Combustion waves in a model with chain branching reaction

In this paper the steady planar travelling waves in the adiabatic model with two-step chain branching reaction mechanism are investigated numerically. The properties of these solutions are demonstrated to have similarities with the properties of non-adiabatic combustion waves that is, there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. It is also shown that the model possesses a new type multiple travelling wave solutions (which we call wave trains) with complex structure of the profiles and varying speeds     

The effect of ambient temperature on the propagation of nonadiabatic combustion waves

In this paper, we undertake an analytical and numerical investigation of the linear stability and properties of travelling nonadiabatic combustion wave for the case of nonzero ambient temperature. Here we consider premixed fuel with one-step exothermic reaction described by Arrhenius law. The speed of the front is estimated analytically by employing the matched asymptotic expansion approach and numerically using the shooting and relaxation methods. It is shown that increasing the ambient temperature results in the growth of both the flame speed and the region of existence of the travelling wave solutions in the parameter space. The linear stability of the travelling wave solution is investigated analytically by using the matched asymptotic expansion method and numerically by employing the Evans function approach. We demonstrate that by increasing the ambient temperature the stability of the propagating wave can also be increased.AMS subject classification: cation: 35K57, 80A25     

Linear stability analysis of a reaction–diffusion model of solid-phase combustion

 The dynamic behavior of a reaction–diffusion model of solid-phase combustion is investigated by using the linear stability analysis method. The diffusion coefficients of the oxygen gas and the vapor of the combustible solid (Mg) are taken as two controlling parameters in the analysis. The bifurcation map obtained shows three dynamic regions. Region I only shows stable combustion. Regions II and III both show stable combustion and oscillatory combustion depending on the ratio of the two diffusion coefficients. Interestingly region II also shows a small range of a bistable state consisting of a stable focus and an oscillating state, which is like the critical phenomena in phase transitions. The results indicate that the occurrence of oscillating combustion requires that the value of the diffusion coefficient of the Mg vapor should be comparable to or less than that of the oxygen gas at the same temperature. Received: 6 November 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002     

Properties of combustion waves in a model with competitive exothermic reactions

We study the properties of travelling combustion waves in a diffusional thermal model with a two-step competitive exothermic-exothermic reaction mechanism. This investigation considers the system in one spatial dimension under adiabatic conditions. Based on the notion of the crossover temperature, the model is examined analytically using the activation energy asymptotic method to predict travelling combustion wave behaviour in the limit of large activation energies. The model is then studied numerically using a shooting-relaxation method over a wide range of parameter values, such as those describing the ratios of enthalpies, pre-exponential factors and activation energies. It is demonstrated that the flame speed as a function of these parameters is a single-valued monotonic function and there are two flame regimes identified—each region representing parameter values when one reaction dominates the other.     

Effect of Lewis acids and low temperature initiators on the allyl transfer reaction involving phthalimido-N-oxyl radical

Previously, we reported allyl transfer reactions of allyl bromide and allyl phthalimido-N-oxyl substrates with hydrocarbons that result in CC bond formation. In both cases, efficient chain transfer processes along with high reaction yields were observed. Since PINO chemistry leads to an environmentally friendly method of hydrocarbon functionalization, additional studies were performed in order to improve the process. To expand the utility of this reaction, we carried out experiments to optimize reaction conditions and tested the effect of Lewis acids and low temperature initiators. Although allyl-PINO substrates reacted slightly slower than the bromides, the reactions were cleaner with little or no side products. The chain lengths for these reactions were compromised at lower temperatures, attributable to the high activation energy required for the hydrogen atom abstraction by PINO. The addition of a Lewis acid catalyst (AlCl₃) improves the product yield and reaction rate, possibly due to the formation of a PINO/AlCl₃ complex which lowers the activation energy for hydrogen abstraction step.     

Study on thermal degradation and combustion behaviors of PC/POSS hybrids

Polycarbonate/polyhedral oligomeric silsesquioxane hybrids were prepared based on bisphenol A polycarbonate (PC) and trisilanolphenyl-POSS (TPOSS) by the melt blending method. Investigation of transmission electronic microscopy and Fourier transform infrared spectroscopy confirms that the nanoscale TPOSS particles were well dispersed in the PC matrix and there is no chemical reaction between the TPOSS particles and PC matrix during the melt blending. The thermal degradation behaviors of the PC/TPOSS hybrids were investigated. The presence of TPOSS significantly affects the thermal degradation process of PC. The combustion behaviors of the hybrids were evaluated by cone calorimetry experiments. The addition of TPOSS significantly decreased the value of peak heat release rate of the hybrids. Moreover, the addition of TPOSS at 2 wt% leads to the maximum decrease of the PHRR. And scanning electron microscopy and X-ray photoelectron spectroscopy were used to explore the char residues of the pure PC and the hybrids.     

