Exploring Side Chain Designs for Enhanced Ion Conductivity of Anion

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C: Energy Conversion and Storage; Energy and Charge Transport

Exploring Side Chain Designs for Enhanced Ion Conductivity of Anion Exchange Membranes by Mesoscale Simulations Ming-Tsung Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01815 • Publication Date (Web): 11 Apr 2019 Downloaded from http://pubs.acs.org on April 11, 2019

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The Journal of Physical Chemistry

Exploring Side Chain Designs for Enhanced Ion Conductivity of Anion Exchange Membranes by Mesoscale Simulations Ming-Tsung Lee* Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, Taipei 10608, Taiwan ABSTRACT: Anion exchange membranes (AEM) are polyelectrolytes functionalized with cationic groups. Studies of AEM in the past few decades suggest that AEM is a competitive alternative to conventional proton exchange membranes in fuel cell (FC) application, mainly because of its alkaline environment that allows the use of non-noble metal for electro-catalysts. Understanding AEM morphology and anion transport is a key for improving the performance of AEMFC. The present work uses dissipative particle dynamics (DPD) to simulate the mesoscale structure of hydrated polyphenylene-oxide (PPO) functionalized with tetramethylamine (TMA) groups on different hydration levels (HL) and ion exchange capacities (IEC). Additional spacers are tethered onto PPO-TMA in order to enhance the nano-segregation of hydrophilic and hydrophobic subdomains, and therefore expand the pathways for ion transportation. A variety of spacers studied include alkyl spacers in PPO-C4-TMA, PPO-C8-TMA, and alkoxy spacers in PPO-E2-TMA. Simulation results show that the diffusivities of anions and water increase with the elevation of HL and IEC, which is consistent with experimental observations. Adding hydrophobic alkyl spacers intensifies the phase segregation and the formation of larger water clusters. The size of the clusters further increases due to the agglomeration with the increase of HL or the length of the alkyl spacers. Nevertheless, hydrophobicity from the side chains results in over-aggregated water phase and therefore form bottleneck within the transport pathways that retards the anion diffusivity. The same issue is observed if the alkyl fragment is tethered on TMA as an extender. A suggested design using less hydrophobic alkoxy spacers, PPO-E2-TMA, outperforms all of the other types of AEM in this work in anion transport by forming narrower channels but more connected network. The provided fundamental information may be useful for designing more versatile AEMFC.

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1. INTRODUCTION Anion exchange membranes (AEMs) are made of ionomers composed of backbone chains and side chains containing cationic groups. Their application in fuel cell (FC) technology has attracted increasing attention recently.1-7 AEMs form hydrophilic channels while being solvated by water, and the transportation of hydroxide anions therein characterizes the conductivity of the membranes and the performance of fuel cells. Compared to now-common proton exchange membrane fuel cells (PEMFC), the alkaline operating environment of AEMFC is one major advantage which allows the use of non-noble metal for electrocatalysts.8-12 The growing interests in AEMFC is also on the grounds that the maturity of fundamental PEMFC research13-27 have led to the design of less expensive batteries in many applications. One major issue of AEMFC is the degradation of membranes due to nucleophilic attack of the hydroxide ions on the cationic groups, which causes both the ion exchange capacity (IEC) and ion conductivity of membranes to decrease over time.28-29 One way to improve the stability of AEM is via the modification of side chains. An earlier work by Tomoi et al. studied styrene-based AEM functionalized by quaternary ammonium (QA) cationic groups. It has been found that the thermal stability of AEM can be improved by tethering “spacers” such as alkylene or alkyleneoxymethylene fragments between the benzene ring and QA, because the reactive benzylic carbons are no longer attached to QA groups.30 Long et al. studied the detailed mechanisms of degradation of tetramethylammonium (TMA) and reaction pathways by quantum DFT. The carbon chain length of the spacers has been found to be highly related to the energy barrier of hydroxide ion attacking the TMA groups.31 Since the hydrated morphology of AEM is altered by adding spacers, its impacts on anion diffusivity has also been discussed. Pan et al. studied polysulfone functionalized with TMA groups and different styles of side chain modifications – tadpole (tethered between backbone and TMA as spacers), pedant (tethered onto cation group as extenders), and side chain (tethered onto backbone without TMA). They have found the optimum conductivity to be 0.1 S/cm at 80 °C using side chain design with 8 alkyl groups.32 Dang and Jannasch systematically studied poly(phenylene oxide)s (PPOs) tethered with cationic chains modified by alkyl spacers and extenders. Based on the SAXS results, they have suggested that the flexible alkyl spacers increase the local mobility of attached cationic groups, and therefore induce the phase separation that forms a better pathway for hydroxide ion transportation. With 1 to 5 units of alkyl spacers, the ion conductivity in their synthesized AEM exceeded 0.1 S/cm, a general requirement for high current density cell outputs, at IEC of 1.3 to 1.5 and hydration level (number of water molecules per hydroxide) of 7 to 14.33 However, it should be noted that Parrondo et al.34 suggested that adding alkyl spacers may not be suitable for all kinds of polymer


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backbones in terms of polymer stability. The IEC of the PPO-C6-TMA (C6 represents a 6-Carbon-units alkyl spacer) they synthesized decreased 33%-39% after 30 days, indicating the degradation of the AEM with alkyl spacers.34 Chen et al. studied poly(ether sulfone)-based AEMs tethered by guanidinium side chains with different spacers. They have found that adding 3 methyl units in spacers leads to a better ion conductivity than adding just 1 or 9 methyl units. Moreover, adding ethylene oxides has significantly increased the ion conductivity due to the interconnectivity of ionic channels and hydrophilicity nature of the EO spacer.35 Dang et al. studied thermal stability of PPO with 8 different hetero-cycloaliphatic TMAs. They discovered that the AEM stability decreased with increasing ring strain and methyl substitution,36 which is consistent with the previous findings.34 They have further suggested that quinuclidinium-based AEM is more thermally stable, yet toxicity and the high cost pose another issue.36 Mohanty et al. systematically tested thermal stability of a series of tethered spacers. They found that AEM with benzylsubstitution near the electronegative atoms (such as oxygen) degrade faster in alkaline media in comparison to alkyl-tethered QAs.37 It should also be noted that their earlier work on SEBS-TMA with different spacers has shown that the steric effects of a bulky spacer (or extender) would result in a poorly defined AEM morphology, low water uptake, and a decrease in the ion conductivity.38 There are also recent contributions on more complicated AEMs with branched side chain modifications, including multiblock copolymer with multi-head cationic groups.39-40 Molecular simulations provide a tool to gain fundamental understandings of AEM such as the membrane morphology and transport properties, and therefore may accelerate experimental investigations. Detailed mechanisms of the transportation for hydroxide ions in comparison with those for protons in water have been discussed by Tuckerman and coworkers.41-43 However, the transportation of anions in AEM are impacted by more factors, including the solvation effects and diffusivities of quaternary ammonium groups and anions,44-47 as well as the morphology of nano-segregated subdomains and ion transportation therein. The morphological studies have been performed by methods in multiple scales for different kinds of polymers. Examples include polysulfone-based QAPS by all-atom molecular dynamics (MD)

