Gaussian Distribution Of Activation Energies Research Articles

The novel oxy-sulfide glassy ionic conductors Na4P2S7-xOx 0 ≤ x ≤ 7: Understanding the features of static and dynamic cations

We present a 23Na nuclear spin dynamics model for interpreting nuclear magnetic resonance (NMR) spin-lattice relaxation and central linewidth data in the invert glass system Na4P2S7-xOx, 0 ≤ x ≤ 7. The glassy nature of this material results in variations in local Na+ cation environments that may be described by a Gaussian distribution of activation energies. A consistent difference between the mean activation energies determined by NMR and DC conductivity measurements was observed, and interpreted using a percolation theory model. From this, the NaNa coordination number in the sodium cation sublattice was obtained. These values were consistent with jumps through tetrahedral faces of the sodium cages for the sulfur rich glasses, x < 5, consistent with proposed models of their short range order (SRO) structures. From NMR spin-echo measurements, we determined the NaNa second moment M2 resulting from the NaNa magnetic dipole interaction of nearest neighbors. Values of M2 obtained as a function of sodium number density N were in agreement with models for uniform sodium distribution, indicating that these invert glass systems form so as to maximize the average NaNa distance. A simple Coulombic attraction model between Na+ cation and X (=S−, O−) anion was applied to calculate the activation energy. In the range 1.5 ≤ x ≤ 7, an increase in activation energy with increasing oxygen content x occurred, and was consistent with the decrease in average anionic radius, and the increase in Coulombic attraction. For small oxygen additions, 0 ≤ x ≤ 1.5, the suggested minimum at low oxygen concentration seen in the activation energies obtained from DC conductivity data is not evident in the model.

Exploring the universality of the alternating conductivity of disordered materials using the Gaussian distribution of activation energies

This paper presents a new approach for the analysis of AC conductivity, = + , in disordered solids which brings together the quasi-universal frequency-dependent conductivity and the idea of a Gaussian distributions of probable activation energy barriers for hopping carriers. An explicit expression for AC conductivity was obtained using a complex dielectric response function and a continuous time random walk treatment applied to a lattice obeying the Kubo’s fluctuation-dissipation theorem. This expression provides an insight into the universality of the form and (k is the dielectric constant), as well into the effect of the Gaussian disorder on exponent s. We discuss the similarities and differences with the Random Free Energy Barrier model equivalent to the long-used box model, and it brings support to an extending expression proposed by J C Dyre and one of the authors. The applicability of the model to experimental observations on poly[(2-methoxy-5-hexyloxy)-p-phenylenevinylene] reveals the dielectric constant, mean energy and variance of the Gaussian distribution for hopping carriers in this disordered conjugated polymer.

Understanding Photoinduced Charge Transfer Dynamics of Single Perylenediimide Dyes in a Polymer Matrix by Bin-Time Dependence of their Fluorescence Blinking Statistics

Fluorescence on–off blinking of single perylenediimide (DMP–PDI) dyes embedded in a disordered matrix of poly(methyl methacrylate) (PMMA) was investigated by single-molecule fluorescence spectroscopy. In particular, we examined the bin-time dependencies of the complementary cumulative distribution functions (cCDF) of the on-time and off-time durations. It appears that intersystem crossing (ISC) within DMP–PDI competes with charge transfer between DMP–PDI and PMMA. The single-molecule and ensemble cCDFs of the on-time and off-time durations (induced by charge transfer) were best described by Weibull functions and log-normal functions, respectively. The dispersive kinetics of the on-time duration were attributed to radical ion pair ISC from triplet charge separation (3CS) state to the corresponding singlet (1CS) state via charge hopping between charge trap sites in PMMA. This process should compete with triplet charge recombination (3CR), which restores the triplet state. On-to-off switching occurs only when 3CS → 1CS ISC overcomes the 3CR process. The resultant Weibull distribution (with A < 1) reflects that the probability of charge hopping rapidly decreases with time. On the other hand, the off-time log-normal kinetics of single-molecules are explained by a Gaussian distribution of activation energies for charge recombination (the so-called Albery model). A simulation study revealed that the ensemble off-time cCDF included power-law kinetics of charge hopping in the polymer matrix.

