Multilayer adsorbates

To derive an explicit expression of the rate of desorption we restrict ourselves to nondissociative adsorption, listing references to other systems— such as multicomponent and multilayer adsorbates with and without precursors—for which such a treatment has been given, later. We look at a situation where the gas phase pressure of a molecular species, P, is different from its value, P, which maintains an adsorbate at coverage 6. There is then an excess flux to re-establish equilibrium between gas phase and adsorbate so that we can write [7-10]... 

Figure 4. Reflection infrared spectra of aniline films (a) aniline multilayer adsorbed on Ni(111) at 165 K (b) poly(aniline) monolayer on Ni(111) at 400 K (c) electrochemically grown poly(aniline) on Pt oxidized at 0.8 V vs. Ag/AgCI(1M) (d) electrochemically grown poly(aniline) on Pt reduced at 0.35 V vs. Ag/AgCI(1M) (e) electrochemically grown poly(aniline) on Pt reduced at 0.0 V vs. Ag/AgCI(1M)...

There are many other examples of the potential use of mixed systems of chitosan + surfactants to be found in the recent research literature. For instance, it has been established that chitosan-surfactant interactions can be successfully used for preparing emulsions stabilized by multilayer adsorbed films (Mun et al., 2006 Chuah et al., 2009). 

Fig. 1 Light absorption in heterogeneous systems. The substrate (S), strongly interacting adsorbate molecules or adducts (A-S) or multilayered adsorbate molecules (A) can be excited...

Figure 1.32a. Schematic representation of the adsorption (1) - (3) and desorption (4) - (6) of a fluid from the gaseous phase in a cylindrical pore with radius a-l (1) stable adsorbed film with radius a - t (2) multilayer adsorbed film at the unstabillty limit r (3) completely filled capillary (4) unsymmetrical state of a partially filled pore at the metastability limit r (5) further desorption at the metastability limit r (6) stable film with radius r. " "...

Here is expressed by eq.2. Ap, depends on the shape of the meniscus in the pore. For the transformation of multilayer adsorption to capillary condensation, Aju, is given by -yV /a, where y and F , denote the surface tension and molar volume of the condensate a = R - / Hence, the chemical potential change of the multilayer adsorbed state, is expressed by eq.4. 

Figure 4. Various semiconductor electrodes, modified with monolayers (covalently attached) of phthalocyanine tethered to the electrode surface (a) or multilayers (adsorbed or sublimed) which aggregate to leave a semiporous surface layer (b) and a uniform phthalocyanine film leading to a p-type semiconductor layer adjacent to the n-type semiconductor substrate (c).

An exception is represented by the Frenkel-Halsey-Hill theory, which describes the multilayer adsorbed film as a liquid perturbed by the presence of a surface. 

The heat measured in step (3) corresponds to the adsorption of an unknown amount of vapor on the carbon surface. Now, in case of a wetting system, we know that the conditions are then fulfilled to have a multilayer adsorbed. This means that the heat measured in step (4) corresponds to the immersion energy of a precovered solid, so that it can be used for the surface area determination by the modified Harkins and Jura method [7]. The addition of the heats measured in steps (3) and (4) after suitable correction leads to the usual immersion energy. If the full wetting is not reached at saturation pressure it is then needed to proceed to step (5). More details about this procedure and the way to get experimental data are described elsewhere [9]. 

A BS. A multilayer-adsorbed porous membrane was prepared via three steps, as shown in Figure 12. (1) Radiation-induced graft... 

The separation factor was determined at various flow rates of the mobile phase ranging from 0.3 to 3 mL/min, i.e., the residence times ranged from 4.6 to 46 s in the BS A-multilayer-adsorbed porous hollow-fiber membrane. As a result, the separation factor was constant... 

In the discussion of the mesopore shape, the contact angle, is assumed to be zero (uniform adsorbed film formation). The lower hysteresis loop of file same adsorbate encloses at a common relative pressure depending to the stability of the adsorbed layer regardless of the different adsorbents due to the so called tensile strength effect. This tensile strength effect is not sufficiently considered for analysis of mesopore structures. The Kelvin equation provides the relationship between the pore radius and the amount of adsorption at a relative pressure. Many researchers developed a method for the calculation of the pore size distribution on the basis of the Kelvin equation with a correction term for the thickness of the multilayer adsorbed film. 

In contrast, when loaded with a sufficiently thick film, a TSM resonator functions as a rheological probe of the properties of surface-attached species. An acoustically thick film is one whose combination of thickness and shear stiffness is such that the acoustic wave significantly deforms it. Consequently, displacement of the outer regions of the film exhibits a phase delay with respect to displacement of the underlying resonator. Multilayer adsorbates may behave in this manner if they are either intrinsically soft or are plasticized by the permeation of a solvent or other small molecules. This situation is more complicated and it is only recently that the theoretical aspects have been treated in quantitative fashion for fluid-immersed films. Accordingly, this case is described subsequently to the simpler gravimetric case and in greater detail. 

