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DOE OSTI2025

Bridging interfacial properties and cell performance: A multiscale model for proton-exchange-membrane fuel cells

Here, to elucidate the impact of local interfaces on mass-transport resistance and overall cell performance of low-loaded proton-exchange-membrane fuel cells (PEMFCs), we present a multiscale modeling framework incorporating a novel modified agglomerate model. The model considers three distinct Pt-electrolyte interfaces: Pt on the carbon surface covered by either ionomer or water film and Pt inside carbon nanopores. Detailed mass-transport voltage-loss breakdowns reveal that coupled agglomerate-interface-scale mass transport dominates the mass-transport loss. The ionomer poisons the exterior-Pt surface through suppressing O 2 adsorption and intrinsic ORR activity, leading to low current-density performance. Conversely, interior-Pt interface enhances the kinetic performance but limits high current-density performance due to its low interfacial permeability. The exterior-Pt/water interface demonstrates superior kinetic performance and mass transport, though its practical implementation requires ensuring proton transport. By coupling the multiscale CL properties with ink parameters, the model identifies an optimal I to C ratio of approximately 0.5, a moderate value where the ionomer content is sufficient to guarantee proton transport without fully covering the Pt surface and forming large agglomeration, thus allowing the utilization of the Pt-water interface and avoiding high mass-transport loss. Overall, the model helps unravel limiting phenomena across different operating regimes and provides routes for optimizing performance.

Cell diagnostic↗

DOE OSTI2023

Modeling the 4D discharge of lithium-ion batteries with a multiscale time-dependent deep learning framework

The lithium-ion battery (LIB) field is moving towards the direction of investigating spatially resolved physical phenomena in the 3D porous microstructure of electrodes. These pore-scale simulations give new insights into the local dynamics of lithiation/de-lithiation and charge transport, Nevertheless, the computational time of these simulations limits the integration of these models in optimization workflows of cycling conditions or electrode manufacturing processes. Machine learning models present a way of assessing in real-time the performance of materials. While several successful techniques for replicating simulations with machine learning have been proposed, this case study presents a more demanding problem, due to the necessity of understanding the behavior of heterogeneous 3D local data, as it evolves in time: this poses both a scientific and a technical challenge. To this end, we propose an autoregressive multiscale convolutional neural network model to predict relevant quantities at the pore-scale in the solid phase: the lithium concentration (in the active material) and potential (in the active material and carbon binder). Here, these are ultimately used to reconstruct the battery discharge curve. 3D images of the electrode microstructures are the input to the network, trained with a dataset of finite element method simulations to predict the discharge behavior of the cathode side in lithium ion batteries. We propose this machine learning model as a proof-of-concept of the applicability of multiscale networks for time-dependent physics problems. The trained model exhibits very high accuracy (with errors lower than 2 %) in forecasting the discharge behavior of new unseen cathodes.

25 ENERGY STORAGE↗

DOE OSTI2020

Efficient bi-directional coupling of 3D computational fluid-particle dynamics and 1D Multiple Path Particle Dosimetry lung models for multiscale modeling of aerosol dosimetry

The development of predictive aerosol dosimetry models has been a major focus of environmental toxicology and pharmaceutical health research for decades. One-dimensional (1D) models successfully predict overall deposition averages but fail to accurately predict local deposition. Computational fluid-particle dynamics (CFPD) models provide site-specific predictions but at a computational cost that prohibits whole lung predictions. Thus, there is a need for developing multiscale strategies to provide a realistic subject-specific picture of the fate of inhaled aerosol in the lungs. CT-based 3D/CFPD models of the large airways were bidirectionally coupled with individualized 1D Navier-Stokes airflow and particle transport based upon the widely used Multiple Path Particle Dosimetry Model (MPPD). Distribution of airflows among lobes was adjusted by measured lobar volume changes observed in CT images between FRC and FRC + 1.5 L. Additionally, as a test of the effectiveness of the coupling procedures, deposition modeling of previous 1 µm aerosol exposure studies was performed. The complete coupled model was run for 3 breaths, with the computation-intense portion being the 3D CFD Lagrangian particle tracking calculation. The average deposition per breath was 11% in the combined multiscale model with site-specific doses available in the CFPD portion of the model and airway- or region-specific deposition available for the MPPD portion. In conclusion, the key methods developed in this study enable predictions of ventilation heterogeneities and aerosol deposition across the lungs that are not captured by 3D or 1D models alone. Overall, these methods can be used as the foundation for multi-scale modeling of the full respiratory system.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2012

