Autocatalytic Kinetics Research Articles

Synthesis and thermal decomposition of ditetrazol-5-ylamine

Ditetrazol-5-ylamine (DTA) was synthesized from cyanuric chloride in four steps. The thermal decomposition of DTA in the solid state was studied by thermogravimetry, volumetry, mass spectrometry, IR spectroscopy, and calorimetry. Under isothermal conditions at 200–242 °C, thermal decomposition obeys the first order autocatalytic kinetics. The kinetic and activation parameters of DTA decomposition were determined. The composition of gaseous reaction products and the structure of condensed residue were studied. The thermal effect of thermal DTA decomposition is 281.4 kJ mol−1. The nitrogen content in a mixture of gaseous products formed by the reaction in a temperature interval of 200–242 °C exceeds 97 vol.%.

Curing kinetics of UV‐initiated cationic photopolymerization of divinyl ether photosensitized by thioxanthone

AbstractPhotodifferential scanning calorimetry was used to investigate the photocuring kinetics of UV‐initiated cationic photopolymerizations of 1,4‐cyclohexane dimethanol divinyl ether (CHVE) monomer with and without a photosensitizer, 2,4‐diethylthioxanthone (DETX), in the presence of a diaryliodonium‐salt photoinitiator. Two kinetics parameters, the rate constant (k) and the order of the initiation reaction (m), were determined for the CHVE system with different amounts of added DETX photosensitizer (0–1 wt %) and at different isothermal temperatures (25–55°C) using an autocatalytic kinetics model. The photosensitized CHVE system exhibited much higher k and m values than did the nonphotosensitized system, which was attributable to the effects of photosensitization. Furthermore, the values of k and m for both CHVE systems increased significantly with increasing isothermal temperature because of a thermal contribution toward increasing the mobility of active species. The addition of DETX lowered the activation energy for the UV‐curable vinyl ether system. The collision factor for the system with DETX was higher than that obtained for the system without DETX, indicating that the reactivity of the former was greater than that of the latter because of the photosensitization effect. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1345–1351, 2005

Photocuring kinetics of UV‐initiated free‐radical photopolymerizations with and without silica nanoparticles

AbstractWe used photodifferential scanning calorimetry to investigate the photocuring kinetics of UV‐initiated free‐radical photopolymerizations of acrylate systems with and without silica nanoparticles. Two kinetics parameters—the rate constant (k) and the order of the initiation reaction (m)—were determined for hybrid organic–inorganic nanocomposite systems containing different amounts of added silica nanoparticles (0–20 wt %) and at different isothermal temperatures (30–100 °C) using an autocatalytic kinetics model. The kinetic analysis revealed that the silica nanoparticles apparently accelerate the cure reaction and cure rate of the UV‐curable acrylate system, most probably due to the synergistic effect of silica nanoparticles during the photopolymerization process. However, a slight decrease in polymerization reactivity that occurred when the silica content increased beyond 15 wt % was attributed to aggregation between silica nanoparticles. We also observed that the addition of silica nanoparticles lowered the activation energy for the UV‐curable acrylate system, and that the collision factor for the system with silica nanoparticles was higher than that obtained for the system without silica nanoparticles, indicating that the reactivity of the former was greater than that of the latter. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 658–670, 2005

Photo-curing kinetics for the UV-initiated cationic polymerization of a cycloaliphatic diepoxide system photosensitized by thioxanthone

Photo-differential scanning calorimetry (photo-DSC) was used to investigate the cure kinetics for the UV-initiated cationic photo-polymerization of cycloaliphatic diepoxide (CADE) systems with and without a photo-sensitizer, 2,4-diethylthioxanthone (DETX), in the presence of a diaryliodonium-salt photo-initiator. Two kinetics parameters—the rate constant ( k) and the order of the initiation reaction ( m)—were determined for the CADE epoxide system for different amounts of added DETX photo-sensitizer (0–1 wt%) and at different isothermal temperatures (25–100 °C) using an autocatalytic kinetics model. The photo-sensitized CADE epoxide system gave much higher k and m values than the nonphoto-sensitized one (due to the photo-sensitization effect). Moreover, k and m for both CADE epoxide systems with and without DETX increased significantly with increasing isothermal temperature due to a thermal contribution towards increasing the mobility of active species. We also observed that the addition of DETX lowered the activation energy for the UV-curable epoxide system; the collision factor for the system with DETX was higher than that obtained for the system without DETX, indicating that the reactivity of the former was greater than that of the latter due to the photo-sensitization effect.

Noise-sustained structures in differential-flow reactors with autocatalytic kinetics.

