After the Paint Has Dried: a Review of Testing

dePolo et al. Herit Sci (2021) 9:68 https://doi.org/10.1186/s40494-021-00529-w

REVIEW Open Access After the paint has dried: a review of testing techniques for studying the mechanical properties of artists’ paint Gwen dePolo1, Marc Walton1, Katrien Keune2,3 and Kenneth R. Shull1*

Abstract While the chemistry of artists’ paints has previously been studied and reviewed, these studies only capture a portion of the properties afecting the response of paint materials. The mechanical properties of artists’ paints relate to the deformation response of these materials when a stress is applied. This response is dependent on many factors, such as paint composition, pigment to binder ratio, temperature, relative humidity, and solvent exposure. Here, thirty years of tensile testing data have been compiled into a single dataset, along with the testing conditions, to provide future researchers with easy access to these data as well some general discussion of their trends. Alongside the more commonly used techniques of tensile testing and dynamic mechanical analysis, new techniques have been developed to more fully investigate the mechanical properties, and are discussed along with salient results. The techniques have been divided into two categories: those that are restricted to use on model systems and those that are applicable to historic samples. Techniques applied to model systems (tensile testing, dynamic mechanic analysis, quartz crystal microbalance, vibration studies) require too large of a sample to be taken from art objects or focus on the mechanical properties of the liquid state (shear rheometry). Techniques applied to historic samples incorporate the use of small sample sizes (nanoindentation), optical techniques (laser shearography), computational simulations (fnite element analysis), and non-invasive comparative mechanical properties (single-sided nuclear magnetic resonance) to investigate and predict the mechanical properties of paints. Keywords: Mechanical properties, Tensile testing, Dynamic mechanical analysis, Shear rheometry, Quartz crystal microbalance, Nanoindentation, Laser shearography, Single-sided nuclear magnetic resonance, Vibration studies, Finite element analysis

Introduction paint flm [1–4]. Te mechanical properties play a key Overview role in assessing its stability over the lifetime, providing Paint is a ubiquitous component of art objects and a information about the stifness, toughness, and the likeli- research subject that has received prominent attention hood of crack formation, among other things. Te most for many years in both industry and cultural heritage. A recent review paper discussing the mechanical properties great amount of research has focused on understanding of paint was published thirty years ago, emphasizing the the chemical changes of the curing processes of paints, role that temperature (T) and relative humidity (RH) play but they only partially capture the overall stability of a on brittleness of these flms [5]. In the present review our aim is to compile the innovative mechanical testing techniques that have been developed in the last two decades, *Correspondence: [email protected] together with the data derived from these experiments. It 1 Department of Materials Science and Engineering, Northwestern University, Evanston, USA is shown how this area of research has grown and begun Full list of author information is available at the end of the article

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to provide possibilities for contributing to improved con- can provide insights about the expected stifness of servation practices. paints since the additives function as rigid fllers within Paints are typically comprised of a pigment for col- the binding medium matrix. Te added fller is typically oration, a binding medium, and other additives that much stifer than the corresponding binding medium can adjust the optical properties and workability of the matrix, and thus contributes to an increased stifness of paint flm. All paint materials have several properties the overall paint [10, 11]. A challenge for researchers is that change over time, initially being a liquid-like flm accurately determining the pigment to binder ratio of that evolves into a solid-like paint flm. Tis transition fully cured historic paints, which provides relevant infor- from liquid- to solid-like behavior can occur two ways: mation for understanding the mechanical properties of through a drying process, where solvents added to the the paint and for understanding an artist’s technique by system evaporate out of the paint flm, or through cur- making paint reconstructions. Two approaches to deter- ing, where crosslinking and other chemical reactions mine pigment to binder ratio that have been previously occur within the pain flm to increase the stifness. Te used various imaging and spectroscopic techniques to timescale over which these drying and/or curing pro- analyze these cross sections. Te frst approach used a cesses occur can vary greatly, from a few hours (acrylics) sequence of µ X-ray difraction (µ XRD), particle induced to months (alkyds) to decades (oil-based paints) [6, 7]. X-ray emission (PIXE) and backscattering spectrometry As the paint transitions from liquid-like to solid-like, the (BS) to determine the light and heavy elements present stifness of the paint flm can typically increase several in a historic paint cross section, using the techniques orders of magnitude. For oil-based paints, the mechani- together to identify the pigment(s) and estimate of the cal properties can continue to change over the long peri- ratio of pigment to binder in the sample [12]. Alterna- ods of time that the curing process is ongoing, motivating tively, researchers have looked into the quantifcation active research into the mechanical properties of these of the ratio between pigment and binder on stable, liq- paints. Alkyd and acrylic paints, since they are modern uid-like paint systems using Fourier Transform Infrared paints that have been in use for less than 100 years, have Spectroscopy (FTIR) and Raman Spectroscopy [13]. Te also been a strong focus of research eforts in the last few use of these spectroscopic techniques becomes dif- decades. Other historic paints, such as distemper or egg cult on dried historic paints where the pigment, binder, tempera, are known to have a short drying phase and to or both are not stable over long periods of time, since form stif, brittle flms [6, 8]. Once tempera paints solid- the particular chemical peaks tracked in this study can ify, the mechanical properties remain fairly stable, so they change quite a bit over longer periods of time. Some have not been the focus of more recent research eforts. more recent work has used X-ray micro- or nano-tomog- Distemper paintings are rare to fnd in a pristine condi- raphy to determine the pigment to binder ratio for the tion, as many have been subjected to a varnish treatment, full volume of a paint sample [14]. which alters the original mechanical properties of the Some studies focused on the mechanical properties flm [9]. of paint have used a measurement of pigment content Te mechanical properties of a paint flm are afected based on volume, pigment volume concentration (PVC), by the paint composition, interactions between paint instead of pigment-to-binder ratio, which is a weight- layers for a composite painting structure, and the envi- based measurement [15–17]. Mathematical models have ronmental conditions (temperature, relative humidity, also been developed to describe the efects of pigment transportation, etc.) to which a paint is subjected. Each particle concentration and shape on the stifness of the of these contributions will be discussed in further detail sample and have been explored in some of the studies in the following sections, followed by an overview of the that will be highlighted in Section 2 [18, 19]. techniques discussed in the review and at what point during the lifetime of a painting they are relevant for use. Paintings as multi‑layer structures Te complexity of paint mechanical properties goes Pigment to binder ratio beyond the efect of a rigid fller on the stifness of the A simplifed defnition of a paint flm is a composite paint. Multiple layers of paint ranging from tens of material comprised of rigid pigment particles suspended microns to 1 mm in thickness are generally utilized in the in a more fexible binding medium. Te concentration of creation of a painting. Tese layers are placed on a sup- pigment or additive present tends to have a strong con- port, forming a multi-layer structure where the mechani- tribution to the mechanical properties of the paint. Te cal properties of a given paint layer can be afected not concentration can also vary widely depending on the only by the environmental fuctuations or conservation desired properties and particular combination of pig- treatments, but also by changes in the surrounding layers ments used in the paint. Tese relative concentrations (Fig. 1) [20]. dePolo et al. Herit Sci (2021) 9:68 Page 3 of 24

formation of new cracks from an impact, transportation, or a drastic change in environmental conditions can increase the chances for paint delamination and paint loss. Te development of craquelure in paint has been an area that has been discussed fairly extensively in a qualitative nature, but has experienced difculties in developing a standardized metric for characterizing the craquelure [21–24]. Some models have been discussed with regards to how ground layers may develop cracks as a result of environmental fuctuations [25]. Research on the craquelure formed using model colloi- dal systems, which can be tuned to have similar particle Fig. 1 The multi-layered structure of a traditional oil painting size and distribution as historic paint layers, has pro- showing the support, glue, ground, preparatory, paint/glaze, and vided some information about the distinctions between varnish layers. The complexity of the layered structure of the painting drying and aging cracks, as well as the insight that as provides an added level of difculty for researchers when studying paintings age, the degree of cracking increases [26]. Te the mechanical properties of paints and how they afect the overall research was also extended to discuss how craquelure stability of the painting. Painting information: Mary Cassatt, The Child’s Bath, 1893, Oil on canvas. The Art Institute of Chicago, Robert on paintings can relate to the mechanical properties of A. Waller Fund. Adapted from a fgure in [20]. the visible and underlying paint layers, as well as the implications of these craquelure in the routine conservation work performed on paintings [27]. Tese colloi- dal system studies provide some experimental data to Obtaining information about this complex multi-layer correlate with the qualitative descriptions of craquelure structure presents challenges to researchers, especially patterns, but it can still be difcult to understand the understanding how each layer contributes to an overall underlying mechanisms infuencing crack formation response of the object and how the material/chemical and propagation within the paint. composition infuences that response.Te range in size of Two distinct length scales need to be considered when single paint layers to entire paintings also provides a chal- discussing crack formation in a paint layer. Te frst lenge for determining which length scale (e.g., micron, of these is the macroscopic scale of the entire paint- millimeter, or meter) and therefore which technique is ing, which determines the stresses that the paint layer is most relevant for understanding the mechanical response exposed to. In fracture mechanics terms these stresses of an object. Any expansion or swelling of a given layer defne the driving force for continued growth of a crack, (such as the swelling of a canvas in response to increased typically expressed in terms of an energetic driving RH) or signifcance diferences in stifness between lay- force, G. Tis quantity has units of energy per unit area, ers (i.e. a much stifer ground layer below a paint layer) and quantifes the energy that is recovered by the over- can lead to small applied strains on the surrounding lay- all system as the crack grows. Crack growth occurs when ers, causing stresses that increase the potential for cracks G exceeds a critical value, Gc , that is characteristic of the to form and propagate through the painting. Paint layers paint. Growth of the crack alters the stress feld around can also be subject to issues of adhesion, which can lead the crack itself, afecting it’s own trajectory and the abil- to delamination or paint loss, which is also problematic. ity of neighboring cracks to grow. Tese interactions Understanding the mechanical properties of these layers determine the craquelure patterns that are observed in the mechanical response to neighboring layers or envi- actual paintings, and motivate the need to understand ronmental fuctuations are relevant when determining the system behavior at the length scale of the cracks the overall structural stability of a painting and will be themselves. Because of the complexities of the experi- discussed within this review. mental geometries in real paintings, numerical fnite element methods have an important role to play at both Craquelure of these length scales, although considerable insight can One of the main concerns for conservators is the for- also be obtained from appropriate analytic expressions. mation or propagation of new cracks within the paint- [27]. Te main point we want to make here is that it is ing due to fuctuations in environmental conditions or generally not sufcient to understand the properties of as a function of transporting a painting. Te craque- the paint in absence of an understanding of the relevant lure present in a painting is acknowledged as an inher- driving forces for crack propagation. Tese driving forces ent part of the drying process of the paint, but the originate from a combination of external forces imposed dePolo et al. Herit Sci (2021) 9:68 Page 4 of 24

