C. Zakri et al., DETERMINATION OF THE INPLANE ELASTIC TENSOR OF CRYSTALLINE DECANOL MONOLAYERS ON WATER BY X-RAY-DIFFRACTION, Physical review. B, Condensed matter, 55(21), 1997, pp. 14163-14172
We show how high-resolution x-ray studies associated with surface tens
ion measurements allow a determination of the elastic constants of cry
stalline 1-decanol monolayers at the water-air interface. The shape an
d position of the power-law diffraction peak yield, respectively, the
shear and compression elastic constants. At low temperature, rotation
scans of the liquid surface around a vertical axis exhibit six sharp p
eaks, proving the existence of the long-range order of bond orientatio
ns, as expected for a hexagonal two-dimensional (2D) crystal. We find
a shear elastic constant of (210 +/- 30) mN/m and a compression modulu
s of (2500 +/- 500) mN/m. These values are compatible with the existen
ce of a 2D solid, according to the Nelson-Halperin melting theory. Bet
ween similar to 12 degrees C and melting (T-m = 14.3 degrees C), the d
rastic broadening of the diffraction line can be interpreted either as
the occurrence of a hexatic phase or as a strong decrease of the shea
r modulus, as expected in the framework of the weak crystallization th
eory.