Simulation study of the equilibrium morphology in ionomers with different architectures

Structure and Diffusion of Ionic PDMS Melts

Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Dissipative Particle Dynamics Modeling of Polyelectrolyte Membrane-Water Interfaces

Previous experiments of water vapor penetration into polyelectrolyte membrane (PEM) thin films have indicated the influence of the water concentration gradient and polymer chemistry on the interface evolution, which will eventually affect the efficiency of the fuel cell operation. Moreover, PEMs of different side chains have shown differences in water cluster structure and diffusion. The evolution of the interface between water and polyelectrolyte membranes (PEMs), which are used in fuel cells and flow batteries, of three different side-chain lengths has been studied using dissipative particle dynamics (DPD) simulations. Higher and faster water uptake is usually beneficial in the operation of fuel cells and flow batteries. The simulated water uptake increased with the increasing side chain length. In addition, the water uptake was rapid initially and slowed down afterwards, which is in agreement with the experimental observations. The water cluster formation rate was also found to increase with the increasing side-chain length, whereas the water cluster shapes were unaffected. Water diffusion in the membranes, which affects proton mobility in the PEMs, increased with the side-chain length at all distances from the interface. In conclusion, side-chain length was found to have a strong influence on the interface water structure and water penetration rates, which can be harnessed for the better design of PEMs. Since the PEM can undergo cycles of dehydration and rehydration, faster water uptake increases the efficiency of these devices. We show that the longer side chains with backbone structure similar to Nafion should be more suitable for fuel cell/flow battery usage.

Improving proton conduction pathways in di- and triblock copolymer membranes: Branched versus linear side chains

Phase separation within a series of polymer membranes in the presence of water is studied by dissipative particle dynamics. Each polymer contains hydrophobic A beads and hydrophilic C beads. Three parent architectures are constructed from a backbone composed of connected hydrophobic A beads to which short ([C]), long ([A₃C]), or symmetrically branched A₅[AC][AC] side chains spring off. Three di-block copolymer derivatives are constructed by covalently bonding an A₃₀ block to each parent architecture. Also three tri-blocks with A₁₅ blocks attached to both ends of each parent architecture are modeled. Monte Carlo tracer diffusion calculations through the water containing pores for 1226 morphologies reveal that water diffusion for parent architectures is slowest and diffusion through the di-blocks is fastest. Furthermore, diffusion increases with side chain length and is highest for branched side chains. This is explained by the increase of water pore size with 〈N_bond〉, which is the average number of bonds that A beads are separated from a nearest C bead. Optimization of 〈N_bond〉 within the amphiphilic parent architecture is expected to be essential in improving proton conduction in polymer electrolyte membranes.

Dependence of Solvent Diffusion on Hydrophobic Block Length within Amphiphilic-Hydrophobic Block Copolymer Membranes

Pore networks and water diffusion within model (amphiphilic-hydrophobic) diblock copolymer membranes in the presence of 16 vol % water is studied by dissipative particle dynamics in combination with Monte Carlo tracer diffusion calculations. The amphiphilic block (parent architecture (A[A₃C])₁₀) is composed of a backbone that contains 10 consecutively connected hydrophobic A beads; to each A bead, a side chain is grafted composed of three connected A beads and a pendant hydrophilic C bead. Hydrophobic blocks are constructed from x covalently bonded A beads, with x = 20, 30, or 50. Water diffusion through the pores is modeled by Monte Carlo tracer diffusion within more than 500 mapped morphologies. Long range water diffusion within the amphiphilic-hydrophobic ((A[A₃C])₁₀-A_x) diblock architectures increases with hydrophobic block length. Diffusion increases with Q = ⟨N_bond⟩|C||1 - C|^-1, where C is the hydrophilic C bead fraction and ⟨N_bond⟩ the average number of bonds that A beads are separated from the nearest C bead. These trends are also anticipated for amphiphilic parent architectures (ACA₃)₁₀, (A₂[C]A₂)₁₀, and (A₂[AC]A)₁₀. This is explained by the squeezing of water from the hydrophobic phase into the amphiphilic phase. Two characteristic distances are observed: The shorter distance corresponds to the interpore (or intercluster) separation within the "parent architecture-water" phase and obeys the earlier obtained linear relation between intercluster distance and ⟨N_bond⟩_amphi of the amphiphilic parent architecture. The longer distance is governed by the phase separation between the amphiphilic-water phase and hydrophobic blocks.

Water Diffusion Dependence on Amphiphilic Block Design in (Amphiphilic-Hydrophobic) Diblock Copolymer Membranes

Polyelectrolyte membranes (PEMs) are applied in polyelectrolyte fuel cells (PEFC). The proton conductive pathways within PEMs are provided by nanometer-sized water containing pores. Large-scale application of PEFC requires the production of low-cost membranes with high proton conductivity and therefore good connected pore networks. Pore network formation within four alternative model diblock (hydrophobic_amphiphilic) copolymers in the presence of water is studied by dissipative particle dynamics. Each hydrophobic block contains 50 consecutively connected hydrophobic (A) fragments, and amphiphilic blocks contain 40 hydrophobic A beads and 10 hydrophilic C beads. For one amphiphilic block the C beads are distributed uniformly along the backbone. For the other architectures C beads are located at the end of the side chains attached at regular intervals along the backbone. Water diffusion through the pores is modeled by Monte Carlo tracer diffusion through mapped morphologies. Diffusion is highest for the grafted architectures and increases with increase of length of the side chains. A consistent picture emerges in which diffusion strongly increases with the value of ⟨Nbond⟩ within the amphiphilic block, where ⟨Nbond⟩ is the average number of bonds between hydrophobic A beads and the nearest C bead.

