Onsager theory: Difference between revisions
Carl McBride (talk | contribs) No edit summary |
Carl McBride (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
The '''Onsager theory''' for the isotropic-[[nematic phase |nematic]] phase transition was developed by [[Lars Onsager]] (Ref. 1). | The '''Onsager theory''' for the isotropic-[[nematic phase |nematic]] phase transition was developed by [[Lars Onsager]] (Ref. 1). | ||
In a 3-dimensional gas of [[hard rods]] there are two contributions to the [[entropy]]: a part due to translation and a part due to orientation. These two contributions are coupled. | In a 3-dimensional gas of [[hard rods]] there are two contributions to the [[entropy]]: a part due to translation and a part due to orientation. These two contributions are coupled. From the point of view of the translational component of the entropy, | ||
a parallel configuration of the rods is favored. This is because the excluded volume is effectively zero. However, from an | |||
orientational point of view a gas of perfectly aligned rods is a very low entropy configuration. | |||
At very low densities the orientational term ''wins'', i.e. there is very little gain in entropy to be made by | |||
reducing the excluded volume via parallel alignments. However, at very high densities it is clear | |||
that a perfectly aligned system is the most favorable. Thus at some point a transition must take place between | |||
the isotropic and nematic phases. | |||
==References== | ==References== | ||
#L. Onsager "THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES", Annals of the New York Academy of Sciences '''51''' pp. 627- (1949) | #L. Onsager "THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES", Annals of the New York Academy of Sciences '''51''' pp. 627- (1949) | ||
Revision as of 16:39, 23 July 2007
The Onsager theory for the isotropic-nematic phase transition was developed by Lars Onsager (Ref. 1). In a 3-dimensional gas of hard rods there are two contributions to the entropy: a part due to translation and a part due to orientation. These two contributions are coupled. From the point of view of the translational component of the entropy, a parallel configuration of the rods is favored. This is because the excluded volume is effectively zero. However, from an orientational point of view a gas of perfectly aligned rods is a very low entropy configuration.
At very low densities the orientational term wins, i.e. there is very little gain in entropy to be made by reducing the excluded volume via parallel alignments. However, at very high densities it is clear that a perfectly aligned system is the most favorable. Thus at some point a transition must take place between the isotropic and nematic phases.
References
- L. Onsager "THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES", Annals of the New York Academy of Sciences 51 pp. 627- (1949)