Gaussian Distribution Of Activation Research Articles

Quasielastic neutron scattering studies on couplings of protein and water dynamics in hydrated elastin.

Performing quasielastic neutron scattering measurements and analyzing both elastic and quasielasic contributions, we study protein and water dynamics of hydrated elastin. At low temperatures, hydration-independent methyl group rotation dominates the findings. It is characterized by a Gaussian distribution of activation energies centered at about Em = 0.17 eV. At ∼195 K, coupled protein-water motion sets in. The hydration water shows diffusive motion, which is described by a Gaussian distribution of activation energies with Em = 0.57 eV. This Arrhenius behavior of water diffusion is consistent with previous results for water reorientation, but at variance with a fragile-to-strong crossover at ∼225 K. The hydration-related elastin backbone motion is localized and can be attributed to the cage rattling motion. We speculate that its onset at ∼195 K is related to a secondary glass transition, which occurs when a β relaxation of the protein has a correlation time of τβ ∼ 100 s. Moreover, we show that its temperature-dependent amplitude has a crossover at the regular glass transition Tg = 320 K of hydrated elastin, where the α relaxation of the protein obeys τα ∼ 100 s. By contrast, we do not observe a protein dynamical transition when water dynamics enters the experimental time window at ∼240 K.

Thermally Induced Structural Evolution of Silicon- and Oxygen-Containing Hydrogenated Amorphous Carbon: A Combined Spectroscopic and Molecular Dynamics Simulation Investigation.

Silicon- and oxygen-containing hydrogenated amorphous carbon (a-C:H:Si:O) coatings are amorphous thin-film materials composed of hydrogenated amorphous carbon (a-C:H), doped with silicon and oxygen. Compared to a-C:H, a-C:H:Si:O exhibits much lower susceptibility to oxidative degradation and higher thermal stability, making a-C:H:Si:O attractive for many applications. However, the physical mechanisms for this improved behavior are not understood. Here, the thermally induced structural evolution of a-C:H:Si:O was investigated in situ by X-ray photoelectron and absorption spectroscopy, as well as molecular dynamics (MD) simulations. The spectroscopy results indicate that upon high vacuum annealing, two thermally activated processes with a Gaussian distribution of activation energies with mean value E and standard deviation σ take place in a-C:H:Si:O: (a) ordering and clustering of sp2 carbon ( E ± σ = 0.22 ± 0.08 eV) and (b) conversion of sp3- to sp2-bonded carbon ( E ± σ = 3.0 ± 1.1 eV). The experimental results are in qualitative agreement with the outcomes of MD simulations performed using a ReaxFF potential. The MD simulations also indicate that the higher thermal stability of a-C:H:Si:O compared to a-C:H (with similar fraction of sp2-bonded carbon and hydrogen content) derives from the significantly lower fraction of strained carbon-carbon sp3 bonds in a-C:H:Si:O compared to a-C:H, which are more likely to break at elevated temperatures.

Relation of short-range and long-range lithium ion dynamics in glass-ceramics: Insights fromLi7NMR field-cycling and field-gradient studies

