Phase transitions in adsorption layers

The dependence of the dimensionless pressure n = ncO /RT (as mo= ,) on the surface coverage 9, calculated for various values of the intermolecular interaction constant a is shown in Fig. 2.19. 

Three different roots of Eq. (2.37) exist for a 2. The region enclosed by the dashed lines (shown in Fig. 2.19 for a = 2.5) corresponds to unstable states of the system. The surface pressure that corresponds to the coexistence of a condensed and gaseous state can be determined by using the so-called Maxwell construction [1, 104, 105]. That is, the areas enclosed by the dashed lines corresponding to this coexistence pressure and the two portions of the loop should be equal to each other on the fl vs A dependence. For a = 2.5 this pressure is marked in Fig. 2.19 by the solid line. 

In spite of the obvious capability of the models described by Eq. (2.37) to provide explanation of the phenomenon of surface condensation due to strong intermolecular interaction, there is evidence that this model is incompatible with the actual physical process governing the two-dimensional condensation of surfactants in either spread or adsorbed interfacial layers. In both regions, precritical and transcritical, Eq. (2.37) involves the same surface layer entities, namely the monomers and no distinction is made between free monomers and molecules involved into 

Applying Eq. (2.114) to experimental data the authors obtained surface pressure FI molar area A isotherms which exhibit horizontal sections. (As F = 1/A, the form of these curves corresponds to a mirror reflection of the curves shown in Fig. 2.19 with respect to the ordinate.) 

This interpretation of the experimental data is erroneous. Indeed, a two-dimensional aggregation (or condensation) in an adsorption layer or a spread insoluble monolayer should be regarded to as the formation of another type of adsorbed particles, namely two-dimensional aggregates (n-mers) or domains. It is important to note that the surface concentration of the 

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Vollhardt D (1999) Phase transition in adsorption layers at the air-water interface. Adv Colloid Interface Sci 79 19-57... 

As pointed out in the preceding chapter phase transitions in adsorption layers as observed in insoluble monolayers (Mbhwald 1993), can also be obtained for soluble surfactants too. Structures in mixed monolayers in particular were investigated by Henon Meunier (1993). These overlapping processes are now starting to be considered in new studies of equilibrium properties (cf Lin et al. 1991, Lunkenheimer Hirte 1992) or in dynamics of insoluble monolayers in terms of nucleation processes (Vollhardt et al. 1993). So far no attempts have been made to consider such transition or structure formation processes are considered in the dynamics of soluble adsorption layers. 

If kinetic processes of adsorption or desorption were observed in time scales t lOO tg, it is difficult to distinguish between impurity effects and specific effects of the surfactant system, such as electrostatic retardation, phase transitions in adsorption layers, conformational changes, structure formations etc. 

The Broekhoff-van Dongen isotherm allows for multilayer adsorption with lateral interactions and predicts the possibility of 2D phase transitions in each layer [17]. The most spectacular evidence for 2D phase transitions concerns the adsorption of heavy noble gases on highly homogeneous non-polar surfaces of low atomic weight (typically, exfoliated graphite obtained by thermal dissociation of its intercalation compound with FeCla). This situation guarantees that the adsorbate-adsorbate interaction prevails on ad-sorbent-adsorbate interaction and makes it possible the observation of phase transitions in each layer. See Ref. [18] for a short overview of this subject. 

The density functional theory appears to be a powerfid tool for studying adsorption on heterogeneous surfaces. In particular, the valuable results have been obtained for adsorption in pores with chemically stractured walls. The interesting, new phenomena, such as bridging, have been discovered in this way. The phase diagrams characterizing various phase transitions in surface layers can be determined quite quickly from the functional density theory. In this context, we emphasize the economy of the computational efforts required for the application of the fimctional density methods. For this reason, the density theory can be under certain conditions, competitive with computer simulations. However, many applications of the density fimctional theory are based on rather crude, oversimplified assumptions, so the conclusions following firom the calculations should be treated very cautiously. 

