Arrhenius-type Law Research Articles

Two state model for sub-exponential fluorescence revisited

A two-state model for the stretched exponential law found in the asymptotic decay of the fluorescence is generalized. By assuming a modification of the Arrhenius law for the detrapping process we find that the exponent characterizing the stretched exponential decay, β, exhibits a number of different behaviors, in qualitative agreement with some recent experimental results. The microscopic origin of these modified Arrhenius-type laws is considered. It is shown that multiphonon absorption can lead to a β which is a decreasing function of temperature, as found experimentally.

Raman spectra and phase transition in betaine potassium iodide dihydrate

Polarized Raman spectra of betaine potassium iodide dihydrate ([(CH3)3N+CH2 COO-]2KI · 2H2O) have been studied in the temperature range 40 - 290 K. The behaviour of betaine external modes and of water internal vibrations provides evidence for a first order phase transition of order-disorder type at 100 K. This phase transition is related to the freezing of the successive reorientations of water molecules. The temperature dependence of the halfwidth of the water stretching band centred at 3489 cm-1 (40 K) obeys an Arrhenius-type law corresponding to different activation energies below and above the critical temperature. The comparison of Raman and dielectric data allows us to identify two types of reorientation of water molecules.

Pyrolysis Behavior of Hybrid-Rocket Solid Fuels Under Rapid Heating Conditions

An experimental investigation of the thermal pyrolysis behavior of several hybrid-rocket solid fuels under rapid heating conditions was conducted to determine pyrolysis laws and to identify and quantify the products of fuel pyrolysis. The study focused on four fuel formulations: pure hydroxyl-terminated polybutadienes (HTPB), 80% HTPB/20% Alex, 80% HTPB/20% Al, and the Joint Industrial Research and Development fuel formulation. A rapid conductive-heating technique was developed and employed to determine Arrhenius-type pyrolysis laws. All four fuels displayed two sets of Arrhenius parameters, depending on the range of surface temperature. For pure HTPB,Ea = 4:91 kcal/mol andA = 11.04mm/s above722K, whileEa = 13:35 kcal/mol andA = 3965mm/s below 722 K. These results agree well with those obtained previously using a lab-scale hybridmotor operating under realistic conditions. The gas chromatograph/mass spectrometer tests of the nonmetalized fuels, using a  ash-heating oven, indicated that the relative concentrations of the pyrolyzed species depended strongly on temperature. For pure HTPB seven major products were identiŽ ed, with 1,3-butadiene representing the dominantproduct at all temperatures tested, up to 1073 K. The measured mole fractions of the pyrolysis products and deduced pyrolysis laws of the fuels studied can be utilized in a comprehensive model simulation for combustion performance predictions.

Structural details and time dependence of the initial susceptibility in iron-rich Fe–Si ribbons

A systematic study of the temperature dependence of the initial susceptibility χ AC versus T of Fe-6.5 wt%Si, Fe-7.5 wt%Si and Fe-11 wt%Si ribbons in the as-quenched state and after annealing at 1373 K for 1 h has been performed. In ribbons with a silicon concentration of 6.5 and 7.5 wt%, the presence of an anomaly in χ AC versus T and a thermal susceptibility hysteresis at high temperatures were observed. This susceptibility anomaly is attributed to the magnetic aftereffect phenomenon originating from the diffusion of pairs of silicon atoms. The occurrence of a magnetic aftereffect is associated with the existence of the B2 type of structure in the sample induced during the process of cooling from high temperature, its formation being sensitive to the cooling rate. The activation energy of the reversible process of the time dependence of the magnetic susceptibility depends on the cooling rate and its value is estimated using an Arrhenius-type law. X-ray diffraction and 57 Fe Mössbauer measurements were included within this study, in order to investigate the crystallographic structure.

