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Special Issue "Nanothermodynamics"

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (30 June 2015)

Special Issue Editors

Guest Editor
Prof. Dr. A. Perez-Madrid

Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Spain
Interests: inhomogeneous systems; energy conversion and storage; small systems; entropic forces; long-range interactions; fluctuations
Guest Editor
Prof. Dr. Iván Santamaría-Holek

UMDI-J Facultad de Ciencias, Universidad Nacional Autónoma de México Campus Juriquilla, Mexico

Special Issue Information

Dear Colleagues,

Recent advances in nanotechnology have favoured a renewed interest in thermodynamics far below macroscopic scales –nanothermodynamics. Such attention to small and nanoscale systems has raised the issue of the applicability of thermodynamic concepts at this level. Roughly speaking, we can say that small and nanoscale systems are those in which the range of interactions is of the order of the size of the system or contain a finite number of particles. However, we can anticipate that results in nanothermodynamics can also be extrapolated to very large self-gravitating systems. Boundary or surface effects, inhomogeneity, non-extensivity, large fluctuations are some of the peculiarities of these systems which can only be revealed through a thermodynamic description. Since the Gibbs-Duhem equation ceases to be valid here, small systems have more degrees of freedom. This means for example, that in general the temperature of the system does not coincide with the bath temperature - except in some particular range of control parameters. Also, confinement causes large fluctuations and unleashes entropic forces in such a way that thermodynamic properties depend on the environment with the concomitant ensemble inequivalence that this brings about. Therefore, the necessity of a particular thermodynamic description adapted to these small and nanoscale systems becomes manifest.

Prof. Dr. A. Perez-Madrid
Prof. Dr. Iván Santamaría-Holek
Guest Editors

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs).

Keywords

  • Ensemble inequivalence
  • symmetry breaking
  • inhomogeneous systems
  • thermal properties
  • fluctuations
  • metastable states
  • nanomotors
  • energy conversion and storage
  • small systems
  • entropic forces
  • long-range interactions

Published Papers (6 papers)

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Research

Jump to: Review

Open AccessArticle Dynamics and Thermodynamics of Nanoclusters
Entropy 2015, 17(10), 7133-7148; doi:10.3390/e17107133
Received: 8 June 2015 / Revised: 22 September 2015 / Accepted: 25 September 2015 / Published: 22 October 2015
Cited by 1 | PDF Full-text (1194 KB) | HTML Full-text | XML Full-text
Abstract
The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained [...] Read more.
The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained in the canonical ensemble. Nanoclusters in the microcanonical ensemble are trapped systems, and inconsistencies will be found if thermodynamic formalism is applied. An analytical model is given for the energy dependence of the phase space volume of nanoclusters, which allows the prediction of both dynamical and thermodynamical properties. Full article
(This article belongs to the Special Issue Nanothermodynamics)
Figures

Open AccessArticle Mesoscopic Thermodynamics for the Dynamics of Small-Scale Systems
Entropy 2015, 17(10), 7201-7212; doi:10.3390/e17107201
Received: 7 September 2015 / Revised: 13 October 2015 / Accepted: 19 October 2015 / Published: 22 October 2015
PDF Full-text (740 KB) | HTML Full-text | XML Full-text
Abstract
We analyze the mesoscopic dynamics of small-scale systems from the perspective of mesoscopic non-equilibrium thermodynamics. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability density of the mesoscopic variables and the nonlinear relationships between activation rates and affinities [...] Read more.
We analyze the mesoscopic dynamics of small-scale systems from the perspective of mesoscopic non-equilibrium thermodynamics. The theory obtains the Fokker–Planck equation as a diffusion equation for the probability density of the mesoscopic variables and the nonlinear relationships between activation rates and affinities proper of activated processes. The situations that can be studied with this formalism include, among others, barrier crossing dynamics and non-linear transport in a great variety of systems. We, in particular, consider the cases of single-molecule stretching and activated processes in small systems. Full article
(This article belongs to the Special Issue Nanothermodynamics)
Figures

