Adsorption from solution 186 isotherm

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Figure 10.2 Schematic isotherm for the simplest cases of chemical adsorption from solution onto a solid substrate. The amount of adsorbate available to adsorb is best gauged by the concentration c...

Equation 10.27 is generally known as Freundlich equation. Equation 10.27 with concentration replaced by pressure was also used to describe the adsorption isotherms of gases on solids, suggesting the incorrect idea that adsorption from solution by a solid could be paralleled with gas or vapor adsorption on the same adsorbents. Whereas in some cases the restriction to dilute solutions was imposed by the solubility of solids (e.g., benzoic acid in water or stearic acid in benzene) it was not imposed on the investigation of mixtures of completely miscible liquids, e.g., acetic acid in water. 

The data which are plotted as isotherms in the case of adsorption from liquid solutions on solid adsorbents are different in nature from those of gas (or vapor) adsorption on the same adsorbents. In fact, while the isotherm for adsorption of a single gas by a solid represents directly the quantity (weight or volume under standard conditions) of gas adsorbed per unit weight of the solid, the experimental measurement in adsorption from solution is the change in concentration of the solution which results from adsorption. The fact that a change in concentration is measured emphasizes that there are at least two components in the solution [13]. 

The material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

One isotherm that is both easy to understand theoretically and widely applicable to experimental data is due to Langmuir and is known as the Langmuir isotherm. In Chapter 9, we see that the same function often describes the adsorption of gases at low pressures, with pressure substituted for concentration as the independent variable. We discuss the derivation of Langmuir s equation again in Chapter 9 specifically as it applies to gas adsorption. Now, however, adsorption from solution is our concern. In this section we consider only adsorption from dilute solutions. In Section 7.9c.4 adsorption over the full range of binary solution concentrations is also mentioned. 

In discussing adsorption from solution, there is nothing that can be done about the multiplicity of possible interactions, except possibly to avoid systems in which highly specific interactions are to be expected. In Chapter 9 we again discuss the Langmuir isotherm as it applies to the adsorption of gases. In that case there are considerably fewer interactions involved in the adsorption process, making it more amenable to analysis. 

Figure 9.2 Schematic plot of eight types of adsorption isotherms commonly observed. If adsorption from the gas phase is studied, the abscissa is the partial pressure P. For adsorption from solution the concentration c is used.

Here, 6 is the relative coverage and KL is a constant, called the Langmuir constant . Tmon is the maximum amount adsorbed which, in the case of Langmuir adsorption, is a mono-layer. Type C adsorption isotherms are characterized by a saturation at high concentrations. A possible reason is that the surface is completely filled with adsorbed molecules. Langmuir adsorption is often observed for the adsorption from solution but only rarely for the adsorption of gases. This type of adsorption isotherm can also be observed for porous materials. Once all pores have been filled the isotherm saturates (see Section 9.4.3). 

An adsorption isotherm is a graph of the amount adsorbed versus the pressure of the vapor phase (or concentration in the case of adsorption from solution). The amounts adsorbed can be described by different variables. The first one is the surface excess I in mol/m2. We use the Gibbs convention (interfacial excess volume Va = 0). For a solid surface the Gibbs dividing plane is localized directly at the solid surface. Then we can convert the number of moles adsorbed Na to the surface excess by... 

Typical Langmuir adsorption isotherms are plotted in figure 9.6 for different values of the Langmuir constant. If adsorption from solution is considered, the pressure P has to be replaced by the concentration c and the Langmuir constant is given in units of L mol-1 instead of Pa"1. 

Experimentally, the investigation of adsorption from solution is much simpler than that of gas adsorption. A known mass of adsorbent solid is shaken with a known volume of solution at a given temperature until there is no further change in the concentration of the supernatant solution. This concentration can be determined by a variety of methods involving chemical or radiochemical analysis, colorimetry, refractive index, etc. The experimental data are usually expressed in terms of an apparent adsorption isotherm in which the amount of solute adsorbed at a given temperature per unit mass of adsorbent - as calculated from the decrease (or increase) of solution concentration - is plotted against the equilibrium concentration. 

Adsorption from solution behaviour can often be predicted qualitatively in terms of the polar/non-polar nature of the solid and of the solution components. This is illustrated by the isotherms shown in Figure 6.12 for the adsorption of fatty acids from toluene solution on to silica gel and from aqueous solution on to carbon. 

Now, to conclude this section, it is necessary to affirm that any one of the equations described here to correlate the relation between the amount adsorbed, ct, with the equilibrium concentration in solution, Ci, corresponds to a particular model for adsorption from solutions. That is, these should be considered as empirical isotherm equations [2],... 

The extent of adsorption can have a profound effect on the rate of the surface reaction. Equilibrium isotherms of many kinds have been reported for adsorption from solution and have been classified by Giles et al. [24-27], The shapes of these adsorption curves often furnish qualitative information on the nature of the solute-surface interactions. Several of the types of isotherm observed in dilute solution are represented reasonably well by three simple and popular isotherm equations, those of Henry, Langmuir, and Freundlich. Their shapes are illustrated in Fig. 1. Each of these isotherms relates the surface concentrations cads (mol m"2) to the bulk equilibrium concentration c of the solute species in question. When few surface sites are occupied, Henry s law adsorption... 

Many more cases of adsorption from solution lead to isotherms in which cads rises with increasing c in dilute solution and then levels off to a limiting... 

