Equilibrium Aspects of Adsorption

The question of whether protein adsorption can be considered as an equilibrium phenomenon has been controversial. The reasons that have led to a widespread belief in the irreversibility of protein adsorption may be summarized as follows. 

Changes in the surface tension of protein solutions occur over long periods of time and this makes it difficult to know with certainty whether constant values are reached. 

Globular protein molecules undergo drastic unfolding to give films having the thickness of a single polypeptide chain at the interface. This has often been termed surface denaturation.  

Interfacial films of protein coagulate under certain conditions, the properties of the coagulated protein being quite different from those of the original crystalline protein. F or example, solubility is lost. 

Proteins are found either not to desorb or to desorb only with great difficulty from quiescent interfaces. Langmuir and Schaefer (1939) calculated, on the basis of the Gibbs adsorption equation, that compression of a monolayer of protein of molecular weight 35,000 by 15 mN m-1 should increase its solubility by a factor of 1095. This results from the large area occupied by the molecule at the interface and the resultant large pressure increment of solubility. The failure of protein monolayers to desorb readily on compression was thus taken as an indication of irreversibility. 

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Activated carbon, in powdered (PAC) or granular (GAC) form, has many applications in drinking water treatment. It can be used for removing taste and odor (T O) compoimds, synthetic organic chemicals (SOCs), and dissolved natural ot] nic matter (DOM) from water. PAC typically has a diameter less than 0.15 mm, and can be applied at various locations in a treatment system (Fig. 1). GAC, with diameters ranging from 0.5 to 2.5 mm, is employed in fixed-bed adsorbers such as granular media filters or post filters. Despite difference in particle size, the adsorption properties of PAC and GAC are fundamentally the same because the characteristics of activated carbon (pore size distribution, internal surface area and smface chemistry) controlling the equilibrium aspects of adsorption are independent of particle size. However, particle size impacts adsorption kinetics. 

This section will deal with the above interfacial aspects starting with the equilibrium aspects of surfactant adsorption at the air/water and oil/water interfaces. Due to the equilibrium aspects of adsorption (rate of adsorption is equal to the rate of desorption) one can apply the second law of thermodynamics as analyzed by Gibbs (see below). This is followed by a section on dynamic aspects of surfactant adsorption, particularly the concept of dynamic surface tension and the techniques that can be applied in its measurement. The adsorption of surfactants both on hydrophobic surfaces (which represent the case of most agrochemical solids) as well as on hydrophilic surfaces (such as oxides) will be analyzed using the Langmuir adsorption isotherms. The structure of surfactant layers on solid surfaces will be described. The subject of polymeric surfactant adsorption will be dealt with separately due to its complex nature, namely irreversibility of adsorption and conformation of the polymer at the solid/liquid interface. 

Equilibrium. Among the aspects of adsorption, equiUbrium is the most studied and published Alany different adsorption equiUbrium equations are used for the gas phase the more important have been presented (see section on Isotherm Models). Equally important is the adsorbed phase mixing rule that is used with these other models to predict multicomponent behavior. 

The important aspect of adsorption processes at a liquid interface is lateral mobility which can lead to lateral excess transport of adsorbed molecules. Lateral transport disturbs the equilibrium state of an adsorption layer. In many important systems, such as emulsions, foams, and bubbly liquids, the properties of a non-equilibrium adsorption layer can be essential. This has been demonstrated in the systematic work of the Russian and Bulgarian schools summarised in monographs like "Thin Liquid Films" by Ivanov, "Coagulation and Dynamics of Thin Films" by Dukhin, Rulyov and Dimitrov, and "Foams and Foam Films" by Krugljakov and Exerowa. These books pay most attention to thick film drainage and stabilisation/destabilisation of thin liquid films. This book is focused on other dynamic processes at liquid interfaces in general or connected with phenomena of emulsions and foams. 

Tiberg, F., Malmsten, M., Linse, P. and Lindman, B., Kinetic and equilibrium aspects of block copolymer adsorption, Langmuir, 1, 2723-2730 (1991). 

Tiberg F, Malmsten M, Linse P, Lindman B. Kinetic and equilibrium aspects of block copolyma adsorption. Langmuir 1991 7 2723-30. 

Several interfacial aspects must be considered when dealing with agrochemical formulations (i) Both equilibrium and dynamic aspects of adsorption of surfactants at the air/liquid interface. These aspects determine spray formation (spray droplet spectrum), impaction and adhesion of droplets on leaf surfaces as well as the various wetting and spreading phenomena, (ii) Adsorption of surfactants at the oil/water interface which determines emulsion formation and their stability. This subject is also important when dealing with microemulsions, (ill) Adsorption of surfactants and polymers at the solid/liquid interface. This is important when dealing with dispersion of agrochemical powders in liquids, preparation of suspension concentrates and their stabilization. 

In this chapter, we review the basic mechanisms underlying adsorption of long-chain molecules on solid surfaces such as oxides. We concentrate on the physical aspects of adsorption and summarize the main theories which have been proposed. This chapter should be viewed as a general introduction to the problem of polymer adsorption at thermodynamical equilibrium. For a selection of previous review articles see Refs 1—4, while more detailed treatments are presented in two books on this subject [5,6]. We do not attempt to explain any specific polymer/oxide system and do not emphasize experimental results and techniques. Rather, we detail how concepts taken from statistical thermodynamics and interfacial science can explain general and universal feamres of polymer adsorption. The present chapter deals with equilibrium properties whereas Chapter 3 by Cohen Stuart and de Keizer is about kinetics. 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

The energetic aspects of underpotential deposition can be investigated by a slow (i.e., a few millivolts per second) potential scan starting at a potential so high that no adsorption takes place. As the potential is lowered, one or more current peaks axe observed, which are caused by the adsorption of the metal ions (see Fig. 4.9). According to the usual convention, the adsorption current is negative (i.e., cathodic). Different peaks may correspond to different adsorption sites, or to different structures of the adsorbate layer. If the potential is scanned further past the equilibrium potential bulk deposition is observed. 

