Phase Behavior of Tapered Diblock Copolymers from Self-Consistent Field Theory.

Tapered diblock copolymers are similar to AB diblock copolymers, but the sharp junction between the A and B blocks is replaced with a gradient region in which composition varies from mostly A to mostly B along its length. The A side of the taper can be attached to the A block (normal) or the B block (inverse). We demonstrate how taper length and direction affect the phase diagrams and density profiles using self-consistent field theory. Adding tapers shifts the order-disorder transition to lower temperature versus the diblock, and this effect is larger for longer tapers and for inverse tapers. However, tapered systems' phase diagrams and interfacial profiles do not simply match those of diblocks at a shifted effective temperature. For instance, we find that normal tapering widens the bicontinuous gyroid region of the phase diagram, while inverse tapering narrows this region, apparently due to differences in polymer organization at the interfaces.

Morphologies of ABC triblock terpolymer melts containing poly(cyclohexadiene): effects of conformational asymmetry.

We have synthesized linear ABC triblock terpolymers containing poly(1,3-cyclohexadiene), PCHD, as an end block and characterized their morphologies in the melt. Specifically, we have studied terpolymers containing polystyrene (PS), polybutadiene (PB), and polyisoprene (PI) as the other blocks. Systematically varying the ratio of 1,2- /1,4-microstructures of poly(1,3-cyclohexadiene), we have studied the effects of conformational asymmetry among the three blocks on the morphologies using transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and self-consistent field theory (SCFT) performed with PolySwift++. Our work reveals that the triblock terpolymer melts containing a high percentage of 1,2-microstructures in the PCHD block are disordered at 110 °C for all the samples, independent of sequence and volume fraction of the blocks. In contrast, the triblock terpolymer melts containing a high percentage of 1,4-microstructure form regular morphologies known from the literature. The accuracy of the SCFT calculations depends on calculating the χ parameters that quantify the repulsive interactions between different monomers. Simulations using χ values obtained from solubility parameters and group contribution methods are unable to reproduce the morphologies as seen in the experiments. However, SCFT calculations accounting for the enhancement of the χ parameter with an increase in the conformational asymmetry lead to an excellent agreement between theory and experiments. These results highlight the importance of conformational asymmetry in tuning the χ parameter and, in turn, morphologies in block copolymers.

Hybrid particle-field simulations of polymer nanocomposites.

We present a theoretical framework and computer simulation methodology for investigating the equilibrium structure and properties of mesostructured polymeric fluids with embedded colloids or nanoparticles. The method is based on a field-theoretic description of the fluid in which particle coordinates and chemical potential field variables are simultaneously updated. The fluid model can contain polymers of arbitrary chemical and architectural complexity, along with particles of all shapes, sizes, and surface treatments. Simulation results are compared with experiments conducted on polystyrene (PS)-functionalized Au nanoparticles in a PS-P2VP diblock copolymer melt.

Field-theoretic simulations of polymer solutions: finite-size and discretization effects.

In this work we analyze the finite-size and discretization effects that occur in field-theoretic polymer simulations. Following our previous work, we study these effects for a polymer solution in the canonical ensemble confined to a slit (with nonadsorbing walls) of width L, and focus on the behavior of two quantities: the chemical potential mu, and the correlation length xi. Our results show that the finite-size effects disappear for both quantities once the lateral size of the system L is larger than approximately 2xi. On the other hand, the chemical potential is dominated by the lattice discretization Deltax. The origins of this dependence are discussed in detail, and a scheme is proposed in which this effect is avoided. Our results also show that the density profiles do not depend on the lattice discretization if Deltax < approximately xi/4. This implies that the correlation length xi, extracted from the density profiles, is free of lattice size and lattice discretization artifacts once L is > approximately 2xi and Deltax < approximately xi/4.

Introducing variable cell shape methods in field theory simulations of polymers.

We propose a new method for carrying out field-theoretic simulations of polymer systems under conditions of prescribed external stress, allowing for shape changes in the simulation box. A compact expression for the deviatoric stress tensor is derived in terms of the chain propagator, and it is used to monitor changes in the box shape according to a simple relaxation scheme. The method allows fully relaxed, stress free configurations to be obtained even in nontrivial morphologies, and it enables the study of morphology transitions induced by external stresses.

Composite mesostructures by nano-confinement.

In a physically confined environment, interfacial interactions, symmetry breaking, structural frustration and confinement-induced entropy loss can play dominant roles in determining molecular organization. Here we present a systematic study of the confined assembly of silica-surfactant composite mesostructures within cylindrical nanochannels of varying diameters. Using exactly the same precursors and reaction conditions that form the two-dimensional hexagonal SBA-15 mesostructured thin film, unprecedented silica mesostructures with chiral mesopores such as single- and double-helical geometries spontaneously form inside individual alumina nanochannels. On tightening the degree of confinement, a transition is observed in the mesopore morphology from a coiled cylindrical to a spherical cage-like geometry. Self-consistent field calculations carried out to account for the observed mesostructures accord well with experiment. The mesostructures produced by confined syntheses are useful as templates for fabricating highly ordered mesostructured nanowires and nanowire arrays.

Continuous polydispersity in a self-consistent field theory for diblock copolymers.

An efficient algorithm is presented for numerically evaluating a self-consistent field theoretic (SCFT) model of an AB diblock copolymer that incorporates continuous polydispersity in one of the blocks. An interesting segregation effect is found in which chains of intermediate molecular weight are concentrated at domain interfaces. This model of continuous polydispersity is also implemented in the random phase approximation (RPA) to study the order-disorder transition and predicts that the stability of the disordered, homogeneous phase decreases as the polydispersity in one of the blocks increases. The RPA predictions are confirmed by SCFT calculations. Our approach and results are particularly relevant to block copolymers prepared by quasiliving synthesis techniques, where the polymerization of one block is much more controlled than the other block.