We are interested in understanding if a 2-D molecule is standing up or lying down on a surface.
A friend of mine is doing research on that: http://dx.doi.org/10.1016/j.cplett.2010.09.051
They use standing x-ray waves on the surface
if the molecules within the layer form a crystalline structure you can use gracing incident diffraction: http://dx.doi.org/10.1021/jp206033x
If the structure is nearly crystalline e.g. they are standing up and are oriented in the same way because of say a bond to the substrate SFG would also do the trick. You could even use it in aqueous media and get more or less time dependant information on conformational changes. Might be useful depending on your experimental setup.
Infrared spectroscopy can be used to elucidate orientation. Have a look at some of Dave Allara or Ralph Nuzzo's papers.
Also, we have used a combination of scanning tunneling microscopy and spectroscopy to do so: ACS Nano 3, 3115 (2009).
I'd recommend to take a look at XPS (X-ray Photoelectron Spectroscopy). A surface analysis technique that may indicate variations in bonding energy among the molecule constituents, via energy shifts in the spectrum.
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