Rheo-optical state of dilute solution of rigid macromolecules in simultaneous hydrodynamic and electric fields is investigated theoretically and experimentally. Macromolecules are taken to be non-electrolytic rigid Brownian spheroids of arbitrary aspect ratio and a dielectric Newtonian fluid is used as a solvent. Both permanent and induced dipole moments are included. Optical state of a solution was investigated through two optical functions, birefringence and extinction angle, and results obtained from analytical studies were discussed and compared with ones from experiments.
First, for clear circumstances, a modeled solution system having above conditions is presented. The governing equation describing the behavior of particles dissolved at the model solution is derived from the torque balance. Final form of that equation is the normalized diffusion equation solved for the orientation distribution function which presumes the probability that the major axis of a spheroid has a particule direction. This equation was expressed in terms of dimensionless field parameters and operators related to respective fields. In addition to optical property of a solution, rheological property can be investigated through the component functions of the stress tensor. Expression of stress tensor pertinent to this model solution were obtained. The converged solutions are used in the prediction of the steady state optical functions such as birefringence and extinction angle over very wide ranges of field strengths.
To solve the problem with arbitrary strength of fields, numerical analysis was performed. The Galerkin method based on spherical harmonics was adopted for the steady state problem and a newly desinged numerical scheme was used to manage with inversion of the huge matrix caused by the strong field problem. Transient Problem could be solved by 4th order Runge-Kutta method. Numerical results up to the saturation field strengths were obtained. Optical properties of the model solultion varied according to not only the absolute strengths of respective fields but also the relative strengths. Thus to interpret the results systematically full ranges of the field strengths were divided into 3 regions.
0.1 and 0.03644 w/v % m-cresol solutions of Poly-γ-benzyl-L-glutamate having molecular weights of 4 sizes ranging from 15,000 to 236.000 were experimented under the combined fields over wide field strengths in witch maximum shear rate was 400 sec$^{-1}$ and electric field was loaded up to 33kv/cm. Transient birefringence and extinction angle were simultaneously measured using the phase-modulated birefringence method. Birefringence experiment using a PBLG solution is usually performed on characteristic time unit of a few msec order and experiments at strong fields is basically restricted by performance of apparatus. Especially, electric birefringence experiment is limited by a dielectric breakdown of a solution caused by strong electric fields and experiments under combined fields are accompanied by the piezoelectric effects.
Experimental characteristics and problems of the component and the combined fields were discussed through the representitive transient experiments. Analyses of steady state results obtained from the combined field experiments were presented. Hydrodynamic interaction between polymer particles was not occurred within experimented conditions, but electric effects were sensitive to both the applied electric field strength and concentration of a solution. Optical state of a solution could be explained to a certain extent by the dimensionless field parameters established in the theory. However, mainly due to electric hindrance, flow instibility by the strong combined fields. and deterioration of a solution by succesive electric experiments, experimental values deviated from theoretically predicted ones. Finally, through the steady state results from the combined field experiments using m-cresol solution of PBLG of M.W. =236,000 optical constant of the solution, permanent dipole strength of PBLG, and its rotational diffusivity were given.
