Widom line

Last updated

In the context of the pressure-temperature phase diagram of a substance and of the supercritical fluid state in particular, the Widom line is a line emanating from the critical point which in a way extends the liquid-vapor coexistence curve above the critical point. It corresponds to the maxima or minima of certain physical properties of the supercritical fluid, such as the speed of sound, isothermal compressibility, isochoric and isobaric heat capacities. A common criterion for locating the Widom line is indeed the maximum in the isobaric heat capacity.

Contents

More generally, the Widom line is defined as the line in the pressure-temperature phase diagram of a fluid substance along which the correlation length has its maximum. [1] It always emanates from a critical point. It has been investigated for various systems, including for example in the context of the hypothesized liquid–liquid critical point (or second critical point) of water. [2]

Similar boundary lines include the Fisher-Widom line and the Frenkel line, which also describe transitions between distinct fluid behaviors.

Overview

Pressure-temperature phase diagram. The supercritical state is at pressures and temperatures above those of the critical point, but below the pressures required for transformation into a solid. The dashed green line shows the anomalous slope of the solid-liquid phase boundary for some substances, including water. Phase-diag2.svg
Pressure–temperature phase diagram. The supercritical state is at pressures and temperatures above those of the critical point, but below the pressures required for transformation into a solid. The dashed green line shows the anomalous slope of the solid-liquid phase boundary for some substances, including water.

Named after theoretical physicist Benjamin Widom, the Widom line is a crucial concept in fluid thermodynamics and critical phenomena.

The Widom line has been suggested [3] to separate liquid-like behaviour and gas-like behaviour in supercritical fluids, where the traditional distinction between liquid and gas no longer exists. Specifically, on the low-pressure side of the line, the fluid exhibits a gas-like behavior, while on the high-pressure side, it behaves more like a liquid. This separation is not a sharp phase change but a continuous crossover in some of the properties of the fluid. It has been observed in laboratory experiments, for example on fluid methane. [4] The concept of Widom line provides a useful framework for characterizing and predicting the properties of fluids, which are important for scientific research as well as various industrial processes. Such a concept is indeed relevant to the physical properties of any single-component fluid at sufficiently high pressures and temperatures, and its study is an active research area.


See also

Related Research Articles

<span class="mw-page-title-main">Boiling point</span> Temperature at which a substance changes from liquid into vapor

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

<span class="mw-page-title-main">Heat engine</span> System that converts heat or thermal energy to mechanical work

A heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the higher temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a lower temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.

<span class="mw-page-title-main">Phase (matter)</span> Region of uniform physical properties

In the physical sciences, a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is a different material, in its own separate phase.

<span class="mw-page-title-main">Triple point</span> Thermodynamic point where three matter phases exist

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation, fusion, and vaporisation curves meet. For example, the triple point of mercury occurs at a temperature of −38.8 °C (−37.8 °F) and a pressure of 0.165 mPa.

<span class="mw-page-title-main">Vapor</span> Substances in the gas phase at a temperature lower than its critical point

In physics, a vapor or vapour is a substance in the gas phase at a temperature lower than its critical temperature, which means that the vapor can be condensed to a liquid by increasing the pressure on it without reducing the temperature of the vapor. A vapor is different from an aerosol. An aerosol is a suspension of tiny particles of liquid, solid, or both within a gas.

<span class="mw-page-title-main">State of matter</span> Forms, such as solid, liquid and gas, which matter can take

In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates and Fermionic condensates, neutron-degenerate matter, and quark–gluon plasma.

<span class="mw-page-title-main">Phase diagram</span> Chart used to show conditions at which physical phases of a substance occur

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases occur and coexist at equilibrium.

In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure, volume and temperature, in thermodynamic equilibrium. If F is the number of degrees of freedom, C is the number of components and P is the number of phases, then

A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist, but below the pressure required to compress it into a solid. It can effuse through porous solids like a gas, overcoming the mass transfer limitations that slow liquid transport through such materials. SCFs are superior to gases in their ability to dissolve materials like liquids or solids. Also, near the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be "fine-tuned".

Supercritical may refer to:

<span class="mw-page-title-main">Critical point (thermodynamics)</span> Temperature and pressure point where phase boundaries disappear

In thermodynamics, a critical point is the end point of a phase equilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas comes into a supercritical phase, and so cannot be liquefied by pressure alone. At the critical point, defined by a critical temperatureTc and a critical pressurepc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition in the absence of an external magnetic field.

<span class="mw-page-title-main">Supercritical drying</span> Process to remove liquid

Supercritical drying, also known as critical point drying, is a process to remove liquid in a precise and controlled way. It is useful in the production of microelectromechanical systems (MEMS), the drying of spices, the production of aerogel, the decaffeination of coffee and in the preparation of biological specimens.

<span class="mw-page-title-main">Supercritical carbon dioxide</span> Carbon dioxide above its critical point

Supercritical carbon dioxide is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure.

