Rigid-rod polymers such as PBO, poly(paraphenylene benzobisoxazole), Figure 1a, are now in commercial development for use as high-performance fibers and for reinforcement at the molecular level in molecular composites. Spinning of liquid crystalline polyphosphoric acid solutions of PBO, followed by washing, drying, and tension heat treatment produces fibers which have the following properties: density of 1.59 g/cm3; tensile strength of 820 kpsi; tensile modulus of 52 Mpsi; compressive strength of 50 kpsi; they are electrically insulating; they do not absorb moisture; and they are insensitive to radiation, including ultraviolet. Since the chain modulus of PBO is estimated to be 730 GPa, the high stiffness also affords the opportunity to reinforce a flexible coil polymer at the molecular level, in analogy to a chopped fiber reinforced composite. The objectives of the molecular composite concept are to eliminate the thermal expansion coefficient mismatch between the fiber and the matrix, as occurs in conventional composites, to eliminate the interface between the fiber and the matrix, and, hopefully, to obtain synergistic effects from the exceptional stiffness of the rigid-rod molecule. These expectations have been confirmed in the case of blending rigid-rod PBZT, poly(paraphenylene benzobisthiazole), Figure 1b, with stiff-chain ABPBI, poly 2,5(6) benzimidazole, Fig. 1c A film with 30% PBZT/70% ABPBI had tensile strength 190 kpsi and tensile modulus of 13 Mpsi when solution spun from a 3% methane sulfonic acid solution into a film. The modulus, as predicted by rule of mixtures, for a film with this composition and with planar isotropic orientation, should be 16 Mpsi. The experimental value is 80% of the theoretical value indicating that the concept of a molecular composite is valid.
Approximate solutions to nonlinear oscillations via an improved He's variational approach