Linear adsorption

The use of CO is complicated by the fact that two forms of adsorption—linear and bridged—have been shown by infrared (IR) spectroscopy to occur on most metal surfaces. For both forms, the molecule usually remains intact (i.e., no dissociation occurs). In the linear form the carbon end is attached to one metal atom, while in the bridged form it is attached to two metal atoms. Hence, if independent IR studies on an identical catalyst, identically reduced, show that all of the CO is either in the linear or the bricked form, then the measurement of CO isotherms can be used to determine metal dispersions. A metal for which CO cannot be used is nickel, due to the rapid formation of nickel carbonyl on clean nickel surfaces. Although CO has a relatively low boiling point, at vet) low metal concentrations (e.g., 0.1% Rh) the amount of CO adsorbed on the support can be as much as 25% of that on the metal a procedure has been developed to accurately correct for this. Also, CO dissociates on some metal surfaces (e.g., W and Mo), on which the method cannot be used. 

Synthetic polymers TSK-GEL GMPWxi TSK-GEL GSOOOPWxl G3000PWxl Large pore size, low adsorption, linear calibration curve... 

A. Damjanovic and M. A. Genshaw, Electrochim. Acta 15 1281 (1970). Experimental proof of Temkin behavior. O adsorption linear with potential. 

Collagen desorption-adsorption linear functions on polyethy-lenes exhibit clearly defined transition points. All collagen which adsorbs in addition to the irreversibly adsorbed layers (represented for polyethylene and grafted polyethylene by their abscissa values 3.0 and 3.7 mg/m ) can be entirely desorbed. Above the transition points the desorption-adsorption slopes are equal to one. 

Most cat- and anions have a chemical affinity for metal (hydr)oxides. Both inner sphere and outer sphere complexes can be formed. In case of an inner sphere complex one or more surface O or OH groups are shared between a metal centre of the metal (hydr)oxide and the centrd element (e.g. P or Cd) of the adsorbed species. The adsorption of a cation bound at a positively charged metal (hydr)oxide usually shows a linear isotherm at low pH and low cation ion concentrations. In a log-log plot of the adsorption linearity of the adsorption isotherm is reflected in the constant slope n with n=l (figure 6). 

Taylor, C.D., M. Neurock, and J.R. Scully, A first-principles model for hydrogen uptake promoted by suUur on Ni(ll 1). Journal of The Electrochemical Society, 2011.158(3) p. F36-F44. Savizi, I.S.P. and M.J. Janik, Acetate and phosphate anion adsorption linear sweep voltammo-grams simulated using density functional theory. Electrochimica Acta, 2011. 56(11) p. 3996-4006. 

Q heat of adsorption linear quadrupole moment r distance between centers of pair pore radius r, ionic radius... 

A comparison of the adsorption energies of the complexes formed by ammonia, pyridine, and isopropylamine with a simple potential-energy model, which assumes that the heat of adsorption linearly scales with gas-phase proton affinities, suggests that proton transfer dominates the interaction between the adsorbate and the acid site [83]. 

Figure 7.12. Calculated effluent profiles for a linear core system (see text) both with and without adsorption. Cases presented are (a) no adsorption, linear adsorption (LO) (b) no adsorption, linear adsorption (LO), Langmuir adsorption (L1,L2) and (c) no adsorption, linear adsorption (LO), Langmuir adsorption (L3).

I. S. P. Savizi and M. J. Janik, Acetate and phosphate anion adsorption linear sweep voltammograms simulated using density functional theory, Electrochim. Act., 2011, 56(11), 3996. 

Many solids show marked swelling as a result of the uptake of a gas or a liquid. In certain cases involving the adsorption of a vapor by a porous solid, a linear relationship exists between the percentage of linear expansion of Ae solid and the film pressure of the adsorbed material [134, 135]. 

Using guest fluorophores, they show that the adsorption energy increases linearly with the alkyl chain length as... 

The adsorption of the surfactant Aerosol OT onto Vulcan Rubber obeys the Langmuir equation [237] the plot of C/x versus C is linear. For C = 0.5 mmol/1, C/x is 100 mol/g, and the line goes essentially through the origin. Calculate the saturation adsorption in micromoles per gram. 

