(488y) Quantification of Molecular Topology Using SANS

A new method to quantify topology in a variety of materials using static scattering will be discussed. Specific examples using long chain branched polyethylene will be used to demonstrate the versatility of this technique. The results will be compared with NMR and rheology measurements. In polyolefins, the method provides a unique measure of the average branch length and the number of "inner" segments. Inner segments are characteristic of hyperbranched molecular topologies where branch-on-branch structures exist. The ability to quantify branch-on-branch structure using dilute solutions of hydrogenous polymers in deuterated solvent makes this method extremely appealing to those studying the synthesis of complex molecular topologies. We have adapted this method to study a wide range of complex topological materials from proteins to bio- and ceramic/carbon nano-aggregates.

Synthetic and biopolymers display chain structures that often contain complex topologies ranging from star structures and dendrimers to randomly branched structures and cyclics, Figure 1. Generally, these topologies dominate the physical properties of these materials [1].

Techniques for the quantification of topology can involve observation of the mass of the molecule and the encompassing size as measured by the hydrodynamic radius under a non-draining assumption for instance. This approach can lead to the mass-fractal dimension, df, which is related to the packing density of an object (through a logarithmic relationship). Complex objects, however, are not fully described by their density and the mass fractal dimension is insufficient to describe transport properties or electrical conductivity for example. At the opposite extreme spectroscopic techniques can describe local features of a complex structure such as the number of branch sites or local interaction between chemical species. Again, in the absence of other information, spectroscopic descriptions are incomplete while they give a good measure of the number of structural bridging sites per molecule for instance.

We have developed new application of static neutron scattering for the direct quantification of topology to quantify the topology of branched structures [2]. For example the mole fraction of a molecule in branches, fBr, can be directly determined using this SANS method. Further, quantitative measures of 1) the convolution or tortuosity of the structure and 2) the connectivity of the branching network can be made [2]. The work is of pivotal interest to many areas of the polymer industry including polyolefins where a picture of branch structure has long been sought to correlate with variation in catalyst, precursor and reaction conditions. This description of topology can further be generalized to describe a much wider range of topologies than long-chain branched polyolefins. In this talk we demonstrate the general usefulness of our topological description of complex structures for long and short chain branched polyethylene. We have already applied this approach to disordered nanomaterials such as chain aggregate structures [3-5], hyperbranched polymers [6], cyclic polymers [5,7] and biomolecules [8].