Abstract
In this paper, the viscosity of water confined in single-walled carbon nanotubes (SWCNTs) with the diameter ranging from 8 to 54 Å is evaluated, which is crucial for the research on the nanoflow but difficult to be obtained. An “Eyring-MD” (molecular dynamics) method combining the Eyring theory of viscosity with the MD simulations is proposed to tackle the particular problems. For the critical energy which is a parameter in the “Eyring-MD” method, the numerical experiment is adopted to explore its dependence on the temperature and the potential energy. To demonstrate the feasibility of the proposed method, the viscosity of water at high pressure is computed and the results are in reasonable agreement with the experimental results. The computational results indicate that the viscosity of water inside SWCNTs increases nonlinearly with enlarging diameter of SWCNTs, which can reflect the size effect on the transports capability of the SWCNTs. The trend of the viscosity is well explained by the variation of the hydrogen bond of the water inside SWCNTs. A fitting equation of the viscosity of the confined water is given, which should be significant for recognizing and studying the transport behavior of fluid through the nanochannels.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alberto S (2006) The mechanism of water diffusion in narrow carbon nanotubes. Nano Lett 6(4):633–639. doi:10.1021/nl052254u
Alenka L, David C (1996) Hydrogen-bond kinetics in liquid water. Nature 379(4):55–57. doi:10.1038/379055a0
Alexiadis A, Kassinos S (2008) The density of water in carbon nanotubes. Chem Eng Sci 63:2047–2056. doi:10.1016/j.ces.2007.12.035
Alfè D, Gillan M (1998) First-principles calculation of transport coefficients. Phys Rev Lett 81(23):5161–5164. doi:10.1103/PhysRevLett.81.5161
Angell CA (1993) Water II is a strong liquid. J Phys Chem 97:6339–6341. doi:10.1021/j100126a005
Bai J, Wang J, Zeng XC (2006) Multiwalled ice helixes and ice nanotubes. Proc Natl Acad Sci 103(52):19664–19667. doi:10.1073/pnas.0608401104
Balasubramanian S, Mundy CJ, Klein ML (1996) Shear viscosity of polar fluids: molecular dynamics calculations of water. J Chem Phys 105(24):11190–11195. doi:10.1063/1.472918
Bertolini D, Tani A (1995) Stress tensor and viscosity of water: molecular dynamics and generalized hydrodynamics results. Phys Rev E 52(2):1699–1710. doi:10.1103/PhysRevE.52.1699
Bianco A, Kostarelos K, Prato M (2005) Applications of carbon nanotubes in drug delivery. Curr Opin Chem Biol 9:674–679. doi:10.1016/j.cbpa.2005.10.005
Bosse D, Bart HJ (2005) Viscosity calculations on the basis of Eyring’s absolute reaction rate theory and COSMOSPACE. Ind Eng Chem Res 44:8428–8435. doi:10.1021/ie048797g
Bryc W (2002) A uniform approximation to the right normal tail integral. Appl Math Comput 127:365–374. doi:10.1016/S0096-3003(01)00015-7
Chen X, Cao GX, Han AJ, Punyamurtula VK, Liu L, Culligan PJ, Kim T, Qiao Y (2008) Nanoscale fluid transport: size and rate effects. Nano Lett 8(9):2988–2992. doi:10.1021/nl802046b
David RL (2003–2004) CRC handbook of chemistry and physics, 84th edn. CRC Press, New York
Eyring H (1936) Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys 4:283–291. doi:10.1063/1.1749836
Giovambattista N, Rossky PJ, Debenedetti PG (2009) Phase transitions induced by nanoconfinement in liquid water. Phys Rev Lett 102:050603. doi:10.1103/PhysRevLett.102.050603
Guo GJ, Zhang YG (2001) Equilibrium molecular dynamics calculation of the bulk viscosity of liquid water. Mol Phys 99(4):283–289. doi:10.1080/00268970010011762
Hallett J (1963) The temperature dependence of the viscosity of supercooled water. Proc Phys Soc 82:1046–1050. doi:10.1088/0370-1328/82/6/326
Han AJ, Lu WY, Punyamurtula VK, Chen X, Surani FB, Kim T, Qiao Y (2008) Effective viscosity of glycerin in a nanoporous silica gel. J Appl Phys 104:124908. doi:10.1063/1.3020535
Hanasaki I, Nakatani A (2006) Flow structure of water in carbon nanotubes: poiseuille type or plug-like? J Chem Phys 124(14):144708. doi:10.1063/1.2187971
Hans WH, William CS, Jed WP, Jeffry DM, Thomas JD, Greg LH, Teresa HG (2004) Development of an improved four-site water model for biomolecular simulations: TIP4P-EW. J Chem Phys 120(20):9665–9678. doi:10.1063/1.1683075
Henkelman G, Jόnsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113:9978. doi:10.1063/1.1329672
Holt JK (2008) Methods for probing water at the nanoscale. Microfluid Nanofluid 5:425–442. doi:10.1007/s10404-008-0301-9
Holt JK, Park HG, Wang YM, Stadermann M, Artyukhin AB, Grigoropoulos CP, Noy A, Bakajin O (2006) Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312:1034–1037. doi:10.1126/science.1126298