A variety of experimental data has been found to fit the Langmuir equation reasonably well. Data are generally plotted according to the linear form, Eq. XVn-9, to obtain the constants b and n from the best fitting straight line. The specific surface area, E, can then be obtained from Eq. XVII-10. A widely used practice is to take to be the molecular area of the adsorbate, estimated from liquid or solid adsorbate densities. On the other hand, the Langmuir model is cast around the concept of adsorption sites, whose spacing one would suppose to be characteristic of the adsorbent. See Section XVII-5B for an additional discussion of the problem. 

One may choose 6(Q,P,T) such that the integral equation can be inverted to give f Q) from the observed isotherm. Hobson [150] chose a local isotherm function that was essentially a stylized van der Waals form with a linear low-pressure region followed by a vertical step tod = 1. Sips [151] showed that Eq. XVII-127 could be converted to a standard transform if the Langmuir adsorption model was used. One writes... 

When plotted according to the linear form of the BET equation, data for the adsorption of N2 on Graphon at 77 K give an intercept of 0.004 and a slope of 1.7 (both in cubic centimeters STP per gram). Calculate E assuming a molecular area of 16 for N2. Calculate also the heat of adsorption for the first layer (the heat of condensation of N2 is 1.3 kcal/mol). Would your answer for Vm be much different if the intercept were taken to be zero (and the slope the same) Comment briefly on the practical significance of your conclusion. 

TPD Temperature programmed desorption After pre-adsorption of gases on a surface, the desorption and/or reaction products are measured while the temperature Increases linearly with time. Coverages, kinetic parameters, reaction mechanism... 

Detailed derivations of the isothemi can be found in many textbooks and exploit either statistical themio-dynaniic methods [1] or independently consider the kinetics of adsorption and desorption in each layer and set these equal to define the equilibrium coverage as a function of pressure [14]. The most conmion fomi of BET isothemi is written as a linear equation and given by ... 

Vlugt T J H, Krishna R and Smit B 1999 Molecular simulations of adsorption isotherms for linear and branched alkanes and their mixtures in silicalite J. Phys. Ohem. B 103 1102-18... 

A rather simpler situation arises when the bulk concentrations are sufficiently small that the adsorption isotherms approach linearity. Then (7,4), for example, shows that... 

Application of Snyder s theory of linear chromatographic adsorption (171) gives the variation in adsorption energy of the thiazole nitrogen atom as a function of this steric hindrance for silica and alumina (see Table III-22). These results show that alumina is more sensitive toward steric effects while silica shows a higher selectivity in the case of polar effects. 

The numerical values of and a, for a particular sample, which will depend on the kind of linear dimension chosen, cannot be calculated a priori except in the very simplest of cases. In practice one nearly always has to be satisfied with an approximate estimate of their values. For this purpose X is best taken as the mean projected diameter d, i.e. the diameter of a circle having the same area as the projected image of the particle, when viewed in a direction normal to the plane of greatest stability is determined microscopically, and it includes no contributions from the thickness of the particle, i.e. from the dimension normal to the plane of greatest stability. For perfect cubes and spheres, the value of the ratio x,/a ( = K, say) is of course equal to 6. For sand. Fair and Hatch found, with rounded particles 6T, with worn particles 6-4, and with sharp particles 7-7. For crushed quartz, Cartwright reports values of K ranging from 14 to 18, but since the specific surface was determined by nitrogen adsorption (p. 61) some internal surface was probably included. f... 

Fig. 2.28. The high-pressure branch is still linear (provided mesopores are absent), but when extrapolated to the adsorption axis it gives a positive intercept which is equivalent to the micropore volume. The slope of the linear branch is now proportional to the external surface area of the solid. Microporosity is dealt with in detail in Chapter 4.

It is sufficient, as Sing has pointed out, merely to replace as normalizing factor by the amount adsorbed at some fixed relative pressure (p/p ), in practice taken as (p/p°), = 0-4. The normalized adsorption n/ o (= j). obtained from the isotherm on a reference sample of the solid, is then plotted against p/p°, to obtain a standard a,-curve rather than a t-curve. The a,-curve can then be used to construct an a,-plot from the isotherm of a test sample of the solid, just as the t-curve can be used to produce a t-plot. If a straight line through the origin results, one may infer that the isotherm under test is identical in shape with the standard the slope b, of the linear branch of the j-plot will be equal totio 4 Just as the slope b, of the t-plot was equal to nja (cf. Equation (2.34)). 

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