Table 1 Summary of the techniques and defning characteristics (age of the paint, type of samples, the amount of strain applied to the sample, how invasive the technique is, and the relevant mechanical properties) for each technique discussed within this review. Technique Paint age Sample type Applied strain Sample size Invasiveness Relevant data

Tensile testing Dried/aged paint Model systems Large strain Bulk Invasive Elastic stifness, ultimate mechanical properties ( E, ef , σT) Dynamic mechani- Dried/aged paint Model systems Small strain Bulk Invasive Solid/liquid-like cal analysis behavior ( E∗, tanφ) Shear rheometry Fresh Paint Model systems Small strain Bulk Invasive Viscosity (η ) Quartz crystal Fresh & dried/aged Model systems Small strain Thin-flm Invasive Elastic stifness, swell- microbalance paint ing ( dρ, |G∗|ρ, φ) Nanoindentation Dried/aged paint Model systems Small strain Single point/small Minimally invasive Elastic stifness, hard- & Historic samples sample size ness ( Er , H) Laser shearography Dried/aged paint Model systems Small strain Area of painting Non-invasive Strain maps & Historic samples Finite element Fresh & dried/aged Model systems & Simulated large Any sample size – Predictive mechanical Analysis+ paint historic samples and/or small responses strain Vibration Studies Dried/aged paint Model systems Small strain Area of painting Minimally invasive Damage risk Single-sided nuclear Dried/aged paint Model systems & _ Single point/small Non-invasive Comparative rtifness magnetic reso- historic samples sample size nance

∗ Defnitions for mechanical properties in relevant data: E: elastic modulus, ef : failure strain, σT : ultimate tensile strength, E : complex elastic modulus, tanφ : loss tangent, ∗ + η : viscosity, dρ : areal density, |G |ρ : magnitude of the complex shear modulus multiplied by the density, Er : reduced elastic modulus, H: hardness. Indicates that the technique is a numerical method

on the object and internal forces generated by the vary- results, there will frst be a brief overview of the mechani- ing response of the diferent layers to environmental cal properties investigated with each technique. conditions. Tensile resting Static mechanics overview Relevant techniques In typical statics measurements of paint systems, a force Te techniques covered within this paper, along with (stress, σ ) is applied to a system to cause a displacement applicability to either model systems or historic sam- (strain, e). Te stresses can be applied in either a normal ples and when they can be used during the lifetime of a or a shear direction to the sample. For paint materials, paint, are shown Table 1. Deciding when to use a given the stresses are commonly applied through the geom- technique depends on the desired mechanical prop- etries shown in Fig. 2. Tese sample geometries take into erty and the goal of the research program, whether it’s consideration some of the structural aspects of the mate- to address questions from art history (i.e., how an artist rial, such as whether it is a membrane system (e.g., an achieved a specifc painting efect), to monitor or assess individual paint layer or painting on a canvas), is attached the condition of historic objects, or to understand the to a rigid support (e.g, painting on a wood panel), or is fundamental responses of mockup paint samples that still in a liquid form (e.g., reproductions of historic reci- can be deformed and subjected to damage more readily pes). Uniaxial tensile testing (Fig. 2a) applies force on than a historic painting. Since there can be some chal- opposing ends of a paint flm, providing material proper- lenges in comparing the results obtained from model ties that will be described shortly. Biaxial tensile testing systems with historic samples (typically due to age and (Fig. 2b) applies tensile forces in two directions, which composition diferences), these techniques have often can be useful when looking at the composite structure of been paired with other analytical techniques to study the a paint layer on a support (i.e. a linen canvas). However, chemical response of a paint and provide a more direct the composite nature of these systems can make it dif- comparison. cult to accurately defne the individual material contribu- For each of the techniques in Table 1, we will discuss tions to the overall behavior. Four point bending (Fig. 2c) the advancements and signifcant results as well as future applies forces on either side of a sample in such a way as directions for their optimization and use to study paints. to cause both compressive and tensile forces at the center To help explain the types of data and the signifcance of of the sample. If there is an adhesive or fller material dePolo et al. Herit Sci (2021) 9:68 Page 5 of 24

c Fig. 3 Typical generic temperature behavior at diferent Fig. 2 Schematics of a uniaxial tensile, b biaxial tensile, and c 4-point temperatures shown with a qualitative load (stress) vs. strain plot. As bending experimental geometries. The grey regions in a indicate the temperature decreases from T4 to T1 , the sample exhibits more where clamps are attached to the sample. The arrows indicate the brittle behavior. This trend is also equivalent to increasing the strain direction of applied force in each experimental geometry rate (or decreasing the measurement time) used for the tensile test

being used on a wooden object, these tests are useful for determining the potential failure conditions of the conservation materials. Te stress-strain behavior for a material can exhibit a range of phenomena, depending on the temperature and timescale of the measurement. In polymeric materials there is a general equivalence between time and temperature, with similar behavior obtained either by decreasing the temperature or increasing the time scale of the measurement. For artist paints, the properties also evolve with time, adding another dimension of complexity. Generic results obtained from a uniaxial tensile test are shown in Fig. 3. While not all of these behaviors are necessarily observed in the same material, the following general Fig. 4 Sample stress (MPa) vs. strain plot for an 8-year-old lead white paint flm in acid refned linseed oil. The relevant mechanical regimes can often be identifed, based on 4 diferent tem- properties that can be determined using these curves are also perature regimes (T 1 , T2 , T3 and T4). displayed on the graph. Data replotted from [28]

• T1: Brittle behavior of a glassy material. Tis is generally observed at sufciently low temperatures. temperature, Tg , which is the point when a polymer tran- • T2: Ductile behavior followed by localized thinning of the sample and failure. sitions from a rubbery, more fexible response to a glassy, more brittle response. A more quantitative example of • T3: Ductile behavior with substantial localized deformation after yield. a tensile test is the stress-strain curve for the 8-year-old lead white sample shown in Fig. 4. Tese curves pro- • T4: uniform deformation of a very soft, rubber material. vide several results that help the researcher understand the overall mechanical behavior of the paints. Te elas- E Note that Fig. 3 is highly qualitative and does not accu- tic modulus ( ) (a.k.a. Young’s modulus) can be deter- rately capture the detailed changes that are observed. mined from the from the slope of the curve at low strains As one follows the blue arrow from T4 to T1 , the poly- and is shown by the line extended from the stress strain mer sample would pass through the glass transition curve. When the paint flm begins to yield, the slope of dePolo et al. Herit Sci (2021) 9:68 Page 6 of 24

the stress strain curve decreases. Te stress at which this As discussed above, the type of pigment used will impact yield point occurs is known as the yield stress ( σY ). Not the pigment to binder ratio of a given sample. Inorganic all paint samples exhibit a yield stress either due to the pigments also tend to be much stifer than the binding softness of the material or to the viscoelastic behavior of media, also leading to a signifcant increase in the stif- the flm. For cases where a yield stress is not present in ness of the sample. Many of the studies focused on the the data, a secant modulus ( Es ) can be calculated using efects of temperature [18, 29, 30, 36, 37, 41, 43, 46, 50, the following equation: 54, 57] and relative humidity [15, 29, 30, 34, 36, 37, 41, σ 43, 44, 46, 52, 57, 59] on the stifness of the sample. Tere E = s e (1) is a general trend across all three binding media classes of increasing stifness as the temperature of a paint where common values of e are less than or equal to 0.05. decreases, shown in Fig. 6, which would indicate that the Te end of a tensile test usually occurs when there is a increase in stifness is controlled more by the properties failure such as a fracture in the paint sample. Te stress of the binding medium than the particular pigment used. ◦ and strain values at this point, the ultimate tensile For all these general classes of binding media, −10 C strength ( σT ) and strain to fracture ( ef ) respectively, are is below their Tg , which leads to a glassier, more brittle useful material properties for characterizing the limits of response from the samples. When the RH is increased for a sample. a paint system, researchers observed a general softening Tese static tensile measurements require larger sam- phenomenon occur since water can act as a plasticizer in ples, making them impractical for measurement of his- most paint flms, leading to a decrease in the stifness that toric paints and requiring the use of either model systems can range from 30-90%.2 [15, 29, 30, 34, 36, 37, 41, 43, or sacrifcial collection samples. Te sample geometry for 44, 46, 52, 57, 59]. When the RH is decreased, the paints tensile tests also requires solid samples, which means the become stifer as less ambient water is present, showing paints have to dry for at least 1 week (acrylic) to 1 month anywhere from 40-300% increase in the stifness. (oil) before measurements can be taken. Te instruments Another common variable for the material response of used for these measurements can be modifed to include paint materials is solvent exposure to assess the efects environmental chambers that control T and RH, some of of solvents commonly used for cleaning paintings [18, the more important practical parameters for understand- 28, 36, 37, 42, 48, 49, 62]. Te most common trend after ing the material properties of paints. exposure to volatile solvents was that the paint flms would become embrittled, exhibiting stifer, more brit- Uniaxial extension tle responses (anywhere from 100-900% increase in the Uniaxial tensile testing of paint samples has been one of stifness) due to the leaching and volatilization of low the most commonly used techniques for investigating molecular weight components. Yet, exposure to non- the mechanical properties of paints in cultural heritage volatile solvents resulted in increased plasticity of the over the last few decades. A summary of the references paint flms (up to a 74% decrease in the stifness) [28]. that have used tensile testing to measure the mechani- Results from uniaxial tensile tests are also dependent on cal properties of paint materials is shown in Table 2. A the strain rate of the test, or how quickly the sample is summary of the data from these references are available deformed. As the strain rate is increased, the paint flm as supplementary information in PDF (Additional fle 1) has less time to respond to the deformation taking place, and Excel (Additional fle 2) fles1. leading to a stifer, glassier response. Hagan et al. varied From the references in Table 2, Fig. 5 provides an the strain rate during their research on acrylic and oil- overview of the range of E from the samples tested as a based paint systems to apply time temperature super- function of age (associated with the curing time) of the position (explained more fully in Sect. 3) to their results samples, which spans four orders of magnitude. While and observe the material response over a wider range of this graph does not show a strong trend in the data, it testing strain rates [18, 19, 46, 50, 54]. Te studies also does highlight one main takeaway about analyzing these considered the efects of PVC as well as the shape of the data: it is difcult to analyze trends in the data using pigment particles on the overall response of the pig- only a single variable from these uniaxial tensile tests. ment/binding medium composite sample using mathematical models focused on fller efects in a composite,