48

as well as by coarse grained (CG) MD simulations,32 poly(vinyl benzyltrimethylammonium)

based membranes by MD simulations coupled with NMR analysis,49-50 PPO-TMA based membranes by MD simulations with reactive force field51 and with polarizable force field,52-53 poly(arylene ether sulfone) with different functional cationic groups by MD simulations,54 and imidazolium-grafted-PPO membrane by MD simulation.55-56 The impacts of different side chain altercations have also been discussed in various computational studies.12, 32, 51-54, 57



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By lumping several atoms into a CG bead, targeting mesoscale, coarse-grained simulations are capable to predict morphologies of hydrated AEM with affordable computational cost. The obtained morphologies may provide guidelines for the forthcoming experimental studies or serve as a starting point for further atomistic simulations based on a top-down perspective. The accuracy of CG methods relies on the nontrivial constructions of the force field, since all the detailed chemical interactions are lost in the CG process. Lu et al.58-59 devised a CGMD method by adapting mW water model60 to study PPOTMA with chloride counterions. Since the long-range Coulombic interactions are replaced by local three body interactions, their model could tackle large time and length scales in the resolution higher than common CG simulations that typically have 4 heavy atoms mapped to 1 bead. Sepehr et al. used dissipative particle dynamics (DPD) simulation to study the morphology of polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene (SEBS) functionalized with alkyl-substituted quaternary ammonium groups, and compared the estimated diffusivities of hydroxide and chloride ions. The interaction parameters have been obtained by linking to DFT calculations of excess energies for bead components developed by same authors.61 DPD has become popular in polymeric systems ever since Groot and Warren mapped the interparticle interaction parameters to the Flory-Huggins parameters.62 Although new modifications are rolling out to overcome limitations of the DPD model,63 the original formalism of Groot and Warren is still generally accepted in predicting the mesoscale characteristics64 owing to the simplicity of the model in which all detailed molecular interactions are replaced by a short ranged particle interaction constant. The model is suitable for polyelectrolyte fuel cells design, as shown in the studies of Dorenbos.65-73 Nevertheless, in order to further improve the capability of DPD in the studies of PEM/AEM systems for more accurate predictions, two major issues should be addressed with improvements. The first is the effects of electrostatic interaction which is overlooked in most DPD studies. Consequently, the application of the smeared charge algorithm74-75 and screening effects,76 as well as its impacts on amphiphilic selfassemblies77-82 should be considered carefully. The other aspect is regarding the truthful representation of actual chemical species using DPD force field. In this regard, alternative physical parameters are suggested in place of the Flory-Huggins parameters such as partition coefficients83-84 or activity coefficient using scale-bridging parameterization85-87 developed by the author and coworkers. In scale-bridging parameterization, the intramolecular force field parameters of DPD models are fitted to reproduce the conformations of reference molecules obtained by all atom MD simulations. The interaction parameters of DPD beads are mapped to bulk properties of bead components, such as isothermal compressibility of pure solvent and infinite dilution activity coefficients of binary mixtures.85-87


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The devised methods are examined by reproducing micellar properties of common nonionic and ionic surfactants,80, 85-87 and have being applied to modeling polyelectrolyte membranes88-89 by incorporating smeared charge to model explicit charge interactions75 and associating potential to describe proton mobility.90 As summarized above, improving membrane properties via side chain modifications is a non-trivial and time-consuming task. Future breakthrough nests on the understanding of the water filled polymer network and the associated dynamics at the nanoscale. Atomistic simulations are accurate in characterizing the local chemistry but computationally expensive; coarse-grained simulations are efficient in capturing essential membrane morphology, but a trivially constructed force field may limit its capability for systematic studies. The purpose of this work is to establish a coarse-grained protocol that can explore the interplay of membrane morphology and ion transfer which are mutually affected by the chemical structure of polymers and side chains, as well as the working conditions. This work adapts scale-bridging parameterization and performs DPD simulations to investigate the morphology of hydrated PPO-TMA with different cationic side chains modified by alkyl and alkoxy fragments. The purpose is to explore the design of AEM for better ion diffusivity. To the best of the author’s knowledge, such a coarse-grained investigation with explicit electrostatic interactions in AEM has not been done before. The rest of this paper is structured as follows. Section 2 describes simulation methods including DPD force fields, chemical structure of AEM and CG models, and force field parameterizations. Section 3 discusses simulation results in different aspects, including hydration level, length of alkyl side chain, types of side chain, ion exchange capacity, and anion diffusivity. Section 4 concludes the key findings, limitations of current model, and ongoing developments. 2. METHODS 2.1. Force field. Dissipative particle dynamics (DPD) method employed here compiles the standard formulations by Groot and Warren,62 the implementation for electrostatic interactions by GonzálezMelchor et al.,75 and the scale-bridging parameterizations developed by the author and coworkers.85-87 The equations are outlined as follows, and the parameters are summarized in Section 2.3. A system is modeled by an ensemble of equal-sized spherical beads, where each bead represents a molecular fragment or several small molecules. For a pair of bead i and bead j, the pairwise forces can be expressed by eq (1): 𝐅𝑖𝑗(𝐫𝑖𝑗) = 𝐅C𝑖𝑗 + 𝐅D𝑖𝑗 + 𝐅R𝑖𝑗 + 𝐅B𝑖𝑗 + 𝐅E𝑖𝑗


