Pre-exponential Constant Research Articles

Kinetics of halide exchange on polystyrene resin and the effect of γ-irradiation

The kinetic behaviour of I −/ ∗I −, Br −/ ∗I − and Cl −/ ∗I − exchanges on strong base anion exchanger has been investigated under conditions of particle diffusion and limited bath technique. Corresponding energy of activation, pre-exponential constant, entropy change and half-time of exchange have been calculated. These parameters increase in the order of I − > Br − > Cl −. Studies on γ-irradiated resin upto 35 Mrad dose showed an increase in the values for the last parameter and a decrease in the values for the first three: for example, activation energy regarding I −/ ∗I − system decreased from 30.4 to 24.6 kJ mol −1.

Thermal degradation study of phenolphthalein polycarbonate

AbstractPhenolphthalein polycarbonate underwent complicated thermal degradation which included random scission, rearrangement, hydrolysis, Friedel‐Crafts acylation, and cross‐linking. The carbonate group and lactone ring were both susceptible to thermal deterioration. Kinetic parameters were determined from the dynamic TGA thermograms. During early stages of degradation the measured reaction order was nearly 1, which suggested a random chain scission mechanism. The measured activation energy was 42.6 kcal/mol, compared with 41.2 kcal/mol calculated from isothermal aging. The Arrhenius preexponential constant was 3.09 × 1011 min−1. Below 80% weight residue the plot of fractional weight against 1/T revealed that complicated reactions with different activation energies occurred simultaneously and resulted in a final overlap of TGA curves for different heating rates indicative of cross‐linking and a lower preexponential constant. The reaction order changed and kept increasing in the last stages of degradation. Pyrolysis of this polymer was performed at 350°C under vacuum, followed by GC‐mass spectroscopic identification of products. The volatile products (17.5%) contained CO2, CO, O2, H2O, phenol, fluorenone, diphenyl carbonate, xanthone, anthraquinone, 2‐hydroxylanthraquinone, 2‐benzoxyanthraquinone, phenolphthalein, and trace amounts of benzoxyphenol and hydroquinone; the other 82.5% of products was insoluble gel. Functional group changes were examined by Fourier transform infrared spectroscopy (FT‐IR). Lactone, carbonate, and aromatic absorptions decreased during degradation. Increasing absorptions at 1739, 1728, 1280–1200, and 1138–1075 cm−1 were believed to result from aromatic ester (1728 cm−1) and phenyl aromatic ester (1739 cm−1) cross‐linkages ortho to the aromatic ether group (increases at 1155 cm−1 and 1280–1200 cm−1). Existence of 2‐hydroxyanthraquinone and xanthone contained in the crosslinked polymer matrix were also detected. Mechanisms for random scission, rearrangement, Friedel‐Crafts acylation, hydrolysis, and cross‐linking were suggested.

Fast Li + conduction in fluoroborate glasses

Following recent measurements of very high d.c. conductivities in complex Li fluoride-borate-sulfate glasses, we have performed systematic measurements in the Li 2OLiFB 2O 3 system. All glasses studied have essentially the same Arrhenius pre-exponential constant. Converting the data to conductivity relaxation times the pre-exponential constant corresponds to a frequency considerably higher than the Li + - cage “rattling” frequency. Connections between the a.c. conductivity and the IR absorptivity are discussed.

The lateral diffusion of boron in polycrystalline silicon and its influence on the fabrication of sub-micron MOSTs

The fabrication of submicron silicon gate MOSTs by the lateral diffusion of boron in polycrystalline silicon (polysilicon) requires knowledge of the relative diffusion kinetics of boron in both polysilicon and silicon dioxide. The kinetics were determined using polysilicon layers deposited by pyrolysis of silane and diffusion from a BN source. An activation energy of 3.26 ± 0.10 eV was found for both lateral and perpendicular diffusion in polysilicon. Values for the pre-exponential rate constants in the Arrhenius relationship of 88.0, 40.0 and 5.73 cm 2 s −1 were found for lateral diffusion in polysilicon deposited at 720, 770 and 820°C respectively. In comparison, a value of 27.6 cm 2 s −1 was found for perpendicular diffusion in polysilicon deposited at 770°C. Corresponding values of 1.76 eV and 4.37 × 10 −7 cm 2 s −1 were found for the conversion of silicon dioxide to borosilicate glass in the region of exposed thin oxide immediately adjacent to the polysilicon gate. Over the temperature range studied, these results give a maximum ratio between the gate length and gate oxide thickness of about 15 in comparison to the ratio of around 40 commonly used for conventional MOSTs. Values for the corresponding diffusion constants were also calculated from the rate constants using the commonly-assumed complementary error function profile. Measurement of the diffusion profiles for electrically active boron shows, however, that the erfc profile is not entirely valid.

