Self-assembly is an effective strategy for the creation of periodic structures at the nanoscale. However, because microelectronic devices use free-form design principles, the insertion point of self-assembling materials into existing nanomanufacturing processes is unclear. We directed ternary blends of diblock copolymers and homopolymers that naturally form periodic arrays to assemble into nonregular device-oriented structures on chemically nanopatterned substrates. Redistribution of homopolymer facilitates the defect-free assembly in locations where the domain dimensions deviate substantially from those formed in the bulk. The ability to pattern nonregular structures using self-assembling materials creates new opportunities for nanoscale manufacturing.

We consider an implementation of umbrella sampling in which the pertinent range of states is subdivided into small windows that are sampled consecutively and linked together. This allows us to simulate without a weight function or to extrapolate the results to the neighboring window in order to estimate a weight function. Additionally, we present a detailed error analysis in which we demonstrate that the error in umbrella sampling is controlled and, in the absence of sampling difficulties, independent of the window sizes. In this case, the efficiency of our implementation is comparable to a multicanonical simulation with a very good weight function, which in our scheme does not need to be known ahead of time. The analysis also allows us to detect sampling difficulties such as correlations between adjacent windows and provides a test of equilibration. We exemplify the scheme by simulating the liquid–vapor coexistence in a Lennard-Jones system.