The Figure Below Shows Two Measurements, One by Self Diffusion and One by Mutual, for A

Dself vs Dmutual PAMAM

The figure below shows two measurements, one by self diffusion and one by mutual, for a charged polymer (a polybase dendrimer). Why is the behavior so different? Which behavior comes closer to reflecting the true molecular dimensions?

This is actually one of our own papers (J. Polym. Sci.--Polym. Phys. Ed. 1996, 34, 1467-1475). It’s a very complicated case. Although I like this paper—a real achievement in dynamic light scattering—the interpretation still troubles me. In the first place, due to the presence of salt and the fact that we worked only at finite concentrations (no extrapolation to zero polymer concentration) everything here is an apparent diameter.

The large rise in the DLS (mutual) diffusion coefficient surely reflects strong thermodynamic nonideality: Dm ~ (dp/dc) so apparent diameter ~ 1/(dp/dc). So, as we add salt, the system “softens” (can execute larger concentration fluctuations) and apparent diameter rises. Assuming that the DLS diameters at the highest salt concentrations have leveled out in terms of their salt response—a big if—then we still have the question of whether the PAMAM concentration itself is low enough to be inverting diffusion to get diameter in the first place. This was not studied—trust me, it was hard enough to get these DLS results at all. So, it is possible that the high-salt DLS diameter represents some kind of PAMAM aggregate. Hard to prove that, though.

The big salt effect is absent in the FPR experiment, because the tracer self diffusion that FPR reports is much less sensitive to thermodynamic driving. Instead, you see an apparent decrease in diameter as salt is added. This makes some sense because any possible intramolecular repulsions of the dendrimer that cause it to expand at low salt would be lessened when salt is added. On the other hand, it could be that the dye attached to the polymer in order to make FPR measurements in the first place would get “tucked inside” as salt is added. I think in the end we settled on that interpretation.

Perhaps DOSY or PFGNMR experiments would be more revealing. Particle tracking, too, but it might be hard to accomplish without the added dye label.