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From the Atomistic to the Macromolecular Scale: Distinct Simulation Approaches for Polyelectrolyte Solutions

  • Jens Smiatek
  • Christian HolmEmail author
Living reference work entry

Abstract

Polyelectrolytes reveal interesting properties in solution. At short length scales, the dissociation of counterions is heavily affected by the chemical structure of the polyelectrolyte, the properties of the solution, and specific ion effects. At larger length scales, the structure of polyelectrolyte solutions is dominated by long-range interactions. In the special case of dissolved polyanions and polycations, polyelectrolyte complexes or multilayers can form. In this review we present distinct simulation approaches to study the corresponding effects at different length scales in more detail. Whereas at short length scales, atomistic molecular dynamics simulation is often the method of choice, semi-coarse-grained and coarse-grained models with a lower level of details reveal their benefits at larger length scales.

Notes

Acknowledgements

We thank Alexander Weyman, Martin Vögele, Anand Narayanan Krishnamoorthy, Florian Fahrenberger, Jonas Landsgesell, Kai Szuttor, Owen A. Hickey, Florian Weik, Tobias Rau, Stefan Kesselheim, Steffen Hardt, Tamal Roy, Andreas Wohlfarth, Klaus-Dieter Kreuer, Lars V. Schäfer, Paulo Telles de Souza, Johannes Zeman, Axel Arnold, Baofu Qiao, Juan J. Cerd\({\grave {\textrm a}}\), Rafael Bordin, Rudi Podgornik, Burkhard D\(\ddot {\textrm u}\)nweg, and Siewert-Jan Marrink for valuable discussions. We thank the Deutsche Forschungsgemeinschaft for funding through AR593/7-1, HO/1108-22-1, HO/1108 26-1, and the Cluster of Excellence Simulation Technology (EXC 310) and the collaborative research center 716 (SFB 716).

