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Paper
Soft Matter, 2009, 5, 203 - 207, DOI: 10.1039/b810134e
Elasticity of two-dimensional crystalline monolayers of fatty acid salts at an air–water surface
Jean Daillant, Jérémy Pignat, Sophie Cantin, Françoise Perrot, Serge Mora and Oleg Konovalov
The elastic properties of organic–inorganic two-dimensional crystals floating at the water surface have been fully characterized by grazing incidence X-ray diffuse scattering and high-resolution diffraction. We show that the strong interaction between the organic molecules and the inorganic divalent cations is enough for these nm thick crystals to behave like true solids, with a residual tension of 1 × 10-4–10-3 N m-1. Their bending rigidity is renormalized as
(q) 
q-
k with k = 0.25 ± 0.07 and a microscopic value 
100 kBT at q = 1 × 109 m-1. The in-plane elastic constants behave like qu with u = 1.41 ± 0.2, obeying the scaling relation u = 2 - 2k. These results are consistent with a long-range phonon-mediated interaction between out-of-plane fluctuations but the values of the exponents differ from those generally obtained in numerical simulations.
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