Horne RA, Courant RA, Johnson DS, Margosian FF (1965) The activation energy of viscous flow of pure water and sea water in the temperature region of maximum density. J Phys Chem 69(11):3988–3991. doi:10.1021/j100895a057
Hummer G, Rasaiah JC, Noworyta JP (2001) Water conduction through the hydrophobic channel of a carbon nanotube. Nature 414:188–190. doi:10.1038/35102535
Joseph S, Aluru NR (2008) Why are carbon nanotubes fast transporters of water? Nano Lett 8(2):452–458. doi:10.1021/nl072385q
Kalra A, Garde S, Hummer G (2003) Osmotic water transport through carbon nanotube membranes. Proc Natl Acad Sci 100(8):10175–10180. doi:10.1073/pnas.1633354100
Kauzmann W, Eyring H (1940) The viscous flow of large molecules. J Am Chem Soc 62(11):3113–3125. doi:10.1021/ja01868a059
Kincaid JF, Eyring H, Stearn AE (1941) The theory of absolute reaction rates and its application to viscosity and diffusion in the liquid state. Chem Rev 28(2):301–365. doi:10.1021/cr60090a005
Koga K, Gao GT, Tanaka H, Zeng XC (2001) Formation of ordered ice nanotubes inside carbon nanotubes. Nature 412:802–805. doi:10.1038/35090532
Lee MJ, Chiu JY, Hwang SM, Lin HM (1999) Viscosity calculations with the Eyring–Patel–Teja model for liquid mixtures. Ind Eng Chem Res 38(7):2867–2876. doi:10.1021/ie980751y
Lei QF, Hou YC, Lin RS (1997) Correlation of viscosities of pure liquids in a wide temperature range. Fluid Phase Equilibr 140:221–231. doi:10.1016/S0378-3812(97)00176-3
Li YX, Xu JL, Li DQ (2010) Molecular dynamics simulation of nanoscale liquid flows. Microfluid Nanofluid. doi:10.1007/s10404-010-0612-5
Liu YC, Wang Q, Wu T, Zhang L (2005) Fluid structure and transport properties of water inside carbon nanotubes. J Chem Phys 123:234701. doi:10.1063/1.2131070
Majumder M, Chopra N, Andrews R, Hinds BJ (2005) Enhanced flow in carbon nanotubes. Nature 438:44. doi:10.1038/438044a
Mallamace F, Branca C, Corsaro C, Leone N, Spooren J, Stanley HE, Chen SH (2010) Dynamical crossover and breakdown of the stokes-einstein relation in confined water and in methanol-diluted bulk water. J Phys Chem B 114:1870. doi:10.1021/jp910038j
Martí J (1999) Analysis of the hydrogen bonding and vibrational spectra of supercritical model water by molecular dynamics simulations. J Chem Phys 110(14):6876–6886. doi:10.1063/1.478593
Mashl RJ, Joseph S, Aluru NR, Jakobsson E (2003) Anomalously immobilized water: a new water phase induced by confinement in nanotubes. Nano Lett 3(5):589–592. doi:10.1021/nl0340226
Poling BE, Prausnitz JM, O’Connell JP (2001) The properties of gases and liquids. McGraw-Hill Companies, New York
Powell RE, Roseveare WE, Eyring H (1941) Diffusion, thermal conductivity, and viscous flow of liquids. Ind Eng Chem 33(4):430–435. doi:10.1021/ie50376a003
Steve P (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19. doi:10.1006/jcph.1995.1039, http://lammps.sandia.gov
Sun YL, Sun MH, Cheng WD, Ma CX, Liu F (2007) The examination of water potentials by simulating viscosity. Comput Mater Sci 38:737–740. doi:10.1016/j.commatsci.2006.05.007
Thomas JA, McGaughey AJH (2008) Reassessing fast water transport through carbon nanotubes. Nano Lett 8(9):2788–2793. doi:10.1021/nl8013617
Tolman RC (1920) Statistical mechanics applied to chemical kinetics. J Am Chem Soc 42:2506
Velikov V, Borick S, Angell CA (2001) The glass transition of water based on hyperquenching experiments. Science 294:2335–2338. doi:10.1021/ja01457a008
Walter J, Moore JR, Eyring H (1938) Theory of the viscosity of unimolecular films. J Chem Phys 6:391–394. doi:10.1063/1.1750274
Walther JH, Jaffe R, Halicioglu T, Koumoutsakos P (2001) Carbon nanotubes in water: structural characteristics and energetics. J Phys Chem B 105:9980–9987. doi:10.1021/jp011344u
Wang HJ, Xi XK, Kleinhammes A, Wu Y (2008) Temperature-induced hydrophobic-hydrophilic transition observed by water adsorption. Science 322:80–83. doi:10.1126/science.1162412
Wonham J (1967) Effect of pressure on the viscosity of water. Nature 215:1053–1054. doi:10.1038/207620a0
Zhu FQ, Tajkhorshid E, Schulten K (2004) Collective diffusion model for water permeation through microscopic channels. Phys Rev Lett 93:224501. doi:10.1103/PhysRevLett.93.224501
Acknowledgments
The supports of the National Natural Science Foundation of China (10721062, 50679013, 90715037, 10902021), the 111 Project (No.B08014), the National Key Basic Research Special Foundation of China (2010CB832704) and the Program for Changjiang Scholars and Innovative Research Team in University of China (PCSIRT) are gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, H., Ye, H., Zheng, Y. et al. Prediction of the viscosity of water confined in carbon nanotubes. Microfluid Nanofluid 10, 403–414 (2011). https://doi.org/10.1007/s10404-010-0678-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10404-010-0678-0