Hydrogen Dynamics in Partially Quasicrystalline Zr69.5Cu12Ni11Al7.5: A Fast Field-Cycling Relaxometric Study

We studied hydrogen dynamics in a partially quasicrystalline hydrogen storage alloy Zr69.5Cu12Ni11Al7.5 by a combination of fast field-cycling nuclear magnetic relaxometry and diffusometry in static fringe field. We demonstrate that proton spin–lattice relaxation cannot be explained using a single activation energy for proton hopping between the interstitial sites. Instead, the behavior is better explained using a Gaussian distribution of activation energies, with the average value closely matching the one obtained in independent direct diffusion measurements. Knowing the diffusion constant and the correlation times for proton jumps, we estimate the average jump length.

Temperature dependent single molecule rotational dynamics in PMA

Temperature dependent measurements of the rotational diffusion of single dye molecules in the polymer poly(methyl acrylate) (PMA) are presented and compared to shear viscosity data and numerical simulations of the rotational diffusion process. It is found that single molecule rotational diffusion very accurately follows the Debye-Stokes-Einstein predictions for the shear viscosity without any additional parameter. We employ a simple model of dynamic changes of the rotational speed of a single molecule. This dynamic heterogeneity model is based on a Gaussian distribution of activation energies in a VFTH (Vogel-Fulcher-Tammann-Hesse) type temperature dependence of the polymer viscosity. The simulations explain all experimental details concerning the stretched exponential single molecule relaxation dynamics and the related distributions. They also reveal that the observed distributions are related to the intrinsic physical properties of the polymer but do not in general reflect the instantaneous spread of local viscous properties.

Broadening effects and ergodicity in deep level photo-thermal spectroscopy of defect states in semi-insulating GaAs: A combined temperature-, pulse-rate- and time-domain study of defect state kinetics

The technique of Deep Level Photo-Thermal Spectroscopy (DLPTS) is extended to the low temperature region in order to cover several defect states in semi-insulating GaAs. Measurements are taken at three different modes, temperature-scanned, pulse-rate-scanned, and time-scanned DLPTS. It is demonstrated that each mode provides unique information about the defect configuration, and the combination of the different modes offers a powerful tool for DLPTS studies of physical optoelectronic processes in SI-GaAs. The non-exponentiality/broadening of experimental data is extensively studied using the two prevalent broadening theories: the stretched exponential and the Gaussian distribution of activation energies. A hierarchical carrier emission model has been proposed for the stretched exponential behavior. Simulations indicate that the two broadening theories exhibit roughly similar broadening effects and good fits to the experimental data. The origin of this similarity indicates an ergodic equivalence of random energy distribution and the constrained hierarchical emission process.

Photodriven Spin Change of Fe(II) Benzimidazole Compounds Anchored to Nanocrystalline TiO2 Thin Films