1 To help understand and look at overarching trends in the mechanical properties of paints studied using uniaxial testing, we compiled a summary of the 2 For all of the ranges presented for changes in stifness as a result of a change reported mechanical property data from studies focusing on oil, alkyd, and in a testing parameter, the range has been estimated across all binding media acrylic paints as well as some paint consolidants and grounds. See Additional and sample compositions in an attempt to show the maximum impact a par- fles 1 and 2 in the Supplementary Information. ticular parameter can have on the stifness. dePolo et al. Herit Sci (2021) 9:68 Page 7 of 24

Table 2 Summary table of the types of paints and testing parameters varied in the studies that used uniaxial tensile testing to investigate mechanical properties Reference Oil Alkyd Acrylic Filler, Temp. RH Solv. exp. Strain rate Sample comp. Aging ground, support

Mecklenburg, 1991 [29] Erlebacher, 1992 [30] Mecklenburg, 1994 [31] Whitmore, 1995 [32] Tumosa, 1999 [28] Mecklenburg, 2001 [33] Carr, 2003 [34] Mirone, 2004 [35] Meckelburg, 2004 [36] Hagan, 2004 [37] Erhardt, 2005[38] Tumosa, 2005 [39] Young, 2007 [40] Hagan, 2007 [15] Young, 2008 [41] Fuesers, 2008 [42] Ormsby, 2008 [43] Fuster-Lopez, 2008 [44] Carlyle, 2008 [45] Hagan, 2009 [46] Hagan, 2010 [18] Hagan, 2011 [19] Tumosa, 2013 [47] Mecklenburg, 2013 [48] Domenech-Carbo, 2013 [49] Hagan, 2015 [50] Fuster-López, 2016 [51] Krzemien, 2016 [52] Penava, 2016 [53] Hagan, 2017 [54] Fuster-López, 2017 [55] Doutre, 2017 [56] Roche, 2018 [57] Fuster-López, 2019 [58] Bridarolli, 2020 [59]

Temp. temperature, RH relative humidity, Solv. Exp. Solvent exposure, Sample comp. Sample composition. Sample composition includes changes in binding medium, pigment type and composition, and sample thickness. Aging refers to both natural and accelerated aging of samples

highlighting the importance of understanding the PVC of of time regardless of pigment, shown in Fig. 7, whereas a paint sample [19]. Tere is a challenge of the composi- the oil and acrylic paint classes do not show any trends tion of the binding medium and PVC not being readily as a function of age due to convolution from other testing available for commercial artists’ paints, but with enough parameters. time and access to analytical tools they can be deter- One of the main drawbacks to using model systems mined. Not all the responses are explained through pig- for paints is their relatively young age; they are typically ment type or fller concentration, though, because the 30 years old at their oldest. While this age range is more alkyd paints continue to increase in stifness as a function relevant for the newer alkyd or acrylic paint classes, it dePolo et al. Herit Sci (2021) 9:68 Page 8 of 24

Fig. 7 Plot showing the elastic modulus (MPa) vs age (years) for the alkyd paints. The wide spread in the value of the elastic modulus for Hansa Yellow is due to solvent exposure. The spread in the data for Fig. 5 Plot showing elastic modulus (MPa) vs aging time (years) from Titanium White is due to temperature variations. Data compiled in uniaxial tensile tests of oil, alkyd, and acrylic paints. The graph does this graph are from [30, 35, 42, 48, 54, 58] not account for testing variables such as T, RH, solvent exposure, or pigment/particle type used in the paint medium, contributing for the wide spread of the modulus data. Data compiled in this graph are at constant strains. Over longer times, the stress begins from [15, 18, 19, 28, 30, 33–37, 39, 41–43, 46–51, 54, 55, 58, 60, 61] to follow a linear trend when plotted against the natural log of time, which allows researchers to create theoretical stress-strain curves that can be more predictive [36, 38]. Tis analysis method provides a good frst approxi- mation for some brittle paints, but it has not been applied to softer paint systems or to paint systems where the stifness remains constant, but the fexibility of the paint flm decreases. Some of the studies shown in Table 2 focus on other materials found in the multi-layered structure of a painting than paint. Researchers have studied the response of grounds to RH to determine ideal storage conditions and the efects of drying shrinkage on the formation of cracks within the ground [52, 56]. Te stifness of canvas as a function of the orientation of the weave of the sample has also been explored using uniaxial extension, demonstrating that the stifness is strongly dependent on the orien- Fig. 6 Plot showing the elastic modulus (MPa) vs temperature (◦ C ) tation that the load is applied to the canvas [53]. Samples from uniaxial tensile tests of oil, alkyd, and acrylic paints. The graph comprised of multiple layers (i.e., paint-paint or canvas- does not account for other testing variables such as age, RH, solvent paint) can provide some insights into the response of the exposure, or pigment/particle type used in the paint medium. Data composite to changes in temperature or relative humid- compiled in this graph are from [15, 18, 19, 28, 30, 33–37, 39, 41–43, 46–51, 54, 55, 58, 60, 61] ity, but it becomes difcult to determine which aspects of the composite structure are contributing to those changes [40, 57, 59, 64]. Uniaxial tensile testing provides researchers with the becomes difcult to draw conclusions about the expected ability to investigate the efects of T, RH, solvent expo- material responses of oil paints that are 50 years or older. sure, and PVC on the mechanical properties of paint, While accelerated aging may be a way to address this but these investigations can only be performed on model issue, previous research has shown that without careful systems due to the relatively large amounts of sample tailoring of the study, accelerated aging of the paint flm required for measurements. enables diferent chemical reaction pathways than natural aging for oil paints, which can make comparisons dif- Biaxial extension fcult [63]. Some theoretical extrapolations can be made When we consider the composite nature of paintings, about the response by observing the changes in stress those mounted on stretchers experience stresses to the dePolo et al. Herit Sci (2021) 9:68 Page 9 of 24

paint layers from two directions, which can be difcult stifness measurements that are not as directly compara- to capture using only the uniaxial extension test. Te way ble to the tensile data shown earlier. Tese more rigid paint that paintings are mounted to stretchers is very similar composite systems can also be more thoroughly studied to how they would be studied using biaxial extension through computational simulation, which will be discussed (Fig. 2b), making this technique a relevant method for more in Sect. 7.2. Tis geometry had targeted benefts of studying these model systems. To address the complexity exploring the response of paints, adhesives, and fllers on of observing stresses in two directions, Young developed rigid substrates, but is not as useful beyond this targeted a biaxial tensile testing system that would be compatible application. with painting mockups [65]. An electronic speckle pattern interferometer was incorporated into the instrumen- Dynamic mechanical analysis tation to help determine the amount of strain occurring Dynamic mechanical analysis (DMA) is a technique ide- in each direction during the tensile tests [66]. Te biaxial ally suited for studying viscoelastic samples such as setup has been used to assess the behavior and interac- paints. Most DMA studies of artists’ paints have used a tion of glue, oil, and four paste grounds when they are similar sample geometry and force application as uni- applied to canvases [45]. Te glue and oil grounds dem- axial tensile testing (see Fig. 2). Unlike tensile testing, onstrated stronger changes as a function of RH than the which applies a fxed stress or strain rate, DMA samples four paste grounds, but the four paste grounds were not undergo oscillatory loading conditions to look at the fre- as stif as the other two grounds [45]. Using the biaxial quency dependent response common to polymer-based geometry to investigate canvases and paint layers allows systems, including artists’ paints. Quantifying this behavior researchers to investigate how the mechanical response is important when planning storage, travel, or exhibition of a canvas-paint composite sample will be afected by conditions and conservation treatments for a work of art. environmental changes since the response of the com- In DMA experiments, the stress is applied as a function of posite system will be diferent dependent on the canvas time ( σ(t) ), which leads to a time dependent expression for weave direction. Due to the isotropic nature of paint the elastic modulus, E(t), which for an oscillatory stress and ∗ samples, when using this geometry both E and Poisson’s strain can also be notated as a complex function, E : ratio (ν) ,the lateral strain that occurs perpendicular to E∗ = E′ + iE′′ = E∗ eiφ, the applied stress, can be determined. One important (2) aspect to keep in mind is that the corners of the sample ′ where E is the storage modulus that describes the solid- will act as stress concentrators when placed under ten- ′′ like behavior of the sample, E is the loss modulus that sion (see Sect. 7.2), which can cause issues during data ∗ describes the liquid-like behavior, |E | is the magnitude analysis. A workaround can be to remove the corners of of the complex elastic modulus, and φ is the viscoelas- the model samples or to use computational simulations tic phase angle, which describes the phase diference to study the impact of the corners of a sample more fully. between the oscillatory stress and strain. Te two right From a materials characterization standpoint biaxial sides of Equation 2 can be related through these two testing provides information that is comparable to what equations: is obtained from uniaxial testing. It’s primary use as described above is in studying the mechanical response E′ = E∗ cos φ (3) of the overall composite painting structure under realistic loading conditions. E′′ = E∗ sin φ. (4) Bending geometries We can combine Eqs. 3 and 4 to get the following expres- As was mentioned earlier, a bending geometry allows one sion for tan φ (also known as tanδ in literature), com- to investigate both compressive and tensile forces applied monly referred to simply as the loss tangent: to a material, especially if those are potential forces that E′′ need to be accounted for in a rigid art object. Young et al. tan . φ = ′ (5) performed a study of adhesives and fllers that are typi- E cally used in the conservation of panel paintings, which For samples that are thermorheologically simple, or have can have a large range of stresses applied as a function of the relaxation times present in the sample that are all environmental shifts (typically T or RH) [67]. With the afected the same way by temperature, frequency sweep bending geometry, it was easier to determine whether experiments can be performed at various temperatures the failure of the joints studied was due to the adhesive ∗ and used to generate a master curve of both E and tanφ or to the wooden support [67]. Te load curves from this using time-temperature superposition [68]. From these research were compressive rather than tensile, generating dePolo et al. Herit Sci (2021) 9:68 Page 10 of 24

