Nanothermodynamics

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N, with dynamics that is readily altered from reversible to irreversible...

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...

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...

In this study, we report the lowest energy structure of bare Cu13 nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu13 cluster, employing a genetic algorithm coupled with density functional theory...

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4 B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics...

This Special Issue concerns recent developments of a theory for energy conversion on the nanoscale, namely nanothermodynamics [...].

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere...

Studies of thermally induced transport in nanostructures provide access to an exciting regime where fluctuations are relevant, enabling the investigation of fundamental thermodynamic concepts and the realization of thermal energy harvesters. We study a serial double quantum dot formed in an InAs/InP nanowire coupled to two electron reservoirs. By means of a specially designed local metallic joule-heater, the temperature of the phonon bath in the vicinity of the double quantum dot can be enhanced. This results in phonon-assisted transport, enabling the conversion of local heat into electrical power in a nanosized heat engine...

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 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...

Single-molecular polymers can be used to analyze to what extent thermodynamics applies when the size of the system is drastically reduced. We have recently verified using molecular-dynamics simulations that isometric and isotensional stretching of a small polymer result in Helmholtz and Gibbs stretching energies, which are not related to a Legendre transform, as they are for sufficiently long polymers. This disparity has also been observed experimentally. Using molecular dynamics simulations of polyethylene-oxide, we document for the first time that the Helmholtz and Gibbs stretching energies can be related by a Legendre-Fenchel transform...

Small system properties are known to depend on geometric variables in ways that are insignificant for macroscopic systems. Small system considerations are therefore usually added to the conventional description as needed. This paper presents a thermodynamic analysis of adsorbed films of any size in a systematic and general way within the framework of Hill's nanothermodynamics. Hill showed how to deal with size and shape as variables in a systematic manner. By doing this, the common thermodynamic equations for adsorption are changed...

As an important property for reflecting the binding forces between atoms, the Debye temperature of nanocrystals can be tuned by size, dimensionality and composition. In order to understand how these factors influence the Debye temperature, in this contribution, a new nanothermodynamic model without any adjustable parameter was established by considering the surface stress and bond number simultaneously. As expected, the Debye temperature decreases with a decrease in size if the dimensionality is given, while the size effect on nanowires is stronger than that on thin films and weaker than that on nanoparticles...

The study of the thermodynamics and structures of iron clusters has been carried on, focusing on small clusters and initial icosahedral and fcc-cuboctahedral structures. Two combined tools are used. First, energy intervals are explored by the Monte Carlo algorithm, called σ-mapping, detailed in the work of Soudan et al. [J. Chem. Phys. 135, 144109 (2011), Paper I]. In its flat histogram version, it provides the classical density of states, gp (Ep ), in terms of the potential energy of the system. Second, the iron system is described by a potential which is called "corrected EAM" (cEAM), explained in the work of Basire et al...

Small systems are known to deviate from the classical thermodynamic description, among other things due to their large surface area to volume ratio compared to corresponding big systems. As a consequence, extensive thermodynamic properties are no longer proportional to the volume, but are instead higher order functions of size and shape. We investigate such functions for second moments of probability distributions of fluctuating properties in the grand-canonical ensemble, focusing specifically on the volume and surface terms of Hadwiger's theorem, explained in Klain, Mathematika, 1995, 42, 329-339...

Understanding the phase diagram is the first step to identifying the structure-performance relationship of a material at the nanoscale. In this work, a modified nanothermodynamical model has been developed to predict the phase diagrams of Ag-Co nanoalloys with the size of 1 ∼ 100 nm, which also overcomes the difference in the predicted results between theory and simulation for the first time. Based on this modified model, the phase diagrams of Ag-Co nanoalloys with various polyhedral morphologies (tetrahedron, cube, octahedron, decahedron, dodecahedron, rhombic dodecahedron, truncated octahedron, cuboctahedron, and icosahedron) have been predicted, showing good agreement with molecular dynamics simulations at the nanoscale of 1 ∼ 4 nm...

The alloy Au-Ag system is an important noble bimetallic phase, both historically (as "Electrum") and now especially in nanotechnology, as it is applied in catalysis and nanomedicine. To comprehend the structural characteristics and the thermodynamic stability of this alloy, a knowledge of its phase diagram is required that considers explicitly its size and shape (morphology) dependence. However, as the experimental determination remains quite challenging at the nanoscale, theoretical guidance can provide significant advantages...

Photodynamic therapy (PDT) involves the action of photons on photosensitive molecules, where atomic oxygen or OH(-) molecular species are locally released on pathogenic human cells, which are mainly carcinogenic, thus causing cell necrosis. The efficacy of PDT depends on the local nanothermodynamic conditions near the cell/nanodrug system that control both the level of intracellular translocation of nanoparticles in the pathogenic cell and their agglomeration on the cell membrane. Dendrimers are considered one of the most effective and promising drug carriers because of their relatively low toxicity and negligible activation of complementary reactions...

The efficiency of penetration of nanodrugs through cell membranes imposes further complexity due to nanothermodynamic and entropic potentials at interfaces. Action of nanodrugs is effective after cell membrane penetration. Contrary to diffusion of water diluted common molecular drugs, nanosize imposes an increasing transport complexity at boundaries and interfaces (e.g., cell membrane). Indeed, tiny dimensional systems brought the concept of "nanothermodynamic potential," which is proportional to the number of nanoentities in a macroscopic system, from either the presence of surface and edge effects at the boundaries of nanoentities or the restriction of the translational and rotational degrees of freedom of molecules within them...

Gold-copper (Au-Cu) phases were employed already by pre-Columbian civilizations, essentially in decorative arts, whereas nowadays, they emerge in nanotechnology as an important catalyst. The knowledge of the phase diagram is critical to understanding the performance of a material. However, experimental determination of nanophase diagrams is rare because calorimetry remains quite challenging at the nanoscale; theoretical investigations, therefore, are welcomed. Using nanothermodynamics, this paper presents the phase diagrams of various polyhedral nanoparticles (tetrahedron, cube, octahedron, decahedron, dodecahedron, rhombic dodecahedron, truncated octahedron, cuboctahedron, and icosahedron) at sizes 4 and 10 nm...