Ferrous tris-chelate compounds based on 2-(2'-pyridyl)benzimidazole (pybzim) have been prepared and characterized for studies of spin equilibria in fluid solution and when anchored to the surface of mesoporous nanocrystalline (anatase) TiO(2) and colloidal ZrO(2) thin films. The solid state structure of Fe(pybzim)(3)(ClO(4))(2).CH(3)CN.H(2)O was determined by single-crystal X-ray diffraction at 110 K to be triclinic, P-1, a = 11.6873(18), b = 12.2318(12), c = 14.723(4) A, alpha = 89.864(13) degrees , beta = 71.430(17) degrees , gamma = 73.788(11) degrees , V = 1907.1(6) A(3), Z = 2, and R = 0.0491. The iron compound has a meridional FeN(6) distorted octahedral geometry with bond lengths expected for a low-spin iron center at 110 K. The visible absorption spectra of Fe(pybzim)(3)(2+) and Fe(pymbA)(3)(2+), where pymbA is 4-(2-pyridin-2-yl-benzimidazol-1-ylmethyl)-benzoic acid, in methanol solution were dominated by metal-to-ligand charge-transfer (MLCT) bands. Variable-temperature UV-visible absorption spectroscopy revealed dramatic changes in the extinction coefficient consistent with a high-spin ((1)A) left harpoon over right harpoon low-spin ((5)T) equilibrium. Thermodynamic parameters for the temperature-dependent spin equilibrium of Fe(pymbA)(3)(2+) in methanol were determined to be DeltaH(HL) = 3270 +/- 210 cm(-1) and DeltaS(HL) = 13.3 +/- 0.8 cm(-1) K(-1). The corresponding values for Fe(pybzimEE)(3)(2+), where pybzimEE is (2-pyridin-2-yl-benzimidazol-1-yl)-acetic acid ethyl ester, in acetonitrile solution were determined to be 3072 +/- 34 cm(-1)and 10.5 +/- 0.1 cm(-1) K(-1). The temperature-dependent effective magnetic moments of Fe(pybzimEE)(3)(2+) in acetonitrile solution were also quantified by the Evans method. Pulsed 532 nm light excitation of Fe(pybzim)(3)(2+) or Fe(pymbA)(3)(2+) in solution resulted in an immediate bleach of the MLCT absorption bands. Relaxation back to the equilibrium state followed a first-order reaction mechanism. Arrhenius analysis of the (5)T --> (1)A rate constant yielded an activation energy, E(a), of 1090 +/- 20 cm(-1) and 710 +/- 10 cm(-1) for Fe(pybzim)(3)(2+) and Fe(pymbA)(3)(2+) in methanol, respectively. The compound Fe(pymbA)(3)(2+) was found to bind to colloidal TiO(2) and ZrO(2) thin films. The absorption spectra of the surface-attached compounds were quantified from 295 to 193 K. Pulsed light excitation of Fe(pymbA)(3)/TiO(2) and Fe(pymbA)(3)/ZrO(2) resulted in the immediate bleach of the MLCT absorption bands. Relaxation was nonexponential but was well described by kinetic models based on a Gaussian distribution of activation energies or a Levy distribution of lifetimes. An Arrhenius analysis of the Gaussian data yielded average activation energies of 660 +/- 80 cm(-1) and 730 +/- 40 cm(-1) for Fe(pymbA)(3)(ClO(4))(2) on TiO(2) and ZrO(2) surfaces, respectively. The Levy distribution analysis did not adequately fit the Arrhenius model.

Broadening effects and ergodicity in deep level photothermal spectroscopy of defect states in semi-insulating GaAs: A combined temperature-, pulse-rate-, and time-domain study of defect state kinetics

The technique of deep level photothermal spectroscopy (DLPTS) is extended to the low temperature region in order to cover several defect states in semi-insulating GaAs. Measurements are taken at three different modes, temperature-scanned, pulse-rate-scanned, and time-scanned DLPTS. It is demonstrated that each mode provides unique information about the defect configuration, and the combination of the different modes offers a powerful tool for DLPTS studies of physical optoelectronic processes in SI-GaAs. The nonexponentiality/broadening of experimental data is extensively studied using the two prevalent broadening theories: the stretched exponential and the Gaussian distribution of activation energies. A hierarchical carrier emission model has been proposed for the stretched exponential behavior. Simulations indicate that the two broadening theories exhibit roughly similar broadening effects and good fits to the experimental data. The origin of this similarity indicates an ergodic equivalence of random energy distribution and the constrained hierarchical emission process.