<span class="mw-page-title-main">Polyamorphism</span> Ability of a substance to exist in more than one distinct amorphous state

Polyamorphism is the ability of a substance to exist in several different amorphous modifications. It is analogous to the polymorphism of crystalline materials. Many amorphous substances can exist with different amorphous characteristics. However, polyamorphism requires two distinct amorphous states with a clear, discontinuous (first-order) phase transition between them. When such a transition occurs between two stable liquid states, a polyamorphic transition may also be referred to as a liquid–liquid phase transition.

Supercritical fluid chromatography (SFC) is a form of normal phase chromatography that uses a supercritical fluid such as carbon dioxide as the mobile phase. It is used for the analysis and purification of low to moderate molecular weight, thermally labile molecules and can also be used for the separation of chiral compounds. Principles are similar to those of high performance liquid chromatography (HPLC); however, SFC typically utilizes carbon dioxide as the mobile phase. Therefore, the entire chromatographic flow path must be pressurized. Because the supercritical phase represents a state whereby bulk liquid and gas properties converge, supercritical fluid chromatography is sometimes called convergence chromatography. The idea of liquid and gas properties convergence was first envisioned by Giddings.

<span class="mw-page-title-main">Transcritical cycle</span> Closed thermodynamic cycle involving fluid

A transcritical cycle is a closed thermodynamic cycle where the working fluid goes through both subcritical and supercritical states. In particular, for power cycles the working fluid is kept in the liquid region during the compression phase and in vapour and/or supercritical conditions during the expansion phase. The ultrasupercritical steam Rankine cycle represents a widespread transcritical cycle in the electricity generation field from fossil fuels, where water is used as working fluid. Other typical applications of transcritical cycles to the purpose of power generation are represented by organic Rankine cycles, which are especially suitable to exploit low temperature heat sources, such as geothermal energy, heat recovery applications or waste to energy plants. With respect to subcritical cycles, the transcritical cycle exploits by definition higher pressure ratios, a feature that ultimately yields higher efficiencies for the majority of the working fluids. Considering then also supercritical cycles as a valid alternative to the transcritical ones, the latter cycles are capable of achieving higher specific works due to the limited relative importance of the work of compression work. This evidences the extreme potential of transcritical cycles to the purpose of producing the most power with the least expenditure.

<span class="mw-page-title-main">Superheated water</span> Pressurized liquid water at temperatures between the boiling and critical points

Superheated water is liquid water under pressure at temperatures between the usual boiling point, 100 °C (212 °F) and the critical temperature, 374 °C (705 °F). It is also known as "subcritical water" or "pressurized hot water". Superheated water is stable because of overpressure that raises the boiling point, or by heating it in a sealed vessel with a headspace, where the liquid water is in equilibrium with vapour at the saturated vapor pressure. This is distinct from the use of the term superheating to refer to water at atmospheric pressure above its normal boiling point, which has not boiled due to a lack of nucleation sites.

Supercritical adsorption also referred to as the adsorption of supercritical fluids, is the adsorption at above-critical temperatures. There are different tacit understandings of supercritical fluids. For example, “a fluid is considered to be ‘supercritical’ when its temperature and pressure exceed the temperature and pressure at the critical point”. In the studies of supercritical extraction, however, “supercritical fluid” is applied for a narrow temperature region of 1-1.2 or to +10 K, which is called the supercritical region.

Supercritical liquid–gas boundaries are lines in the pressure-temperature (pT) diagram that delimit more liquid-like and more gas-like states of a supercritical fluid. They comprise the Fisher–Widom line, the Widom line, and the Frenkel line.

In thermodynamics, the Frenkel line is a proposed boundary on the phase diagram of a supercritical fluid, separating regions of qualitatively different behavior. Fluids on opposite sides of the line have been described as "liquidlike" or "gaslike", and exhibit different behaviors in terms of oscillation, excitation modes, and diffusion.

References

  1. H. E. Stanley, P. Kumar, G. Franzese, L. Xu, Z. Yan, M. G. Mazza, S. V. Buldyrev, S.-H. Chen and F. Mallamace "Liquid polyamorphism: Possible relation to the anomalous behaviour of water", European Physical Journal - Special Topics 161 pp. 1-17 (2008)
  2. Limei Xu, Pradeep Kumar, S. V. Buldyrev, S.-H. Chen, P. H. Poole, F. Sciortino, and H. E. Stanley "Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition", PNAS 102 pp. 16558-16562 (2005)
  3. Simeoni, Giovanna Giulia; Bryk, Taras; Gorelli, Federico Aiace; Krisch, Michael; Ruocco, Giancarlo; Santoro, Mario; Scopigno, Tullio (2010). "The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids". Nature Physics. 6 (7): 503–507. Bibcode:2010NatPh...6..503S. doi: 10.1038/nphys1683 . ISSN   1745-2473.
  4. U. Ranieri, F. Formisano, F. A. Gorelli, M. Santoro, M. M. Koza, A. De Francesco, L. E. Bove "Crossover from gas-like to liquid-like molecular diffusion in a simple supercritical fluid", Nature Communications 15, 4142 (2024)