## 2 Materials and Methods
### Principles of Grazing Incidence Scattering  
A description of grazing incidence scattering and the distorted wave Born approximation (DWBA) can be found in the literature, e.g., in Refs. [9; 23; 26]. Here we just mention briefly the main characteristics of a soft matter GISANS experiment. Typically, soft samples undergo structural changes when adsorbing to a solid substrate. For example, spherical microgel particles can be distorted and compressed when adsorbed at an interface [13]. Studying such soft matter systems consisting of polymer layers of the order of 100 nm is a challenging task due to the essentially very small scattering volume. Nevertheless, neutron reflectometry and scattering under grazing incidence allows us to obtain valuable information on the scattering length density normal to the surface as well as on lateral (in-plane) correlations at the interface, which correspond to thermal density fluctuations or spacial arrangements with a characteristic length scale [27]. GISANS scattering is normally treated in the DWBA, which takes into account multiple scattering processes at the interface [25; 27; 28]. According to Ref. [29] the diffuse scattered intensity (that accompanies the specular reflection) coming from lateral scattering length density fluctuations with intensity:  
\[I(q)\sim\langle[F_{DWBA}(q)]^{2}\rangle S(q), \tag{1}\]  
where the term \(F_{DWBA}(q)\) is a DWBA form factor accounting for different scattering scenarios with multiple scattering events as described e.g., in Ref. [23]. GISANS is therefore predestined for studying the lateral inhomogeneities. In the case of soft matter samples, lateral structuring is rather blurred and lacking clear Bragg peaks or Bragg sheets, therefore a more detailed modelling of the experiment is needed. In grazing incidence small-angle scattering (GISAS) experiment incident radiation impinges at a shallow incident angle \(\alpha_{i}\) (\(<\)1\({}^{\circ}\)) and the scattered intensity is detected with a position sensitive detector as a function of scattering (\(\alpha_{f}\)) and out-of-plane (\(\psi\)) angles (see Figure 1). The sample surface is the \((x,y)\)-plane with the incident neutron beam coming along the \(x\)-axis, and the scattering plane where the detector is located is the \((y,z)\)-plane [30]. At \(\alpha_{f}=\alpha_{i}\) specular reflection occurs. The interesting part however for GISANS is the off-specular or diffuse scattering, where \(\alpha_{f}\
eq\alpha_{i}\)[31]. A characteristic part of the detector image in a GISANS experiment is the so-called Yoneda peak [32], which appears at \(\alpha_{f}=\alpha_{c}\), with the critical angle of total reflection, \(\alpha_{c}\). The cut through the 2D detector pattern at the position of the Yoneda peak provides information on correlations in the lateral density distribution, for example the average inter-particle distance, the size and the shape of the nanostructures in the near surface region [26; 33]. When \(\alpha_{i}>\alpha_{c}\), the beam is partly reflected and partly refracted, the thin film is then fully illuminated. If the incidence angle at which the neutron beam hits the sample surface is smaller than the critical angle of total reflection, \(\alpha_{i}<\alpha_{c}\), the beam is totally reflected and a specular reflection appears on the detector. However, inside the medium an evanescent intensity distribution with the signature of a propagating wave in \(z\)-direction parallel to the surface is induced. This \"evanescent wave\" arises as a real part of the solution of the Schrodinger equation at \(\alpha_{i}<\alpha_{c}\) (a mathematical description of the evanescent wave nature can be found elsewhere [34; 35; 36]). The evanescent wave (EW) probes the sample only to a short distance from the probed interface (up to 100 nm) [16]. The intensity of the EW drops exponentially with the distance. In this work, we used the software BornAgain [25] to mimic a GISANS experiment as close as possible with its 2D detector image for a given incident angle.