Nuclear magnetic resonance study of hydrogen mobility in LaY 2Ni 9H x and CeY 2Ni 9H x

In order to investigate the mobility of hydrogen in the ternary compounds LaY 2Ni 9 and CeY 2Ni 9, we have measured the proton nuclear magnetic resonance (NMR) spectra and the proton spin–lattice relaxation rates R 1 for LaY 2Ni 9H x ( x=0.78 and 10.3) and CeY 2Ni 9H x ( x=0.79 and 7.2). The measurements have been performed at the resonance frequencies of 14, 23.8 and 90 MHz over the temperature range of 11–404 K. For LaY 2Ni 9H x , the behavior of R 1 is consistent with the presence of a considerable contribution due to motionally modulated dipole–dipole interaction between nuclear spins. This contribution can be satisfactorily described in terms of the Bloembergen–Purcell–Pound model with a Gaussian distribution of activation energies for hydrogen diffusion; the value of the average activation energy resulting from such a description for LaY 2Ni 9H 10.3 is approximately 0.36 eV. For CeY 2Ni 9H x compounds, the measured proton spin–lattice relaxation rates are dominated by the contribution due to the interaction between proton spins and paramagnetic centers over the entire temperature range studied. Only qualitative information on H mobility in these compounds has been obtained from the narrowing of NMR spectra. Possible paths of H diffusion in LaY 2Ni 9H x and CeY 2Ni 9H x are discussed in terms of the distances between the interstitial sites occupied by hydrogen.

Numerical analysis of new distributed activation energy model for the representation of biomass pyrolysis kinetics

AbstractThere are a considerable number of chemical reactions involved in biomass pyrolysis and many different models have been proposed for analysing biomass pyrolysis kinetics. The most accurate and up to date approach for kinetic description of biomass pyrolysis is to adopt the distributed activation energy model (DAEM). The conventional DAEM assumes the Gaussian distribution of activation energies and the same frequency factor for all parallel reactions. However, the Gaussian distribution cannot be directly used for the distribution of activation energies, and the uniform frequency factor approximation is not always valid especially for the initial and final stages of biomass pyrolysis process. In this paper, a new DAEM using a linear relationship between the natural logarithm of the frequency factor and the activation energy and a modified Gaussian distribution for the representation of biomass pyrolysis kinetics has been presented. To obtain the realistic values of the kinetic parameters, some numer...

TG-FTIR pyrolysis of coal and secondary biomass fuels: Determination of pyrolysis kinetic parameters for main species and NOx precursors

Co-firing of secondary biomass fuels with coal in coal-fired pulverized fuel boilers is facing increased application in large-scale power production. Fundamental knowledge on the thermochemical behavior of biomass and waste fuels is still lacking, especially regarding the release of the fuel bound nitrogen. Characterization of chicken litter (CL), biomass mix (BM) and meat and bone meal (MBM) and an HV coal blend was performed using TG-FTIR analysis. Three heating rate profiles were applied (10, 30 and 100 °C/min), with a final temperature of 900 °C. NH3 was found to be the major gaseous N-product, while HCN and HNCO were also released in substantial amounts. Kinetic parameters for the pyrolysis of biomass fuels were obtained using a model based on parallel first-order reactions with a Gaussian distribution of activation energies. Input files for the coal FG-DVC (functional group-devolatilization, vaporization, cross-linking) and FG-BioMass pyrolysis models were prepared. The fit of model parameters to TG-FTIR product-evolution data was found to be generally good, but the model-predicted yields for some species did not fit experimental data at all heating rates equally well. This problem can be overcome by improvements in the FG-BioMass model. The results of this study can be used to have an improved input of initial pyrolysis in CFD modeling of co-fired boilers.

