Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Abstract

Disjoining pressure was discovered by Derjaguin in 1930’s, which describes the difference between the pressure of a strongly confined fluid and the corresponding one in a bulk phase. It has been revealed recently that the disjoining pressure is at the origin of distinct differential and integral surface tensions for strongly confined fluids. Here we show how the twin concept, disjoining chemical potential, arises in a reminiscent way although it comes out eighty years later. This twin concept advances our understanding of nanoscale thermodynamics. Ensemble-dependence (or environment-dependence) is one hallmark of thermodynamics of small systems. We show that integral surface tension is ensemble-dependent while differential surface tension is not. Moreover, two generalized Gibbs-Duhem equations involving integral surface tensions are derived, as well as two additional adsorption equations relating surface tensions to adsorption-induced strains. All the results obtained in this work further evidence that an approach alternative of Hill’s nanothermodynamics is possible, by extending Gibbs surface thermodynamics instead of resorting to Hill’s replica trick. Moreover, we find a compression-expansion hysteresis without any underlying phase transition.

Thermodynamics, statistical mechanics and the vanishing pore width limit of confined fluids

“…When the pore becomes narrower and narrower, some characteristic behaviors of small systems manifest themselves more and more. For example, differential and integral pressures ( p , and ), differential and integral surface tensions ( γ and ), differential and integral chemical potentials ( μ and ) are no longer the same 9 , 13 , 14 . The definitions of these differential and integral thermodynamic functions are recalled: ( : grand potential), , , , , .…”

“…T. L. Hill has been a pioneer for developing a thermodynamic approach for small systems 2 – 6 . Recently, W. Dong has shown that if the surface contribution is adequately accounted for, an alternative approach is possible, which is based on the more traditional surface thermodynamics 13 , 14 . It is to be emphasized that the thermodynamic formalism presented in this section applies for any arbitrarily small pore width.…”

“…T. L. Hill was the pioneer who tried to extend thermodynamics for small systems 2 , 3 . His approach, named now as nanothermodynamics 4 – 6 , is attracting much renewed interest 7 – 14 (see the monograph of Bedeaux, Kjelstrup and Schnell 7 for a recent review). Is it necessary to resort to Hill’s nanothermodynamics to study the dimensional cross-over problem described above?…”

Rewritable nano print of ionic liquids utilizing focused ion beam induced film wetting

“…At millimeter to micrometer range, the surface tension dominates, and the majority of traditional microfluidics methods belong to such region, with the spatial resolution difficult to approach nanoscale. When the system size reduces to nanometer region, the interfacial overlapping 31,33 emerges. The disjoining pressure increases rapidly when film thickness approaches sub-nanometer and dominates system energy.…”

“…Actually, when the liquid film thickness approaches nanometer scale, the interfacial overlapping dominates the system free energy [31][32][33] instead of surface tension. Such phenomenon usually called disjoining pressure has been proved to be capable of stabilizing liquid nanofilm [34][35][36] .…”