(1)


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The first three terms on the RHS act only when two particles fall within the cutoff radius 𝑟𝑐, which is of the range as bead diameters. Drag forces 𝐅D𝑖𝑗 and random forces 𝐅R𝑖𝑗 together act as a thermostat, and the related stochastic and drag coefficients are chosen according to Groot and Warren’s suggestions.62 Conservative forces 𝐅C𝑖𝑗 are determined by the degree of bead overlapping and the repulsion parameter, aij, is parameterized using a top-down approach:85-87

(

𝐅C𝑖𝑗 = 𝑎𝑖𝑗 1 ―

|𝑟𝑖𝑗| 𝐫𝒊𝒋 𝑟𝑐 |𝑟𝑖𝑗|

)

for 𝑟𝑖𝑗 ≤ 𝑟𝑐 ,and 𝐅C𝑖𝑗 = 0 for 𝑟𝑖𝑗 > 𝑟𝑐.

(2)

The calibration curves are constructed in the following way: DPD simulations are first performed at different values of aij, and the calculated thermodynamic properties are mapped to bulk properties in order to relate bead parameters to a specific chemistry of their composing molecules. For the same bead type (i.e. i = j), aii is fitted to isothermal compressibility of the bulk water, and its value is proportional to the coarse-grained size Nm, the number of water molecules per water bead. For different bead types, the mismatch parameter aij (defined as aij = aij − aii) is fitted to the infinite dilution activity coefficient of the reference compounds of bead i and bead j. The relations between ln𝛾∞ 𝑖𝑗 and aij are built by sampling the insertion energy using the particle insertion method.91 Bond forces 𝐅B𝑖𝑗 in eq. (3) are used to maintain connectivity or rigidity for a chain molecule through 12 bonds (for nearest neighbors) and 1-3 bonds (for 2nd neighbors). The bond potential is either harmonic as in eq. (4) or finitely extendible non-linear elastic (FENE) as in eq. (5). The bond parameters are, contrary to aij, parameterized using a bottom-up approach.85-87 All-atom MD simulations are carried out for obtaining the conformation of the AEM composing chains. 1-2 bond and 1-3 bond parameters are obtained by matching intramolecular distributions from DPD simulations of the coarse-grained AEM model to the atomistic conformation from MD simulations. This method has been applied to the modelling of sPS88 and Nafion.89 Details of the mapping procedure and the determination of bond parameters are discussed later. 𝐅B𝑖𝑗 = ―

∂𝑈(𝑟𝑖𝑗) 𝐫𝒊𝒋

(

∂𝑟𝑖𝑗

)|

𝑟𝑖𝑗|

𝐾 𝑈(𝑟𝑖𝑗) = (𝑟𝑖𝑗 ― 𝑟0)2 2 𝐾

(

𝑈(𝑟𝑖𝑗) = ― 2 𝑟2𝑚ln 1 ―

(𝑟𝑖𝑗 ― 𝑟0)2 𝑟2𝑚

) for 𝑟

𝑖𝑗

< 𝑟0 + 𝑟𝑚; 𝑈(𝑟𝑖𝑗) = ∞ for 𝑟𝑖𝑗 ≥ 𝑟0 + 𝑟𝑚

(3) (4) (5)

Electrostatic forces 𝐅E𝑖𝑗 apply only to charged bead pairs. In order to avoid the divergence of Coulombic energy when charged beads are fully overlapped, charge smearing technique74-75 is adapted to distribute a


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𝑞𝑒

(

point charge to an electronic cloud by a Slater-type function 𝑓(𝑟) = 𝜋𝜆3exp ―

)

2𝑟 75 𝜆 .

When a pair of

charged beads are distant, Coulombic forces of the smeared charges are consistent with those of point charges. The Coulombic forces converge to a finite value at 𝑟𝑖𝑗 = 0, and the magnitude is decided by the smearing length of the Slater-type model. Following the choices of previous studies of PEM,88-90 the effective smearing length is set to 0.25 rc. More discussions on the smearing functions, smearing length,76 and the role of explicit electrostatics in modeling charged polymers78-79, 81 and surfactants80, 82 can be found in the literature. 2.2. Systems and Models. Polyphenylene oxide tetramethylammines (PPO-TMAs) with two levels of ion exchange capacity (IEC) are investigated, chosen based on previous experimental34 (IEC = 1.7 to 2.0) and simulational58 (IEC = 3.2) studies. To explore the effects of side chain composition, alkyl and alkoxy fragments are added to PPO-TMA as spacers if tethered on the PPO backbone, or as extenders if tethered on TMA cationic groups. The type 1 spacer S1 is hydrophobic, and four units and eight units of methylene (labelled as C4 and C8 in Table 1) are used to cover the range of literature values.34 The type 2 spacer S2 is hydrophilic, and two units of ethylene oxide (labelled as E2 in Table 1) are chosen to avoid overassembling of hydrophobic spacers and extenders.32 All of the PPO-TMA based models listed in Table 1 have chloride counter ions, and are a commonly studied precursor form of AEM with hydroxide anions.38 In DPD simulations, molecules are dissected or grouped into spherical beads which occupy a similar volume (i.e. equal rc for all bead types). Based on a reference all-atom MD simulation (details are discussed in the Section 2.3) of PPO, Connolly volume92 of an PPO monomer is found to be equal to the volume of four water molecules, which determines the bead diameter rc as 7.1 Å.77 As illustrated in Figure 1, molecular fragments in other bead types of a similar size are then determined accordingly: A cation C bead includes a TMA cation group solvated with one water molecule, an anion A bead represents a chloride ion solvated with three water molecules, a type 1 spacer S1 bead represents four CH2 units, and a type 2 spacer S2 bead represents two CH2OCH2 units. The mapping of alkyl and alkoxy groups are consistent with previous studies for CnEm nonionic surfactants77,

85

based on the scattering length of

C12E6.93 All bead types are summarized in Table 1. Table 1. Top: Polymers studied in this work, their coarse-grained structures, and theoretical ion exchange capacity (IEC). Bottom: Coarse-grained bead types and corresponding molecular contents. Name PPO-TMA

