The Dynamics of Adsorption

The surface residence time, tsurf, is related to the heat of adsorption, AH, and temperature, T, through a Frenkel-type relationship  

If we assume that t0= 10 13 s (vibrational frequency)-1, then for a heat of adsorption AH of 40 kJ mol-1 and a surface temperature of 295 K the residence time zsurf is 3 x 10-6 s and for 80 kJ mol-1 it is 102 s as T decreases the value of the surface residence time increases rapidly for a given value of AH. Decreasing the temperature is one possible approach to simulating a high-pressure study in that surface coverage increases in both cases the reaction, however, must not be kinetically controlled. 

For a molecule characterised by a AH value of 40 k.I mol 1 and undergoing facile surface diffusion, i.e. a A/ dir value close to zero, then each molecule will visit, during its surface lifetime (10 r s), approximately 107 surface sites. Since the surface concentration a is given by a = NtSUIf, then for a AH value of 40 kJ mol-1 and zsurf= 10-6 s at 295 K, the value of a is 109 molecules cm-2. These model calculations are illustrative but it is obvious that no conventional spectroscopic method is available that could monitor molecules present at a concentration 10-6 monolayers. These molecules may, however, contribute, if highly reactive, to the mechanism of a heterogeneously catalysed reaction we shall return to this important concept in discussing the role of transient states in catalytic reactions. 

These are well-founded basic physico-chemical principles applied to molecules adsorbed at solid surfaces, but what is new is that they have been made relevant to understanding chemical reactivity by our experimental 

Pb(110) at 77 K and warming to 140 K with (b) electron energy loss spectrum confirming the presence of surface hydroxyls at 160K when molecularly adsorbed water has desorbed. Both the oxide overlayer at Pb(110) and the atomically clean surface are unreactive to water. H abstraction was effected by transient Os states, which were also active in NH3 oxidation. (Reproduced from Refs. 40, 42). 

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In principle, therefore, these valuable techniques can provide all of the information needed to specify the molecular structure of the electrode/electrolyte solution interphase, the dynamics of adsorption/... 

Excellent reference to gain an enhanced understanding of the fundamentals of the dynamics of adsorption phenomena at liquid interfaces. An in-depth theoretical description of methods to determine dynamic interfacial tensions is included in the book. 

The approach to time resolution of very fast processes described above has been used to study a variety of gas phase chemical reactions stimulated by pulses of either photons or electrons (37) While similar studies have not yet been performed for processes occurring at solid surfaces, it should be feasible to do so. Thus, for example, the dynamics of adsorption and reaction at a single crystal surface, could be studied using a chopped molecular beam as the source of reactants. Alternatively, a pulsed photon beam could be used to repeatedly stimulate a reaction between adsorbed species. 

An important goal of investigations of the fundamental nature of catalysis is to provide a detailed analysis and characterization of the active surface sites and their role in the dynamics of adsorption and catalysis at the molecular level, whether induced by thermal energy (catalysis) and/or by photonic energy (photocatalysis). ... 

Gee AT, Hayden BE (2000) The dynamics of adsorption on Pt(533) step mediated molecular chemisorption and dissociation. J Chem Phys 113 10333... 

Some key adsorbates and reaction intermediates relevant to fuel-cell anodes are H2 as the fuel, CO and CO2 as poisons in hydrogen reformate feeds, and water as a co-adsorbate and potential oxidant. In the case of the cathode, oxygen is clearly the most important reactant. In the case of a number of these molecules, such as H2, O2, and H2O, not only is the molecular adsorption important on platinum (or promoted platinum catalysts), but the dissociative adsorption of the molecules is important as well. With this in mind, some details concerning the dynamics of adsorption of these molecules, the associated dissociation barriers, molecular degrees of freedom, and energy partition are important to the overall catalytic processes. In addition to the... 

