Highly anisotropic rigidity of ''ribbon-like'' polymers .1. Chain conformation in dilute solutions

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 l(2) than their in-plane persistence length l. In the first paper of this series, we mostly investigate 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 Ohm = l(2)d(2)l(-3) where d is the chain diameter. For small values of Ohm, (l(2) similar to l), the chain behaves as a standard semiflexible chain with isotropic rigidity. For large values of Ohm, (Ohm greater than or similar to 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 less than or similar to L less than or similar to l(2)) and a three-dimensional swollen coil conformation at larger length scale. In the intermediate range of Ohm, l(2)/d(2) less than or similar to Ohm less than or similar to 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.