Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density

  • Jahin Patwary
  • Guang Chen
  • Siddhartha DasEmail author
Research Paper


Nanochannels, functionalized by grafting with a layer of charged polyelectrolyte (PE), have been employed for a large number of applications such as flow control, ion sensing, ion manipulation, current rectification and nanoionic diode fabrication. Recently, we established that such PE-grafted nanochannels, often denoted as “soft” nanochannels, can be employed for highly efficient, streaming-current-induced electrochemomechanical energy conversion in the presence of a background pressure-driven transport. In this paper, we extend our calculation for the practically realizable situation when the PE layer demonstrates a pH-dependent charge density. Consideration of such pH dependence necessitates consideration of hydrogen and hydroxyl ions in the electric double layer charge distribution, cubic distribution of the monomer profile, and a PE layer-induced drag force that accounts for this given distribution of the monomer profile. Our results express a hitherto unknown dependence of the streaming electric field (or the streaming potential) and the efficiency of the resultant energy conversion on parameters such as the pH of the surrounding electrolyte and the \(\hbox {pK}_{\mathrm{a}}\) of the ionizable group that ionizes to produce the PE charge—we demonstrate that increase in the pH and the PE layer thickness and decrease in the \(\hbox {pK}_{\mathrm{a}}\) and the ion concentration substantially enhance the energy conversion efficiency.


Electric Double Layer Polymer Brush Streaming Potential Exclude Volume Effect Electric Double Layer Thickness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors gratefully acknowledge NSF LSAMP Bridge to Doctorate programme for providing financial support to Mr. Jahin Patwary.


  1. Adiga SP, Brenner DW (2005) Flow control through polymer-grafted smart nanofluidic channels: molecular dynamics simulations. Nano Lett 12:2509–2514CrossRefGoogle Scholar
  2. Adiga SP, Brenner DW (2007) Toward designing smart nanovalves: modeling of flow control through nanopores via the helix coil transition of grafted polypeptide chains. Macromolecules 40:1342–1348CrossRefGoogle Scholar
  3. Adiga SP, Brenner DW (2012) Stimuli-responsive polymer brushes for flow control through nanopores. J Funct Biomater 3:239–256CrossRefGoogle Scholar
  4. Ali M, Yameen B, Neumann R, Ensinger W, Knoll W, Azzaroni O (2008) Biosensing and supramolecular bioconjugation in single conical polymer nanochannels. Facile incorporation of biorecognition elements into nanoconfined geometries. J Am Chem Soc 130:16351–16357CrossRefGoogle Scholar
  5. Ali M, Tahir MN, Siwy Z, Neumann R, Tremel W, Ensinger W (2011) Hydrogen peroxide sensing with horseradish peroxidase-modified polymer single conical nanochannels. Anal Chem 83:1673–1680CrossRefGoogle Scholar
  6. Andrews J, Das S (2015) Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates. RSC Adv 5:46873–46880CrossRefGoogle Scholar
  7. Azzaroni O (2012) Polymer brushes here, there, and everywhere: recent advances in their practical applications and emerging opportunities in multiple research fields. J Pol Sci 50:3225–3258CrossRefGoogle Scholar
  8. Bandopadhyay A, Chakraborty S (2012) Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids. Appl Phys Lett 101:153112CrossRefGoogle Scholar
  9. Bandopadhyay A, Dhar J, Chakraborty S (2013) Effects of solvent-mediated nonelectrostatic ion–ion interactions on a streaming potential in microchannels and nanochannels. Phys Rev E 88:033014CrossRefGoogle Scholar