ab c ϕ

Fig. 8 Plots showing master curves for the a complex elastic modulus (| E∗| ) versus frequency, b tan φ versus temperature, and c the shift factors ( aT ) versus temperature obtained from a DMA experiment on a commercial Galkyd alkyd binding medium that has been aged for 159 days. The complex elastic modulus shows the frequency dependent behavior of the Galkyd binding medium, tanφ provides an estimate of the glass transition temperature for this system, and the shift factors can provide insights into the overall polymer behavior of the Galkyd system. Data reproduced from [69]

master curves of the complex elastic modulus versus Using a shear stress geometry and temperature range ◦ ′ shifted frequency, the glassy and rubbery regimes of a from 5 − 100 C , an increase of G (loss shear modulus, ′ sample are visible. Te peak of a tanφ versus tempera- defned in a similar way to the E ) and signifcant reduc- ture plot is a measure of the glass transition temperature, tion in tan(δ) for the burnt sienna samples indicated Tg , where the sample transitions from rubbery behavior leaching and embrittlement after solvent exposure; the above the Tg to a more brittle, glassy response below Tg . lead white samples showed minimal change in response Due to the nature of polymer relaxation times, the Tg is after solvent exposure [70]. Samples of the same pig- also partially dependent on the frequency of the meas- ments aged 15 years were explored over a range of rela- urement. In a typical amorphous polymer, increasing tive humidities (54–94%) and compared to composite the frequency of measurement by an order of magnitude samples of canvas, primer, and a white oil paint layer ◦ increases Tg by about 3 C, which is important to remem- from a rear primed painting, which demonstrated a sof- ber when comparing data between diferent techniques tening behavior with an increase in relative humidity that use a diferent base frequency, such as will be dis- [71]. Foster et al. modifed a DMA system to work with cussed in Sect. 5. Shift factors ( aT ) are used to align the a controlled RH chamber in order to study how the RH ∗ E and tanφ to the values for a given reference tempera- and curing process of polyester/melamine paint systems ture by shifting the data horizontally along the frequency afect the glass transition temperature [72]. Te analysis ′ axis, using the underlying assumption for time-temper- performed on E and tan φ master curves is a good exam- ature-superposition to apply these shift factors. Figure 8 ple and illustrates just how much information is obtained ∗ provides example master curves of |E | as a function of through these experiments. frequency and of tanφ and aT as a function of tempera- Ormsby et al. focused on acrylic paints, specifcally ture for an alkyd binding medium commercially made by investigating the efects of solvent exposure on the chem- Galkyd and aged for 159 days before testing. In Fig. 8a, ical, optical, and physical properties of the samples [73]. ∗ |E | spans over 15 decades of frequency, showing the rub- Comparisons between acrylic brands and exposure meth- bery-like behavior on the lower left of the graph and the ods of swabbing or immersion were considered, showing glassy behavior on the upper right. Te tanφ curve shows a strong efect on the dimensional extension of samples ◦ a peak around 26 C , which would be a rough estimate after being immersed in the solvents, especially more of the Tg for this alkyd binding medium. Mathematical polar solvents. Te Tg of the samples would increase with models are often used to describe the shift factors and extended immersed solvent exposure, showing an oppo- predict the response of the polymers [68], but are not dis- site trend than previous data on oil paints, most likely cussed in this review. due to embrittlement of the acrylic paints as a result of Hedley et al. presented some of the earliest foun- the solvent exposure. Te samples that were swabbed dational work using DMA on artists’ paints to assess experienced signifcantly smaller changes in the DMA changes in mechanical responses of lead white (“medium data, leading to the conclusion that using swabs for sol- lean”) and burnt sienna (“medium rich”) samples after vent exposure will reduce the overall changes to the bulk exposure to solvents typically used for cleaning [70]. properties of the paint compared to full immersion of the dePolo et al. Herit Sci (2021) 9:68 Page 11 of 24

paint flm, even if some surfactants are lost at the surface using DMA and nanoindentation indicated that full of the flm [73]. Titanium white acrylic paints exposed to immersion had the higher chance of embrittling the paint temperature and RH sweeps showed typical responses flms than the sponge cleaning, highlighting the impor- corresponding to an embrittlement/decrease in Tg with a tance of choosing the appropriate method and solvent decrease in RH, indicating a strong relationship between when preparing to clean a specifc paint [78]. A study that the water content of the paint and the mechanical prop- focused on the material response of composite sample ′ erties [74]. Some samples that were thermally aged exhib- was Bridarolli et al., which assessed the change in E of ited smaller tan(δ) , peaks, indicating stifer flms than the consolidants that are commonly used as treatments on naturally aged flms and potentially better coalescence of degraded canvases as a function of relative humidity to the paint flms. Te onset of a brittle response from alkyd determine their efectiveness and viability for use in con- and acrylic based grounds was investigated using the Tg servation treatments [59]. from DMA to help confrm the ductile to brittle transi- Most research on paint samples using DMA have ◦ ◦ tion as temperatures were dropped from 20 C to −10 C emphasized the importance of Tg in assessing the over- [41]. Phenix performed an extensive survey of Tg values all response of the paint as well as providing a metric for of oil paints and how they were afected by the type of understanding the type of response (i.e. more glassy/brit- pigment and the age of the paint sample (1–16 years), tle or rubbery/ductile) to expect from paint samples. Tg fnding that the range of Tg s varied widely with sample of a paint is also an important parameter to know when composition [75]. Most samples in the study demon- adding an infll to a painting to ensure there are not strated an increase in Tg with age, indicating an embrit- added stresses created within the paint layers through a tlement efect that could pose potential long term issues mismatch of mechanical properties. Due to the amount for paintings stored in a museum environment. and geometry of the sample necessary to perform these Te application of time-temperature superposition to measurements, model systems are typically used, intro- DMA data collected over a range of temperatures allows ducing challenges when drawing conclusions about researchers to access a much wider range of measure- the behavior of “young” paint samples (1–15 years) and ment frequencies than typically accessed with other using them to predict the behavior of older paint sam- methods. Sturdy et al. used DMA to understand the ples (100+ years).When time-temperature superposi- material response of a commercially produced alkyd tion is used for a DMA experiment, one can obtain more based binding medium (Galkyd) as a function of curing information about a single paint flm than from a typical time and fller content of zinc oxide, providing a sur- tensile testing experiment. Tere are some nuances to be vey of the efects of fller content and the compatibility aware of when determining the Tg of the paint sample, between DMA, the quartz crystal microbalance (QCM), but the papers in this section provide guidance towards and nanoindentation for studying paint materials [17, understanding those nuances. 69]. Tese studies also compared the material responses measured using DMA and the QCM, demonstrating that Shear rheometry both techniques are able to capture the glassy material Shear rheometry can be viewed as a version of DMA that response well. Verifying the general response regime of is used in a shear geometry and well suited for samples a viscoelastic system using the Tg is also fairly common; with a liquid character. It has been used to study historic a linseed oil with zinc/lead white ionomer system deter- paint formulations, varnish, and glaze recipes, with an mined the Tg of samples with DMA to inform difusion emphasis on understanding on how the recipe infuenced models for solvent exposure of the ionomer systems, the overall texture and visual presentation of paintings which are used to study the mechanisms controlling the today. Tese experiments are typically performed using formation of metal carboxylates, or metal soaps, within a either the parallel plate geometry, shown in Fig. 9a, or paint flm [76]. More recently, the mechanical properties the cone and plate geometry, shown in Fig. 9b. Samples of oil paints aged 6 years with several additives including studied using these geometries experience shear forces, fatty acids (both with and without a metal base), linseed resulting in the measurement of a complex shear mod- ∗ ∗ oil, and alumina hydrate were observed and quantifed ulus, G , analogous to the complex elastic modulus, E using the DMA to studying commercial Winsor & New- defned in Sect. 3. For isotropic materials, which have the ton oil paints, commonly used by contemporary artists same bulk properties in all directions, the shear modulus [77]. With more linseed oil, the Tg of paints decreased, can be related to elastic modulus through the following while alumina hydrate increased the Tg ; the added fatty expression that also involves Poisson’s ratio, ν, T acids did not have a consistent efect on the g [77]. E = 2G(1 + ν). Quantifcation of the efects of solvent exposure (immer- (6) sion and sponge) for a water-sensitive yellow ochre paint dePolo et al. Herit Sci (2021) 9:68 Page 12 of 24

