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This research addressed fundamental issues in the mesoscopic thermodynamics of asymmetric fluid interfaces, namely, the nature of the asymmetric interfacial profile and the curvature dependence of the interfacial tension. In some fundamentally and practically important fluid systems exhibiting smooth interfaces, such as near-critical fluids and polymer solutions, the amplitude of the first curvature correction to the interfacial tension, known as Tolman’s length, may become as large as the thickness of the interface itself. Tolman’s length depends crucially on the degree of asymmetry in the fluid phase coexistence and on the mesoscopic fluctuations of density or concentration. We have performed a theoretical study of these effects on the behavior of curved interfaces in soft matter. The approach we have adopted is semi-phenomenological, based on “gradient theory” and scaling ideas in mesoscopic thermodynamics. The research impacts filtration through micro porous media in oil recovery, microfluidics, nanoscale liquid bridges, nucleation phenomena, and all instances where science and technology deal with fluid droplets at submicron and nano scales. In particular, the interfacial properties of highly asymmetric polymer solutions and polymer blends, ionic fluids near the critical points of phase separation, and two-dimensional phase separation on the surface of vesicles and lamellae are some of the principle subjects of our investigations.

As previously reported (see Narrative Progress Report 2009), we have generalized the theory of “complete scaling” to mesoscopically inhomogeneous fluids, including systems with smooth interfaces. Complete scaling is a theory which maps the thermodynamics of asymmetric fluids i.e. those fluids with asymmetric phase coexistence, onto the well-developed thermodynamics of symmetric models, such as the lattice gas model. Complete scaling was originally formulated to treat critical phenomena in bulk systems. It postulates that the “theoretical” field variables of the symmetric models can be represented as linear combinations of the physical field variables which describe the actual asymmetric fluid. We have introduced another field variable, which controls the density inhomogeneity, into the field mixing. This allows us to successfully map the complicated thermodynamics of the fluctuation-affected asymmetric interfaces onto the relatively simple thermodynamics of the lattice-gas interface. We have calculated the asymmetric interfacial profile near the critical point of vapor-liquid and liquid-liquid separation and applied the results to such highly asymmetric systems as ethane-heptane mixtures near the vapor-liquid critical point and methanol-hexane-water mixtures near the liquid-liquid critical point. We have also calculated Tolman’s length, the first curvature correction to the surface tension, and have verified and extended the previously proposed phenomenological relation between Tolman’s length, the thickness of the interface and the bulk densities of the coexisting fluid phases. This result, in turn, lead to the introduction of a new critical amplitude ratio. The ratio depends on a newly proposed asymmetry of the bulk correlation length in the two coexisting phases. We have suggested a light scattering experiment to verify the universality of the ratio and the asymmetry in the correlation length. The findings from this work were published in May, 2010 in Phys. Rev. Lett. 104, 205702, with the expectation that a full-size paper, containing various applications, will be published by the end of this year.

More recently, we have turned our attention to understanding the limitations of the complete scaling approach. Most theories of critical phenomena rely on renormalization group (RG) methods, where as complete scaling is a mixture of RG results and phenomenology. The previously developed RG results for fluids have not been able to fully describe the experimentally observed effects of fluid asymmetry, where as complete scaling is in good agreement in with experiments. We have investigated the connection between the complete scaling approach and the RG results and have found them to be compatible. This puts complete scaling on more rigorous theoretical footing and provides a guiding principle for interpreting the RG results in a manner consistent with experiment. This connection in turn allows us to quantify and control the effects of the approximations used in the previous calculations of Tolman’s length and the interfacial profile. These new results will be published as a separate paper.

In addition to the previously reported conference presentations, we have also reported these results at the 5th International Conference on the Physics of Liquid Matter: Modern Problems (Kiev, May 2010). A Chapter “Thermodynamics of Fluids at Meso and Nano Scale” in the IUPAC book “Applied Thermodynamics of Fluids”, which reviews some fundamental results of this study, is now in press. One student, Christopher Bertrand, was supported by the PRF grant for the 2009-2010 academic year. He will defend his PhD on November 8, 2010. The research activities described above constitute the bulk of the work in his dissertation.