## 3 Results and Discussion
### Experimental Analysis of Indents in a Matrix  
During the experimental indentation, usually matrix with a certain number of indents is set up. Thus, it is of an interest to explore the influence of the distance between indents with different orientations and a number of neighbors. Here, three different orientations (0\({}^{\circ}\), 90\({}^{\circ}\) and 45\({}^{\circ}\)) as shown in Figure 1 are considered for a 3 by 3 matrix. The average percentage difference values for three indents in the same row or column, \(\overline{D}\)%, with different orientations are shown in Figure 8. As per the schematics presented in Figure 1, for 0\({}^{\circ}\) orientation, the three groups are defined as: the first group includes 1 st, 2 nd, and 3 rd indent, the second group--4 th, 5 th, and 6 th indent, and the third group--7 th, 8 th, and 9 th indents. While the groups for 90\({}^{\circ}\) orientation are following: the first group--1 st, 4 th, and 7 th indents, the second group--2 nd, 5 th, and 8 th indents, and the third group--3 rd, 6 th, and 9 th indents. As expected, the hardness and reduced modulus become stable with increasing separation and reduced indent overlap. Less than 1% average difference between each indent was measured when the _d/h_ \(\sim\) 7-8 for, \(h\) = 5 \(\upmu\)m (Figure 8c,**e**) and 10 \(\upmu\)m (Supporting Information S3, Figure S3.1). Optical images of matrix indentation indicate that _d/h_ = 7-8 is already the first spacing where indents hardly touch with pyramidal shape corners. However, it is also evident that a small portion of the indent will still be imprinted on the piled-up or crazed part of the PS sample at nominal separation of 7 (Figure 6b), which was not observed for indents performed in a single row (Figure 6a). This is expected, as with the matrix method in total larger area and volume of material is disturbed during the indentation. The absolute values (Figure 9; Figure S3.2) become more or less constant when _d/h_ = 10, where indents are completely separated. As  
Figure 7: Typical load–displacement curves at low nominal separations. Example is given for \(h\) = 5 \(\upmu\)m recorded at constant load of 140 mN. in the case of indents in a single rows or columns, indent orientation does not show any significant influence at large separations. However, is it highly affected when indents are close, with the highest deviation in values observed at orientation of 0\({}^{\circ}\) for \(h=5\) um and 10 um. The influence of orientation at 45\({}^{\circ}\) was not determined experimentally, as the matrix was too small to have sufficient data, but it is expected to show a similar response as for the horizontal and vertical values. The effect of 45\({}^{\circ}\) orientation was investigated with FEA and will be presented in the next chapter. In the case of \(h=1\) um, \(H\) and \(Er\) values between the indent sets show a higher deviation (\(\sim\)1-2%) even at large separations. In addition, the influence of orientation is more pronounced in this case even if it is not very significant at larger separations. Why the values deviate so much, is not clear. Depth of 1 um for the nanoindentation is deep enough to be considered as measuring \"bulk\", tip apex imperfections can be ignored, and the diamond contact area approach the ideal equation. There might be some influence of the indentation size effect for PS [34; 35], as measured values tend to differ with increasing depth, as shown in Table 2. The larger deviation at smaller depth might be related to the sample itself. In this work, commercial flat polystyrene sheets were used. As samples are transparent, visual inspection did not show any external or internal flaws. A closer look at the surface with optical microscope showed only flat surfaces with no defects. Yet, it is not clear how the sheets were manufactured, if plasticizers were used, and how all of it might affect the surface layer. The sample ageing also cannot be excluded, even if they were kept in a closed container at room temperature away from any heat sources.