Determination of the in-plane elastic tensor of crystalline decanol monolayers on water by x-ray diffraction

Abstract

We show how high-resolution x-ray studies associated with surface tension measurements allow a determination of the elastic constants of crystalline 1-decanol monolayers at the water-air interface. The shape and 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 peaks, proving the existence of the long-range order of bond orientations, as expected for a hexagonal two-dimensional ͑2D͒ crystal. We find a shear elastic constant of (210Ϯ30) mN/m and a compression modulus of (2500 Ϯ500) mN/m. These values are compatible with the existence of a 2D solid, according to the Nelson-Halperin melting theory. Between ϳ12°C and melting (T m ϭ14.3°C), the drastic broadening of the diffraction line can be interpreted either as the occurrence of a hexatic phase or as a strong decrease of the shear modulus, as expected in the framework of the weak crystallization theory.

Langmuir monolayers as disordered solids: Disorder and elastic fluctuations in mesophases

“…This explains an effect already observed. 7,8 Moreover, we have considered the time-evolution and frequency dependence of the elastic response and offered interpretation of the difference between the observed static and high-frequency shear elasticity, 16 as well as for anomalous shear viscosity. 17 Positional order of the monolayers, as observed by x-ray scattering, 6 may be expected to be influenced by the disorder of the clusters and their correlation.…”

“…Our findings explain the observations of ''viscosity'' made by Copeland et al, 17 and by other, more recent, experiments on shear elasticity of Langmuir monolayers. 7,8,16 Implications for diffuse scattering Clearly, the ''anomalous'' elastic properties of the mesophases are related to disorder due to the existence of mesoscopic elastic domains. This disorder is seen in x-ray scattering experiments and manifests itself in the anomalous broadening of diffraction peaks at temperatures around the LS/S transition.…”

“…The way the elastic interaction renormalizes the elastic properties of the mesophases is also discussed. Results are examined in the context of recent experiments on the microscopic 7 and macroscopic 8 elasticity of the monolayers and kinetic aspects of the elastic response are also considered. New studies of the positional disorder in LS, and S phases 6 stimulate an additional discussion on the contribution of the elastic domains to the x-ray diffuse scattering.…”

“…Moreover, grazing incidence x-ray diffraction experiments have shown the monolayers to be crystalline in both compressed and uncompressed states, 5 and, very recently, this has also been shown for high-temperature ͑LS͒ and low-temperature ͑S͒ phases. 6 In recent elegant studies of the shear elasticity of monolayers, 7,8 it has been confirmed that these phases are more crystalline in nature, rather than hexatic. These findings strongly support our previously introduced model of Langmuir monolayers as disordered solids, 3,9 as do other studies 10,11 that demonstrate mesophases can be treated as two-dimensional ͑2D͒ solids.…”

Dynamics in Ultrathin Films: Particle Tracking Microrheology of Langmuir Monolayers

“…It is well known that long-chain n-alcohols for m stable Langmuir monolayers at the air/water surface, with a complex 2-D phase diagram qualitatively similar to that of the fatty acids and esters [59]. Moreover, at the spreading pressure, surface induced solidification has been reported for some of the monolayers [60,61]. We have studied the monolayer of n-dodecanol at 22 ºC over the whole range.…”