Finite element analysis of the Poisson–Boltzmann equation coupled with chemical equilibriums: redistribution and transport of protons in nanophase separated polymeric acid–base proton exchange membranes

References

• Kreuer K. On the complexity of proton conduction phenomena. Solid State Ionics. 2000;136–137:149–160.10.1016/S0167-2738(00)00301-5
   Web of Science ®Google Scholar
• Yang C, Costamagna P, Srinivasan S, et al. Approaches and technical challenges to high temperature operation of proton exchange membrane fuel cells. J Power Sources. 2001;103:1–9.10.1016/S0378-7753(01)00812-6
   Web of Science ®Google Scholar
• Zhang J, Xie Z, Zhang J, et al. High temperature PEM fuel cells. J Power Sources. 2006;160:872–891.10.1016/j.jpowsour.2006.05.034
   Web of Science ®Google Scholar
• Yan L, Zhu S, Ji X, et al. Proton hopping in phosphoric acid solvated NAFION membrane: a molecular simulation study. J Phys Chem B. 2007;111:6357–6363.10.1021/jp071005m
   PubMed Web of Science ®Google Scholar
• Singh B, Duong NMH, Henkensmeier D, et al. Influence of different side-groups and cross-links on phosphoric acid doped radel-based polysulfone membranes for high temperature polymer electrolyte fuel cells. Electrochim Acta. 2017;224:306–313.10.1016/j.electacta.2016.12.088
   Web of Science ®Google Scholar
• He Y, Zhang H, Li Y, et al. Synergistic proton transfer through nanofibrous composite membranes by suitably combining proton carriers from the nanofiber mat and pore-filling matrix. J Mater Chem A. 2015;3:21832–21841.10.1039/C5TA03601A
   Web of Science ®Google Scholar
• Li G, Zhao C, Li X, et al. Novel side-chain-type sulfonated diphenyl-based poly(arylene ether sulfone)s with a hydrogen-bonded network as proton exchange membranes. Polym Chem. 2015;6:5911–5920.10.1039/C5PY00700C
   Web of Science ®Google Scholar
• Fu Y, Manthiram A, Guiver MD. Blend membranes based on sulfonated poly(ether ether ketone) and polysulfone bearing benzimidazole side groups for proton exchange membrane fuel cells. Electrochem Commun. 2006;8:1386–1390.10.1016/j.elecom.2006.06.018
   Web of Science ®Google Scholar
• Fu Y, Manthiram A, Guiver MD. Acid–base blend membranes based on 2-amino-benzimidazole and sulfonated poly(ether ether ketone) for direct methanol fuel cells. Electrochem Commun. 2007;9:905–910.10.1016/j.elecom.2006.12.001
   Web of Science ®Google Scholar
• Wu D, Xu T, Wu L, et al. Hybrid acid–base polymer membranes prepared for application in fuel cells. J Power Sources. 2009;186:286–292.10.1016/j.jpowsour.2008.10.028
   Web of Science ®Google Scholar
• Niu R, Kong L, Zheng L, et al. Novel graphitic carbon nitride nanosheets/sulfonated poly(ether ether ketone) acid–base hybrid membrane for vanadium redox flow battery. J Membr Sci. 2017;525:220–228.10.1016/j.memsci.2016.10.049
   Web of Science ®Google Scholar
• Zhang YP, Yue BH, Han SY, et al. Synergetic proton conducting effect in acid–base composite of phosphonic acid functionalized polystyrene and triazolyl functionalized polystyrene. RSC Adv. 2014;4:33702–33712.10.1039/C4RA04514A
   Web of Science ®Google Scholar
• Yue BH, Yan LM, Han SY, et al. Proton transport pathways in an acid–base complex consisting of a phosphonic acid group and a 1,2,3-triazolyl group. J Phys Chem B. 2013;117:7941–7949.10.1021/jp404684e
   PubMed Web of Science ®Google Scholar
• Xie LQ, Liu HT, Han SY, et al. Hydrogen bond and proton transport in acid–base complexes and amphoteric molecules by density functional theory calculations and 1H and 31P nuclear magnetic resonance spectroscopy. J Phys Chem B. 2013;117:16345–16355.10.1021/jp4094386
   PubMed Web of Science ®Google Scholar
• Yue B, Zeng G, Zhang Y, et al. Improved performance of acid–base composite of phosphonic acid functionalized polysulfone and triazolyl functionalized polysulfone for PEM fuel cells. Solid State Ionics. 2017;300:10–17.10.1016/j.ssi.2016.11.011
   Web of Science ®Google Scholar
• Ahmadzadeh K. Interaction potential energy between finite rectangular cellulose nanofibrils [ dissertation]. Stockholm (SE): KTH Royal Institute of Technology; 2015.
   Google Scholar
• Zhang X, Zhang J, Shi Y, et al. Potential of mean force between like-charged nanoparticles: many-body effect. Sci Rep. 2016;6:1–12.
