Redheads equation

BSSE Basis Set Superposition Error. TDS Thermal Desorption Spectroscopy. DFT Density Functional Theory. IRS InfraRed Spectroscopy. Clausius-Clapeyron evaluation of pressure and temperature dependent IR-intensities with the Clausius-Clapeyron equation. Redhead evaluation of TDS data with the Redhead equation [651. 

On setting dRIdt = 0 (and using Eq. XVIII-1), we obtain an equation due to Redhead [89] ... 

If the desorption rate is second-order, as is often the case for hydrogen on a metal surface, so that appears in Eq. XVIII-1, an equation analogous to Eq. XVIII-3 can be derived by the Redhead procedure. Derive this equation. In a particular case, H2 on Cu3Pt(III) surface, A was taken to be 1 x 10 cm /atom, the maximum desorption rate was at 225 K, 6 at the maximum was 0.5. Monolayer coverage was 4.2 x 10 atoms/cm, and = 5.5 K/sec. Calculate the desorption enthalpy (from Ref. 110). 

Redhead [89] gives the approximate equation EjRTm - ln(A7) //3)- 3.64. Check the usefulness of this equation by comparing with the answers to Problems 5 and 6. 

In estimating the value of Ed by means of the transcendental equations (28), the circumstance utilized is that the variation of em for a given change in Tm is much less than the variation of exp(em) (31). Until now, only particular solutions have been available for the hyperbolic and linear heating schedules and for the first-order and second-order desorptions. They can be found for example in the fundamental papers by Redhead (31) and Carter (32) or in the review by Contour and Proud homme (106), and therefore will not be repeated here. Recently, a universal procedure for the... 

One can then use the standard Redhead analysis to the data of Fig. 5.24. To this end one uses the Redhead equation in its generalized form derived by Falconer and Madix 48... 

Figure 8,16. Activation energy of desorption, Ed, of 02 from Ru02 as a function of the applied potential21,25 as extracted from TPD and the modified Redhead equation of Falconer and Madix.25,26 Reprinted from ref. 21 with permission from Elsevier Science.

The simultaneous desorption peaks observed at 560-580 K in TPR are of reaction-limited desorption. The peak temperatures of these peaks do not depend on the coverage of methoxy species, indicating that the desorption rate (reaction rate) on both surfaces has a first-order relation to the coverage of methoxy species. Activation energy (Ea) and the preexponential factor (v) for a first-order process are given by the following Redhead equation [12] ... 

Performing a Redhead analysis of the TPD. an estimation of the activation energy (Ea) of hydrogen desorption from npSi can be derived from the following equation [7], where v is the evolution rate, and p is the linear temperature ramp rate. 

If we know that the desorption follows first order kinetics (n=l) and we have an educated guess on the value of A (e.g from transition state theory), Redheads equation makes it easy to determine E from a measurement of the peak temperature, T. 

Finally, a caution about the Redhead equation. The requirement n=l is not explicit in the equation. For this reason nothing prevents that the equation is applied in situations where the order of the desorption is unknown or, even worse, when the order is known to be different from 1. To describe E obtained in this fashion as an approximation is an understatement, completely wrong is a better description. 

Equation (2-16) is approximately correct for first-order desorption and for values of v/p between 108 and 1013 K 1. It is very often applied to determine Edes from a single TPD spectrum. The critical point, however, is that one must choose a value for v, the general choice being 1013 s 1, independent of coverage. As we explain below, this choice is only valid when there is little change in entropy between the molecule in the ground state and the transition state [27, 29, 30]. The Redhead formula should only be used if a reliable value for the prefactor is available ... 

Desorption energy Bd = AHdes ) mol Heat of adsorption derived from TPD Ei = feBTmJln(vT a,a/P) -const] (Redhead equation)... 

The conclusive proof came only recently and was based on MgO single crystal experiments. A single crystal surface is expected to have a small number (almost negligible) of defects. On a UHV cleaved MgO single crystal [85,86], the CO thermal desorption spectra (TDS) showed a peak at T 57 K and a broad feature at 76 K. The adsorption energy, calculated via the Redhead equation... 

DFT calculations of the vibrational frequencies of these adsorbed species produced spectra of which those deriving from intermediate 1 more closely resembled the HREEL spectrum of the surface. The authors calculate an activation energy of 55 kj/mol for cyclisation of intermediate 1 from the peak maximum temperature of 300 K for EO desorption using the Redhead equation [35] and an... 

The method of determining these desorption energies differs between authors. The approach adopted by Redhead (22) is to use the Polanyi-Wigner equation for desorption, that is... 

Redhead (22) and Rigby (23), using these equations, assume a value of 10 sec for vj. 

McCabe and Schmidt [275] have used a revised form of the Redhead equation, eqn. (116), including coverage variations of Ed, viz. 

Given such postulated, but not general, rate equations, a variety of methods is available for evaluating the rate parameters. We will consider the uniqueness or otherwise of the rate parameters subsequently, but first we will describe briefly the analytical procedures with specific reference to their application to metal—semiconductor systems. The simplest, and in many cases most accurate, is the peak temperature method first described by Redhead [63]. AE can be directly obtained by measuring the temperature, Tp, at which the desorption rate is a maximum, then by setting d2n/dt2 = 0, an expression for AE can be derived in terms of v, Tp and the known heating rate 3 v is usually assumed to be 1013 s-1. 

Method (ii). Redhead [63] derived equations for desorption rate maxima for various orders of reaction, but the expressions are rather insensitive to order so, again, evaluation of the pre-exponential term does not necessarily provide physically useful information. Because Tp can be obtained accurately, however, the energy term can also be precisely estimated and where the adsorbate—surface interaction dominates the adsorbate—adsorbate interaction, it provides a reliable value for the... 

Recently, Redhead (1995) presented a new empirical equation to cover the multilayer adsorption region, and his purpose is to extend the range of validity of the proposed equation to higher pressure range. His empirical equation takes the following form... 

Redhead s equation of the form (3.7-1) was chosen based on the fact that ... 

The range of validity of the Redhead s equation is such that at the lower limit of the relative pressure, the coverage is a monolayer, that is ... 

Previous work by Wachs et al. demonstrated that the information obtained during the temperature programmed surface reaction of adsorbed intermediate species over powdered samples enables us to determine kinetic parameters, such as the activation energy Ea of a surface reaction [20]. The authors demonstrated that the Redhead equation allows determining the activation energy Ea,... 

Strength of oxygen dissociatively chemisorbed on Pt supported on YSZ. Increasing eV R and e0 by 0.6 eV causes a 150°C decrease in Tp and a 0.6-eV decrease in E. The latter is computed by varying the heating rate p via the modified Redhead equation of Falconer and Madix ... 

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