Adsorption, rate

From the kinetic theory of gases, in a gaseous system the rate of collisions, rcoi, between gas-phase molecules and unit surface area per unit time is proportional to the mean molecular velocity, v, and the concentration of molecules, C  

Boltzmann s constant, T is absolute temperature, and m is the mass of the molecule. From the ideal gas law, PV = nRT or, in units of molecules, M, PV = MkfiT, one obtains C = M/V = P/kaT and the collision rate can be written in terms of the pressure, P, in this system  

Not all of these collisions result in chemisorption, thus a sticking probability, s, is defined to represent the fraction of collisions that do provide chemisorption, thus the adsorption rate is  

The sticking probability is seldom equal to unity for any one of the following reasons. 

Activation Energy - Chemisorption can be an activated process therefore, only those molecules possessing the required activation energy can be chemisorbed. However, many, if not most, chemisorption processes on clean metal surfaces are nonactivated at temperatures near or above 300 K, especially for nondissodative adsorption. 

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Alternative approaches treat the adsorbed layer as an ideal solution or in terms of a Polanyi potential model (see Refs. 12-14 and Section XVII-7) a related approach has been presented by Myers and Sircar [15]. Adsorption rates have been modeled as diffusion controlled [16,17]. 

Rate effects may not be chemical kinetic ones. Benson and co-worker [84], in a study of the rate of adsorption of water on lyophilized proteins, comment that the empirical rates of adsorption were very markedly complicated by the fact that the samples were appreciably heated by the heat evolved on adsorption. In fact, it appeared that the actual adsorption rates were very fast and that the time dependence of the adsorbate pressure above the adsorbent was simply due to the time variation of the temperature of the sample as it cooled after the initial heating when adsorbate was first introduced. 

Mention was made in Section XVIII-2E of programmed desorption this technique gives specific information about both the adsorption and the desorption of specific molecular states, at least when applied to single-crystal surfaces. The kinetic theory involved is essentially that used in Section XVI-3A. It will be recalled that the adsorption rate was there taken to be simply the rate at which molecules from the gas phase would strike a site area times the fraction of unoccupied sites. If the adsorption is activated, the fraction of molecules hitting and sticking that can proceed to a chemisorbed state is given by exp(-E /RT). The adsorption rate constant of Eq. XVII-13 becomes... 

Where E is appreciable, adsorption rates may be followed by ordinary means. In a rather old but still informative study, Scholten and co-workers [130] were able to follow the adsorption of N2 on an iron catalyst gravimetrically, and reported the rate law... 

Despite the difference ia the nature of the surface, the adsorptive behavior of the molecular sieve carbons resembles that of the small pore zeoHtes. As their name implies, molecular sieve separations are possible on these adsorbents based on the differences ia adsorption rate, which, ia the extreme limit, may iavolve complete exclusion of the larger molecules from the micropores. 

In practice the kinetics are usually more complex than might be expected on this basis, siace the activation energy generally varies with surface coverage as a result of energetic heterogeneity and/or sorbate-sorbate iateraction. As a result, the adsorption rate is commonly given by the Elovich equation (15) ... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Table 7-2 summarizes the cases when all substances are in adsorptive equilibrium and the surface reac tion controls. In Table 7-3, substance A is not in adsorptive equilibrium, so its adsorption rate is controUing. 

TABLE 7-3 Adsorption-rate Controlling (Rapid Surface Reaction)... 

Adsorption rate of substance A is controlling in each case. When an inert substance I is adsorbed, the term K pi is to be added to the adsorption term. SOURCE From Walas, Reaction Kinetics for Chemical Engineers, McGraw HiU, 1959 Butterworths, 1989. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

Each application for carbon treatment must be cognizant of the characteristics of the contaminant to be removed and designed with the proper carbon type in order to attain optimum results. Basically, there are two forms of activated carbon powdered and granular. The former are particles that are less than U.S. Sieve Series No. 50, while the latter are larger. The adsorption rate is influenced by carbon particle size, but not the adsorptive capacity which is related to the total surface area. —... 

In order to study the influence of surface disorder in the MM reaction, Frachenbourg et al. [91] have considered a substratum which has two types of randomly distributed sites with different adsorption rates. It is found that such a kind of disorder can sustain a reactive steady state, in contrast to the standard MM process on homogeneous surfaces. 

The desorption rate contains an exponential factor with a chemical potential (Iq for desorption into the vapor phase, since it is a thermally excited process. In a nonequilibrium situation, the chemical potential increases by Afi and increases the adsorption rate The rate difference is given as... 

In this equation, Mp is the monomer concentration within forming particles, pa is the adsorption rate of oligomeric radicals by the forming particles, Vp is the volume fraction of forming particles within the system, and kp and k, are the rate constants of propagation and termination, respectively. 

A general conclusion regarding H2 adsorption on alkali modified metal surfaces is that alkali addition results in a pronounced decrease of the dissociation adsorption rate of hydrogen as well as of the saturation coverage. 

This backdonation of electron density from the metal surface also results in an unusually low N-N streching frequency in the a-N2 state compared to the one in the y-N2 state, i.e. 1415 cm 1 and 2100 cm"1, respectively, for Fe(l 11)68. Thus the propensity for dissociation of the a-N2 state is comparatively higher and this state is considered as a precursor for dissociation. Because of the weak adsorption of the y-state both the corresponding adsorption rate and saturation coverage for molecular nitrogen are strongly dependent on the adsorption temperature. At room temperature on most transition metals the initial sticking coefficient does not exceed 10 3. 

The influence of the presence of sulfur adatoms on the adsorption and decomposition of methanol and other alcohols on metal surfaces is in general twofold. It involves reduction of the adsorption rate and the adsorptive capacity of the surface as well as significant modification of the decomposition reaction path. For example, on Ni(100) methanol is adsorbed dissociatively at temperatures as low as -100K and decomposes to CO and hydrogen at temperatures higher than 300 K. As shown in Fig. 2.38 preadsorption of sulfur on Ni(100) inhibits the complete decomposition of adsorbed methanol and favors the production of HCHO in a narrow range of sulfur coverage (between 0.2 and 0.5). 

The influence of electronegative additives on the CO hydrogenation reaction corresponds mainly to a reduction in the overall catalyst activity.131 This is shown for example in Fig. 2.42 which compares the steady-state methanation activities of Ni, Co, Fe and Ru catalysts relative to their fresh, unpoisoned activities as a function of gas phase H2S concentration. The distribution of the reaction products is also affected, leading to an increase in the relative amount of higher unsaturated hydrocarbons at the expense of methane formation.6 Model kinetic studies of the effect of sulfur on the methanation reaction on Ni(lOO)132,135 and Ru(OOl)133,134 at near atmospheric pressure attribute this behavior to the inhibition effect of sulfur to the dissociative adsorption rate of hydrogen but also to the drastic decrease in the... 

Opcn-ciitnit actks am strength of adsorption Weak adsorption Raft DuSit.i e order in i > v. cdk adsorption Rate positive order in A 5r/f pA>()... 

The FTE SAMs have a good hydrophobic property. Ohio et al. [36] have compared the variation of contact angles with immersing time in a neat FTE and a 100 mM FTE solution. The contact angles of water and hexadecane increased to about 110° and 73° from the initial value 76° and 36°, respectively, after 24 h immersion. Their works also indicate that the adsorption rate in 100 mM FTE solution is slightly faster than that in neat FTE. 

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