Characterization of entanglements in glassy polymeric ensembles using the Gaussian linking number.

We propose a method for enumerating entanglements between long chained, linear polymers that is based on the Gaussian linking number. The linking number is calculated between closely approaching segments of the macromolecular chains. Topological features of an entanglement, i.e., the extent to which one open segment winds around another, are reflected by the linking number. We show that using this measure, we can track disentanglement events through a deformation history and gain insights into how large scale disentanglements lead to failure. Incorporating an additional step where the topological entanglements identified along each chain are optimally clustered using standard clustering algorithms, we can also obtain a measure of the average number of rheological constraints that exist along each chain in an ensemble. Comparisons with other methods of enumerating entanglements, especially the primitive path analysis, are also made. Our results indicate that the linking number between two entangled segments in the undeformed state is a good indicator of the strength of the entanglement. Also, disentanglements occurring overwhelmingly around chain ends are an important cause of failure when a triaxial stress state exists in the polymer.

Mechanistic origin and prediction of enhanced ductility in magnesium alloys.

Pure magnesium exhibits poor ductility owing to pyramidal [Formula: see text] dislocation transformations to immobile structures, making this lowest-density structural metal unusable for many applications where it could enhance energy efficiency. We show why magnesium can be made ductile by specific dilute solute additions, which increase the [Formula: see text] cross-slip and multiplication rates to levels much faster than the deleterious [Formula: see text] transformation, enabling both favorable texture during processing and continued plastic straining during deformation. A quantitative theory establishes the conditions for ductility as a function of alloy composition in very good agreement with experiments on many existing magnesium alloys, and the solute-enhanced cross-slip mechanism is confirmed by transmission electron microscopy observations in magnesium-yttrium. The mechanistic theory can quickly screen for alloy compositions favoring conditions for high ductility and may help in the development of high-formability magnesium alloys.