Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions

Nucleation of surface nanobubbles in electrochemistry: Analysis with nucleation theorem

The formation of single bubbles at nanoelectrodes during electrochemical reactions allows to accurately identify the critical nucleus for bubble formation. As demonstrated before, combining nanoelectrode experiments and an analysis approach based on classical nucleation theory (CNT) delivers useful insight into bubble nucleation. In this work we propose an alternative approach to analyze the critical nuclei by applying the nucleation theorem (NT), which is able to overcome the inherent shortcomings of CNT. The size of the critical nucleus can be calculated more accurately by fitting experimental data in a simple form of the NT. Simulating the local gas concentration using a finite element approach, and considering the effect of gas oversaturation on the interfacial tension and the real gas compressibility, we obtain a more realistic estimation of the critical nuclei morphology. With the NT-based analysis presented, we re-analyze the nucleation data reported before. The properties of the critical nuclei obtained here are roughly consistent with those obtained from the CNT-based approach. In addition, we confirm that the critical nucleus for bubble formation in high gas oversaturation is featured with a contact angle much larger than Young's contact angle.

Molecular Insights into the Salinity Effects on Movability of Oil-Brine in Shale Nanopore-Throat Systems

Low-salinity flooding has been well recognized as a promising strategy to increase shale oil recovery, but the underlying mechanism remains unclarified, especially for complex nanopore networks filled with oil-brine fluids. In this study, the pressure-driven flow of an oil-brine fluid with varying salinities in shale nanopore-throat channels was first investigated based on molecular dynamics simulations. The critical pressure driving oil to intrude into a nanothroat filled with brine of varying salinities was determined. Simulation results indicate that the salinity of brine exhibits great effects on the movability of oil, and low salinity favors the increase of oil movability. Further analysis of the interactions between fluid and pore walls as well as the displacement pressures reveals dual effects of brine salinity on oil transportation in a nanopore-throat. On the one hand, hydrated cations anchoring onto throat walls enlarge the effective flow width in the throat before the hydration complexes reach the maximum. On the other hand, the interfacial tension between oil and brine increases with the brine salinity, which increases the capillary resistance and leads to a higher displacement pressure. These findings highlight the effects of brine salinity on oil movability in a nanopore-throat, which will promote the understanding of oil accumulation and dissipation in petroleum systems, as well as help to develop enhanced oil recovery.

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

Temperature, particle number and volume are the independent variables of the Helmholtz free energy for a bulk fluid. For a fluid confined in a slit pore between two walls, they are usually complemented by the surface area. However, an alternative choice is possible with the volume replaced by the pore width. Although the formulations with such two sets of independent variables are different, we show they are equivalent and present their relations. Corresponding general statistical-mechanics results are also presented. When the pore width becomes very small, the system behaves rather like a two-dimensional (2D) fluid and one can wonder if thermodynamics still holds. We find it remains valid even in the limit of vanishing pore width and show how to treat the divergences in the normal pressure and the chemical potential so that the corresponding 2D results can be obtained. Thus, we show that the Gibbs surface thermodynamics is perfectly capable of describing small systems.

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

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.

Legendre-Fenchel transforms capture layering transitions in porous media

We have investigated the state of a nanoconfined fluid in a slit pore in the canonical and isobaric ensembles. The systems were simulated with molecular dynamics simulations. The fluid has a transition to a close-packed structure when the height of the slit approaches the particle diameter. The Helmholtz energy is a non-convex function of the slit height if the number of particles does not exceed that of one monolayer. As a consequence, the Legendre transform cannot be applied to obtain the Gibbs energy. The Gibbs energy of a non-deformable slit pore can be transformed into the Helmholtz energy of a deformable slit pore using the Legendre-Fenchel transform. The Legendre-Fenchel transform corresponds to the Maxwell construction of equal areas.

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary systems with probability a priori where the thermodynamic infinite-size limit is replaced by a multiple-measurement limit. A duality symmetry between Massieu's and Gibbs's entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as a dual pair. If a system has a thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.

Gibbs thermodynamics and surface properties at the nanoscale

Gibbs's classical thermodynamic framework approximates systems as infinitely large phases separated by infinitely thin surfaces. The range of validity of this classical framework naturally comes under scrutiny as we become interested in the properties of ever smaller systems. This Communication clarifies that while Gibbs's original framework of bulk phase thermodynamics did require modifications to describe the properties of very small (i.e., non-additive) phases, his classical framework remains fundamentally valid to describe the thermodynamic properties of surfaces. We explain why classical surface laws are applicable at the nanoscale, as suggested by simulations and confirmed by experiments. We also show that a generalized Gibbs-Tolman-Koenig-Buff equation and the resulting Tolman's law for surface tension are obtained from a classical thermodynamic analysis in the Tolman region, a region of interaction between the system and the environment.