Models (B-C)x(B)y

x (x + y = 20) 5


Theoretical IEC 1.8


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PPO-TMA (IEC3) PPO-C4-TMA PPO-C8-TMA PPO-TMA-C4 PPO-E2-TMA

(B-C)x(B)y (B-S1-C)x(B)y (B-S1-S1-C)x(B)y (B-C-S1)x(B)y (B-S2-C)x(B)y

10 6 6 6 6

3.2 1.9 1.7 1.9 1.8

Bead type W B C A S1 S2

Bead component 4∙H2O (CH3)2C6H3O (CH3)3NCH2 Cl− + 3∙H2O (CH2)4 (CH2OCH2)2

Bead content four water molecules backbone PPO monomer tetra-methyl ammonium cation solvated chloride anion spacer type 1: butyl spacer type 2: ethylene oxide dimer

Charge 0 0 +1 -1 0 0

Figure 1. Chemical structure of repeating units and tethered cationic groups of AEM studied in this work. Coarse-grained beads are shaded in colors and the types are indexed in purple. 2.3. Parameterization. To describe interparticle interactions and molecular structure for the general DPD force field in eq. (1), repulsion parameters in eq. (2) and bond coefficients in eq. (4)-(5) are determined by adapting previously developed method.85 Repulsion parameters between particles of the same type aii are set to the same value for all bead types, to be mapped to the isothermal compressibility of water.62, 77 For the coarse grained size of rc = 7.1 Å or Nm = 4, aii equals 106.1. Repulsion parameters between particles of different types aij (or the corresponding mismatch parameters aij = aij

aii) are

mapped to mutual solubility of composing molecules in particles i and j. The calibration relation in eq. (6) between the infinite dilution activity coefficient ∞ and mismatch parameter aij is constructed using a hybrid DPD-MC method with particle insertion implementation.85


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ln𝛾∞ 𝑖𝑗 = ln

() 𝑏𝑖

𝑏𝑗

(6)

+ 0.32∆𝑎𝑖𝑗

The 1st term on the RHS is a correction resulted from chemical potential sampled by Widom insertion method91 when transferring from molecular basis to particle basis, where bi is the number of molecules in a bead i. Take the interactions between B bead (PPO) and W bead (water) as an example, experimental water uptake of PPO is 7∙10-4 wt%,94 which is equivalent to a water mole fraction of 0.005. With this solubility for determining the infinite dilution activity coefficient of water and the correction term of ln(1/4) for Nm = 4, the estimated aBW is 12.4. This mismatch parameter is also used for describing the interactions between PPO and other hydrophilic components (hydrated TMA and chloride ions). Following the previous work,85 repulsion parameters involving alkyl and alkoxy fragments are determined based on the solubility of octane in water and activity of water in a PEO-400 melt. The mismatch parameter between PPO backbone and alkyl spacers equals one third of that between PPO and water, as suggested by Groot and Rabone77 for fragments whose mutual solubility isn’t available. Mismatch parameters between all hydrophilic beads (C, A, W) are set to zero due to the fact that TMAs and chloride ion are soluble in water. Such approximation is used in the previous work88, 90 and other DPD studies of polymer electrolytes.78-79, 81

The repulsion parameters used in this work are summarized in Table. 2.

Table 2. Repulsion parameters (mismatch parameters in parentheses) for all kinds of beads as well as 1-2 and 1-3 bond parameters for PPO-TMA and tethered spacers S1 (alkyl) and S2 (alkoxy). The middle beads in 1-3 bonds are marked in parentheses. aij (aij) S1 B S2 C A W

S1 106.1 112.5 (+6.4) 125.2 (+19.1) 125.2 (+19.1) 125.2 (+19.1)

connecting beads B-B B-(B)-B S1-X & S2-X, (X=S1, S2, C) B-X, (X=S1, S2, C) B-(X)-X, (X=S1, S2, C)

B

S2

C

A

W

106.1 107.6 (+1.5) 118.5 (+12.4) 118.5 (+12.4) 118.5 (+12.4)

106.1 107.6 (+1.5) 107.6 (+1.5) 107.6 (+1.5)

106.1 106.1 106.1

106.1 106.1

106.1

bond type harmonic FENE harmonic harmonic harmonic

K 2000 440 80 80 40

r0 rm (FENE) 0.69 1.34 3.0 0.8 0.8 1.6



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DPD models are related to the target PPO-TMA by reproducing backbone conformations of a reference all-atom MD simulation. A single 10-mer PPO chain ([C6H2(CH3)2O]10, M.W. = 1200) is solvated by 3989 water molecules. The general Amber force field (GAFF) is chosen for PPO force field and TIP3P water model is used for water force field, where the initial configurations and simulation input files are prepared by ACPYPE95 and AmberTool.96 The MD simulations are run for 6 ns using Gromacs package97 in the NPT ensemble at normal conditions. The calculated Connolly volume92 of 10-mer PPO sampled from 20 different configurations is 1223.2 ± 3.4 Å3, which is equivalent to the size of 40 water molecules (c.a. 30 Å3 per H2O). This results in our choice of coarse-grained level as Nm = 4 mentioned earlier. 1-2 and 1-3 bond forces for modelled PPO backbones are parameterized based on the configurations of the reference molecule averaged from 5000 frames. The 10mer PPO is modelled by DPD with 10 B beads connected by harmonic 1-2 bonds and FENE 1-3 bonds. The choice of FENE type 1-3 bonds are required to reproduce asymmetric intramolecular behavior of chained molecules as suggested in the literature.85 By mapping each PPO monomer to a DPD bead, the bead-bead distances for the nearest neighbor (r12), 2nd neighbor (r13), 3rd neighbor (r14), are calculated accordingly to describe intramolecular distributions, as shown in in Figure 2. By matching the r12 and r13 configurational profiles from DPD simulations to the profiles from MD simulations, bond coefficients K, r0, and rm are characterized and summarized in Table 2. It is noteworthy that the MD profiles are reproduced by the proposed DPD model well up to r16, which is better than the previous work for alkyl chains and alkoxy chains,85 as a result of the more regular aromatic structure of PPO. All of the other bond coefficients for side chains are estimated by correlate 12 and 1-3 harmonic bond coefficients to the number of covalent bonds between neighboring beads.87 This approximation is validated by reproducing micellar properties of nonionic surfactants.86