Classical dynamical simulation of spontaneous alloying

“Spontaneous alloying” observed by Yasuda, Mori et al. for metallic small clusters is simulated using classical Hamiltonian dynamics. Very rapid alloying occurs homogeneously and cooperatively starting from the solid phase of the cluster if the heat of solution is negative and the size of cluster is less than a critical size. Analysis of 2D models reveals that the alloying rate obeys an Arrhenius-type law, which predicts the alloying time much less than second at room temperature. Evidences manifesting that the spontaneous alloying proceeds in the solid phase without melting are also presented. The simulation reproduces the essential features of the experiments.

Polymer design for pervaporation membranes: influence of the soft segment size of block copolymers (polyurethaneimides or polyureaimides) on their pervaporation features

Three sets of new block copolymers PUI with increasing soft segment lengths were obtained by a method which allows the control of the material structure by a step-by-step polycondensation: polyetherurethaneimides (PEG-MDI-AP), polyetherureaimides (JFA ED-MDI-AP) and polyesterurethaneimides (PCL-MDI-AP) with soft block molecular weights in the range of 300–2000. At 30°C, all the PUI exhibited selectivity towards ethanol during the pervaporation of EtOH/ethyl tert-butylether mixtures close to the azeotropic composition and the PV fluxes were related to the polymer structure in a quantitative way. They were shown to vary exponentially with the soft segment weight fraction in the case of PUI polyethers whereas linear relationships described the partial and total fluxes obtained with PUI polyesters. The second part of the investigations dealt with the influence of the soft segment length on the PV features of PUI at higher temperatures. Despite one particular polymer leading to a significant deviation from the usual behaviour, the PV mass transfer of both permeants in all the PUI investigated obeys an Arrhenius type law in the temperature range of 30–60°C. The activation energies could be related to the material structure qualitatively, showing an important decrease of these parameters for the polymers with the longest soft segment.

Influence of NiCu alloying on Sepiolite-supported nickel catalysts in the liquid-phase selective hydrogenation of fatty acid ethyl esters

The role of Cu in Sepiolite-supported bimetallic NiCu catalysts has been evaluated through the results obtained in a kinetic study on the influence of temperature in the consecutive hydrogenation of ethyl linolate to ethyl oleate and ethyl stearate, respectively. Liquid-phase hydrogenation reactions (individual and consecutive) were carried out under hydrogen pressure of 0.41 MPa in a temperature range between 305 and 337 K. Thus, the relative reactivities of linoleic and oleic ethyl esters, R L,O, as well as the corresponding relative adsorption constants, K L,O, were obtained at all temperatures studied. According to the results, in both of the Sepiolite supported catalysts studied, selectivity values steadily increased with temperature in the interval studied. Besides, R L,O and K L,O exhibited an Arrhenius type law with temperature that enabled us to obtain several kinetic parameters affecting the selectivity of the consecutive hydrogenation process and closely related to the electronic density of supported nickel which is modified by NiCu alloying.

Stochastic equations of motion for epitaxial growth.

We report an analytic derivation of the Langevin equations of motion for the surface of a solid that evolves under typical epitaxial-growth conditions. Our treatment begins with a master-equation description of the microscopic dynamics of a solid-on-solid model and presumes that all surface processes obey Arrhenius-type rate laws. Our basic model takes account of atomic deposition from a low-density vapor, thermal desorption, and surface diffusion. Refinements to the model include the effects of hot-atom knockout processes and asymmetric energy barriers near step edges. A regularization scheme is described that permits a (nonrigorous) passage to the continuum limit when the surface is rough. The resulting stochastic differential equation for the surface-height profile generically leads to the behavior at long length and time scales first described by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)] (due to desorption). If evaporation is negligible, the asymptotic behavior is characteristic of a linear model introduced by Edwards and Wilkinson [Proc. R. Soc. London, Ser. A 381, 17 (1982)] (due to asymmetric step barriers and/or knockout events). If the latter are absent as well, the surface roughness is determined by an equation independently analyzed by Villain [J. Phys. I 1, 19 (1991)] and Lai and Das Sarma [Phys. Rev. Lett. 66, 2348 (1991)] (which includes only deposition and site-to-site hopping). The consequences of reflection-symmetry breaking in the basic microscopic processes are discussed in connection with step-barrier asymmetry and Metropolis kinetic algorithms.

