperatures.     

Kinetic study by differential scanning calorimetry of the bulk copolymerization of 2‐hydroxyethylmethacrylate with ethyleneglycoldimethacrylate

This article presents a kinetic study of the copolymerization of 2‐hydroxyethylmethacrylate (HEMA) with ethyleneglycoldimethacrylate (EGDMA). First, the rate constant of decomposition, k_d, of azobisisobutyronitrile (AIBN) used to initiate the copolymerization was investigated. Then, the reactivity ratios, r₁ and r₂, of the monomers (HEMA and EGDMA), and the termination rate constant, k_t, were determined. Rate constants were obtained by differential scanning calorimetry (DSC) experiments. The decomposition rate constant of AIBN follows an Arrhenius law in the temperature range 320–400 K. Copolymerizations were carried out in the pans of the DSC apparatus at 353 K. The reactivity ratios, determined after analysis of the mixture composition by gas chromatography, exploitation of the data using the Meyer and Lowry equation, and a numerical method, were found equal to r₁ = 0.811 and r₂ = 6.548. Also from the reaction rate obtained by DSC, the dependence of the termination rate constant with conversion and temperature has been established. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1220–1228, 2001     

A kinetic study on the autocatalytic cure reaction of a cyanate ester resin

The cure of a novolac‐type cyanate ester monomer, which reacts to form a polycyanurate network, was investigated by using differential scanning calorimeter. The conversions and the rates of cure were determined from the exothermic curves at several isothermal temperatures (513–553 K). The experimental data, showing an autocatalytic behavior, conforms to the kinetic model proposed by Kamal, which includes two reaction orders, m and n, and two rate constants, k₁ and k₂. These kinetic parameters for each curing temperature were obtained by using Kenny's graphic‐analytical technique. The overall reaction order was about 1.99 (m = 0.99, n = 1.0) and the activation energies for the rate constants, k₁ and k₂, were 80.9 and 82.3 kJ/mol, respectively. The results show that the autocatalytic model predicted the curing kinetics very well at high curing temperatures. However, at low curing temperatures, deviation from experimental data was observed after gelation occurred. The kinetic model was, therefore, modified to predict the cure kinetics over the whole range of conversion. After modification, the overall reaction order slightly decreased to be 1.94 (m = 0.95, n = 0.99), and the activation energies for the rate constants, k₁ and k₂, were found to be 86.4 and 80.2 kJ/mol. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3067–3079, 2004     

Binary biopolymeric beads of alginate and gelatin as potential adsorbent for removal of toxic Ni2+ ions: A dynamic and equilibrium study

Binary biopolymeric beads of alginate and gelatin were prepared and characterized by IR spectral and scanning electron micrograph techniques. On to the surfaces of the prepared beads were performed static and dynamic adsorption studies of Ni²⁺ ions at fixed pH and ionic strength of the aqueous metal ion solutions. The adsorption data were applied to Langmuir and Freundlich isotherm equations and various static parameters were calculated. The dynamic nature of adsorption was quantified in terms of several kinetic constants such as rate constants for adsorption (k₁), Lagergreen rate constant (k_ad), interparticle diffusion rate constant (k_p), and pore diffusion coefficient (D ). The influence of various experimental parameters such as solid to liquid ratio, pH, temperature, presence of salts, and chemical composition of biopolymeric beads on the adsorption of nickel ions was investigated. Various thermodynamic parameters were also calculated. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2581–2590, 2007     

A pseudo first order rate model for the adsorption of an organic adsorbate in aqueous solution

Five low rank, coal‐based adsorbents, i.e. coal, grus, two chars, and an activated carbon were used to adsorb a low molecular weight organic compound from aqueous solution. The rates of adsorption were found to conform to pseudo first order kinetics with good correlation (r² greater than 0.996). This kinetic model was used to calculate pseudo first order rate constants (k₁^′ min ⁻¹) and relative rate constants (rate constant/unit mass of adsorbent, k₁^″ min⁻¹ g⁻¹) for the adsorption process. Rate properties have been explained in terms of both a diffusion and chemically controlled rate determining step. Rate constants for the five adsorbents vary as expected on the basis of their physical properties, that is slowest for grus (compressed coal) and fastest for the activated carbon. © 1999 Society of Chemical Industry     

