3D Quantum thermodynamic description of the non-equilibrium behavior of an unbounded system at an atomistic level

• Published in: Journal of physics. Conference series 2010-06, Vol.237 (1), p.012022
• Main Authors: Smith, C E, Sciacovelli, A, Spakovsky, M R von, Verda, V
• Format: Article
• Language: English
• Subjects: Carbon; Carbon nanotubes; Eigenvalues; Eigenvectors; Equations of motion; Equilibrium; Evolution; Hydrogen; Physics; Spatial distribution; Thermodynamic equilibrium
• ISSN: 1742-6596; 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/237/1/012022

Quantum thermodynamics (QT) provides a general framework for the description of non-equilibrium phenomena at any level, particularly the atomistic one. This theory and its dynamical postulate are used here to model the storage of hydrogen on and in a carbon nanotube. The tube is placed at the center of a tank with a volume of 250 nm3. The thermodynamic system of interest is the hydrogen, which is assumed isolated and having boundaries that coincide with the walls of the tank and the carbon nanotube. The hydrogen is initially prepared in a state far from stable equilibrium (i.e., with the hydrogen molecules probabilistically near one of the outer tank walls) after which the system is allowed to relax (evolve) to a state of stable equilibrium. To predict this evolution in state, the so-called energy eigenvalue problem, which entails a many-body problem that for dilute and moderately dense gases can be modeled using virial expansion theory, is first solved for the geometry involved. The energy eigenvalues and eigenstates of the system found are then used by the nonlinear Beretta equation of motion of QT to determine the evolution of the thermodynamic state of the system as well as the 3D spatial distributions of the hydrogen molecules in time. The simulation results provide a quantification of the entropy generated due to irreversibilities at an atomistic level and show in detail the trajectory of the thermodynamic state of the system as the hydrogen molecules, which are initially arranged to be far from the carbon nanotube, spread out in the system and eventually become probabilistically more concentrated near the carbon atoms, which make up the nanotube.