Assembled Structures of Perfluorosulfonic Acid Ionomers Investigated by Anisotropic Modeling and Simulations

Nafion, a classic of perfluorosulfonic acid ionomers, has broad applications in proton conduction, attributed from the unique structures. However, a satisfactory structure model from theoretical calculation and simulation that can match with the well-known experimental observations is still absent. We performed GPU-accelerated molecular dynamics simulations to investigate the assembled structures of Nafion at different water contents based on an anisotropic coarse-grained model equipped with Gay–Berne potential. Accurate parameters for the coarse-grained model are collected by matching energy profiles based on density functional theory calculations. The results show that the hydrophilic phase in Nafion assemblies undergoes a crossover from isolated spherical clusters to interconnected cluster/channel networks with the increase of water content. We found the crystalline domains in polymer matrix and they are suppressed at elevated water content. These microphase-separated structures achieve quantitative agreement with existing experimental observations, including morphologies from electron microscopy and intensity profiles from scattering experiments. This work suggests that accurate consideration of the anisotropy is a key to reveal the formation of unique assembled structures of perfluorosulfonic acid ionomers at different water contents

The average simulation cost per step of GALAMOST (GALA) and LAMMPS (LAMM) with the GB (+GB) or the MGB (+MGB) interaction as a function of the number of particles in simulation systems.

<p>The average simulation cost per step of GALAMOST (GALA) and LAMMPS (LAMM) with the GB (+GB) or the MGB (+MGB) interaction as a function of the number of particles in simulation systems.</p

The average end-to-end distance (<i>R</i>_<i>f</i>) of backbone for MCLCP and SCLCP.

<p>The average end-to-end distance (<i>R</i>_<i>f</i>) of backbone for MCLCP and SCLCP.</p

The radial distribution function <i>g</i>(<i>r</i>) and the orientational correlation functions <i>g</i>₂(<i>r</i>) at various temperatures for small molecular, MCLCP and SCLCP systems.

<p>The three vertical dash lines label the location of the side-by-side and cross, the 2^nd nearest side-by-side and T-shape, and the end-to-end packing of mesogens from left to right.</p

Schematics of LC molecules (A) in small molecular LC (SMALL, B), main-chain polymers (MCLCP, C) and side-chain polymers (SCLCP, D).

<p>Ellipsoids are mesogens, spheres are backbone connectors in SCLCP and the springs demonstrate harmonic interactions. <i>θ</i> is the angle between the major axis of the two adjacent GB mesogens (<b>u</b>_<i>i</i>, <b>u</b>_<i>j</i>) for MCLCP (C), while it is the angle between the major axis of the GB mesogen (<b>u</b>_<i>i</i>) and the vector from the center of the GB mesogens to the adjacent LJ beads on backbone (<b>r</b>_<i>ij</i>) for SCLCP (D). The site-site vector <b>S</b>_<i>ij</i> connects the two adjacent GB/GB sites or GB/LJ sites placed in terminal position for MCLCP and SCLCP, respectively.</p

The average simulation cost per step of GALAMOST and LAMMPS for pair force, neighbor list and integration, the three major time consuming functions in MD simulation.

<p>The average simulation cost per step of GALAMOST and LAMMPS for pair force, neighbor list and integration, the three major time consuming functions in MD simulation.</p

Snapshots of typical phases for mesogens in small molecules (up), MCLCP (middle) and SCLCP (bottom) with temperature increasing from left to right.

<p>Snapshots of typical phases for mesogens in small molecules (up), MCLCP (middle) and SCLCP (bottom) with temperature increasing from left to right.</p

The vectors and parameters of two interacted ellipsoids (left), the interaction profile of GB potential (solid lines) and its modified form (MGB, dotted lines).

<p>Interaction profiles in four orientations including side-by-side, cross, T-shape and end-to-end from left to right are presented.</p

Orientational order parameter <i>S</i> of mesogens in small molecules as a function of temperature and simulation approaches.

<p>Orientational order parameter <i>S</i> of mesogens in small molecules as a function of temperature and simulation approaches.</p

The phase diagram of mesogens in small molecular LC obtained by GPU-accelerated simulation equipped with coarse grained GB potential.

<p>Solid circles mark our simulation results and lines are plotted for guide only. The X-axis is converted to number density for the comparison with de Miguel’s report.</p