Macromolecules 1982, 15, 87-93
87
Rotational and Translational Diffusion in Semidilute Solutions of Rigid-Rod Macromolecules K. M. Zero and R. Pecora* Department of Chemistry, Stanford University, Stanford, California 94305. Received July 20, 1981
ABSTRACT Dynamic light scattering studies were done on solutions of poly(y-benzyl L-glutamate) (PBLG) in 1,2-dichloroethane. In this solvent, PBLG exists as a rigid CY helix with a length per residue of 1.5 8, and a diameter of 15 A. The concentrationof the solutions ranged between 4 and 50 mg/mL, and the molecular weights of the PBLG were between 150000 and 210000. The rotational diffusion coefficients were inversely proportional to the concentration squared and to about the eighth power of the length for concentrations above 5 mg/mL and roughly equivalent to the infinite-dilution values below 5 mg/mL. The translational diffusion coefficients had little concentration dependence and were roughly two-thirds of the predicted infinite-dilution value.
I. Introduction For dilute solutions, the overall dimensions of a polymer can be related to the translational and rotational diffusion
7 , = 0.19 - 4.2(1/6 - 0.39)'
coefficients by simple equations derived from hydrodynamics.1-6 Thus, any technique, such as dynamic light scattering, which can measure these diffusion coefficients should also yield information about molecular dimensions. However, because the intensity of scattered light is relatively low, the diffusion coefficienta for truly dilute solutions are difficult to measure. This is especially true for the rotational diffusion coefficients, which usually require the measurement of extremely weak depolarized scattered light intensity fluctuations. In addition, some particles may change shape with concentration (as in certain micellar systems) and thus cannot be studied in dilute solutions. The effect of concentration on the motions of flexible polymers has been thoroughly investigated by numerous authomW However, the motions of semiflexible and rigid polymers have large, complicated concentration dependences, particularly for long rodlike molecules, which have not been extensively investigated. In this article we present a study of the translation and rotation of rodlike macromolecules of known size and compare the time constants obtained with theory in the hope that a welldefined relationship between their motions and concentration can be established.
where L is the length of the rod, d is the diameter of the rod, and .rt8 is the viscosity of the solvent. These relations assume that the rods are large enough so that stick boundary conditions hold; i.e., they behave as macroscopic rods in a viscous medium. For much more concentrated solutions, one would expect a decrease in these values due to hindrance by neighboring rods. Doi and Edwards*" have presented a theory of restricted rotational diffusion for number concentrations of rods ranging from greater than l / L 3 to 27r/dL2, Le., where the solutions are still isotropic but exhibit strong steric repulsions between rods. In this treatment, the translational motion of each rod parallel to its axis is assumed to be unhindered while motion perpendicular to its axis is restricted to about the distance to the nearest neighboring rod, which we shall call a,. For small values of a, ( l / L 3
