Surface interfacial model

The surface complexation models used are only qualitatively correct at the molecular level, even though good quantitative description of titration data and adsorption isotherms and surface charge can be obtained by curve fitting techniques. Titration and adsorption experiments are not sensitive to the detailed structure of the interfacial region (Sposito, 1984) but the equilibrium constants given reflect - in a mean field statistical sense - quantitatively the extent of interaction. 

Mechanisms of Sorption Processes. Kinetic studies are valuable for hypothesizing mechanisms of reactions in homogeneous solution, but the interpretation of kinetic data for sorption processes is more difficult. Recently it has been shown that the mechanisms of very fast adsorption reactions may be interpreted from the results of chemical relaxation studies (25-27). Yasunaga and Ikeda (Chapter 12) summarize recent studies that have utilized relaxation techniques to examine the adsorption of cations and anions on hydrous oxide and aluminosilicate surfaces. Hayes and Leckie (Chapter 7) present new interpretations for the mechanism of lead ion adsorption by goethite. In both papers it is concluded that the kinetic and equilibrium adsorption data are consistent with the rate relationships derived from an interfacial model in which metal ions are located nearer to the surface than adsorbed counterions. 

Selected entries from Methods in Enzymology [vol, page(s)] Activation of lipolytic enzymes by interfaces, 64, 341 model for lipase action on insoluble lipids, 64, 345 interfacial enzyme inactivation, 64, 347 reversibility of the adsorption step, 64, 347 monolayer substrates, 64, 349 kinetic models applicable to partly soluble amphiphilic lipids, 64, 353 surface dilution model, 64, 355 and 364 practical aspects, 64, 357. 

Boussinesq (B4) proposed that the lack of internal circulation in bubbles and drops is due to an interfacial monolayer which acts as a viscous membrane. A constitutive equation involving two parameters, surface shear viscosity and surface dilational viscosity, in addition to surface tension, was proposed for the interface. This model, commonly called the Newtonian surface fluid model (W2), has been extended by Scriven (S3). Boussinesq obtained an exact solution to the creeping flow equations, analogous to the Hadamard-Rybczinski result but with surface viscosity included. The resulting terminal velocity is... 

Surface and Interfacial Tension. Some properties of liquid surfaces are suggestive of a skin that exercises a contracting force or tension parallel to the surface. Mathematical models based on this effect have been used in explanation of surface phenomena, such as capillary rise. The terms surface tension (gas—liquid or gas—solid interface) and interfacial tension (liquid—liquid or liquid—solid) relate to these models which do not reflect the actual behavior of molecules and ions at interfaces. Surface tension is the force per unit length required to create a new unit area of gas—liquid surface (mN/m (= dyn/cm)). It is numerically equal to the free-surface energy. Similady, interfacial tension is the force per unit length required to create a new unit area of liquid—liquid interface and is numerically equal to the interfacial free energy. 

The adsorption of block copolymers from a selective solvent was considered by Ligoure (1991). He predicted the existence of surface micelles (see Fig. 3.22) in the case when the block interacting unfavourably with the solvent only partially wets the surface. The model predicts a critical surface micellar concentration (csmc) that differs from the bulk cmc. When the contact angle, which characterizes the interfacial interactions between the copolymer, adsorbing surface, and solvent is lower than some universal value, surface micelles were predicted to appear at a lower copolymer concentration than bulk ones. Experimental results on surfaces are discussed in Section 3.8.4. 

Van der Waals theory is a typical example of a mean field theory in the sense that z is the only position variable. The interfacial layer has the same averaged properties everywhere parallel to the surface. This model works well as long as the temperature is far below its critical value. When T - T fluctuations in the density profile start to become important so that taking average values becomes less accurate. This is the main reason why [2.5.29] is not a good approximation. 

Metal mobility in soils is governed by interfacial processes, such as dissolution. The role of DOM in such processes will be determined by the nature t organic matter-surface associations. The surface complexation model pro-odes a conceptual framework for estimating the contributions of specific DOM components, particularly LMW organic ligands, to the mobilization f metals in soils. With this framework, the effects of humic substances on mineral dissolution can be interpreted to provide some insight into hu--mate-surface interactions. 

In the area of interfacial charging at the solid/liquid interface of metal oxide aqueous suspensions, the "surface complexation or site binding concept is commonly used [3-20]. This concept is characterised by consideration of specific ionic reactions with surface groups, rather than assuming simple binding of ions to the surface or their accumulation at the interface (adsorption). In the past decade several different models were introduced on the basis of the surface complexation model (SCM) they differ in the assumed structure of the electrical interfacial layer (EIL) and in the proposed mechanisms and stoichiometries of surface reactions leading to surface charge. 

To make Pick s law tractable for engineering calculations, several theories, or models, have been discussed. Their application usually introduces some empiricism, since distance of diffusion and extent of interfacial area are usually indeterminate. For most calculations, the time-tested film model is appropriate, not because it represents with validity the physical situation, but rather because it is supported by a wealth of experience as well as the ready availability of data, particularly molecular diffusion coefficients. The penetration and surface-renewal models have specialized applications and also depend on empirically derived parameters. 

Figure 10-16. Interfacial model of mica surfaces covered with adsorbed monolayers of stearic acid.

This idea is a consequent transfer of the three-dimensional van der Waals equation into the interfacial model developed by Cassel and Huckel (cf. Appendix 2B.1). The advantages of Frumkin s position is a more realistic consideration of the real properties of a two-dimensional surface state of the adsorption layer of soluble surfactants. This equation is comparable to a real gas isotherm. This means that the surface molecular area of the adsorbed molecules are taken into consideration. Frumkin (1925) additionally introduced, on the basis of the van der Waals equation, the intermolecular interacting force of adsorbed molecules represented by a . 

Figure 1 Relationships of S with interfacial tension and emulsifying activity of proteins. I, bovine serum albumin 2, /3-lactoglobulin 3. trypsin 4, ovalbumin 5, conalbuntin 6, lysozyme 7, K-casein 8, 9, I0, II, and 12, denatured ovalbumin by heating at 85°C for l, 2, 3, 4, and 5 min respectively 13, 14, 15, 16. 17, and 18. denatured lysozyme by heating at 85"C for l, 2, 3, 4, 5, and 6 min respectively 19, 20, 21, 22, and 23, ovalbumin bound with 0.2, 0.3, 1.7, 5.7, and 7.9 mol of sodium dodecyl sulfate/mol of protein respectively 24, 25, 26, 27, and 28, ovalbumin bound with 0.3, 0.9, 3.1,4.8, and 8.2 mol of linoleate/mol of protein respectively. Interfacial tension measured at corn oil/0.20c protein interface with a Fisher Surface Tensiontat Model 21. Emulsifying activity index calculated from the absorbance at 500 nm of the supernatant after centrifuging blended mixtures of 2 ml of corn oil and 6 ml of 0.5% protein in 0.01 M phosphate buffer, pH 7.4 S initial slope of fluorescence intensity (FI) vs. percent protein plot. 10 /al of 3.6 mM m-parinaric acid solution was added to 2 ml of 0.002 to 0.1% protein in 0.01 M phosphate buffer, pH 7.4, containing 0.002% SDS. FI was measured at 420 nm by exciting at 325 nm. (From Ref. 2. Reprinted by permission.)...

---