The area is an important surface parameter for catalytic studies. It is needed to evaluate the rate constant of the surface reaction from the kinetics as well as to allow a fair comparison to be made of the effectiveness of different catalysts. Areas are commonly determined by nitrogen or krypton gas adsorption interpreted by the Brunauer-Emmett Teller (BET) isotherm [30, 32], A number of other methods has been proposed and utilised including microscopy, isotopic exchange, chromatography, gas permeability, adsorption from solution, and negative adsorption (desorption) of co-ions [30, 33]. 

The first recorded isotherms of adsorption from solution were probably those reported by van Bemmelen in 1881 (Forrester and Giles, 1972). In his investigations of the absorptive power of soils, van Bemmelen noted the importance of the colloidal structure and drew attention to the relevance of the final state (i.e. equilibrium concentration) of the solution in contact with the soil. 

Langmufr s work on gas adsorption and insoluble monolayers prepared the way for more progress to be made in the interpretation of adsorption from solution data. In the light of the Langmuir theory, it seemed logical to suppose that the plateau of a solute isotherm represented monolayer completion and that the monolayer capacity could be derived by application of the Langmuir equation. 

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. 

Since the reduced and relative surface excess isotherms convey composite information on the adsorption of the two components, there is a strong incentive to determine the individual (or separate ) isotherms, i.e. the adsorbed amount n (or ) versus concentration, mole fraction or mass fraction. It will be recalled that this implies some assumptions about the thickness, composition and structure of the adsorbed layer, and therefore is not to be recommended for reporting adsorption from solution data in a standard form. Indeed, this second step is already part of the theoretical interpretation of the adsorption mechanisms. 

We may divide the experimental techniques available for the study of adsorption from solution into three main categories (a) for the determination of adsorption isotherms, (b) for the measurement of the energies involved, and (c) for the provision of extra information on the properties of the adsorbed layer. 

Values of apparent surface area can be derived only if the solute isotherm exhibits a long saturation plateau. Unfortunately, the derived values are often of questionable significance since the exact structure of the monolayer (containing both solute and solvent) is rarely known. The study of microporosity by adsorption from solution measurements is in its infancy, but the use of comparison plots appears to be a promising approach. 

There are a number of different factors which may affect the level of uptake and the energetics of adsorption from solution the chemistry and electrical properties of the solid surface and the molecular/micellar/polymeric structure of the solution must all be taken into account. Whenever possible, a study of both adsorption isotherms and enthalpies of displacement is worthwhile, but it is often necessary to complement these measurements with others including electrophoretic mobilities, FI7R spectra-and various types of microscopy. 

For a description of isotherms for adsorption from solution, see figs. 2.8 and 2.23. 

As discussed In some detail in chapter 1. for a rigorous test of adsorption models, especially in terms of isotherms. It is necessary to have data for several decades of bulk concentration at one s disposal. Because of analytical limitations, such information is usually restricted to a few decades for adsorption from solution. ... 

The matter discussed in sec. 2.3 concerned the phenomenology of adsorption from solution. To make further progress, model assumptions have to be made to arrive at isotherm equations for the individual components. These assumptions are similar to those for gas adsorption secs. 1.4-1.7) and Include issues such as is the adsorption mono- or multlmolecular. localized or mobile is the surface homogeneous or heterogeneous, porous or non-porous is the adsorbate ideal or non-ideal and is the molecular cross-section constant over the entire composition range In addition to all of this the solution can be ideal or nonideal, the molecules may be monomers or oligomers and their interactions simple (as in liquid krypton) or strongly associative (as in water). 

Adsorption from solution is an exchange process. Consequences of this "first law" pervade all attempts to define individual (or partial) isotherms. Any assumption made on the adsorption of component 1 involves an assumption regarding component 2 deriving an equation for 1 implies deriving an equation for 2. This is (or should be) reflected in all models, and all thermodynamics and statistical thermodynamics should be consistent with this principle. 

Just as with gas adsorption, an isosteric enthalpy of adsorption can also be defined for adsorption from solution. In sec. 2.3d we have refrained from deriving from isotherms, measured at different temperatures because a... 

The second basic problem in adsorption from solutions deals with the physical interpretation the parameter n which may be determined from the excess isotherms. The total excess isotherm is given by the expression ... 

The most studies of adsorption from solution have been concerned with the adsorption from two-component mixture, for example [1,2], Practical use of adsorption however deals with the adsorption from multicomponent systems. In liquid chromatography in a many cases for the separation of mixture of solutes the multicomponent eluents are used. The most difficulties in the investigation of adsorption from multicomponent systems arise at the determination of some component concentration at once in equilibrium solution over the adsorbent. Moreover for the determination of adsorption isotherm in this case large experimental data are needed. 

The isotherm of adsorption from solution may be determined by frontal chromatograms [6-8]. In [6] it was shown that if to take into consideration the broadening the band owing to diffusion, the adsorption isotherms determined by the column chromatography and in a batch process are coincided. This method can be used for the calculation of S-shape isotherm of adsorption. The isotherm of adsorption can be determined by frontal chromatography if the adsorbents have not fine pores [7]. 

The thermodynamic characteristic of adsorption from solutions can be determined from the dependence of adsorption on temperature. But the determination of adsorption isotherms from solution at different temperatures is the rather complicate problems. Liquid chromatography may be very useful method for the determination of thermodynamic characteristics of adsorption at small coverage [11] because of the measurement of retention volume (the Henry constant) at different temperatures of the chromatographic columns makes it possible to calculate the heats of adsorption and the differential standard change entropy of adsorption from ... 

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