Block copolymers (BCPs) self-assemble into periodic arrays of lamella, cylinders, spheres and gyroids with characteristic feature sizes of 3-100nm, making them ideal for fabrication of nanostructured materials. For many applications including separation membranes and nanopatterning, it is necessary to use block copolymer in thin film geometries and with domain orientations perpendicular to substrates. Chapter 2 discusses the effects of surface and interfacial energy on the self-assembly of PS-cylinder forming PS-b-PMMA thin films. These are less studied than the standard PMMA-cylinder forming BCPs. We explore using this BCP as a sacrificial template for the formation of nanoporous metal oxide films with tunable pore sizes. The fabricated nanoporous membrane is transferred onto a macroporous support for protein separation studies. Directed self-assembly (DSA) of BCPs utilizes topographic or chemical contrast guide patterns to provide long-range orientational order. DSA has great potential for next generation lithography as it enables low processing cost and feature density multiplication. Defectivity is the biggest challenge for moving DSA into high-volume manufacturing. Current defectivity studies reply on surface or cross-sectional 2D metrologies. These data are not enough to describe the 3D nature of DSA morphologies and probe hidden defects under the surface. In chapter 3, we describe a 3D metrology for graphoepitaxial DSA contact-hole shrink process (to make vias) using the post-DSA membrane fabrication technique and STEM tomography. The 3D reconstruction results reveal relationships between guide patterns of different surface chemistry and geometry and types of defects in DSA morphologies. In addition to patterning contacts using graphoepitaxial patterns, DSA using chemoepitaxial patterns is a very effective technology for line/space patterning over large area. It is of particularly interest in bit patterned media (BPM) applications. In BPM, an areal density of 5 Tb/in¬2 corresponds to an 11 nm bit pitch size, which is a huge challenge for any existing lithography techniques. Chapter 4 investigates the combination of two commonly used pitch splitting techniques: DSA and self-aligned double patterning (SADP) to reach a total density multiplication factor of 8. Starting from guiding lines with 84 nm pitch, a final line/space pattern with pitch as small as 10.5 nm is demonstrated. This combined DSA and SADP strategy could avoid many sacrificial layers and etch/deposition steps to reach the same aggressive pitch scaling compared to self-aligned octuplet patterning (SAOP). While DSA is approaching maturity for use in the semiconductor industry, researchers can develop high-resolution nanofabrication using DSA technology to solve problems in the condensed matter physics community. One revolutionary idea is to control the thermal transport by periodic nanostructures, or phononic crystal patterning. Chapter 5 describes the approach to fabricate DSA templated phononic crystal devices which have well-defined hexagonal packed holes with 38 nm pitch in suspended silicon nitride bridges. A great reduction in thermal conductivity is observed from thermoreflectance measurements. This work has applications into novel thermoelectric devices and highly sensitive bolometric radiation detectors.