Thermodynamics of adsorption

The adsorption of a gas at a solid surface is exothermic. This is required by the thermodynamic condition for a spontaneous process, illustrated by the Eq. 1.12  

In fact, adsorption being necessarily accompanied by a decrease in entropy (Aa5 0) in that the degrees of freedom of the molecules in the adsorbed state are lower than in the gaseous state vide infra Sect. 1.5.3 for details), it turns out that the Aa// term, i.e. the enthalpy change accompanying adsorption, must be negative [1, 13, 

Heat is not a state function and the value of the heat of adsorption depends on both the experimental conditions and the employed method of measurement. As a consequence, any physical interpretation of the experimentally determined heats of adsorption requires an accurate thermodynamic definition. 

Only a few fundamental concepts will be summarized and discussed here, in that a detailed description of the thermodynamics of adsorption is out of the scopes of this Chapter. The interested reader is addressed to the exhaustive review on this subject published in 1992 by Cardona-Martinez and Dumesic [13]. 

Thermodynamics requires a precise and accurate use of quantities the convention suggested by lUPAC for a proper thermodynamics nomenclature is here summarized. For any extensive quantity X we define (i) the mean molar quantity x = j, which is the quantity normalized to the amount of matter expressed as moles n, and is indicated by the lower case ii) the correspondent differential quantity, which is defined as the derivative of the quantity X with respect to the amount of matter expressed as moles n, and is indicated by the bar lower case x. 

Derivation of the Gibbs adsorption isotherm. Determination of the adsorption of surfactants at liquid interfaces. Laboratory project to determine the surface area of the common adsorbent, powdered activated charcoal. 

The complex three-dimensional structure of these materials is determined by their carbon-based polymers (such as cellulose and lignin), and it is this backbone that gives the final carbon structure after thermal degradation. These materials, therefore, produce a very porous high-surface-area carbon solid. In addition, the carbon has to be activated so that it will interact with and physisorb (i.e., adsorb physically, without forming a chemical bond) a wide range of compounds. This activation process involves controlled oxidation of the surface to produce polar sites. 

The attachment of molecules to the surface of a solid by adsorption is a broad subject. This chapter is focused on the adsorption of gases in high-capacity solid adsorbents such as active carbon or zeolites. These commercial adsorbents owe their enormous capacity to an extensive network of nanopores of various shapes (cylinders, slits) with specific volumes in the range from 100 to 1000 cm kg . Applications of adsorption exploit the ability of nanoporous materials to adsorb one component of a gas preferentially. For example, the preferential adsorption of nitrogen from air passed through an adsorption column packed with zeolite creates a product stream of nearly pure oxygen. 

Thermodynamics has the remarkable ability to connect seemingly unrelated properties. For example, the temperature coefficient of adsorption is directly proportional to the heat of immersion of the solid adsorbent in the gas. The most important application of thermodynamics to adsorption is the calculation of phase equilibrium between a gaseous mixture and a solid adsorbent. 

The basis for thermodynamic calculations is the adsorption isotherm, which gives the amount of gas adsorbed in the nanopores as a function of the external pressure. Adsorption isotherms are measured experimentally or calculated from theory using molecular simulations. Potential functions are used to constmct a detailed molecular model for atom-atom interactions and a distribution of point charges is used to reproduce the polarity of the solid material and the adsorbing molecules. Recently, ab initio quantum chemistry has been applied to the theoretical determination of these potentials, as discussed in another chapter of this book. 

Thermodynamics applies only to equilibrium adsorption isotherms. Equilibrium means that any point can be reached from either direction by raising (adsorption) or lowering (desorption) the pressure at constant temperature. If the desorption isotherm does not coincide with the adsorption isotherm, then equilibrium has not been achieved and the usual thermodynamic equations do not apply. The mismatch of adsorption and desorption, which is called hysteresis, does not occur in pores smaller than 2 nm but is observed when the pores are large enough for the adsorbing molecules to condense to a liquid. For adsorption of supercritical gases or for 

Molecular simulations yield absolute adsorption or the actual number of molecules in the nanopores. Experiments measure excess adsorption, which is the number of molecules in the nanopores in excess of the amount that would be present in the pore volume at the equilibrium density of the bulk gas. The difference between absolute and excess adsorption is negligible at the sub-atmospheric pressures of greatest interest. For supercritical gases adsorbed at high pressure (e.g. 100 bar), the difference between absolute and excess adsorption is too large to ignore.  