We use various $^{7}\mathrm{Li}$ NMR methods to investigate lithium ion dynamics in ${70\mathrm{Li}}_{2}{\mathrm{S}\ensuremath{-}30\mathrm{P}}_{2}{\mathrm{S}}_{5}$ glass and glass-ceramic obtained from this glass after heat treatment. We employ $^{7}\mathrm{Li}$ spin-lattice relaxometry, including field-cycling measurements, and line-shape analysis to investigate short-range ion jumps as well as $^{7}\mathrm{Li}$ field-gradient approaches to characterize long-range ion diffusion. The results show that ceramization substantially enhances the lithium ion mobility on all length scales. For the ${70\mathrm{Li}}_{2}{\mathrm{S}\ensuremath{-}30\mathrm{P}}_{2}{\mathrm{S}}_{5}$ glass-ceramic, no evidence is found that bimodal dynamics result from different ion mobilities in glassy and crystalline regions of this sample. Rather, $^{7}\mathrm{Li}$ field-cycling relaxometry shows that dynamic susceptibilities in broad frequency and temperature ranges can be described by thermally activated jumps governed by a Gaussian distribution of activation energies $g({E}_{\mathrm{a}})$ with temperature-independent mean value ${E}_{\mathrm{m}}=0.43\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and standard deviation $\ensuremath{\sigma}=0.07\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. Moreover, use of this distribution allows us to rationalize $^{7}\mathrm{Li}$ line-shape results for the local ion jumps. In addition, this information about short-range ion dynamics further explains $^{7}\mathrm{Li}$ field-gradient results for long-range ion diffusion. In particular, we quantitatively show that, consistent with our experimental results, the temperature dependence of the self-diffusion coefficient $D$ is not described by the mean activation energy ${E}_{\mathrm{m}}$ of the local ion jumps, but by a significantly smaller apparent value whenever the distribution of correlation times $G(log\ensuremath{\tau})$ of the jump motion derives from an invariant distribution of activation energies and, hence, continuously broadens upon cooling. This effect occurs because the harmonic mean, which determines the results of diffusivity or also conductivity studies, continuously separates from the peak position of $G(log\ensuremath{\tau})$ when the width of this distribution increases.

Effective noise-suppressed and artifact-reduced reconstruction of SPECT data using a preconditioned alternating projection algorithm.

The authors have recently developed a preconditioned alternating projection algorithm (PAPA) with total variation (TV) regularizer for solving the penalized-likelihood optimization model for single-photon emission computed tomography (SPECT) reconstruction. This algorithm belongs to a novel class of fixed-point proximity methods. The goal of this work is to investigate how PAPA performs while dealing with realistic noisy SPECT data, to compare its performance with more conventional methods, and to address issues with TV artifacts by proposing a novel form of the algorithm invoking high-order TV regularization, denoted as HOTV-PAPA, which has been explored and studied extensively in the present work. Using Monte Carlo methods, the authors simulate noisy SPECT data from two water cylinders; one contains lumpy "warm" background and "hot" lesions of various sizes with Gaussian activity distribution, and the other is a reference cylinder without hot lesions. The authors study the performance of HOTV-PAPA and compare it with PAPA using first-order TV regularization (TV-PAPA), the Panin-Zeng-Gullberg one-step-late method with TV regularization (TV-OSL), and an expectation-maximization algorithm with Gaussian postfilter (GPF-EM). The authors select penalty-weights (hyperparameters) by qualitatively balancing the trade-off between resolution and image noise separately for TV-PAPA and TV-OSL. However, the authors arrived at the same penalty-weight value for both of them. The authors set the first penalty-weight in HOTV-PAPA equal to the optimal penalty-weight found for TV-PAPA. The second penalty-weight needed for HOTV-PAPA is tuned by balancing resolution and the severity of staircase artifacts. The authors adjust the Gaussian postfilter to approximately match the local point spread function of GPF-EM and HOTV-PAPA. The authors examine hot lesion detectability, study local spatial resolution, analyze background noise properties, estimate mean square errors (MSEs), and report the convergence speed and computation time. HOTV-PAPA yields the best signal-to-noise ratio, followed by TV-PAPA and TV-OSL/GPF-EM. The local spatial resolution of HOTV-PAPA is somewhat worse than that of TV-PAPA and TV-OSL. Images reconstructed using HOTV-PAPA have the lowest local noise power spectrum (LNPS) amplitudes, followed by TV-PAPA, TV-OSL, and GPF-EM. The LNPS peak of GPF-EM is shifted toward higher spatial frequencies than those for the three other methods. The PAPA-type methods exhibit much lower ensemble noise, ensemble voxel variance, and image roughness. HOTV-PAPA performs best in these categories. Whereas images reconstructed using both TV-PAPA and TV-OSL are degraded by severe staircase artifacts; HOTV-PAPA substantially reduces such artifacts. It also converges faster than the other three methods and exhibits the lowest overall reconstruction error level, as measured by MSE. For high-noise simulated SPECT data, HOTV-PAPA outperforms TV-PAPA, GPF-EM, and TV-OSL in terms of hot lesion detectability, noise suppression, MSE, and computational efficiency. Unlike TV-PAPA and TV-OSL, HOTV-PAPA does not create sizable staircase artifacts. Moreover, HOTV-PAPA effectively suppresses noise, with only limited loss of local spatial resolution. Of the four methods, HOTV-PAPA shows the best lesion detectability, thanks to its superior noise suppression. HOTV-PAPA shows promise for clinically useful reconstructions of low-dose SPECT data.