Properties of combustion waves in the model with competitive exo- and endothermic reactions

In this paper we investigate the properties of the travelling combustion wave solutions in a diffusion-thermal model with a two-step competitive exo–endothermic reaction mechanism in one spatial dimension under adiabatic conditions. The model is analysed both numerically and analytically using asymptotic analysis. It is demonstrated that depending on the parameter values, the flame speed as a function of parameters is either a single-valued monotonic function or a double-valued c-shaped function with the turning point type of behaviour. For the case of single-valued flame speed, two flame regimes are identified: the regime with exo- and endothermic reaction domination. Two different routes to extinction are found as well as regions of the existence of combustion waves in the parameter space. Prospects of further work are also discussed.     

Reaction of donor-acceptor cyclopropanes with 1,3-diphenylisobenzofuran. Lewis acid effect on the reaction pathway

Reaction of donor-acceptor cyclopropanes with 1,3-diphenylisobenzofuran in the presence of lanthanide triflates, as well as CuOTf, Sn(OTf)₂, SnCl₂, ZnCl₂, GaCl₃, and MgI₂, proceeds as a formal [3+4]-cycloaddition leading to a newly formed seven-membered ring. This reaction was found to be typical of cyclopropane-1,1-diesters and dinitriles, as well as 1-nitrocyclo-propanecarboxylates containing aromatic, heteroaromatic, and vinylic substituents at the C(2) atom of the small ring. When Me₃SiOTf, TiCl₄, SnCl₄, or BF₃·OEt₂ were used as initiators, unusual cyclic hemiacetals were formed via the conjugate 1,4-addition of a cyclopropane and a nucleophile to the diene moiety.     

The effect of solvent on a Lewis acid catalyzed Diels-Alder reaction,using computed and experimental kinetic isotope effects

A new transition structure for the Diels-Alder reaction between isoprene and acrolein catalyzed by Et(2)AlCl is found to reconcile reported discrepancies between computed and observed secondary kinetic isotope effects (KIEs). Including the effect of solvent realigns the computed results with experiment demonstrating the importance of nonbond interactions at transition structures. Comparison of experimental and newly predicted KIE data reaffirms the ability of theory and experiment to probe the mechanism and transition structure geometry of organic reactions.     

Chain length effect on the crystal thermal stability of oligoesters crystallized in thin layers

Specific heat of two fractions of oligomeric ethylene adipates (EA-2 with molecular weight <M _n>=1700 and EA-4 <M _n>=4000) containing up to 85 weight parts of untreated Aerosil-175, was measured in the temperature range 150–400 K. Detailed analysis of experimental data in terms of equations (1) and (2) led to the conclusion that significantly higher rate of decrease of both crystalline melting point as well as true (i. e., corrected for crystallinity) enthalpy of fusion with inverse value of distance between filler particles for EA-2 reflects higher affinity of end hydroxyl groups of oligomer chains in extended conformation towards polar Aerosil surface, as compared to that for middle-chain segments of EA-4 molecules which presumably are in a coiled conformation in the melt, and fold back on themselves on crystallization. On the other hand, sudden drop of experimental heats of fusion and crystallinities for both oligomers at filler contents above 50 weight parts is attributed to drastic jump of nucleation barrier for crystallization due to severe loss of conformational entropy of oligomer chains which either form ties between filler particles, with end groups anchored on the latter (as in the case of EA-2), or are squeezed in coiled conformation, with middle-chain segments on the periphery of coils interacting with neighboring filler particles (EA-4).     

The analysis of combustion products : The effect of hydrogen peroxide on the reaction of potassium permanganate with organic peroxides in acid solution

Although methyl and ethyl hydroperoxides alone do not react with potassium permanganate in acid solution at room temperature, they can be oxidised by this reagent in the presence of hydrogen peroxide. The apparent equivalents (as compared with hydrogen peroxide) are much lower than usual but, in the presence of excess hydrogen peroxide, the titre due to the organic peroxide is proportional to its original concentration. This forms the basis of a simple titration method which, though empirical, is both rapid and accurate. Since t-butyl hydroperoxide does not react in this way, it may be possible to differentiate the higher peroxides from lower peroxides.     

Thermal waves scattering by a subsurface sphere in a semi-infinite exponentially graded material using non-Fourier's model

In this study, the multiple scattering of thermal waves and temperature distribution resulting from a subsurface sphere in a semi-infinite exponentially graded material are investigated, and the analytical expression of the temperature at the surface of the graded material is obtained. Non-Fourier heat conduction equation is applied to solve the temperature at the surface, and the image method is used to satisfy the semi-infinite boundary condition of graded material. The thermal wave fields are expressed using wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the sphere. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented for the first time. The temperature distribution and phase difference at the surface of the semi-infinite material with different parameters are graphically presented. Analyses show that the hyperbolic heat conduction equation cannot be regarded as a continuation of the parabolic heat conduction equation at very short time scale. The effects of the incident wave number, the structural and physical parameters on the distribution of temperature and phase difference in the semi-infinite material are also examined.     

Synthesis and effect of hyperbranched (3-hydroxyphenyl) phosphate as a curing agent on the thermal and combustion behaviours of novolac epoxy resin

A novel type of hyperbranched (3-hydroxyphenyl) phosphate (HHPP) with high functionality as a curing agent of epoxy resins was synthesized and characterized by FTIR, ¹H NMR and vapor phase osmometry (VPO). The cured epoxy resin with HHPP possessed improved glass transition temperature. The thermostability and flame retardancy of O-cresol novolac epoxy resin cured with different contents of HHPP were investigated by thermogravimetric analysis (TGA), limiting oxygen index (LOI) and cone calorimetry. The obtained results show that the samples containing a higher percentage of HHPP exhibit relatively lower thermostability at lower temperature while higher thermostability at elevated temperature and more char was formed compared with those containing a lower percentage of HHPP. The LOI value increased from 22.0 to 30.0 when HHPP, instead of 1,3-dihydroxybenzene, was used as a curing agent. The 25 wt% addition of HHPP in the curing agent complex effectively decreased the heat release rate and improved the char yield to the content nearly similar as those of the epoxy resin cured with pure HHPP.     

The effects of Lewis acid on the 1,3-dipolar cycloaddition reaction of C-arylaldonitrones with alkenes

The regio- and stereoselectivity of the 1,3-dipolar cycloaddition reactions of C-aryl-N-alkylaldonitrones (1a-e) with some alkenes were found to be affected significantly by the addition of Lewis acid. The rate of the reaction was also affected by adding the Lewis acid. In the reactions using allyl alcohol as a dipolarophile an addition of Lewis acid caused a remarkable acceleration of the reaction and a great change in the stereoselectivity. In the reactions using ethyl acrylate as a dipolarophile the regioselectivity was reversed whether the reaction was performed in the presence or the absence of Lewis acid; i.e. isoxazolidine-5-carboxylates were obtained mainly in the absence of Lewis acid although isoxazolidine-4-carboxylates were obtained mainly in the presence of Lewis acid. When the reaction of C,N-diarylaldonitrones (1k, 1m, 1n) with ethyl acrylate was carried out in the presence of Lewis acid, the cleavage of the N-O bond of the cycloadducts giving gamma-aminoalcohols was also observed besides a reverse phenomenon of regioselectivity.     

Theoretical analysis of the effect of Lewis acid catalysts on reactivity in the Diels-Alder reaction of 2-azabutadiene with ethylene

The catalytic effect of a Lewis acid on the reaction of 2-azabutadiene with ethylene has been analyzed theoretically. It is found that catalytic action favors the electronic transference from ethylene to the diene through the iminic carbon atom leading to an increase in the asynchronicity and a stronger interaction between the diabatic curves corresponding to the transferred configuration and the zero configuration causing a decrease in the activation energy, and an earlier character of the transition structure for the process.     

Modeling the effect of ion-induced shock waves and DNA breakage with the reactive CHARMM force field

Ion-induced DNA damage is an important effect underlying ion beam cancer therapy. This article introduces the methodology of modeling DNA damage induced by a shock wave caused by a projectile ion. Specifically it is demonstrated how single- and double strand breaks in a DNA molecule could be described by the reactive CHARMM (rCHARMM) force field implemented in the program MBN Explorer. The entire workflow of performing the shock wave simulations, including obtaining the crucial simulation parameters, is described in seven steps. Two exemplary analyses are provided for a case study simulation serving to: (a) quantify the shock wave propagation and (b) describe the dynamics of formation of DNA breaks. The article concludes by discussing the computational cost of the simulations and revealing the possible maximal computational time for different simulation set-ups.     

The effect of a centrifugal field on a diels-alder reaction

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, p. 2151, September, 1989.     

The simple model and linear stability analysis of the electrode process with the NDR region caused by the potential-dependent convective transport

In our earlier report on the experimental studies of convection coupled with electrochemical processes of Hg ions at the mercury electrode we showed that the potential-dependent onset and decay of this convection can give rise to the N-shaped negative differential resistance (NNDR) in the current–potential characteristics. As a consequence, the presence of appropriate serial ohmic resistance in the electric circuit caused bistability. Since the rather poorly reproducible nature of this convection makes the precise experimental studies difficult, we elaborated the simple model which extracts the basic dynamical properties of the system under study. The model involves the electrode potential and the Nernst layer thickness for the convective diffusion as the dynamical variables. Using linear stability analysis we derived the stability criteria and constructed the bifurcation diagram, showing bistability, in accordance with the experimental data, but not predicting the oscillatory behavior.     

Study of catalytic effect of ammonium molybdate on the bisphthalonitrile resins curing reaction with aromatic amine

A kind of catalyst, ammonium molybdate was developed in this paper to promote the curing reaction of bisphthalonitrile resins with aromatic amine as curing agent, and the catalytic effect was studied by differential scanning calorimetry (DSC), rheometric measurements and thermogravimetric analysis (TGA). The results indicated that the catalyst could improve the curing rate and increase the curing degree, which could be regulated by the content of the catalyst used in the reaction.