Morphology and diffusion within model membranes: Application of bond counting method to architectures with bimodal side chain length distributions

How fork-length asymmetry affects solvent connectivity and diffusion in grafted polymeric model membranes

The hydrophilic pore morphology and solvent diffusion within model (amphiphilic) polymer membranes are simulated by dissipative particle dynamics (DPD). The polymers are composed of a backbone of 18 covalently bonded A beads to which at regular intervals side chains are attached. The side chains are composed of linear Ap chains (i.e., -A1-A2…Ap) from which two branches, [AsC] and [ArC], split off (s ≤ r). C beads serve as functionalized hydrophilic pendent sites. The branch lengths (s + 1 and r + 1) are varied. Five repeat unit designs (with general formula A3[Ap[AsC][ArC]]) are considered: A2[A3C][A3C] (symmetric branching), A2[A2C][A4C], A2[AC][A5C], A2[C][A6C] (highly asymmetric branching), and A4[AC][A3C]. The distribution of water (W) and W diffusion through nanophase segregated hydrophilic pores is studied. For similar primary length p, an increase in side chain symmetry favors hydrophilic pore connectivity and long-range water transport. C beads located on the longer [ArC] branches reveal the highest C bead mobility and are more strongly associated with water than the C beads on the shorter [AsC] branches. The connectivity of hydrophilic (W and W + C) phases through mapped replica of selected snapshots obtained from Monte Carlo tracer diffusion simulations is in line with trends found from the W bead diffusivities during DPD simulations. The diffusive pathways for protons (H+) in proton exchange membranes and for hydronium (OH-) in anion exchange membranes are the same as for solvents. Therefore, control of the side chain architecture is an interesting design parameter for optimizing membrane conductivities.

Simulated and Experimental Trends Regarding Water Uptake in Polymeric Electrolyte Membranes

Polymeric membranes in an anion or a proton exchange membrane fuel cell need sufficient hydration in order to provide a high hydroxide ion or proton conductivity. The water uptake for six model ionomer membranes, all of the same ion exchange capacity, is modeled by dissipative particle dynamics. The architectures cover three types of families that are of potential interest in fuel cell membrane research. All architectures consist of connected hydrophobic backbone A beads, to which side chains are grafted. For the type I family, the hydrophilic (functional) C beads are pendent on (amphiphilic) [AxC] side chains. The type II architecture contains both hydrophobic [A4] and short hydrophilic [C] side chains. For type III, the C beads are embedded along various locations within the [AxCAy] side chains (x + y = constant). For similar equilibrium time, the membrane water volume fraction increases with side chain length x for type I, and for type III, it increases with the distance x that C beads are separated from the backbone. Among the architectures (types I and III) for which the number of covalent C-A bonds are the same, the water uptake increases with the average number of A-A and A-C bonds (dpd springs) between A beads and the nearest C bead. A picture emerges in which for similar ion exchange capacity model membranes water uptake increases as a function of ⟨Nbondphob-phyl⟩.

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.

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.