A kinetic model of persulfate–bisulfite-initiated acrylonitrile polymerization

The molecular weight distribution has been derived for a homopolymer polymerized in a continuous-feed reactor under homogeneous conditions. The derived equations are then compared with data obtained on polymers of acrylonitrile–co(vinyl acetate) prepared under heterogeneous conditions with the potassium peroxydisulfate–sodium bisulfite–iron redox system. The termination reaction is assumed to be effected completely by recombination of active radicals with no disproportionation. The only transfer reaction considered is the transfer-to-activator reaction The transfer and termination reactions produce polymers with different acid groups as endgroups. Each molecule, on the average, contains one sulfonate group, whereas the concentration of sulfate groups depends upon the extent of the transfer-to-activator reaction. The basic dye acceptance of the polymer depends on the number of acid groups in the polymer and hence on the activator and catalyst concentrations. Analysis of the basic dye acceptance and conversion data at a variety of catalyst and activator concentrations yields the following parameters at 50°C: k_p/k = 1.01 (1./mole sec)^1/2, k_tr/k_p = 0.2063, and k₁ [see eq. (1)] = 50.7 l./mole sec. Owing to the heterogeneous nature of the polymerization, the weight-average molecular weight of the polymer depends only on the activator concentration and the conversion and not directly on the catalyst concentration as predicted.     

‘Nano-tree’—type spherical polymer brush particles as templates for metallic nanoparticles

We present a new type of spherical polymer brush particles that consist of a solid poly(styrene) core (diameter: ca. 100 nm) onto which chains of a bottlebrush polymer have been densely grafted. These systems were prepared in aqueous dispersion by photo emulsion-polymerization using the macromonomer poly(ethylene glycol) methacrylate (PEGMA). In opposite to conventional spherical polyelectrolyte brushes carrying linear polymer chains, the system prepared here has a shell consisting of regularly branched chains (‘nano-tree’-type morphology). The branches consist of oligo(ethylene glycol) chains (n=13) terminated by a hydroxyl group. We demonstrate that these particles can be used as nanoreactors for the generation and immobilization of well-defined silver nanoparticles. Cryo-TEM and FESEM images show that Ag nanoparticles with diameter of ∼7.5±2 nm are homogeneously embedded into the PS-PEGMA brushes. Moreover, the composite particles exhibit an excellent colloidal stability. The catalytic activity is investigated by monitoring the reduction of 4-nitrophenol by NaBH₄ in presence of these silver nano-composite particles. The rate constant k_app was found to be strictly proportional to the total surface of the nanoparticles in the system. The study of the temperature dependence shows that the rate constants k_app obtained at different temperatures leads to an activation energy of 62 kJ/mol.     

Rheo‐kinetic evaluation on the formation of urethane networks based on hydroxyl‐terminated polybutadiene

Rheo‐kinetic studies on bulk polymerization reaction between hydroxyl‐terminated polybutadiene (HTPB) and di‐isocyanates such as toluene‐di‐isocyanate (TDI), hexamethylene‐di‐isocyanate (HMDI), and isophorone‐di‐isocyanate (IPDI) were undertaken by following the buildup of viscosity of the reaction mixture during the cure reaction. Rheo‐kinetic plots were obtained by plotting ln (viscosity) vs. time. The cure reaction was found to proceed in two stages with TDI and IPDI, and in a single stage with HMDI. The rate constants for the two stages k₁ and k₂ were determined from the rheo‐kinetic plots. The rate constants in both the stages were found to increase with catalyst concentration and decrease with NCO/OH equivalent ratio (r‐value). The ratio between the rate constants, k₁/k₂ also increased with catalyst concentration and r‐value. The extent of cure reaction at the point of stage separation (x_i) increased with catalyst concentration and r‐value. Increase in temperature caused merger of stages. Arrhenus parameters for the uncatalyzed HTPB‐isocyanate reactions were evaluated. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1869–1876, 2001