Adsorbed layer definition

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

It is useful to define the tenns coverage and monolayer for adsorbed layers, since different conventions are used in the literature. The surface coverage measures the two-dimensional density of adsorbates. The most connnon definition of coverage sets it to be equal to one monolayer (1 ML) when each two-dimensional surface unit cell of the unreconstructed substrate is occupied by one adsorbate (the adsorbate may be an atom or a molecule). Thus, an overlayer with a coverage of 1 ML has as many atoms (or molecules) as does the outennost single atomic layer of the substrate. 

It is thus tempting to define the first saturated layer as being one monolayer, and this often done, causing some confiision. One therefore also often uses tenns like saturated monolayer to indicate such a single adsorbate layer that has reached its maximal two-dimensional density. Sometimes, however, the word saturated is omitted from this definition, resulting m a different notion of monolayer and coverage. One way to reduce possible confiision is to use, for contrast with the saturated monolayer, the tenn fractional monolayer for the tenn that refers to the substrate unit cell rather than the adsorbate size as the criterion for the monolayer density. 

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

Molecules in adsorbed layers have also a definite orientation. If a complete layer is formed over a surface, with those groups possessing the greatest attraction for the surface turned inward, we have virtually a new surface with properties determined by the nature of the groups which are directed outwards. There seems to be no very good reason why this, in certain cases, should not adsorb a second layer of molecules. Indeed, the assumption that this double-layer adsorption occurs has occasionally been found helpful. But there is a large difference between this extension of the single-layer theory and the atmospheric. theory. 

The equilibrium between the gas phase and the adsorbed layer according to the theory of the definite saturation limit. 

It is assumed that the surface of a solid consists of a definite number of areas of atomic size, sites each of these sites is capable to bind one particle, atom or molecule, in an adsorption process. The adsorbed layer is ideal if (1) all surface sites are identical and (2) the interaction between adsorbed particles may be neglected. 

This review has surveyed the present status of theoretical and experimental studies on the adsorption of macromolecules, with particular reference to the determination of conformations of adsorbed macromolecules. No definitive experimental method is as yet available for this determination. At present, the conformation of adsorbed macromolecules can only be inferred from a comparison of experimental data of such properties as the adsorbed amount T, the fraction p of adsorbed trains and the thickness of the adsorbed layer with the existing theories formulated on various conformational models as depicted in Fig. X. 

Adsorption is the process of analyte accumulation on the surface under the influence of the surface forces. Determination of the total amount of the analyte adsorbed on the surface requires the definition of the volume where this accumulation is observed, usually called the adsorbed layer volume (U ). In chromatographic systems, adsorbents have large surface area, and even very small variation in the adsorbed layer thickness lead to a significant variation on the adsorbed layer volume. There is no uniform approach to the definition of this volume or adsorbed layer thickness in the literature [14,21,22]. 

Assumption 5 In the definition of the isotherm, the convention is adopted that the solvent (if pure) or the weak solvent (in a mixed mobile phase) is not adsorbed [8]. Riedo and Kov ts [9] have given a detailed discussion of this problem. They have shown that the retention in liquid-solid i.e., adsorption) chromatography can best be described in terms of the Gibbs excess free energy of adsorption. But it is impossible to define the surface concentration of an adsorbate without defining the interface between the adsorbed layer and the bulk solvent. This in turn requires a convention regarding the adsorption equilibrium [8,9]. The most convenient convention for liquid chromatography is to decide that the mobile phase (if pure) or the weak solvent (if the mobile phase is a mixture) is not adsorbed [8]. Then, the mass balance of the weak solvent disappears. If the additive is not adsorbed itself or is weakly adsorbed, its mass balance may be omitted [30]. 

In adsorption studies the size ratio parameter, n, is defined as the number of solvent molecules replaced from the adsorbed layer by one molecule of the adsorbate. This is a definition at a molecular level. An alternative definition of n as a purely thermodynamic quantity is given by the ratio... 

The accuracy with which this can be expressed as square meters of surface depends on the exactness with which the number of adsorbed layers can be determined, and on the closeness with which one can approximate the average area covered by each adsorbed molecule. Beyond this, the definition of the area so measured presents some difficulty. Langmuir has pointed out that there must be spaces of all sizes and shapes on a charcoal surface. On a plane surface, a single adsorbed molecule, may be attached to a single carbon atom whereas, in crevices and pores the same size molecule may cover several carbon atoms. Much depends on the size and orientation of an adsorbed molecule. Thus, an aliphatic acid molecule that lies flat on the surface will cover more carbon atoms than when attached at one end. Therefore, it is to be anticipated that the measured surface will depend on the structure of the adsorbate.1,2... 

Drauglis published describes experiments that would definitely prove the multilayer organization but the experimental set up was not sensitive enough to characterize layers of thickness lower than 100 a The model proposed implied that the first adsorbed layers extend their order through some 100 to 10 000 A which is exactly what LC do. 

Coil-like macromolecules, however, may form a great many contacts with a substrate, and the shape of the adsorbed coil molecule may be very different according to polymer-substrate, polymer-solvent, polymer-polymer, and substrate-solvent interactions (Figure 12-5). The number and order of adsorbed segments leads to a definite macroconformation, and a definite macroconformation, in turn, determines the thickness of and polymer concentration in the adsorbed layer. 

The formula (1.48) or formulas based on another definition of the effective charge [40, 43, 46, 77] can be used for evaluating the degree of the bond polarity (the valency) from IR spectra of thin films if the density N of the electric dipoles is known from independent measurements [46, 78]. This parameter is of considerable importance, since it allows one to calculate the derivative of the surface potential with respect to the thickness of the adsorbate layer [79] and the interionic distance [40, 43, 46],... 

A—B diblock copolymers adsorb spontaneously at the interface between two immiscible A and B homopolymers. Our objective here is to make quantitative predictions of the nature of the adsorbed layer, fri this case, the phase behavior depends on (Mily one x parameter, that between the A and B homopolymers, and the statistical segment lengths of the A and B chains. The specific example that we will smdy is the adsorption of a SPB(89)-SPB(63) diblock copolymer at the interface between SPB(89) and SPB(63) homopolymers at room temperamre [A = SPB(89) and B = SPB(63)]. For this system, x = 0.0064 (system 33 in Table 19.1), I A = 0.49 nm, and /b = 0.75 nm. We consider the interface between SPB(89) and SPB(63) homopolymers with Na = 4,230 and Nr =3,600. It is straightforward to show that the two homopolymeis are highly immiscible because xAave =6.2 which is much greater than 2 (see Eq. (19.8) for definition of Nave)- We consider the adsorption of a SPB(89)-SPB(63) diblock copolymer with NAb = 790 and Nsb = 730 where the subscript b refers to the chains comprising the block copolymer. We consider two flat homopolymer-rich phases with the diblock copolymer adsorbed at the interface. The z-axis of our coordinate frame is perpendicular to the interface. The results of SCFT predictions for 0 e volume fraction of the A-B... 

Eqs. 5 and 6 could be applied to formulate computer programs that calculate the final values of Rp(j) for a given gradient program and the retention-eluait composition relationships for selected systems. The systems vay often applied in MD contain thin layers of adsorbents with definite groups like diol, cyano, or amine. " The basic equation describing the retention of solutes in such systems has the form of Eq. 2 or the following formula ... 

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