Two-dimensional gas

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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:

Contents

  1. the issue being studied actually takes place in two dimensions (as certain surface molecular phenomena); or,
  2. the two-dimensional form of the problem is more tractable than the analogous mathematically more complex three-dimensional problem.

While physicists have studied simple 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 Elastischer stoss 2D.gif
Two-dimensional elastic collision

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 equilibrium velocity 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.

Electron gas

Diagram of cyclotron operation from Lawrence's 1934 patent. Cyclotron patent.png
Diagram of cyclotron operation from Lawrence's 1934 patent.

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 ]

See also

Related Research Articles

The following outline is provided as an overview of and topical guide to chemistry:

<span class="mw-page-title-main">Molecule</span> Electrically neutral group of two or more atoms

A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.

<span class="mw-page-title-main">Metallic bonding</span> Type of chemical bond in metals

Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and lustre.

<span class="mw-page-title-main">Physical chemistry</span> Physics applied to chemical systems

Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mechanics, analytical dynamics and chemical equilibria.

Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together is called the "physical sciences".

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, neuroscience, computer science, information theory and sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.

<span class="mw-page-title-main">Theoretical chemistry</span> Branch of chemistry

Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation.

<span class="mw-page-title-main">Surface science</span> Study of physical and chemical phenomena that occur at the interface of two phases

Surface science is the study of physical and chemical phenomena that occur at the interface of two phases, including solid–liquid interfaces, solid–gas interfaces, solid–vacuum interfaces, and liquid–gas interfaces. It includes the fields of surface chemistry and surface physics. Some related practical applications are classed as surface engineering. The science encompasses concepts such as heterogeneous catalysis, semiconductor device fabrication, fuel cells, self-assembled monolayers, and adhesives. Surface science is closely related to interface and colloid science. Interfacial chemistry and physics are common subjects for both. The methods are different. In addition, interface and colloid science studies macroscopic phenomena that occur in heterogeneous systems due to peculiarities of interfaces.

A thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films is a fundamental step in many applications. A familiar example is the household mirror, which typically has a thin metal coating on the back of a sheet of glass to form a reflective interface. The process of silvering was once commonly used to produce mirrors, while more recently the metal layer is deposited using techniques such as sputtering. Advances in thin film deposition techniques during the 20th century have enabled a wide range of technological breakthroughs in areas such as magnetic recording media, electronic semiconductor devices, integrated passive devices, LEDs, optical coatings, hard coatings on cutting tools, and for both energy generation and storage. It is also being applied to pharmaceuticals, via thin-film drug delivery. A stack of thin films is called a multilayer.

<span class="mw-page-title-main">Heterogeneous catalysis</span> Type of catalysis involving reactants & catalysts in different phases of matter

Heterogeneous catalysis is catalysis where the phase of catalysts differs from that of the reactants or products. The process contrasts with homogeneous catalysis where the reactants, products and catalyst exist in the same phase. Phase distinguishes between not only solid, liquid, and gas components, but also immiscible mixtures, or anywhere an interface is present.

Desorption is the physical process where adsorbed atoms or molecules are released from a surface into the surrounding vacuum or fluid. This occurs when a molecule gains enough energy to overcome the activation barrier and the binding energy that keep it attached to the surface.

<span class="mw-page-title-main">Self-assembled monolayer</span>

Self-assembled monolayers (SAM) of organic molecules are molecular assemblies formed spontaneously on surfaces by adsorption and are organized into more or less large ordered domains. In some cases molecules that form the monolayer do not interact strongly with the substrate. This is the case for instance of the two-dimensional supramolecular networks of e.g. perylenetetracarboxylic dianhydride (PTCDA) on gold or of e.g. porphyrins on highly oriented pyrolitic graphite (HOPG). In other cases the molecules possess a head group that has a strong affinity to the substrate and anchors the molecule to it. Such a SAM consisting of a head group, tail and functional end group is depicted in Figure 1. Common head groups include thiols, silanes, phosphonates, etc.

Inelastic electron tunneling spectroscopy (IETS) is an experimental tool for studying the vibrations of molecular adsorbates on metal oxides. It yields vibrational spectra of the adsorbates with high resolution (< 0.5 meV) and high sensitivity (< 1013 molecules are required to provide a spectrum). An additional advantage is the fact that optically forbidden transitions may be observed as well. Within IETS, an oxide layer with molecules adsorbed on it is put between two metal plates. A bias voltage is applied between the two contacts. An energy diagram of the metal-oxide-metal device under bias is shown in the top figure. The metal contacts are characterized by a constant density of states, filled up to the Fermi energy. The metals are assumed to be equal. The adsorbates are situated on the oxide material. They are represented by a single bridge electronic level, which is the upper dashed line. If the insulator is thin enough, there is a finite probability that the incident electron tunnels through the barrier. Since the energy of the electron is not changed by this process, it is an elastic process. This is shown in the left figure.