Fig. 10 Schematic of a quartz crystal used on the QCM. The grey is the AT-cut quartz crystal, which has a resonant frequency of 5 MHz. The gold layers are the electrodes which conduct the oscillating a b voltage, shown in the circle at the lower right of the diagram. The Fig. 9 Schematic of the cone and plate geometry for shear purple layer is a sample that has been deposited onto the crystal and rheometry. The blue portion is the sample, the purple arm is the base typically has a thickness less than 10 µm plate, and the orange portion is the top plate, which is either a fat plate or a cone. The angle θ indicates the angle of the cone, which is typically between 0.25 and 4◦ . The arrows indicate the direction of force applied to the sample. The fgure is modifed from an image stress and pigment concentration [16]. Rheology has also licensed under the Creative Commons Attribution-Share Alike 3.0 been used to characterize plant-oil based inks (similar Unported recipes to oil-based paints) to optimize their properties as well as adhesive combinations to maximize their efectiveness as consolidant materials [87–89]. Tixo- For liquids and relatively soft polymers at temperatures tropic behavior and the efects of pigment concentra- above their glass transition temperature, ν ≈ 0.5 and tions on the fow of the paint through rheology provides E ≈ 3G . In an oscillatory experiment where the complex both important conservation data explaining causes of ∗ ∗ ∗ ′ ′ shear modulus, G , is obtained, E ≈ 3G , E ≈ 3G and sagging, drippings, or faking of paintings as well as art ′′ ′′ ′ ′′ E ≈ 3G , where G and G are the storage and loss historical insights into how historical recipes can be cor- = ′ shear moduli, defned as described in Sect. 3, but with G , related to artist technique. ′′ ∗ ′ ′′ ∗ G and G replacing E , E and E . Quartz crystal microbalance Originally developed for use in industry, shear rheometry has been used for about 70 years to understand the Originally used as a technique for studying small mass mechanical properties of paints. Due to the longstand- changes, the QCM has been developed to study the vis- ing use of the technique, best practices for measuring coelastic properties of biological and polymer-based sys- the mechanical properties of historic recipes have been tems [90]. Many of the advancements in determining the described in some detail [79, 80]. One of the earliest viscoelastic properties over the past decade have been reported discussions about the composition of the paint developed by the Johannsmann group [91, 92]. Te QCM afecting the rheological behavior of the paint examined measures the impedance spectra of a quartz crystal when the state of white impastos used by Rembrandt, conclud- an oscillating voltage is applied to electrodes on either ing that the proportions of pigment and driers resulted surface of the crystal as shown in Fig. 10. When a sample in a thixotropic behavior of the paint, with the viscosity flm is deposited on one surface of the crystal, the reso- decreasing with increasing strain rate. Not only did such nant frequencies are shifted, allowing one to determine insights provide a greater understanding of Rembrandt’s both the mass and mechanical properties of the sample. paint structures, it was shown that these data could be Resonant frequencies of quartz crystals are typically used to relate the artist’s technique to the measured yield in the megahertz (MHz) regime, which means the QCM stress of the paint [81]. Further surveys of the efects of probes material responses in the “glassy regime” for most adding resins, solvents, and pigments on the viscosity polymer and paint systems. Sample preparation is impor- and resulting yield stress of paints, glazes, and varnishes tant because the thickness of the sample plays a critical has broadened the knowledge base for thinking about role in the ability to obtain meaningful data. A broader how these historic recipes infuenced the response and discussion about the range of material properties probed characteristic appearance that we associate with these by the QCM and the required thicknesses to detect those materials [82–84]. More recent research has focused properties has been previously published by the Shull on studying the rheological properties of gumtion, an group [93, 94]. In brief, polymer samples prepared to experimental paint material that added resin to the oils target viscoelastic properties can range from hundreds µm to decrease the drying time of the paint, and the efects of nanometers to 10 in thickness. Such small sam- of fllers such as calcite on the workability of lead white ple sizes can efectively be treated as a skin layer since paints [85, 86]. For instance, the amount of pigment Van there is minimal difusion required before a sample is Gogh needed to create the impasto efects in his paint- equilibrated with its environment. Having an exposed ings was connected to the relationship between the yield surface of the sample also facilitates measurements of dePolo et al. Herit Sci (2021) 9:68 Page 13 of 24

a b c

Fig. 11 Representative QCM data during the drying and curing of a commercial Galkyd alkyd binding medium sample showing a normalized ∗ mass, b the complex shear modulus of the third harmonic multiplied by density (| G3 |ρ ), and c) the viscoelastic phase angle ( φ ) as a function of time. The three regions shown on the plot are representative of the I) solvent evaporation, II) oxygen uptake, and III) long term curing behavior of the alkyd samples. Data reproduced from [69]

temperature, humidity, and solvated atmospheres, and to incorporate solvent exposure for understanding the the use of non-invasive molecular characterization tech- swelling behavior of paints, providing the capability to niques (e.g., FTIR, Raman). For paint model systems, study the efects of plasticization on the overall stabil- data collection can begin within a few minutes of casting, ity of a paint sample. Samples can also be exposed to UV rather than having to wait for months before the sample light to understand the efects on the mechanical proper- becomes touch dry, allowing the study of paint model ties of paints with photosensitive pigments, and the tem- systems through the entire curing process. perature-dependent response of the the sample can also Te curing behavior of a commercial alkyd binding be probed [93]. Tese temperature-dependent measure- medium was measured over the course of three years, ments are a particular focus of ongoing research because as well as the efects of temperature and the fller efects they probe molecular relaxations in the material that are when zinc oxide was added [17, 69, 95]. Analyzing both likely coupled to the ductile/brittle transition in the mate- the mass and the mechanical properties of a sample rial, complementing information obtained from more can provide a clearer picture about how the material traditional measurements of the glass transition tempera- responses of paint flms change as a function of their ture. While these samples can be exposed to a wide range environment as demonstrated in Fig. 11. From these data, of environmental conditions, it is dependent on good Sturdy et al. determined three distinct regions during the contact between the sample surface and the quartz crys- curing process of the alkyd paint system: solvent evapo- tal, making it difcult to use the QCM to study historic ration (region I) taking place in the frst few hours of data paint samples directly. Tese studies provide initial steps collection, short term curing where oxygen uptake hap- for being able to understand more fully the initial curing pens (region II) during the frst day, and long term curing stages of binding media, how they afect the overall paint over the following three years (region III). It is possi- material response, and begin to investigate more targeted ble to see the impact of these mass fuctuations on the questions related to curing and degradation processes in mechanical properties, with the short term curing region paints. showing the steepest rise in stifness (shown by the sharp ∗ increase in |G3 |ρ (product of the magnitude of the com- Nanoindentation plex shear modulus at 15 MHz and the flm density) and Technique background decrease in φ (viscoelastic phase angle at 15 MHz) of All the techniques described up to this point in the Fig. 11b and c). Even after three years, the complex shear review require the use of model systems in order to modulus of the alkyd samples continued to increase, sup- obtain the mechanical properties of paints. Tese tech- porting the understanding that paint systems continue niques provide useful information and can allow a to experience chemical changes years after they are cast wider range of experiments to be performed (especially onto the quartz crystal. Te QCM is versatile enough those that are more destructive in nature), but there dePolo et al. Herit Sci (2021) 9:68 Page 14 of 24

Fig. 12 Geometry of a a Berkovich tip and b a spherical tip commonly used in indentation experiments on paint materials. The angle, α , is 65.35◦ for a standard Berkovich tip. The fgure is based on images available in the public domain through Wikimedia Commons

can be difculties relating these results back to actual historic paints. One technique well suited to bridge the Fig. 13 Typical load-displacement curve for indentation of the gap between model systems and historic paint samples polyester resin used to embed the paint samples, labeled to illustrate is nanoindentation. Te small sample size required to the values of Pmax , δmax and S obtain data about the modulus, stifness, and hardness of a paint sample is well suited for use on cross sections from paintings. Typically, the indentations are ≈ 2-5 μm wide, making them nearly invisible to the naked following expression for S is used to extract the elastic eye. Oliver and Pharr have outlined the methodol- properties: ogy for contact mechanics of elastic-plastic materials, 2 . S = amaxEr (7) which has been widely incorporated into nanoindentation analysis [96]. Oyen and Cook summarized how Here Er is the reduced modulus obtained from plane contact mechanics analysis can be expanded to include strain geometries like the indentation experiments of a wider range of tip shapes, two of which are shown in interest here. It involves the following combination of the Fig. 12, and accommodate material responses that are elastic modulus and Poisson’s ratio: viscous, expanding contact mechanics to use on biolog- E E = . ical and polymeric based materials [97]. r (1 − ν2) (8) Material properties are obtained from load-displacement curves, such as the one shown in Fig. 13. Note Te quantity amax is the contact radius radius established that a displacement of zero is defned as the point for δ = δmax , which for a parabolic indenter is given by where initial contact is made between the indenter the following expression: and the material. Because most paint materials have a time-dependent response, the detailed protocol con- amax = δmaxR, (9) trol for controlling the displacement will afect the measurement. Te load-displacement curve shown in where R is the radius of curvature of the indenter at its Fig. 13 shows an experimental protocol where the dis- tip. placement increased at a constant rate from zero to a For non-parabolic indenters and those for situations maximum value of δmax during a loading time of ≈1s. where material yielding needs to be accounted for (as Te displacement is then fxed at this maximum value with the Berkovich indenters shown in Fig. 12a, a gen- for ≈ 1 minute, and is then decreased at the same rate eralization of Eqs. 7 and 9 needs to be utilized. Te as that used for the loading portion of the experiment. most commonly used procedure was developed by Oli- It is also common to have the holding condition be ver and Pharr [96], and involves the following: based on a fxed load. Te elastic modulus is obtained a a from the unloading stifness, S, defned as the slope of 1 Replacement of max with an efective radius, eﬀ . the initial portion of the unloading curve (see Fig. 13). Te area of a circle with this radius is the same as the For a parabolic indenter where the contact between actual maximum contact area between the indenter the indenter and the material has a radius of a, the and the material: dePolo et al. Herit Sci (2021) 9:68 Page 15 of 24