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Figure 2. Probability of bead-bead distance rij for neighboring beads (r12), 2nd neighboring beads (r13), and up to 5th neighboring beads (r16) for a solvated 10-mer PPO chain. Results obtained from MD simulations are drawn in dashed black lines, and those from fitted DPD simulations are drawn in red long dashed lines. MD-DPD fitting for alkyl and alkoxy chains obtained previously85 are reprinted here for comparison. 3. RESULTS AND DISCUSSION. All DPD simulations in this work are performed by DL_MESO98 version 2.6 with the force field constructed above. Periodic simulation box is sized 30 rc (equivalent to 21.3 nm), packed with modelled polymer and solvent molecules at bead density equal to 3 commonly used in DPD simulations.62 Each simulation runs for 2 million steps on time step size of 0.01. Using integrated velocity Verlet thermostat in the NVT ensemble, temperature fluctuation is lower than 0.01 degrees. Choosing a small time step size allows for higher accuracy in diffusivity calculations.88, 90 In a typical DPD simulation for self-assembly behavior, a bigger time step size of 0.06  is allowed.74 Parameters for electrostatic interactions are chosen according to the previous studies,88, 75 with the permittivity scaled to 12.6 for Nm = 4 based on Γ = 20.08 ∙ 𝑁𝑚 ―

1 3 74 .

Table 3. Systems simulated in this work, categorized by the hydration level , the number of water molecules per TMA group. NA is the number of anion beads A, NW is the number of water beads W, and NAEM is the number of AEM molecules. DA/DW is the diffusivity of A bead divided by that of W bead. DA is the estimated diffusion coefficient of anion, and IC is the corresponding ionic conductivity. A/V is the



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specific pore area of the hydrophilic channels (if developed), and dmax is the corresponding maximum cross section diameter. AEM



NAEM

PPO-TMA

10

2160 16200 10800

0.95

0.83

0.058

-

-

PPO-C4-TMA

10

1620 32400

8100

0.95

0.85

0.056

0.14

1.75

PPO-C8-TMA

10

1306 31344

7836

0.90

0.78

0.046

0.21

1.75

PPO-TMA (IEC3) 10

1191 28584

7146

0.98

1.47

0.117

0.50

2.18

PPO-TMA

20

1723 15507 10338

0.92

1.15

0.060

0.39

2.72

PPO-C4-TMA

20

1528 13752

9168

0.93

1.18

0.059

0.34

2.88

PPO-C8-TMA

20

1306 31344

7836

0.98

1.16

0.053

0.28

3.17

PPO-TMA-C4

20

1306 31344

7836

0.98

1.12

0.056

0.21

4.99

PPO-E2-TMA

20

1245 31125 12450

0.99

1.30

0.065

0.38

2.72

0.97

1.70

0.098

0.54

2.72

PPO-TMA (IEC3) 20

NW

900 45000

NA

9000

DA/DW DA [105cm2/s] IC [S/cm] A/V [nm-1] dmax [nm]

3.1. Effects of hydration level on AEM nano-segregation. Table 3 lists eight systems simulated in this work, exploring the structure of AEM and the corresponding influences on the ion capacity, cationic side chain, and hydration level. The hydration level  is defined as the number of water molecules per cationic group. Two levels of  are studied to cover the common range of hydration in literature, and  = 20 is usually considered as the “wet” condition.32, 50, 53, 58, 64 With absorbed water, amphiphilic PPO-TMA molecules self-assemble into hydrophobic and hydrophilic sub-domains. Hydrophilic channels, formed by percolated water and hydrated anions, are enclosed by cationic sidechains and aggregated hydrophobic AEM backbones. When these channels are formed, the width and the connectivity of the channels impact the transportation of the mobile components through the membranes. Figures 3a and 3d illustrate the development of water clusters in PPO-TMA-Cl membranes. Although the distribution of the cation groups suggest that the system undergoes nanosegregation, water beads aggregate into small and separated clusters at  = 10 with no visual sign of percolation. The connectivity of these clusters starts to enhance when water content raises to  = 20. Figures 3c and 3f create an isosurface around the percolated water domains, showing the growth of water channels typically found in hydrated polymer electrolyte membranes.99 In addition to isosurface, a digitized morphology is also created to obtain a more precise image of segregated AEM structure. The simulation box is mapped to a lattice model, where each lattice site is characterized by its occupying beads. The grid of the lattice is set to a half of the bead diameter, and the


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“mobility” of the lattice site ms is determined by n surrounding beads within one cutoff distance from the site. The mobility of a particle i, mi, is set to +1 for A and W beads, and mi is 1 for other beads from chain molecules. The site is mobile if ms is equal to or large than zero, as defined by eq (7): 𝑛

𝑚𝑠 =

∑(1 ― 𝑟 )𝑚 𝑖=1

𝑟𝑖𝑠 𝑐

𝑖

(7)

The digitized nano-structure of the hydrated AEM is shown in Figures 3b and 3e. The boundaries of hydrophilic channels are well-defined, allowing the following analysis of the pore size distribution (PSD), which is crucial to understand the transportation of the mobile components in terms of the AEM morphology.

Figure 3. Morphologies of hydrated PPO-TMA-Cl on the hydration level of  = 10 (1st row) and  = 20 (2nd row) in different visualization modes. Bead-based modes (panels a and d) are on the left: W and A beads are in cyan, C beads are in blue, and B beads are in white. Digitized modes are in the middle (panels b and e): mobile phase is in blue, and immobile phase is in red. Isosurface representations (panels c and f) are on the right: mobile phase is in blue, and immobile phase is in white. Isosurface images (QuickSurf



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in VMD drawing method) is created based on the comparison with the digitized AEM structure in its maximum surface quality. The radius scale is 0.5, density isovalue is 0.2, and grid spacing is 0.5. The radial distribution function (RDF, or g(r)) between two water beads is commonly used to describe the clustering of water molecules in hydrated polymer electrolyte membranes.100 RDF of W-W for the two systems discussed in Figure 3 are shown in Figure 4, averaged over 150 frames (from 0.5 million steps to 2 million steps, per ten thousand steps). When g(r) of W-W falls below unity after the 1st dominant peak, W beads start to anti-correlate with each other, and the value of such an r indicates the average cluster size because of the hydrophobic-hydrophilic boundary involved. As shown in Figure 4, the water cluster grows from 1.2 nm to 1.8 nm as  increases from 10 to 20. The position of the 2nd dominant peak is treated as the average cluster spacing, and it increases from 3.3 nm to 4.2 nm. Both quantities validate the swollen hydrophilic domain observed in visual inspections.


