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If anyone has an example of a polymer whose monomers form an ideal mix with its solvant, or an experiment where a polymer behaves in some way or the other like an ideal chain, that'll be great. ThorinMuglindir 10:41, 29 October 2005 (UTC)
Hey ThorinMuglindir. A solvent in which a polymer displays ideal behavior is typically called a theta solvent. Generally if you have a solvent that is a fluid made up of the monomers of the polymer you get what is called screening of the excluded volume effects and the resulting behavior is ideal (ideal simply means we can ignore the excluded volume interactions and hence model the polymer as a random walk). In terms of the Helmholtz free energy the coefficient of the first term in the virial expansion is zero since tau=0 or T=theta. Practically there is no real ideal solvent since the temperature can never be exactly theta, but if T is close enough to theta the thermal blob size can be much greater than the typical size of the polymer and hence the behavior is ideal (all chains look ideal if they are below the thermal blob size). I think a typical example is polyethylene and polystyrene but don't quote me on that. I think a qualitative explanation of what makes a solvent an ideal solvent is probably more important since it would be hard to get data to add a graph in order to truly convince people that it is a reasonable model (although I guess a reference could be given to a text where it could be found). Here and in the polymer physics article somebody should put in the Helmholtz free energy for the chain...
Hi
There is an sever Error in the Artikel The End to End distance is Normal distributed, but the End-to-End Vektors are NOT! There you have to take into account, that the Ammound of vectors with a certain end to End distance R is Proportional to the Survace of an Sphere with the Radius R so the Korrekt Formular is
or [[User:Patrickruediger, 10:04, 7.December 2006
It may be worth noting that the probability distribution given in the article is only true for the end-to-end vector in the thermodynamic limit. The exact solution is dimension-dependent and can only be given as a series solution. See Yamakawa 'Modern Theory of Polymer Solutions' (1971, Harper and Row) for the complete derivation. ScottRShannon 02:06, 24 April 2006 (UTC)
There was a small issue with the change in thermodynamical ensemble at the very end of the article. In the "fixed force" ensemble, it's a mean end-to-end vector, but it's not a mean force, the force is fixed by the operator as . I had to come back with my previous account, since stacy can not (yet?) upload images. The image also had to be corrected in the same way. Sorry about that mistake from a few years ago. ThorinMuglindir ( talk) 15:34, 22 May 2008 (UTC)
The third ensemble is missing: See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1303618/pdf/3418.pdf , https://journals.aps.org/pra/abstract/10.1103/PhysRevA.34.3486 — Preceding unsigned comment added by 129.69.120.91 ( talk) 07:25, 10 December 2018 (UTC)
However, since the components of the vectors are uncorrelated for the random walk we are considering,
This is completely wrong. The components are correlated, since |rᵢ| is fixed. The correlation disappears only in the limit of infinitely many links. -- Ilya-zz ( talk) 10:16, 17 August 2020 (UTC)