Mapping coexistence lines via free-energy extrapolation: Application to order-disorder phase transitions of hard-core mixtures

In this work, a variant of the Gibbs-Duhem integration (GDI) method is proposed to trace phase coexistence lines that combines some of the advantages of the original GDI methods such as robustness in handling large system sizes, with the ability of histogram-based methods (but without using histograms) to estimate free-energies and hence avoid the need of on-the-fly corrector schemes. This is done by fitting to an appropriate polynomial function not the coexistence curve itself (as in GDI schemes) but the underlying free-energy function of each phase. The availability of a free-energy model allows the post-processing of the simulated data to obtain improved estimates of the coexistence line. The proposed method is used to elucidate the phase behavior for two non-trivial hard-core mixtures: a binary blend of spheres and cubes and a system of size-polydisperse cubes. The relative size of the spheres and cubes in the first mixture is chosen such that the resulting eutectic pressure-composition phase diagram is nearly symmetric in that the maximum solubility of cubes in the sphere-rich solid (∼20%) is comparable to the maximum solubility of spheres in the cube-rich solid. In the polydisperse cube system, the solid-liquid coexistence line is mapped out for an imposed Gaussian activity distribution, which produces near-Gaussian particle-size distributions in each phase. A terminal polydispersity of 11.3% is found, beyond which the cubic solid phase would not be stable, and near which significant size fractionation between the solid and isotropic phases is predicted.

NMR Study of Reorientational Motion in Alkaline-Earth Borohydrides: β and γ Phases of Mg(BH4)2 and α and β Phases of Ca(BH4)2

To study the reorientational motion of BH4 groups in β and γ phases of Mg(BH4)2 and in α and β phases of Ca(BH4)2, we have performed nuclear magnetic resonance (NMR) measurements of the 1H and 11B spin–lattice relaxation rates in these compounds over wide ranges of temperature and resonance frequency. It is found that at low temperatures the reorientational motion in β phases of Mg(BH4)2 and Ca(BH4)2 is considerably faster than in other studied phases of these alkaline-earth borohydrides. The behavior of the measured spin–lattice relaxation rates in both β phases can be satisfactorily described in terms of a Gaussian distribution of activation energies Ea with the average Ea values of 138 meV for β-Mg(BH4)2 and 116 meV for β-Ca(BH4)2. The α phase of Ca(BH4)2 is characterized by the activation energy of 286 ± 7 meV. For the novel porous γ phase of Mg(BH4)2, the main reorientational process responsible for the observed spin–lattice relaxation rate maximum can be described by the activation energy of 276 ± 5 meV. The barriers for reorientational motion in different phases of alkaline-earth borohydrides are discussed on the basis of changes in the local environment of BH4 groups.

SU‐GG‐J‐189: Use of a Clinically Relevant Digital PET Chest Phantom to Investigate the Threshold Required to Define a PET‐Based Target Volume