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Figure 4. Radial distribution functions of water beads W in PPO-TMA-Cl at the hydration level of  = 10 (dashed line) and  = 20 (solid line). Bottom figure zooms to show the position of the first interception with g(r) = 1. 3.2. Effects of hydrophobic spacer length. Experimental work suggested that adding a C5 spacer may impact the morphology of PPO-TMA-Cl and the ion diffusivity of chloride ions.34 Therefore, alkyl spacers are added to PPO-TMA in order to enhance the aggregation of the hydrophobic sub-domains. Three systems (PPO-TMA, PPO-C4-TMA, PPO-C8-TMA) are compared under the same IEC (see Table 1) and two hydration levels. Judging from the g(r) of water beads in Figure 5a, it is clear that both PPO-C4-TMA and PPO-C8-TMA have an increased size of water clusters with a pore diameter larger than 2 nm. As presented in Figure 5c-e, the evolution of nano-segregation in PPO-TMA, PPO-C4-TMA, PPO-C8-TMA (top to down) suggests that increasing spacer chain length leads to a fewer number of individual subdomains with more agglomerated configurations and more expanded hydrophilic channels.



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Figure 5. Comparisons of hydrated PPO-TMA, PPO-C4-TMA, and PPO-C8-TMA membranes: (a) Radial distribution function of water beads W in terms of bead-bead distance r. (b) Pore size distribution in terms of pore diameter d. PPO-TMA are in black dashed lines, PPO-C4-TMA are in black solid lines, and PPOC8-TMA are in red solid lines. (c-e) Iso-surface snapshots for nano-segregation of mobile and immobile subdomains in (c) PPO-TMA, (d) PPO-C4-TMA, and (e) PPO-C8-TMA. While the increase of the averaged size of water channels suggests that adding hydrophobic fragments to the cationic sidechains as spacers may promote the segregation of hydrophobic and hydrophilic subphases, the bottleneck between chunky water clusters is observable in Figure 5e. This raises a concern that the overly extended hydrophobic sidechains may cause AEM molecules to overly aggregate and prohibit the distribution of water molecules in sustained channels.


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To further look into this issue, pore size distribution (PSD) analysis is performed using Poreblazer version 3.0.2101 to understand the geometry of the percolated water clusters (i.e. the “pores” of the polymer matrix). Using the digitized structures described above, a probe particle is randomly placed in the system and explore the accessible area (i.e. mobile phase) by Monte Carlo procedure that finds the biggest spherical domain that contains the probe particle without overlapping with the immobile sites. The probe particle is treated as a hard sphere with a diameter equal to rc. Properties including the maximum pore size (dmax in Table 3) and specific pore area (A/V in Table 3) are computed. As reported in Table 3, the maximum pore diameter increases with the water content for all cases. PPOC8-TMA at  = 20 generates pores with a maximum diameter larger than 3 nm. At a lower hydration level, PPO-C8-TMA seems outachieve PPO-C4-TMA by providing more accessible pore area, whereas the maximum pore diameter remains the same. However, a high water content enhances the self-assembly of alkyl-TMA side chains and the accessible specific pore area of PPO-C8-TMA is smaller than PPO-C4TMA and PPO-TMA. As the pore size distribution in Figure 5b shows, adding C4 spaces leads to a more populated pore size of 2.2 nm and clusters smaller than 1.6 nm are diminished. In the presence of C8 spacers, a third major peak at 2.8 nm is developed and pores larger than 3 nm start to appear. 3.3. Effects of side chain type. As surveyed in the Introduction, several works (MD simulations32, 51 and experiments32-33) show interests in using alkyl fragments as extenders33 (or referred as a tadpole type32). PPO-TMA-C4 is then studied here compared to PPO-C4-TMA discussed in Section 3.2. Since explicit electrostatic interactions have not been employed in previous AEM studies using a coarse-grained description such as DPD, the current comparison may serve as a guidance when devise long range interactions in the DPD model. The compositions of PPO-TMA-C4 and PPO-C4-TMA systems are the same. The only difference is that the charged cationic groups now locate near the polymer backbones. Figures 6a and 6b compares the water clustering in hydrated PPO-TMA with C4 fragments as spacers and extenders, respectively. As seen from the visualization in Figure 6b, radial distribution function in Figure 7a, and the maximum pore diameter in Table 3, water clusters as large as 5 nm is developed in hydrated PPO-TMA-C4. In the case of PPO-C4-TMA, charged TMA groups have more flexibility to cluster with water. For PPO-TMA-C4, the charged beads are attached to the PPO backbone and have more direct impact on backbone conformations. The dissociated anions on the hydrophobic-hydrophilic interface stabilize the cationic groups, making the backbone of PPO-TMA-C4 to stretch more than that of PPO-C4-TMA, as shown in Figure 7d. Meanwhile, the addition of C4 fragments provides the same extent of hydrophobicity as mentioned in section 3.1, thus driving the nano-segregation at high water contents.



Page 18 of 32

Altogether, water molecules are clustering into bigger but irregular-shaped domains along with the smaller ones. Peaks of PSD in Figure 7e indicates that typical water clusters in PPO-TMA around 2 nm are less populated and the agglomerations of larger sizes are clearly seen. With the formation of large clusters, the decrease in the peak height for C-A and A-W correlations shown in Figure 7b and 7c suggest that more anions tend to be dispersed in and migrated through the water medium away from the charged cationic groups, which at first sight may enhance the ionic mobility. However, the decrease in the specific pore area for PPO-TMA-C4 in Table 3 also indicates that the tadpole type PPO-TMA-C4 could suffer from the same issue as PPO-C8-TMA, for which the ion transportation may be hindered as a result of overly assembled AEM forming bottlenecks for water channels.

