Kinetic Self-Assembly of Metals on Co-polymer Templates

In this work we seek to understand some of the fundamental processes that govern self-assembly at the nanoscale in the context of the formation of metallic structures on patterned co-polymer templates. To this end we focus on the experiments conducted by Lopes {\it et al} (Nature, 2001), where morphologies resulting from the evaporation-deposition of different metals on PS-b-PMMA phase separated templates were studied. We show that the different morphologies obtained can be understood in terms of the relative importance of the energetics and kinetics. We then focus on a particular morphology: micron long wire-like states obtained by the evaporation-deposition of silver on the template. We show the existence of ``non-trivial'' correlations between adjacent wires that can be understood based on a purely kinetic mechanism. We also compare these correlations quantitatively to those obtained from simulations done with the relevant experimental parameters and find them in good agreement.Comment: 18 pages, 18 figures, submitted to Phys. Rev.

Active matter clusters at interfaces

Collective and directed motility or swarming is an emergent phenomenon displayed by many self-organized assemblies of active biological matter such as clusters of embryonic cells during tissue development, cancerous cells during tumor formation and metastasis, colonies of bacteria in a biofilm, or even flocks of birds and schools of fish at the macro-scale. Such clusters typically encounter very heterogeneous environments. What happens when a cluster encounters an interface between two different environments has implications for its function and fate. Here we study this problem by using a mathematical model of a cluster that treats it as a single cohesive unit that moves in two dimensions by exerting a force/torque per unit area whose magnitude depends on the nature of the local environment. We find that low speed (overdamped) clusters encountering an interface with a moderate difference in properties can lead to refraction or even total internal reflection of the cluster. For large speeds (underdamped), where inertia dominates, the clusters show more complex behaviors crossing the interface multiple times and deviating from the predictable refraction and reflection for the low velocity clusters. We then present an extreme limit of the model in the absense of rotational damping where clusters can become stuck spiraling along the interface or move in large circular trajectories after leaving the interface. Our results show a wide range of behaviors that occur when collectively moving active biological matter moves across interfaces and these insights can be used to control motion by patterning environments.Comment: 15 pages, 7 figure

Statistically Locked-in Transport Through Periodic Potential Landscapes

Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments on colloidal spheres flowing through arrays of optical traps do indeed reveal such a hierarchy,but not with the predicted structure. The microscopic trajectories, moreover,appear to be random, with commensurability emerging only in a statistical sense. We introduce an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in states.Comment: REVTeX with EPS figures, 4 pages, 4 figure

Chelated Antimony Compounds

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