Many high Χ block copolymer (BCP) systems often have one block which shows a strong preference to wet the free interface at the top of the film. This property makes it difficult to form vertically aligned lamellae which are desired for many directed self-assembly (DSA) applications. To better understand this behavior, simulations of thin films of BCPs were carried out using a coarse-grained molecular dynamics (MD) model. The property that leads one block to preferentially wet the free interface over the other is a difference in cohesive energy density (CED) between the two blocks. Our simulation allows for the systematic variation in the CED of each block to investigate how the magnitude of these differences affects self-assembly behavior. BCPs with no CED differences between the blocks show large ranges of underlayer compositions where vertical lamellae will form that are minimally affected by changing Χ of the BCP. The range where vertical lamellae will form can be thought of as a process window. Increasing the CED asymmetry of the BCP (i.e. the difference in CED between blocks) causes a reduction in the process window and also causes a shift in the underlayer composition that is the center of the window. Increasing Χ increases the process window for vertical lamellae in CED asymmetric systems. This behavior is determined by the trade-off in energy due to three interfacial interactions: A-B interface, film-free surface interface, and film-underlayer interface. At the limits of very high CED asymmetry and low Χ, there may be no underlayer compositions where vertical lamellae will form. A simplified model was also developed that can accurately predict these process windows for different CED asymmetry and Χ values on the order of seconds and minutes compared to hours and days for the full simulation.