A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: classical ideal gas elements such as rigid disks undergoing elastic collisions; elementary particles, or any ensemble of individual objects in physics which obeys laws of motion without binding interactions. The concept of a two-dimensional gas is used either because:
the issue being studied actually takes place in two dimensions (as certain surface molecular phenomena); or,
the two-dimensional form of the problem is more tractable than the analogous mathematically more complex three-dimensional problem.
Research at Princeton University in the early 1960s[2] posed the question of whether the Maxwell–Boltzmann statistics and other thermodynamic laws could be derived from Newtonian laws applied to multi-body systems rather than through the conventional methods of statistical mechanics. While this question appears intractable from a three-dimensional closed form solution, the problem behaves differently in two-dimensional space. In particular an ideal two-dimensional gas was examined from the standpoint of relaxation time to equilibriumvelocity distribution given several arbitrary initial conditions of the ideal gas. Relaxation times were shown to be very fast: on the order of mean free time .
In 1996 a computational approach was taken to the classical mechanics non-equilibrium problem of heat flow within a two-dimensional gas.[3] This simulation work showed that for N>1500, good agreement with continuous systems is obtained.
While the principle of the cyclotron to create a two-dimensional array of electrons has existed since 1934, the tool was originally not really used to analyze interactions among the electrons (e.g. two-dimensional gas dynamics). An early research investigation explored cyclotron resonance behavior and the de Haas–van Alphen effect in a two-dimensional electron gas.[4] The investigator was able to demonstrate that for a two-dimensional gas, the de Haas–van Alphen oscillation period is independent of the short-range electron interactions.
Later applications to Bose gas
In 1991 a theoretical proof was made that a Bose gas can exist in two dimensions.[5] In the same work an experimental recommendation was made that could verify the hypothesis.
Experimental research with a molecular gas
In general, 2D molecular gases are experimentally observed on weakly interacting surfaces such as metals, graphene etc. at a non-cryogenic temperature and a low surface coverage. As a direct observation of individual molecules is not possible due to fast diffusion of molecules on a surface, experiments are either indirect (observing an interaction of a 2D gas with surroundings, e.g. condensation of a 2D gas) or integral (measuring integral properties of 2D gases, e.g. by diffraction methods).
An example of the indirect observation of a 2D gas is the study of Stranick et al. who used a scanning tunnelling microscope in ultrahigh vacuum (UHV) to image an interaction of a two-dimensional benzene gas layer in contact with a planar solid interface at 77 kelvins.[6] The experimenters were able to observe mobile benzene molecules on the surface of Cu(111), to which a planar monomolecular film of solid benzene adhered. Thus the scientists could witness the equilibrium of the gas in contact with its solid state.
Integral methods that are able to characterize a 2D gas usually fall into a category of diffraction (see for example study of Kroger et al.[7]). The exception is the work of Matvija et al. who used a scanning tunneling microscope to directly visualize a local time-averaged density of molecules on a surface.[8] This method is of special importance as it provides an opportunity to probe local properties of 2D gases; for instance it enables to directly visualize a pair correlation function of a 2D molecular gas in a real space.
If the surface coverage of adsorbates is increased, a 2D liquid is formed,[9] followed by a 2D solid. It was shown that the transition from a 2D gas to a 2D solid state can be controlled by a scanning tunneling microscope which can affect the local density of molecules via an electric field.[10]
Implications for future research
A multiplicity of theoretical physics research directions exist for study via a two-dimensional gas, such as:[citation needed]
Complex quantum mechanics phenomena, whose solutions may be more appropriate in a two-dimensional environment;
Stranick, S. J.; Kamna, M. M.; Weiss, P. S, Atomic Scale Dynamics of a Two-Dimensional Gas-Solid Interface, Pennsylvania State University, Park Dept. of Chemistry, 3 June 1994
Matvija, Peter; Rozbořil, Filip; Sobotík, Pavel; Ošťádal, Ivan; Kocán, Pavel (2017). "Pair correlation function of a 2D molecular gas directly visualized by scanning tunneling microscopy". The Journal of Physical Chemistry Letters. 8 (17): 4268–4272. doi:10.1021/acs.jpclett.7b01965. PMID28830146.
Thomas Waldmann; Jens Klein; Harry E. Hoster; R. Jürgen Behm (2012), "Stabilization of Large Adsorbates by Rotational Entropy: A Time-Resolved Variable-Temperature STM Study", ChemPhysChem (in German), vol.14, no.1, pp.162–169, doi:10.1002/cphc.201200531, PMID23047526, S2CID36848079
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