Thermodynamics surface phases

Despite the importance of the precipitation of calcium phosphates, there is still considerable uncertainty as to the nature of the phases formed in the early stages of the precipitation reactions under differing conditions of supersaturation, pH, and temperature. Although thermodynamic considerations yield the driving force for the precipitation, the course of the reaction is frequently mediated by kinetic factors. Whether dicalcium phosphate dihydrate (CaHPO HoO, DCPD), octacalcium phosphate (Ca HfPO, 2.5 H20, OCP), hydroxyapatite (Cag (PO fOH), HAP), amorphous calcium phosphate (ACP), or a defect apatite form from aqueous solution depends both upon the driving force for the precipitation and upon the initiating surface phase. Thermodynamically, the relative supersaturation, o, is given by... 

The micrographs in Fig. 7.88 show clearly how from a knowledge of the AG -concentration diagrams it is possible to select the exact reaction conditions for the production of tailor-made outermost surface phase layers of the most desired composition and thus of the optimum physical and chemical properties for a given system. In addition it shows that according to thermodynamics, there can be predictable differences in the composition of the same outermost phase layer prepared at the same conditions of temperature but under slightly different vapour pressures. 

The surface-phase layers will difier in character depending on the stractures of metal and oxide. On certain metals (zinc, cadmium, magnesium, etc.), loose, highly porous layers are formed which can attain appreciable thicknesses. On other metals (aluminum, bismuth, titanium, etc.), compact layers with low or zero porosity are formed which are no thicker than 1 pm. In a number of cases (e.g., on iron), compact films are formed wfiicfi fiave a distorted lattice, owing to the influence of substrate metal stracture and of the effect of chemical surface forces. The physicochemical and thermodynamic parameters of such films differ from tfiose of ordinary bulk oxides. Because of the internal stresses in the distorted lattice, such films are stable only when their thickness is insignificant (e.g., up to 3 to 5 nm). 

For the non-oxidative activation of light alkanes, the direct alkylation of toluene with ethane was chosen as an industrially relevant model reaction. The catalytic performance of ZSM-5 zeolites, which are good catalysts for this model reaction, was compared to the one of zeolite MCM-22, which is used in industry for the alkylation of aromatics with alkenes in the liquid phase. The catalytic experiments were carried out in a fixed-bed reactor and in a batch reactor. The results show that the shape-selective properties of zeolite ZSM-5 are more appropriate to favor the dehydroalkylation reaction, whereas on zeolite MCM-22 with its large cavities in the pore system and half-cavities on the external surface the thermodynamically favored side reaction with its large transition state, the disproportionation of toluene, prevails. 

Precipitation can occur if a water is supersaturated with respect to a solid phase however, if the growth of a thermodynamically stable phase is slow, a metastable phase may form. Disordered, amorphous phases such as ferric hydroxide, aluminum hydroxide, and allophane are thermodynamically unstable with respect to crystalline phases nonetheless, these disordered phases are frequently found in nature. The rates of crystallization of these phases are strongly controlled by the presence of adsorbed ions on the surfaces of precipitates (99). Zawacki et al. (Chapter 32) present evidence that adsorption of alkaline earth ions greatly influences the formation and growth of calcium phosphates. While hydroxyapatite was the thermodynamically stable phase under the conditions studied by these authors, it is shown that several different metastable phases may form, depending upon the degree of supersaturation and the initiating surface phase. 

If one adds an inorganic salt, such as NaCl, instead of detergent, then no foam is formed. Foam formation indicates that the surface-active agent adsorbs at the surface, and forms a TLF (consisting of two layers of amphiphile molecules and some water). This has led to many theoretical analyses of surfactant concentration (in the bulk phase) and surface tension (consequent on the presence of surfactant molecules at the surface). The thermodynamics of surface adsorption has been extensively described by the Gibbs adsorption theory (Chattoraj and Birdi, 1984). 

The statistical thermodynamic approach to the derivation of an adsorption isotherm goes as follows. First, suitable partition functions describing the bulk and surface phases are devised. The bulk phase is usually assumed to be that of an ideal gas. From the surface phase, the equation of state of the two-dimensional matter may be determined if desired, although this quantity ceases to be essential. The relationships just given are used to evaluate the chemical potential of the adsorbate in both the bulk and the surface. Equating the surface and bulk chemical potentials provides the equilibrium isotherm. 

How is an equation of state related to an adsorption isotherm What is the basic thermodynamic principle that governs the equilibrium between the surface phase and bulk phase ... 

The corresponding expression for the thermodynamic energy of a surface phase cr is... 

It is commonly assumed that transfer processes can be modeled by bulk phase thermodynamics and that surface or interfacial effects are negligible. These assumptions may, in the case of partitioning into amphiphilic structures formed by micelles or bilayer membranes, not always be appropriate. These interfacial solvents have a large surface to volume ratio, similar to interfacial solvents used in reversed-phase liquid chromatography. The partitioning into such phases is the basis of the chromatographic separation. 

It has commonly been assumed that transfer processes can be modeled in terms of simple bulk-phase thermodynamics. However, in many circumstances this assumption seems to be incorrect. Bulk thermodynamics cannot be applied when the solutes (especially amphiphilic drugs) partition into amphiphilic aggregates such as bilayer membranes. It is important to remember that a bilayer consisting of phospholipids is a solvent with an interfacial phase and a high surface/volume ratio. 

S-shaped current potential curves emerge when a surface phase transition of an organic adsorbate is coupled with a faradaic reaction of some electroactive species. As a representative of such a system, the periodate reduction on Au(lll) single crystal electrodes in the presence of camphor was studied [160], Camphor adsorbed on Au(lll) electrodes exhibits two first-order phase transitions upon variation of the electrode potential [161]. In a cyclic voltammogram, the phase transition manifests itself in a pair of needle-like peaks (Fig. 28 (A)). Between the peak pairs, a condensed, well-ordered camphor film exists. At more negative potentials, the camphor coverage is low, while the state of the adsorbate at positive potentials beyond the second phase transition is not yet known. The small hystereses between the respective anodic and cathodic peaks are caused by the finite nucleation rate of the respective thermodynamically stable phase. 

The thermodynamic development is similar to Gibbs s theory and may be carried out as follows (cf. 2). If a is the total internal energy of the surface phase, for an area A, and rf its entropy,... 

The surface phase. While this may not be a separate phase in the thermodynamic sense, adsorption of a growing radical on the particle surface would confine the reaction to this locus throughout much of the life of the chain. 

We take up this topic not only because of its intrinsic interest, but because it is pedagogically valuable to note the various descriptions that arise from the multitude of available choices for the basic thermodynamic potential functions. The system under consideration consists of a thin layer of atoms held on the surface of a solid or liquid exposed to a gas phase. The solid or liquid is termed the adsorbent. whereas the material held on the surface is called the adsorbate the process by which the thin surface layer is formed from the transfer of gas molecules to the surface phase is called adsorption. 

In summary, an attempt has been made in sections 5.2 and 5.3 to provide a number of formulations for the thermodynamic properties of surface phases. Special emphasis has been placed on the key role of the Gibbs adsorption equation as a link between the experimentally available isotherm data, and the determination of molar or differential entropies, enthalpies,... 

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