π 2 = . aeﬀ Amax (10) [98]. Comparisons between reconstructed and historic paint samples of white pigments used by Van Gogh dem- 2 Defnition of a contact depth, δc , which accounts for onstrated that the age of the sample had a direct efect on deformation of the material outside the contact zone. the resulting reduced modulus (with the modulus of his- Te Oliver and Pharr expression for δc is: toric samples being up to an order of magnitude higher than the reconstructed samples), highlighting one of the Pmax δc = δmax − 0.75 . (11) main issues for studying model systems [99]. However, S the authors of this study also concluded that it can be dif- 3 Use of a relationship between Amax and δmax which fcult to determine an accurate modulus for a paint due depends only on the indenter geometry. For a Berko- to the fller behavior of pigment particles in the paint vich indenter this relationship is: samples. Te presence of these stifer pigment particles causes signifcant increases in the reduced modulus near 24.5 2. Amax = δc (12) the particles. More recent studies using nanoindentation have incorporated comparisons of the data from nanoin- For a parabolic indenter of with tip radius of curva- dentation with data from DMA and dynamic vapor ture R, this relationship is: sorption to understand how each technique showed the 2 . changes in mechanical properties when subjected to Amax = πδcR (13) variations in RH [100]. Measurements on the same zinc Tese equations enable the maximum contact radius oxide flled alkyd samples with DMA, QCM and nanoin- (or the efective maximum contact radius, aeﬀ ) to be dentation have confrmed the compatibility of the three obtained from load-displacement relations directly with- techniques when the frequency of the measurement is out direct visualization of the contact radius, a determi- appropriately taken into account [17]. Fujisawa et al. add 2 nation of the reduced modulus, E/ 1 − ν . a compliance term to their determination of mechani- Te other property that is often obtained from a cal properties to account for edge efects of the stifer nanoindentation experiment is the hardness, H, given by embedding resin on a paint sample [101]. A more sys- the ratio of the load to the projected contact area: tematic study with nanoindentation focused on understanding edge efects for cross sections mounted in resin, Pmax H = . showing how these efects impact the data obtained from A (14) max the experiments [102]. Since paint samples are typically While a value of H can be obtained from Eq. 14 for any mounted in resin materials that can exhibit a higher tip shape, it is usually used with tips with sharp edges, modulus, Freeman et al. explored the minimum size like the Berkovich tip. In these cases the material deforms required of cross sections to be able to minimize an artif- plastically in the regions near the indenter edges, and the cial stifening afect from the resin substrate. Initial steps hardness is taken as a measure of the yield stress of the have been taken towards mapping the mechanical prop- material. In these cases indentation necessarily involves erties of an entire painting cross section, which will be an irreversible deformation of the material, and limits meas- important method for being able to probe the mechani- urements of historic samples to regions of the paint that cal properties of historic paints more readily [103]. More are not visible (small portions taken from underneath work remains to be done in order to refne this mapping the frame, for example). Indentation probes a volume of technique and adapt it to paintings. Resolving efects of the sample with dimensions controlled by amax, and this solvent cleaning for a water sensitive oil paint were stud- length scale controls both the depth that is sampled ied with nanoindentation as well as DMA to determine in the measurement and the lateral resolution that is how much surface and bulk mechanical properties would obtained. Tis length scale is in turn controlled by the be efected, where most of the data for sponge cleaned size of the indenter tip and the depth of the indent in the samples exhibited statistically insignifcant changes [78]. sample, and is much smaller for atomic force microscopy In tandem with expanding the use of nanoindentation (AFM) than for nanoindentation. through mapping and optimizing the analysis of cross sections, atomic force microscopy has the potential to Advancements for artists’ paints be applied to painting cross sections to obtain mechanical properties. Since the AFM tip is smaller than the tip In cultural heritage research, nanoindentation has been of a nanoindenter, it can provide a higher resolution of used to correlate changes of mechanical properties with the surface mechanical property data across the paint optical and chemical changes as a function of aging or sample. One issue that needs to be considered with the light exposure for natural and synthetic binding media dePolo et al. Herit Sci (2021) 9:68 Page 16 of 24

environment and be stable enough to provide interfero- grams that were sensitive to changes in the painting after thermal loading, but not sensitive to slight environmental changes in the surrounding conditions [108, 109]. Te sensitivity of the phase maps obtained through laser shearography helps researchers observe defects such as cracks, paint losses, and delaminations more easily, especially if the defects are subsurface. Te maps are also capable of serving as a diagnostic tool for cultural heritage, guiding attention to areas that need more immediate attention during a conservation survey. Te sensitivity of laser shearography to detect delaminations, impacts on a painting surface, and the propagation of cracks through paint layers was successfully demonstrated with mockup samples [110]. Te use of strain maps to show the potential areas of concern and highlight areas of potential Fig. 14 Schematic of a shearography setup for measuring slight degradation in the paintings have been optimized for thermal changes in paintings as a result of a difuse light source. The ease of interpretation by conservators [111]. Shearogra- laser light from the optical head is used to obtain the phase maps of phy has also been paired with other imaging techniques the surface before and after the thermal loading of the painting. The such as terahertz imaging, fringe projections to observe phase shifting is achieved using a piezoelectric transducer driver (PZT 3D topographic maps, and refectance transformation driver) and an analog output card (DAQ). Modeled after and adapted from Klausmeyer et al. [107] imaging to provide more complete datasets for diagnos- ing defects and changes in a painting after environmental fuctuations or transport [107, 112, 113]. Some optimization of strain maps from the displacement gradients was AFM is that for very small contact dimensions the efect also performed on a test painting to quantify the strain of adhesive interactions become more important. When experienced by a painting as a result of cycling lights in these efects are appropriately accounted for, the AFM a museum setting [107, 114]. Comparing the phase maps can be used to quantify the viscoelastic properties of a of defects in paintings to simulated phase maps gener- material. Te approach has been validated for an acrylic ated using fnite element analysis (see Section 7.2), allow system [104, 105], and similar approaches can in prin- researchers to understand the nature of defects within a ciple be used to investigate the properties of aged paint painting and to vary the parameters of the defect until systems. A variety of complications exist when applying the simulated map matches the experimentally observed the technique to heterogeneous systems like actual art- map, which can be useful for understanding how difer- ist’s paints [106], but the availability of commercial AFM ent defects/areas of degradation within a painting can instrumentation with the ability to obtain load/displace- afect the resulting phase map [115]. ment curves over a small region of the sample may prove Laser shearography shows great promise as a diagnosis to be useful in the feld of cultural heritage. and monitoring tool for performing preliminary conservation surveys and tracking the state of a painting, espe- Developing research directions cially after transport for an exhibition. Te mobility of Laser shearography the setup allows it to be fairly cost efective for a museum One technique developed in the last couple of dec- setup. While it takes some time to gain the experience ades to observe changes in the mechanical properties of to interpret the data from the phase maps, the strain paintings is laser shearography. As shown in the sche- maps are a useful tool for understanding the mechani- matic in Fig. 14, interference patterns of a painting are cal response of the painting to slight fuctuations in its collected before and after a slight thermal, acoustic, or environment. vibrational excitation caused by the difuse light sources in the image. Te interference patterns are used to cre- Finite element analysis ate a phase map of the painting surface, which can be Technique background unwrapped to generate a displacement gradient map, also When a paint layer is considered in the context of a known as a strain map. painting, there can be range of complex stresses applied Kalms et al. focused on developing a setup that to the layer by the neighboring layers and quantifying would be mobile enough to easily set up in a museum the stresses can be difcult using free standing flms. dePolo et al. Herit Sci (2021) 9:68 Page 17 of 24

One way to look at understanding these stresses is to use fnite element analysis (FEA), which is capable of modeling the feld responses (such as stresses or strains) for complicated objects. A brief description of the process for using FEA is that the geometry is discretized into smaller elements, a simplifed material model is chosen that resembles the expected response from the object, boundary and load conditions are applied, then the solu- tions are calculated to determine the feld responses to the given load. When the geometry is defned, material properties need to be inputted, which typically include the elastic modulus, Poisson’s ratio, and hygric or thermal expansion coefcients, depending on the type of loading the object will experience. Tese material properties are usually informed from experimental data using one of the techniques previously discussed in this review. Fig. 15 A stress feld surrounding a crack tip depicting the horizontal How the material will respond to a load also needs to be stresses in a gesso ground layer, indicating that the highest stresses in the ground layer are occurring at the crack tip, which is functioning defned; the most common responses are isotropic (the as a stress concentrator. The FEA simulation used to create this stress same response in all directions) for paints or grounds and feld is based on the simulations used in Bratasz et al. [116] orthotropic (some directional dependence) for wood and some canvas substrates. Te ability to break down the object geometry into smaller elements allows easier comparison of the stress/strain response on the micro and results from a FEA model need to be validated against macroscopic scale, which is one of the strengths of this either experimental values (e.g. the expected results technique. Selection of a material model is determined by from the experiment that provided the material property the expected response from a material. Te two models inputs) or against analytical models. A balance also needs that have been applied to cultural heritage objects are a to be struck between the computational expense of run- linear elastic model, assuming a fairly elastic response of ning the model with its overall accuracy, which can make the material, or a visco-hyperelastic model, which allows it difcult to model some non-linear behavior that would for more time dependent deformation of the object [123]. be expected from paints and paintings. Te boundary and load conditions are used to constrain the geometry and explicitly defne the scenario being Application to cultural heritage modeled, for example, a strain being applied as a dis- An area of cultural heritage research that has begun placement along one axis of the model. Te results from using FEA more often focuses on understanding craque- a simulation are typically displayed as feld maps, such as lure development and the mechanisms governing crack the stress feld depicting the horizontal stresses in a gesso opening or delamination. For the papers discussed in this ground layer shown in Fig. 15. For this particular exam- section, all use a linear elastic model as their material ple, the highest areas of stress are immediately next to model unless otherwise specifed. Mecklenburg’s work the crack tip, which is functioning as a stress concentra- using FEA focused on the understanding of the response tor within this layer. From these stress felds, the energy of paintings to T or RH fuctuations, out of plane bend- release rate can be determined by integrating the area ing of the canvas due to vibrations from transport, and around the crack tip. Comparing the value of the energy an impact force on the side and corner of a painting to Gc release rate to values of obtained from measurements simulate a painting being dropped, comparing the result- on model materials will indicate if the crack would con- ing simulated craquelure patterns to ones observed in tinue to propagate under these conditions. painting mock ups [29, 61, 117]. Further studies of vibra- FEA is a very powerful method and allows the compar- tions afecting canvas paintings have been carried out to ison of a range of material properties and scenarios in a assess the vibrational modes that are most relevant to relatively short time compared to preparing that range of consider [118]. Bratasz et al. used a more targeted FEA experiments, there are also some things to keep in mind approach to study the behavior of gesso ground layers on when reviewing the results of a simulation. Te outputs a wood substrate, focusing on how the response of the from a simulation are heavily dependent on the material ground layer translates to the development of a craque- properties inputted, which can make it challenging to lure pattern that is less susceptible to environmental fuc- extend the use of a simulation beyond its initial goal. Te tuations [116, 119]. Eumelen et al. have investigated the dePolo et al. Herit Sci (2021) 9:68 Page 18 of 24

