Directed self-assembly (DSA) of block copolymers has attracted attention for its use as a simple, cost- effective patterning tool for creating vertical interconnect access (VIA) channels in nanoelectronic devices.1, 2 This technique supplements existing lithographic technologies to allow for the creation of high-resolution cylindrical holes whose diameter and placement can be precisely controlled. In this study, we use self-consistent field theory (SCFT) simulations to investigate the equilibrium configurations of under-filled DSA systems with air-polymer interactions. We report on a series of SCFT simulations of our three species (PMMA-b-PS diblock and air) model in cylindrical confinement to explore the role of template diameter, under-fill fraction (i.e. volume fraction of air), air-polymer surface interaction and polymer-side wall/substrate interactions on equilibrium morphologies in an under-filled template with a free top surface. We identify parameters and system configurations where a meniscus appears and explore cases with PMMA-attractive, PS-attractive, and all-neutral walls to understand the effects of wall properties on meniscus geometry and DSA morphology. An important outcome is an understanding of the parameters that control the contact angle of the meniscus with the wall, as it is one of the simplest quantitative measures of the meniscus shape. Ultimately, we seek to identify DSA formulations, templates, and surface treatments with predictable central cylinder diameter and a shallow contact angle, as these factors would facilitate broad process windows and ease of manufacturing.