Diffusion flame stabilization and extinction under naturally convective flows

The stabilization and extinction phenomena for a two-dimensional diffusion flame around the leading edge of an upright solid fuel under naturally convective environments are studied theoretically. The governing system consists of two-dimensional Navier-Stokes' momentum (including a body force term), energy, species, and continuity equations, together with a finite-rate chemical kinetics described by a second-order Arrhenius-type rate equation. The burning rate of fuel is expressed by an Arrhenius-type pyrolysis law. The nondimensional model is solved numerically. Two parametric Studies, based on changing gravity level and ambinet oxygen index, respectively, are investigated. Under the variation of gravity, both Damkohler number and preexponential factor for fuel pyrolysis are changed. Two quenching limits are identified separately at a very low and a high gravity level. The envelope flame exists when gravity is less than 1.95 g. As gravity is increased, there appears a transition to open-tip flame, stabilized on the side of fuel plate. A similar trend is found when ambient oxygen index is decreased from the higher value to the lower one but only with a quenching limit that is blowoff. The detailed flame structures for envelope and open-tip flames are illustrated graphically.

Molecular-dynamics simulation of methane adsorbed on MgO: Evidence for a Kosterlitz-Thouless transition

A realistic model of a monolayer molecular crystal of methane adsorbed on the (100) surface of MgO has been studied by means of molecular dynamics. The model treates the atomicity of the MgO substrate explicitly. Large corrugations in energy are found for both the translational and rotational motion of methane across the substrate. The preferred configurations of adsorption is over an Mg2+ ion in a tripod-down orientation. The orientationally ordered low-energy states of the monolayer have been found. Finite-size-scaling calculations on systems of different sizes indicate, however, that the ordered state exhibits only quasi-long-range order. The disclinations in the ordered phase exist in low concentrations and in bound pairs. Evidence is presented for a Kosterlitz-Thouless-type unbinding transition occurring at T c ≈ 27 K. No evidence is found for a first-order transition. The specific heat exhibits an anomaly at T ≈ 32 K. The disclination density in the region of the transition is reported; below T c, this density can be fitted to an Arrhenius-type law, yielding an estimate of the core enegy for a bound vortex-antivortex pair.

AIPO 4-supported nickel catalysts IX. Liquid-phase selective hydrogenation of propargyl alcohols

The liquid-phase consecutive hydrogenation of propargyl alcohols (2-propyn-l-ol, 3-butyn-2-ol, and 2-methyl-3-butyn-2-ol) has been carried out at 293–323 K and in an initial hydrogen pressure range of 0.3–0.7 MPa on three nickel catalysts at 20 wt% supported on two different types of AIPO 4. A bimetallic NiCu catalyst was also employed as a catalyst. Furthermore, individual hydrogenation of related allyl alcohols was carried out under identical experimental conditions. Thus, by introducing a modification in the classical kinetic equation of competitive hydrogenations, the relative reactivities R D,T as well as the relative adsorption constants K D,T were successfully obtained in the consecutive process. The independence of R D,T with respect to the temperature and the Arrheniustype law obtained from In K vs T −1 was ascribed to the existence of a linear free-energy relationship (LFER) which also manifested itself in the existence of a linear correlation between the activation parameters ΔH≠ and ΔS≠ (and between E a and In A) known as the “compensation effect”. On the basis of these results, valuable information was obtained concerning not only the mechanism of the liquid-phase catalytic hydrogenation of propargyl alcohols but also the parameters affecting the selectivity of the process.