Purpose: To examine the relationship between the threshold required to segment PET‐based target volumes placed in inhomogeneous background provided by a digital PET chest phantom. Method and Materials: We placed four spheres of uniform activity and sizes ranging from 2–13ml in the lung, mediastinum and lung/mediastinum boundary in the chest of a digital PET phantom. The intensity of the spheres was adjusted to obtain different target to background (T/B) ratios and the threshold as a percent of the maximum image intensity required to get the true tumor volume was estimated. We also constructed a spherical target of non‐uniform activity by placing a spatial Gaussian activity distribution in the larger (13ml) sphere and adjusting its intensity to obtain various T/B ratios. Results: The results suggest that a threshold varying from 37–55% may be required to segment the true target volume depending on the location and size of the target. Smaller targets and ones placed in higher background activities (such as the mediastinum) require higher thresholds than larger targets or the ones placed in lower intensity background (such as the lung). Adding inhomogeneity in the intensity of the target results in lower thresholds required and smaller difference between the threshold required to segment targets in higher and lower image intensity backgrounds. Conclusion: For the first time to our knowledge we present a study investigating PET‐based threshold segmentation in a realistic situation, where the target's background activity is similar to what is seen in clinical cases. The most important finding of this study is the indication that lesions in the mediastinum require higher thresholds than the ones in normal lung or at the boundary between lung and mediastinum.

Analysis of volatile species kinetics during typical medical waste materials pyrolysis using a distributed activation energy model

The complex reactions of typical medical waste materials pyrolysis and the evolution of different volatile species can be well represented by a Distributed Activation Energy Model (DAEM). In this study, A thermogravimetric analyser (TGA), coupled with Fourier transform infrared analysis of evolving products (TG-FTIR), were used to perform kinetic analysis of typical medical waste materials pyrolysis. A simple direct search method was used for the determination of DAEM kinetic parameters and the yield of individual pyrolysis products under any given heating condition. The agreement between the model prediction and the experimental data was generally good. The results can be used as inputs to a pyrolysis model based on first-order kinetic expression with a Gaussian Distribution of Activation Energies as a sub-model to CFD code.

Tacticity effects on the barriers to rotation of the ester methyl group in poly (methyl methacrylate): a deuteron magnetic resonance study.

In isotactic poly(methyl methacrylate) (PMMA), we investigate the dynamics of the ester methyl groups by means of deuteron magnetic resonance (DMR) in a deuterated sample. We find that the motion of the CD(3)-group affects the deuteron spin-lattice relaxation as well as the DMR line shape in a characteristic way. Quadrupolar order spin lattice relaxation measurements between T=291 K and T=70 K reveal a broad temperature dependent probability distribution of autocorrelation times tau(c) for the 2pi/3 reorientation. This broad distribution corresponds to a temperature independent Gaussian distribution of activation energies rho(E(a)) with variance sigma(E(a) )=13.8+/-0.5 meV (1.33 kJ/mol). The line shape transition between T=70 K and T=23 K is explained with the freezing in of the methyl group reorientation. By comparing our results in an 88% isotactic sample with results obtained from a 50% syndiotactic, 30% atactic, and 20% isotactic sample of a previous investigation, we demonstrate the higher local order of the 88% isotactic sample, which corresponds to a ratio of 1.6 in the relative width sigma(E(a) )/E(a) of the E(a) distribution. We show that different stereospecific forms of PMMA can be easily distinguished by the characteristics of their line shape transition between T=70 K and T=23 K.

The influence of transformation twins on the seismic-frequency elastic and anelastic properties of perovskite: dynamical mechanical analysis of single crystal LaAlO3

