PHOTON SCIENCE

Gas, liquid, and solid are familiar states of matter – but the structure of liquids, especially on the surfaces, remain elusive. It is important for fundamental science and many applications where liquid surfaces serve as substrates, from lipid monolayers that model biomembranes to on-liquid-surface synthesis of two-dimensional materials. Its key question is to measure the layer structure of a liquid surface.

In the 1980s the first synchrotron X-ray reflectivity (XRR) experiments on liquid surfaces at DORIS II at DESY and at NSLS at Brookhaven National Laboratory (BNL) in the US led to the ‘capillary wave model’ (CWM). It quantifies the contribution of the thermally excited roughness of a liquid surface to the X-ray scattering. The standard CWM handles “floppy” interfaces such as neat water but falters when a film stiffens the surface. Fourty years later, another collaboration, this time between PETRA III beamline P08 at DESY and NSLS-II beamline 12ID-OPLS at BNL, takes a major step forward to close the gap. By introducing the ‘extended capillary wave model’ (eCWM), a unified theory that interprets x-ray scattering from the liquid surfaces without and with mechanical stiffness, they were able to cover the regime encountered for lipid monolayers and other films. Building on the eCWM, they established ‘pseudoreflectivity’ (pseudo-XRR), a new way to obtain reflectivity from fixed grazing incidence X-ray scattering (GIXS) in a single shot – faster and more precisely than the conventional angle-scanned XRR. These studies are published in the Journal of Applied Crystallography and the Physical Review Research.

The physics behind the eCWM is compact. Liquid surfaces are roughened by the thermally excited capillary waves of which the amplitudes depend on temperature, surface tension, and mechanical stiffness. However, this thermal roughness “blurs” the time and ensemble averaged structure measured by XRR. “We were inspired by the standard CWM to solve this challenge by also utilizing the diffuse scattering.” says DESY scientist Chen Shen. This model uses a single expression that describes both the specular reflectivity and the off-specular diffuse scattering. This is a concise product of three factors: the intrinsic structure factor (the ‘unblurred’ density profile), a thermal roughness factor which depends on temperature, surface tension, and bending modulus, and a factor for an ideal flat interface (that reduces to Fresnel reflectivity at specular position). It recovers the standard CWM at zero bending rigidity. The consequence for experiments is decisive: the eCWM analysis allows to decouple the thermal roughness from the X-ray data, providing the high-resolution intrinsic layer structure and the bending rigidity simultaneously.

The eCWM enables a much simpler and quicker way of measuring XRR from liquid surfaces. The conventional X-ray reflectometry requires a complicated crystal optics to deflect the beam downwards over a large incident angle range with respect to the liquid surface. After closer examination of the theory, the team realized that the specular reflectivity and the diffuse scattering differ only by a special value (Qxy) inside the roughness factor. Using the ratio of their roughness factors would enable the conversion from the diffuse signal into the XRR. This raised the following question for the team: “GIXS measures the diffuse scattering around the total reflection. So can’t we measure GIXS at a fixed incidence and use eCWM to compute the XRR curve?” This ‘pseudo-XRR’ idea was validated by measuring both conventional XRR and GIXS on the same samples at the NSLS-II beamline 12ID-OPLS: the pseudo-XRR computed from GIXS was identical to the scanned reflectivity. At the low-background Langmuir trough GID setup at the PETRA III beamline P08, a 20-second pseudo-XRR data acquisition now reaches down to ~10^-13 in reflectivity, a ten thousand times larger dynamic range compared to a 900-second conventional XRR scan and without need for complex beam-deflection optics. Its fixed incident angle is set with a mirror, and the background is easily suppressed along the fixed beam path.

For facility users, the impact is immediate: the GIXS pseudo-XRR technique is available at the Langmuir trough GID setup at P08 at PETRA III and at the OPLS endstation of 12ID at NSLS-II. “This pseudo-XRR approach provides the users curves ready for analysis with standard reflectivity software, lowering the barrier to adoption. Moreover, it is ‘elegant’ to introduce the roughness factor to account for the thermal roughness in the equation.” says Brookhaven scientist Benjamin M. Ocko, who was also among the pioneers for liquid surface XRR. The team of researchers is now exploring the boundary of this approach beyond the lipid and the surfactant layers. This development is especially valuable for biomembranes, surfactant films, and other systems where time resolution and radiation sensitivity are crucial. Forty years after CWM opened the door to liquid surfaces, the eCWM and pseudo-XRR invite us to continue along this path, which the next generation of light sources such as PETRA IV at DESY make even more promising.


Reference:

C. Shen, H. Zhang, B. Klösgen, B. M. Ocko, Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering, Physical Review Research (2025). DOI: 10.1103/znt1-fmx6

C. Shen, H. Zhang, B. M. Ocko, Reconstructing the reflectivity of liquid surfaces from grazing incidence X-ray off-specular scattering data, J Appl Crystallogr (2024), DOI: 10.1107/s1600576724002887