We have studied the formation of noise-sustained structures in a differential-flow reactor with cubic autocatalytic kinetics (the Gray-Scott model). In this system the interplay between advection, diffusion, reaction, and noise fluctuations leads to the formation of noise-sustained patterns in the key species. Numerical integration in one and two spatial dimensions shows that the structures are nonlocally cross correlated. Near threshold, the observed correlation is related to the properties of the convectively unstable critical modes.

Hydrothermal stability of aromatic carboxylic acids

The chemical behavior of aromatic carboxylic acids in water at elevated temperatures has implications for industrial chemistry, fuel processing and waste treatment processes. Therefore, the hydrothermal reactions of six different aromatic carboxylic acids were investigated from 250–410 °C at times up to 240 min. Benzoic acid was the most stable of the six, showing negligible degradation after 1 h of hydrothermal treatment at 350 °C. Terephthalic acid, 2,6-naphthalene dicarboxylic acid and isophthalic acid were stable after 1 h at 300 °C, but they decarboxylated to form monoacids in 10–15% yields at 350 °C. Trimellitic anhydride decomposed completely after 30 min at 350 °C, but showed no appreciable decomposition after 30 min at 250 °C. Terephthalic acid and isophthalic acid were the main degradation products, but o-phthalic acid was also formed in small amounts at 350 °C. The o-phthalic acid conversion to benzoic acid was 73% after 60 min at 300 °C, but the diacid remained stable at 250 °C for 1 h. An autocatalytic kinetics model provided a good description of the trimellitic anhydride and terephthalic acid decomposition at 300 and 410 °C, respectively.

Polymerization mechanisms and curing kinetics of novel polymercaptan curing system containing epoxy/nitrogen

AbstractThe bis[3‐(2,3‐epoxypropylthio)phenyl]‐sulfone (BEPTPhS)/trimercaptothioethylamine (TMTEA) system has a self‐catalytic effect and can cure without any other accelerator. The curing kinetics of the BEPTPhS/TMTEA system was studied by means of the dynamic and isothermal differential scanning calorimetry method. The dynamic kinetic parameters were calculated with the aid of the Kissinger and Ozawa methods. The kinetic reaction mechanism in the isothermal reaction of BEPTPhS/TMTEA was shown to follow autocatalytic kinetics. The isothermal kinetic parameters, including k1, k2, m, and n, from the model proposed by Kamal were determined by fitting the experimental data; a good description of the curing kinetics was obtained, although deviations were observed at low conversions. The Arrhenius kinetic analysis indicated that the activation energy decreased with the increase of the reaction conversion, which indicated a change of the reaction mechanism. The isothermal kinetic analysis and Arrhenius kinetic analysis both demonstrated that the catalytic effect of the nitrogen atom in TMTEA predominated at low conversions and the autocatalytic effect predominated at high conversions. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 000–000, 2002

Hydrotrope-Induced Autocatalysis in the Biphasic Alkaline Hydrolysis of Aromatic Esters

The alkaline hydrolysis of aromatic esters exhibits autocatalytic kinetics when performed under two-phase conditions without any mixing solvent. The molecular structures of such aromatic esters determine whether the autocatalysis occurs or not. It has been established that enhancing the solubility of the hydrophobic ester in water by the hydrotropic salts yielded by the hydrolysis itself accelerates the apparent reaction rate. By kinetically independent measurements, the solubilization process of the ester was verified to be the rate-determining step. It has been observed that the solubilization process can be influenced by factors such as the initial addition of hydrotropic salt, the volumetric ratio of the oil/aqueous phase, and the concentration of alkali.

Curing kinetics of boron-containing phenol-formaldehyde resin formed from paraformaldehyde

A boron-containing phenol–formaldehyde resin (BPFR) was synthesized from boric acid, phenol, and paraformaldehyde. The curing reaction of BPFR was studied by Fourier-transform infrared spectrometry and differential scanning calorimetry. According to the heat evolution behavior during the curing process, several influencing factors on isothermal curing reaction were evaluated. The results show that the isothermal kinetic reaction of BPFR follows autocatalytic kinetics mechanism, and kinetic parameters m, n, k1, and k2, were derived, respectively. In the latter reaction stage, the curing reaction becomes controlled mainly by diffusion. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 638–644, 2002

A simple kinetic model to describe the progression of prion disease

A simple mathematical model based on bistationary autocatalytic kinetics is proposed to describe a possible progression of prion disease. The model accounts for both the sporadic and the infectious manifestation of the disease. Peculiarly, it shows how the disease grows if the concentration of the infectious agent (the prion PrPSc) is added to the metabolic system over a threshold concentration, while for a lower concentration the disease cannot grow.