The low-frequency mechanical properties of single crystal LaAlO3 have been investigated as a function of temperature, frequency and applied force using the technique of dynamical mechanical analysis (DMA) in three-point bend geometry. LaAlO3 undergoes a cubic to rhombohedral phase transition below 550 ◦ C. The mechanical response in the low-temperature rhombohedral phase is shown to be dominated by the viscous motion of transformation twin domain walls, resulting in a factor of 10 decrease in the storage modulus relative to the high-temperature cubic phase (super-elastic softening) and a significant increase in attenuation. Super-elastic softening is observed down to 200 ◦ C, below which the mobility of the domain walls decreases markedly, causing a rapid increase in storage modulus and a pronounced peak in attenuation (domain wall freezing). The frequency dependence of the storage modulus close to the freezing temperature is accurately described by a modified Burgers model with a Gaussian distribution of activation energies with mean value 84.1(1) kJ/mol and S.D. 10.3(1) kJ/mol. This activation energy suggests that domain walls are pinned predominantly by oxygen vacancies. Detailed analysis of the dynamic force-deflection curves reveals three distinct regimes of mechanical response. In the elastic regime, the domain walls are pinned and unable to move. The elastic response is linear with a slope determined by the intrinsic stiffness of the lattice, the initial susceptibility of the pinning potential and the bending of twin walls between the pinning sites. In the super-elastic regime, the domain walls unpin and displace by an amount determined by the balance between the applied and restoring forces. The value of the apparent super-elastic modulus is shown to be independent of the spontaneous strain and hence independent of temperature. At high values of the applied force, adjacent domain walls come into contact with each other and prevent further super-elastic deformation (saturation). The strain in the saturation regime scales with the spontaneous strain and the resulting modulus is strongly temperature dependent. The possible effects of domain wall motion on the seismic properties of minerals are discussed. It is concluded that, if these results are directly transferred to mantle-forming (Mg, Fe)(Si, Al)O 3 perovskite, the strain amplitude of a typical seismic wave would be sufficient to cause super-elastic softening. However, pinning of domain walls by oxygen vacancies leads to very short relaxation times at mantle temperatures. If translated to (Mg, Fe)(Si, Al)O 3, these would be too short to amount to significant seismic attenuation. Increased pinning of ferroelastic domain walls by defects, impurities and grain boundaries

An experimental comparison of in-situ gamma spectrometric methods for quantifying Cs-137 radioactive contamination in the ground

In-situ gamma spectrometry is a potentially powerful method for rapid quantification of radioactive contamination in the ground using an above-ground detector. The accuracy of the technique, however, depends on having information on the activity variation with depth. Three methods have previously been proposed for deriving this information using information obtained in the field. This paper describes these methods and models used to approximate activity-depth distributions and presents an experimental comparison for a range of sites of differing activity concentrations and sources of contamination. It was found that the Lead Plate Method in conjunction with a modified gaussian activity distribution model gave the best results estimating activity concentrations on average to within a factor of 1.5 of the true value.

Monte Carlo study of freezing of polydisperse hard spheres.

We have established the solid-fluid coexistence region for a system of polydisperse hard spheres with near Gaussian diameter distributions, as a function of polydispersity. Our approach employs Monte Carlo simulation in the isobaric semigrand ensemble with a Gaussian activity distribution. Gibbs-Duhem integration is used to trace the coexistence pressure as a function of the variance of the imposed activity distribution. Significantly, we observe a ``terminal'' polydispersity above which there can be no fluid-solid coexistence. The terminus arises quite naturally as the Gibbs-Duhem integration path leads the pressure to infinity. This pressure divergence is an artifact of the method used to evaluate the freezing transition, because the sphere diameters vanish in this limit. A simple rescaling of the pressure with the average diameter brings the terminal pressure to a finite value. Nevertheless, the existence of this terminus only at infinite pressure precludes the construction of a continuous path from the solid to the fluid. At the terminus the polydispersity is 5.7% for the solid and 11.8% for the fluid while the volume fractions are 0.588 and 0.547 for the solid and fluid, respectively. Substantial fractionation observed at high values of the polydispersity (\ensuremath{\gtrsim}5%) implies that the ``constrained eutectic'' assumption made in previous theoretical studies is not generally valid. Our results for the terminal polydispersity are consistent with experiments performed on polydisperse colloidal suspensions. \textcopyright{} 1996 The American Physical Society.

Hydrogen diffusion in amorphous Ni35Ti65studied by NMR

The relaxation rates Gamma 1 and Gamma 2 of hydrogen in amorphous Ni35Ti65 have been observed in the temperature range from 100K to 450K at the external fields 0.2 T, 0.8 T and 2.1 T. The temperature and field dependences of the Gamma 1 relaxation rate indicates that the diffusion of hydrogen cannot be described by one thermally activated process but with a gaussian distribution of activation energies with a maximum at Q=0.35 eV, and half-width Delta Q12/=0.16 eV. The pre-exponential factor tau 0=7*10-13 s was found to be of the same order as for crystalline materials in the adiabatic limit.

