Rational approximations of the integral of the Arrhenius function

1977 ◽  
Vol 11 (3) ◽  
pp. 445-447 ◽  
Author(s):  
G. I. Senum ◽  
R. T. Yang
Keyword(s):  
Rational Approximations ◽  
Arrhenius Function

scholarly journals Agreed – there is no need to switch the modified Arrhenius function back to the old form

2021 ◽  
Vol 231 (6) ◽  
pp. 2117-2117
Author(s):  
Joseph R. Stinziano ◽  
Bridget K. Murphy
Keyword(s):  
Arrhenius Function

scholarly journals Water vapor transmission properties of acrylic organic coatings

2020 ◽  
Author(s):  
Réka Lilla Kovács ◽  
Lajos Daróczi ◽  
Péter Barkóczy ◽  
Eszter Baradács ◽  
Eszter Bakonyi ◽  
...  
Keyword(s):  
Water Vapor ◽  
Transmission Rate ◽  
Performance Testing ◽  
Preexponential Factor ◽  
Diffusion Activation Energy ◽  
Vapor Permeability ◽  
Coating Materials ◽  
Comparative Performance ◽  
Water Vapor Transmission ◽  
Arrhenius Function

AbstractIn this work, we evaluate the water vapor transmission rate (WVTR), the permeability (P), solubility (S), and diffusion (D) coefficients of Paraloid B44, Paraloid B72, and Incralac coatings in the temperature range of 5–35°C. The Arrhenius function—diffusion activation energy and preexponential factor—has also been determined from the data: $$D_{B44} = 35.2\;{\text{cm}}^{2} \;{\text{s}}^{ - 1} \exp \left( { - 25\;{\text{kJ mol}}^{ - 1} /{\text{RT}}} \right)$$ D B 44 = 35.2 cm 2 s - 1 exp - 25 kJ mol - 1 / RT ; $$D_{B72} = 9.5\;{\text{cm}}^{2} \;{\text{s}}^{ - 1} \exp \left( { - 23\;{\text{kJ mol}}^{ - 1} /{\text{RT}}} \right)$$ D B 72 = 9.5 cm 2 s - 1 exp - 23 kJ mol - 1 / RT ; $$D_{\text{Incralac}} = 622.8\;{\text{cm}}^{2} \;{\text{s}}^{ - 1} { \exp }\left( { - 28\;{\text{kJ mol}}^{ - 1} /{\text{RT}}} \right)$$ D Incralac = 622.8 cm 2 s - 1 exp - 28 kJ mol - 1 / RT . These resins are important coating materials, for example, for conservators to protect metallic artifacts, such as statues, against corrosion. Despite Paraloid B44 and B72 resins being considered as reference materials in conservation practice, that is, new coating materials (either water vapor retarders or transmitters) are often compared to them, there are no comprehensive data for the quantities describing the vapor permeability (P, S, D) of these materials. The measurements are based on the ISO cup-method using substrate/coating composite samples. The strength of this technique is that it can also be used when the coating is non-self-supporting; nevertheless, P, S, and D can be deduced for the coating layer itself, and it seems to be a standardizable procedure for comparative performance testing of coating materials. Paraloid B72 layers exhibited higher WVTRs—from 39 to 315 g m−2 day−1 as the temperature increased from 5 to 35°C—compared to Paraloid B44 and Incralac coatings—from 17 to 190 g m−2 day−1, respectively. The transmission rate parameters were also compared to the results of corrosion tests. Incralac was the most effective corrosion inhibitor, and the performance of the B44 was better than the B72, which is in good agreement with the transmission rate tests.

Macromodeling of I/O Buffers via Compressed Tensor Representations and Rational Approximations

2016 ◽  
Vol 6 (10) ◽  
pp. 1522-1534 ◽  
Author(s):  
Gianni Signorini ◽  
Claudio Siviero ◽  
Stefano Grivet-Talocia ◽  
Igor S. Stievano
Keyword(s):  
Rational Approximations ◽  
Tensor Representations

On Rational Approximations of Groups of Operators

1980 ◽  
Vol 17 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Philip Brenner ◽  
Vidar Thomée
Keyword(s):  
Rational Approximations

Surprisingly Accurate Rational Approximations

2002 ◽  
Vol 75 (4) ◽  
pp. 307-310 ◽  
Author(s):  
Tom M. Apostol ◽  
Mamikon A. Mnatsakanian
Keyword(s):  
Rational Approximations

Temperature profiles in endothermic and exothermic reactions and the interpretation of experimental rate data

1970 ◽  
Vol 320 (1540) ◽  
pp. 71-100 ◽  
Keyword(s):  
Steady State ◽  
Correction Factor ◽  
Exothermic Reaction ◽  
Kinetic Studies ◽  
Activation Energies ◽  
Uniform Temperature ◽  
Exothermic Reactions ◽  
Arrhenius Function ◽  
Point To Point ◽  
Reacting Systems

Any endothermic or exothermic reaction is accompanied by self-cooling or self-heating. In reacting systems in which heat transfer is controlled by conduction, non-uniform temperature-position profiles are established. Examples of this situation are the exothermic decomposition of gaseous diethyl peroxide and the endothermic decomposition of nitrosyl chloride at low pressures (when convection is unimportant). In kinetic studies, allowance must be made for the non-uniform temperature to derive accurate isothermal velocity constants and Arrhenius parameters. In the present paper, the necessary corrections have been derived for a reactant in the steady state whose reaction rate varies exponentially with temperature and in which the temperature excess varies from point to point, being zero at the boundary (Frank-Kamenetskii’s conditions). The geometries considered are the slab, cylinder and sphere. The temperature gradient at the surface in the steady state ( Г ) occupies a key position, and this is exploited to find the correction factor required to convert 'observed’ rate constants to isothermal conditions, and thence to correct ‘observed’ activation energies and pre-exponential factors. The correction factor is found to be simply related to Frank- Kamenetskii’s δ (a dimensionless measure of heat-release rate). A similar analysis is given for systems hotter or cooler than their surroundings but uniform in temperature—such as well stirred fluid systems or small solid crystals (Semenov’s conditions). In these circumstances, systems of arbitrary geometry may be studied, and no approximation need be made to the Arrhenius function. For either type of boundary condition, uncorrected activation energies are overestimates in exothermic reactions and underestimates in endothermic reactions. Explicit relations are derived for making corrections. Boundary conditions intermediate between the two extremes investigated can also be treated though the resulting expressions are more cumbersome. In an appendix, an alternative ‘experimental’ approach is made to the elimination of errors from measured reaction velocities. This approach identifies the measured velocities with a temperature intermediate between those at centre and surface. The optimum choice, which weights the central and surface temperatures in the ratios 2:1 (slab), 1:1 (cylinder) and 2:3 (sphere), gives exactly correct results for the cylinder and acceptable precision for the slab and sphere even to within 5 K of the explosion limit. Other correction methods are also discussed.

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