Eyring equation


Testing the Eyring Equation  [c.97]

Testing the Eyring Equation  [c.97]

While the Eyring equation gives a relationship between and 7 which allows for both Newtonian and pseudoplastic behavior, the result does not appear too promising. To begin with, the inverse hyperbolic sine function is discouraging and, worse yet, the relationship involves four adjustable parameters kj, 6, X, and A. Having this many parameters imparts a flexibility to the theory which enhances the chance of fitting it to experimental data. On the other hand, we might be hard pressed to find suitable values for these parameters to evaluate rj via Eq. (2.25). Furthermore, the possibility of extracting useful molecular information from an equation which contains so many parameters seems slim. To assess this situation more thoroughly, let us reexamine the parameters in Eq. (2.25) and the grouping in which they occur.  [c.97]

Testing the Eyring Equation  [c.99]

Examination of Table 2.2 and Fig. 2.5 enables us to judge the success of the Eyring equation. In the region of first deviations from Newtonian behavior the agreement between theory and experiment is excellent. Since the parameters are fitted with these data, no great significance should be attached to the fact that the agreement occurs here rather than elsewhere. Perhaps an equally good fit could be obtained with other parameters for a different range of experimental values. For the parameters used, theory and experiment agree to within 0.5% over an order of magnitude variation of 7 and within 10% for one and a half orders of magnitude. On the log-log scale of Fig. 2.5 the agreement is excellent up to a 7 value of about 1.0 sec", at which point theoretical viscosities are less than experimental. One useful application of the Eyring equation is to extrapolate shearing forces, viscosities, and so on, over modest ranges from the conditions where they are measured.  [c.100]

This guarded assessment does not mean that the effort involved in deriving the Eyring equation was wasted-far from it. Several points might be noted  [c.100]

Testing the Eyring Equation  [c.101]

Testing the Eyring Equation  [c.729]

EYPEL-F Eyring equation  [c.389]

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.).  [c.1511]

The free enthalpy of activation, aG, of the ring inversion at 253 K is calculated from the logarithmic form of the Eyring equation  [c.190]

This is a phenomenological equation, relating observables what we seek is the molecular basis for this expression. Eyring s approach focuses attention on the energy barrier along the reaction coordinate as the source of this insight. The molecular situation at the top of the energy barrier is described as an activated complex, so the corresponding theory is called the activated complex theory.  [c.91]

We shall refer to Eq. (2.28) as the Eyring viscosity equation.  [c.96]

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary.  [c.98]

The semiempirical methods combine experimental data with theory as a way to circumvent the calculational difficulties of pure theory. The first of these methods leads to what are called London-Eyring-Polanyi (LEP) potential energy surfaces. Consider the triatomic ABC system. For any pair of atoms the energy as a function of intermolecular distance r is represented by the Morse equation, Eq. (5-16),  [c.196]

The final term on the right-hand side is just the Coulomb repulsion between the stationary nuclei. We think of the nuclei as being clamped in position for the purpose of calculating the electronic energy and the electronic wavefunction. We then change the nuclear positions and recalculate the energies and the electronic wavefunction. Should we be interested in the nuclear motions (vibrational and rotational), we have to solve the relevant nuclear Schrodinger equation. Don t get this confused with MM calculations the nuclear Schrodinger equation is a full quantum-mechanical equation, which has to be solved by standard techniques. You might like to read Eyring, Walter and Kimball (EWK) s classic text Quantum Chemistry (1944) to see how it is done.  [c.75]

L Solution of the third equation gives the second-order corrections, and so on. It is shown in the standard textbooks (e.g. Eyring, Walter and Kimball, 1944) that the solutions are  [c.198]

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are  [c.9]

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are  [c.10]

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are  [c.11]

Combining equation (A3,4,95). equation (A3,4,96) and equation (A3.4.97) one obtains the first Eyring equation for iinimolecular rate constants  [c.780]

Next let us briefly consider how the Eyring equation might be modified to improve its agreement with experiment. As noted in item (4) above, the relaxation time plays a very important role in the theoretical development and the practical application of the Eyring model. A little reflection readily convinces us that it is also the greatest weakness of the theory. Specifically, it seems highly improbable that the slithering of a polymer chain through a tangle of similar chains would be characterized by a single relaxation time. For some of the flow segments, the barrier to displacement may be the consequence of weak London forces which attract all molecules to each other. For other segments the barrier may be much higher owing to a virtual knotting of chains together through entanglements. The response time of a heavily entangled chain is expected to be significantly longer than that for a segment which moves the same way as a nontangled small molecule. This leads us to the idea that a whole spectrum of relaxation times rather than a single value might be a more suitable way to describe the flow process.  [c.101]

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1) Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)
Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up.  [c.76]


See pages that mention the term Eyring equation : [c.780]    [c.405]    [c.62]    [c.870]    [c.196]   
Structure Elucidation by NMR in Organic Chemistry (2002) -- [ c.62 , c.189 , c.190 ]