Diffusion at interfaces

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Diffusion at the liquid-vapour interface is both interesting and controversial. The very definition of particles "at" the interface is difficult. The diffusion coefficient will in this case be a diagonal tensor; two of its elements are equal and correspond to parallel diffusion (along the interface), the third one corresponds to normal, or perpendicular diffusion (across the interface). Since the particles are continuously leaving and entering the interfacial region, it is also important to study this dynamical process by, e.g., the residence time.

Typically, slabs corresponding to the interfacial region are obtained, and diffusion processes are considered for each of them separately. The three Cartesian components may be mixed [1,8], or separated, as in most of the other references below. Sometimes diffusion is only tracked down for times shorter than the residence time [5,8]. The work by Liu et al. [10] employs a refined treatment using Smoluchowski equations. Its subtlety, combined by the application to perhaps the most interesting system, the liquid water surface, makes this reference quite important. See also Ref [17] (as yet unpublished) for a criticism of these techniques, and a consideration of the problem from the point of view of the intrinsic surface.


pure system Ref
ST-2 Water [2]
TIP4P/FQ Water [9], [11]
SPC/E Water [5]
Dimethyl sulfoxide [7]
Ethanol [8]
liquid metals [13]


mixture Ref
two inmiscible LJs [1], [10]
water/1,2-dichloroethane [3]
water/nitrobenzene [6]
surfactants on water [16]
ions at surfaces [12]

Confined fluids:

system Ref
water on surfaces [4]
LJ on solid [15]
water diffusion across channels [14]


  1. M. Meyer, M. Mareschal, and M. Hayoun "Computer modeling of a liquid–liquid interface", Journal of Chemical Physics 89 pp. 1067-1073 (1988)
  2. R. Michael Townsend and Stuart A. Rice "Molecular dynamics studies of the liquid–vapor interface of water", Journal of Chemical Physics 94 pp. 2207-2218 (1991)
  3. Ilan Benjamin "Theoretical study of the water/1,2-dichloroethane interface: Structure, dynamics, and conformational equilibria at the liquid–liquid interface", Journal of Chemical Physics 97 pp. 1432-1445 (1992)
  4. Song Hi Lee and Peter J. Rossky "A comparison of the structure and dynamics of liquid water at hydrophobic and hydrophilic surfaces—a molecular dynamics simulation study", Journal of Chemical Physics 100 pp. 3334-3345 (1994)
  5. R. S. Taylor, L. X. Dang, and B. C. Garrett "Molecular Dynamics Simulations of the Liquid/Vapor Interface of SPC/E Water", Journal of Physical Chemistry 100 11720 (1996)
  6. Michael, D. Benjamin "Molecular dynamics simulation of the water/nitrobenzene interface", Journal of Electroanalytical Chemistry 450 pp. 335-345, (1998)
  7. Sanjib Senapati "A molecular dynamics simulation study of the dimethyl sulfoxide liquid–vapor interface", Journal of Chemical Physics 117 pp. 1812-1816 (2002)
  8. Ramona S. Taylor and Roseanne L. Shields "Molecular-dynamics simulations of the ethanol liquid–vapor interface", Journal of Chemical Physics 119 pp. 12569-12576 (2003)
  9. Pu Liu, Edward Harder, and B. J. Berne "On the Calculation of Diffusion Coefficients in Confined Fluids and Interfaces with an Application to the Liquid-Vapor Interface of Water", Journal of Physical Chemistry B 108 pp. 6595-6602 (2004)
  10. Jörn B. Buhn, Philippe A. Bopp, and Manfred J. Hampe "A molecular dynamics study of a liquid–liquid interface: structure and dynamics" Fluid Phase Equilibria 224 pp. 221-230 (2004)
  11. Pu Liu, Edward Harder, and B. J. Berne "Hydrogen-Bond Dynamics in the Air-Water Interface", Journal of Physical Chemistry B 109 pp. 2949-2955 (2005)
  12. Tsun-Mei Chang and Liem X. Dang "Recent Advances in Molecular Simulations of Ion Solvation at Liquid Interfaces", Chemical Reviews 106 pp 1305-1322 (2006)
  13. Luis E González and David J González "Ab initio study of the atomic motion in liquid metal surfaces: comparison with Lennard-Jones systems", Journal of Physics: Condensed Matter 18 pp. 11021-11030 (2006)
  14. Vincent J. van Hijkoop, Anton J. Dammers, Kourosh Malek, and Marc-Olivier Coppens "Water diffusion through a membrane protein channel: A first passage time approach", Journal of Chemical Physics 127 085101 (2007)
  15. J. A. Thomas and A. J. H. McGaughey "Effect of surface wettability on liquid density, structure, and diffusion near a solid surface", Journal of Chemical Physics 126 034707 (2007)
  16. Javier Rodriguez and Daniel Laria "Computer simulations of catanionic surfactants adsorbed at air/water interfaces. II. Full coverage", Journal of Chemical Physics 127 124704 (2007)
  17. Daniel Duque, Pedro Tarazona, and Enrique Chacón "Diffusion at the liquid-vapor interface", Journal of Chemical Physics 128 134704 (2008)