In the development of new block copolymers (BCPs) that can satisfy the multiple covarying properties necessary to meet manufacturing criteria in nanolithography, a body of recent work has explored the use of BCPs exhibiting a block containing groups amenable to click chemistry towards access to high-throughput libraries of block random copolymers (BRCs). These recent advances demonstrate the ability to select compositions of a random block accessed by click chemistry to achieve equal surface energy between the random and non-random block, thereby granting the BCP the ability to perpendicularly assemble in the thin film state when subjected to a thermal anneal process. Simultaneously, the choice of specific pairs of functional groups in the random block that meet this first mandate allows for a wide range of differences in the Flory-Huggins interaction parameter (χ) between BRCs, and therefore segregation strength (χN) and feature size (L₀) from the same parent polymer of identical degree of polymerization (N). This thesis seeks to expand on this precedent to explore both the polymer physics associated with phase separation behavior and the application of BRCs to directed self-assembly as an industrially significant process for patterning. The first chapter of this thesis introduces the research needs of the use of block copolymers in the semiconductor industry and how their chemical design can serve as a fundamental means of addressing them. The second chapter details ways of using A-b-(B-r-C) BCPs accessed via thiol-epoxy click chemistry to investigate scaling behavior in lamellar pitch and interfacial width with variable N and constant χ using resonant soft X-ray scattering (RSoXR). The third chapter introduces another click chemistry approach to synthesizing A-b-(B-r-C) BCPs, where each copolymer component can be chemically selected towards engineering dry etch contrast within its design via the incorporation of silicon groups in the random block against the identity of the homopolymer block. The fourth chapter investigates the behaviors of BCP libraries bearing a “double amide” side chain structure, which exhibited unusual and previously unreported behavior in L₀ when functionalized by select R groups, and where computational insights into partial charge contributions and radial distribution functions shed light on the effects of dipole moment and packing on observed behavior. The final chapter considers the future potential of BCPs bearing mixed composition and sequence in one block, both as accessed via click chemistry and by other approaches. Two immediate ventures being actively pursued are described: the use of A-b-(B-r-C) BCPs of variable etch contrast to assess the effects of this property on line roughness in pattern transfer, and preliminary work on precisely defining sequence in a copolymer block using solid-phase peptoid synthesis.