growth behavior of metal soaps combined the chemical information related to the difusion of metal soaps into aggregates with estimated mechanical properties for a paint layer to both understand the directionality of metal soap formation and the most likely regions for cracks to form within the model from the stresses caused by the aggregates [120]. More recent investigations from Bosco et al. have been focused on understanding the underlying deformation mechanisms that can lead to crack opening or delamination when a paint layer is exposed to fexural stresses as a result of increased moisture [121, 122]. An additional area where FEA can be applied for cultural heritage research is to simulate long term fatigue behavior. Te simulations can study the potential for cyclic fatigue that would cause failure or delamination of a paint layer, which was performed using a visco-hyperelastic material model since the timescales of fatigue responses tend to be more viscoelastic in nature [123]. Computational simulations studying fatigue behavior in paintings provide the fexibility to test multiple parameters and draw preliminary conclusions on a faster timescale than can be done with experiments, which is useful for informing conservator practice on a wide range of paintings varying in composition and structural support in a relatively short time. FEA can also be used to generate displacement felds as a result of thermal excitation, as was shown by Buchta et al. when observing defects using laser shearography [115]. While being able to test a wide range of parameters using FEA simulations is a strong beneft of the tech- Fig. 16 The a schematic of a vibration fatigue stage setup for nique, there is a major caveat: one needs to insure the mock up pastel paintings and b a modifed Wöhler curve showing results are physically relevant. Accurate determination the vibration level versus the number of cycles of vibrations. The of the critical energy release rate, Gc , mentioned above, is dashed curve is the fatigue limit for the mock up, above which (and one example. Informing the models using material prop- emphasized by the shaded region of the plot) the pastel mock up would be damaged by the vibrations. The schematic of the setup is erties for the paints or paintings of interest is a key step based of the setup used in [127] towards validating and extending the model.

Vibration studies through the detection of background vibrations in Another potential source of damage to paintings is museum as well as exposure of model systems to sus- from vibrations causing faking or crack formation, tained periods of vibration to determine thresholds whether from transport conditions, acute scenarios for damage to objects. Wei et al. assessed the afects of such as a construction project, or more difuse ambi- these background vibrations within a museum setting ent noise in or around a museum. When these vibra- to understand some thresholds of safety for paintings tions occur, they tend to apply an oscillating stress over and objects, determining it to be somewhat lower than a longer period of time, which can lead to longer term expected [125]. A particular case study where vibra- fatigue responses of the painting. Conservative limits tions are more problematic are pastel paintings, or for vibrations during a construction along with a pro- paintings where powdery pigment layers are applied to posed plan for assessment of a construction project was the support. Due to the low level of adhesion between outlined thoroughly by Johnson et al. to determine a the paint layers and support, pastel paintings are a vibration range of 1.5–4.0 mm/s depending on the fre- useful case study for assessing the potential limit of quency of the vibration [124]. Assessing these sources material loss due to vibrations before the painting is of vibration and understanding the efects on the lon- noticeably damaged [126]. gevity of objects in the museum has been assessed dePolo et al. Herit Sci (2021) 9:68 Page 19 of 24

Shown in Fig. 16, a biaxial tension setup with mockup PVC values were studied to determine if the compara- canvases is used to generate modifed Wöhler curves tive results could be quantifed as a function of increas- (displacement of material versus number of cycles) to ing PVC [14, 129–132]. One of these studies looked to correlate the amount of vibration sustained by an object extend their fndings with young model systems to see with the overall loss of material and minimum amount if they could develop a protocol for determining the age of acceptable loss from pastel paintings as determined of paint materials based on the response of the relaxa- by imaging and conservator observation [126]. Within tions times, which was unfortunately inconclusive [131]. this setup, a laser interferometer is used to track the Single-sided NMR has also been used to study the efects amplitude of the vibrations and the camera is used of solvent exposure on the stifness of paints. Te frst to monitor the overall surface damage of the canvas. study assesses previous solvent treatments of a 17th cen- Tese fatigue tests can provide useful information tury painting through comparison with another similar about the amount of vibration that can be sustained painting from the Pipenpoyse Wedding Set, demonstrat- before damage, which when paired with information ing that a cleaning treatment performed on one of the about display and travel of an object, can help curators paintings had a statistically signifcant efect on the stif- and conservators determine the best lifetime decisions ness, most likely due to a redistribution of low molecu- to maintain the best conditions for a pastel painting as lar weight molecules through the paint layer.[133]. A long as possible. While pastel paintings are more sensi- more recent study used both single-sided NMR and solid tive to damage by vibration than other paintings, these phase microextraction to investigate the efectiveness of types of fatigue tests can be used to assess the chances swab or gel cleaning of more green solvents for painting of new craquelure formation in an object, especially cleaning and is able to demonstrate that the gel method after travel or acute exposure to sustained vibrations. produces a reduced paint response and showed less pen- Eforts in this area have focused on understanding the etration into the paint layer than the swab method [134]. efects of pigment size on the stability of the pastel While this technique does not provide absolute informa- painting, incorporating high speed imaging to under- tion about the stifness of the paint layer, single-sided stand the resonant vibration modes of a canvas more NMR can provide relevant information about stifness fully, and working on more directly relating the data changes over the depth profle of a paint layer, which from mockup samples to actual museum objects. Te can be especially useful when investigating the solvent latter point would allow the use of Wöhler curves as response of a paint material. a predictive tool for determining if moving a pastel is within a safe limit. Conclusions When considering the mechanical properties of paints, Single‑sided nuclear magnetic resonance there are quite a few factors that need to be considered. Paintings that undergo solvent exposure for cleaning It is important to understand the material properties of treatments tend to experience embrittlement of the sur- both the binding medium and the pigment, which can face paint layers. A more thorough review discussing be partially informed from chemical analysis, as well as the chemical changes and implications has been recently the pigment concentration and how it afects the overall published [128]. A fairly novel way of studying paint- properties of the paint. Since paintings are multi-layered ings has been explored by researchers to correlate the structures, there also have to be considerations for the mechanical properties with chemical changes in paint interactions (both chemical and mechanical) between is single-sided nuclear magnetic resonance (NMR), or layers. Beyond the paint composition and structure, the NMR relaxometry [129]. Tis technique uses a NMR- environmental factors (e.g., T, RH, vibrations, and solvent MOUSE (Mobile Universal Surface Explorer) to look at exposure) can afect the response of the paint and need the relaxation times within a layer using a locally gener- to be accounted for when considering a conservation ated magnetic feld and detector. Transverse relaxation treatment. times (T 2 ), related to spin-spin interactions of the mate- Several techniques have been developed over recent rial being studied, can be recorded in depth profles and decades to help provide this information. Tensile testing, can be related to the stifness of a material. If a material DMA, rheology, and the QCM can provide information has reduced intermolecular motion (such as a cross- about the mechanical properties of paints from the liquid linked paint material), T2 will decrease as the stifness to the solid state, creating a data set that is more com- increases [129]. Single-sided NMR has been employed prehensive and complete than any dataset provided by a to look at both PVC and the efects of solvent on paint- single technique. Tese techniques are limited to model ing materials. Model systems of traditional oil paints, systems, but with the correct assumptions and compari- water-miscible oil paints, and acrylic paints with varying sons to historic samples, the data can be used to inform dePolo et al. Herit Sci (2021) 9:68 Page 20 of 24

conservation treatments. Techniques that are directly (e.g., such as determining an artist’s historic formulation) applicable to historic objects have been developed and and to expand the knowledge base of relevant materials adapted from industrial applications for cultural heritage, in ways that beneft the conservation community. Te which expands the breadth of knowledge accessible to purpose of this review has been to describe past work conservators. Nanoindentation can provide an estimate while highlighting newer capabilities that we expect to be of the stifness of a paint cross section and allow a con- useful in addressing these aims, in hope that the interdis- servator to explore the temperature and solvent response ciplinary collaborations enabling success would continue of the cross section before beginning a treatment. Laser to fourish. shearography, since it is both portable and non-invasive, is a technique that will be most useful for both initial Abbreviations surveys of a new painting in the collection (pinpoint- T: Temperature; RH: Relative humidity; µXRD: µ-X-ray difraction; PIXE: ing areas most in need of deeper investigation) and for a Particle induced X-ray emission; BS: Backscattering spectrometry; FTIR: Fourier transform infrared spectroscopy; PVC: Pigment volume concentration; DMA: painting traveling on exhibition (to track the amount of Dynamic mechanical analysis; QCM: Quartz crystal microbalance; MHz: damage accumulated as a result of travel). Computational Megahertz; AFM: Atomic force microscopy; FEA: Finite element analysis; NMR: studies using FEA can allow researchers to consider both Nuclear magnetic resonance; NMR-MOUSE: Nuclear magnetic resonance- mobile universal surface explorer. the macroscopic and microscopic length scales afecting the mechanical properties of a paint simultaneously as Supplementary Information well as explore a wide parameter space more rapidly than The online version contains supplementary material available at https://doi. experiments, given that the models are well informed and org/10.1186/s40494-021-00529-w. verifed via theories or experimental comparison. Studies analyzing the vibration response of model systems and Additional fle 1. Appendix: Tensile testing tables. generating predictive curves that can be used to assess Additional fle 2. Excel spreadsheet containing the tensile testing data objects in a museum, especially more sensitive objects shown in Additional fle 1. such as pastel paintings, give some insights into how much travel and exhibition an object can endure before Acknowledgements it needs restoration or to be retired. Single-sided NMR The authors would like to thank Alan Phenix and Arnaud Lesaine for helpful is emerging as a non-invasive technique that can provide conversations surrounding the references selected for this review paper and useful depth profles of comparative stifness measure- Marc Vermeulen for his time proofreading this manuscript. ments, which can provide information about PVC orpre- Author contributions vious solvent exposure of a painting sample. GD—writing, data compilation, and data analysis, MW—conceptualization and editing, KK—review and editing, KRS—data analysis, conceptualization, To continue progressing the feld and to provide rel- and editing. All authors read and approved the fnal manuscript. evant information for conservators, research eforts expanding the breadth of pigments investigated with Funding This work was supported by the NSF (OISE-1743748) and is also part of NU- these techniques will provide data to compare to when ACCESS’s broad portfolio of activities, which is made possibly by generous determining a conservation treatment for an object. support of the Andrew W. Mellon Foundation. Information about paint samples can also be expanded by Availability of data and materials combining any of the techniques discussed in the paper, The uniaxial tensile testing datasets analyzed during the current study are requiring an understanding of how the techniques can available through supplementary information as both a PDF fle (Additional complement each other. Extrapolating expected mate- fle 1) and an Excel fle (Additional fle 2). All other data sets presented and the rial responses of historic paints from relatively young codes used to generate fgures are available from the authors upon request. model systems continues to be a challenge for researchers and requires systematic eforts to look at aging trends Declarations and see if they can be extrapolated to longer times for a Competing interests wider range of paint materials. Expanding the eforts of Not applicable performing optical or in situ measurements of paintings Author details to obtain mechanical properties is very appealing, espe- 1 Department of Materials Science and Engineering, Northwestern Univer- cially when surveying objects for conservation treatment sity, Evanston, USA. 2 Van’t Hof Institute for Molecular Science, University of Amsterdam, Science Park, Amsterdam, The Netherlands. 3 Conservation [135]. One potential way to push this direction forward is and Science, Rijksmuseum Amsterdam, Amsterdam, The Netherlands. to collaborate with industry, adapting their existing tech- nology to work for paintings [136]. Te choice of which Received: 18 December 2020 Accepted: 5 May 2021 techniques are most relevant to use is also two potential research aims: to answer technical art history questions dePolo et al. Herit Sci (2021) 9:68 Page 21 of 24

