Heterogeneous chain propagation in low-pressure flames

An analysis of papers on hydrogen combustion at low pressures is performed, which refines the contribution of the catalytic reactions on the reactor wall to the gas-phase part of the process. A new model for the heterogeneous loss of active reaction centers was proposed and tested experimentally to explain inconsistencies that occur in some papers. In this model, the diffusion region of chain termination is formed under standard experimental conditions in vacuum oxyhydrogen flames at a reactor gas pressure a thousand times lower than the boundary pressure postulated by the previous models as the pressure below which the diffusion region of chain termination cannot be formed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 10–18, March–April, 2006.     

Heterogeneous chain propagation on a quartz surface

Results of experimental and analytical studies of heterogeneous chain processes on quartz are given. A calculation is made of the ignition of an oxyhydrogen mixture in a quartz reactor under conditions of intense heterogeneous negative interaction of chains in the kinetic and diffusion regions. An energy criterion was developed experimentally that allows one to distinguish the range of reactions with an elevated probability of heterogeneous chain propagation on quartz. The possibility of the formation of atoms and radicals on the surface of quartz and conditions for their passage into the bulk are studied. The possibility of passage of hydrogen atoms from a microporous SiO₂ surface into the bulk is analyzed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 3, pp. 42–52, May–June, 2006.     

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     

Catalytic Combustion of the Stoichiometric n-Butane/Air Mixture on Isothermally Heated Platinum Wire

The catalytic combustion of the stoichiometric n-butane–air mixture per se or diluted with N₂, on a platinum wire at different initial pressures (10–70 kPa) and temperatures (690–1,080 K) was studied. The chemical heat flow rate, dQ _r/dt, of the surface reaction was measured in isothermal and isobaric conditions and the overall kinetic parameters were evaluated for both steady state and initial transient catalytic combustion. At low total pressure (10 kPa), the temperature dependence of dQ _r/dt indicated a normal (Arrhenius) behavior for 690 < T < 900 K, while at higher temperatures, over 900 K, an anti-Arrhenius behavior was found. The obtained results are consistent with a diffusion-controlled process, accompanied by reactant depletion around the catalytic surface, at higher temperatures.     

Kinetics and mechanism of cationic oligomerization of styrene using poly(styrenesulphonic acid) resin as catalyst

The cationic oligomerization of styrene in benzene using poly(styrenesulphonic acid) resin as catalyst, was carried out under nitrogen. A kinetic model involving initiation, propagation, chain transfer to monomer and spontaneous termination steps, is proposed to fit the experimental kinetic data. It is found that (1) the propagation constant decreases with increasing chain length and remains constant as $\text{n ≧ 5}$; (2) the constant for chain transfer to monomer is also chain length dependent and reaches a maximum at n = 4.     

Kinetics of all-trans-β-carotene degradation on heating with and without phenylalanine

All-trans-β-carotene was heated in liquid paraffin at 210°C for 15 min in the presence and the absence of phenylalanine to assess the effect of the amino acid on the rate of degradation of all-trans-β-carotene. The curve that represents all-trans-β-carotene degradation in both model systems is formed of two distinct parts that correspond, respectively, to the propagation and termination phases of an autocatalytic reaction. The reaction over 1–15 min followed first-order reaction kinetics in both systems, and the rate constant obtained was 2.8 times lower in the presence of phenylalanine. The kinetic behavior and the rate constant for color loss were similar to those for all-trans-β-carotene degradation for each model system.     

Suspension,bulk, and emulsion polymerization of vinyl chloride—mechanism,kinetics, and reactor modelling

A review of relevant microscopic processes, both chemical and physical, which occur during suspension, bulk and emulsion polymerization (both before and after pressure drop) is given. The state of the art of kinetic modelling of monomer consumption rate, reactor pressure, molecular weight and short and long chain branching development and polymer chain microstructure is illustrated. The effects of diffusion-controlled termination and propagation reactions and the significant decrease in initiator efficiency and decomposition rate constant at high monomer conversions on the relative rates of various chemical reactions are discussed. The application of temperature programming and semibatch operation are emphasized. Finally, attempts to model polymer particle morphology are described.     