Co/pH and V o/pH results are sensitive to different aspects of the surface chemistry of oxides. Surface charge data allow the determination of the parameters which describe counterion complexation. Surface potential data allow the determination of the ratio /3 —< slaDL- Given assumptions about the magnitude of the site density Ns and the Stern capacitance C t, this quantity can be combined with the pHp2C to yield values of Ka and Ka2. Surface charge/pH data contain direct information about the counterion adsorption capacitances in their slope. To find the equilibrium constants for adsorption, a plot such as those in Figures 7 and 8 can be used, provided that Ka and Kai are independently known from V o/pH curves. 

Although the overwhelming majority of theoretical papers in liquid chromatography are dealing with the various aspects of RP-HPLC separation, theoretical advances have also been achieved in some other separation modes. Thus, a theoretical study on the relation between the kinetic and equilibrium quantities in size-exclusion chromatography has been published, hi adsorption chromatography the probability of adsorbing an analyte molecule in the mobile phase exactly r-times is described by... 

The second application concerned aspects of UHV technology. In UHV systems at equilibrium, the predominant gas load arises from the outgassing of internal surfaces. The factors influencing outgassing, including adsorption/desorption, were discussed (Examples 6.10-6.12). Outgassing from the interior of materials (diffusive outgassing), which can arise with both metallic- and non-metallic materials exposed to vacuum, was quantified in Examples 6.13-6.15. 

The Frumkin epoch in electrochemistry [i-iii] commemorates the interplay of electrochemical kinetics and equilibrium interfacial phenomena. The most famous findings are the - Frumkin adsorption isotherm (1925) Frumkin s slow discharge theory (1933, see also - Frumkin correction), the rotating ring disk electrode (1959), and various aspects of surface thermodynamics related to the notion of the point of zero charge. His contributions to the theory of polarographic maxima, kinetics of multi-step electrode reactions, and corrosion science are also well-known. An important feature of the Frumkin school was the development of numerous original experimental techniques for certain problems. The Frumkin school also pioneered the experimental style of ultra-pure conditions in electrochemical experiments [i]. A list of publications of Frumkin until 1965 is available in [iv], and later publications are listed in [ii]. 

In retrospect, the early adsorption models identified most of the significant aspects of the adsorption problem. The relationship between adsorption energy and average chain configuration was explored extensively. The assumptions necessary for the calculations, however, limited the utility of these models in predicting the behavior of real systems and, hence, their credibility. Improved analyses of excluded volume and equilibrium required a more comprehensive mathematical framework. 

One of the most intriguing aspects of surface diffusion is the strong dependence of the diffusivity on sorbate concentration. The dependence of surface diffusivities on pressure, temperature and composition is much more complicated than those of the molecular and Knudsen diffusivities, because of all the complexities of porous medium geometry, surface structure, adsorption equilibrium, mobility of adsorbed molecules, etc. 

An additional aspect of surface structure determination involves the relationship between swface structure and reactivity. The study of adsorbates on well ordered solids constitutes much of the structural work being carried out today. When an atom or molecule adsorbs on a clean substrate, its equilibrium position is determined by its interactions with the surface atoms, and its interactions with neighboring adsorbates. For physically adsorbed species, adsorbate adsorbate interactions can equal the interaction between the adsorbate and substrate and affect the structure of the overlayer. However the adsorbate adsorbate interactions are typically small when compared to the forces in chemical bonds formed upon adsorption and adsorbate-substrate interactions dominate in chemisorbed systems. 

In the description of adsorption, not only static (equilibrium) features but also kinetic aspects are of importance and we shall consider some of these aspects in sec. 1.5a. Some Information is already available in secs. I.6.5d and e. where diffusion transport to and from surfaces has been discussed. One of the more Important equations that we derived is (1.6.5.36), describing the increase of r with time t due to (semi-infinite) diffusion onto a flat surface. Replacing the concentration c in that equation by the number of moles n per volume V, we have for an ideal gas c = p/RT, so that [1.6.5.36) can be written as... 

To examine the dynamical aspect of the hysteretic behavior, we consider the system geometry shown in Fig. 4. The porous material of length L in the z-direction is bounded by the gas reservoirs at z = 0 and z = L. Periodic boundary conditions are imposed on the X and y-directions. In typical experimental situations, starting from a (quasi)-equilibrium state, the external vapor pressure of the gas reservoir is instantaneously changed by a small amount, which induces gradual relaxations of the system into a new state. This geometry was used in recent work on dynamics of off-lattice models of adsorption (Sarkisov and Monson,... 

A final aspect of the development of an adsorption model is description of the equilibrium behaviour for a particular adsorbent/adsorbate combination as a function of the residual liquid phase concentration of the adsorbate, i.e. ... 

Adsorption from solution is discussed by Adamson, but with emphasis on the equilibrium aspects, rather than the kinetics. The subject can conveniently be divided into adsorption of non-electrolytes and adsorption of electrolytes. The former can be treated for dilute solutions, in a similar manner to adsorption of gases on solid surfaces. Multilayer adsorption has been observed however, so that... 

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