Arrhenius type

The stabihty of pure hydrogen peroxide solutions increases with increasing concentration and is maximum between pH 3.5—4.5. The decomposition rate of ultrapure hydrogen peroxide increases 2.2—2.3-fold for each 10 °C rise in temperature from ambient to about 100 °C. This approximates an Arrhenius-type response with activation energy of about 58 kJ/mol (13.9 kcal/mol). However, decomposition increases as low as 1.6-fold for each 10 °C rise have been noted for impure, unstabilized solutions. 

The temperature dependence of melt viscosity at temperatures considerably above T approximates an exponential function of the Arrhenius type. However, near the glass transition the viscosity temperature relationship for many polymers is in better agreement with the WLF treatment (24). 

The relationship between i j, and temperature can be described by an Arrhenius type of equation ... 

The diffusion coefficient varies with temperature according to the following Arrhenius-type equation ... 

An Arrhenius-type relationship is obtained, with a slope determined by the energy of formation of the defects. 

The relationship between the ionic conductivity oi and the temperature T can either be derived from the diffusivity D or the mobility u assuming Arrhenius-type behavior ... 

D, W. Blair, CombustFlame 20 (1), 105—9 (1973) CA 78, 113515 (1973) A simple heat-transfer model is coupled with an Arrhenius-type pyrolysis law to study the effect of solid-state heat-transfer losses on burning rates of solid rocket-proplnt strands. Such heat-transfer losses materially affect the burning rates and also cause extinction phenomena similar to some that had been observed exptly. Strand diam and compn, adiabatic burning rate, and the heat-transfer film coeff at the strand surface are important variables. Results of theoretical analysis are applied to AP-based composite solid proplnts... 

An early attempt to apply an Arrhenius-type equation to a decomposition reaction was by Polyani and Wigner [512] using the expression... 

Data after Balke(9.) Ito( ) and Hayden and Melville ( ) were correlated with an Arrhenius type plot giving the following equation which was used in all the simulations. 

In semi-crystalline polymers at least two effects play a role in the diffusion of the reactive endgroups. Firstly, the restriction in endgroup movement due to the lowering of the temperature, which usually follows an Arrhenius type equation. Secondly, the restriction of the molecular mobility as a result of the presence of the crystalline phase whose size and structure changes on annealing. 

Increasing temperature permits greater thermal motion of diffusant and elastomer chains, thereby easing the passage of diffusant, and increasing rates Arrhenius-type expressions apply to the diffusion coefficient applying at each temperature," so that plots of the logarithm of D versus reciprocal temperature (K) are linear. A similar linear relationship also exists for solubUity coefficient s at different temperatures because Q = Ds, the same approach applies to permeation coefficient Q as well. 

The polymer rheology is modeled by extending the usual power-law equation to include second-order shear-rate effects and temperature dependence assuming Arrhenius type relationship. 

The product distribution of the HDS of thiophene over the Mo(lOO) surface is shown in Table III compared with that reported by Kolboe over a MoS catalyst (14). It is clear that the two are very similar ana that our catalyst mimics the MoS catalyst very closely in this respect. An Arrhenius plot fpigure 2) made in the temperature region mentioned above shows that butadiene is the only product whose rate of formation shows true Arrhenius type dependence and yields an activation energy of 14.4 kcal/mole. At high temperatures the rate of butane formation deviates even more sharply than that of the butenes and does so at lower temperatures (9). 

By using a liquid with a known kinematic viscosity such as distilled water, the values of Ci and Cj can be determined. Ejima et al. have measured the viscosity of alkali chloride melts. The equations obtained, both the quadratic temperature equation and the Arrhenius equation, are given in Table 12, which shows that the equation of the Arrhenius type fits better than the quadratic equation. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

Plotting of Inkj (j=l,2,3) versus 1/T shows that only k exhibits Arrhenius type of behavior. However, given the large standard deviations of the other two estimated parameters one cannot draw definite conclusions about these two parameters. 

Writing Arrhenius-type expressions, kj=Aj< x/ (-Ej/RT), for the kinetic constants, the mathematical model with six unknown parameters (Ab A2, A3, E, E2 and E3) becomes... 

The objective is to determine the parameters and their standard errors by the Gauss-Newton method for each temperature and then check to see if the parameter estimates obey Arrhenius type behavior. 

The parameter values were then plotted versus the inverse temperature and were found to follow an Arrhenius type relationship... 

Let us reconsider the hydrogenation of 3-hydroxypropanal (HPA) to 1,3-propanediol (PD) over Ni/Si02/Al203 catalyst powder that used as an example earlier. For the same mathematical model of the system you are asked to regress simultaneously the data provided in Table 16.23 as well as the additional data given here in Table 16.28 for experiments performed at 60°C (333 K) and 80°C (353 K). Obviously an Arrhenius type relationship must be used in this case. Zhu et al. (1997) reported parameters for the above conditions and they are shown in Table 16.28. 

Examine whether any of the estimated parameters follow an Arrhenius-type relationship. If they do, re-estimate these parameters simultaneously. A better way to numerically evaluate Arrhenius type constants is through the use of a reference value. For example, if we consider the death rate, kd as a function of temperature we have... 

In all the above three-component models as well as in the four-component models presented next, an Arrhenius-type temperature dependence is assumed for all the kinetic parameters. Namely each parameter k, is of the form A,erJc>(-El/RT). 

Figures 18.13, through 18.17 show the experimental data and the calculations based on model I for the low temperature oxidation at 50, 75, 100, 125 and 150TZ of a North Bodo oil sands bitumen with a 5% oxygen gas. As seen, there is generally good agreement between the experimental data and the results obtained by the simple three pseudo-component model at all temperatures except the run at 125 TT. The only drawback of the model is that it cannot calculate the HO/LO split. The estimated parameter values for model I and N are shown in Table 18.2. The observed large standard deviations in the parameter estimates is rather typical for Arrhenius type expressions.

This behavior is in between that of a liquid and a solid. As an example, PDMS properties obey an Arrhenius-type temperature dependence because PDMS is far above its glass transition temperature (about — 125°C). The temperature shift factors are... 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

---