References

  1. Andelman D (1995) Handbook of biological physics. School of Physics and Astronomy, Tel Aviv University, p 603, chap 12Google Scholar
  2. Antypov D, Holm C (2006) Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes. Phys Rev Lett 96:088302Google Scholar
  3. Antypov D, Barbosa MC, Holm C (2005) A simple non-local approach to treat size correlations within poisson-boltzmann theory. Phys Rev E 71:061106Google Scholar
  4. Arnold A, Fahrenberger F, Holm C, Lenz O, Bolten M, Dachsel H, Halver R, Kabadshow I, Gähler F, Heber F, Iseringhausen J, Hofmann M, Pippig M, Potts D, Sutmann G (2013) Comparison of scalable fast methods for long-range interactions. Phys Rev E 88:063308.  https://doi.org/10.1103/PhysRevE.88.063308
  5. Batys P, Luukkonen S, Sammalkorpi M (2017) Ability of Poisson–Boltzmann equation to capture molecular dynamics predicted ion distribution around polyelectrolytes. Phys Chem Chem Phys 19:24583–24593CrossRefGoogle Scholar
  6. Bordin JR, Podgornik R, Holm C (2016) Static polarizability effects on counterion distributions near charged dielectric surfaces: A coarse-grained molecular dynamics study employing the drude model. Eur Phys J Special Top 225(8):1693–1705.  https://doi.org/10.1140/epjst/e2016-60150-1ADSCrossRefGoogle Scholar
  7. Brini E, Algaer EA, Ganguly P, Li C, Rodriguez-Ropero F, van der Vegt NFA (2013) Systematic coarse-graining methods for soft matter simulations – a review. Soft Matter 9:2108–2119. https://doi.org/10.1039/C2SM27201FADSCrossRefGoogle Scholar
  8. Cerdà JJ, Qiao B, Holm C (2009) Understanding polyelectrolyte multilayers: an open challenge for simulations. Soft Matter 5:4412–4425. https://doi.org/10.1039/b912800jADSCrossRefGoogle Scholar
  9. Collins KD (2004) Ions from the Hofmeister series and osmolytes: effects on proteins in solution and in the crystallization process. Methods 34(3):300–311. https://doi.org/10.1016/j.ymeth.2004.03.021CrossRefGoogle Scholar
  10. de Gennes PG (1979) Scaling concepts in polymer physics. Cornell University Press, Ithaca. http://books.google.com/books?id=ApzfJ2LYwGUC&lpg=PP1&num=15&pg=PP1#v=onepage&q&f=false
  11. Deserno M, Holm C (1998) How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines. J Chem Phys 109:7678ADSCrossRefGoogle Scholar
  12. Deserno M, Holm C (2001) Cell-model and poisson-boltzmann-theory: a brief introduction. In: Holm C, Kékicheff P, Podgornik R (eds) Electrostatic effects in soft matter and biophysics, NATO science series II – mathematics, physics and chemistry, vol 46. Kluwer Academic Publishers, Dordrecht, pp 27–50CrossRefGoogle Scholar
  13. Deserno M, Holm C, May S (2000) Fraction of condensed counterions around a charged rod: comparison of Poisson-Boltzmann theory and computer simulations. Macromolecules 33:199–206. https://doi.org/10.1021/ma990897oADSCrossRefGoogle Scholar
  14. Deserno M, Holm C, Blaul J, Ballauff M, Rehahn M (2001) The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment. Eur Phys J E 5:97–103ADSCrossRefGoogle Scholar
  15. Dobrynin AV (2008) Theory and simulations of charged polymers: from solution properties to polymer nanomaterials. Curr Opin Colloid Interface Sci 13:376–388. https://doi.org/10.1016/j.cocis.2008.03.006, http://www.sciencedirect.com/science/article/pii/S1359029408000411CrossRefGoogle Scholar
  16. Dobrynin AV, Rubinstein M (2005) Theory of polyelectrolytes in solutions and at surfaces. Prog Polym Sci 30(11):1049–1118. https://doi.org/10.1016/j.progpolymsci.2005.07.006, http://www.sciencedirect.com/science/article/B6TX2-4H2G8WN-1/2/4b378f3016fcf641ad1821b4ded9d389CrossRefGoogle Scholar
  17. Dobrynin AV, Rubinstein M, Obukhov SP (1996) Cascade of transitions of polyelectrolytes in poor solvents. Macromolecules 29(8):2974ADSCrossRefGoogle Scholar
  18. Doi M, Edwards SF (1988) The theory of polymer dynamics, vol 73. Oxford University Press, New YorkGoogle Scholar
  19. Dormidontova EE, Erukhimovich IY, Khokhlov AR (1994) Microphase separation in poor-solvent polyelectrolyte solutions: phase diagram. Macromol Theory Simul 3(4):661–675CrossRefGoogle Scholar
