## LSU Historical Dissertations and Theses

1994

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Chemistry

Paul Russo

#### Abstract

The self-diffusion coefficient (D$\sb{\rm s}$) of fluorescent dye labeled poly-$\gamma$-benzyl-L-glutamates (LPBLG) in pyridine solutions was measured by fluorescence photobleaching recovery (FPR). Intrinsic viscosity and static light scattering measurements showed that the LPBLGs did not aggregate in pyridine and that the rod structure of LPBLG was not perturbed by labeling. The measured concentrations spanned from dilute to the most concentrated isotropic solutions, and the axial ratios from 7 to 80 (M$\sb{\rm W}$ ranged from 20 000 to 232 000). The objective of this FPR study was to focus directly on the translational diffusion of a single LPBLG molecule in the absence of the thermodynamic driving force, which has been difficult to resolve from the dynamic light scattering measurements. After being corrected by the reduction in solvent mobility, the reduced self-diffusion coefficient of different molecular weight LPBLGs could be nearly superimposed on a single curve when plotted against the normalized concentration $\nu$dL$\sp2$, where $\nu$ was the number density, d = 20 A was the hydrodynamic diameter and L was the length of the LPBLG molecule. According to the concentration dependence of D$\sb{\rm S}$, short LPBLG solutions had two concentration regimes, while long LPBLG solutions exhibited three concentration regimes. Below $\nu$dL$\sp2\approx$ 0.8, the diffusion coefficient did not change much with concentration within the experimental error. D$\sb{\rm S}$ experienced substantial reduction only when the excluded volume effect became significant; the crossover concentration was proportional to L$\sp{-2}$. At $\nu$dL$\sp2\approx$ 4, the normalized diffusion coefficient was reduced to 0.1. A power law fit of the superimposed curve in the regime of 0.8 $\le \nu$ dL$\sp2 \le$ 4 gave D$\sb{\rm S} \sim$ L$\sp{-1.8 \pm \ 0.1}$c$\sp{-1.13 \pm 0.04}.$ In this region the experimental curve could also be fit with the calculated D$\sb{\rm S}$ by combining the green function formulated longitudinal and transverse diffusion coefficients. Above $\nu$dL$\sp2 \approx$ 4 short LPBLG solutions underwent the liquid crystal transition, but the long LPBLGs had a delayed transition and entered into a third dynamic regime in which the D$\sb{\rm S}$ became less concentration dependent. The normalized self-friction factor and the mutual-friction factor showed different concentration dependencies. This discrepancy could be explained by the additional cross term of the velocity correlation function when expressing the mutual-friction factors.

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