Multilayer Adsorption Film

Presented analysis allows one to make the following conclusions  

The simplest model of normal mechemism of layers formation from a unicomponent ffow on the substrate leads to the Poisson distribution of relief points over the heights. 

After fflling a few first monolayers, the mean height and squared corrugation become linear functions of time. This is confirmed both by suialytical investigations and computer simulations. 

The film quality can be characterized by the parameter 9(00), that depends on the film growth mechanism. Therefore, the further development of multilayer films formation theory must be connected with the study of the detailed kinetics of processes in adsorption layers. 

The problem of kinetic boundary condition (KBC) was briefly discussed in Chap.6 in connection with the scattering problem. Here KBC will be considered in more detail. This problem is an important one providing a bridge between two different phases and taking into account effects of mutual interference of surface and gaseous systems. 

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Let us describe a phenomenological model of the multilayer film growth that is a simplified version of the general kinetic model of multilayer adsorption presented in Chap.6. The latter model allows one to evaluate the distribution function 0(fi,R,t) by solving general equation (6.1.19) and then to calculate main parameters of a multilayer adsorption film (h. A, H). 

In the case of multilayer adsorption it seems reasonable to suppose that condensation to a liquid film occurs (as in curves T or of Fig. XVII-13). If one now assumes that the amount adsorbed can be attributed entirely to such a film, and that the liquid is negligibly compressible, the thickness x of the film is related to n by... 

There is little doubt that, at least with type II isotherms, we can tell the approximate point at which multilayer adsorption sets in. The concept of a two-dimensional phase seems relatively sterile as applied to multilayer adsorption, except insofar as such isotherm equations may be used as empirically convenient, since the thickness of the adsorbed film is not easily allowed to become variable. 

Returning to multilayer adsorption, the potential model appears to be fundamentally correct. It accounts for the empirical fact that systems at the same value of / rin P/F ) are in essentially corresponding states, and that the multilayer approaches bulk liquid in properties as P approaches F. However, the specific treatments must be regarded as still somewhat primitive. The various proposed functions for U r) can only be rather approximate. Even the general-appearing Eq. XVn-79 cannot be correct, since it does not allow for structural perturbations that make the film different from bulk liquid. Such perturbations should in general be present and must be present in the case of liquids that do not spread on the adsorbent (Section X-7). The last term of Eq. XVII-80, while reasonable, represents at best a semiempirical attempt to take structural perturbation into account. 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

Multihydroxy surfactants, 24 148 Multijunction (MJ) stack arrays, 22 137-138, 139-140 Multilayer adsorption, 1 591 Multilayer barrier film, properties of,... 

By size of pore one can mean the diameter of an equivalent cylindrical or the distance between the sides of a slit-shaped pore (i.e., in general a diameter of the largest circle that can be inscribed in a flat cross section of a pore of arbitrary form). The basis of this classification is that each of the size ranges corresponds to characteristic adsorption effect that is manifested in the isotherm of adsorption [53,115], In micropores, the interaction potential is significantly higher than in wider pores, owing to the proximity of the walls. This explains that such pores become totally full with adsorbate at low relative pressures. In mesopores, one will observe formation of mono- and then multilayer molecular film forming over the walls. After formation of a multilayer molecular film,... 

So far we only have considered adsorption phenomena in the submonolayer range. It is well known, however, that for certain substrate-adsorbate partners it is possible to observe multilayer adsorption phenomena or adsorption of fluid films which may undergo wetting transitions from a microscopic to a macroscopic thickness. 

Indeed, a direct relationship between the lifetimes of films and foams and the mechanical properties of the adsorption layers has been proven to exist [e.g. 13,39,61-63], A decrease in stability with the increase in surface viscosity and layer strength has been reported in some earlier works. The structural-mechanical factor in the various systems, for instance, in multilayer stratified films, protein systems, liquid crystals, could act in either directions it might stabilise or destabilise them. Hence, quantitative data about the effect of this factor on the kinetics of thinning, ability (or inability) to form equilibrium films, especially black films, response to the external local disturbances, etc. could be derived only when it is considered along with the other stabilising (kinetic and thermodynamic) factors. Similar quantitative relations have not been established yet. Evidence on this influence can be found in [e.g. 2,13,39,44,63-65]. 

