The directed self assembly of block copolymers is an exciting complimentary technique for the fabrication of nanoscale structures for lithographic applications. Typically a directed self assembly process is driven through substrates with chemical (chemoepitaxy) or topographical (graphoepitaxy) guiding features. These patterning strategies have led to the ability to assemble structures with a high degree of perfection over large areas. However, a guiding pattern has not been created which assembles the desired features with a defect density that is commensurate with industrial standards of 1 defect/100cm2. This work focuses on using molecular simulations on the Theoretically Informed Coarse Grained model to provide design rules for substrate patterns which drive the assembly of desired, device-oriented morphologies., Prior to the work presented in Chapter 2, the TICG model has been used in conjunction with a chemical pattern that is approximated as a a hard-impenetrable surface. As many experimental systems use polymer brushes to help guide the polymer melt deposited on the,substrate, this work analyzes the consequences of such an assumption by comparing a model where the polymer brush is explicitly implemented to the hard-wall substrate used in the past. Then, a methodology which utilizes a evolutionary optimization method is used to map the parameters of the more detailed model to the hard-surface model. This provides a qualitative understanding of how to interpret the model parameters used in previous works in the context of real experimental pattern designs., Chapter 3 discuss the concept of competitive assemblies in regards to defining a thermodynamic processing window in design space for assembling lines-and-spaces. The most competitive assembly to the desired orientation of the lamella is defined as a rotation of,assembled lamella to the underlying pattern. Thermodynamic integration is used to calculate the free-energy difference between these assemblies over chemical patterns with varied design parameters. Local maximums in the free-energy difference are observed over pattern designs that are in qualitatively agreement with the pattern designs which produce the most perfect assemblies in experiments. The analysis is extended to study how choice of chemistry impacts this thermodynamic selection for the desired morphology. , Finally, Chapter 4 provides insight into the kinetics of patterned directed self-assembly by investigating cylinder forming block copolymers within cylindrical connements. Through the use of the string method, the minimum free-energy path between a defective state and the desired assembled morphology is calculated and clear transition states are highlighted. The effects of key parameters of the confinement design on the calculated minimum free energy path are calculated to identify design rules which should lead to a better understanding of optimal connement design for eliminating defects. In addition, a specific modification to existing cylindrical confinements is discussed as a possibility for tackling the problem of placement accuracy for a cylinder that is assembled within the confinement.