Arrhenius type equations

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

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

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. 

If one assumes that the reaction rate in the gas phase is given by a one-step, kth-order Arrhenius-type equation and substitutes this in Eq. (3.83), one gets... 

Consider the activation energy for various radical chain polymerizations. For a polymerization initiated by the thermal decomposition of an initiator, the polymerization rate depends on the ratio of three rate constants kp (kj/k,) 2 in accordance with Eq. 3-32. The temperature dependence of this ratio, obtained by combining three separate Arrhenius-type equations, is given by... 

Diffusivity. The diffusivity of water in the prepreg (either fresh or cured), follows an Arrhenius-type equation [13]... 

The rates of chemical and biochemical reactions usually increase with temperature. The dependence of the reaction rate on temperature can usually be represented by the following Arrhenius-type equation over a wide temperature range ... 

Anisothermal Transport Across a Phase Boundary. Once we know the effect of temperature on equilibrium position, we need know only its effects on diffusivities and the condensation coefficient to complete our task. The Stephan-Maxwell equation states that diffusivity in the vapor increases with the square root of the absolute temperature. In the condensed phase the temperature effect is expressed by an Arrhenius-type equation. 

The table which follows gives the activation energy E (as calcd from the above Arrhenius type equation), as well as the value B for various initiating agents and extrapolated temperatures in °C, such as a) t -maximum temp for 0% ignitions b) t° oo-minimum temp for 100% ignitions and c) t° sec ignition temp when delay was 5 sec... 

An Arrhenius type equation is obtained for the apparent reaction rate constant. Equations for the apparent activation energy and for the frequency factor are established as functions of Hamaker s Constant, ionic strength, surface potentials and particle radius. 

Results are shown in Figs. 12 and 13. All blend specimens were set iso-thermally above LCST and kept there for a maximum of 5 min. As will be seen, this corresponds only in some cases to an early stage of spinodal decomposition depending on temperature. The diffusion coefficients governing the dynamics of phase dissolution below LCST are in the order of 10"14 cm2 s"1. Figure 12 reflects the influence of the mobility coefficient on the phase dissolution. As can be seen, the apparent diffusion coefficient increases with increasing temperature of phase dissolution which expresses primarily the temperature dependence of the mobility coefficient. Furthermore, it becomes evident that the mobility obeys an Arrhenius-type equation. Similar results have been reported for phase dis-... 

For the variation of the electrical conductivity with temperature an Arrhenius type equation is used ... 

Independent of the order of the kinetic expression, the effect of temperature in all these processes can be easily introduced in the kinetic constant by means of an Arrhenius type equation (4.29). The effect of temperature is especially important in electrochemical oxidation processes, where the action of oxidants electrochemically generated will be very significant... 

These shift factors are reported in Fig. 11 as a function of the inverse of the absolute temperature. The temperature dependence of these quantities it clearly follows an Arrhenius type equation in the form ... 

Activated surface diffusion or configurational diffusion occurs in molecules with a diameter larger than 60% of the pore diameter, as is the case in pervaporation with zeolite membranes [113]. Diffusion is an activated process and the diffusivity follows an Arrhenius-type equation ... 

Despite these possible complications, many authors have found that the effect of temperature on decomposition rate can be described by an Arrhenius-type equation i.e. plots of log k against 1/T are linear. This then enables the stability to be predicted at room... 

For solid-solid and solid-vapor equilibria, which often occur at temperatures below the eutectic temperature, Teu, the solubility can be described by an Arrhenius-type equation. For solid-liquid equilibria at temperatures above Teu, the temperature dependence is more complex and will be discussed in detail in the following sections. 

Owing to the exothermic behavior of the adsorption, the retention time increases at lower temperatures. An Arrhenius-type equation describes the retention factor s dependence on temperature (Eq. 4.11)... 

The model is formulated on the premise that the decomposing hydrate particle is surrounded by a cloud of the product gas hence the driving force for the decomposition process is expressed in terms of the fugacity difference given in Eq. (1). The process of decomposition possibly involves (1) destruction of the clathrate host (water) lattice at the surface of the particle, and (2) and desorption of the guest (hydrate former) molecules from the surface. The particle size distribution was incorporated in the calculations for the determination of the intrinsic rate constants.The following Arrhenius type equation is used to represent the effect of temperature on the intrinsic rate constant ... 

The reciprocals of the quadrupole relaxation time, l/T and l/T, are reasonably represented by an Arrhenius-type equation as given in Eq. (8),... 

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