The polymers of the present invention comprise a rigid-rod backbone comprising at least about 25 monomer units, preferably at least about 100 monomer units, joined together by covalent bonds, non-limiting examples of which are carbon-carbon, carbon-nitrogen, carbon-oxygen, carbon-sulfur, nitrogen-nitrogen, silicon-oxygen or silicon-carbon covalent bonds, wherein at least about 95%, and preferably 99%, of the bonds are substantially parallel, the polymer and its monomers being soluble in a common solvent system. Solubilizing groups are attached to the rigid-rod backbone, that is, to some of the monomer units of the backbone. The polymer can be a copolymer of two or more monomers.