Solubility and Diffusion of Sulfur in Polymeric Materials

Radiotracer techniques were used to study the sorption of sulfur vapor by silicone and epoxy polymers and to obtain information on the diffusion of sulfur in these materials. Sulfur was found to enter silicone polymers solely by a physical solution process which obeys Henry's law. The heat of solution is large (−0.43 eV) and at room temperature the solubility coefficient is at least five orders of magnitude greater than for many fully gaseous solutes, a result which fits an empirical rule relating the solubility coefficient of a given solute to its boiling point. Sorption of sulfur by a flexibilized anhydride-cured diglycidyletherbisphenol-A (DGEBA) epoxy is somewhat more complicated and appears to involve a double process of physical solution and chemical reaction. The rapid diffusion of sulfur in silicone rubber necessitated measurements of the diffusion coefficient D by a vacuum desorption technique. The activation energy Q and pre-exponential constant D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> are found to be 0.74 eV and 4×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s, respectively. Corresponding values for the epoxy, as determined by a steady state permeation method, are 1.06 eV and 3×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s. These relatively large activation energies and pre-exponential factors are thought to reflect the large size of the S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</inf> molecule. Near room temperature, the difference in the activation energies causes sulfur diffusion to occur at least four orders of magnitude more slowly in the epoxy, which makes this material much more attractive for encapsulation applications requiring an effective diffusion barrier to elemental sulfur present as a pollutant of the atmosphere.

Diffusion and diffusion creep in olivine and ultrabasic rocks.

The applicability of Winchell's compensation law relating the activation energy to the pre-exponential constant is examined for diffusion in orthosilicate, and the diffusion coefficients of oxygen, silicon, magnesium and iron in olivine are estimated. Effects of high solid pressure and the partial pressure of H2O on diffusion are also evaluated by means of the compensation law and Liempt's empirical law between melting temperature and activation energy. The rate of diffusion creep in ultrabasic rocks is evaluated. The ratecontrolling process of creep changes with temperature; oxygen lattice diffusion is the rate-controlling process at high temperatures, while the oxygen grain boundary diffusion dominates at low temperatures. The strain rate by diffusion creep is so small that diffusion creep cannot be the dominant mechanism for flow at the actively deforming part in the upper mantle. The time and distance required to reach a state of chemical equilibrium between two geologic media in contact are also evaluated by using the values of the diffusion coefficients.

Monopropellant droplet decomposition for large activation energies

The quasi-steady decomposition of a monopropellant droplet in a quiescent atmosphere is analyzed, in the limit of large activation energy, for a gas phase decomposition reaction of the Arrhenius type. An analytical relation is obtained for the pre-exponential rate constant, or the Damköhler number, as a function of the droplet vaporization rate. The curve giving the vaporization rate in terms of the Damköhler number has, for low values of the temperature at infinity, an S shaped form which exhibits ignition-extinction characteristics. With increasing values of the droplet vaporization rate above the pure vaporization value we pass from a nearly frozen regime, under which ignition conditions occur due to the large temperature sensitivity of the reaction rate, to a complete decomposition regime, in which practically all the fuel is decomposed in a thin reactive-diffusion zone, separated from the droplet surface by a transport region of lower temperature. For sufficiently large Damköhler numbers, the thin reaction zone is located close to the droplet surface, so that the flame structure becomes planar: a linear relation between the droplet radius and time is obtained in this case. The non planar effects are responsible for the extinction of the flame at low Damköhler numbers and ambient temperatures below the adiabatic flame temperature. For sufficiently low values of the ambient temperature, an intermediate regime exists in which the enhancement of the vaporization rate is due only to the fraction of the vaporized fuel decomposed at a thin reaction zone, not far from the droplet, where the temperature reaches its maximum value; the remaining fuel is decomposed very far from the droplet.

Effect of temperature on the chemical relaxation process in rubbers

The effect of temperature on the chemical relaxation of rubbers has been investigated. With reference to nine industrial rubbers it has been shown that during storage in the stressed state (at e=const) chemical relaxation is chiefly determined by two processes proceeding at different rates. Furthermore, the chemical relaxation of rubbers is determined not only by the rate constants of these two processes but also by the pre-exponential constants C0i, the relationship between which varies with increase in temperature. It is possible to extrapolate the rate constants (ki) and pre-exponential constants (C0i) from elevated temperatures (110–50° C) to temperatures in the range 20–25° C. An equation is proposed that makes it possible to calculate the change in the elastic properties of rubbers in the stressed state at storage temperatures (20–25° C) by means of results obtained at elevated temperatures.

