# Nanoindentation of Historic and Artists' Paints
## 4 Characterization of Artists' Paints
### Cross-Sectional Samples
#### 4.2.2 Indentation near Sample Edge  
Two main issues associated with testing embedded cross-sectional samples are infiltration of the embedding medium into the sample and edge effect. Figure 10 shows the Berkovich indentation imprints on the cross-sectional surfaces of a 0.26 mm-thick TiO\({}_{2}\) acrylic paint film (generated with 9 mN maximum load) and its surrounding Technovit  
Figure 9: Cleaning of a Berkovich indenter contaminated with Liquitex acrylic gesso by successive indentings into polycarbonate; (**a**) the imprint of the first test (**left**) showing the paint residue on the sample surface and that of the sixth test (**right**) showing no signs of contamination, and (**b**) comparison of stiffness versus contact depth for the first and sixth tests. 2000 LC liquid as the embedding resin material (generated with 100 mN maximum load). While all indents on the are identical in both size and shape, an indent on the paint near the sample-resin interface is smaller. This is attributed to the liquid resin infiltrating the paint during the embedding process, thereby increasing the measured hardness of the paint sample near the interface in cured condition. Infiltration of the embedding resin is not the only factor responsible for the overestimation of the measured hardness near the paint-resin interface. Indentation tests performed on an embedded, submillimeter cross-sectional paint sample may also overestimate mechanical properties due to the presence of surrounding resin that is stiffer than the paint itself [48,49]. The extent of paint modulus overestimation is greater at test locations closer to the interface with a stiffer embedding material and can be further exacerbated by infiltration of the embedding resin into the paint sample. Such a phenomenon (possible when the sample is porous, and the embedding material is liquid-like) irreversibly changes the composition of the paint material. The simplest approach to avoiding both edge and infiltration effects is to perform measurements away from the sample-resin interface. This approach, however, is impractical for minute cross-sectional samples especially because the impact from the edge and infiltration effects is difficult to assess for samples of unknown mechanical properties. The dilemma is well illustrated in [14] where the authors practically exhausted the available surface area of a small Van Gogh paint sample to maximize the number of indents and obtain as much information as possible about the paint properties. While mitigating both the edge and infiltration effects in an embedded paint sample may be difficult or impossible, use of an appropriate contact mechanics model may account for the edge effect alone (i.e., in the absence of infiltration). Using the concept of structural compliance proposed by [PERSON] et al. [49], a method to correct for the edge effect in dynamic sharp indentation was developed and applied to a viscoelastic paint film embedded in a noninfiltrating, light-curing fixing paste [17]. The method established the correct modulus value near the edge of a TiO\({}_{2}\) acrylic paint sample embedded in a \(\sim\)10 times stiffer medium. The only assumption used in this method is that the modulus of the paint does not change with depth from the surface. This assumption is reasonable, since a gradient in paint properties is expected in the direction of the film thickness, but not parallel to the film surface. The decision to employ a noninfiltrating embedding medium for the preparation of paint cross-sections typically means selection of a resin with an even greater stiffness mismatch between the paint and the resin in cured condition. For example, the storage modulus of light-cured Technovit(r) 2000 LC liquid is equal to \(\sim\)4 GPa [16], whereas the storage modulus of light-cured Technovit(r) 2000 LC fixing paste is \(\sim\)15 GPa [17]. A larger difference between the moduli of paint and resin results in a more pronounced edge effect, but this may be mitigated by use of the previously discussed structural compliance method.