Mesoscopic and Nanoscale Thermodynamics: Fundamentals for Emerging Technologies

Thermodynamics is a keystone in engineering and science, bridging the gap between fundamentals and applications. New emerging technologies and materials deal with biomembrane and gene engineering, micro-reactor chemistry and microcapsule drug delivery, micro-fluids and porous media, nanoparticles and nanostructures, supercritical extraction and artificial organs. Engineers often have to design processes and products where classical thermodynamics may become insufficient, e.g., strongly fluctuating and nano-size systems, or dissipative systems under conditions far away from equilibrium. Mesoscopic thermodynamics can be defined as a semi-phenomenological approach to the systems and phenomena in which a length - intermediate between the atomistic scale and the macroscopic scale - emerges and where such a length explicitly affects the thermodynamic properties. Finite-size and fluctuation thermodynamics, critical phenomena in fluids and solids as well as that in soft-matter materials (such as complex fluids), wetting and interfacial phenomena, self-organized criticality and guided selfassembly, thermodynamics of pattern formation and fractals are examples of the topics addressed in the mesoscopic thermodynamics. While conventional methods of statistical mechanics remain to be the fundamental background of mesoscopic thermodynamics, an approach based on the Landau-Ginzburg local free-energy functional and on the local order parameter(s) can be successfully applied to describing apparently very different phenomena on mesoscales - from the critical fluctuations to the near-surface and interfacial density profile, from micelles and microemulsions to porous media and nanoparticles. This approach emphasizes universality and utilizes a number of powerful theoretical concepts, such as renormalization-group theory, finite-size scaling, percolation theory, coupling between different order parameters and emergence of multicriticality. As an example of finding simplicity in complexity , new experimental results on a competition of mesoscales and a coupled critical dynamics ( avoided crossing and critical microrheology ) in high-molecular-weight polymer solutions will be discussed.