Theoretical studies of the properties of the individual components of nanocat-alytic systems (including metal nanoclusters, finite or extended supporting substrates, and molecular reactants and products), and of their assemblies (that is, a metal cluster anchored to the surface of a solid support material with molecular reactants adsorbed on either the cluster, the support surface, or both), employ an arsenal of diverse theoretical methodologies and techniques for a recent perspective article about computations in materials science and condensed matter studies [254], These theoretical tools include quantum mechanical electronic structure calculations coupled with structural optimizations (that is, determination of equilibrium, ground state nuclear configurations), searches for reaction pathways and microscopic reaction mechanisms, ab initio investigations of the dynamics of adsorption and reactive processes, statistical mechanical techniques (quantum, semiclassical, and classical) for determination of reaction rates, and evaluation of probabilities for reactive encounters between adsorbed reactants using kinetic equation for multiparticle adsorption, surface diffusion, and collisions between mobile adsorbed species, as well as explorations of spatiotemporal distributions of reactants and products. 

The results revealed a significant effect of surface-active and nonsurface active polysaccharides on the properties of adsorbed protein films at the air-water interface. To explain the observed effects on the dynamics of adsorption, the rates of diffusion and rearrangement and the surface dilatational modulus were taken into accoimt (i) the competitive adsorption, (ii) the complexation, and (iii) the existence of a limited thermodynamic compatibility between protein and polysaccharide at the air-water interface and in the aqueous bulk phase. 

The ability of polymeric materials to act at interfaces depends on the manner in which they respond to mechanical stress through their surface viscoelasticity (Gau et al., 1993). In addition, the dynamics of adsorption provides information concerning the processes that occur during surface adsorption. 

In distinction to the equilibrium state the dynamics of adsorption is characterised by time dependence and inhomogeneous distributions of surface and bulk concentration. This is accompanied by hydrodynamic convection and convective diffusion as transport process for the molecules between the bulk phase and the adsorption layer. 

This section is dedicated to some selected examples of the very broad spectrum of surface phenomena directly influenced by the dynamics of adsorption of surfactants. There are books and monographs which show these and other examples in much more detail (Adamson 1990, Dorfler 1994, Hunter 1992, Ivanov 1988, Krugljakov Exerowa 1990, Lyklema 1991, Schulze 1984). However, to make the reader acquainted with some of the huge variety of applications, we inserted this section into the book. 

The first three chapters should be regarded as an introduction to the broad area of the dynamics of adsorption, while subsequent chapters contain original results, some of them not yet published. 

This dynamic character of the adsorption equilibrium has contributed significantly to developments in non-equilibrium thermodynamics. The balance of adsorption and desorption fluxes as the first step in the description of the dynamics of adsorption is a key point in this book. The second step is the introduction of a sublayer concentration and the diffusion layer to describe the non-equilibrium state in the bulk phase. While the system surface-bulk is in nonequilibrium the presence of local equilibrium is assumed between the adsorption layer and the sublayer as the third important step. This allows us to generalise Eq. (2.36) to Eqs (2.36a) and (2.36b). The first examples of dynamic adsorption layers of rising bubbles were given already by Frumkin Levich (1947) and Levich s book (1962) on "Physico-Chemical Hydrodynamics" (cf. Chapter 8) offered the first theories. Simultaneously, Frumkin Levich... 

The aim of this chapter is to present the fundamentals of adsorption at liquid interfaces and a selection of techniques, for their experimental investigation. The chapter will summarise the theoretical models that describe the dynamics of adsorption of surfactants, surfactant mixtures, polymers and polymer/surfactant mixtures. Besides analytical solutions, which are in part very complex and difficult to apply, approximate and asymptotic solutions are given and their range of application is demonstrated. For methods like the dynamic drop volume method, the maximum bubble pressure method, and harmonic or transient relaxation methods, specific initial and boundary conditions have to be considered in the theories. The chapter will end with the description of the background of several experimental technique and the discussion of data obtained with different methods. 

There are two general ideas to describe the dynamics of adsorption at liquid interfaces. The diffusion controlled model assumes the diffusional transport of interfacially active molecules from the bulk to the interface to be the rate-controlling process, while the so-called kinetic controlled model is based on transfer mechanisms of molecules from the solution to the adsorbed state and vice versa. A schematic picture of the interfacial region is shown in Fig. 4.1. showing the different contributions, transport in the bulk and the transfer process. 

