Ensemble statistique

En physique statistique, un ensemble statistique est une abstraction qui consiste à considérer une collection de copies virtuelles (ou répliques) d'un système physique dans l'ensemble des états accessibles où il est susceptible de se trouver, compte tenu des contraintes extérieures qui lui sont imposées, telles le volume, le nombre de particules, l'énergie et la température. Cette notion, introduite par le physicien américain Josiah Willard Gibbs en 1902, est un concept central de la physique statistique. En effet l'état microscopique d'un système physique fluctue en général au cours du temps, même si celui-ci est à l'équilibre. Sauf pour des systèmes très simples il est impossible de connaître exactement à tout instant ces fluctuations, ne serait ce qu'en raison du très grand nombre de degrés de liberté microscopiques du système. Or les grandeurs physiques, telles l'énergie, la pression et la densité, résultent en principe de l'évaluation de moyennes temporelles qu'il est pratiquemen

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (6)

Publications associées

Chargement

Personnes associées

Chargement

Unités associées

Chargement

Concepts associés (36)

Concepts associés

Chargement

Cours associés (15)

Cours associés

Chargement

Séances de cours associées (30)

Séances de cours associées

Chargement

High-Throughput Sizing, Counting, and Elemental Analysis of Anisotropic Multimetallic Nanoparticles with Single-Particle Inductively Coupled Plasma Mass Spectrometry

Ayush Agarwal, Natalia Gasilova, Cedric David Koolen, Mo Li, Wen Luo, Andreas Züttel

Nanoparticles (NPs) have wide applications in physical and chemical processes, and their individual properties (e.g., shape, size, and composition) and ensemble properties (e.g., distribution and homogeneity) can significantly affect the performance. However, the extrapolation of information from a single particle to the ensemble remains a challenge due to the lack of suitable techniques. Herein, we report a high-throughput single-particle inductively coupled plasma mass spectrometry (SP-ICP-MS)-based protocol to simultaneously determine the size, count, and elemental makeup of several thousands of (an)isotropic NPs independent of composition, size, shape, and dispersing medium with atomistic precision in a matter of minutes. By introducing highly diluted nebulized aqueous dispersions of NPs directly into the plasma torch of an ICP-MS instrument, individual NPs are atomized and ionized, resulting in ion plumes that can be registered by the mass analyzer. Our proposed protocol includes a phase transfer step for NPs synthesized in organic media, which are otherwise incompatible with ICP-MS instruments, and a modeling tool that extends the measurement of particle morphologies beyond spherical to include cubes, truncated octahedra, and tetrahedra, exemplified by anisotropic Cu NPs. Finally, we demonstrate the versatility of our method by studying the doping of bulk-dilute (

2022

Chargement

Isobaric first-principles molecular dynamics of liquid water with nonlocal van der Waals interactions

Giacomo Francesco Leonardo Miceli, Alfredo Pasquarello

We investigate the structural properties of liquid water at near ambient conditions using first-principles molecular dynamics simulations based on a semilocal density functional augmented with nonlocal van der Waals interactions. The adopted scheme offers the advantage of simulating liquid water at essentially the same computational cost of standard semilocal functionals. Applied to the water dimer and to ice I-h, we find that the hydrogen-bond energy is only slightly enhanced compared to a standard semilocal functional. We simulate liquid water through molecular dynamics in the N pH statistical ensemble allowing for fluctuations of the system density. The structure of the liquid departs from that found with a semilocal functional leading to more compact structural arrangements. This indicates that the directionality of the hydrogen-bond interaction has a diminished role as compared to the overall attractions, as expected when dispersion interactions are accounted for. This is substantiated through a detailed analysis comprising the study of the partial radial distribution functions, various local order indices, the hydrogen-bond network, and the selfdiffusion coefficient. The explicit treatment of the van der Waals interactions leads to an overall improved description of liquid water. (c) 2015 AIP Publishing LLC.

American Institute of Physics2015

Chargement

Scaling analyses for hyperpolarization transfer across a spin-diffusion barrier and into bulk solid media

Bradley Floyd Chmelka, David Lyndon Emsley, Arthur César Pinon

By analogy to heat and mass transfer film theory, a general approach is introduced for determining hyperpolarization transfer rates between dilute electron spins and a surrounding nuclear ensemble. These analyses provide new quantitative relationships for understanding, predicting, and optimizing the effectiveness of hyperpolarization protocols, such as Dynamic Nuclear Polarization (DNP) under magic-angle spinning conditions. An empirical DNP polarization-transfer coefficient is measured as a function of the bulk matrix H-1 spin density and indicates the presence of two distinct kinetic regimes associated with different rate-limiting polarization transfer phenomena. Dimensional property relationships are derived and used to evaluate the competitive rates of spin polarization generation, propagation, and dissipation that govern hyperpolarization transfer between large coupled spin ensembles. The quantitative analyses agree closely with experimental measurements for the accumulation, propagation, and dissipation of hyperpolarization in solids and provide evidence for kinetically-limited transfer associated with a spin-diffusion barrier. The results and classical approach yield general design criteria for analyzing and optimizing polarization transfer processes involving complex interfaces and composite media for applications in materials science, physical chemistry and nuclear spintronics.

ROYAL SOC CHEMISTRY2021

Chargement

Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any

Willard Gibbs

Josiah Willard Gibbs ( ; New Haven, - New Haven, ) est un physico-chimiste américain. Son travail sur l'application à la chimie de la thermodynamique joue un grand rôle dans la transformation de la

Fonction de partition

En physique statistique, la fonction de partition Z est une grandeur fondamentale qui englobe les propriétés statistiques d'un système à l'équilibre thermodynamique. C'est une fonction de la tempéra

PHYS-441: Statistical physics of biomacromolecules

Introduction to the application of the notions and methods of theoretical physics to problems in biology.

PHYS-315: Statistical physics I

L'objectif du cours est d'introduire les concepts fondamentaux de la physique statistique.

PHYS-316: Statistical physics II

Introduction à la théorie des transitions de phase