It is very important to select thermodynamic quantities that are invariant with respect to the position of the dividing interface, especially for the discussion on the surface quantities based on experimental results. The volume is expressed by the following equation with respect to component 

After introducing (8.32) into (8.30) and rearranging, we obtain the following equation for the relative adsorption of Fof / with respect to component 1 (by convention, the solvent is designated component 1)  

The relative adsorption amount F d) turns out to be invariant with respect to the dividing interface, as is clear from the definite values of the variables in the right-hand side of the last equality, even though F, and Fi depend on the location of the dividing surface. 

The next step is to make clear the Gibbs adsorption amount, using the above relative adsorption. Recall (8.27), in which the interfacial tension is a function of i -H 2 independent variables. However, the Gibbs phase rule permits only i independent variables for two phases including i components. Therefore, the problem is how to reduce the number of intensive variables by two while keeping thermodynamical consistency. The Gibbs-Duhem equations for two homogeneous phases a and respectively, are 

We have now reduced the degrees of freedom by one, employing (8.29) with respect to the volume. On the other hand, from (8.34) and (8.35), the Gibbs-Duhem equations per unit volume for homogeneous bulk phases become the following  

As we have already seen in Section 3.2.4, a pure liquid decreases its surface free energy by diminishing its surface area to the minimum possible, with molecules leaving the surface for the interior under the action of the inward attractive force exerted on the surface molecules. Surface molecules orient themselves so that the functional groups with the largest 

In molecular energy terms, adsorption occurs when a molecule loses sufficient energy to the atoms in a surface by exciting them vibrationally or electronically to become effectively bound to the surface. An ensemble of adsorbed molecules is called an adlayer (or monolayer if only a single molecular layer forms), and the average time of stay of a molecule upon the surface is called the mean stay time. 

For some time there has been a certain amount of confusion about the application of thermodynamics to adsorption data. However, it seems possible now, after the work of Cassel (80), Coolidge (81), Rowley and Innes (82), Hill (18,83), Gorter and Frederikse (84), Hansen (85), 

Everett (86), Kington and Aston (87), and Guggenheim (87a), to say that general agreement has been reached on all questions of thermodynamic correctness or incorrectness. There is still some difference of opinion as to relative utility and completeness of different approaches, etc., but at the present time these are to a large extent matters of personal taste. Future work will perhaps lead to general agreement even on some of these questions. 

We shall summarize below the present status of the more important aspects of this subject. This seems worth while since the papers listed above overlap each other considerably and contain more detail than is necessary for applications to experimental data. 

We consider a one-component gas and a one-component sorbent throughout for simplicity. 

In accordance with common thermodynamic practice we use in this section the gas constant R and moles instead of the Boltzmann constant k and molecules.  

Solid surface will have molecules arranged at the surface in a very well-defined geometrical arrangement. This will give rise to surface forces, which will determine the adsorption of a particular substance. On any solid surface, one can expect a certain number of possible adsorption sites per gram (N, ). This is the number of sites where any adsorbate can freely adsorb. There will be a 

It is known that at equilibrium, these rates must be equal  

A typical adsorption experiment is carried out as follows. The solid sample (e.g., activated charcoal) is shaken in contact with a solution with known concentration of acetic add. After equilibrium is reached (approximately after 24 h), the amount of acetic adsorbed is determined. One can determine the concentration of acetic acid by titration with NaOH solution. 

One may also use solutions of dyes (such as methylene blue), and after adsorption, the amount of dye in solution is measured by any convenient spectroscopic method (VIS or UV or flourescence spectroscopy). 

It has long been known that the adsorption of a gas on a solid surface is always accompanied by the evolution of heat. Various attempts have been made to arrive at a satisfactory thermodynamic analysis of heat of adsorption data, and within the past few years broad agreement has been achieved in setting up a general system of adsorption thermodynamics. Here we are not concerned with the derivation of the various thermodynamic functions but only with the more relevant definitions and the principles involved in the thermodynamic analysis of adsorption data. For more detailed treatments, appropriate texts should be consulted.  

