Positional order and thermal expansion of surface crystalline N-alkane monolayers

We report a high-resolution synchrotron grazing incidence x-ray diffraction measurement of a surface crystalline monolayer at the liquid-vapor interface of the n-alkane eicosane (C₂₀H₄₂) just above its melting temperature. The peak width of the surface monolayer rotator phase is shown to be resolution limited and implies positional correlations of at least ∼1 μm. The high resolution allowed determination of the temperature dependence of the peak position over the narrow (3 °C) temperature range of the surface crystal phase. The two-dimensional thermal expansion was determined to be (dA/dT)/A=1.8(±0.1)×10^-3°C^-1, which is comparable to the expansion in similar chain length bulk n-alkane rotator phases. Our data are consistent with the power-law shaped scattering tails expected from quasi-long-range order in two dimensions.