An Analysis of the Thermodynamics of Dislocation Glide

AbstractA general treatment of thermally activated dislocation motion is presented following the approach first suggested by Basinski and making use of Leibniz's formula to analyze the properties of arbitrarily shaped obstacles. The small region surrounding a dislocation obstacle is shown to be an acceptable thermodynamic system with the effective stress, defined as the difference between the applied stress and the long range internal stress evaluated at the obstacle, as an appropriate thermodynamic variable. All of the thermodynamic properties of such a local system are self consistent. The question of the choice of a thermodynamic system is discussed in connection with the results of prior treatments of the problem. Whether one considers a local system using the effective stress as the operative thermodynamic variable, or the entire crystal as a system using the applied stress, the value of the effective stress and the conditions for which it is zero must be known, in general, in order to relate measured thermodynamic quantities to the properties of an obstacle. The thermodynamic methods are illustrated with the use of a simple sinusoidal model for the backstress produced by an obstacle. The difficult problem of relating the stress and temperature dependence of plastic flow to the results of thermodynamic analysis is treated. The discussion indicates that serious errors can be made either when the effective stress is not precisely known, as is commonly the case for high temperature creep, or when the stress and temperature dependence of the preexponential constant are not taken into account.

The Role of Surface Stress on Hydrogen Absorption by 4340 Steel

Abstract The reaction kinetics of stressed, high strength steel with cathodically generated hydrogen are shown to follow the first-order rate equation, with rate constant k = −5 × 105 exp [−9700/RT] in which the activation energy is equivalent to that for diffusion of hydrogen in iron. The pre-exponential constant, however, is several orders of magnitude greater than that obtained for diffusion and is discussed in terms of the number of reactive sites. While the number of incipient sites is believed to be comparable to the number of subgrain (domain) boundaries in martensity (1012 cm−2), a stress of 85 ksi activates approximately 107 sites/cm2. These sites are not activated by a surface tensile stress of less than 40 to 50 ksi. When these sites are activated, however, hydrogen diffuses to the area of higher tensile stress. In the case of ferritic structure, the hydrogen reaction rate does not increase with the magnitude of the tensile stress.

Obsidian-H2O viscosities at 1000 and 2000 bars in the temperature range 700° to 900°C

Viscosities of synthetically hydrated obsidians have been measured by the falling-sphere technique at two values of the H2O content. At 4.3 per cent H2O, by weight, the common logarithm of the viscosity in poises ranges from 6.51 at 800°C to 5.88 at 900°C, and at 6.2 per cent H2O from 6.54 at 700°C to 5.25 at 850°C. The effect of pressure on the viscosity is shown experimentally to be slight at these temperatures. The data are consistent with viscosity isotherms determined by Friedman, Long, and Smith on rhyolite glass at H2O contents to 1.25 per cent. Activation energies and pre-exponential constants determined from this work and that of Friedman et al. show striking similarities to data for binary alkali oxide-silica systems. This suggests that the discrete ion theory of silicate melts proposed by Bockris and co-workers is applicable to silicate-H2O systems. On the basis of this model a generalized graph is presented which permits approximate predictions of viscosities of framework silicate-H2O systems for H2O contents up to about 10 per cent by weight and temperatures in the range 500° to 1200°C.

Comparison of Three Equations for the Spacing of Nuclear Levels

The equations of Bethe, Weisskopf and of Lang and Le Couteur for the spacing of nuclear levels have been compared using the experimental data for 40 nuclei. The average errors obtained by the three equations are not very different. Bethe’s equation has been found to give the best results. Odd-even effects on the pre-exponential constants in the three equations have been discussed.

Diffusion of arsenic in germanium from the vapour phase

The diffusion of arsenic in germanium has been measured. The diffusion constants and the concentrations of As at the surface in equilibrium with gaseous arsenic of a certain pressure have been determined at different temperatures. From the temperature dependence, the activation energy of diffusion and the pre-exponential constant have been calculated. It is found that, if the diffusion is carried out via the vapour phase and if the diffusion vessel contains zones of different temperatures, the surface concentration of the arsenic depends on the geometry of the vessel, when working in the absence of an inert gas. This effect is caused by the fact that the degree of dissociation of the gaseous As molecules above the germanium sample depends on the geometry of the vessel. A method is described how to get rid of thermal conversion.