There are many other experimental method for studying the dynamics of adsorption at liquid interfaces. First of all, many other techniques exist to measure dynamic surface and interfacial tensions. Only a subjective selection of some more experimental developments are given in the following section. Moreover, other than surface and interfacial techniques are discussed in this chapter too, such as radiotracer, ellipsometer, electric potential, and spectroscopic methods. 

Although many other experimental set-ups were developed to study the dynamics of adsorption, mainly via surface and interfacial tensions, of solutions of surface active compounds and polymers, they cannot all be described in detail here. More are given in textbooks of surface chemistry, e.g. by Adamson (1990) or Edwards et al. (1991). The last original technique, briefly discussed in this chapter, is the overflowing cylinder method used for example by Bergink-Martens et al. (1990). 

One of the older techniques for measuring directly the adsorbed amoimt of surfactant molecules or polymers at liquid interfaces is the radiotracer technique. Its idea is the measurement of the radiation emitted by radio-labelled molecules, adsorbed at an interface (Sally et al. 1950, Flengas Rideal 1959). Because of the background radiation the method yields relative data only. Using equilibrium adsorption isotherms, the dynamics of adsorption can also be followed by the radiotracer method. Experiments were performed with various surfactant systems (Matuura et al. 1958, 1959, 1961, 1962, Tajima 1970, Konya et al. 1973, Muramatsu et al. 1973, Okumura et al. 1974) and adsorbed polymers (Frommer Miller 1966, Adams et al. 1971, Graham Phillips 1979b). Due to the development of more efficient methods the use of this technique has been reduced. 

Many of these topics were originally developed or inspired by B.V. Derjaguin and his school. For this reason this book is dedicated to B.V. Derjaguin to honour his outstanding contribution to the dynamics of adsorption layers and its application to other fields of colloid and surface science. 

The dynamics of adsorption of alkanes is totally different. Both methane and propane were detected at reactor outlet already after the first pulse, revealing a very low sticking probability compared to CO and O2. Methane produced no thermal effect on the catalyst, whereas propane caused a weak temperature rise (about 0.2 °C). 

As mentioned above, the study of the dynamics of adsorption layers at liquid interfaces is mainly restricted to surface and interfacial tension measurements. Only for slow adsorption processes, methods such as radiotracer technique [163, 164], the significantly improved surface ellipsometry [165, 166], or the very recently developed technique of neutron reflectivity [167, 168, 169, 170] can be used to directly follow the change of surface concentration with time. Neutron reflectivity allows even distinguishing between different species adsorbed at a fluid interface [171, 172, 173]. These techniques are reviewed in more detail in the preceding chapter 3 as they yield data most of all for the equilibrium state of adsorption layers. 

In this paragraph we give examples for each of the mentioned cases, starting with a simple surfactant system that follows essentially the classical diffusion model. Then the effect of reorientation and aggregation of adsorbed molecules will be discussed by demonstrating experimental dynamic surface tension data. The adsorption dynamics of ionic surfactants has not been studied systematically so that these systems cannot be presented here extensively. Also the dynamics of adsorption at the interface between two liquids is at the beginning and we present here an impressive example. 

Software package WardTordai to calculate the dynamics of adsorption for various adsorption isotherms, available via sintech t-online.de... 

The similar model was first proposed by Bohart and Adams [128] for one component adsorption. It is widely used to describe the dynamics of adsorption when chemical reaction takes place. Equation (34) represents the differential mass balance for component i in a fixed bed adsorber with corresponding boundary conditions (Eq. (36) and (37)). At an initial time, t = 0, the bed is free from adsorbates and reaction products. Concentrations of adsorbates in a gas phase, Ci, and an adsorbed phase, qi, are equal to zero at any point of the bed. Inlet concentrations of each gas components are constant and equal to Coi, at any moment of time. 

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