Scott W. Sides

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.

Parallel algorithm for numerical self-consistent field theory simulations of block copolymer structure

An efficient algorithm is presented for numerically evaluating a self-consistent field theoretic (SCFT) model of block copolymer structure. This algorithm is implemented on a distributed memory parallel cluster in order to solve the SCFT equations on large computational grids. Simulation results are presented for a two-component molten mixture of a symmetric ABA triblock copolymer with an A homopolymer. These results illustrate a case in which simulating a large system is required to resolve features with a wide range of length scales.

Interactions and structure of poly(dimethylsiloxane) at silicon dioxide surfaces: Electronic structure and molecular dynamics studies

Electronic structure studies are used to probe the interactions and molecular dynamics simulations are used to study the structure of thin poly(dimethylsiloxane) (PDMS) films near hydroxylated SiO2 substrates. Results of the electronic structure calculations show that the PDMS end groups, rather than atoms such as oxygen in the PDMS backbone structure, dominate interactions at the interface. Methyl–terminated PDMS binds weakly with the substrate via interactions between H atoms on PDMS methyl groups and O atoms on the substrate hydroxyl groups, while hydroxyl–terminated PDMS binds strongly with the substrate via hydrogen bonding between hydroxyl groups on PDMS and the substrate. To study the effect of temperature and type of substrate on the structural ordering of the PDMS liquid near the solid/liquid and liquid/air interfaces, molecular dynamics simulations for two temperatures (300 and 400 K) are carried out for three hydroxylated SiO2 substrates (α–quartz, β–cristobalite and amorphous SiO2). A direct c...

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.

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.

Microphase separation in thin films of lamellar forming polydisperse di-block copolymers

Despite the ubiquity of polydispersity in chain lengths of di-block copolymers, its effects on microphase separation in thin films have eluded a clear understanding. In this work, we have studied effects of polydispersity on the microphase separation in thin films of lamellar forming di-block copolymers using self-consistent field theory (SCFT) and neutron reflectivity experiments. Di-block copolymers containing a polydisperse block of poly(glycidylmethacrylate) (PGMA) connected to a near-monodisperse block poly(2-vinyl-4,4-dimethyl-d6 azlactone) (PVDMA-d6) are considered in this work. Effects of chain length polydispersity, film thickness, substrate–monomer and monomer–monomer interactions on the microphase segregation are studied using SCFT. The theoretical study reveals that in comparison to a film created with monodisperse di-block copolymers, an increase in polydispersity tends to decrease the number of lamellar strata that can be packed in a film of given thickness. This is a direct consequence of an increase in lamellar domain spacing with an increase in polydispersity index. Furthermore, it is shown that polydispersity induces conformational asymmetry and an increase in the polydispersity index leads to an increase in the effective Kuhn segment length of the polydisperse blocks. It is shown that the conformational asymmetry effects, which are entropic in origin and of increasing importance as film thickness decreases, drive the polydisperse blocks to the middle of the films despite favorable substrate interactions. These predictions are verified by results from neutron reflectivity experiments on thin films made from moderately polydisperse PGMA-PVDMA-d6 di-block copolymer deposited on silicon substrates. Finally, results from SCFT are used to predict neutron reflectivity profiles, providing a facile and robust route to obtain useful physical insights into the structure of polydisperse diblock copolymers at interfaces.

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

Different strategies for coupling fine-coarse grid patches are explored in the context of the adaptive mesh refinement (AMR) method. We show that applying linear interpolation to fill in the fine grid ghost values can produce a finite volume stencil of comparable accuracy to quadratic interpolation provided the cell volumes are adjusted. The volume of fine cells expands whereas the volume of neighboring coarse cells contracts. The amount by which the cells contract/expand depends on whether the interface is a face, an edge, or a corner. It is shown that quadratic or better interpolation is required when the conductivity is spatially varying, anisotropic, the refinement ratio is other than two, or when the fine-coarse interface is concave.

Morphology diagrams for A2B copolymer melts: real-space self-consistent field theory

Morphology diagrams for A2B copolymer melts are constructed using real-space self-consistent field theory (SCFT). In particular, the effect of architectural asymmetry on the morphology diagram is studied. It is shown that asymmetry in the lengths of A arms in the A2B copolymer melts aids in the microphase separation. As a result, the disorder-order transition boundaries for the A2B copolymer melts are shown to shift downward in terms of χN, χ and N being the Florys chi parameter and the total number of the Kuhn segments, respectively, in comparison with the A2B copolymers containing symmetric A arms. Furthermore, perforated lamellar (PL) and a micelle-like (M) microphase segregated morphologies are found to compete with the classical morphologies namely, lamellar, cylinders, spheres and gyroid. The PL morphology is found to be stable for A2B copolymers containing asymmetric A arms and M is found to be metastable for the parameter range explored in this work.