Uptake curves

TPD is frequently used to detenuine (relative) surface coverages. The area below a TPD spectrum of a certain species is proportional to the total amount that desorbs. In this way one can detennine uptake curves that correlate gas exposure to surface coverage. If tire pumping rate of the UHV system is sufiBciently high, the mass spectrometer signal for a particular desorption product is linearly proportional to the desorption rate of the adsorbate [20, 21] ... 

For a step change in sorbate concentration at the particle surface (r = R) at time 2ero, assuming isothermal conditions and diffusion control, the expression for the uptake curve maybe derived from the appropriate solution of this differential equation ... 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

Fig. 9. Uptake curves for N2 in two samples of carbon molecular sieve showing conformity with diffusion model (eq. 24) for sample 1 (A), and with surface resistance model (eq. 26) for example 2 (0)j LDF = linear driving force. Data from ref. 18.

Figure 2,13, CO uptake curves for clean and K covered Pt(l 11) at 300 K.41,42 Reprinted with permission from Elsevier Science.

Figure 2.18. NO uptake curves for clean (solid line) and 0.18 ML K-covered (dashed line) Rh(100).55 Reprinted with permission from the American Institute of Physics.

Figure 2.20. Oxygen uptake curves for K (left)61 and Cs (right)60 dosed Ru(001) at T=300 K.60,61 Reprinted with permission from Elsevier Science.

For example, consider the dissociative adsorption of methane on a Ni(lOO) surface. If the experiment is performed above 350 K, methane dissociates into carbon atoms and hydrogen that desorbs instantaneously. Consequently, one determines the uptake by measuring (e.g. with Auger electron spectroscopy) how much carbon is deposited after exposure of the surface to a certain amount of methane. A plot of the resulting carbon coverage against the methane exposure represents the uptake curve. 

Figure 7.1 shows a calculated set of uptake curves obtained at different temperatures, while experimental results for methane on nickel are given in Fig. 7.2. 

Figure 7.1. Uptake curves for first and second order adsorption as a function of gas dose given in Pascal seconds. In this example, the sticking coefficient is strongly activated, with an activation energy of 60 kj moTb...

The reader is left to make this trivial conversion. Please note that the slope of the uptake curve at zero coverage equals So(T), and that the above derivation implicitly assumes that the adsorbates do not interact, which is seldom the case. Hence, sticking coefRcients in the limit of zero coverage are the most meaningful quantity. 

Figure 7.3. Uptake curves of hydrogen on Cu(lOO). Here the dosage has been converted into the equivalent number of monolayers (ML). Note that the sticking coefficient is very low and that 1.8 bar of H2 was required. The insert shows Arrhenius plots ofthe extracted...

Figure 16 Cumulative phosphorus uptake curves (per unit root length) predicted for two tomato cultivars Knox and C37 ) grown in a soil fertilised to two P-levels. (From Ref. 28.)...

Figure 1 Moisture uptake curves for LiCl hydrate. 

This should be compared with the hydrogen uptake curve for the corresponding 10,000 TON homogeneously catalyzed reactions shown in Figure... 

Figure 1 Hydrogen uptake curves for 1-hexene hydrogenations run at 35°C and 50 psig of hydrogen in 10% toluene/EtOH with a stirring rate of 1700 rpm. a) AHC-Wilk catalyst b) Homogeneous Wilkinson s catalyst.

Assuming zero order kinetics, the reaction rate constants can be calculated from the slope of the hydrogen uptake curve. Table 1 shows that the first three catalysts have similar rate constants on catalyst weight basis, from 5.6xl0"3 to... 

Figure 1 Hydrogen uptake curves of 3%Pd/CPS4 and 5%Pd and 10%Pd on CPS1, CPS2 and CPS4. The reaction conditions are 10 g 4-(benzyloxy) phenol in 100 methanol, hydrogen pressure 1.1 bar, agitation rate 200 rpm, temperature 35°C, catalyst loading 3wt%.

For large K, values, the uptake curve depends only upon the value of the parameter (1 representing the ratio of characteristic time constants for diffusion in the pores and in the subparticles. For small (1 values, diffusion in the subparticles is controlling and the solution coincides with Eq. (16-96) with r, replacing rp. For large (3 values, pore diffusion is controlling, and the solution coincides with Eq. (16-96) with ZpDp/iZp + pplQ replacing D . 

Figure 4. Equilibrium water uptake curve for Nafion membrane (a) measurement at 30 (b) measurement...

Fig. 2 displays a set of FTIR spectra obtained for the uptake of benzene into H-ZSM-5 at 415 K employing the experimental device and procedure as described in the Experimental Section. One recognizes the increase in absorbance of the typical benzene band at 1478 cm as a function of time (spectra 1 to 4). The maximum absorbance, A, of such bands can be used as a measure of the amount sorbed, M, at time t into the porous structure of the zeolite crystallites. Therefore, evaluation of the sequence of these spectral uptake curves can provide data which may be used in the appropriate solution (equ. 1) of Fick s second law, and this generates the desired diffusivities [22] ... 

Fig. 3. Oxygen transport by perfluorocarbons versus hemoglobin (Hb) (a) In the case of PFCs, O2 dissolution is characterized by loose, nondirectional van der Waals interactions. Oxygen solubility follows Henry s law, that is, is directly proportional to the gas s partial pressure (curve c). (b) In the case of Hb, a strong, localized chemical bond is established with the iron atom of a heme. Successive binding of four O2 molecules to the four hemes of Hb is cooperative, and saturation occurs when all four iron atoms are bound. Hence, the sigmoid shape of the O2 uptake curve, which levels off when the partial pressure of O2 on earth is attained (curve d) [20].

The hygroscopicity of the commercial sorbitol samples was investigated with an automated moisture balance system, where the relative humidity (RH) could be varied over the range of 0 to 90% [32], EMC sorption values were calculated from the raw data at each relative humidity and are summarized in Table 5, and moisture uptake curves for the sorbitol... 

Fig, 15. Effect of nickel content on the rate of hydrogenation of styrene by alloy catalysis. Curve A . Hydrogen uptake. Curve B Number of holes per atom in the Sd-band. Curve C Coefficient of the electronic specific heat term [D. A. Dowden and P. W, Reynolds, Disc. Faraday Soc. 8, 187 (1950)]. 

Co-Oxidation in Presence of Added N,N -di-sec-butyl-/>-phenylene-diamine. Figure 3 shows typical oxygen uptake curves obtained if DSBPD is added at concentrations around 10"2 to 10 4M to the indene-thiophenol reaction mixture. The reproducibility was good. The products after oxygen absorption was complete and the hydroperoxide had been allowed to decay were substantially the same as those obtained in the absence of DSBPD. Uptake of oxygen was extremely slow when either of the main reactants was omitted. 

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