The study of block copolymer self-assembly in solution has been an active subject for years. As one of the most versatile molecules in nature, it is a chemical and biological building block for life. Lipids in aqueous solution self-organize to a bilayer structure that effectively compartmentalize cellular spaces for complex biochemical processes. Industrial products related to block copolymer self-assembly in solution have been created through intensive experimental and engineering efforts. Although models for block copolymer melts have been successful, a consistent theoretical understanding of block copolymers in solution has not kept with the applications. Challenges arise from its nature that block copolymer self-assembly in solution is a multiscale and multidimensional problem. Extremely diluted block copolymer solutions are homogeneous that can be well understood by an equation of state model. Inhomogeneity appears when the polymer concentration is above critical micelle concentration and the block copolymers form isolated micelles in dilute solution. Longrange ordered lyotropic liquid crystals of multidimensional mesophases are formed in concentrated solution when the block copolymers of individual micelles overlap.

This thesis aims to develop a consistent thermodynamic model for block copolymer self-assembly in solution in multiscale and multidimension, based on a particular molecular density functional theory (DFT): interfacial statistical associating fluid theory (iSAFT). This DFT model ultimately predicts phase behaviors of self-assembly in solution, explains thermodynamic factors that influence the phase behaviors from a microscopic view at molecular level, and provides a guidance to design operating conditions and to select candidate materials for the related applications.

Key contributions of this thesis include: 1. A quantitative approach to predict critical micelle concentrations and aggregation numbers of micelles of both diblock copolymers and triblock copolymers, and to explain inhomogeneous micellar solubilization in dilute aqueous solution; 2. Description of solvent regulated mesophase behaviors of block copolymers in solution having two-dimensional inhomogeneity, and how solvent selectivity and molecular packing parameter affect the phase behaviors in concentrated solution; 3. A new efficient numerical algorithm for molecular density functional theory with application to iSAFT to improve convergence, stability, and performance of DFT solution algorithm in cylindrical geometry.