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.
While
two body interactions on a plane for centuries, the attention given to the two-dimensional gas (having many bodies in motion) is a 20th-century pursuit. Applications have led to better understanding of superconductivity,[1] gas thermodynamics, certain solid state problems and several questions in quantum mechanics
.
Classical mechanics
Two-dimensional elastic collision
Research at
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.
Electron gas
See also:
Lawrence's
1934 patent.
While the principle of 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
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
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