  20. Dünweg B (1993) Molecular dynamics algorithms and hydrodynamic screening. J Chem Phys 99(9):6977–82ADSCrossRefGoogle Scholar
  21. Dünweg B, Ladd AJC (2009) Lattice boltzmann simulations of soft matter systems. In: Advanced computer simulation approaches for soft matter sciences III. Advances in polymer science, vol 221. Springer, Berlin, pp 89–166. https://doi.org/10.1007/12_2008_4
  22. Ermak DL, McCammon J (1978) Brownian dynamics with hydrodynamic interactions. J Chem Phys 69:1352ADSCrossRefGoogle Scholar
  23. Fahrenberger F, Holm C (2014) Computing the coulomb interaction in inhomogeneous dielectric media via a local electrostatics lattice algorithm. Phys Rev E 90:063304.  https://doi.org/10.1103/PhysRevE.90.063304
  24. Fahrenberger F, Hickey OA, Smiatek J, Holm C (2015a) Importance of varying permittivity on the conductivity of polyelectrolyte solutions. Phys Rev Lett 115:118301. http://link.aps.org/doi/10.1103/PhysRevLett.115.118301
  25. Fahrenberger F, Hickey OA, Smiatek J, Holm C (2015b) The influence of charged-induced variations in the local permittivity on the static and dynamic properties of polyelectrolyte solutions. J Chem Phys 143:243140. http://scitation.aip.org/content/aip/journal/jcp/143/24/10.1063/1.4936666ADSCrossRefGoogle Scholar
  26. Farhat T, Yassin G, Dubas ST, Schlenoff JB (1999) Water and ion pairing in polyelectrolyte multilayers. Langmuir 15(20):6621–6623CrossRefGoogle Scholar
  27. Frank S, Winkler RG (2009) Mesoscale hydrodynamic simulation of short polyelectrolytes in electric fields. J Chem Phys 131(23):234905. https://doi.org/10.1063/1.3274681ADSCrossRefGoogle Scholar
  28. Fritz D, Koschke K, Harmandaris VA, van der Vegt NF, Kremer K (2011) Multiscale modeling of soft matter: scaling of dynamics. Phys Chem Chem Phys 13(22):10412–10420CrossRefGoogle Scholar
  29. Fyta M, Netz RR (2012) Ionic force field optimization based on single-ion and ion-pair solvation properties: going beyond standard mixing rules. J Chem Phys 136(12). https://doi.org/10.1063/1.3693330ADSCrossRefGoogle Scholar
  30. Gompper G, Ihle T, Kroll DM, Winkler RG (2008) Multi-particle collision dynamics: a particle-based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv Polym Sci 221:1–87Google Scholar
  31. Grass K, Böhme U, Scheler U, Cottet H, Holm C (2008) Importance of hydrodynamic shielding for the dynamic behavior of short polyelectrolyte chains. Phys Rev Lett 100:096104Google Scholar
  32. Groot RD, Warren PB (1997) Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107(11):4423–4435ADSCrossRefGoogle Scholar
  33. Heyda J, Dzubiella J (2012) Ion-specific counterion condensation on charged peptides: Poisson–boltzmann vs. atomistic simulations. Soft Matter 8(36):9338–9344ADSCrossRefGoogle Scholar
  34. Hickey OA, Shendruk TN, Harden JL, Slater GW (2012) Simulations of free-solution electrophoresis of polyelectrolytes with a finite debye length using the debye-hückel approximation. Phys Rev Lett 109:098302.  https://doi.org/10.1103/PhysRevLett.109.098302
  35. Hsu CW, Fyta M, Lakatos G, Melchionna S, Kaxiras E (2012) Ab initio determination of coarse-grained interactions in double-stranded DNA. J Chem Phys 137(10):105102ADSCrossRefGoogle Scholar
  36. Jorgensen WL, Maxwell DS, Tirado-Rives J (1996) Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chem Soc 118(45):11225–11236CrossRefGoogle Scholar
  37. Kremer K, Grest GS (1990) Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J Chem Phys 92(8):5057–5086ADSCrossRefGoogle Scholar
  38. Krishnamoorthy AN, Zeman J, Holm C, Smiatek J (2016) Preferential solvation and ion association properties in aqueous dimethyl sulfoxide solutions. Phys Chem Chem Phys 18:31312–31322. https://doi.org/10.1039/C6CP05909KCrossRefGoogle Scholar
  39. Kunz W (ed) (2010) Specific ion effects. World Scientific, SingaporeGoogle Scholar
  40. Landsgesell J, Holm C, Smiatek J (2017a) Simulation of weak polyelectrolytes: a comparison between the constant ph and the reaction ensemble method. Eur Phys J Special Top 226:725–736.  https://doi.org/10.1140/epjst/e2016-60324-3ADSCrossRefGoogle Scholar
