Orientation behavior of carbon fiber axes in polymer solutions under magnetic field estimated in terms of orientation distribution function

Orientation behavior of carbon fibers (CFs) in polymer solution/gel under magnetic field was estimated in terms of the orientation distribution function. The estimation was done by a series of spherical harmonics of the orientation distribution function of the reciprocal lattice vector of the (002) plane measured for the composite films. Despite a number of papers concerning the orientation of CFs and carbon nanotubes under magnetic field, all estimations have been done in terms of the second-order orientation factor of the (002) plane. The work described in this paper was first successful for the direct estimation of orientation of CF axes within the dried film in terms of orientation function by considering a random orientation of the CF axes around the magnetic field direction. In this experiment, poly(vinyl alcohol) (PVA) was adopted as the solution to disperse CFs and to prepare the composite films by evaporating solvent. The normalized function obtained experimentally was analyzed in comparison with the magnetic orientation of CFs in solution or gel at the equilibrium state calculated by the magnetic energy of CF. Furthermore, the orientation of the CFs up to the equilibrium state in the given systems was estimated as a function of time by a common diffusion equation. The calculated results indicated that the preferential orientation of CFs with respect to the magnetic field direction becomes promoted with elapsing time. This tendency became significant, when the contents of CFs and/or PVA were less than the critical concentration within the dispersion solution. The experimental and theoretical results, however, provided that the preferential orientation degree became lower drastically, when the PVA content and/or the CF content were beyond their critical concentration. This was due to a drastic decrease in viscosity of the dispersion solution before gelation/crystallization.