Macroscopic properties coexistence

Figure 2. Schematic representation of the four conceptually different paths (the heavy lines) one may utilize to attack the phase-coexistence problem. Each figure depicts a configuration space spanned by two macroscopic properties (such as energy, density. ..) the contours link macrostates of equal probability, for some given conditions c (such as temperature, pressure. ..). The two mountaintops locate the equilibrium macro states associated with the two competing phases, under these conditions. They are separated by a probability ravine (free-energy barrier). In case (a) the path comprises two disjoint sections confined to each of the two phases and terminating in appropriate reference macrostates. In (b) the path skirts the ravine. In (c) it passes through the ravine. In (d) it leaps the ravine.

Microemulsions and most surfactants in dilute solutions and dispersions self-assemble into a variety of microstructures spherical or wormlike micelles, swollen micelles, vesicles, and liposomes. Such systems are of biological and technological importance, e.g., in detergency, drug delivery, catalysis, enhanced oil recovery, flammability control, and nanoscale particle production. The macroscopic properties—rheology, surface tension, and conductivity—of these systems depend on their microstructure. As these microstructures are small (1-1000 nm) and sometimes several microstructures can coexist in the same solution, it is difficult to determine their structure. Conventional techniques like radiation scattering, although useful, provide only indirect evidence of microstructures, and the structures deduced are model-dependent. 

A system of interest may be macroscopically homogeneous or inliomogeneous. The inliomogeneity may arise on account of interfaces between coexisting phases in a system or due to the system s finite size and proximity to its external surface. Near the surfaces and interfaces, the system s translational synnnetry is broken this has important consequences. The spatial structure of an inliomogeneous system is its average equilibrium property and has to be incorporated in the overall theoretical stnicture, in order to study spatio-temporal correlations due to themial fluctuations around an inliomogeneous spatial profile. This is also illustrated in section A3.3.2. 

These contact angles can be related to the physical state of the surface. The 100 facet is better wetted than the 111 one because the 100 surface is partly premelted. But, the liquid-like disordered monolayer is too thin to have the properties of the macroscopic liquid, and this "adsorbed liquid layer" coexists with a non-wetting macroscopic liquid. This so-called "incomplete surface melting" has also been observed on a pure single crystal of ice. ... 

Perhaps the most striking property of a microemulsion in equilibrium with an excess phase is the very low interfacial tension between the macroscopic phases. In the case where the microemulsion coexists simultaneously with a water-rich and an oil-rich excess phase, the interfacial tension between the latter two phases becomes ultra-low [70,71 ]. This striking phenomenon is related to the formation and properties of the amphiphilic film within the microemulsion. Within this internal amphiphilic film the surfactant molecules optimise the area occupied until lateral interaction and screening of the direct water-oil contact is minimised [2, 42, 72]. Needless to say that low interfacial tensions play a major role in the use of micro emulsions in technical applications [73] as, e.g. in enhanced oil recovery (see Section 10.2 in Chapter 10) and washing processes (see Section 10.3 in Chapter 10). Suitable methods to measure interfacial tensions as low as 10 3 mN m 1 are the sessile or pendent drop technique [74]. Ultra-low interfacial tensions (as low as 10 r> mN m-1) can be determined with the surface light scattering [75] and the spinning drop technique [76]. 

Supercritical fluids in the highly compressible regime are of particular interest, because it is in this regime that one can easily access the intermediate solvent densities, and thus the associated intermediate solvent properties, which are obscured in subcritical fluids by the liquid-vapor coexistence curve. However, a large macroscopic compressibility arises from a balance of energetic and entropic forces which, concomitantly, give rise to interesting microscopic behaviors. These microscopic consequences must be accounted for if one is to accurately predict reaction rates in compressible SCFs. 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

The typical surface-active or surfactant molecule consists of at least one polar hydrophilic part and one apolar hydrophobic part, such as a hydrocarbon or fluorocarbon chain. Although there is normally only one headgroup per surfactant molecule, there are frequently several nonpolar tails. These can be linear or branched, the most common being single and linear. Because of the coexistence of two opposite types of behavior inside the same molecule, surfactants can build different submicroscopic aggregates in water that can organize themselves into various supramolecular structures of macroscopic dimensions and different properties. The variety of supramolecules ranges from micelles to liquid crystalline... 

In this paragraph we focus on the properties of interfaces between coexisting phases, i.e., planar interfaces between macroscopic domains. Let S. denote the area of the (planar) interface, so we calculate the free energy that an interface costs per unit area, the interfacial tension y, via ... 

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