  41. Landsgesell J, Holm C, Smiatek J (2017b) Wang-landau reaction ensemble method: simulation of weak polyelectrolytes and general acid-base reactions. J Chem Theory Comput 13(2):852–862.  https://doi.org/10.1021/acs.jctc.6b00791CrossRefGoogle Scholar
  42. Lemkul JA, Huang J, Roux B, MacKerell Jr AD (2016) An empirical polarizable force field based on the classical drude oscillator model: development history and recent applications. Chem Rev 116(9):4983–5013.  https://doi.org/10.1021/acs.chemrev.5b00505CrossRefGoogle Scholar
  43. Li YC, Wen TC, Wei HH (2012) Electrophoretic stretching of tethered polymer chains by travelling-wave electric fields: tunable stretching, expedited coil–stretch transition, and a new paradigm of dynamic molecular probing. Soft Matter 8(6):1977–1990ADSCrossRefGoogle Scholar
  44. Limbach HJ, Holm C (2003) Single-chain properties of polyelectrolytes in poor solvent. J Phys Chem B 107(32):8041–8055CrossRefGoogle Scholar
  45. Limbach HJ, Holm C, Kremer K (2002) Structure of polyelectrolytes in poor solvent. Europhys Lett 60(4):566–572ADSCrossRefGoogle Scholar
  46. Limbach HJ, Sayar M, Holm C (2004) Polyelectrolyte bundles. J Phys Condens Matter 16(22):2135–2144ADSGoogle Scholar
  47. Lo Nostro P, Ninham BW (2012) Hofmeister phenomena: an update on ion specificity in biology. Chem Rev 112(4):2286–2322. https://doi.org/10.1021/cr200271jCrossRefGoogle Scholar
  48. Lu BZ, Zhou YC, Holst MJ, McCammon JA (2008) Recent progress in numerical methods for the poisson-boltzmann equation in biophysical applications. Commun Comput Phys 3(5):973–1009Google Scholar
  49. Lu K, Rudzinski JF, Noid W, Milner ST, Maranas JK (2014) Scaling behavior and local structure of ion aggregates in single-ion conductors. Soft Matter 10(7):978–989ADSCrossRefGoogle Scholar
  50. Lund M, Vácha R, Jungwirth P (2008) Specific ion binding to macromolecules: effects of hydrophobicity and ion pairing. Langmuir 24(7):3387–3391CrossRefGoogle Scholar
  51. Lyubartsev A, Laaksonen A (1999) Effective potentials for ion–DNA interactions. J Chem Phys 111(24):11,207–11,215ADSCrossRefGoogle Scholar
  52. Manning GS (1969) Limiting laws and counterion condensation in polyelectrolyte solutions I. colligative properties. J Chem Phys 51:924–933ADSCrossRefGoogle Scholar
  53. Manning GS (1996) Counterion condensation theory constructed from different models. Physica A 231(1–3):236–253ADSCrossRefGoogle Scholar
  54. Marcus Y (2009) Effect of ions on the structure of water: structure making and breaking. Chem Rev 109(3):1346–1370. https://doi.org/10.1021/cr8003828CrossRefGoogle Scholar
  55. Marcus Y, Hefter G (2006) Ion pairing. Chem Rev 106(11):4585–4621CrossRefGoogle Scholar
  56. Marrink SJ, Tieleman DP (2013) Perspective on the MARTINI model. Chem Soc Rev 42(16):6801–6822. https://doi.org/10.1039/C3CS60093ACrossRefGoogle Scholar
  57. Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH (2007) The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B 111(27):7812–7824. https://doi.org/10.1021/jp071097fCrossRefGoogle Scholar
  58. Marrink SJ, Periole X, Tieleman DP, de Vries AH (2010) Comment on using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models by M. Winger, D. Trzesniak, R. Baron and WF van Gunsteren. Phys Chem Chem Phys 2009, 11, 1934. Phys Chem Chem Phys 12(9):2254–2256Google Scholar
  59. McNaught AD, Wilkinson A (1997) Compendium of chemical terminology, vol 1669. Blackwell Science OxfordGoogle Scholar
  60. Mecerreyes D (2011) Polymeric ionic liquids: broadening the properties and applications of polyelectrolytes. Prog Polym Sci 36(12):1629–1648. https://doi.org/10.1016/j.progpolymsci.2011.05.007CrossRefGoogle Scholar
  61. Micciulla S, Sanchez PA, Smiatek J, Qiao B, Sega M, Laschewsky A, Holm C, von Klitzing R (2014) Layer-by-layer formation of oligoelectrolyte multilayers: a combined experimental and computational study. Soft Mater 12:S14. https://doi.org/10.1080/1539445X.2014.930046, http://www.tandfonline.com/eprint/eCn9vDIc5aMbyBmB6DV5/fullCrossRefGoogle Scholar
