Adsorption isotherms liquid-solid equilibria

Originally derived for the study of gas-solid equilibria, the T6th isotherm [64] accounts for adsorption on a heterogeneous surface, with no adsorbate-adsorbate interactions. It has three parameters. The heterogeneous surface has a unimodal adsorption energy distribution with a width related to the value of the parameter t. Like the Langmuir isotherm, it can be extended to the case of liquid-solid equilibrium. Its equation is... 

The adsorption isotherm is the equilibrium relationship between the concentration in the fluid phase and the concentration in the adsorbent particles at a given temperature. For gases, the concentration is usually given in mole percent or as a partial pressure. For liquids, the concentration is often expressed in mass units, such as part per million. The concentration of adsorbate on the solid is given as mass adsorbed per unit mass of original adsorbent. 

Various parameters such as adsorption and desorption isotherms, diffusion coefficients, liquid/gas, gas/solid and liquid/solid equilibrium distribution coefficients, as well as mass transfer coefficients and many other physicochemical property values have to be used in the models proposed for supercritical fluid extractions. These parameter values are either obtained from existing correlations, or from independent data sources using parameter estimation. However, in those cases where the above stated means are not sufficient to estimate the values of all parameters used in the model, the researcher(s) may be forced to use the model and the associated data to evaluate best fit or optimal values for the missing parameters. The fact is that, the number of reliable correlation s and methods for the SFE are still quite scarce. 

The equilibrium model for the adsorption of polymers at solid-liquid interfaces recently presented by Hogg and Mirville (1) has been evaluated at some length. It has been shown that, for polymers consisting of a reasonably large number of segments, the adsorption isotherms can be closely approximated by an expression of the form ... 

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

Quantifying adsorption of contaminants from gaseous or liquid phases onto the solid phase should be considered valid only when an equilibrium state has been achieved, under controlled environmental conditions. Determination of contaminant adsorption on surfaces, that is, interpretation of adsorption isotherms and the resulting coefficients, help in quantifying and predicting the extent of adsorption. The accuracy of the measurements is important in relation to the heterogeneity of geosorbents in a particular site. The spatial variability of the solid phase is not confined only to field conditions variability is present at all scales, and its effects are apparent even in well-controlled laboratory-scale experiments. 

The BET method (Brunauer, Emmett and Teller, 1938) with N2 as the adsorbate, is by far the most common method of measuring the surface areas of Fe oxides. Various commerical instruments are available for these measurements. The method involves measuring the extent of adsorption of N2 (at the boiling temperature of liquid N2 - 77 K) on the outgassed solid as a function of the relative pressure, p/po. he. the adsorption isotherm p is the partial pressure of the adsorbate and po is its equilibrium vapour pressure. The following linear relationship exists between the amount adsorbed, v, (cm g ) and the relative vapour pressure, p/po, ... 

Adsorption experiments are conducted at constant temperature, and an empirical or theoretical representation of the amount adsorbed as a function of the equilibrium gas pressure is called an adsorption isotherm. Adsorption isotherms are studied for a variety of reasons, some of which focus on the adsorbate while others are more concerned with the solid adsorbent. In Chapter 7 we saw that adsorbed molecules can be described as existing in an assortment of two-dimensional states. Although the discussion in that chapter was concerned with adsorption at liquid surfaces, there is no reason to doubt that similar two-dimensional states describe adsorption at solid surfaces also. Adsorption also provides some information about solid surfaces. The total area accessible to adsorption for a unit mass of solid —the specific area Asp — is the most widely encountered result determined from adsorption studies. The energy of adsorbate-adsorbent interaction is also of considerable interest, as we see below. 

Adsorption isotherms are used to quantitatively describe adsorption at the solid/ liquid interface (Hinz, 2001). They represent the distribution of the solute species between the liquid solvent phase and solid sorbent phase at a constant temperature under equilibrium conditions. While adsorbed amounts as a function of equilibrium solute concentration quantify the process, the shape of the isotherm can provide qualitative information on the nature of solute-surface interactions. Giles et al. (1974) distinguished four types of isotherms high affinity (H), Langmuir (L), constant partition (C), and sigmoidal-shaped (S) they are represented schematically in Figure 3.3. 

These equations are supplemented by the equilibrium relationship between the solid and local liquid phase concentrations. Langmuir isotherm was chosen for the adsorption isotherm of a target product or by product ... 

In the case of adsorption from solution, the apparent adsorption of a solute at the liquid-solid interface is usually evaluated by measuring the decrease in its concentration when brought into contact with the adsorbent. The adsorption isotherm is then plotted as the apparent adsorption of the solute against the equilibrium concentration. 

Assessment of wettability from the gas adsorption isotherm. If the solid is covered with a liquid film in equilibrium with saturated vapour p°, the spreading pressure of the film can be derived from Equation (2.22). Thus ... 

