Highly Anisotropic Rigidity of “Ribbon-like” Polymers: I. Chain Conformation in Dilute Solutions

Irina A. Nyrkova; Alexander N. Semenov; Jean-Francois Joanny; Alexei R. Khokhlov

doi:doi:10.1051/jp2:1996139

Numéro		J. Phys. II France Volume 6, Numéro 10, October 1996


Page(s)		1411 - 1428
DOI		https://doi.org/10.1051/jp2:1996139

DOI: 10.1051/jp2:1996139
J. Phys. II France 6 (1996) 1411-1428

Highly Anisotropic Rigidity of "Ribbon-like" Polymers: I. Chain Conformation in Dilute Solutions

Irina A. Nyrkova^{1, 2}, Alexander N. Semenov^{1, 2, 3, 4}, Jean-Francois Joanny² and Alexei R. Khokhlov¹

¹ Physics Department, Moscow State University, Moscow 117234, Russia
² Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France
³ Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
⁴ Nesmeyanov Institute of Organo-Element Compounds of Russian Academy of Science, 28 Vavilova Str., Moscow 117812, Russia

(Received 12 May 1995, revised 25 April 1996, accepted 2 July 1996)

Abstract
We discuss the solution properties of polymers with a highly anisotropic rigidity which bend rather freely in a plane (the plane of main flexibility) and are extremely rigid in the direction perpendicular to this plane. Examples of these polymers are the ladder polymers recently synthesized or living polymers formed by the aggregation of peptide rodlike fragments. These polymers have a much higher out of plane persistence length l₂ than their in-plane persistence length l. In the first paper of this series, we mostly inverstigate the conformation of single chains in solution (at extremely low concentrations). The conformation of an isolated chain with a highly anisotropic rigidity essentially depends on the dimensionless parameter $\Omega = l_2d^2l^{-3}$ where d is the chain diameter. For small values of $\Omega, (l_2\sim l)$ , the chain behaves as a standard semiflexible chain with isotropic rigidity. For large values of $\Omega, (\Omega \gtrsim 1)$ , the chain adopts a one-dimensional rodlike conformation at length scales smaller than l, an anisotropic disc-like conformation at intermediate scales (corresponding to a contour length L such that $l\lesssim L \lesssim l_2$ ) and a three-dimensional swollen coil conformation at larger length scale. In the intermediate range of $\Omega, l^2/d^2\lesssim \Omega\lesssim 1$ , the same three regimes are expected but the excluded volume interactions do not play any role in the disc-like regime. At the end of the paper we discuss qualitatively the possible liquid crystalline phases (with nematic or smectic symmetry) which can emerge in these solutions at higher concentration.