Adsorption thickness

Short-Chain Organics. Adsorption of an organic dispersant can reduce polarizabiHty attraction between particles, ie, provide semisteric stabilization, if A < A.p < A or A < A.p < A (T = dispersant) and the adsorption layer is thick. Adsorption in aqueous systems generally does not foUow the simple Langmuir profile because the organic tails on adsorbed molecules at adjacent sites attract each other strongly. 

Non-dairy creams (cream alternatives) are O/W emulsions stabilized by milk proteins. A relatively thick adsorption layer provides stability, mostly by steric stabilization and partly by electrostatic stabilization [829]. Figure 13.3 shows an example of a soybean-oil and milk-protein emulsion stabilized by fat globules and protein membranes. Stabilizers, such as hydrocolloid polysaccharides, are added to increase the continuous phase viscosity and reduce the extent of creaming. They must be stable enough to have a useful shelf-life but de-stabilize in a specific way when they are... 

D. C. Jones and Cutting (unpublished 1937) have very recently confirmed the predominance of the lateral adhesion in these adsorbed films, and also the validity of Traube s rule. When the vapour phase is nearly saturated with the hydrocarbon they find films more than one molecule thick. Adsorption on heavy water is rather less than on ordinary water. 

Theoretical. In deriving a theoretical expression for k, we have developed a reaction mechanism model for calcite dissolution which expands on the adsorption layer heterogeneous reaction model of Mullin ( ). We assume that a thin (possibly only a few molecules thick) "adsorption layer" (or "surface layer") exists adjacent to the crystal surface, between the crystal surface and the hydrodynamic boundary layer. Species in the adsorption layer are loosely bound to the crystal surface and have relatively low mobility, particularly in comparison with species mobility in the boundary layer. The crystal surface is believed to be sparsely covered by reaction sites at discontinuities in the surface ( 3). To distinguish between species activities in the bulk fluid, at the base of the boundary layer (near the crystal surface), and in the adsorption layer, we use the subscripts (B), (o), and (s), respectively. 

Contact angle Wettability, film thickness, adsorption properties PI... 

Numerous mathematical models exist the ones to be considered, however, are only those which are not of the empirical or semiempirical type the assumptions of which appear correct from a thermodynamical and statistical-mechanical point of view and the numerical solution of which does not present an unrealistically large computational task even in the case of thick adsorption layers. One of these is the so-called lattice model. Aversion of this model suitable for the description of the structure and thermodynamical properties of multimolecular adsorption layers was used in our calculations. 

J. O. Indekeu, Thin-thick adsorption phase-transitions and competing short-range forces, Europhys. Lett. 10 (1989) 165-170. 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

Madey and co-workers followed the reduction of titanium with XPS during the deposition of metal overlayers on TiOi [87]. This shows the reduction of surface TiOj molecules on adsorption of reactive metals. Film growth is readily monitored by the disappearance of the XPS signal from the underlying surface [88, 89]. This approach can be applied to polymer surfaces [90] and to determine the thickness of polymer layers on metals [91]. Because it is often used for chemical analysis, the method is sometimes referred to as electron spectroscopy for chemical analysis (ESCA). Since x-rays are very penetrating, a grazing incidence angle is often used to emphasize the contribution from the surface atoms. 

An interesting question that arises is what happens when a thick adsorbed film (such as reported at for various liquids on glass [144] and for water on pyrolytic carbon [135]) is layered over with bulk liquid. That is, if the solid is immersed in the liquid adsorbate, is the same distinct and relatively thick interfacial film still present, forming some kind of discontinuity or interface with bulk liquid, or is there now a smooth gradation in properties from the surface to the bulk region This type of question seems not to have been studied, although the answer should be of importance in fluid flow problems and in formulating better models for adsorption phenomena from solution (see Section XI-1). 

Electrolyte adsorption on metals is important in electrochemistry [167,168]. One study reports the adsorption of various anions an Ag, Au, Rh, and Ni electrodes using ellipsometry. Adsorbed film thicknesses now also depend on applied potential. 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

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... 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

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. 

The existence of a characteristic isotherm (or of a r-plot) gives a very important piece of information about the adsorption potential, at least for polar solids for which the observation holds. The direct implication is that film thickness f, or alternatively n/n is determined by P/I independent of the nature of the adsorbent. We can thus write... 

N2 as adsorbate, was quite similar to that for N2 on a directly prepared and probably amorphous ice powder [35, 141], On the other hand, N2 adsorption on carbon with increasing thickness of preadsorbed methanol decreased steadily—no limiting isotherm was reached [139]. 

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... 

In the pioneer work of Foster the correction due to film thinning had to be neglected, but with the coming of the BET and related methods for the evaluation of specific surface, it became possible to estimate the thickness of the adsorbed film on the walls. A number of procedures have been devised for the calculation of pore size distribution, in which the adsorption contribution is allowed for. All of them are necessarily somewhat tedious and require close attention to detail, and at some stage or another involve the assumption of a pore model. The model-less method of Brunauer and his colleagues represents an attempt to postpone the introduction of a model to a late stage in the calculations. 

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