Editing Diffusion at interfaces

[[Diffusion]] at the [[Gas-liquid_phase_transitions | 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 equation]]s.
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See also Ref [17] (still unpublished) for a criticism of these techniques, and
a consideration of the problem from the point of view of the [[capillary waves | intrinsic surface]].


== Systems ==

{| border="1"
|- 
| pure system || Ref
|-
|[[ST2  | ST-2 Water ]] || [2]
|- 
|[[TIP4P/FQ  | TIP4P/FQ Water ]] || [9], [11]
|-
|[[SPC/E  | SPC/E Water ]] || [5]
|-
|Dimethyl sulfoxide || [7]
|-
|[[Ethanol]] || [8]
|-
|[[Metallic liquids |liquid metals]] || [13]
|-
|}

[[Mixtures]]:

{| border="1"
|-
| mixture || Ref
|-
| two inmiscible [[Lennard-Jones_model | LJs]] || [1], [10]
|-
| water/1,2-dichloroethane || [3]
|-
| water/nitrobenzene || [6]
|-
| surfactants on water || [16]
|-
| ions at surfaces || [12]
|-
|}


[[Confined systems |Confined fluids]]:
{| border="1"
|- 
| system || Ref
|-
| water on surfaces || [4]
|-
| [[Lennard-Jones_model | LJ]] on solid || [15]
|-
| water diffusion across chanels || [14]
|-
|}

==References==
#[http://dx.doi.org/10.1063/1.455259 M. Meyer, M. Mareschal, and M. Hayoun "Computer modeling of a liquid–liquid interface", Journal of Chemical Physics '''89''' pp. 1067-1073 (1988)]
#[http://dx.doi.org/10.1063/1.2424934 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)]
#[http://dx.doi.org/10.1063/1.1625643 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) ]
#[http://dx.doi.org/10.1063/1.466425 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) ]
#[http://pubs.acs.org/cgi-bin/abstract.cgi/jpchax/1996/100/i28/abs/jp960615b.html  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)]
#[http://dx.doi.org/10.1016/S0022-0728(97)00653-0   Michael, D. Benjamin "Molecular dynamics simulation of the water/nitrobenzene interface", Journal of Electroanalytical Chemistry '''450'''  pp. 335-345, (1998)]
#[http://dx.doi.org/10.1063/1.1489898 Sanjib Senapati "A molecular dynamics simulation study of the dimethyl sulfoxide liquid–vapor interface", Journal of Chemical Physics '''117''' pp. 1812-1816 (2002)  ]
#[http://dx.doi.org/10.1063/1.1625643 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)]
#[http://dx.doi.org/10.1021/jp0375057 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)]
#[http://dx.doi.org/10.1016/j.fluid.2004.02.012 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)]
#[http://dx.doi.org/10.1021/jp046807l 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)]
#[http://dx.doi.org/10.1021/cr0403640 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)]
#[http://dx.doi.org/10.1088/0953-8984/18/48/030 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)]
#[http://dx.doi.org/10.1063/1.2761897 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)]
#[http://dx.doi.org/10.1063/1.2424934 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)]
#[http://dx.doi.org/10.1063/1.2779876 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)]
[[Category: Non-equilibrium thermodynamics]]
#D. Duque, P. Tarazona, and E. Chacón "Diffusion at the liquid-vapor interface", to be published