Surface adsorption binary systems

Batch adsorption experiments by Yee and Fein (2002) using aqueous Cd, B. subtilis, and quartz as a function of pH showed that the thermodynamic stability constants, determined from binary systems, could successfully describe the distribution of Cd between the aqueous phase and the bacterial and mineral surfaces. The constants could also be used to estimate the distribution of mass in systems, and construct a surface complexation model. 

In the case of surface adsorption, at constant surface tension ofsolutions, an equation of the same form as equation 12 is obtained for the binary surfactant mixture system (15,16) ... 

It is evident that the non-ideal solution theory of surface adsorption and micellization is a convenient and useful tool for obtaining the surface and the micelle compositions and for studing the molecular interaction in the binary surfactant system. 

As already discussed in Chapter 1, the relative tendency of a surfactant component to adsorb on a given surface or to form micelles can vary greatly with surfactant structure. The adsorption of each component could be measured below the CMC at various concentrations of each surfactant in a mixture. A matrix could be constructed to tabulate the (hopefully unique) monomer concentration of each component in the mixture corresponding to any combination of adsorption levels for the various components present. For example, for a binary system of surfactants A and B, when adsorption of A is 0.5 mmole/g and that of B is 0.3 mmole/g, there should be only one unique combination of monomer concentrations of surfactant A and of surfactant B which would result in this adsorption (e.g., 1 mM of A and 1.5 mM of B). Uell above the CMC, where most of the surfactant in solution is present as micelles, micellar composition is approximately equal to solution composition and is, therefore, known. If individual surfactant component adsorption is also measured here, it would allow computation of each surfactant monomer concentration (from the aforementioned matrix) in equilibrium with the mixed micelles. Other processes dependent on monomer concentration or surfactant component activities only could also be used in a similar fashion to determine monomer—micelle equilibrium. 

Finally, intraparticle diffusion appears to be an important factor in adsorption kinetics for many types of systems. In the past it has been customary to define such mass transfer quantitatively in terms of an effective diffusivity. However, even in gas-solid systems more than one process can be involved for porous particles. Thus, two-dimensional migration on the pore surface, surface diffusion, is a potential contribution. Liquid systems appear to be more complex, and, with electrolytes, it has been shown that the electric potential induced by counter-diffusing ions should be taken into account. A realistic description of intraparticle mass transfer in such cases requires more than a single rate coefficient for a binary system. 

The equations (20) to (30) provide the basis for predicting the adsorption rate profiles for the binary system. The input parameters required for the model are the single-solute film transfer and surface diffusion coefficients, the single-solute isotherm constants and the mixture equilibria coefficients. The rate parameters were obtained from single solute rate data (20), and the equilibrium parameters were obtained from single and multi-solute equilibrium data. 

There are two properties of the metal crystals in binary systems that seem worthy of special consideration. First, since the crystals are small, they have a relatively high ratio of surface to bulk atoms hence, if bond formation during adsorption is related to a change in physical properties, as, for instance, for the case of ferromagnetism, relatively strong effects can be expected. For this reason the study of the change in ferromagnetism consequent upon adsorption was started. It was later completed by photoelectric emission and conductivity work on films, since for these studies binary catalysts are unsuitable for obvious reasons. 

Secondly, since the metal surface is large and relatively stable to a prolonged sojourn at higher temperatures, the binary systems appear interesting objects from the point of view of the study of adsorption equilibria. Contrary to films, they permit a study of equilibrium situations in which only a small fraction of the surface is covered, and therefore they serve to open a quite extensive field of investigations. 

This expression describes the analyte retention in binary system using only the total volume of the liquid phase in the column, Vq, and total adsorbent surface area S as parameters and the derivative of the excess adsorption by the analyte equihbrium concentration. It is important to note that the position of Gibbs dividing plane in the system has not been defined yet. 

The examples discussed in the previous sections Illustrate models for deriving Isotherms for binary systems. A variety of variants (e.g. mobile adsorbates), alternatives (e.g. models based on computer simulations) and extensions (e.g. multimolecular adsorption. Inclusion of surface heterogeneity, can be, and have been, proposed. The extensions usually require more parameters so that agreement with experiment is more readily obtained, but as long as various models are not compared against the evidence, discrimination is impossible. As there are numerous theoretical (e.g. distinction between molecules in the first and second layer) and experimental (presence of minor admixtures, tenaciously adsorbing on part of the surface) variables one tends to enter a domain of diminishing returns. On the other hand, there are detailed models for certain specific, well-defined situations. Here we shall review some approaches for the sake of illustration. 

The next procedure and the calculation of the surface adsorption of the third component is analogical as it was shown for binary systems. 

The first attempt to model sorption in these suspensions was based on the adsorptive additivity approach. The model parameters which best fit the sorption data for pure Fe(OH)3 and Si02 suspensions were identified (Table II) and using these values the binary systems were modeled by including surface sites from both pure solids in the calculations. However, because this approach overestimated the overall removal of ions from solution in almost all cases, dissolution and sorption of silicate were then incorporated into the model. 

Role of Adsorbed Surfactant Layer. Foams, irrespective of the nature of liquid and gas involved, require a third component for stabilization of thin films (lamellae) of the liquid. In the familiar case of aqueous soap films, this third component is the soap, a surface-active chemical that adsorbs at the gas—liquid interface and lowers the surface tension of water. The two effects, adsorption at the liquid surface and the depression of surface tension, are intimately linked and occur concomitantly. The adsorption is defined as the excess moles of solute per unit area of the liquid surface. In a binary system, this surface excess can be directly related to the lowering of surface tension by Gibbs adsorption equation ... 