  10. Barbati AC, Kirby BJ (2012) Soft diffuse interfaces in electrokinetics—theory and experiment for transport in charged diffuse layers. Soft Matter 8:10598–10613CrossRefGoogle Scholar
  11. Chakraborty S, Das S (2008) Streaming-field-induced convective transport and its influence on the electroviscous effects in narrow fluidic confinement beyond the Debye-Hückel limit. Phys Rev E 77:037303CrossRefGoogle Scholar
  12. Chanda S, Das S (2014) Effect of finite ion sizes in an electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution. Phys Rev E 89:012307CrossRefGoogle Scholar
  13. Chanda S, Sinha S, Das S (2014) Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters. Soft Matter 10:7558–7568CrossRefGoogle Scholar
  14. Chen G, Das S (2015a) Electrostatics of soft charged interfaces with pH-dependent charge density: effect of consideration of appropriate hydrogen ion concentration distribution. RSC Adv 5:4493–4501CrossRefGoogle Scholar
  15. Chen G, Das S (2015b) Electroosmotic transport in polyelectrolyte-grafted nanochannels with pH-dependent charge density. J Appl Phys 117:185304CrossRefGoogle Scholar
  16. Chen G, Das S (2015c) Scaling laws and ionic current inversion in polyelectrolyte-grafted nanochannels. J Phys Chem B 119:12714–12726CrossRefGoogle Scholar
  17. Chen G, Das S (2015d) Streaming potential and electroviscous effects in soft nanochannels beyond Debye–Hückel linearization. J Colloid Interface Sci 445:357–363CrossRefGoogle Scholar
  18. Chien M, Wang G, Yu W (2007) Modeling ion diffusion current in nanochannel using infinitesimal distribution resistor–capacitor circuits. Jpn J Appl Phys 46:7436–7440CrossRefGoogle Scholar
  19. Daiguji H, Yang P, Szeri AJ, Majumdar A (2004) Electrochemomechanical energy conversion in nanofluidic channels. Nano Lett 4:2315–2321CrossRefGoogle Scholar
  20. Das S, Chakraborty S (2009) Influence of streaming potential on the transport and separation of charged spherical solutes in nanochannels subjected to particle-wall interactions. Langmuir 25:9863–9872CrossRefGoogle Scholar
  21. Das T, Das S, Chakraborty S (2009) Influences of streaming potential on cross stream migration of flexible polymer molecules in nanochannel flows. J Chem Phys 130:244904CrossRefGoogle Scholar
  22. Das S, Chakraborty S (2010) Effect of conductivity variations within the electric double layer on the streaming potential estimation in narrow fluidic confinements. Langmuir 26:11589–11596CrossRefGoogle Scholar
  23. Das S (2014) Explicit interrelationship between Donnan and surface potentials and explicit quantification of capacitance of charged soft interfaces with pH-dependent charge density. Colloids Surf A 462:69–74CrossRefGoogle Scholar
  24. Das S, Banik M, Chen G, Sinha S, Mukherjee R (2015) Polyelectrolyte brushes: theory, modelling, synthesis and applications. Soft Matter 11:8550–8583CrossRefGoogle Scholar
  25. de Gennes P-G (1976) Dynamics of entangled polymer solutions. II. Inclusion of hydrodynamic interactions. Macromolecules 9:594–598CrossRefGoogle Scholar
  26. Dolan AK, Edwards SF (1974) Theory of the stabilization of colloids by adsorbed polymer. Proc R Soc Lond Ser A 337:509–516CrossRefGoogle Scholar
  27. Dolan AK, Edwards SF (1975) The effect of excluded volume on polymer dispersant action. Proc R Soc Lond Ser A 343:427–442CrossRefGoogle Scholar
  28. Donath E, Voigt E (1986) Streaming current and streaming potential on structured surfaces. J Colloid Interface Sci 109:122–139CrossRefGoogle Scholar
  29. Duval JFL, Zimmermann R, Cordeiro AL, Rein N, Werner C (2009) Electrokinetics of diffuse soft interfaces. IV. Analysis of streaming current measurements at thermoresponsive thin films. Langmuir 25:10691–10703CrossRefGoogle Scholar
