A study of diblock copolymer/charged particle nanoporous membranes; morphology, design and transport property modeling

A combination of self-consistent field theory and density functional theory was used to examine the stable, 3-dimensional equilibrium morphologies formed by diblock copolymers with a neutral or charged nanoparticle attached either between the two blocks or at the end of copolymer. Particle size was varied between one and four tenths of the radius of gyration of the copolymer. Phase diagrams were constructed and analyzed in terms of thermodynamic diagrams to understand the molecular-level self-assembly processes with the aim of determining the appropriate morphologies used as nanoporous membranes, (i.e. the periodic, hexagonal arrays of cylinders wherein the particles would primarily be located within the interface between the two blocks). Key factors were determined to be the particle position, particle size, interactions between the blocks and particles, and the copolymer composition and molecular weight.

Self-assembly of a diblock copolymer under an external field was also investigated by overlaying a free energy for an entropic chain, herein modeled as finitely-extensible nonlinear elastic dumbbell, onto the standard diblock copolymer free energy expression along with the associated energy of the external field. The additional influence of the external field, dramatically affected the overall chain extension and orientation, thus commensurately affecting the free energy. As a consequence, the stable, equilibrium properties of the diblock copolymer system were directly responsive to changes in the global properties. The results demonstrated a promising strategy for controlling the polymer segmental orientation, the domain densities, as well as the microphase domain dimensions.

We also studied the conductivity of perfluorosulfonate acid (PFSA) polymer membranes using a nanoporous network model. The transport of hydronium ions inside the network was expressed by an extended Nernst-Einstein equation. Percolation theory was used to modify the diffusion coefficient and to illustrate the transport mechanism. The conductivity of typical PFSA membranes was quantified in terms of water content, equivalent weight, temperature, and polymer architecture. Theoretical predictions of this model were compared against experimental data for four different membranes: Nafion, Membrane C, a Dow membrane, and a 3M membrane at different water contents and temperatures. The comparisons displayed qualitative and quantitative agreement between theory and experiment.