Figure 6. System visualization for hydrated (a) PPO-C4-TMA, (b) PPO-TMA-C4, and (c) PPO-E2-TMA. Bead color: B (white), S (black), C (green), A (blue), and W (cyan).


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Figure 7. (a-d) RDF and (d) PSD of hydrated AEM at  = 20. PPO-C4-TMA in black dashed lines, PPOTMA-C4 in black solid lines, PPO-E2-TMA in red solid lines, and PPO-TMA in green solid lines. An alternative design is suggested here to avoid the over-aggregation of PPO-TMA with alkyl spacers at the wet condition by using oligo-ethylene oxide as spacers. More specifically, (CH2OCH2)2 are added



Page 20 of 32

in PPO-TMA as spacers, and the polymer is labelled as PPO-E2-TMA. The goal is to increase the length of the side chain, moving the charged group away from the polymer backbone for water solvation without a substantial increase in the hydrophobicity from the spacers. Based on the experimental scattering volume of a C12E6 surfactant,93 the length of (CH2)4 in C4 spacers is equivalent to that of (CH2OCH2)2 in E2 spacers. In the simulations, the segregated structure of hydrated PPO-E2-TMA is very similar to that of PPO-TMA, and their maximum pore diameters and specific pore areas are the same in Table 3. Several characteristics suggest that PPO-E2-TMA may provide a better environment for ion transportation compared to PPO-TMA: The pores with size smaller than 1.5 nm are diminished in the PSD analysis in Figure 7e, the 1st dominant peak of W-W correlation in Figure 7a decreases, and the overall correlations for A-W and C-A in Figures 7b and 7c increase. As can be seen in Figure 6c, small water clusters merge into a more connected network, and the dissociated anions are solvated better to promote ion transport. The positive impacts of adding less hydrophobic spacers on anionic diffusivity is discussed in Section 3.5. 3.4. Effects of ion capacity. Aside from modifying cationic side chains to promote segregation in hydrated AEM, another straightforward way is to add more cationic groups which increase the IEC. Although the additional cationic sidechains locally hinder the diffusion of anions due to electrostatic attractions between ions carrying opposite charges, the increase of IEC directly raises the limit of water uptake. For the devised model PPO-TMA (IEC3), every other monomer along the PPO backbone is tethered with one TMA group, yielding the IEC equivalent to that investigated in ref.58 In the simulations, the whole system is swollen with water while the packing and spacing of hydrophobic subdomains are visually similar to those in PPO-TMA (IEC=1.8). For  = 20, the pore size distributions of PPO-TMA at two IEC levels are similar, so are the maximum developed pore sizes (see Table 3). This indicates that the morphology of segregation is not influenced by an enhanced IEC at a high water content, and the AEM molecules are well-dissolved in water with only local packing of the polymer backbone. The abundant water molecules form a continuous network, and the system is structured as a percolated 3D pores. RDF of W-W in Figure 8a shows that water in PPO-TMA (IEC3) forms a more bulk-water-like structure since the membrane is swollen. This bulk-water-like characteristic for PPO-TMA (IEC3) also makes anions less correlated with the cations, as suggested in the RDF of C-A in Figure 8b.


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Figure 8. RDF of (a) W-W and (b) C-A of hydrated PPO-TMA (IEC=1.8) at  = 10 (black dashed lines), PPO-TMA (IEC=1.8) at  = 20 (black solid lines), PPO-TMA (IEC=3.2) at  = 10 (red dashed lines), PPO-TMA (IEC=3.2) at  = 10 (red solid lines). RDF of the bulk water using the same W-W repulsion parameters are shown in green solid line for comparison. Before closing this subsection, a summary is drawn for morphological study of hydrated AEM in terms of the chemical structure of polyelectrolytes. First of all, increasing IEC and the hydration level both drive the percolation of water, enhance the dissociation of anions from the cationic groups, and may further improve ion transport. Adding a spacer between PPO and TMA, even with a non-hydrophobic fragment such as polyethylene oxide, improves the formation of sustained water channels. If the hydrophobicity of AEM spacers is increased, nano-segregation of hydrophilic and hydrophobic subdomains as well as an increase in the size of water clusters are expected. However, if the hydrophobic spacer is too long, or the spacer is tethered as an extender of TMA (tadpole type), the over-aggregated water clusters eventually form bottlenecks that could prohibit ion transport at a high water content. 3.5. Diffusion of water and anions through the membranes. Diffusion coefficients of water and hydrated cations are estimated by calculating the mean square displacement (MSD) of beads, which is averaged for 5000 W beads and A beads in each simulation using the Diffusion program in M.DynaMix version 5.2.8.102 For each species, diffusion coefficient is calculated by eq (8). In all of the simulated



Page 22 of 32

systems, the mean square displacement [𝑅𝑖(𝑡0 + 𝑡) ― 𝑅𝑖(𝑡0)]2 reaches the linear regime within the simulation time t. 𝐷=

1 〈[𝑅 (𝑡 + 𝑡) ― 𝑅𝑖(𝑡0)]2〉 6𝑡 𝑖 0

(8)

Physical unit of time ( ) in DPD simulations is determined by mapping the self-diffusion coefficient of water beads DW to the diffusion coefficient of water Dwater. Care should be taken while mapping these two diffusion coefficients with a factor of Nm. The mean square replacement of a water bead is a result of the replacement of Nm composing water molecules. In this work one water bead represents four water molecules with 𝐷𝑊 = 𝐷𝑤𝑎𝑡𝑒𝑟 4 , and therefore the time unit  equals 83.5 ps, which is consistent with the literature value.77 Diffusion coefficients of W beads and A beads in the hydrated AEM systems studied above are first calculated and then converted to physical quantities by comparing with the diffusion coefficient of W beads in the bulk system. Table 3 lists the diffusion coefficient of hydrated anions DA, and the ratio of diffusion coefficients for anion and water beads, DA/DW, where DW is for the hydrated AEM, not for the bulk solvent. For AEMs with the same cationic side chains, increasing the hydration level enhances the diffusion coefficient of the hydrated anion beads A. This trend is the same as increasing the IEC at the same hydration level. At a lower hydration level with  = 10, adding a C4 alkyl spacer on PPO-TMA increases the diffusion coefficient of anions. However, DA for PPO-C8-TMA is smaller than that for PPO-TMA, consistent with the observation of bottleneck-forming of water channels in the AEM mentioned above, which does hinder the overall anion transportation. At the hydration level of  = 20, while DA for PPOC8-TMA is lower than DA for PPO-C4-TMA, it is slightly higher than DA for PPO-TMA. As shown in Figure 9 and Table 3, as  increases from 10 to 20, dmax in PPO-C8-TMA shifts from 1.8 nm to over 3 nm, which indicates that the AEM is swollen at a higher hydration level and domains of clustering water channels locally facilitate water diffusion. For PPO-TMA-C4, however, the over-aggregated water clusters of 5 nm result in trapped domains (as seen in Figure 7d) and DA is even lower than that for PPOTMA. Finally, DA of PPO-E2-TMA is the highest among all of the systems investigated at IEC=1.8, further emphasizing the importance of water cluster channeling.