  62. Michalowsky J, Schäfer LV, Holm C, Smiatek J (2017) A refined polarizable water model for the coarse-grained MARTINI force field with long-range electrostatic interactions. J Chem Phys 146(5):054501. https://doi.org/10.1063/1.4974833ADSCrossRefGoogle Scholar
  63. Micka U, Holm C, Kremer K (1999) Strongly charged, flexible polyelectrolytes in poor solvents – a molecular dynamics study. Langmuir 15:4033CrossRefGoogle Scholar
  64. Mukhopadhyay A, Fenley AT, Tolokh IS, Onufriev AV (2012) Charge hydration asymmetry: the basic principle and how to use it to test and improve water models. J Phys Chem B 116(32):9776–9783CrossRefGoogle Scholar
  65. Ober MMCK, Thomas EL (1997) Competing interactions and levels of ordering in self-organizing polymeric materials. Science 277:1225–1232CrossRefGoogle Scholar
  66. Pagonabarraga I, Rotenberg B, Frenkel D (2010) Recent advances in the modelling and simulation of electrokinetic effects: bridging the gap between atomistic and macroscopic descriptions. Phys Chem Chem Phys 12:9566–9580. https://doi.org/10.1039/C004012FCrossRefGoogle Scholar
  67. Praprotnik M, Junghans C, Site LD, Kremer K (2008) Simulation approaches to soft matter: generic statistical properties vs. chemical details. Comput Phys Commun 179(1–3):51ADSCrossRefGoogle Scholar
  68. Qiao B, Sega M, Holm C (2011) An atomistic study of a poly(styrene sulfonate)/poly(diallyldimethylammonium) bilayer: the role of surface properties and charge reversal. Phys Chem Chem Phys 13(36):16336–16342. https://doi.org/10.1039/C1CP21777ACrossRefGoogle Scholar
  69. Qiao B, Sega M, Holm C (2012) Properties of water in the interfacial region of a polyelectrolyte bilayer adsorbed onto a substrate studied by computer simulations. Phys Chem Chem Phys 14:11425–11432. https://doi.org/10.1039/C2CP41115FCrossRefGoogle Scholar
  70. Rau T, Weik F, Holm C (2017) A dsDNA model optimized for electrokinetic applications. Soft Matter 3918–3926. https://doi.org/10.1039/C7SM00270J, http://pubs.rsc.org/en/content/articlehtml/2017/sm/c7sm00270jADSCrossRefGoogle Scholar
  71. Reith D, Müller B, Müller-Plathe F, Wiegand S (2002) How does the chain extension of poly (acrylic acid) scale in aqueous solution? a combined study with light scattering and computer simulation. J Chem Phys 116(20):9100–9106ADSCrossRefGoogle Scholar
  72. Reith D, Pütz M, Müller-Plathe F (2003) Deriving effective mesoscale potentials from atomistic simulations. J Comput Chem 24(13):1624–1636CrossRefGoogle Scholar
  73. Roy T, Szuttor K, Smiatek J, Holm C, Hardt S (2017) Stretching of surface-tethered polymers in pressure-driven flow under confinement. Soft Matter 13:6189–6196. https://doi.org/10.1039/C7SM00306DADSCrossRefGoogle Scholar
  74. Savelyev A, Papoian GA (2010) Chemically accurate coarse graining of double-stranded DNA. Proceedings of the National Academy of Sciences of the United States of America 107(47):20340–20345.  https://doi.org/10.1073/pnas.1001163107ADSCrossRefGoogle Scholar
  75. Schmid F (1998) Self-consistent-field theories for complex fluids. J Phys Condens Matter 10(37):8105ADSGoogle Scholar
  76. Senftle TP, Hong S, Islam MM, Kylasa SB, Zheng Y, Shi YK, Junkermeier C, Engel-Herbert R, Janik MJ, Aktulga HM, Verstraelen T, Grama A, van Duin ACT (2016) The ReaxFF reactive force-field: development, applications and future directions. Comput Mater 2:15011.  https://doi.org/10.1038/npjcompumats.2015.11
  77. Slater GW, Holm C, Chubynsky MV, de Haan HW, Dubé A, Grass K, Hickey OA, Kingsburry C, Sean D, Shendruk TN, Zhan L (2009) Modeling the separation of macromolecules: a review of current computer simulation methods. Electrophoresis 30(5):792–818.  https://doi.org/10.1002/elps.200800673CrossRefGoogle Scholar
  78. Smiatek J, Schmid F (2010) Polyelectrolyte electrophoresis in nanochannels: a dissipative particle dynamics simulation. J Phys Chem B 114(19):6266–6272. https://doi.org/10.1021/jp100128p, http://pubs.acs.org/doi/abs/10.1021/jp100128pCrossRefGoogle Scholar
  79. Smiatek J, Schmid F (2011) Mesoscopic simulations of electroosmotic flow and electrophoresis in nanochannels. Comput Phys Commun 182(9):1941–1944. https://doi.org/10.1016/j.cpc.2010.11.021, http://www.sciencedirect.com/science/article/pii/S0010465510004674. Computer Physics Communications Special Edition for Conference on Computational Physics Trondheim, Norway, June 23–26, 2010ADSCrossRefGoogle Scholar