  30. Duval JFL, Gaboriaud F (2010) Progress in electrohydrodynamics of soft microbial particle interphases. Curr Opin Colloid Interface Sci 15:184–195CrossRefGoogle Scholar
  31. Duval JFL, Kütter D, Werner C, Zimmermann R (2011a) Electrohydrodynamics of soft polyelectrolyte multilayers: point of zero-streaming current. Langmuir 27:10739–10752CrossRefGoogle Scholar
  32. Duval JFL, Kütter D, Nitschke M, Werner C, Zimmermann R (2011b) Interrelations between charging, structure and electrokinetics of nanometric polyelectrolyte films. J Colloid Interface Sci 362:439–449CrossRefGoogle Scholar
  33. Duval JFL, Merlin J, Anantha P (2011c) Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye–Hückel approximation and Deryagin formulation. Phys Chem Chem Phys 13:1037–1053CrossRefGoogle Scholar
  34. Duval JFL, van Leeuwen HP (2004) Electrokinetics of diffuse soft interfaces. 1. Limit of low Donnan potentials. Langmuir 20:10324–10336CrossRefGoogle Scholar
  35. Fredrickson GH, Pincus P (1991) Drainage of compressed polymer layers: dynamics of a “squeezed sponge”. Langmuir 7:786–795CrossRefGoogle Scholar
  36. Freed KF, Edwards SF (1974) Polymer viscosity in concentrated solutions. J Chem Phys 61:3626–3633CrossRefGoogle Scholar
  37. Harden JL, Cates ME (1996) Deformation of grafted polymer layers in strong shear flows. Phys Rev E 53:3782–3787CrossRefGoogle Scholar
  38. Heyden F H J v d, Bonthuis DJ, Stein D, Meyer C, Dekker C (2006) Electrokinetic energy conversion efficiency in nanofluidic channels. Nano Lett 6:2232–2237CrossRefGoogle Scholar
  39. Israels R, Leermakers FAM, Fleer GJ, Zhulina EB (1994) Charged polymeric brushes: structure and scaling relations. Macromolecules 27:3249–3261CrossRefGoogle Scholar
  40. Keh HJ, Ding JM (2003) Electrokinetic flow in a capillary with a charge-regulating surface polymer layer. J Colloid Interface Sci 263:645–660CrossRefGoogle Scholar
  41. Keh HJ, Liu YC (1995) Electrokinetic flow in a circular capillary with a surface charge layer. J Colloid Interface Sci 172:222–229CrossRefGoogle Scholar
  42. Klein J (1994) Shear of polymer brushes. Colloids Surf A 86:63–76CrossRefGoogle Scholar
  43. Lyatskaya YV, Leermakers FAM, Fleer GJ, Zhulina EB, Birshteint TM (1995) Analytical self-consistent-field model of weak polyacid brushes. Macromolecules 28:3562–3569CrossRefGoogle Scholar
  44. Ma HC, Keh HJ (2007) Diffusioosmosis of electrolyte solutions in a capillary slit with adsorbed polyelectrolyte layers. J Colloid Interface Sci 313:686–696CrossRefGoogle Scholar
  45. McDaniel K, Valcius F, Andrews J, Das S (2015) Electrostatic potential distribution of a soft spherical particle with a charged core and pH-dependent charge density. Colloids Surf B 127:143–147CrossRefGoogle Scholar
  46. Milne Z, Yeh L-H, Chou T-H, Qian S (2014) Tunable Donnan potential and electrokinetic flow in a biomimetic gated nanochannel with pH-regulated polyelectrolyte brushes. J Phys Chem C 118:19806–19813CrossRefGoogle Scholar
  47. Milner ST, Witten TA, Cates ME (1988a) A parabolic density profile for grafted polymers. Europhys Lett 5:413CrossRefGoogle Scholar
  48. Milner ST, Witten TA, Cates ME (1988b) Theory of the grafted polymer brush. Macromolecules 21:2610–2619CrossRefGoogle Scholar
  49. Milner ST, Witten TA, Cates ME (1989) Effects of polydispersity in the end-grafted polymer brush. Macromolecules 22:853–861CrossRefGoogle Scholar
  50. Milner ST (1991) Polymer brushes. Science 251:905–914CrossRefGoogle Scholar
  51. Morrison FA, Osterle JF (1965) Electrokinetic energy conversion in ultrafine capillaries. J Chem Phys 43:2111–2115CrossRefGoogle Scholar
  52. Netz RR, Andelman D (2003) Neutral and charged polymers at interfaces. Phys Rep 380:1–95CrossRefzbMATHGoogle Scholar