RAFT with Bulk and Solution Polymerization: An Approach to Mathematical Modelling and Validation

Reversible addition fragmentation chain transfer (RAFT)-mediated polymerization is a novel technique used to impart a living character in free radical polymerization. A mathematical model accounting for the concentrations of the propagating, intermediate, dormant and dead chains is developed based on their reaction pathways. The kinetic scheme used includes initiation, propagation, pre-equilibrium, core-equilibrium and termination of the propagating radicals along with termination reactions of the carbon-centered intermediate radical. This model is combined with chain-length dependant termination model in order to account for the decreased termination rate. The model has been validated against experimental data for solution polymerization of styrene with dithiobenzoate at 80°C. The fragmentation rate coefficient was used as a model parameter and a value equal to 6×10⁴ sec^?1 was found to provide a good agreement with the experimental data. The model predictions indicate that the observed retardation can be attributed to the cross termination of the intermediate radical and, to some extent, to the RAFT effect on increasing the average termination rate coefficient. The hypothesised irreversible self termination was found to have a negligible effect on the polymerization rate. While the linear growth of the number average molecular weight along with the low polydispersity, reveal the living nature of RAFT agent and the importance of the transfer constant in controlling these properties.     

Effect of nano-nucleating agent addition on the isothermal and nonisothermal crystallization kinetics of isotactic polypropylene

Using differential scanning calorimetry (DSC) technique, a comparative study has been made of the isothermal and nonisothermal crystallization kinetics of nonnucleated isotactic polypropylene (iPP) and of nucleated iPP with 0.5 wt% of single-walled carbon nanotubes (SWCNTs) as a nucleating agent. The Avrami exponents (n) of iPP and nucleated iPP are close to 3.0 for isothermal crystallization. These results indicate that the addition of nucleating agents did not change the crystallization growth patterns of the neat polymer and that crystal growth was heterogeneous three-dimensional spherulitic. The results show that the addition of SWCNTs can shorten the crystallization half-time (t _1/2) and increase the crystallization rate of iPP. In the nonisothermal crystallization process, the Ozawa model failed to describe the crystallization behavior of nucleated iPP. The Cazé–Chuah model successfully described the nonisothermal crystallization process of iPP and its nanocomposite. A kinetic treatment based on the Ziabicki theory is presented to describe the kinetic crystallizability, in order to characterize the nonisothermal crystallization kinetics of iPP and nucleated iPP. Polarized light microscopy (PLM) experiments reveal that SWCNTs served as nucleating sites, resulting in a decrease of the spherulite size.     

Kinetics studies of dimethyl carbonate synthesis from urea and methanol over ZnO catalyst

A kinetic experiment of dimethyl carbonate (DMC) synthesis by urea methanol over ZnO catalyst was carried out in an isothermal fixed-bed reactor. A kinetic model based on the mole fraction was proposed and the kinetic parameters were estimated from the experimental results. The model predictions were compared with the experimental data and fair agreements were found. The effects of the reaction temperature (443–473 K), space time (0–4.7 h mol⁻¹ kg _cat ) and urea mass percent (5–9%) in feed on DMC mole fraction were investigated. It was found that the reactions are mainly influenced by the reaction temperature and space time rather than urea mass percent in feed. The experimental and simulated results indicated that the reaction from MC to DMC was the rate-controlling step in the DMC synthesis process from urea and methanol. It is important to remove the DMC and byproduct ammonia to achieve a high selectivity of DMC. This implies that reactive distillation might be used in the DMC synthesis on an industrial scale to achieve a higher selectivity of DMC.     

Free-radical polymerization of styrene with a binary mixture of symmetrical bifunctional initiators

The kinetics of bulk styrene polymerization catalyzed by a binary mixture of symmetrical bifunctional initiators has been investigated. When the bifunctional initiators having different thermal stabilities are mixed, an unsymmetry in the initiator functions is formed in situ via propagation, chain transfer, and termination reactions. For the quantification of the polymerization kinetics, a kinetic model has been developed using the molecular species modeling technique. For various polymerization conditions, good agreements between the model predictions and experimental data have been obtained. It is shown that polymerization rate and molecular weight can be easily regulated under isothermal reaction condition by changing the initiator composition. A comparison of the detailed kinetic model with a simple kinetic model for monofunctional initiators has also been made to illustrate the molecular weight increasing effect of the bifunctional initiator system. © 1992 John Wiley & Sons, Inc.     