Multiscale studies of the three-dimensional dayside X-line

We review recent experience from the Cluster, Double Star, and THEMIS missions for lessons that apply to the upcoming Magnetospheric Multiscale Mission (MMS) being developed for launch in 2014. On global scales, simulation and statistical studies lead to mean configurations of dayside reconnection, implying specific relative alignments of the inflow magnetic fields and X-line, with implications for MMS operations designed to maximize the number of close encounters with the diffusion region. At intermediate MHD-to-ion scales, reconstruction of features created by one or two X-lines have developed to the point where data from a cluster of spacecraft can determine their temporal trends and the approximate three-dimensional X-line structure. Recent petascale particle-in-cell (PIC) simulations of reconnection encompass three spatial dimensions with excellent resolution, and make striking predictions of electron scale physics that creates complex interacting flux ropes under component reconnection. High time resolution measurements from MMS will determine the detailed electron scale kinetics embedded within the global and MHD–ion scale contexts. These developments will lead to the refinement of our three-dimensional multiscale picture of reconnection, yielding improved understanding of the global, MHD, and local physics controlling the onset or quenching, variability, and mean rate of reconnection. This in turn will enable improved predictability of the structural features created by transient reconnection, and their space weather consequences.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Parallel multiscale simulations of a brain aneurysm

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Multiscale modeling and computation of optically manipulated nano devices

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, and use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Constrained approximation of effective generators for multiscale stochastic reaction networks and application to conditioned path sampling

Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement to the constrained approach, which is a method for computing effective dynamics of slowly changing quantities in these systems, but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA can cause errors in the estimation of effective dynamics for systems where the difference in timescales between the “fast” and “slow” variables is not so pronounced. This new application of the constrained approach allows us to compute the effective generator of the slow variables, without the need for expensive stochastic simulations. This is achieved by finding the null space of the generator of the constrained system. For complex systems where this is not possible, or where the constrained subsystem is itself multiscale, the constrained approach can then be applied iteratively. This results in breaking the problem down into finding the solutions to many small eigenvalue problems, which can be efficiently solved using standard methods. Since this methodology does not rely on the quasi steady-state assumption, the effective dynamics that are approximated are highly accurate, and in the case of systems with only monomolecular reactions, are exact. We will demonstrate this with some numerics, and also use the effective generators to sample paths of the slow variables which are conditioned on their endpoints, a task which would be computationally intractable for the generator of the full system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

A multiscale Bayesian data integration approach for mapping air dose rates around the Fukushima Daiichi Nuclear Power Plant

This paper presents a multiscale data integration method to estimate the spatial distribution of air dose rates in the regional scale around the Fukushima Daiichi Nuclear Power Plant. We integrate various types of datasets, such as ground-based walk and car surveys, and airborne surveys, all of which have different scales, resolutions, spatial coverage, and accuracy. This method is based on geostatistics to represent spatial heterogeneous structures, and also on Bayesian hierarchical models to integrate multiscale, multi-type datasets in a consistent manner. The Bayesian method allows us to quantify the uncertainty in the estimates, and to provide the confidence intervals that are critical for robust decision-making. Although this approach is primarily data-driven, it has great flexibility to include mechanistic models for representing radiation transport or other complex correlations. Here, we demonstrate our approach using three types of datasets collected at the same time over Fukushima City in Japan: (1) coarse-resolution airborne surveys covering the entire area, (2) car surveys along major roads, and (3) walk surveys in multiple neighborhoods. Results show that the method can successfully integrate three types of datasets and create an integrated map (including the confidence intervals) of air dose rates over the domain in high resolution. Moreover, this study provides us with various insights into the characteristics of each dataset, as well as radiocaesium distribution. In particular, the urban areas show high heterogeneity in the contaminant distribution due to human activities as well as large discrepancy among different surveys due to such heterogeneity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

A concurrent irradiation-mechanics multiscale coupling model

The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. Here, we present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

42 ENGINEERING↗

DOE OSTI2024

A multiscale model to understand the interface chemistry, contacts, and dynamics during lithium stripping

A reversible Li-metal electrode, paired with a solid electrolyte, is critical for attaining higher energy density and safer batteries beyond the current lithium-ion cells. A stable stripping process may be even harder to attain as the stripping process will remove Li-atoms from the surface, and naturally reduce surface contact area, if not self-corrected by other mechanisms, such as diffusion and plastic deformation under an applied external stack pressure. Here, we capture these mechanisms occurring at multiple length- and time- scales, i.e., interface interactions, vacancy hopping, and plastic deformation, by integrating density functional theory (DFT) simulations, kinetic Monte Carlo (KMC), and continuum finite element method (FEM). By assuming the self-affine nature of multiscale contacts, we predict the steady-state contact area as a function of stripping current density, interface wettability, and stack pressure. We further estimate the exponential increase of overpotential due to contact area loss to maintain the same stripping current density. We demonstrate that a lithiophilic interface requires less stack pressure to reach the same steady-state contact area fraction than a lithiophobic interface. A “tolerable steady-state” contact area loss for maintaining stable stripping is estimated at 20 %, corresponding to a 10 % increase in overpotential. To constrain contact loss within the tolerance, the required stack pressure is 0.1, 0.5, and 2 times the yield strength of lithium metal for three distinct interfaces, lithiophilic Li/lithium oxide(Li2O), Li/lithium lanthanum zirconium oxide(LLZO), and lithiophoblic Li/lithium fluoride(LiF), respectively. The modeling results agree with experiments on the impact of the stack pressure quantitatively, while the discrepancy in stripping rate sensitivity is attributed to the simplifying interface interaction in our simulations. Overall, this multiscale simulation framework demonstrates the importance of electrochemical-mechanical coupling in understanding the dynamics of the Li/SE interface during stripping.

