|
|
| Line 1: |
Line 1: |
| 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. | | The writer's name is Andera and she believes it sounds fairly great. I am truly fond of to go to karaoke but I've been using on new issues recently. For years he's been residing in Alaska and he doesn't strategy on changing it. He works as a bookkeeper.<br><br>my web blog: psychic phone readings ([http://help.ksu.edu.sa/node/65129 http://help.ksu.edu.sa/node/65129]) |
| | |
| 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]]
| |
The writer's name is Andera and she believes it sounds fairly great. I am truly fond of to go to karaoke but I've been using on new issues recently. For years he's been residing in Alaska and he doesn't strategy on changing it. He works as a bookkeeper.
my web blog: psychic phone readings (http://help.ksu.edu.sa/node/65129)