In dealing with physical adsorption it is usually assumed that the adsorbent is inert, so that the loss or gain of energy is due solely to the change in state of the adsorptive brought about by the addition or removal of the adsorbate. This approach allows us to write 

Similarly, one may define the molar integral enthalpy of adsorption, SJt as 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as 

Similarly, the differential molar enthalpy of adsorption, Ji is defined as 

---

We take up here some aspects of the thermodynamics of adsorption that are of special relevance to gas adsorption. Two types of processes are of interest ... 

D. Nicholson, N. D. Parsonage. Computer Simulation and the Statistical Thermodynamics of Adsorption. New York Academic Press, 1983. 

Temperature programmed desorption, TPD detection of backspillover species, 228 of oxygen, 228 Thermodynamics of adsorption, 306 of spillover, 104, 499 Three phase boundaries charge transfer at, 114 electrocatalysis at, 115 length, measurement of, 243 normalized length, 243 Time constants ofNEMCA analysis of, 198 and backspillover, 198 prediction of, 200... 

The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface specific techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface specific experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid-liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electrified interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8-21]. 

Thermodynamics of adsorption at liquid interfaces has been well established [22-24]. Of particular interest in view of biochemical and pharmaceutical applications is the adsorption of ionic substances, as many of biologically active compounds are ionic under the physiological conditions. For studying the adsorption of ionic components at the liquid-liquid interface, the polarized liquid-liquid interface is advantageous in that the adsorption of ionic components can be examined by strictly controlling the electrical state of the interface, which is in contrast to the adsorption studies at the air-water or nonpolar oil-water interfaces [25]. 

These TPD techniques reflect the kinetics (not thermodynamics) of adsorption, and are quite useful for determining trends across series of catalysts, but are often not suitable for the derivation of quantitative information on surface kinetics or energetics, in particular on ill-defined real catalysts. Besides averaging the results from desorption from different sites, TPD detection is also complicated in porous catalysts by simultaneous diffusion and readsorption processes [58],... 

In contrast to this, there is little information available (11) on the thermodynamics of adsorption of alkyl betaines and no data on the thermodynamic parameters of adsorption or micellization for sulfobetaines. 

THERMODYNAMICS OF ADSORPTION the rate of adsorption a [solute conc.][l - 9]N ... 

In recent papers (1-2), we have shown how the thermodynamics of adsorption of nonionic surfactants on latex surfaces can be described in terms of a few simple parameters that may be used to predict the relative strength of adsorption of surfactants with different hydro-philic/hydrophobic balance on surfaces of different polarity. 

Thermst-Desorpaon-Spectroscopy (TDS) Heel Desorbed atoms and molecules Nature of adsorbed species > Thermodynamics of adsorption / desorption processes... 

The thermodynamics of adsorption of a given species are thus characterised by bifl and Ai/ads,i. By fitting the breakthrough curves, expressions for the kinetics of adsorption/desorption can be developed Fig. 27 shows simulated, as well as measured, breakthrough curves. 

Although we started out this chapter by discussing insoluble monolayers, it is evident that we have slipped into examples for which soluble amphipathics are being considered. In the next section we examine the thermodynamics of adsorption from solution. 

It is convenient to divide the extent of adsorption into three categories submonolayer, monolayer, and multilayer. We discuss them in this order. The thermodynamics of adsorption may be developed around experimental isotherms or around calorimetric data. We begin with the definition of adsorption isotherms and how they are determined experimentally (Section 9.2). 

Adsorption measurements of gaseous bases are often used for the determination of surface acidity. The chief advantage of this method over those discussed previously is that adsorption can be measured at or near temperatures at which catalyzed reactions occur. A variety of bases and techniques have been used as described in previous reviews (/ -3). Two representative approaches will be discussed in this critique one consists of using chemisorption measurements of a suitable base at a given set of conditions to count acid sties on a catalyst surface the other is a more comprehensive approach in which adsorption is measured at several temperatures to enable the determination of the thermodynamics of adsorption as a function of surface coverage. 

---