Feng, Min↗

DOE OSTI2012

Multiscale microstructural characterization of Sn-rich alloys by three dimensional (3D) X-ray synchrotron tomography and focused ion beam (FIB) tomography

Sn-rich (Pb-free) alloys serve as electrical and mechanical interconnects in electronic packaging. It is critical to quantify the microstructures of Sn-rich alloys to obtain a fundamental understanding of their properties. In this work, the intermetallic precipitates in Sn-3.5Ag and Sn-0.7Cu, and globular lamellae in Sn-37Pb solder joints were visualized and quantified using 3D X-ray synchrotron tomography and focused ion beam (FIB) tomography. 3D reconstructions were analyzed to extract statistics on particle size and spatial distribution. In the Sn-Pb alloy the interconnectivity of Sn-rich and Pb-rich constituents was quantified. It will be shown that multiscale characterization using 3D X-ray and FIB tomography enabled the characterization of the complex morphology, distribution, and statistics of precipitates and contiguous phases over a range of length scales. - Highlights: Black-Right-Pointing-Pointer Multiscale characterization by X-ray synchrotron and focused ion beam tomography. Black-Right-Pointing-Pointer Characterized microstructural features in several Sn-based alloys. Black-Right-Pointing-Pointer Quantified size, fraction, and clustering of microstructural features.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Multiscale geographically and temporally weighted regression (MGTWR): exploring the spatiotemporal heterogeneity of EV market adoption

As an innovative vehicle technology, electric vehicles are experiencing growing sales and have made significant inroads into the traditional automotive market in the United States and around the world. However, EV adoption rates vary significantly across space and over time, influenced by a complex interplay of socio-economic and infrastructural factors alongside federal and state policies. Here, this paper presents a comprehensive spatial–temporal investigation of EV market adoption within one city in the US, that of Chicago, utilizing Multiscale Geographically and Temporally Weighted Regression (MGTWR) alongside Multiscale Geographically Weighted Regression (MGWR). The aim is to unravel the spatial and temporal dynamics affecting EV adoption and to explore how the influence of various determinants of EV adoption, such as demographic factors and economic conditions, vary spatially. Moreover, by utilizing MGTWR, we provide insights into the evolution of these relationships over time, offering a predictive outlook on future EV market growth. Our findings, with an 86.6% prediction accuracy for EV market adoption, tailored policy measures to support accelerated EV adoption. Methodologically, this work advances MGWR frameworks by integrating temporal dynamics to examine nonstationary processes in spatially disaggregated contexts. These findings offer evidence–based guidance for policymakers, urban planners, and stakeholders in the automotive industry, supporting the transition toward a more sustainable and efficient transportation system.

EV Market Adoption↗

DOE OSTI2021

A seamless multiscale operator neural network for inferring bubble dynamics

Modelling multiscale systems from nanoscale to macroscale requires the use of atomistic and continuum methods and, correspondingly, different computer codes. Here, we develop a seamless method based on DeepONet, which is a composite deep neural network (a branch and a trunk network) for regressing operators. In particular, we consider bubble growth dynamics, and we model tiny bubbles of initial size from 100 nm to 10 $\mathrm {\mu }\textrm {m}$ , modelled by the Rayleigh–Plesset equation in the continuum regime above 1 $\mathrm {\mu }\textrm {m}$ and the dissipative particle dynamics method for bubbles below 1 $\mathrm {\mu }\textrm {m}$ in the atomistic regime. After an offline training based on data from both regimes, DeepONet can make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. The framework of DeepONet is general and can be used for unifying physical models of different scales in diverse multiscale applications.