   PubMed Web of Science ®Google Scholar
• Xie F, Turesson M, Woodward CE, et al. Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers. Phys Chem Chem Phys. 2016;18:11422–11434.10.1039/C5CP07814H
   PubMed Web of Science ®Google Scholar
• Bossa GV, Roth J, Bohinc K, et al. The apparent charge of nanoparticles trapped at a water interface. Soft Matter. 2016;12:4229–4240.10.1039/C6SM00334F
   PubMed Web of Science ®Google Scholar
• Li B, Wen J, Zhou S. Mean-field theory and computation of electrostatics with ionic concentration dependent dielectrics. Commun Math Sci. 2016;14:249–271.10.4310/CMS.2016.v14.n1.a10
   PubMed Web of Science ®Google Scholar
• Ozden E, Tari I. Proton exchange membrane fuel cell degradation: a parametric analysis using computational fluid dynamics. J Power Sources. 2016;304:64–73.10.1016/j.jpowsour.2015.11.042
   Web of Science ®Google Scholar
• Jahnke T, Futter G, Latz A, et al. Performance and degradation of proton exchange membrane fuel cells: state of the art in modeling from atomistic to system scale. J Power Sources. 2016;304:207–233.10.1016/j.jpowsour.2015.11.041
   Web of Science ®Google Scholar
• Cwirko EH, Carbonell RG. Interpretation of transport coefficients in Nafion using a parallel pore model. J Membr Sci. 1992;67:227–247.10.1016/0376-7388(92)80027-H
   Web of Science ®Google Scholar
• Weber AZ, Newman J. Modeling transport in polymer-electrolyte fuel cells. Chem Rev. 2004;104:4679–4726.10.1021/cr020729l
   PubMed Web of Science ®Google Scholar
• Kreuer KD, Paddison SJ, Spohr E, et al. Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology. Chem Rev. 2004;104:4637–4678.10.1021/cr020715f
   PubMed Web of Science ®Google Scholar
• Eikerling M, Kornyshev A, Kuznetsov A, et al. Mechanisms of proton conductance in polymer electrolyte membranes. J Phys Chem B. 2001;105:3646–3662.10.1021/jp003182s
   Web of Science ®Google Scholar
• Eikerling M, Kornyshev A. Proton transfer in a single pore of a polymer electrolyte membrane. J Electroanal Chem. 2001;502:1–14.10.1016/S0022-0728(00)00368-5
   Web of Science ®Google Scholar
• Qiao R, Aluru N. Ion concentrations and velocity profiles in nanochannel electroosmotic flows. J Chem Phys. 2003;118:4692–4701.10.1063/1.1543140
   Web of Science ®Google Scholar
• Qiao R, Aluru NR. Multiscale simulation of electroosmotic transport using embedding techniques. Int J Multiscale Comput. 2004;2:1–16.
   Web of Science ®Google Scholar
• Keh HJ, Ma HC. The effect of diffusioosmosis on water transport in polymer electrolyte fuel cells. J Power Sources. 2008;180:711–718.10.1016/j.jpowsour.2008.02.072
   Web of Science ®Google Scholar
• Berg P, Ladipo K. Exact solution of an electro-osmotic flow problem in a cylindrical channel of polymer electrolyte membranes. Proc R Soc A Math Phys Eng Sci. 2009;465:2663–2679.10.1098/rspa.2009.0067
   Web of Science ®Google Scholar
• Chen Y, Ni Z, Wang G, et al. Electroosmotic flow in nanotubes with high surface charge densities. Nano Lett. 2008;8:42–48.10.1021/nl0718566
   PubMed Web of Science ®Google Scholar
• Commer P, Cherstvy A, Spohr E, et al. The effect of water content on proton transport in polymer electrolyte membranes. Fuel Cells. 2002;2:127–136.10.1002/fuce.200290011
   Web of Science ®Google Scholar
• Hu Y, Li X, Yan L, Yue, B. Improving the overall characteristics of proton exchange membranes via nanophase separation techniques: a progress review. Fuel Cells. 2017;2017:3–17.
   Web of Science ®Google Scholar
• Hinderberger D, Spiess HW, Jeschke G. Radial counterion distributions in polyelectrolyte solutions determined by EPR spectroscopy. Europhys Lett. 2005;70:102.10.1209/epl/i2004-10459-y
   Google Scholar
• Wu Y, Wang F, Tan Z. Calculating potential of mean force between like-charged nanoparticles: a comprehensive study on salt effects. Phys Lett A. 2013;377:1911–1919.10.1016/j.physleta.2013.05.011
   Web of Science ®Google Scholar
• Baker NA, Sept D, Joseph S, et al. Electrostatics of nanosystems: application to microtubules and the ribosome. Proc Natl Acad Sci. 2001;98:10037–10041.10.1073/pnas.181342398
   PubMed Web of Science ®Google Scholar
• Eikerling M, Kornyshev A, Stimming U. Electrophysical properties of polymer electrolyte membranes: a random network model. J Phys Chem B. 1997;101:10807–10820.10.1021/jp972288t
   Web of Science ®Google Scholar
• Paddison SJ, Reagor DW, Zawodzinski TA Jr. High frequency dielectric studies of hydrated Nafion. J Electroanal Chem. 1998;459:91–97.10.1016/S0022-0728(98)00321-0
   Web of Science ®Google Scholar
• Karimi G, Li X. Electroosmotic flow through polymer electrolyte membranes in PEM fuel cells. J Power Sources. 2005;140:1–11.10.1016/j.jpowsour.2005.02.009
   Web of Science ®Google Scholar
• Sata N, Eberman K, Eberl K, et al. Mesoscopic fast ion conduction in nanometre-scale planar heterostructures. Nature. 2000;408:946–949.10.1038/35050047
   PubMed Web of Science ®Google Scholar
• Han SY, Yue BH, Yan LM. Improving the performances of poly(vinylphosphonic acid) by compositing or copolymerization with poly(4-(alpha-methyl)vinyl-1H-1,2,3-triazole). Electrochim Acta. 2014;138:256–263.10.1016/j.electacta.2014.06.121
   Web of Science ®Google Scholar