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The '''hydrodynamic radius''' of a [[macromolecule]] or [[colloid]] particle has two meanings. Some books use it as a synonym for the [[Stokes radius]]. | |||
<ref > {{cite book | author = Gert R. Strobl | |||
| title= The Physics of Polymers Concepts for Understanding Their Structures and Behavior| publisher=Springer-Verlag | year=1996 | isbn = 3-540-60768-4 }} Section 6.4 page 290. </ref> | |||
Others books define a theoretical hydrodynamic radius <math>R_{\rm hyd}</math>. They consider the macromolecule or colloid particle to be a collection of <math>N</math> subparticles. This is done most commonly for [[polymer]]s; the subparticles would then be the units of the polymer. <math>R_{\rm hyd}</math> is defined by | |||
:<math> | |||
\frac{1}{R_{\rm hyd}} \ \stackrel{\mathrm{def}}{=}\ \frac{1}{N^{2}} \left\langle \sum_{i \neq j} \frac{1}{r_{ij}} \right\rangle | |||
</math> | |||
where <math>r_{ij}</math> is the distance between subparticles <math>i</math> and <math>j</math>, and where the angular brackets <math>\langle \ldots \rangle</math> represent an [[ensemble average]]. | |||
<ref > {{cite book | author = J. Des Cloizeaux and G. Jannink | |||
| title= Polymers in Solution Their Modelling and Structure | publisher=Clarendon Press | year=1990 | isbn = 0-19-852036-0 }} Chapter 10, Section 7.4, pages 415-417. </ref> The theoretical hydrodynamic radius <math>R_{\rm hyd}</math> was originally an estimate by [[John Gamble Kirkwood]] of the [[Stokes radius]] of a polymer. | |||
The theoretical hydrodynamic radius <math>R_{\rm hyd}</math> arises in the study of the dynamic properties of polymers moving in a [[solvent]]. It is often similar in magnitude to the [[radius of gyration]]. | |||
==Notes== | |||
<references/> | |||
==References== | |||
Grosberg AY and Khokhlov AR. (1994) ''Statistical Physics of Macromolecules'' (translated by Atanov YA), AIP Press. ISBN 1-56396-071-0 | |||
[[Category:Polymer physics]] | |||
Revision as of 07:37, 7 January 2014
The hydrodynamic radius of a macromolecule or colloid particle has two meanings. Some books use it as a synonym for the Stokes radius. [1]
Others books define a theoretical hydrodynamic radius . They consider the macromolecule or colloid particle to be a collection of subparticles. This is done most commonly for polymers; the subparticles would then be the units of the polymer. is defined by
where is the distance between subparticles and , and where the angular brackets represent an ensemble average. [2] The theoretical hydrodynamic radius was originally an estimate by John Gamble Kirkwood of the Stokes radius of a polymer.
The theoretical hydrodynamic radius arises in the study of the dynamic properties of polymers moving in a solvent. It is often similar in magnitude to the radius of gyration.
Notes
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Section 6.4 page 290. - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Chapter 10, Section 7.4, pages 415-417.
References
Grosberg AY and Khokhlov AR. (1994) Statistical Physics of Macromolecules (translated by Atanov YA), AIP Press. ISBN 1-56396-071-0