  53. Ohshima H (1995) Electrophoresis of soft particles. Adv Colloid Interface Sci 62:189–235CrossRefGoogle Scholar
  54. Ohshima H (2009) Theory of electrostatics and electrokinetics of soft particles. Sci Technol Adv Mater 10:1–13CrossRefGoogle Scholar
  55. Ohshima H (2012) Electrical phenomena in a suspension of soft particles. Soft Matter 8:3511–3514CrossRefGoogle Scholar
  56. Ohshima H, Kondo T (1990) Electrokinetic flow between two parallel plates with surface charge layers: electro-osmosis and streaming potential. J Colloid Interface Sci 135:443–448CrossRefGoogle Scholar
  57. Quan G, Wang M, Tong C (2014) A numerical study of spherical polyelectrolyte brushes by the self-consistent field theory. Polymer 55:6604–6613CrossRefGoogle Scholar
  58. Siwy Z, Trofin L, Kohli P, Baker LA, Trautmann C, Martin CR (2005) Protein biosensors based on biofunctionalized conical gold nanotubes. J Am Chem Soc 127:5000–5001CrossRefGoogle Scholar
  59. Starov VM, Solomentsev YE (1993a) Influence of gel layers on electrokinetic phenomena: 1. Streaming potential. J Colloid Interface Sci 158:159–165CrossRefGoogle Scholar
  60. Starov VM, Solomentsev YE (1993b) Influence of gel layers on electrokinetic phenomena: 2. Effect of ions interaction with the gel layer. J Colloid Interface Sci 158:166–170CrossRefGoogle Scholar
  61. Wang Q, Taniguchi T, Fredrickson GH (2004) Self-consistent field theory of polyelectrolyte systems. J Phys Chem B 108:6733–6744CrossRefGoogle Scholar
  62. Wang M, Tong C (2014) RSC Adv 4:20769–20780Google Scholar
  63. Witte KN, Kim S, Won Y-Y (2009) Self-consistent field theory study of the effect of grafting density on the height of a weak polyelectrolyte brush. J Phys Chem B 113:11076–11084CrossRefGoogle Scholar
  64. Xia F, Guo W, Mao Y, Hou X, Xue J, Xia H, Wang L, Song Y, Ji H, Ouyang Q, Wang Y, Jiang L (2008) Gating of single synthetic nanopores by proton-driven dna molecular motors. J Am Chem Soc 130:8345–8350CrossRefGoogle Scholar
  65. Yameen B, Ali M, Neumann R, Ensinger W, Knoll W, Azzaroni O (2009) Single conical nanopores displaying pH-tunable rectifying characteristics. J Am Chem Soc 131:2070–2071CrossRefGoogle Scholar
  66. Yang J, Lu F, Kostiuk LW, Kwok DY (2003) Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena. J Micromech Microeng 13:963–970CrossRefGoogle Scholar
  67. Zhulina YB, Pryamitsyn VA, Borisov OV (1989) Structure and conformational transitions in grafted polymer chain layers. A new theory. Pol Sci USSR 31:205–216CrossRefGoogle Scholar
  68. Zhulina EB, Borisov OV (1997) Structure and interaction of weakly charged polyelectrolyte brushes: self-consistent field theory. J Chem Phys 107:5952–5967CrossRefGoogle Scholar
  69. Zhulina EB, Borisov OV (2011) Poisson–Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush. Langmuir 27:10615–10633CrossRefGoogle Scholar
  70. Zimmermann R, Kuckling D, Kaufmann M, Werner C, Duval JFL (2010) Electrokinetics of poly(N-isopropylacrylamid)-co-carboxyacrylamid soft thin-film. Evidence for diffuse segment distribution in swollen state. Langmuir 26:18169–18181CrossRefGoogle Scholar
  71. Zimmermann R, Dukhin SS, Werner C, Duval JFL (2013) On the use of electrokinetics for unraveling charging and structure of soft planar polymer films. Curr Opin Colloid Interface Sci 18:83–92CrossRefGoogle Scholar
  72. Zimmermann R, Romeis D, Bihannic I, Stuart MC, Sommer J-W, Wernerad C, Duval JFL (2014) Electrokinetics as an alternative to neutron reflectivity for evaluation of segment density distribution in PEO brushes. Soft Matter 10:7804–7809CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA

Personalised recommendations