Controlling the orientation of nanostructured thin films of block copolymers (BCPs) is essential for next-generation lithography using BCPs. According to conventional wisdom, the orientation of BCP thin films is mainly determined by molecular interactions (enthalpy-driven orientation). Here, we show that the entropic effect can be used to control the orientation of BCP thin films. Specifically, we used the architecture of star-block copolymers consisting of polystyrene (PS) and poly­(dimethylsiloxane) (PDMS) blocks to regulate the entropic contribution to the self-assembled nanostructures. The study unequivocally demonstrate that for star-block copolymers with the same volume fractions of PS and PDMS, perpendicularly oriented BCP nanostructures could be induced via an entropic effect regulated by the number of arms. Also, the feasibility of using the star-block copolymer thin films for practical applications is demonstrated by using the thin film as a mask for nanolithography or as a template for the fabrication of nanoporous monolith.

The phase behavior of AB diblock copolymers mixed with C homopolymers (AB/C), in which A and C are capable of forming hydrogen-bonds, is examined using selfconsistent field theory. The study focuses on the modeling of hydrogen-bonding in polymers. Specifically, we examine two models for the formation of hydrogen-bonds between polymer chains. The first commonly used model assumes a large attractive interaction parameter between the A/C monomers. This model reproduces correct phase transition sequences as compared with experiments, but it fails to correctly describe the change of lamellar spacing induced by the addition of the C homopolymers.The second model is based on the fact that hydrogen-bonding leads to A/C complexation. We show that the interpolymer complexation model predicts correctly the order-order phase transition sequences and the decrease of lamellar spacing for strong hydrogen-bonding. Our analysis demonstrates that hydrogen-bonding of polymers should be modeled by interpolymer complexation.iii

The line tension or edge energy of bilayer membranes self-assembled from binary amphiphilic molecules is studied using self-consistent-field theory (SCFT). Specifically, solutions of the SCFT equations corresponding to an infinite membrane with a circular pore, or an open membrane, are obtained for a coarse-grained model in which the amphiphilic species and hydrophilic solvents are represented by ABandED diblock copolymers and C homopolymers, respectively. The edge energy of the membrane is extracted from the free energy of the open membranes. Results for membranes composed of mixtures of symmetric and cone- or inverse cone-shaped amphiphilic molecules with neutral and/or repulsive interactions are obtained and analyzed. It is observed that an increase in the concentration of the cone-shaped species leads to a decrease of the line tension. In contrast, adding inverse cone-shaped copolymers results in an increase of the line tension. Furthermore, the density profile of the copolymers reveals that the line tension is regulated by the distribution of the amphiphiles at the bilayer edge.

We examine the behavior of lamellar phases of charged/neutral diblock copolymer thin films containing mobile ions in the presence of an external electric field. We employ self-consistent field theory and focus on the aligning effect of the electric field on the lamellae. Of particular interest are the effects of the mobile ions on the critical field, the value required to reorient the lamellae from the parallel configuration favored by the surface interaction to the perpendicular orientation favored by the field. We find that the critical field depends strongly on whether the neutral or charged species is favored by the substrates. In the case in which the neutral species is favored, the addition of charges decreases the critical electric field significantly. The effect is greater when the mobile ions are confined to the charged lamellae. In contrast, when the charged species is favored by the substrate, the addition of mobile ions stabilizes the parallel configuration and thus results in an increase in the critical electric field. The presence of ions in the system introduces a new mixed phase in addition to those reported previously.

The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.