  80. Smiatek J, Sega M, Holm C, Schiller UD, Schmid F (2009) Mesoscopic simulations of the counterion-induced electro-osmotic flow: a comparative study. Journal of Chemical Physics 130(244702). https://doi.org/10.1063/1.3152844ADSCrossRefGoogle Scholar
  81. Smiatek J, Harishchandra RK, Rubner O, Galla HJ, Heuer A (2012) Properties of compatible solutes in aqueous solution. Biophys Chem 160(1):62–68. https://doi.org/10.1016/j.bpc.2011.09.007CrossRefGoogle Scholar
  82. Smiatek J, Wohlfarth A, Holm C (2014) The solvation and ion condensation properties for sulfonated polyelectrolytes in different solvents-a computational study. New J Phys 16(2):025001. http://stacks.iop.org/1367-2630/16/i=2/a=025001CrossRefGoogle Scholar
  83. Stevens MJ, Kremer K (1993a) Form factor of salt-free linear polyelectrolytes. Macromolecules 26:4717ADSCrossRefGoogle Scholar
  84. Stevens MJ, Kremer K (1993b) Structure of salt-free linear polyelectrolytes. Phys Rev Lett 71:2228ADSCrossRefGoogle Scholar
  85. Szuttor K, Roy T, Hardt S, Holm C, Smiatek J (2017) The stretching force on a tethered polymer in pressure-driven flow. J Chem Phys 147(3):034902. https://doi.org/10.1063/1.4993619ADSCrossRefGoogle Scholar
  86. Uusitalo JJ, Ingólfsson HI, Akhshi P, Tieleman DP, Marrink SJ (2015) MARTINI coarse-grained force field: extension to DNA. J Chem Theory Comput 11(8):3932–3945CrossRefGoogle Scholar
  87. Vögele M, Holm C, Smiatek J (2015a) Coarse-grained simulations of polyelectrolyte complexes: MARTINI models for poly(styrene sulfonate) and poly(diallyldimethylammonium). J Chem Phys 143:243151. https://doi.org/10.1063/1.4937805, http://scitation.aip.org/content/aip/journal/jcp/143/24/10.1063/1.4937805ADSCrossRefGoogle Scholar
  88. Vögele M, Holm C, Smiatek J (2015b) Properties of the polarizable MARTINI water model: a comparative study for aqueous electrolyte solutions. J Mol Liq 212:103–110. https://doi.org/10.1016/j.molliq.2015.08.062, http://www.sciencedirect.com/science/article/pii/S0167732215304657CrossRefGoogle Scholar
  89. Weeks JD, Chandler D, Andersen HC (1971) Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54:5237ADSCrossRefGoogle Scholar
  90. Weik F, Kesselheim S, Holm C (2016) A coarse-grained DNA model for the prediction of current signals in DNA translocation experiments. J Chem Phys 145(19):194106. https://doi.org/10.1063/1.4967458ADSCrossRefGoogle Scholar
  91. Weyman A, Bier M, Holm C, Smiatek J (2018) Microphase separation and the formation of ion conductivity channels in poly (ionic liquid) s: A coarse-grained molecular dynamics study. J Chem Phys 148:193824ADSCrossRefGoogle Scholar
  92. Winger M, Trzesniak D, Baron R, van Gunsteren WF (2009) On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models. Phys Chem Chem Phys 11(12):1934–1941Google Scholar
  93. Wohlfarth A, Smiatek J, Kreuer KD, Takamuku S, Jannasch P, Maier J (2015) Proton dissociation of sulfonated polysulfones: influence of molecular structure and conformation. Macromolecules 48(4):1134–1143. https://doi.org/10.1021/ma502550fADSCrossRefGoogle Scholar
  94. Yesylevskyy SO, Schäfer LV, Sengupta D, Marrink SJ (2010) Polarizable water model for the coarse-grained MARTINI force field. PLoS Comput Biol 6(6):e1000810.  https://doi.org/10.1371/journal.pcbi.1000810ADSCrossRefGoogle Scholar
  95. Yuan J, Mecerreyes D, Antonietti M (2013) Poly(ionic liquid)s: an update. Prog Polym Sci 38:1009–1036. https://doi.org/10.1016/j.progpolymsci.2013.04.002CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Computational PhysicsUniversity of StuttgartStuttgartGermany
  2. 2.Helmholtz Institute Münster (HI MS), Ionics in Energy Storage, Forschungszentrum Jülich GmbHMünsterGermany
  3. 3.Institute for Computational PhysicsUniversity of StuttgartStuttgartGermany

Section editors and affiliations

  • Kurt Kremer
    • 1
  1. 1.MPI for Polymer ResearchMainzGermany

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