Until relatively recently, the fact that an experimental isotherm necessarily contained composite information concerning the adsorption of the two components of a binary solution was considered to be a major problem. For a rigorous interpretation it was felt necessary to process the data to obtain the so-called individual adsorption isotherm or separate adsorption isotherm of each component. However, this is not at all straightforward and requires the introduction of a number of assumptions relating to the structure of the adsorbed layer. The main problem is of course to know the composition of the adsorbed layer. One assumption often used in the case of volatile components is that introduced by Williams (1913) the solid will adsorb the same amount of each component from the vapour in equilibrium with the solution as from the solution itself. This of course implies that the adsorbed layer has the same composition at the liquid-solid and gas-solid interfaces and it requires numerous gravimetric measurements from the vapour... 

Adsorption is a process in which a species in a fluid (liquid or gas) mixture adheres to the surface of a solid with which the fluid is in contact. (This process should not be confused with absorption, in which a component of a gas mixture dissolves in a liquid solvent.) The solid is the adsorbent, and the species that adheres to the surface is the adsorbate. Good adsorbents such as activated carbon have extremely high specific surface areas (m surface/g solid), enabling small quantities of adsorbent to remove large quantities of adsorbate from fluid mixtures. An adsorption isotherm is a plot or equation that relates the equilibrium amount of an adsorbate held by a given mass of adsorbent to the adsorbate partial pressure or concentration in the surrounding gas at a specified temperature. 

Material balance calculations on separation processes follow the same procedures used in Chapters 4 and 5. If the product streams leaving a unit include two phases in equilibrium, an equilibrium relationship for each species distributed between the phases should be counted in the degree-of-freedom analysis and included in the calculations. If a species is distributed between gas and liquid phases (as in distillation, absorption, and condensation), use tabulated vapor-liquid equilibrium data, Raoult s law, or Henry s law. If a solid solute is in equilibrium with a liquid solution, use tabulated solubility data. If a solute is distributed between two immiscible liquid phases, use a tabulated distribution coefficient or equilibrium data. If an adsorbate is distributed between a solid surface and a gas phase, use an adsorption isotherm. 

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]. 

Some essential discoveries concerning the organization of the adsorbed layer derive from the various spectroscopic measurements [38-46]. Here considerable experimental evidence is consistent with the postulate that ionic surfactants form localized aggregates on the solid surface. Microscopic properties like polarity and viscosity as well as aggregation number of such adsorbate microstructures for different regions in the adsorption isotherm of the sodium dedecyl sulfate/water/alumina system were determined by fluorescence decay (FDS) and electron spin resonance (ESR) spectroscopic methods. Two types of molecular probes incorporated in the solid-liquid interface under in situ equilibrium conditions... 

Immersion energy is an integral quantity, which corresponds to the average interaction of the liquid with the entire solid. Each experiment only provides one figure, whereas, e.g., adsorption isotherms can discriminate between various kinds of successive interactions as the equilibrium pressure increases. Nevertheless, a careful analysis of the parameters contributing to the immersion energy allows to derive a most useful information about the sohd surface. The immersion energy depends indeed on... 

For dilute solutions of surfactants then, the number of moles of surface-active solute adsorbed per unit mass of the solid substrate can be calculated from the concentrations of the solute in the liquid phase before and after the solution is mixed with the finely divided solid adsorbent and the mixture is shaken until equilibrium has been reached. Then n is plotted against C to yield the adsorption isotherm. A variety of analytical techniques are available for determining the change in concentration of the surfactant (Rosen, 1972). 

Physical chemists distinguish between adsorption and absorption. Adsorption is a surface phenomenon. Consider a solid or liquid phase (the adsorbent), in contact with another, fluid, phase. Molecules present in the fluid phase may now adsorb onto the interface between the phases, i.e., form a (usually monomolecular) layer of adsorbate. This is discussed in more detail in Section 10.2. The amount adsorbed is governed by the activity of the adsorbate. For any combination of adsorbate, adsorbent, and temperature, an adsorption isotherm can be determined, i.e., a curve that gives the equilibrium relation between the amount adsorbed per unit surface area, and the activity of the adsorbate. Powdered solid materials in contact... 

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

Desiccants. A solid desiccant is simply an adsorbent which has a high affinity and capacity for adsorption of moisture so that it can be used for selective adsorption of moisture from a gas (or liquid) stream. The main requirements for an efficient desiccant are therefore a highly polar surface and a high specific area (small pores). The most widely used desiccants (qv) are silica gel, activated alumina, and the aluminum rich zeolites (4A or 13X). The equilibrium adsorption isotherms for moisture on these materials have characteristically different shapes (Fig. 3), making them suitable for different applications. 

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