Molecular scale electronics, also called single-molecule electronics, is a branch of nanotechnology that uses single molecules, or nanoscale collections of single molecules, as electronic components. Because single molecules constitute the smallest stable structures imaginable, this miniaturization is the ultimate goal for shrinking electrical circuits.

Adsorption is the adhesion of ions or molecules onto the surface of another phase. Adsorption may occur via physisorption and chemisorption. Ions and molecules can adsorb to many types of surfaces including polymer surfaces. A polymer is a large molecule composed of repeating subunits bound together by covalent bonds. In dilute solution, polymers form globule structures. When a polymer adsorbs to a surface that it interacts favorably with, the globule is essentially squashed, and the polymer has a pancake structure.

The strength of metal oxide adhesion effectively determines the wetting of the metal-oxide interface. The strength of this adhesion is important, for instance, in production of light bulbs and fiber-matrix composites that depend on the optimization of wetting to create metal-ceramic interfaces. The strength of adhesion also determines the extent of dispersion on catalytically active metal. Metal oxide adhesion is important for applications such as complementary metal oxide semiconductor devices. These devices make possible the high packing densities of modern integrated circuits.

A two-dimensional liquid is a collection of objects constrained to move in a planar space or other two-dimensional space in a liquid state.

The pseudo Jahn–Teller effect (PJTE), occasionally also known as second-order JTE, is a direct extension of the Jahn–Teller effect (JTE) where spontaneous symmetry breaking in polyatomic systems occurs even when the relevant electronic states are not degenerate. The PJTE can occur under the influence of sufficiently low-lying electronic excited states of appropriate symmetry. "The pseudo Jahn–Teller effect is the only source of instability and distortions of high-symmetry configurations of polyatomic systems in nondegenerate states, and it contributes significantly to the instability in degenerate states".

Artificial lattice is a term encompassing every atomic-scale structures designed and controlled to confine electrons onto a chosen lattice. Research has been done on multiple geometries and one of the most notable being what is called molecular graphene. Molecular graphene is a part of two-dimensional artificial lattices.

Shirley Chiang is an American microscopist focused on the high-resolution imaging of surfaces, including the use of scanning tunneling microscopy and low-energy electron microscopy, and known for capturing the first image showing the ring structure of benzene molecules. She is a professor at the University of California, Davis, in the Department of Physics and Astronomy, and editor-in-chief of the MDPI journal Nanomaterials.

References

  1. Feld; et al. (2011). "Observation of a pairing pseudogap in a two-dimensional gas". Nature. 480 (7375): 75–78. arXiv: 1110.2418 . Bibcode:2011Natur.480...75F. doi:10.1038/nature10627. PMID   22129727. S2CID   4425050.
  2. C.M.Hogan, Non-equilibrium statistical mechanics of a two-dimensional gas, Dissertation, Princeton University, Department of Physics, May 4, 1964
  3. D. Risso and P. Cordero, Two-Dimensional Gas of Disks: Thermal Conductivity , Journal of Statistical Physics , volume 82, pages 1453–1466, (1996)
  4. Kohn, Walter (1961). "Cyclotron Resonance and de Haas–van Alphen Oscillations of an Interacting Electron Gas". Physical Review . 123 (4): 1242–1244. Bibcode:1961PhRv..123.1242K. doi:10.1103/physrev.123.1242.
  5. Vanderlei Bagnato and Daniel Kleppner. Bose–Einstein condensation in low-dimensional traps, American Physical Society, 8 April 1991
  6. 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
  7. Kroger, I. (2009). "Tuning intermolecular interaction in long-range-ordered submonolayer organic films". Nature Physics. 5 (2): 153–158. Bibcode:2009NatPh...5..153S. doi:10.1038/nphys1176.
  8. 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. PMID   28830146.
  9. 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, PMID   23047526, S2CID   36848079
  10. Matvija, Peter; Rozbořil, Filip; Sobotík, Pavel; Ošťádal, Ivan; Pieczyrak, Barbara; Jurczyszyn, Leszek; Kocán, Pavel (2017). "Electric-field-controlled phase transition in a 2D molecular layer". Scientific Reports. 7 (1): 7357. Bibcode:2017NatSR...7.7357M. doi:10.1038/s41598-017-07277-7. PMC   5544747 . PMID   28779091.