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Figure 9. Pore size distribution and visualized snapshots (same style as in Figure 3 – B and S1 beads in white, C beads in white, and W and A beads in cyan) for PPO-C8-TMA at the hydration level of  = 10 and  = 20. Given the diffusion coefficient obtained above, the ion conductivities are estimated using Nernst equation in eq. (9), and are reported in Table 3. 𝜎𝑖𝑜𝑛 =

𝐹2 𝐷 𝐶 𝑅𝑇 𝐴 𝐴

(9)

First of all, the comparison between the obtained ion conductivities for PPO-TMA and PPO-C4-TMA is consistent with the experimental observation34 that adding alkyl spacers (C5 in the experiment) does not improve ion conductivity if IEC of PPO-TMA remains the same. The calculated diffusion coefficient for chloride ions is similar to a DPD simulation study for SEBS-based TMA-functionalized AEM.64 The computed ion conductivity of PPO-C4-TMA is 58 mS/cm, which is one half of an experimental work (with OH− anion)36 but fifty times larger than another study (with Cl− anion).34 While the ion conductivity predicted by current DPD simulations semi-quantitatively agrees with available experimental data,34, 36 further improvements of the model are suggested to provide better descriptions for the mechanisms of anion transportation. The main limitation of the current DPD model is the lack of local association forces that describe the dissociation-association equilibrium between charged anions and cationic groups. The explicit consideration of electrostatic interactions does capture certain extent of the effects which are crucial for a charged polymer, as exhibited in the morphological results presented above. However, the short-range Coulombic potential is only of a few kBT at a complete overlap between the beads, which is much lower



Page 24 of 32

than the repulsive forces which are of tens to over a hundred kBT. This means that anions would still dissociate from the cationic hosts even when the AEM is completely dry, and the electrostatic resistance for anions resulted from the clustering cationic groups at the hydrophobic-hydrophilic interface is much smaller than expected. In other words, the diffusivity of anions here may be over-estimated, as evidenced by the relative diffusivity of anion and water beads in Table 3 where anion beads move nearly as fast as water beads. Although the retardation of anions as a result of immobile cationic interface is not truthfully captured, the predicted morphology could still provide a qualitative guideline for the AEM design. The determination of how various mesoscopic structures are related to the anion transport mechanism should be made with caution. 4. CONCLUSION. In this work, DPD simulations are performed to model mesoscale morphology and ion transportation of hydrated anion exchange membranes PPO-TMA-Cl. The structure of AEM impacted by a variety of factors, including IEC, water content, and tethered cationic side chains modified by spacers or extenders, are discussed. Increasing water content or IEC both improve diffusion of chloride ions, which is consistent with experimental observations. Adding alkyl C4 spacers onto the PPO-TMA backbone enhances the nano-segregation of hydrophilic and hydrophobic domains, as a result of the agglomeration of water clusters into connected network. Although such a design seems to improve the transportation of mobile components, water clusters may over-aggregate if the length of alkyl spacers further increase or the C4 fragments are tethered as extenders onto TMA groups. In these cases, the generation of bottlenecks destructs the hydrophilic channels, and hence may decrease the diffusion coefficients of water and anions. Aside from carefully choosing the spacer length based on AEM’s working conditions and water content, a possible suggested design that may avoid this issue is to add hydrophilic fragments as the whole or part of the spacers. PPO-TMA tethered with polyethylene oxide spacers outperforms other spacers at the same IEC and hydration level in enhancing anion conductivity. While DPD simulations with explicit charge considerations and scale bridging parameterization act as a suitable tool to explore possible polyelectrolytes for AEMFC design in morphological aspects, some modifications of the model are still desired in order to improve the ability of more quantitative prediction for ion conductivity. Local associating potential is needed to describe dissociation-association equilibrium between ionic pairs, which is not fully reproduced by the smeared charge approach. For AEM with hydroxide counterions, this can be achieved by incorporating a previous development by the author and


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coworkers88, 90 for modeling proton transport in proton exchange membranes. The associating potential shall be re-parameterized to reproduce the diffusion coefficient of hydroxide ions in the bulk water, the dissociation constant from its host cations, and most ideally the complexation of the ions with nearby water network.103 Subsequently, models for halogen counterions including chloride ions in this work shall be developed in a similar fashion. However, such parameterization might be limited by the lack of experimental data or atomistic simulations as AEM with chloride ions is only the precursor of AEM with hydroxide ions, and has so far drawn less attention. Therefore, ion-ion association potential shall be parameterized in systems with similar amphiphilic nature such as micellar properties of ionic surfactants of the same/similar chemistry. The performance of the model can be assessed by comparing with DPD studies in literature with careful treatment of explicit charge algorithms.78-79, 81-82 ■ AUTHOR INFORMATION Corresponding Author * Email: [email protected] ORCID Ming-Tsung Lee: 0000-0002-9326-8107 Notes The author declares no competing financial interest. ■ ACKNOWLEDGEMENTS This work was supported by MOST (Ministry of Science and Technology) in Taiwan under grant number MOST 106-2218-E-027-019-MY3. Computing equipment was purchased with the help of the School of Engineering and the Department of Chemical Engineering and Biotechnology at National Taipei University of Technology.



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Exploring Side Chain Designs for Enhanced Ion Conductivity of Anion

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