In this review we consider several systems in detail, ranging from idealized models for adsorbates with purely repulsive interactions to the adsorption of spherical particles (noble gases) and/or (nearly) ellipsoidal molecules (N2, CO). Of particular interest are the stable phases in monolayers and the phase transitions between these phases when the coverage and temperature in the system are varied. Most of the phase transitions in these systems occur at fairly low temperatures, and for many aspects of the behavior quantum effects need to be considered. For several other theoretical studies of adsorbed layer phenomena see Refs. 59-89. 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Damaskin and Baturina [171] have studied unstable states during coumarin adsorption on mercury electrode. These instabilities were attributed to the nonequilibrium phase transitions in the adsorption layer, during which the orientation of coumarin molecules changed at the electrode surface. 

The region of jump-like changes in the dAsurface tension (see Fig. 3.77). This jump [364,365] is explained with a phase transition in the adsorption layer. Other authors have also noticed the flexion in Ao(C) isotherm and have considered it to be a transition from liquid-crystalline to gel state of the adsorption layer, e.g. in solutions of dodecylamine hydrochloride [374]. This transition can be found experimentally also from AV(C) dependence. As it is seen from Fig. 3.77 the minimum of AV coincides with the flexion point of Ao(lgC) isotherm. 

The adsorption and structure of anions such as bromide, cyanide, sulfate/bisulfate, and iodide on metal electrodes have been extensively studied by in-situ STM in electrolyte solutions. Figure 41a displays a cyclic voltammogram for an Au(lll) electrode in 1-mM KI solution. The anodic/cathodic peaks below 0 V versus Ag/AgI are associated with adsorption/desorption of iodine at the surface. The smaller peaks at 0.5V are due to a phase transition in the adsorbed iodine layer, as can be observed by STM images taken at various electrode potentials. STM images shown in Figure 41b taken at a potential of —0.2 V show a periodic structure with perfect... 

A successful application of Eq. (3.41) is the calculation of surface tensions of mixed Ci2S04Na/1-dodecanol solution [95]. It was shown in [25] that 1-dodecanol forms surface aggregates (see Fig. 3.5). As the Ci2S04Na adsorption is completed before any appreciable adsorption of 1-dodecanol starts, and 1-dodecanol adsorbs due to the diffusion mechanism the Eq. (3.41) remains valid also for the dynamic surface pressure. The approximate model correctly predicts the existence of a significant shift towards shorter times corresponding to the critical point of phase transition in the mixed surface layer. The time of the aggregation onset of 1-dodecanol in the mixed solution is 4 times lower as compared to the individual 1-dodecanol solution [95]. 

Measurements of electrode impedance offer an extra bonus an electrode placed in an ionic solution is surrounded by the electrical double layer having the corresponding double-layer capacity that contributes to the overall electrode impedance. The value of the double-layer capacity sensitively reflects the interfacial properties of substances present in the solution and therefore the impedance technique is suitable for the investigation of adsorption at the interface, the phase transition in monolayers, the interaction of biosurfactants with counter ions, the inhibition properties of polymers, the analysis of electro-inactive compounds on the basis of adsoprtion effects, and other topics. The theory of electrode impedance has been well formulated and a complete set of diagnostic criteria for the elucidation of electrochemical processes is available. With the increasing availability of ready-made instrumentation an increased number of applications in biochemical studies is also to be expected. 

Phase transition. IH liquid signals have further been applied to investigate the phase transitions of polymers in adsorption layers by monitoring the change in mobility of polymer... 

At Pj)= 100 bar, disappearance of the phase transition is observed at x > 1 21. At higher relative pressures, the adsorption curve goes around the phase envelope, as the curve M in Fig. 26. However, aU of the forms of the AAE predict a nonzero thickness of the adsorbed layer for these relative pressures. This problem is similar to the corresponding problem for the Kelvin equation Both equations predict existence of the Kelvin radius or of an adsorbed film in the regions where they do not exist. To the best of our knowledge, the only way to check the boundary for capillary condensation or for the phase transition in the adsorbate is to perform direct numerical calculations. 

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