Mechanics↗

DOE OSTI2024

Multiscale Modeling of Plutonium Radiation Chemistry in Nitric Acid Solutions. 1. Cobalt-60 Gamma Irradiation of Pu(IV)

We report careful manipulation of the plutonium oxidation states is essential in the study and utilization of its rich redox chemistry. To achieve this level of control, a comprehensive mechanistic understanding of radiation-induced plutonium redox chemistry is critical due to the unavoidable exposure of plutonium to ionizing radiation fields, both inherent and from in-process applications. To this end, we have developed an experimentally evaluated multiscale computer model for the prediction of gamma radiation-induced Pu(IV) redox chemistry in concentrated nitric acid solutions (1.0, 3.0, and 6.0 M). Under these acidic, aqueous solution conditions, cobalt-60 gamma irradiation afforded marginal net conversion of Pu(IV) to Pu(VI), the extent of which was dependent on the concentration of HNO 3 and absorbed gamma dose. Multiscale calculations, which are in excellent agreement with experimental data, indicate that this observation is due to a combination of inherent plutonium disproportionation reactions and several radiation-induced processes, including redox cycling between Pu(IV) and Pu(III), as achieved by the reduction of Pu(IV) by nitrous acid and hydrogen peroxide, the oxidation of Pu(III) by nitrate and hydroxyl radicals, and the sequential oxidation of Pu(IV) to Pu(V) and Pu(VI) by the remaining available yield of nitrate radicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model

We report molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. The SLIC/CDC multiscale model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). The SLIC/CDC model predicts Gibbs energies of solvation for a database of 500 solutes in water with average accuracy better than 1 kcal/mol both for experimental measurements and for explicit-solvent molecular dynamics simulations. The separate SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent accessible surface area (SASA) nonpolar energy mode. The SLIC/SASA model predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems and better than 1.6 kcal/mol average accuracy in ionic liquids. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

New Insights into Low-Temperature Oxidation of Propane from Synchrotron Photoionization Mass Spectrometry and Multiscale Informatics Modeling

We investigated the low-temperature oxidation of propane at 4 Torr and temperatures of 530, 600, and 670 K. The oxidation is initiated by pulsed laser photolysis of oxalyl chloride, (COCl)2, at 248 nm, which rapidly generates a ~1:1 mixture of 1-propyl (n-propyl) and 2-propyl (i-propyl) radicals via the fast Cl + propane reaction. Reactants, intermediates and products are probed with isomeric selectivity by time-resolved multiplexed photoionization mass spectrometry (MPIMS) with tunable synchrotron vacuum UV radiation as the ionization source. At all three temperatures, the major stable product species is propene, formed in the C3H7 + O2 reactions by direct HO2-elimination from both n- and i-propyl peroxy radicals. The experimentally derived propene yields relative to the initial concentration of Cl atoms are (20 ± 4)% at 530 K, (55 ± 11)% at 600 K, and (86 ± 17)% at 670 K at a reaction time of 20 ms. The lower yield of propene at low temperature reflects substantial formation of propyl peroxy radicals, which do not completely decompose on the experimental time scale. In addition, we detect the C3H6O isomers methyloxirane, oxetane, acetone and propanal as minor products. Our measured yields of oxetane and methyloxirane, which are co-products of OH radicals, suggest a revision of the OH formation pathways in models of low-temperature propane oxidation. The experimental results are modeled and interpreted using a multi-scale informatics approach that is presented in detail in a separate publication (Burke, M. P.; Goldsmith, C. F.; Klippenstein, S. J.; Welz, O.; Huang H.; Antonov I. O.; Savee J. D.; Osborn D. L.; Zádor, J.; Taatjes, C. A.; Sheps, L., Multi-Scale Informatics for Low-Temperature Propane Oxidation: Further Complexities in Studies of Complex Rections, submitted, 2015). The model predicts the time profiles and yields of the experimentally observed primary products well, and shows satisfactory agreement for products formed mostly via secondary radical-radical reactions.

Combustion↗

DOE OSTI2021

A Multiscale Simulation Study of Influence of Morphology on Ion Transport in Block Copolymeric Ionic Liquids

In this work, we present results of a multiscale simulation study involving coarse-graining and reverse-mapping steps probing at an atomistic resolution the influence of morphology on ion transport in block copolymer polymeric ionic liquids. We provide a detailed description of the multiscale simulation methodology and then describe the results in the context of four microphase-separated morphologies: two lamella systems, a cylinder, and a gyroid morphology. For the framework adopted in this study (in which the total number of ions was maintained fixed), morphology had little influence on the fraction of ions segregating to the interface and the coordination and hopping characteristics of such interfacially present ions. Such results manifested in anion mobilities being insensitive to the morphology once the dimensionality of the morphology was accounted for. Overall, our results are consistent with the hypothesis that the mobility of ions in such microphase-separated morphologies, after accounting for the dimensionality effects, can be roughly correlated to a linear superposition based on the fraction of bulk anions, which possess mobilities unperturbed from their values in the conducting homopolymers, and the interfacial anions, which exhibit much lower mobilities.

36 MATERIALS SCIENCE↗