This PhD thesis is devoted to a theoretical study of polymer and ’polymer like’ systems in strictly two dimensions. Polymer systems in reduced dimensions are of high experimental and technological interest and present theoretical challenges due to their strong non-mean-field-like behavior manifested by various non-trivial universal power law exponents. We focus on the strictly 2D limit where chain crossing is forbidden and study as function of density and of chain rigidity conformational and elastic properties of three system classes: flexible and semiflexible polymers at finite temperature and macroscopic athermal polymers (fibers) with imposed quenched curvature. For flexible polymers it is shown that although dense self-avoiding polymers are segregated with Flory exponent ν = 1/2 , they do not behave as Gaussian chains. In particular a non-zero contact exponent θ2 = 3/4 implies a fractal perimeter dimension of dp = 5/4. As a consequence and in agreement with the generalized Porod law, the intramolecular structure factor F(q) reveals a non-Gaussian behavior and the demixing temperature of 2D polymer blends is expected to be reduced. We also investigate the effects of chain rigidity on 2D polymer systems and found that universal behavior is not changed when the persistence length is not too large compared to the semidilute blob size. The nature of the nematic phase transition at higher rigidities, which is in the 2D case the subject of a long standing debate, is also briefly explored. Preliminary results seem to indicate a first order transition. Finally, motivated by recent theoretical work on elastic moduli of fiber bundles, we study the effects of spontaneous curvature at zero temperature. We show that by playing on the disorder of the Fourier mode amplitudes of the ground state, it is possible to tune the compression modulus, in qualitative agreement with theory.
