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The '''Noro–Frenkel law of corresponding states''' is an equation in [[thermodynamics]] that describes the critical temperature of the liquid-gas transition T as a function of the range of the attractive potential ''R''. It states that, all short-ranged spherically symmetric pair-wise additive attractive potentials are characterised by the same thermodynamics properties if compared at the same reduced density and second [[virial coefficient]]<ref>
{{cite journal
  |author=M.G. Noro and D. Frenkel
|year=2000
|title=Extended corresponding-states behavior for particles with variable range attractions
  |journal=[[Journal of Chemical Physics]]
|volume=113
|issue=8 |pages=2941
|doi=10.1063/1.1288684
|arxiv = cond-mat/0004033 |bibcode = 2000JChPh.113.2941N }}</ref>
 
==Description==
 
[[Johannes Diderik van der Waals]]'s [[Theorem of corresponding states|law of corresponding states]] expresses the fact that there are basic similarities in the thermodynamic properties of all simple gases. Its essential feature is that if we scale the thermodynamic variables that describe an [[equation of state]] (temperature, pressure, and volume) with respect to their values at the liquid-gas critical point, all simple fluids obey the same reduced equation of state.
 
[[Massimo G. Noro]] and [[Daan Frenkel]] formulated an extended law of corresponding states that predicts the phase behaviour of short-ranged potentials on the basis of the effective pair potential alone – extending the validity of the van der Waals law to systems interacting through pair potentials with different functional forms.
 
The Noro–Frenkel law suggests to condensate the three quantities which are expected to play a role in the thermodynamics behavior of a system (hard-core size, interaction energy and range) into a combination of only two quantities: an effective hard core diameter and the reduced second virial coefficient. Noro and Frenkel suggested to determine the effective hard core diameter following the expression suggested by Barker<ref>
{{cite journal
  |author=J.A. Barker and D. Henderson
|year=1976
|title=What is "liquid"? Understanding the states of matter
|journal=[[Reviews of Modern Physics]]
|volume=48
|issue=4 |pages=587
|doi=10.1103/RevModPhys.48.587
|bibcode = 1976RvMP...48..587B }}</ref> based on the separation of the potential into attractive ''V''<sub>att</sub> and repulsive ''V''<sub>rep</sub> parts used in the Weeks–Chandler– Andersen method.<ref>
{{cite journal
|author=H.C. Andersen, J.D. Weeks, and D. Chandler
|year=1971
|title=Relationship between the Hard-Sphere Fluid and Fluids with Realistic Repulsive Forces
|journal=[[Physical Review A]]
|volume=4
|issue=4 |pages=1579
|doi=10.1103/PhysRevA.4.1597
|bibcode = 1971PhRvA...4.1597A }}</ref> The reduced second virial coefficient, i.e., the second virial coefficient ''B''<sub>2</sub> divided by the second virial coefficient of hard spheres with the effective diameter can be calculated (or experimentally measured) once the potential is know. ''B''<sub>2</sub> is defined as
:<math>B_2=2\pi\int_0^\infty r^2\left[ 1-e^{-V(r)/k_\text{B}T} \right] dr</math>
 
==Applications==
 
The Noro–Frenkel law is particularly useful for the description of colloidal and globular protein solutions,<ref>
{{cite journal
|author=R.P. Sear
|year=1999
|title=Phase behavior of a simple model of globular proteins
|journal=[[Journal of Chemical Physics]]
  |volume=111
|issue=10 |pages=4800
|doi=10.1063/1.479243
|arxiv = cond-mat/9904426 |bibcode = 1999JChPh.111.4800S }}</ref> for which the range of the potential is indeed significantly smaller than the particle size. For these systems the thermodynamic properties can be re-written as a function of only two parameters, the reduced density (using the effective diameter as length scale) and the reduced second-virial coefficient ''B''{{su|b=2|p=*}}. The gas-liquid critical point of all systems satisfying the extended law of corresponding states are characterized by same values of ''B''{{su|b=2|p=*}} at the critical point.
 
The Noro-Frenkel law can be generalized to particles with limited valency (i.e. to non spherical interactions).<ref>
{{cite journal
|author=G. Foffi and F. Sciortino
|year=2007
|title=On the possibility of extending the Noro-Frenkel generalized law of correspondent states to nonisotropic patchy interactions
|journal=[[Journal of Physical Chemistry B]]
|volume=111 |issue=33 |pages=9702
|doi=10.1021/jp074253r
|pmid=17672500
}}</ref> Particles interacting with different potential ranges but identical valence behave again according to the generalized law, but with a different value for each valence of ''B''{{su|b=2|p=*}} at the critical point.
 
==See also==
*[[Theorem of corresponding states]]
*[[Van der Waals equation]]
*[[Equation of state]]s
*[[Daan Frenkel]]
*[[Massimo G. Noro]]
 
==References==
{{reflist}}
 
{{DEFAULTSORT:Noro-Frenkel law of corresponding states}}
[[Category:Thermodynamics]]
[[Category:Condensed matter physics]]

Revision as of 10:41, 14 December 2013

The Noro–Frenkel law of corresponding states is an equation in thermodynamics that describes the critical temperature of the liquid-gas transition T as a function of the range of the attractive potential R. It states that, all short-ranged spherically symmetric pair-wise additive attractive potentials are characterised by the same thermodynamics properties if compared at the same reduced density and second virial coefficient[1]

Description

Johannes Diderik van der Waals's law of corresponding states expresses the fact that there are basic similarities in the thermodynamic properties of all simple gases. Its essential feature is that if we scale the thermodynamic variables that describe an equation of state (temperature, pressure, and volume) with respect to their values at the liquid-gas critical point, all simple fluids obey the same reduced equation of state.

Massimo G. Noro and Daan Frenkel formulated an extended law of corresponding states that predicts the phase behaviour of short-ranged potentials on the basis of the effective pair potential alone – extending the validity of the van der Waals law to systems interacting through pair potentials with different functional forms.

The Noro–Frenkel law suggests to condensate the three quantities which are expected to play a role in the thermodynamics behavior of a system (hard-core size, interaction energy and range) into a combination of only two quantities: an effective hard core diameter and the reduced second virial coefficient. Noro and Frenkel suggested to determine the effective hard core diameter following the expression suggested by Barker[2] based on the separation of the potential into attractive Vatt and repulsive Vrep parts used in the Weeks–Chandler– Andersen method.[3] The reduced second virial coefficient, i.e., the second virial coefficient B2 divided by the second virial coefficient of hard spheres with the effective diameter can be calculated (or experimentally measured) once the potential is know. B2 is defined as

B2=2π0r2[1eV(r)/kBT]dr

Applications

The Noro–Frenkel law is particularly useful for the description of colloidal and globular protein solutions,[4] for which the range of the potential is indeed significantly smaller than the particle size. For these systems the thermodynamic properties can be re-written as a function of only two parameters, the reduced density (using the effective diameter as length scale) and the reduced second-virial coefficient BTemplate:Su. The gas-liquid critical point of all systems satisfying the extended law of corresponding states are characterized by same values of BTemplate:Su at the critical point.

The Noro-Frenkel law can be generalized to particles with limited valency (i.e. to non spherical interactions).[5] Particles interacting with different potential ranges but identical valence behave again according to the generalized law, but with a different value for each valence of BTemplate:Su at the critical point.

See also

References

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang