World Library  
Flag as Inappropriate
Email this Article

Excluded volume

Article Id: WHEBN0005821204
Reproduction Date:

Title: Excluded volume  
Author: World Heritage Encyclopedia
Language: English
Subject: Polymer physics, Self-avoiding walk, Pervaded volume, Theta solvent, Macromolecule
Collection: Polymer Physics
Publisher: World Heritage Encyclopedia

Excluded volume

The concept of excluded volume was introduced by Werner Kuhn in 1934 and applied to polymer molecules shortly thereafter by Paul Flory.


  • In liquid state theory 1
  • In polymer science 2
  • See also 3
  • References 4

In liquid state theory

In liquid state theory, the 'excluded volume' of a molecule is the volume that is inaccessible to other molecules in the system as a result of the presence of the first molecule.[1] The excluded volume of a hard sphere is eight times its volume—however, for a two-molecule system, this volume is distributed among the two particles, giving the conventional result of four times the volume;[2] this is an important quantity in the Van der Waals equation of state. The calculation of the excluded volume for particles with non-spherical shapes is usually difficult, since it depends on the relative orientation of the particles. The distance of closest approach of hard ellipses and their excluded area has been recently considered.

In polymer science

In polymer science, excluded volume refers to the idea that one part of a long chain molecule can not occupy space that is already occupied by another part of the same molecule.[3] Excluded volume causes the ends of a polymer chain in a solution to be further apart (on average) than they would be were there no excluded volume (e.g. in case of ideal chain model). The recognition that excluded volume was an important factor in analyzing long-chain molecules in solutions provided an important conceptual breakthrough, and led to the explanation of several puzzling experimental results of the day. It also led to the concept of the theta point, the set of conditions at which an experiment can be conducted that causes the excluded volume effect to be neutralized. At the theta point, the chain reverts to ideal chain characteristics.[4] The long-range interactions arising from excluded volume are eliminated, allowing the experimenter to more easily measure short-range features such as structural geometry, bond rotation potentials, and steric interactions between near-neighboring groups. Flory correctly identified that the chain dimension in polymer melts would have the size computed for a chain in ideal solution if excluded volume interactions were neutralized by experimenting at the theta point.

See also


  1. ^ Hill T. L., An Introduction to Statistical Thermodynamics,Dover Publications, New York, 1986, p 288
  2. ^ Mortimer, Robert G., Physical Chemistry, Academic Press, 3rd Edition, p 423
  3. ^ Hill T. L., An Introduction to Statistical Thermodynamics,Dover Publications, New York, 1986, p 225
  4. ^ Rubinstein M., Colby R. H., Polymer Physics, Oxford University Press, New York, 2003, p 49

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.