Application of the Thermorheologically Complex Nonlinear Adam-Gibbs Model for the Glass Transition to Molecular Motion in Hydrated Proteins

The nonlinear thermorheologically complex Adam Gibbs (extended “Scherer-Hodge”) model for the glass transition is applied to enthalpy relaxation data reported by Sartor, Mayer, and Johari for hydrated methemoglobin. A sensible range in values for the average localized activation energy is obtained (100–200 kJ mol −1). The standard deviation in the inferred Gaussian distribution of activation energies, computed from the reported KWW β-parameter, is ∼30% of the average, consistent with the suggestion that some relaxation processes in hydrated proteins have exceptionally low activation energies.

Conformational Thermodynamic and Kinetic Parameters of Methyl-Substituted 1,3-Butadienes

The s-trans/s-cis conformational equilibria of 10 methyl-substituted 1,3-butadienes [(E)- and (Z)-1,3-pentadiene; 2-methyl-1,3-butadiene; (E)-2-methyl-1,3-pentadiene; 2,3-dimethyl-1,3-butadiene; (E,E)-, (E,Z)-, and (Z,Z)-2,4-hexadiene; 2,5-dimethyl-2,4-hexadiene; and (E,E)-2,4-dimethyl-2,4-hexadiene] were explored by trapping high-temperature conformational equilibria by cryogenic deposition. The vapor state enthalpy differences of these s-trans/s-cis conformers, DeltaH(t equilibrium c), were determined by varying the equilibrating temperature and integrating the resulting matrix isolated IR spectra. The results obtained are in good agreement with ab initio calculations at the G3 level. From these thermodynamic parameters, methyl group nonbonded interactions in conjugated 1,3-butadienes were delineated. Rates of decay of s-cis conformers to their s-trans rotamers were obtained in the solid-state by warming up trapped high-temperature equilibrated samples formed from neat depositions. These data were analyzed in terms of dispersive kinetics with matrix site effects in the solid-state modeled by a Gaussian distribution of activation energies. The activation barriers thus obtained were compared with G3 calculations of the enthalpies of activation.

Pyrolysis of Miscanthus Giganteus and wood pellets: TG-FTIR analysis and reaction kinetics ☆

Characterisation of two biomass fuels (pelletised Miscanthus Giganteus and wood) was performed using thermogravimetric analysis with measurement of products by means of Fourier transform infrared spectroscopy (TG-FTIR). Three heating rate profiles were applied (10, 30 and 100 °C/min), with a final temperature of 900 °C. HCN and HNCO were found to be the major N-products, while the NH 3 fraction was detected to a minor extent. Kinetic parameters were obtained from the TG-FTIR results using a model based on parallel first-order reactions with a Gaussian distribution of activation energies. On the basis of the above kinetic analysis and product yields, input files for the functional group–devolatilisation, vaporisation, cross-linking biomass-pyrolysis model were prepared. The fit of model parameters to TG-FTIR product-evolution data was found to be generally good, but the model-predicted yields for some species did not fit experimental data at all heating rates. Further improvements in the model are needed to resolve above difficulty.

Modeling the evolution of volatile species during tobacco pyrolysis

A great need exists for comprehensive biomass-pyrolysis models that could predict yields and evolution patterns of selected volatile products as a function of feedstock characteristics and process conditions. Low heating rate data obtained from a thermogravimetric analyzer (TGA), coupled with Fourier transform infrared analysis of evolving products (TG-FTIR), were used to perform kinetic analysis of tobacco pyrolysis. The results were utilized to create input to a biomass-pyrolysis model based on first-order kinetic expressions with a Gaussian distribution of activation energies. Pyrolysis simulations were carried out for high heating rate conditions, and predicted product yields were compared with literature data.