Aqueous corrosion of natural and nuclear waste glasses II. Mechanisms of vapor hydration of nuclear waste glasses

Results of recent vapor phase hydration experiments performed on nuclear waste glasses at various temperatures and relative humidities are presented. Hydration rates were determined using a variety of techniques, including specimen weight gain measurement, alteration layer thickness measured using optical microscopy or scanning electron microscopy (SEM), and near-surface concentration profiles obtained using secondary ion mass spectrometry (SIMS). For the three nuclear waste glass formulations studied, previously observed differences in reaction products and rates of hydration in liquid and vapor environments were confirmed. At 100% relative humidity (RH) and at temperatures between 75° and 240°C, the rate of hydration of SRL 131 glass followed and Arrhenius-type rate law with an activation energy of 17.9 kcal/mol. A significantly higher apparent activation energy was estimated for SRL 131 glass hydrated at 95% RH. The vapor hydration rate of SRL 131 glass decreased with RH and was negligible below humidity of 70% RH at 202° C. Potential mechanisms that may govern the vapor hydration of glass are reviewed and several lines of evidence including the parametric dependence of vapor hydration rate observed in the present work are consistent with a molecular water diffusion model. In the context of such a model, the dependence of hydration rates on RH is explained through a relationship between p H 2O and concentration of absorbed molecular water at the outermost surface of hydrated glasses.

Measurement of effective diffusivities of ionic and non-ionic solutes through beef and pork muscles using a diffusion cell

A diffusion cell in conjunction with a new mathematical model was used to measure the apparent diffusion coefficients of sodium chloride, potassium nitrate and glucose through beef semitendinosus and pork longissimus dorsi muscles. The apparent diffusion coefficient was obtained within less than 180 min with a coefficient of variation less than 10% in most cases. The influence of temperature can be adequately explained by the Arrhenius-type law with activation energy between 19 and 26 kJ/mol depending on the diffusant. However, these values were not significantly different. Finally, we showed that the apparent diffusion coefficient of sodium chloride is not affected by the direction of the muscle fibre to the axes of diffusion while glucose diffusion parallel to the muscle fibre can be three times greater than diffusion at a right angle to the muscle fibre.

Anharmonic interactions in solids: a Raman investigation of some vibrational states in ammonium fluorosilicate

The temperature dependence of the stretching vibration of ammonium ions in cubic and trigonal ammonium fluorosilicate has been measured between 10K and room temperature. The half-width of the symmetric stretching mode exhibits a temperature dependence that can be fitted to an Arrhenius-type law. This behaviour is discussed in terms of anharmonic components of the potential function and it is suggested that the temperature dependence of the linewidth is due to the phenomenon of exchange modulation, whereby the excited vibrational state is elastically scattered by a torsional vibration of the ammonium ion.

Deuterium separation by multiphoton dissociation of dichlorofluoromethane

Absorption and dissociation probabilities of CHCl2F and CDCl2F were investigated by a pulsed CO2 laser in the wavenumber region of largest selectivity for deuterium. The absorption of CHCl2F, which is a difference band, can largely be suppressed by cooling. At 200 K and at 920 cm−1 absorption selectivities up to 4000 were found by extrapolation. In the presence of buffer gas, CDCl2F can be multiphoton excited nearly like a linear absorber (“harmonic oscillator”). This is interpreted by a nearly resonant collisional relaxation v7 to v2 and by the smallness of the cross anharmonicity x27. The dissociation selectivityS was 24,000 at natural abundance. Such large values were measured by a chromatographic method.S depends only onp D, the partial pressure of the deuterated species. This dependence is approximately ln S∝p D −1 . It can be rationalized by considering only the average energy transferred to the nonresonant molecules by collisions with CDCl2F. The above functional shape is related to an Arrhenius type law. Comparison with trifluoromethane for D separation shows that CHCl2F has primarily two advantages: its rapid H-D exchange with water and the less stringent requirements of laser energy and pulse length.

