When Thermodynamic Properties of Adsorbed Films Depend on Size: Fundamental Theory and Case Study

Strøm, Bjørn André; He, Jianying; Bedeaux, Dick; Kjelstrup, Signe

doi:10.3390/nano10091691

Cited by 13 publications

(12 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The subdivision potential, introduced by Hill as a measure of smallness, deviates from zero in the last relation, also when the integral pressure does not depend on the size of the area, with height h and surface area

as control variables. A dependency on the area is relevant when adsorption takes place on small spheres [ 24 ]. A slit pore with large walls may be expected to be small for small heights h , since the confined fluid is not bulk-like.…”

Section: Resultsmentioning

confidence: 99%

“…The approach following Gibbs is most popular [ 15 , 16 , 17 , 18 , 19 ]. However, the method of Hill may offer an attractive alternative [ 20 , 21 , 22 , 23 , 24 , 25 ], partly because it may provide an independent check on Gibbs procedure, but also because general geometric scaling relations are obtainable from Hill’s method. We will see that this is also the case in the present study.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

2021

Self Cite

View full text Add to dashboard Cite

We have described for the first time the thermodynamic state of a highly confined single-phase and single-component fluid in a slit pore using Hill’s thermodynamics of small systems. Hill’s theory has been named nanothermodynamics. We started by constructing an ensemble of slit pores for controlled temperature, volume, surface area, and chemical potential. We have presented the integral and differential properties according to Hill, and used them to define the disjoining pressure on the new basis. We identified all thermodynamic pressures by their mechanical counterparts in a consistent manner, and have given evidence that the identification holds true using molecular simulations. We computed the entropy and energy densities, and found in agreement with the literature, that the structures at the wall are of an energetic, not entropic nature. We have shown that the subdivision potential is unequal to zero for small wall surface areas. We have showed how Hill’s method can be used to find new Maxwell relations of a confined fluid, in addition to a scaling relation, which applies when the walls are far enough apart. By this expansion of nanothermodynamics, we have set the stage for further developments of the thermodynamics of confined fluids, a field that is central in nanotechnology.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many finite-size contributions to energy can be included in the net Hamiltonian of the system. Indeed, already in 1872 Gibbs included surface energies proportional to N 2/3 , and recent results have greatly extended these ideas to include shape-dependent terms [53][54][55].…”

Section: An Introduction To Nanothermodynamicsmentioning

confidence: 99%

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Chamberlin¹,

Clark²,

Mújica³

et al. 2021

Preprint

View full text Add to dashboard Cite

Here we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for atoms that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the Ising-like spins we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to equilibrium thermal fluctuations found in many materials.

show abstract

“…In contrast to Landsberg’s approach, Hill’s thermodynamic theory is not based on modified energy levels, but rather on the introduction of a subdivision potential to account for nonadditive effects. Hill’s theory has proven fruitful to describe nanoscale phenomena [ 24 , 25 , 26 , 27 , 28 , 29 ], and also the nonadditivity that occurs in macroscopic systems subject to long-range interactions [ 2 ].…”

Section: Introductionmentioning

confidence: 99%

Statistical Mechanics at Strong Coupling: A Bridge between Landsberg’s Energy Levels and Hill’s Nanothermodynamics

Miguel

Rubı́

2020

Nanomaterials

View full text Add to dashboard Cite

We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill’s nanothermodynamics.

show abstract

When Thermodynamic Properties of Adsorbed Films Depend on Size: Fundamental Theory and Case Study

Cited by 13 publications

References 23 publications

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Statistical Mechanics at Strong Coupling: A Bridge between Landsberg’s Energy Levels and Hill’s Nanothermodynamics

Contact Info

Product

Resources

About