Russell B. Thompson

Improved convergence in block copolymer self-consistent field theory by Anderson mixing

A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.

Nanoparticle-regulated phase behavior of ordered block copolymers

Although block copolymer motifs have received considerable attention as supramolecular templates for inorganic nanoparticles, experimental observations of a nanostructured diblock copolymer containing inorganic nanoparticles-supported by theoretical trends predicted from a hybrid self-consistent field/density functional theory-confirm that nanoparticle size and selectivity can likewise stabilize the copolymer nanostructure by increasing its order-disorder transition temperature.

Origins of the failure of classical nucleation theory for nanocellular polymer foams

DOI: 10.1039/C1SM05575E (Paper) Soft Matter, 2011, 7, 7351-7358 This journal is

Origins of Elastic Properties in Ordered Block Copolymer/Nanoparticle Composites

We predict a diblock copolymer melt in the lamellar phase with added spherical nanoparticles that have an affinity for one block to have a lower tensile modulus than a pure diblock copolymer system. This weakening is due to the swelling of the lamellar domain by nanoparticles and the displacement of polymer by elastically inert fillers. Despite the overall decrease in the tensile modulus of a polydomain sample, the shear modulus for a single domain increases dramatically.

Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

Molecularly asymmetric triblock copolymers progressively grown from a parent diblock copolymer can be used to elucidate the phase and property transformation from diblock to network-forming triblock copolymer. In this study, we use several theoretical formalisms and simulation methods to examine the molecular-level characteristics accompanying this transformation, and show that reported macroscopic-level transitions correspond to the onset of an equilibrium network. Midblock conformational fractions and copolymer morphologies are provided as functions of copolymer composition and temperature.

Elastic moduli of multiblock copolymers in the lamellar phase.

We study the linear elastic response of multiblock copolymer melts in the lamellar phase, where the molecules are composed of tethered symmetric AB diblock copolymers. We use a self-consistent field theory method, and introduce a real space approach to calculate the tensile and shear moduli as a function of block number. The former is found to be in qualitative agreement with experiment. We find that the increase in bridging fraction with block number, that follows the increase in modulus, is not responsible for the increase in modulus. It is demonstrated that the change in modulus is due to an increase in mixing of repulsive A and B monomers. Under extension, this increase originates from a widening of the interface, and more molecules pulled free of the interface. Under compression, only the second of these two processes acts to increase the modulus.

Reduction of polymer surface tension by crystallized polymer nanoparticles

Self-consistent field theory is applied to investigate the effects of crystallized polymer nanoparticles on polymer surface tension. It is predicted that the nanoparticles locate preferentially at the polymer surface and significantly reduce the surface tension, in agreement with experiment. In addition to the reduction of surface tension, the width of the polymer surface is found to narrow. The reduced width and surface tension are due to the smaller spatial extent of the nanoparticles compared to the polymer. This allows the interface to become less diffuse and so reduces the energies of interaction at the surface, which lowers the surface tension. The solubility of the surrounding solvent phase into the polymer melt is mostly unchanged, a very slight decrease being detectable. The solubility is constant because away from the interface, the system is homogeneous and the replacement of polymer with nanoparticles has little effect.

Bidirectional mapping between self-consistent field theory and molecular dynamics: application to immiscible homopolymer blends.

A bidirectional mapping scheme that bridges particle-based and field-based descriptions for polymers is presented. Initial application is made to immiscible homopolymer blends. The forward mapping (upscaling) approach is based on the use of molecular dynamics simulations to calculate interfacial density profiles for polymer molecular weights that can be readily relaxed using standard simulation methods. These profiles are used to determine the optimal, effective interaction parameter that appears in the one-parameter self-consistent field theory treatment employed in the present work. Reverse mapping from a field representation to a particle-based description is accomplished by the application of a density-biased Monte Carlo method that generates representative chain configurations in the blend using statistical weights derived from fields obtained from self-consistent field theory.

Benchmarking a self-consistent field theory for small amphiphilic molecules

A minimalist self-consistent field theory for small amphiphilic molecules is presented. The equations for this model are less involved than those for block copolymers and are easily implemented computationally. A new convergence technique based on a variant of Anderson mixing is also presented which allows the equations to be solved more rapidly than block copolymer self-consistent field theory. The computational speed up and simplicity of equations result from a lack of configurational degrees of freedom in the amphiphilic molecular model. The omission of polymeric flexibility leads to qualitatively different predictions compared to known diblock copolymer behaviour.

The Self-Assembly of Particles with Isotropic Interactions

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, motivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding kinetic effects. It is found that non-trivial morphologies are possible and that, for this effectively one component system, these parallel the phases of diblock copolymer melts for certain parameter choices, despite the absence of connectivity or packing frustration in the model. An explanation for the morphological similarity between these architecturally disparate systems is given. For other parameter choices, it is found that meta-stable and defected phases become more common, and that similarity with block copolymer morphologies decreases.