Relating the structure factors of two-dimensional materials in planar and spherical geometries

TL;DR

This paper derives an approximate relationship between structure factors of two-dimensional materials in planar and spherical geometries, facilitating model-free comparisons across different experimental and simulation setups.

Contribution

It introduces a novel approximate relationship linking structure factors in planar and spherical geometries for 2D materials, aiding cross-geometry analysis.

Findings

The relationship is useful for comparing structure factors across geometries.

It is demonstrated with a Gaussian material supporting different phases.

The method enables model-free analysis within its applicability range.

Abstract

Scattering structure factors provide essential insight into material properties and are routinely obtained in experiments, computer simulations, and theoretical analyses. Different approaches favor different geometries of the material. In case of lipid bilayers, scattering experiments can be performed on spherical vesicles, while simulations and theory often consider planar membrane patches. We derive an approximate relationship between the structure functions of such a material in planar and spherical geometries. We illustrate the usefulness of this relationship in a case study of a Gaussian material that supports both homogeneous and microemulsion phases. Within its range of applicability, this relationship enables a model-free comparison of structure factors of the same material in different geometries.