Höfling F, Dietrich S
Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany.
Zuse Institut Berlin, Takustr. 7, 14195 Berlin, Germany.
J Chem Phys. 2024 Mar 14;160(10). doi: 10.1063/5.0186955.
Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.
掠入射X射线衍射（GIXRD）是一种散射技术，它能够让人们在分子尺度上表征流体界面的结构，包括表面张力和界面粗糙度的测量。然而，非零波数下相应的标准数据分析被批评为没有定论，因为散射强度受到来自体相不可避免的散射的污染。在此，我们基于一组与实验相关的最小假设，提出一个体相贡献的物理上自洽的模型，从而克服了这种模糊性。为此，我们推导了背景散射的显式积分表达式，它可以根据共存体相的静态结构因子作为独立输入进行数值确定。关于从计算机模拟推断的GIXRD数据的解释，我们扩展了模型，以考虑体相的有限尺寸，这在模拟中是不可避免的。通过渐近分析揭示了对散射强度的主导贡献之外的相应领先阶修正，在模拟情况下，它的特征是线性系统尺寸与X射线穿透深度之间的竞争。具体而言，我们通过广泛的高精度计算机模拟，计算了具有截断对相互作用的Lennard-Jones流体在平面液-气界面处散射的预期GIXRD强度。报告的数据涵盖了沿着整个液-气共存线的流体状态的界面和体相性质。敏感性分析表明，我们的发现对于平均界面位置的详细定义是稳健的。我们得出结论，先前关于介观尺度上表面张力增强的说法可以通过散射实验进行明确的检验。
