Thermodynamics at the Meso- and Nanoscale
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Thermodynamics is a keystone in engineering and science, bridging the gap between fundamentals and applications. However, when one compares the content of traditional courses in thermodynamics with what engineers often do in practice, one notices a gap and the gap is widening every year. New emerging technologies and products deal with subjects such as biomembrane and gene engineering, microreactor chemistry and microcapsule drug delivery, microfluids and porous media, nanoparticles and nanostructures, supercritical-fluid extraction and artificial organs. Engineers often must design processes for systems where classical thermodynamics (in particular, the Second Law) becomes insufficient, as in the case of strongly fluctuating and nanosize systems, or dissipative systems under conditions far away from equilibrium. Mesoscopic thermodynamics can be defined as a semiphenomenological approach to phenomena in systems where a length—intermediate between the atomistic scale and the macroscopic scale—emerges and where such a length explicitly affects the thermodynamic properties and phase behavior. Finite-size and fluctuation thermodynamics, critical phenomena in fluids and solids as well as in soft-matter materials (such as complex fluids), wetting and interfacial phenomena, self-organized criticality and dissipative structures, thermodynamics of pattern formation and fractals are examples of topics addressed in mesoscopic thermodynamics (equilibrium and nonequilibrium). While conventional methods of statistical mechanics remain the fundamental background of mesoscopic thermodynamics, coarse-grained approaches emphasizing universality rather than microscopic details, such as the Landau–Ginzburg local free-energy functional, can be successfully applied to describe what seem to be very different phenomena on mesoscales: from critical fluctuations to near-surface and interfacial density profiles, from micelles and microemulsions to porous media, from thin layers to nanoparticles. For this purpose, one can utilize a number of powerful theoretical concepts, such as renormalization-group theory, finite-size scaling, percolation theory, and coupling between different order parameters so as to predict the properties at meso- and nanoscales.