Numerical Simulation of Single Aluminum Particle Combustion (Review)

A two-dimensional, unsteady-state, kinetic-diffusion-vaporization-controlled numerical model for aluminum particle combustion is presented. The model solves the conservation equations, while accounting for species generation and destruction with a 15-reaction kinetic mechanism. Two of the major phenomena that differentiate aluminum combustion from hydrocarbon-droplet combustion, namely, condensation of the aluminum-oxide product and subsequent deposition of part of the condensed oxide onto the particle, are accounted for in detail with a submodel for each phenomenon. The effect of the oxide cap in the distortion of the species and temperature profiles around the particle is included into the model. The results obtained from the model, which include two-dimensional species and temperature profiles, are analyzed and compared with experimental data. The combustion process is found to approach a diffusion-controlled process for the oxidizers (O₂, CO₂, and H₂O) and conditions treated. The flame-zone location and thickness are found to vary with the oxidizer. The result shows that the exponent of the particle-diameter dependence of the burning time is not a constant and changes from ≈1.2 for smaller-diameter particles to ≈1.9 for larger-diameter particles. Owing to deposition of the aluminum oxide onto the particle surface, the particle velocity oscillates. The effect of pressure is analyzed for a few oxidizers. __________ Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 6, pp. 15–33, November–December, 2005.     

Continuous precipitation polymerization of vinylidene fluoride in supercritical carbon dioxide: A model for understanding the molecular-weight distribution

Poly(vinylidene fluoride) (PVDF) that is synthesized by precipitation polymerization in supercritical carbon dioxide (scCO₂) has a bimodal molecular weight distribution (MWD) and a very broad polydispersity index (PDI) under certain reaction conditions. Different models have been formulated to account for this behavior. This paper presents a homogenous model for a continuous stirred-tank reactor (CSTR) that includes the change of the termination reaction from kinetic control to diffusion control as the chain length of the polymeric radicals increases, and accounts for the change in the termination rate constant with macroradical chain length in the diffusion-controlled region. The model also includes the chain transfer to polymer reaction. Comparison of the model output with experimental data demonstrates that changes of the MWD, including the development of a bimodal distribution, with such reaction conditions as monomer concentration and average residence time are successfully predicted. In addition, the model can capture the occurrence of gelation, which appears to be responsible for a region of inoperability that was observed in the polymerization experiments. The success of this homogeneous model is consistent with recent research demonstrating that the CO₂-rich phase is the main locus of polymerization for the precipitation polymerization of vinylidene fluoride and vinylidene fluoride/hexafluoropropylene mixtures in scCO₂, at the conditions that have been studied to date.     

Macrokinetics of physicochemical condensation in two-phase systems of the gas-solid body type

The macrokinetics of the phase evolution at the microscopic level under isothermal and nonisothermal conditions is analyzed theoretically within the framework of a two-scale approach for describing physicochemical condensation processes in two-phase systems. Scenarios are established for the transformation of the condensed particles in a chemically active medium, taking into account the exothermal nature of the reaction, the finiteness of heat- and mass-transfer rates, and the phase transformations. The equilibrium constant of the heterogeneous reactions is shown to have a significant effect on the conditions of evaporation, or the increase in the incipient condensation phase. An analytical criterion is obtained for controlling the phase transformation in a reaction-capable medium, and it is supported by numerical calculations. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 3, pp. 37–45, May–June 1998.     

High-conversion diffusion-controlled polymerization of styrene. I

A kinetic model based on the free volume theory has been proposed for the polymerization of styrene. The model, which is capable of describing the course of polymerization in both bulk and solution, accounts for diffusion-controlled termination and propagation and gives a limiting conversion.     

Selecting the conditions of molding iron oxide catalysts for dehydrogenation

The effect of the conditions for molding iron oxide catalysts for dehydrogenation of iso-amylenes to isoprene on their operation characteristics was studied. The investigation of laboratory samples allowed us to determine the optimum molding pressure (200–250 MPa) under which high mechanical strength (strength factor K _G = 33.4–37.3 N/mm), the stability of the kinetic characteristics in the dehydrogenation reaction, and the formation of 15–50 nm pores, ensuring the occurrence of the process in the kinetic region, were attained. we propose using the extrudate density as an indirect criterion for estimating the molding pressure under industrial conditions of extrusion. It was shown that in order to develop high strength properties (K _G ∼ 29.1 N/mm) of the catalysts upon their production under industrial conditions and to ensure the occurrence of the reaction in the kinetic region, the extrudate density must be 2.40–2.46 g/cm³. The obtained results were verified via paste molding on various industrial extruders, thereby enabling us to recommend the type of molding extrusion equipment.     

