Curvature effects, interfacial

Up to now we have considered interfacial phenomena in systems where the interfacial boundaries separating coexisting phases were essentially flat (i.e., with large radius of curvature). The interfacial curvature changes the thermodynamic properties of systems and is responsible for a number of important phenomena, such as capillary effects. The large interfacial curvature is typical of finely dispersed systems, and hence one has to take into account its effects on the thermodynamic properties of such systems. 

The interfacial free energy associated with the creation of the micellar core-water interface, as well as with the shielding part of that interface. This contribution is obtained from available hydrocarbon-water interfacial tension data, and the interfacial area per monomer. The effect of interfacial curvature on interfacial tension was obtained from the Tolman equation [23]. 

In Sec. II we discuss the mechanism by which the interfacial tension may become ultralow. After that, in Sec. Ill we mention curvature effects of the oil/water interface. Subsequently, a number of models for thermodynamic calculations are described (Sec. IV). In Secs. V-VII we discuss droplet-type microemulsions in some detail. Section Vdescribes a thermodynamic formalism that incorporates the interfacial free energy (as influenced by the curvature) and the free energy of mixing of droplets and continuous medium and ultimately leads to equations for the size distribution of microemulsion droplets. This size distribution is important because measurable properties can be calculated... 

Nielsen AE, Bindra PS (1973) Effect of curvature on interfacial tension in liquid systems measured by homogeneous nucleation. Croat Chem Acta 45 31-52... 

Paek, E., A. J. Pak, and G. S. Hwang. 2013. Curvature effects on the interfacial capacitance of carbon nanotubes in an ionic liquid. Journal of Physical Chemistry C 117 23539-23546. 

Because many practical situations involve surfaces and interfaces with high degrees of curvature, it is important to understand the effect of curvature on interfacial properties. As pointed out in Chapters 2 and 6, there will develop a pressure differential across any curved surface, with the pressure being greater on the concave side of the interface. In other words, the pressure inside a bubble will always be greater than that in the continuous phase. The Young-Laplace equation... 

In all the preceding discussion of terms having the gAy form, yhas been interpreted as a surface tension, the factor g serving to correct for the molecular-scale curvature effect. But a stuface tension is measured at the macroscopic air-liquid interface, and in the solution case we are actually interested in the tension at a molecular scale solute-solvent interface. This may be more closely related to an interfacial tension than to a surface tension. As a consequence, if we attempt to find (say) g2A2 by dividing by we may be dividing by the wrong munber. 

We now consider how dU might change for a fluid interface if the reference surface S is deformed. Both the area and curvature of S can change but if the radii of curvature are much greater than the interfacial thickness, we might expect curvature effects to be small, so that... 

Fletcher (46) showed experimentally that the interfacial partition coefficients of different solutes depend on both the external salinity and on the interfacial curvature. Leodidis and Hatton (37b) extended this work by illustrating a curvature dependence of the interfacial partition coefficient Kx- Figures 9.12 (37a) and 9.13 (37b) demonstrate this curvature effect. The term 1/Vko is directly related to the curvature 1// , if / w is the radius of the droplet. When the curvature is increasing, the partition coefficient is decreasing. This is attributed to an increase of the rigidity of the interface, which induces a squeezing-out effect, as in the lamellar phase. Thus, a local equilibrium of solute adsorption at the interface can be directly linked to the mean curvature of the surfactant film. 

There is an important caveat in all the dehquescence studies of NaCl reviewed by Martin. The samples were polycrystalhne, or if a single grain, their surfaces were irregular and not defined. Since it is known that surface curvature, steps and defects can effect interfacial properties [2,3,6,26,27,44], Cantrell et al. [89] undertook to study dehquescence of cleaved NaCl (001) faces placed in a temperature and humidity controlled environment. The onset of dissolution (deliquescence) was monitored by the appearance of a thick film of brine as determined from its infrared spectrum. The infrared signatures of neat water and brine are quite distinct, so the film grown was brine and not water. Photometry was used to determine the brine thickness which... 

The derivation of Young s equation in its form (2) assumes that the solid is homogeneous and the interfacial tensions have the same value at all points in each interface. Even in the absence of curvature effects, interactions between the three interfaces will occur in the region of contact33 35 these will modify the... 

In the last two sections the formal theory of surface thermodynamics is used to describe material characteristics. The effect of interfaces on some important heterogeneous phase equilibria is summarized in Section 6.2. Here the focus is on the effect of the curvature of the interface. In Section 6.3 adsorption is covered. Physical and chemical adsorption and the effect of interface or surface energies on the segregation of chemical species in the interfacial region are covered. Of special importance again are solid-gas or liquid-gas interfaces and adsorption isotherms, and the thermodynamics of physically adsorbed species is here the main focus. 

---