Amalie L. Frischknecht

Ionic Aggregate Structure in Ionomer Melts: Effect of Molecular Architecture on Aggregates and the Ionomer Peak

We perform a comprehensive set of coarse-grained molecular dynamics simulations of ionomer melts with varying polymer architectures and compare the results to experiments in order to understand ionic aggregation on a molecular level. The model ionomers contain periodically or randomly spaced charged beads, placed either within or pendant to the polymer backbone, with the counterions treated explicitly. The ionic aggregate structure was determined as a function of the spacing of charged beads and also depends on whether the charged beads are in the polymer backbone or pendant to the backbone. The low wavevector ionomer peak in the counterion scattering is observed for all systems, and it is sharpest for ionomers with periodically spaced pendant charged beads with a large spacing between charged beads. Changing to a random or a shorter spacing moves the peak to lower wavevector. We present new experimental X-ray scattering data on Na(+)-neutralized poly(ethylene-co-acrylic acid) ionomers that show the same two trends in the ionomer peak, for similarly structured ionomers. The order within and between aggregates, and how this relates to various models used to fit the ionomer peak, is quantified and discussed.

Numerical challenges in the application of density functional theory to biology and nanotechnology

This paper summarizes our efforts to develop fast algorithms for density functional theory (DFT) calculations of inhomogeneous fluids. Our goal is to apply DFTs to a variety of problems in nanotechnology and biology. To this end we have developed DFT codes to treat both atomic fluid models and polymeric fluids. We have developed both three-dimensional real space and Fourier space algorithms. The former rely on a matrix-based Newtons method while the latter couple fast Fourier transforms with a matrix-free Newtons method. Efficient computation of phase diagrams and investigation of multiple solutions is facilitated with phase transition tracking algorithms and arclength continuation algorithms. We have explored the performance that can be obtained by application of massively parallel computing, and have begun application of the codes to a variety of two-and three-dimensional systems. In this paper, we summarize our algorithm development work as well as briefly discuss a few applications including adsorption and transport in ion channel proteins, capillary condensation in disordered porous media and confinement effects in a diblock copolymer fluid.

Expanded chain dimensions in polymer melts with nanoparticle fillers

We apply the self-consistent polymer reference interaction site model (SC/PRISM) to liquid state calculations of the chain dimensions in polymer melts with added nanoparticle fillers. The nanoparticles are assumed to be smaller than the polymer radius of gyration and are attracted to the polymer so that they are miscible. We find that the nanoparticles perturb the chain dimensions, causing an increase in the radius of gyration with increasing nanoparticle volume fractions, assuming reasonable interaction energies between the various components. The magnitude of the expansion is in qualitative agreement with recent neutron scattering results and suggests that the SC/PRISM approach is reasonable when dealing with these apparent nonlinear phenomena present in nanocomposites in the protein limit.

Using arbitrary trial distributions to improve intramolecular sampling in configurational-bias Monte Carlo

A new formulation of configurational-bias Monte Carlo that uses arbitrary distributions to generate trial bond lengths, angles and dihedrals is described and shown to provide similar acceptance rates with substantially less computational effort. Several different trial distributions are studied and a linear combination of the ideal distribution plus Gaussian distributions automatically fit to the energetic and ideal terms is found to give the best results. The use of these arbitrary trial distributions enables a new formulation of coupled–decoupled configurational bias Monte Carlo that has significantly higher acceptance rates for cyclic molecules. The chemical potential measured via a modified Widom insertion is found to be ill-defined in the case of a molecule that has flexible bond lengths due to the unbounded probability distribution that describes the distance between any two atoms. We propose a simple standard state that allows the computation of consistent chemical potentials for molecules with flexible bonds. We show that the chemical potential via Widom insertion is not computed properly for molecules with Coulombic interactions when the number of trials for any of the nonbonded selection steps is greater than one. Finally, we demonstrate the power of the new algorithms by sampling the side-chain conformations of a polypeptide.