Modelling linear and branched amphiphilic star polymer electrolyte membranes and verification of the bond counting method

Water diffusion through hydrated amphiphilic star polymer membranes depends strongly on hydrophilic position within the linear and Y-shaped arms.

Water diffusion within hydrated model grafted polymeric membranes with bimodal side chain length distributions

The effect of bimodal side chain length distributions on pore morphology and solvent diffusion within hydrated amphiphilic polymeric membranes is predicted. Seven polymeric architectures are constructed from hydrophobic backbones from which at regular intervals side chains branch off that are alternatingly short (composed of p hydrophobic A fragments or beads) and long (q A fragments, q > p). The side chains are end-linked with a hydrophilic C fragment. Pore morphologies at a water volume fraction of 0.16 are calculated by dissipative particle dynamics (DPD). Water diffusion through the water containing pores is calculated by tracer diffusion calculations through 140 selected snapshots and from the water bead motions. Diffusion constants decrease with difference in side chain lengths, q - p. Overall, the distance between pores also decreases with q - p. The results are explained by counting for every architecture the average number of bonds 〈N(bond)〉 between an A and the nearest C fragment. These results are in line with a database that contains more than 60 architectures. Diffusion constants tend to increase linearly with 〈N(bond)〉|C|(-1)|A|, where |C| and |A| are the C and A bead fractions within the architecture. 〈N(bond)〉 is therefore expected to be an interesting design parameter for obtaining low percolation thresholds for solvent and/or proton diffusion.

Self-assembly in Nafion membranes upon hydration: water mobility and adsorption isotherms

By means of dissipative particle dynamics (DPD) and Monte Carlo (MC) simulations, we explored geometrical, transport, and sorption properties of hydrated Nafion-type polyelectrolyte membranes. Composed of a perfluorinated backbone with sulfonate side chains, Nafion self-assembles upon hydration and segregates into interpenetrating hydrophilic and hydrophobic subphases. This segregated morphology determines the transport properties of Nafion membranes that are widely used as compartment separators in fuel cells and other electrochemical devices, as well as permselective diffusion barriers in protective fabrics. We introduced a coarse-grained model of Nafion, which accounts explicitly for polymer rigidity and electrostatic interactions between anionic side chains and hydrated metal cations. In a series of DPD simulations with increasing content of water, a classical percolation transition from a system of isolated water clusters to a 3D network of hydrophilic channels was observed. The hydrophilic subphase connectivity and water diffusion were studied by constructing digitized replicas of self-assembled morphologies and performing random walk simulations. A non-monotonic dependence of the tracer diffusivity on the water content was found. This unexpected behavior was explained by the formation of large and mostly isolated water domains detected at high water content and high equivalent polymer weight. Using MC simulations, we calculated the chemical potential of water in the hydrated polymer and constructed the water sorption isotherms, which extended to the oversaturated conditions. We determined that the maximum diffusivity and the onset of formation of large water domains corresponded to the saturation conditions at 100% humidity. The oversaturated membrane morphologies generated in the canonical ensemble DPD simulations correspond to the metastable and unstable states of Nafion membrane that are not realized in the experiments.

Transport in supported polyelectrolyte brushes

Functional polymers have a wide variety of applications ranging from energy storage to drug delivery. For energy storage applications, desirable material properties include low cost, high charge storage and/or mobility, and low rates of degradation. Isotropic thin films have been used for many of these types of applications, but research suggests that different structures such as polymer brushes can improve charge transport by an order of magnitude. Supported polymer brush structures produced by "grafting-from" polymerization methods offer a framework for a controlled study of these materials on the molecular scale. Using these materials, researchers can study the basis of hindered diffusion because they contain a relatively homogeneous polyelectrolyte membrane. In addition, researchers can use fluorescent molecular probes with different charges to examine steric and Coulombic contributions to transport near and within polymer brushes. In this Account, we discuss recent progress in using fluorescence correlation spectroscopy, single-molecule polarization-resolved spectroscopy, and a novel three-dimensional orientational technique to understand the transport of charged dye probes interacting with the strong polyanionic brush, poly(styrene sulfonate). Our preliminary experiments demonstrate that a cationic dye, Rhodamine 6G, probes the brush as a counterion, and diffusion is therefore dominated by Coulombic forces, which results in a 10,000-fold decrease in the diffusion coefficient in comparison with free diffusion. We also support our experimental results with molecular dynamics simulations. Further experiments show that, up to 50% of the time, Rhodamine 6G translates within the brush without significant rotational diffusion, which indicates a strong deviation from Fickian transport mechanisms (in which translational and rotational diffusion are related directly through parameters such as chemical potential, size, solution viscosity, and thermal properties). To understand this oriented transport, we discuss the development of an experimental technique that allows us to quantify the three-dimensional orientation on the time scale of intrabrush transport. This method allowed us to identify a unique orientational transport direction for Rhodamine 6G within the poly(styrene sulfonate) brush and to report preliminary evidence for orientational dye "hopping".

Simulation study of poled low-water ionomers with different architectures

The role of the ionomer architecture in the formation of ordered structures in poled membranes is investigated by molecular dynamics computer simulations. It is shown that the length of the sidechain L(s) controls both the areal density of cylindrical aggregates N(c) and the diameter of these cylinders in the poled membrane. The backbone segment length L(b) tunes the average diameter D(s) of cylindrical clusters and the average number of sulfonates N(s) in each cluster. A simple empirical formula is noted for the dependence of the number density of induced rod-like aggregates on the sidechain length L(s) within the parameter range considered in this study.