As in the binary system, 0, =Xj, but for the ionic solutes 0, =2x] and 02=2xj. In Eq. (3.32) the factor 2 can be omitted when the molar area of the ions toi is introduced instead of (B. After consideration of the surface-to-bulk distribution of both electroneutral combinations of ions, we arrive at the equation for the adsorption isotherm of the two surfactants RiX and R2X, respectively... 

It was predicted that in the case of the binary systems NaF-NaX or KF-KX (X = Cl , Br , I ), investigated at constant molal ionic strength at a mercury electrode, the treatment would lead to the specifically adsorbed surface excess of Cl , Br , I , provided that the specific adsorption of F is considered negligible, which seems a reasonable assumption. Likewise, it was demonstrated that the determination of Fcg+ for Cs+ from mixtures of the type liCl-CsCl is possible if the specific adsorption of Ii+ is assumed to be weak. 

The mathematical treatment set forth here is not confined to the case of surface adsorption. J. J. Hermans has stressed that exactly the same reasoning may be applied to the equilibrium of the gas phase with a solid structure containing throughout its body a number of N mutually independent active spots per unit volume, in which the molecules of the gas phase may penetrate by diffusion and where they can be bound according to the conditions 1 and 2 (p. 516). Such conditions may very well apply to certain instances of adsorption of gases or vapours in gel-like systems (cf. Section 6a 3 y.) giving rise to solid solutions which should theoretically be considered as homogeneous binary systems. ... 

Finn and Monson [139] first tested the predictability of IAS theory for binary systems using the isothermal isobaric Monte Carlo simulation on a single surface. However, this system does not represent real adsorption systems. Tan and Gubbins [140,141] conducted detailed studies on the binary equilibria of the methane-ethane system in slit-shaped micropores using the nonlocal density function theory (NLDFT). The selectivity of ethane to methane was studied in terms of pore width, temperature, pressure, and molar fractions. 

Maknsten, M. and Lassen, B. 1994. Competitive adsorption at hydrophobic surfaces from binary protein systems./. Colloid Interface Sci. 166 490 98. 

It is the objective of this paper to discuss fundamental aspects of the thermodynamics of adsorption at the solid-liquid interface, with emphasis on providing proper definitions of experimental variables such as the surface excess, selectivity, amount adsorbed, and the relationships among them. Types of surfactant adsorption isotherms for binary systems are discussed, and it is shown that an extreme caution must be taken when interpreting isotherms for surfactant mixtures. It is hoped that this discussion will facilitate a better understanding and interpretation of experimental results reported in the literature. 

Adsorption isotherm—binary systems Surfactant adsorption from a liquid onto a solid surface is usually determined from a change of surfactant concentration in the bulk liquid phase after contact of the liquid with the solid adsorbent ... 

Minka and Myers (8) have extended the concept of surface excess and selectivity to multicomponent mixtures. They applied a theory of an ideal adsorbed phase to predict the adsorption behavior of ternary mixtures from adsorption measurements in binary systems. Having binary data in the form of Equation (10) a ternary isotherm is calculated as follows ... 

Fainerman and Miller [35] found that displacement of an initially adsorbed surfactant by a second, more surface-active species allowed measurement of the desorption rate of the former. For example, competitive adsorption of sodium decyl sulfate and the nonionic Triton X-165 gave a desorption rate constant for the former of 40 s". Mul-queen and coworkers [36] recently developed a diffusion-based model to describe the kinetics of surface adsorption in multicomponent systems, based upon the Ward-Tor-dai equation. Experimental work with a binary mixture of two nonionic alkyl ethoxy-late surfectants [37] showed good agreement with the model, demonstrating a similar temporal adsorption profile to that found by Diamant and Andehnan [34],... 

Djikaev and Tabazadeh developed a model by including adsorption as well as Henry s law to describe trace gas uptake into cloud droplets for binary systems (water and the trace gas) [241]. Testing properties for both soluble and insoluble organic species, they found that a large fraction of the organic will remain near the gas-liquid interface if it is surface active, which could affect the surface tension and cloud physics. 

Brusatori and Van Tassel [20] presented a kinetic model of protein adsorption/surface-induced transition kinetics evaluated by the scale particle theory (SPT). Assuming that proteins (or, more generally, particles ) on the surface are at all times in an equilibrium distribution, they could express the probability functions that an incoming protein finds a space available for adsorption to the surface and an adsorbed protein has sufficient space to spread in terms of the reversible work required to create cavities in a binary system of reversibly and irreversibly adsorbed states. They foimd that the scale particle theory compared well with the computer simulation in the limit of a lower spreading rate (i.e., smaller surface-induced unfolding rate constant) and a relatively faster rate of surface filling. 

To understand the functional nature of gas-solid equilibria for physical adsorption processes, one may develop a relation between and the gas phase composition using equation (3.3.43h) and the illustrations thereafter. Two alternate approaches will he illustrated here using the same basic equation (3.3.43b) and a binary system of species i = 1,2. Recognize that S is the total interfacial area per unit mass of adsorbent and therefore may be expressed as where S is the molar surface... 

Clifford etalP initiated the application of XPS to the characterization of sulfide mineral surfaces in flotation systems. These authors concluded that the adsorption of amyl (pentyl) xanthate and diethyl dithiophosphate on a range of binary and ternary metal sulfides could be observed with difficulty by following the simultaneous increase in the C, S, and P molar ratios. ... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

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