AlPO 4-supported nickel catalysts : VI. Support effects on the individual and competitive hydrogenation of allyl alcohol and its α and β methyl derivatives

Individual and competitive liquid-phase hydrogenation of allyl alcohols (2-propen-1-ol, 2-methyl-2-propen-1-ol, and 2-buten-1-ol) has been carried out at 293–313 K and 0.41 MPa of initial hydrogen pressure on nickel catalysts at 20 wt% supported on Al 2O 3, SiO 2, and on three different types of AlPO 4. Furthermore, unsupported bulk nickel was employed as catalyst. The independence of the relative reactivities, R, with respect to the temperature and the Arrhenius-type law obtained for the relative adsorption constants, K, from ln K vs T −1, in all studied catalysts, was associated with the existence of a linear free-energy relationship (LFER) which also manifested itself in a linear relationship between the differential adsorption heat, Δω, and differential entropy factors, Δ S. According to the values of both kinds of parameters (Δω and Δ S) for every catalyst, it was concluded that the steric effects on the CH 3 adsorption decreased in the order Ni A1PO 4 -P > Ni AlPO 4 -F > Ni SiO 2 > Ni Al 2O 3 > Ni AlPO 4 -B > Ni bulk ; which is exactly the opposite of the inductive effect. -P, -F, and -B refer to the precipitation agent employed in the synthesis of AlPO 4: propylene oxide, ammonia, and ethylene oxide, respectively. Such LFER also manifested itself in the existence of a linear correlation between log A and E a (Arrhenius constant and apparent activation energy, respectively) known as “compensation effect.” The existence of this LFER is adscribed to the independence of the true activation energy from substituent and catalyst effects in these hydrogenation processes.

Elementarerweichungen in Amorphen Polymeren

Thermally stimulated recovery behaviour of amorphous polymers is described in terms of a continuous distribution of sharply defined elementary softening processes in the polymer. It is proposed that each of these elementary processes is the result of a co-operative site-change mechanism. On exceeding the activation temperature for the process, the viscoelastic time constants fall abruptly by many orders of magnitude, as opposed to following an Arrhenius-type law. The implications of this type of behaviour are discussed.

The connection between carrier lifetime and doping density in nondegenerate semiconductors

It is assumed that there exists a temperature Tf at which dominant recombination centers in the form of electrically neutral, mechanical defects (e.g., vacancies) are frozen into a semiconductor matrix. For this process we assume an Arrhenius-type law with an activation energy. From this assumption there follows by standard semiconductor statistics the doping dependencies of (a) the defect concentration and (b) the minority carrier lifetimes. The analysis can in principle be applied to any defect in any semiconductor which satisfies the above assumptions, provided the cross sections and related data are known. For the case of silicon we have deduced a set of parameters to fit the optimal experimental lifetimes. Assuming the unknown defects to have two charge states, neutral and negative, it is inferred that the levels lie near midgap and have recombination coefficients of order 10−9 cm3 s−1.

Influences of Upstream Versus Downstream Heat Loss/Gain on Stability of Premixed Flames

Abstract Influences of upstream versus downstream volumetric heat loss/gain on the linear stability of laminar premixed flames are investigated. A single-step irreversible reaction governed by Arrhenius-type rate law is considered within the framework of a diffusional-thermal stability model. The resulting dispersion relations show that while both upstream and downstream losses enhance the tendency towards instability, downstream loss is more effective in promoting instability. The characteristics of cellular as well as the travelling-wave type instabilities in the presence of heat loss/gain from either the downstream or upstream side of the flame have been determined. Also, the impact of these various modes of heat loss/gain on the rate of growth of the characteristic cell size of cellular flames is assessed. The dispersion relation describing the stability of non-adiabatic flames with a two-reactant chemical model is determined as being similar to that corresponding to the single-reactant model. The pra...

Temperature-independent relaxation in a lamellar block copolymer

IT has long been assumed that all processes giving rise to stress relaxation in high polymers are very dependent on temperature. The peak in mechanical or dielectric loss factor (tanδ) can be used to characterise the most probable relaxation time of a high polymer solid. The temperature locus of this relaxation time is described by a simple Arrhenius-type law for low temperature, glassy state processes1 and by the Williams, Landel and Ferry expression2 for ‘Tg’ processes. We now report results for an elastomer exhibiting a unique relaxation process which remains essentially constant in position and magnitude over a temperature range of more than 100 K.