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The '''Stokes radius''' or '''Stokes-Einstein radius''' (named after [[George Gabriel Stokes]]) of a solute is the radius of a hard sphere that diffuses at the same rate as that solute. It is closely related to solute mobility, factoring in not only size but also solvent effects. A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger but weaker ion.
 
Stokes radius is sometimes used synonymously with effective hydrated radius in solution.<ref>{{cite book|last=Atkins|first=Peter|title=Physical Chemistry|year=2010|publisher=Oxford UP|location=Oxford|edition=9|coauthors=Julio De Paula}}</ref> [[Hydrodynamic radius]], ''R''<sub>''H''</sub>, can refer to the Stokes radius of a polymer or other macromolecule.
 
==Spherical Case==
According to [[Stokes’ law]], a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient <math>f</math>:
 
<math>F_{drag}=fs=(6 \pi \eta a)s</math>
 
where <math> \eta </math> is the liquid's [[viscosity]], <math> s </math> is the sphere's drift speed, and <math> a </math> is its radius. Because [[Electrical mobility|ionic mobility]] <math> \mu </math> is directly proportional to drift speed, it is inversely proportional to the frictional coefficient:
 
<math> \mu = \frac{ze}{f} </math>
 
where <math> ze </math> represents ionic charge in integer multiples of electron charges.
 
In 1905, Albert Einstein found the diffusion coefficient <math> D </math> of an ion to be proportional to its mobility:
 
<math> D = \frac{\mu k_B T}{q} = \frac{k_b T}{f} </math>
 
where <math> k_B </math> is the [[Boltzmann constant]] and <math>q</math> is [[electrical charge]]. This is known as the [[Einstein relation (kinetic theory)|Einstein relation]]. Substituting in the frictional coefficient of a perfect sphere from Stokes’ law yields
 
<math> D = \frac{k_b T}{6 \pi \eta a} </math>
 
which can be rearranged to solve for <math>a</math>, the radius:
 
<math> R_H = a = \frac{k_b T}{6 \pi \eta D} </math>
 
In non-spherical systems, the frictional coefficient is determined by the size and shape of the species under consideration.
 
==Research Applications==
Stokes radii are often determined experimentally by gel-permeation or gel-filtration chromatography.<ref>{{cite journal|last=Alamillo|first=J.|coauthors=Jacobo Cardenas, Manuel Pineda|title=Purification and Molecular Properties of Urate Oxidase from Chlamydomonas Reinhardtii|journal=Biochimica Et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology|year=1991|volume=1076|issue=2|pages=203–08}}</ref><ref>{{cite journal|last=Dutta|first=Samarajnee|coauthors=Debasish Bhattacharyya|title=Size of Unfolded and Dissociated Subunits versus That of Native Multimeric Proteins|journal=Journal of Biological Physics|year=2001|volume=27|pages=59–71}}</ref><ref name="fourth">{{cite journal|last=Elliott|first=C.|coauthors=H. Joseph Goren|title=Adipocyte Insulin-binding Species: The 40 Å Stoke's Radius Protein|journal=Biochemistry and Cell Biology|year=1984|volume=62|issue=7|pages=566–70}}</ref><ref>{{cite journal|last=Uversky|first=V.N.|title=Use of Fast Protein Size-exclusion Liquid Chromatography to Study the Unfolding of Proteins Which Denature through the Molten Globule|journal=Biochemistry|year=1993|volume=32|issue=48|pages=13288–98}}</ref> They are useful in characterizing biological species due to the size-dependence of processes like enzyme-substrate interaction and membrane diffusion.<ref name="fourth" /> The Stokes radii of sediment, soil, and aerosol particles are considered in ecological measurements and models.<ref>{{cite journal|last=Ellis|first=W.G.|coauthors=J.T. Merrill|title=Trajectories for Saharan Dust Transported to Barbados Using Stokes's Law to Describe Gravitational Settling|journal=Journal of Applied Meterology|year=1995|volume=34|issue=7|pages=1716–26}}</ref> They likewise play a role in the study of polymer and other macromolecular systems.<ref name="fourth" />
 
==See also==
* [[Capillary electrophoresis]]
* [[Hydrodynamic radius]]
* [[Dynamic light scattering]]
* [[Stokes' law]]
* [[Equivalent spherical diameter]]
 
== References ==
{{Reflist}}
 
{{DEFAULTSORT:Stokes Radius}}
[[Category:Fluid dynamics]]

Revision as of 04:19, 1 August 2013

The Stokes radius or Stokes-Einstein radius (named after George Gabriel Stokes) of a solute is the radius of a hard sphere that diffuses at the same rate as that solute. It is closely related to solute mobility, factoring in not only size but also solvent effects. A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger but weaker ion.

Stokes radius is sometimes used synonymously with effective hydrated radius in solution.[1] Hydrodynamic radius, RH, can refer to the Stokes radius of a polymer or other macromolecule.

Spherical Case

According to Stokes’ law, a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient :

where is the liquid's viscosity, is the sphere's drift speed, and is its radius. Because ionic mobility is directly proportional to drift speed, it is inversely proportional to the frictional coefficient:

where represents ionic charge in integer multiples of electron charges.

In 1905, Albert Einstein found the diffusion coefficient of an ion to be proportional to its mobility:

where is the Boltzmann constant and is electrical charge. This is known as the Einstein relation. Substituting in the frictional coefficient of a perfect sphere from Stokes’ law yields

which can be rearranged to solve for , the radius:

In non-spherical systems, the frictional coefficient is determined by the size and shape of the species under consideration.

Research Applications

Stokes radii are often determined experimentally by gel-permeation or gel-filtration chromatography.[2][3][4][5] They are useful in characterizing biological species due to the size-dependence of processes like enzyme-substrate interaction and membrane diffusion.[4] The Stokes radii of sediment, soil, and aerosol particles are considered in ecological measurements and models.[6] They likewise play a role in the study of polymer and other macromolecular systems.[4]

See also

References

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    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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    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
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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