Curing behavior and thermal property of epoxy resin with boron-containing phenol-formaldehyde resin

The curing reaction of bisphenol-A epoxy resin (BPAER) with boron-containing phenol–formaldehyde resin (BPFR) was studied by isothermal and dynamic differential scanning calorimetry (DSC). The kinetic reaction mechanism in the isothermal reaction of BPAER-BPFR was shown to follow autocatalytic kinetics. The activation energy in the dynamic cure reaction was derived. The influence of the composition of BPAER and BPFR on the reaction was evaluated. In addition, the glass transition temperatures (Tgs) were measured for the BPAER-BPFR samples cured partially at isothermal temperatures. With the curing conditions varying, different glass transition behaviors were observed. By monitoring the variation in these Tgs, the curing process and the thermal property of BPAER–BPFR are clearly illustrated. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1054–1061, 2000

Ester containing aggregates in the autocatalytic biphasic hydrolysis of ethyl alkanoate

Autocatalytic kinetics are observed during the biphasic alkaline hydrolysis of C-4, C-6 and C-8 (butanoate, hexanoate and octanaoate) ethyl esters. Ethanol and alkanoate anions are the products of the reaction. A kinetic model including spontaneous dissolution of the organic phase into the aqueous phase, aqueous hydrolysis of the ester, formation of ester containing aggregates and micellisation has been proposed. For C-4, taking into account salting-in and solvent effects is sufficient to reproduce the autocatalytic behaviour. For C-8, the major autocatalytic process is an ester containing aggregates (ECA) mediated phase transfer. For C-6, it appears that the role of ECA is double. Small sized ECA which are formed at the beginning of the reaction do not perform rapid phase transfer and trap surfactant molecules. Larger ECA which appear at the end of the reaction are the main phase transfer agent. Using an empirical formula to describe the size of the interface, the model is able to reproduce the effect of a variation of the volumic ratio of the two phases as well as the effect of stirring rate and non-emulsified experiments.

Silver Formation, Particle Size Distribution, and Morphology in Photothermographic Systems

Spectroscopic measurements of photothermographic systems at development temperatures show how Ag particles form during the course of the development process. In standard systems, development follows autocatalytic kinetics. Systems containing infectious developers exhibit more unusual kinetics which do not generally fit simple mathematical models. In standard photothermographic systems, Ag particles have a median diameter of approximately 0.065 μm. The median diameter is reduced to 0.028 μm and the particles are generally more spherical in the presence of an infectious developer. Intermediate sizes and morphologies are possible with low levels of infectious development. Particle size and morphology correlates to light absorption and Ag covering power. Standard photothermographic development proceeds sequentially, while infectious development occurs in parallel.

Differential scanning calorimetry of phenol–formaldehyde resins cure-accelerated by carbonates

One of the drawbacks of phenol–formaldehyde (PF) resol resin is its slow cure which requires longer hot-pressing time for the manufacture of wood composite products, especially for thick fibreboard products. In this study, PF resol resin was modified with three carbonates (i.e. propylene carbonate, sodium carbonate and potassium carbonate) to accelerate the cure of the resin for the manufacture of medium density fibreboard. The thermal behaviour of carbonate-modified PF resol resins was characterized with differential scanning calorimetry (d.s.c.) using three different thermal scanning methods (single-heating rate, multi-heating rate and isothermal method). The results of the single-heating rate method were not consistent when compared to the other two methods. The rate constants were calculated with the activation energy and pre-exponential factor obtained by the multi-heating method. The calculated rate constant increased with increasing carbonate level and the temperature selected. The isothermal method revealed that the curing of propylene carbonate-modified resins follows autocatalytic kinetics while the other two additives showed nth-order kinetics with a partial autocatalytic effect.

Origin of Autocatalysis in the Biphasic Alkaline Hydrolysis of C-4 to C-8 Ethyl Alkanoates

The alkaline hydrolysis of C-4 to C-8 (butanoate to octanoate) ethyl esters shows autocatalytic kinetics when performed under two-phase conditions without any mixing solvent. Alkanoate anions and ethanol are the products of the reaction. A dynamic model is proposed that describes quantitatively this kinetic behavior. The model includes the main processes occurring in the biphasic medium and the corresponding thermodynamic calculations of the average size and stoichiometry of the molecular aggregates. Modeling indicates that salting-in and solvent effects caused by the alkanoate anions and ethanol determine the autocatalytic kinetics in the hydrolysis of C-4 ethyl ester where no aggregation occurs. In the C-5 to C-8 experiments, ester-containing micelles (ECM) are mainly formed by cooperative aggregation of alkanoate anions with ester molecules. ECM is formed only after a threshold concentration of the alkanoate anion has been reached. In a phase-transfer-like process, ECM carries ester molecules into the aqueous phase, where hydrolysis takes place yielding alkanoate anions. Additionally, in C-6 and C-7 ethyl ester hydrolysis, autocatalysis appears to be delayed, since acceleration only starts after the extent of hydrolysis has reached a certain level. A transient storage of alkanoate anions in a reservoir has been assumed to explain this delay. Collective adsorption of alkanoate anions at the oil−water interface, which occurs without any threshold concentration, could play the role of such a transient storage. The model also shows that empty micelles are without any kinetic importance, since they are formed at the end of reaction after the ester is completely depleted.

