We determine the effective mobility radius for fractal aggregate particles. Our method is to use static light scattering to measure the radius of gyration R(g) of the aggregates, and dynamic light scattering to measure the diffusion coefficient hence the mobility radius R(m). The range of our results can be specified by the Knudsen number Kn, which is the mean free path of the medium molecules divided by the radius of the aggregate. Our results apply to the entire range of Kn from the continuum limit (Kn=0) to the free molecular limit (Kn>>1). In the continuum regime we find R(m)/R(g)=0.97+/-0.05 when the aggregate fractal dimension is D(f) approximately 2.15, and 0.70+/-0.05 when D(f) approximately 1.75. The latter result is independent of Kn for Kn < or approximately 1.3. The free molecular mobility goes as R(m)=aN(0.44+/-0.03), where a is the monomer radius and N is the number of monomers per aggregate. Since R(g) approximately aN(1/D(f)), R(m)/R(g) is not a constant when Kn is large. We find for all Kn that the functionality of R(m)/R(g) must always begin with the correct N-->1 limit, and this affects experimental observation.
Gold nanocrystal superlattices were synthesized in colloidal form by ligating the nanocrystal surface with
dodecanethiol ligand. Formation and dissolution of the superlattices in the colloid were studied by UV−vis
spectroscopy and dynamic light scattering. The phase boundary between nanocrystals and their superlattices
in solution was found to be similar to the case of macroscopic crystals made of atoms or molecules. Lowering
the temperature across the phase boundary resulted in nucleation of nanocrystals into superlattices and the
superlattice size depended on the rate of nucleation. UV−vis spectroscopy and dynamic light scattering also
showed that thermal dissolution of the superlattices occurred after the temperature of the colloid was raised
across the phase boundary.
We consider the large qR(g), where q is the magnitude of the scattering wave vector and R(g) is the aggregate radius of gyration, part of the structure factor of fractal aggregates, and quantify the coefficient C of the power law, S(q) approximately C(qR(g))(-D), where D is the fractal dimension, for various structure factors proposed in the literature. With the aid of earlier work, we conclude the most accurate structure factors have C=1.0. We then calculate the effects of polydispersity on this coefficient, and show the effects are significant, enough so to allow a measurement of the distribution width. These concepts are accurately supported with scattering data from a diffusion limited aerosol and a reaction limited colloid.
A theoretical description of the aggregation kernel homogeneity for fractal aggregates in the slip regime is developed. Experimental values of the kernel homogeneity were determined with dynamic light scattering measurements on titania and silica aerosols at pressures of 1/10 to one atmosphere. These experiments yielded aggregates with a fractal dimension of ca. 1.75 and aggregate radii to cover a range of Knudsen numbers of 0.04 -3.8. Measurement of the fractal aggregate mobility radius as a function of time during aggregation gave the homogeneity. Agreement of theory and experiment is in general successful.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.