Heterogeneous denaturation of enzymes: A distributed activation energy model with nonuniform activities

A model is proposed for the denaturation of enzymes based on heterogeneous enzyme subpopulations with nonuniform initial activities and nonzero final activities. The more frequently used simple first-order deactivation model is a special case of the model corresponding to the standard deviation of Gaussian distribution of activation energies approaching zero. Parametric studies made with the model are capable of simulating the reported trends in experimental data on the thermal profile and activity time behavior of native as well as modified enzymes with a minimum number of adjustable parameters. The model predictions are found to be in good agreement with data reported in the literature.

Thermal desorption spectroscopy of he from Ni at and below saturation

Abstract Trapping of helium after implantation at energies of 8 to 150 keV and fluences up to 1019 He-ions/cm2 in nickel at room temperature is studied by measuring the thermal desorption spectra during linear heating up to 1000°C. At several annealing stages the trapped helium is measured by means of the nuclear reaction 3He(d, α)H and the target surface is observed by laser scattering and with the scanning electron microscope. The thermal desorption spectra depend strongly on the implantation fluence but only slightly on the implantation energy, indicating a similar trapping of He in the lattice for the implantation energies used here, The temperature at which desorption starts decreases with increasing fluence. Above the critical fluence for blistering an additional low temperature (150°C) desorption maximum is found. The desorption peak at 150°C can be approximated theoretically with a single jump desorption process of first order and a Gaussian distribution of activation energies around 1 eV. The mea...

Approximate solution technique for nonisothermal, gaussian distributed activation energy models

The literature on combustion and pyrolysis contains many references to pyrolytic reaction models based on the concept of a Gaussian distribution of activation energies. Such models have been used to describe the pyrolysis of coal [1-12], oil shale [13], and cellulose [14] ; they are seen as particularly appropriate for describing the pyrolysis of certain natural products containing a variety of chemically distinct functional groups. It has been pointed out that the use of a single first-order reaction rate model to describe overall volatiles formation can give rise to activation energies which are too low to be realistic for chemical processes (even in situations in which transport limitations play no role) [2, 6]. As a compromise between detailed individual product evolution models [1, 7, 10, 13 15-17] and the single pseudoreaction models, a few groups have modeled the overall rate of weight loss during pyrolysis as being governed by a Gaussian distribution of activation energies [4-6, 8, 9, 14]. This approach recognizes the fact that there are many distinct chemical pathways available for formation of volatiles, but does not get involved with the actual identification of all volatile species. In one test case, analysis of detailed product formation kinetics has shown the Gaussian distribution concept to be reasonable [17]. It is sometimes necessary to use models which distinguish between the evolution of different types of volatiles. Among the detailed individual volatile product formation models, a growing

Cellulose pyrolysis kinetics and char formation mechanism

The pyrolysis of cellulose was studied by electrically heating in helium single strips (0.75 cm×2.5 cm) of low ash (<0.07%) predried filter paper (≈0.01 cm thick) supported inside a folded wire mesh heating element mounted in a sealed vessel. The samples were rapidly brought to a desired temperature, held there for a desired time and then rapidly cooled. Extents of conversion to volatiles, measured by weighing samples before and after experiments of known duration, were determined as a function of residence time (0.2–75,600 s), final temperature (250–1,000°C), heating rate (400–10,000°C/s), and ambient pressure (0.0005–1 atm). Pyrolysis kinetics was determined by nonisothermal techniques to account for substantial reaction occurring during sample heat-up and cool-down. All of the cellulose was converted to volatiles without char formation, except when an extended heating period at a low temperature (e.g., an hour or longer at 250°C) preceded the pyrolysis at higher temperatures. The latter procedure resulted in char yields of about 2% by weight of the original cellulose. The kinetics data are well described by a single-reaction first-order decomposition model with an activation energy of 33.4 kcal/mole and a frequency factor of 6.79×10 9 s −1 . The correlation is slightly improved by use of a multiple-reaction model based on a set of independent parallel first-order reactions represented by a Gaussian distribution of activation energies with a mean of 37.0 kcal/mole and a standard deviation of 1.1 kcal/mole. Selected experiments at reduced pressures (0.0005 atm), elevated heating rates (10,000°C/s), or both resulted in rate constants smaller than those obtained at 400°C/s and 1 atm. The results indicate that the residence time of volatile products within the pyrolyzing cellulose matrix is extremely important in determining conversion. Suggested pathways for cellulose pyrolysis that are consistent with these findings and with much of the pertinent literature involve primary decomposition to an oxygen-rich intermediate (probably levoglucosan) which then participates in three processes to extents depending on experimental conditions: (a) direct escape from the decomposing material into the ambient gas; (b) polymerization, cross-linking and cracking to form char and (c) pyrolysis to smaller volatiles some of which inhibit the char formation in (b) or autocatalyze (c). Accordingly, char is not a primary product, and the yield of char is zero for extremely short residence times of the primary products within the matrix of the decomposing material or for conditions that permit complete inhibition of char formation by secondary pyrolysis products.

