Departmental Papers (CBE)

Document Type

Journal Article

Date of this Version

January 2003


The elastic properties of planar, C4-symmetric networks under stress and at nonzero temperature are determined by simulation and mean field approximations. Attached at fourfold coordinated junction vertices, the networks are self-avoiding in that their elements (or bonds) may not intersect each other. Two different models are considered for the potential energy of the elements: either Hooke’s law springs or flexible tethers (square well potential). For certain ranges of stress and temperature, the properties of the networks are captured by one of several models: at large tensions, the networks behave like a uniform system of square plaquettes, while at large compressions or high temperatures, they display many characteristics of an ideal gas. Under less severe conditions, mean field models with more general shapes (parallelograms) reproduce many essential features of both networks. Lastly, the spring network expands without limit at a two-dimensional tension equal to the force constant of the spring; however, it does not appear to collapse under compression, except at zero temperature.


Copyright American Physical Society. Reprinted from Physical Review E, Volume 67, Issue 1, Article 011903, January 2003, 10 pages.
Publisher URL:



Date Posted: 21 December 2005

This document has been peer reviewed.