A very versatile approach to the formation of multilayer films has been developed by Decher, based on polyelectrolytes. If a solid substrate with ionic groups at the surface is dipped into a solution of a complementary polyelectrolyte, an ultrathin, essentially monomolecular film of the polyion is adsorbed [340]. The adsorption is based on pairing of surface bound ionic sites with oppositely charged ions, bound to the macromolecule. The polymers adsorb in an irregular flattened coil structure and only part of the polymer ions can be paired with the surface ions (Figure 29a). Ionic sites which remain with small counterions provide anchor points for a next layer formed by a complementary polyelectrolyte [342,343]. This way multilayer polyelectrolyte films can be prepared layer-by-layer just by dipping a suitable substrate alternately in an aqueous solution of polyanions and polycations. The technique can be employed with nearly all soluble charged polymers and results in films with a... 

All the techniques discussed so far refer to clean surfaces or surfaces with adsorbed molecules. When thicker adsorbed layers are present on the surface, the properties of these layers start to resemble those of the corresponding bulk phases. For Instance, for thin water layers on solid surfaces the dielectric permittivity (bulk water. A more or less gradual transition takes place towards wetting films to which we shall return in Volume III and. as far as multilayer adsorption is concerned, in sec. 1.5 g, h. 

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. " "...

This result is in a qualitative agreement with the experimental t-plot of Ar adsorption at 87 K on MCM 41 samples (see Figure 2(b)) using the data given in reference [13], As for simulation data, we assume that the density of the adsorbate equals that of the 3D-liquid and we have determined the thickness of the adsorbed film as the ratio of the adsorbed volume with the surface of the sample. Assuming pores of MCM 41 are cylinders, the specific surface S of each sample was determined via the relation between the porous volume V (given by the adsorbed amount after capillary condensation) and the diameter d of the pores S = 4V/d. Comparison of the different t-curves indicates that there is a pore size (5.1 nm) above which no confinement effect occurs on multilayer adsorption. Below this value, the thickness of the adsorbed film increases as the pore diameter decreases, t-curves are often analysed with the Frenkel-Halsey-Hill equation [14] /n... 

It is easy to see that adsorption energies are dependent on the curvature of the interface. Consider first adsorption on a planar interface. At low pressures, p, a sub-monolayer, gas-like, and eventually a two-dimensional liquid described by a Langmuir isotherm (or decorations thereof) forms. At higher pressures still (p/ps>0.35, where ps is the saturated vapour pressure) multilayer adsorption isotherms can occur depending on adsorbate, molecular size and adsorbate-substrate interactions. This regime is usually described by the theory of Brxmauer-Emmet-Teller (BET). In this domain, ln(p/pg) = 1/t, where t is the thickness of the film. 

As an example of a high boiling adsorbate, adsorption data for n-heptane on graphite may be considered. Harkins, Jura, and Loeser [43] reported afilm pressure at saturation of 63 dynes per cm.for this system. For comparison, we may cite the value for monolayer coverage given by Chessick, Zettlemoyer, and Wu [20], which was 27.6 dynes per cm. Thus, the relative contributions of monolayer adsorption and multilayer adsorption to the film pressures at saturation are quite comparable... 

The BJH, Cl and DH methods assume the same general picture of the adsorption-desorption process. Adsorption in mesopores of a given size is pictured as the multilayer adsorption followed by capillary condensation (filling of the pore core, i.e., the space that is unoccupied 1 the multilayer film on the pore walls) at a relative pressure determined by the pore diameter. The desorption is pictured as capillary evaporation (emptying of the pore core with retention of the multilayer film) at a relative pressure related to the pore diameter followed by thinning of the multilayer. 

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. 

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