Langmuirian adsorption

A more general criterion for linearity can be derived noting that the denominator of the Langmuirian adsorption isotherms must approach 1, and consequently ... 

General Model with Two Types of Langmuirian Adsorption Sites Coupled to First-Order Internalisation Processes... 

O(10 9)molm 2, one can still accept the linear regime hypothesis (10% occupancy), but an increase of the bulk concentration can overrule this assumption. For such situations, a more detailed analysis with Langmuirian adsorption is required. 

Kankare, J. and Vinokurov, I. A. (1999). Kinetics of Langmuirian adsorption onto planar, spherical, and cylindrical surfaces, Langmuir, 15, 5591-5599. 

At very low adsorption densities, metal ion adsorption exhibits Langmuiriaij behavior. However, above some critical adsorption density, r (i.e., when approximately 0.01% of surface sites are occupied), the intensity of metal lon/interactions decreases with increasing surface-site occupancy. A corollary of this model is that K has a unique value at adsorption densities below r for a specific adsorbate and adsorbent. By extension, 0a[Pg.181]

Postulation of eqns. (154) is in accordance with the assumption of Langmuirian adsorption. If the isotherm is more complex, it should be admitted that the rate constants are functions of 0 (e.g. fc, exp ( gd)... 

In several photocatalytic reactions, a linear relation between the rate of photocatalytic reaction and amount of substrate(s) adsorbed on the surface of photocatalyst has been reported.3,1(M2) When the Langmuirian adsorption isotherm was expected, this behavior was sometimes called Langmuir-Hinshelwood (L-H) mechanism even if only a kind of adsorbed substrate was assumed. Strictly speaking, however, this is wrong, because L-H mechanism involves the surface reaction of two kinds of adsorbed species, which is not realized in photocatalytic... 

Finally, a hydrophobic interaction was used by Hashimoto43 to perform the separation of phenylalanine and NaCl. In this case, NaCl, having almost no interaction with the packing, had a linear adsorption isotherm when the phenylalanine exhibited a classical Langmuirian adsorption isotherm. 

An exaggerated emphasis on heats of chemisorption has probably been harmful in the proper understanding of the role of chemisorption in surface phenomena. Thus the marked nonuniformity of all surfaces with respect to heats of chemisorption has led to rather elaborate treatments where models of surface heterogeneity (statistical distribution of energy sites) or, less successfully, specific forces of interaction between adsorbed species have been invoked to explain the non-Langmuirian adsorption isotherms. For instance the Frumkin isotherm can be obtained with a linear variation of heats of adsorption with coverage, and the Freundlich isotherm is attributed to an exponential variation of heats of adsorption. 

Rudzinski W. and Panczyk T The langmuirian adsorption kinetics revised A farewell to the XX-th century theories , Adsorption, 8 (2002) pp.23-34. 

The key equation describing competitive Langmuirian adsorption on such amphoteric carbons, in terms of fractional surface coverage 0 of molecules (M) and ions (M or M ) of a partially dissociated organic solute on a homogeneous surface, is... 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

In return for this complication, the TS-CST-SSR can yield very interesting results with much less effort than the TS-PF-SSR. This comes from the very different contacting pattern inherent in the TS-CST-SSR configuration as compared to the TS-PF-SSR, that allows the direct measurement of several quantities of interest. In Chapter 5 we have elaborated on the necessary theory and a mode of operation for the TS-CST-SSR. There it was shown how, in the special case of Langmuirian adsorption, this type of reactor will yield, in one run, more information than is available from a TS-PF-SSR experiment consisting of several runs. 

Adsorption. Consider an equimolar mixture of gases A and B and that each compound obeys Langmuirian adsorption behavior ... 

Most adsorbed phenoxazine derivatives give slightly broader peaks than what is theoretically stipulated for a Langmuirian adsorption process. The number n, whether evaluated from the o.5 or from eqn.(l), is usually somewhat lower than two, reflecting interactions between the adsorbed molecules. The immobilization process may strongly influence the properties of the adsorbed species, which is clearly revealed for Nile Blue in Fig.3. Both the energy level, as well as the various pKa-values of the oxidized and the reduced forms, are changed on adsorption. " ... 

One sees that for Langmuirian adsorption the Gibbs elasticity grows linearly with the surfactant concentration cj. Since the concentration of the monomeric surfactant cannot exceed the critical micellization concentration, Cj[Pg.624]

Data present absolute masses adsorbed (m ) calculated from Eq. (1.34), i. e. assuming V = and V = m /p with pj = 0.600 g/cm having been determined via tbe optimization procedure (1.33) using the Langmuirian adsorption isotherm (AI)... 

Reinmuth WH (1961) Diffusion to a plane with Langmuirian adsorption. J Phys Chem 65 473-... 

The analysis is straightforward in cases where adsorbate interaction effects do not play a role. This is the case either under Langmuirian adsorption conditions or in the saturation limit, 6>o 1. The former is an unrealistic assumption, since it is known that Temkin conditions prevail, illustrated in the seminal work of Sepa et al. (1981). Under the latter assumption, one can proceed to determine values of the effective transfer coefficient in the Butler-Volmer equation. Each quasi-equilibrium step, represented by a factor K in vqrr, contributes an amount of ( — to... 

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