A wide-line NMR study of reorientation of some spherical-top molecules enclathrated in water

NMR spectra at temperatures down to 1.8 K are given for the 19F resonance of SF6 and CF4 in H2O and D2O clathrates and for the 1H resonance in CH4–D2O and CH4–tetrahydrofuran-d8–D2O clathrates. The second moments correspond effectively to isotropic reorientation of encaged SF6, CF4, and CH4 molecules at temperatures above 13, 22, and 4 K, respectively. The CH4 spectra are only slightly broadened at 1.8 K. For SF6 and CF4 a low-temperature transition in second moment is characterized by the superposition on the rigid lattice band of a narrow component whose intensity increases progressively with rise of temperature. This ’’apparent phase-change effect,’’ after Resing, is attributed to a very broad distribution of reorientational correlation times, here associated with orientational disorder of the water molecules of the lattice. The behavior during the transition agrees with a model which assumes a Gaussian distribution of activation energies about a mean value of 207 cal/mol for SF6 and 360 cal/mol for CF4.

Rapid devolatilization of pulverized coal

The rapid devolatilization of a lignite and a bituminous coal was studied by electrically heating in helium approximately monolayer samples of small particles supported on wire mesh heating elements. The samples were rapidly brought to a desired temperature, held there for a desired time, and then rapidly cooled. Devolatilization rates, measured by weighing samples before and after experiments of known duration, were determined as a function of residence time (0.05–20 sec), temperature (400–1100°C), heating rate (102–104°C/sec), pressure (0.001–100 atm), and particle size (50–1000 μm). Devolatilization kinetics were determined by non-isothermal techniques since substantial reaction occurred during heating even under the most rapid heating rates. Weight loss from both coals was essentially complete within a fraction to a few seconds depending upon temperature, and increased with increasing final temperature up to 900 to 950°C. Weight loss (corrected to its value at a fixed temperature) was found to be independent of pressure, heating rate and particle size for the lignite, i.e., it depended only on temperature and time; but for the bituminous coal it increased with decreasing pressure, decreasing particle size and, to a small extent, increasing heating rate. The general reaction scheme appears to involve thermal decomposition forming volatiles and initiating a sequence of secondary polymerization and char-forming reactions. The kinetics and yields of the primary decomposition are successfully described by a set of independent first-order parallel reactions represented by a Gaussian distribution of activation energies around a mean of 56 kcal/mole for the lignite, with a standard deviation of 11, and 51 kcal/mole for the bituminous coal at 69 atm and 70 μm particle diameter, with a standard deviation of 7. For the bituminous coal it was necessary in addition to allow for pressure- and particle-size-dependent secondary reactions representing competition between char-forming reactions and diffusional escape of volatiles. Attempts to correlate the data in terms of a single first-order reaction lead to an overall activation energy (∼10 kcal/mole) that is considerably lower than the mean activation energy of the multiple-reaction system, and to a different set of kinetic parameters for each set of experimental conditions. Conditions such as lower pressure, smaller particle size, and better particle dispersion which help to diminish the effect of secondary reactions appear to be more important than rapid heating in the production of volatile yields in excess of the volatile content obtained by proximate analysis.