Travelling waves in a differential flow reactor with simple autocatalytic kinetics

A simple prototype model for a differential flow reactor in which the possible initiation and propagation of a reaction-diffusion-convection travelling-wave solution (TWS) in the simple isothermal autocatalytic system A+mB→ (m+1)B, rate kabm (m ≥ 1) is studied with special attention being paid to the most realistic cases (m=1,2). The physical problem considered is such that the reactant A (present initially at uniform concentration) is immobilised within the reactor. A reaction is then initiated by allowing the autocatalyst species to enter and to flow through the reaction region with a constant velocity. The structure of the permanent-form travelling waves supported by the system is considered and a solution obtained valid when the flow rate (of the autocatalyst) is very large. General properties of the corresponding initial-value problem (IVP) are derived and it is shown that the TWS are the only long-time solutions supported by the system. Finally, these results are complemented with numerical solutions of the IVP which confirm the analytical results and allow the influence of the parameters of the problem not accessible to the theoretical analysis to be determined.

Nitrile reaction in high‐temperature water: Kinetics and mechanism

AbstractThe reaction pathways, kinetics and mechanisms underlying the hydrolysis of aliphatic and aromatic nitriles in high‐temperature water (HTW) were investigated. The reaction products were the associated amides and carboxylic acids. Autocatalytic kinetics were observed and confirmed by experiment and analysis of the physical chemistry of the HTW reaction environment. A model incorporating two autocatalytic steps captured the observed kinetics well, and the associated optimized rate constants highlighted the key differences in the reaction chemistry of aliphatic and aromatic nitriles. The rate behavior of nitrile hydrolysis at these conditions has tangible consequences regarding optimal processing strategies.

The propagation of travelling waves in an open cubic autocatalytic chemical system

The reaction-diffusion travelling waves that can be initiated in an open isothermal chemical system governed by cubic autocatalytic kinetics are discussed. The system is shown to be capable of sustaining up to three spatially uniform steady states, the (trivial) unreacted state, which is always stable (a node), and two nontrivial states, one of which is always unstable (a saddle point). The third state can change its stability through Hopf bifurcation (both subcritical and supercritical). This allows the possibility of two sorts of travelling wave being established; there are wave profiles which connect the unreacted state ahead to the nontrivial state at the rear, and wave profiles (pulse waves) which have the unreacted state at both the front and rear. The conditions under which a particular wave is initiated are considered by both a discussion of the (ordinary) differential equations governing the travelling waves and by numerical integrations of an initial-value problem. This treatment also reveals the possibility of a stable travelling wave propagating through the system, leaving behind a temporally unstable stationary state. Under these conditions, spatiotemporal chaotic behaviour is seen to develop after the passage of the wave.

The chemical mechanism of beta-haematin formation studied by Mössbauer spectroscopy.

Spontaneous formation of beta-haematin (malaria pigment) from haematin in acetate solution follows pseudo-zero-order and not autocatalytic kinetics. Acetate appears to facilitate the reaction by solubilizing the haematin and acting as a phase-transfer catalyst, a role which, in vivo, could be fulfilled by carboxylic acids or amino acids.

A novel exit boundary condition for the axial dispersion model

A new modification of the Danckwerts' exit boundary condition for the axial dispersion model is proposed. According to the novel boundary condition, the concentration gradient at the reactor exit is a fraction of the gradient predicted by the plug flow model. The fraction is a function of the Peclet number. A family of suitable function expressions has been derived. The exit boundary condition provides a smooth transition from the complete back-mixing model with a zero concentration gradient to the plug flow model with a finite concentration gradient. The boundary condition is illustrated via two examples: a first-order reaction and an autocatalytic reaction. The correct asymptotics for the boundary condition have been demonstrated by an analytical solution of the first-order reaction model. Numerical solution of the autocatalytic kinetics with global orthogonal collocation indicates that the use of the modified boundary condition improves the performance of the numerical algorithm compared to the performance obtained using the classical Danckwerts' boundary condition.