Density functional theory for inhomogeneous polymer systems. II. Application to block copolymer thin films

We use polymer reference interaction site model (PRISM)-based density functional theory (DFT) to study the structures and morphologies of block copolymer thin films. The polymers are modeled as freely jointed chains, allowing numerical solution of the nonlinear DFT equations. The use of PRISM with DFT allows the inclusion of compressibility and local packing effects due to the finite size of the monomers. We also employ a pseudo-arclength continuation algorithm to locate phase transitions and new morphologies. We study symmetric diblock copolymers confined between two parallel surfaces which both attract one component of the diblock, for two different values of AB segregation strength and for various surface interactions. The predicted equilibrium morphologies are in good qualitative agreement with previous self-consistent field calculations and are consistent with experiment. We are able to resolve the detailed packing structure near the surfaces. We find that packing effects enhance the stability of the...

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.

Density functional theory for inhomogeneous polymer systems. I. Numerical methods

We present a new real space Newton-based computational approach to computing the properties of inhomogeneous polymer systems with density functional theory (DFT). The DFT is made computationally efficient by modeling the polymers as freely jointed chains and obtaining direct correlation functions from polymer reference interaction site model calculations. The code we present can solve the DFT equations in up to three dimensions using a parallel implementation. In addition we describe our implementation of an arc-length continuation algorithm, which allows us to explore the phase space of possible solutions to the DFT equations. These numerical tools are applied in this paper to hard chains near hard walls and briefly to block copolymer systems. The method is shown to be accurate and efficient. Arc-length continuation calculations of the diblock copolymer systems illustrate the care required to obtain a complete understanding of the structures that may be found with this polymer-DFT approach.

Surface-induced phase behavior of polymer/nanoparticle blends with attractions.

In an athermal blend of nanoparticles and homopolymer near a hard wall, there is a first order phase transition in which the nanoparticles segregate to the wall and form a densely packed monolayer above a certain nanoparticle density. Previous investigations of this phase transition employed a fluids density functional theory (DFT) at constant packing fraction. Here we report further DFT calculations to probe the robustness of this phase transition. We find that the phase transition also occurs in athermal systems at constant pressure, the more natural experimental condition than constant packing fraction. Adding nanoparticle-polymer attractions increases the nanoparticle transition density, while sufficiently strong attractions suppress the first-order transition entirely. In this case the systems display a continuous transition to a bulk layered state. Adding attractions between the polymers and the wall has a similar effect of delaying and then suppressing the first-order nanoparticle segregation transition, but does not lead to any continuous phase transitions.

Two- and three-body interactions among nanoparticles in a polymer melt

We perform direct three-dimensional density functional theory (DFT) calculations of two- and three-body interactions in polymer nanocomposites. The nanoparticles are modeled as hard spheres, immersed in a hard-sphere homopolymer melt of freely jointed chains. The two-particle potential of mean force obtained from the DFT is in near quantitative agreement with the potential of mean force obtained from self-consistent polymer reference interaction site model theory. Three-body interactions among three nanoparticles are found to be significant, such that it is not possible to describe these systems with a polymer-mediated two-body interaction calculated from the potential of mean force.

Hydrogen-bonded aggregates in precise acid copolymers

We perform atomistic molecular dynamics simulations of melts of four precise acid copolymers, two poly(ethylene-co-acrylic acid) (PEAA) copolymers, and two poly(ethylene-co-sulfonic acid) (PESA) copolymers. The acid groups are spaced by either 9 or 21 carbons along the polymer backbones. Hydrogen bonding causes the acid groups to form aggregates. These aggregates give rise to a low wavevector peak in the structure factors, in agreement with X-ray scattering data for the PEAA materials. The structure factors for the PESA copolymers are very similar to those for the PEAA copolymers, indicating a similar distance between aggregates which depends on the spacer length but not on the nature of the acid group. The PEAA copolymers are found to form more dimers and other small aggregates than do the PESA copolymers, while the PESA copolymers have both more free acid groups and more large aggregates.