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.     

Crystallization behavior of polyamide 11/multiwalled carbon nanotube composites

Differential scanning calorimetry (DSC) was used to investigate the isothermal and nonisothermal crystallization kinetics of polyamide11 (PA11)/multiwalled carbon nanotube (MWNTs) composites. The Avrami equation was used for describing the isothermal crystallization behavior of neat PA11 and its nanocomposites. For nonisothermal studies, the Avrami model, the Ozawa model, and the method combining the Avrami and Ozawa theories were employed. It was found that the Avrami exponent n decreased with the addition of MWNTs during the isothermal crystallization, indicating that the MWNTs accelerated the crystallization process as nucleating agent. The kinetic analysis of nonisothermal crystallization process showed that the presence of carbon nanotubes hindered the mobility of polymer chain segments and dominated the nonisothermal crystallization process. The MWNTs played two competing roles on the crystallization of PA11 nanocomposites: on the one hand, the MWNTs serve as heterogeneous nucleating agent promoting the crystallization process of PA11; on the other hand, the MWNTs hinder the mobility of the polymer chains thus retarding the crystal growth process of PA11. The activation energies of PA11/MWNTs composites for the isothermal and nonisothermal crystallization are lower than neat PA11. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.     

Kinetic model for autoxidation of β-carotene in organic solutions

Autoxidation of β-carotene was studied experimentally using n-decane as a solvent under various reaction conditions of temperature and dissolved oxygen concentration A novel kinetic model was proposed on the basis of an autocatalytic free-radical chain reaction mechanism. A secondary initiation reaction by decomposition of hydroperoxide and reactions concerned with a β-carotene-derived C-centered radical in propagation and termination processes were taken into consideration in the model. There were four unknown kinetic constants, and the constants were estimated by fitting the model with the experimental data. The fitted results are in good agreement with the experimental data in all stages of the kinetics of autoxidation and over a wide range of oxygen concentrations. The model described not only the appearance of the induction stage but also the effect of the oxygen concentration on the autoxidation rate. In addition, the model predicted the behavior of autoxidation in another solvent at low temperature that had been reported by other researchers.     

Comparison of the oxidizability of various glycerophospholipids in bilayers by the oxygen uptake method

The aims of this study were twofold: develop a convenient and rapid procedure for assessing the oxidizability of small quantities of glycerophospholipids in bilayers by the oxygen uptake method, and determine and compare the oxidizability of various glycerophospholipids in bilayers. Our purpose was to educidate phospholipid oxidation characteristics in membranes. The quantitative autoxidation kinetics of dilinoleoyl phosphatidylcholine (DLPC) (18∶2/18∶2) was studied in large unilamellar vesicles (LUV) in aqueous dispersions with watersoluble initiator—2,2′-azobis(2-amidinopropane) dihydrochloride—and inhibitor 2-carboxy-2,5,7,8-tetramethyl-6-chromanol. The kinetic data indicated a high efficiency of free radical production, resulting in shortening of measuring time; the very low kinetic chain length, particularly in the induction period, suggested the possibility of including large errors in thekinetics data. Nevertheless, the autoxidation of DLPC obeyed the classic rate law: R _p =k _p [LH]R _i ^1/2 /(2k _t )^1/2 (where R _p -rate of oxygen consumption, k _p =rate constant for chain propagation, [LH]-substrate concentration; R _i ^1/2 -square root of rate of chain initiation, and 2k _t =rate constant for chain termination) in a mixed bilayer system with saturated dimyristoyl PC (14∶0/14∶0), which provided precise and reproducible data. Therefore, the system was used to assess the relative oxidizability of each glycerophospholipid DLPC (18∶2/18∶2), dilinolenoyl PC (18∶3/18∶3), 1-palmitoyl-2-linoleoyl PC (16∶0/18∶2), 1-palmitoyl-2-arachidonoyl PC (16∶0/20∶4), 1-palmitoyl-2-docosahexaenoyl PC (16∶0/22∶6), and dilinoleoyl PE (18∶2/18∶2) in bilayers. The results suggested that the oxidizability of glycerophospholipid in bilayers is substantially influenced by the number of intramolecular oxidizable acyl chains and the content of bis-allylic hydrogen in a structured environment, and showed deviation of the rate law for autoxidation in PC and PE mixed LUV, which possibly was due to nonhomogeneous phospholipid distribution in vesicles.