Open AccessArticle Reaction Kinetic Parameters and Surface Thermodynamic Properties of Cu2O Nanocubes
Entropy 2015, 17(8), 5437-5449; doi:10.3390/e17085437
Received: 15 May 2015 / Revised: 18 June 2015 / Accepted: 1 July 2015 / Published: 30 July 2015
Cited by 2 | PDF Full-text (1688 KB) | HTML Full-text | XML Full-text
Abstract
Cuprous oxide (Cu2O) nanocubes were synthesized by reducing Cu(OH)2 in the presence of sodium citrate at room temperature. The samples were characterized in detail by field-emission scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, X-ray powder diffraction, [...] Read more.
Cuprous oxide (Cu2O) nanocubes were synthesized by reducing Cu(OH)2 in the presence of sodium citrate at room temperature. The samples were characterized in detail by field-emission scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, X-ray powder diffraction, and N2 absorption (BET specific surface area). The equations for acquiring reaction kinetic parameters and surface thermodynamic properties of Cu2O nanocubes were deduced by establishment of the relations between thermodynamic functions of Cu2O nanocubes and these of the bulk Cu2O. Combined with thermochemical cycle, transition state theory, basic theory of chemical thermodynamics, and in situ microcalorimetry, reaction kinetic parameters, specific surface enthalpy, specific surface Gibbs free energy, and specific surface entropy of Cu2O nanocubes were successfully determined. We also introduced a universal route for gaining reaction kinetic parameters and surface thermodynamic properties of nanomaterials. Full article
(This article belongs to the Special Issue Nanothermodynamics)
Open AccessArticle Synthesis and Surface Thermodynamic Functions of CaMoO4 Nanocakes
Entropy 2015, 17(5), 2741-2748; doi:10.3390/e17052741
Received: 25 January 2015 / Revised: 13 April 2015 / Accepted: 16 April 2015 / Published: 30 April 2015
Cited by 3 | PDF Full-text (475 KB) | HTML Full-text | XML Full-text
Abstract
CaMoO4 nanocakes with uniform size and morphology were prepared on a large scale via a room temperature reverse-microemulsion method. The products were characterized in detail by X-ray powder diffraction, field-emission scanning electron microscopy, transmission electron microscopy, and high-resolution transmission electron microscopy. [...] Read more.
CaMoO4 nanocakes with uniform size and morphology were prepared on a large scale via a room temperature reverse-microemulsion method. The products were characterized in detail by X-ray powder diffraction, field-emission scanning electron microscopy, transmission electron microscopy, and high-resolution transmission electron microscopy. By establishing the relations between the thermodynamic functions of nano-CaMoO4 and bulk-CaMoO4 reaction systems, the equations for calculating the surface thermodynamic functions of nano-CaMoO4 were derived. Then, combined with in-situ microcalorimetry, the molar surface enthalpy, molar surface Gibbs free energy, and molar surface entropy of the prepared CaMoO4 nanocakes at 298.15 K were successfully obtained as (19.674 ± 0.017) kJ·mol−1, (619.704 ± 0.016) J·mol−1, and (63.908 ± 0.057) J·mol−1·K−1, respectively. Full article
(This article belongs to the Special Issue Nanothermodynamics)
Open AccessArticle A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics)
Entropy 2015, 17(3), 1309-1328; doi:10.3390/e17031309
Received: 31 January 2015 / Revised: 5 March 2015 / Accepted: 10 March 2015 / Published: 16 March 2015
Cited by 8 | PDF Full-text (773 KB) | HTML Full-text | XML Full-text
Abstract
The interest in designing nanosystems is continuously growing. Engineers apply a great number of optimization methods to design macroscopic systems. If these methods could be introduced into the design of small systems, a great improvement in nanotechnologies could be achieved. To do [...] Read more.
The interest in designing nanosystems is continuously growing. Engineers apply a great number of optimization methods to design macroscopic systems. If these methods could be introduced into the design of small systems, a great improvement in nanotechnologies could be achieved. To do so, however, it is necessary to extend classical thermodynamic analysis to small systems, but irreversibility is also present in small systems, as the Loschmidt paradox highlighted. Here, the use of the recent improvement of the Gouy-Stodola theorem to complex systems (GSGL approach), based on the use of entropy generation, is suggested to obtain the extension of classical thermodynamics to nanothermodynamics. The result is a new approach to nanosystems which avoids the difficulties highlighted in the usual analysis of the small systems, such as the definition of temperature for nanosystems. Full article
(This article belongs to the Special Issue Nanothermodynamics)

Review

Jump to: Research

Open AccessReview The Big World of Nanothermodynamics
Entropy 2015, 17(1), 52-73; doi:10.3390/e17010052
Received: 11 November 2014 / Accepted: 23 December 2014 / Published: 31 December 2014
Cited by 5 | PDF Full-text (7067 KB) | HTML Full-text | XML Full-text
Abstract
Nanothermodynamics extends standard thermodynamics to facilitate finite-size effects on the scale of nanometers. A key ingredient is Hill’s subdivision potential that accommodates the non-extensive energy of independent small systems, similar to how Gibbs’ chemical potential accommodates distinct particles. Nanothermodynamics is essential for [...] Read more.
Nanothermodynamics extends standard thermodynamics to facilitate finite-size effects on the scale of nanometers. A key ingredient is Hill’s subdivision potential that accommodates the non-extensive energy of independent small systems, similar to how Gibbs’ chemical potential accommodates distinct particles. Nanothermodynamics is essential for characterizing the thermal equilibrium distribution of independently relaxing regions inside bulk samples, as is found for the primary response of most materials using various experimental techniques. The subdivision potential ensures strict adherence to the laws of thermodynamics: total energy is conserved by including an instantaneous contribution from the entropy of local configurations, and total entropy remains maximized by coupling to a thermal bath. A unique feature of nanothermodynamics is the completely-open nanocanonical ensemble. Another feature is that particles within each region become statistically indistinguishable, which avoids non-extensive entropy, and mimics quantum-mechanical behavior. Applied to mean-field theory, nanothermodynamics gives a heterogeneous distribution of regions that yields stretched-exponential relaxation and super-Arrhenius activation. Applied to Monte Carlo simulations, there is a nonlinear correction to Boltzmann’s factor that improves agreement between the Ising model and measured non-classical critical scaling in magnetic materials. Nanothermodynamics also provides a fundamental mechanism for the 1/f noise found in many materials. Full article
(This article belongs to the Special Issue Nanothermodynamics)

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