A-factor pre-exponential

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

Fig. 44a. Theoretical molecular weight distribution of a polymer sample degraded along the central streamline at different strain rates, calculated with a pre-exponential factor A = 1014s-1 (I) strain rate e = 75000s-1 (II) strain rate e = 88000s-1 (III) strain rate e = 190000 s- b Theoretical molecular weight distribution of a polymer sample degraded along the central streamline at different strain rates, calculated with A = 104 s-1 (I) strain rate e = 100000 s -1 (II) strain rate e = 120000 s 1 (III) strain rate e = 300000 s -1 (Solid line polymer before degradation, dotted line, degraded polymer)...

Some of the rate constants discussed above are summarized in Table VI. The uncertainties (often very large) in these rate constants have already been indicated. Most of the rate constants have preexponential factors somewhat greater than the corresponding factors for neutral species reactions, which agrees with theory. At 2000°K. for two molecules each of mass 20 atomic units and a collision cross-section of 15 A2, simple bimolecular collision theory gives a pre-exponential factor of 3 X 10-10 cm.3 molecule-1 sec.-1... 

Equation (12) also contains a pre-exponential factor. In Section 3.8.4 we treated desorption kinetics in terms of transition state theory (Figure 3.14 summarizes the situations we may encounter). If the transition state of a desorbing molecule resembles the chemisorbed state, we expect pre-exponential factors on the order of ek T/h = 10 s . However, if the molecule is adsorbed in an immobilized state but desorbs via a mobile precursor, the pre-exponential factors may be two to three orders of magnitude higher than the standard value of 10 s . ... 

Because the Arrhenius plots of both TPD experiments are straight lines over a large portion of the data points, the reaction between CO and O is, most likely, an elementary step, with an activation energy of 103 5 kj mol and a pre-exponential factor of s . This analysis is again only valid if coverage dependencies play... 

A pre-exponential factor and activation energy for each rate constant must be established. All forward rate constants involving alkyne adsorption (ki, k2, and ks) are assumed to have equal pre-exponential factors specified by the collision limit (assuming a sticking coefficient of one). All adsorption steps are assumed to be non-activated. Both desorption constants (k.i and k ) are assumed to have preexponential factors equal to 10 3 sec, as expected from transition-state theory [28]. Both desorption activation energies (26.1 kcal/mol for methyl acetylene and 25.3 kcal/mol for trimethylbenzene) were derived from TPD results [1]. 

The photovoltage is esentially determined by the ratio of the photo- and saturation current. Since io oomrs as a pre-exponential factor in Eq. 1 it determines also the dark current. Actually this is the main reason that it limits the photovoltage via Eq. 2, The value of io depends on the mechanism of charge transfer at the interface under forward bias and is normally different for a pn-junction and a metal-semiconductor contact. In the first case electrons are injected into the p-region and holes into the n-region. These minority carriers recombine somewhere in the bulk as illustrated in Fig. 1 c. In such a minority carrier device the forward current is essentially determined... 

Pt, a key requirement is seen to be a pre-exponential factor in (1.10) significantly larger than zero, which requires, in turn that 0qx bo lowered significantly under 1 by bringing cath close to ft(H20)/Pt-0H,ds Rm abnost 400 mV. 

The procedure of limiting the RHR and finding a pre—exponential factor for each test series proved to be very robust... 

A pre-exponential factor in Arrhenius equation, (mor1 m3)" 1 s 1, equation 3.1-8 area, m2... 

The experimental data corresponding to one labeled arm in stars of f=12 (good solvent) [68] shows, as expected, Kratky plot ordinates that increase monotonously with q. However, the plateau is only obtained with an apparent critical exponent of 2/3 (i.e., greater than the theoretical value, v-3/5). This seems an indication of the arm stretching effect, though the scaling and RG theoretical predictions describe this effect only in terms of a pre-exponential factor [11,42]. 

A Pre-exponential factor for surface reaction B Pre-exponential factor for gas phase reaction D Diffusion coefficient E Activation energy... 

In the light of these estimates, Reaction 3 does not seem unreasonable it would be about 2 kcal. per mole endothermic, and might therefore be expected to have an activation energy of about 8 kcal. per mole, and a pre-exponential factor of around 2 X 10"12 cc. molecule"1 sec."1 (12). 

The forward rate constant is represented in Arrhenius form with a pre-exponential factor as A = 2.1 x 1012 s-1 and an activation energy of E = 206.4 kJ/mol. 

By preparing an Arrhenius plot (i.e., In kK versus 7 -1), estimate a pre-exponential factor A and an activation energy E for the surface reaction. Assume that the reaction is first order in CH4. Is there observable curvature in the Arrhenius plot ... 

The rate constant of polymerization that they deduced for THF at 20° C was 1.66 x 10 a 1/mole sec. From studies of the polymerization in the temperature range 0—40° C they derived an activation energy, E , of 13.3 kcal/mole and a pre-exponential factor, A, of 1.64 X 1081/mole sec. Using these values for E0 and A we have calculated a value of 3.7 X 10-3 1/mole sec for kp at 0° C. This is in good agreement with the value, 4.83 x 10 31/mole sec, reported by Vofsi and Tobolsky (32). 

By using the value of kp at 20° C and the value of the equilibrium monomer concentration, the rate constant calculated for the depropagation reaction, ka, was 4.67 X 10-2 sec-1 at 20° C. An activation energy of 19.4 kcal/mole and a pre-exponential factor of 1.65 x 1013 sec-1 were calculated for the depropagation reaction. 

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