Because the free energy of adsorption per mole of oxygen decreases with amount of oxygen adsorbed (the O-substrate bond becomes weaker), multilayer adsorbed oxygen on metal M eventually favors transformation to a crystalline stoichiometric oxide. In other words, AG for O-Mads + n02 (n02)-0-Mads... 

W is the adsorption Vm is the liquid molar volume pf is the fluid density in occupied pores pni is the density of the multilayered adsorbate in pores is the radius of pores occupied at the pressure p Oss is the collision diameter of the surface atoms... 

Transition from gas (subscript g) to liquid (1) or fluid in the form of multilayered adsorbate in pores (m) can be linked to the corresponding fugacity f. 

Ackley, M. W. Multilayer Adsorbent Beds for PSA Gas Separation. EP 0875279A2, (1998), to Praxair. 

Notaro, F., Mulhaupt, J. T., Leavitt, F. W., and Ackley, M. W. Adsorption process and system using multilayer adsorbent beds. U.S. Patent 5,810,909 (1998), to Praxair. 

A characteristic parameter of a porous material is its so-called BET-surface. This is the surface of a monolayer adsorbate of N2-molecules at boiling temperature of N2 at po = 1 atm, namely 77.3 K [1.3]. It is determined by nitrogen adsorption experiments at this temperature for pressures (p/po) < 1 The mass of the monolayer load (mO is determined by fitting data (m ) to the adsorption isotherm equation developed by Bmnauer, Emmett and Teller in 1938, originally designed for multilayer adsorbates [1.1-1.3, 1.57]. 

Type VI isotherms present stepwise multilayer adsorbates, the layers becoming more pronounced at low temperatures. 

The BET-isotherm has been derived by statistical mechanical methods by Hill and later again by W. Steele (1974) [7.5], [7.43], It can be shown that the infinitive number of adsorbate layers assumption used in deriving (7.70), is a reasonable approximation for multilayer adsorbates with more than 4 layers. Though admolecular interactions are not explicitly taken into account in (7.70), today this isotherm provides the basis for a standardized method to determine the mesoporous surface of porous sorbent materials by N2-adsorption at T = 77 K or Ar-adsorption at T = 87 K, i. e. ps = 0.1 MPa. For this normally only the initial portion of a measured isotherm (0 < p/ps < 0.35) is used. Details are given in [7.1, 7.5, 7.44-7.47] and in the respective ISO-documents published meanwhile [7.14]. 

In Eq. (354), k and k are kinetic constants of the rate of adsorption and desorption, respectively, is the average heat of adsorption taking place on the first (already adsorbed) layer, is the total (monolayer plus multilayer) adsorbed amount, and n is the amount of gas adsorbed onto the first layer only. From the definitions of n, rf and n it follows that... 

The heterogeneity effects in the formation of multilayer adsorbed films have not been very intensively studied in terms of the lattice models. In general, one can expect a certain rounding of the sharp steps occurring on adsorption isotherms. We will discuss the problem of possible phase transitions in the surface films in Section VII. 

In case of multilayer adsorbate (P> 2) certmn hypotheses on the capture mechanism and interaction potential of colliding particle with the adsorbate are necessary for the calculation of the adsorption probabilities. Particularly, in some cases the expressions (7.1.6) and (7.1.7) are valid. Omitting the question of the calculation of detailed adsoi-ption-desorption probabilities let us formulate a model based on ideas of the two-layer adsorption model and BET-approximation for the adsorption isotherms of multilayer fihns (Flood 1967). The main assumptions of this generalized kinetic BET-model are ... 

This solution describes the following physical effects. When 6 1 (a rarefied multilayer adsorbate) a(2) w o(2) and he is defined entirely by the coverages of the first two layers. If 6 1... 

As it has been shown, the model qualitatively describes a number of features of growth dynamics for ideal and nonideal adsorbate. Possible generalizations of this model can be based on more precise adsorption isotherms of multilayer adsorbate (csdculated in other than the meem field approximation) and including more realistic diffusion and adsorption coefficients dependence on the coverage. 

Here, the target of measurement by infrared ER spectrometry is a thin film deposited on a flat surface of a dielectric material. Multilayered adsorbed species (adsorbates) may also be a target, but, if a quantitative analysis of their observed spectra is to be performed, each layer in the adsorbate film should have a flat and parallel structure. For this reason, the discussion in this chapter assumes that thin films like a Langmuir-Blodgett (LB) film [4], which has an ideally flat layer, are the target of study. A dielectric substrate is made of a nonmetallic material and includes semiconductors the surface of water is also regarded as a dielectric substrate. Monolayers spread onto the surface of water are often analyzed by ER spectrometry. 

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