Evolved gas analysis of some solid fuels by TG-FTIR

Co-firing of secondary biomass fuels with coal in coal-fired pulverized fuel boilers is facing increased application in large-scale power production. Fundamental knowledge on the thermochemical behavior of biomass and waste fuels is still lacking, especially regarding the release of the fuel bound nitrogen. Characterization of chicken litter (CL), biomass mix (BM) and meat and bone meal (MBM) and an HV coal blend was performed using TG-FTIR analysis. Three heating rate profiles were applied (10, 30 and 100 °C/min), with a final temperature of 900 °C. NH3 was found to be the major gaseous N-product, while HCN and HNCO were also released in substantial amounts. Kinetic parameters for the pyrolysis of biomass fuels were obtained using a model based on parallel first-order reactions with a Gaussian distribution of activation energies. Input files for the coal FG-DVC (functional group-devolatilization, vaporization, cross-linking) and FG-BioMass pyrolysis models were prepared. The fit of model parameters to TG-FTIR product-evolution data was found to be generally good, but the model-predicted yields for some species did not fit experimental data at all heating rates equally well. This problem can be overcome by improvements in the FG-BioMass model. The results of this study can be used to have an improved input of initial pyrolysis in CFD modeling of co-fired boilers.

Rate constants for the reaction of H2 with defects at the SiO2/Si(111) interface

A radio frequency probe has been used to monitor changes in charge-carrier recombination centers at a SiO2/Si interface by following the steady-state photogenerated carrier concentration in the silicon. A silicon surface covered with ∼200 Å of thermal oxide was exposed to gaseous molecular hydrogen at temperatures between 135 and 300 °C. The reaction was found to occur with a nonexponential rate law that could be described by a cluster of rate constants governed by a Gaussian distribution of activation energies. At high temperatures, the dominant reaction was found to be that of “Pb” centers with a rate law that is consistent with that previously obtained by electron paramagnetic resonance. At low temperatures the reaction is dominated by the passivation of a carrier recombination center with a much lower activation energy. This new species makes up about 25% of the total recombination center concentration at the Si/SiO2 interface. Almost 20% of the recombination centers could not be passivated by H2.

31P NMR relaxation in glassy 0.35 LiF·0.65 LiPO 3

LiF doped LiPO 3 glasses have been investigated by means of nuclear magnetic resonance. Spin–lattice relaxation rates of the stationary 31 P nucleus have been measured in both the laboratory and the rotating frame of reference, thus covering the wide frequency range from about 34 kHz to 81 MHz. The temperature and frequency dependence of the rates is described by the Bloembergen–Purcell–Pound model, modified with a Gaussian distribution of activation energies. For doped and undoped samples, the derived values for the activation energy of the lithium motion compare well with those obtained by DC conductivity measurements. We also report on aging effects in the glassy samples.

Pyrolysis of pitch

Kinetics of thermal pyrolysis of pitches from two heavy oil upgrading processes have been studied using thermogravimetric analysis. Experiments were carried out at atmospheric pressure with heating rates of 25–150°C min −1 to a final temperature of 800°C. At temperatures below 150°C, there is little devolatilization of either pitch. At higher temperatures, the pyrolysis takes place in two stages. Heating rate had a minor effect on the weight loss at a given temperature. Single-stage, first-order reaction methods, including models which incorporate a Gaussian distribution of activation energies, were found to be inadequate to interpret the thermogravimetric analysis results. A two-stage model which reflects changes in the chemical constitution or structure as conversion prcoeeds was necessary to describe the dependence of devolatilization rates on remaining volatile content. The transition between these two stages is a sharp one, occurring at about 450°C for both pitches. The magnitudes of the activation energies suggest that both stages are kinetically controlled.

Wide frequency range 31P relaxation in the ion conducting glass LiPO 3

Spin–lattice relaxation studies on the stationary 31P nucleus have been performed in order to investigate to which extent the dynamics of the mobile lithium ions are reflected in the behavior of the glassy network. The temperature dependence of the 31P relaxation, which is governed by the heteronuclear dipole–dipole interaction between lithium and phosphorus, can be described in terms of a Gaussian distribution of activation energies and that over a wide frequency range from about 34 kHz to 81 MHz. A relaxation rate maximum, which provides useful information about correlation times and activation energies of the lithium-ion diffusion process, could only be observed in the rotating frame relaxation measurements.