References 19. Hagan EWS, Charalambides MN, Young CRT, Learner TJS, Hackney S. 1. van Gorkum R, Bouwman E. The oxidative drying of alkyd paint cata- Micromechanics models for predicting tensile properties of latex paint lysed by metal complexes. Coord Chem Rev. 2005;249(17):1709–1728. flms. In: Proulx T, editor. Time dependent constitutive behavior and http://www.sciencedirect.com/science/article/pii/S0010854505000342. fracture/failure processes, Volume 3. Conference proceedings of the 2. Juita DBZ, Kennedy EM, Mackie JC. Low temperature oxidation of society for experimental mechanics series. New York, NY: Springer; linseed oil: a review. Fire Sci Rev. 2012;1(1):3. https://doi.org/10.1186/ 2011. p. 297–306. 2193-0414-1-3. 20. Leonardi R. Nuclear physics and painting: sub-topic of the wide and 3. Soucek MD, Khattab T, Wu J. Review of autoxidation and driers. Prog fascinating feld of science and art. Nucl Phys A. 2005;752:659–674. Org Coat. 2012;73(4):435–454. https://linkinghub.elsevier.com/retrieve/ http://www.sciencedirect.com/science/article/pii/S0375947405002241. pii/S0300944011002529. 21. Keck S. Mechanical alteration of the paint flm. Stud Conserv. 4. Honzíček J. Curing of air-drying paints: a critical review | industrial and 1969;14(1):9–30. engineering chemistry research. Ind Eng Chem Res. 2019;58(28):12485– 22. Bucklow S. The description of craquelure patterns. Stud Conserv. 505. https://doi.org/10.1021/acs.iecr.9b02567. 1997;42(3):129–40. https://doi.org/10.1179/sic.1997.42.3.129. 5. Michalski SW. Paintings—their response to temperature, relative 23. Bucklow SL. A stylometric analysis of craquelure. Comput Humanit. humidity, shock, and vibration. In: Mecklenburg M, editor. Art in transit: 1998;31:503–21. studies in the transport of paintings. Washington, D.C.: National Gallery 24. Bucklow S. Classifcation of craquelure. In: Hill Stoner J, Rushfeld R, edi- of Art; 1991. https://www.academia.edu/741944/1991_Paintings_-_ tors. Conservation of easel paintings: principles and practice. London/ Their_Response_to_Temperature_Relative_Humidity_Shock_and_ New York: Butterowrth-Heinemann; 2012. p. 285–90. Vibration. 25. Michalski SW. Crack mechanisms in gilding. In: Gilded wood: conserva- 6. van Loon A, Noble P, Burnstock A. Ageing and deterioration of tradi- tion and history. Madison, Connecticut: Sound View Press; 1991. p. tional oil and tempera paints. In: Conservation of easel paintings. 1st 171–181. https://www.academia.edu/741952/1991_Crack_mecha edn. Routledge series in conservation and museology. London/New nisms_in_gilding. York: Routledge; 2012. p. 214–41. 26. Giorgiutti-Dauphiné F, Pauchard L. Painting cracks: a way to investigate 7. Learner T. Modern paints. In: Conservation of easel paintings. 1st edn. the pictorial matter. J Appl Phys. 2016;120(6):065107. http://aip.scita Routledge series in conservation and museology. London/New York: tion.org/doi/10.1063/1.4960438. Routledge; 2012. p. 242–251. 27. Pauchard L, Giorgiutti-Dauphiné F. Craquelures and pictorial matter. J 8. Hermens E, Townsend JH. Binding media in western easel painting. In: Cult Herit. 2020;46:361–373. https://www.sciencedirect.com/science/ Conservation of easel paintings. 1st edn. Routledge series in conserva- article/pii/S1296207420304398. tion and museology. London/New York: Routledge; 2012. p. 207–213. 28. Tumosa CS, Millard J, Erhardt D, Mecklenburg MF. Efects of solvents 9. Rothe A. Andrea Mantega’s “Adoration of the Magi”. In: Historical on the physical properties of paint flms. Preprints, ICOM Committee painting techniques, materials, and studio practice. Preprints from the for Conservation, 12th Triennial Meeting, Lyon. 1999;1:347–352. http:// Symposium at the University of Leiden, the Netherlands. The Getty repository.si.edu/xmlui/handle/10088/35962. Conservation Institute; 1995. p. 111–116. 29. Mecklenburg MF, Tumosa CS. An introduction into the mechanical 10. Sato K. The mechanical properties of flled polymers. Prog Org Coat. behavior of paintings under rapid loading conditions. In: Art in transit: 1976;4(4):271–302. http://www.sciencedirect.com/science/article/pii/ studies in the transport of paintings. Washington D.C.: National Gallery 0300944076800100. of Art; 1991. p. 137–171. 11. Perera DY. Efect of pigmentation on organic coating characteristics. 30. Erlebacher JD, Brown E, Mecklenburg MF, Tumosa CS. The efects of Prog Org Coat. 2004;50(4):247–262. http://www.sciencedirect.com/ temperature and relative humidity on the mechanical properties of science/article/pii/S0300944004000694. modern painting materials. In: Materials issues in art and archaeology 12. de Viguerie L, Beck L, Salomon J, Pichon L, Walter P. Composition of III. vol. 267. San Francisco: Materials Research Society; 1992. p. 359–370. renaissance paint layers: simultaneous particle induced X-ray emission http://repository.si.edu/xmlui/handle/10088/35967. and backscattering spectrometry. Anal Chem. 2009;81(19):7960–6. 31. Mecklenburg MF, Tumosa CS, Erlebacher JD. Mechanical behavior of https://doi.org/10.1021/ac901141v. artist’s acrylic paints under equilibrium conditions. In: Division of poly- 13. Wiesinger R, Pagnin L, Anghelone M, Moretto LM, Orsega EF, Schreiner mer chemistry. vol. 35. Washington, D.C.: American Chemical Society; M. Pigment and binder concentrations in modern paint samples deter- 1994. p. 297–298. http://repository.si.edu/xmlui/handle/10088/10305. mined by IR and Raman spectroscopy. Angewandte Chemie Int Edn. 32. Whitmore PM, Colaluca VG. The natural and accelerated aging of an 2018;57(25):7401–7. https://doi.org/10.1002/anie.201713413. acrylic artists’ medium. Stud Conserv. 1995;40(1):51–64. https://www. 14. Liu X, Di Tullio V, Lin YC, De Andrade V, Zhao C, Lin CH, et al. jstor.org/stable/1506611. Nano- to microscale three-dimensional morphology relevant to 33. Mecklenburg MF, Tumosa CS. Traditional oil paints: the efects of long- transport properties in reactive porous composite paint flms. term chemical and mechanical properties on restoration eforts. MRS Sci Rep. 2020;10(1):18320. https://www.nature.com/articles/ Bull. 2001;26(01):51–54. http://www.journals.cambridge.org/abstract_ s41598-020-75040-6. S0883769400023058. 15. Hagan E, Charalambides M, Learner TJS, Murray A, Young CT. Factors 34. Carr DJ, Young CRT, Phenix A, Hibberd RD. Development of a physical afecting the mechanical properties of modern paints. In: Modern model of a typical nineteenth-century English canvas painting. Stud paints uncovered: proceedings from the modern paints uncovered Conserv. 2003;48(3):145–54. https://doi.org/10.1179/sic.2003.48.3.145. symposium. Los Angeles: Getty Conservation Institute; 2007. p. 35. Mirone G, Marton B, Vancso GJ. Elastic modulus profles in the cross 227–235. sections of drying alkyd coating flms: modelling and experiments. Eur 16. Salvant Plisson J, de Viguerie L, Tahroucht L, Menu M, Ducouret G. Polym J. 2004;40(3):549–560. https://linkinghub.elsevier.com/retrieve/ Rheology of white paints: how van gogh achieved his famous impasto. pii/S0014305703002726. Colloids Surf A Physicochem Eng Aspects. 2014;458:134–141. http:// 36. Mecklenburg MF, Tumosa CS, Erhardt D. The changing mechanical www.sciencedirect.com/science/article/pii/S092777571400212X. properties of aging oil paints. In: Vandiver PB, Mass JM, Murray A, edi- 17. Sturdy LF, Wright MS, Yee A, Casadio F, Faber KT, Shull KR. Efects of zinc tors. Materials issues in art and archeology VII. Warrendale, PA: Materials oxide fller on the curing and mechanical response of alkyd coatings. Research Society; 2004. p. 13–24. http://repository.si.edu/xmlui/handle/ Polymer. 2020;191:122222. http://www.sciencedirect.com/science/artic 10088/36019. le/pii/S0032386120300641. 37. Hagan E, Murray A. Efects of water exposure on the mechanical 18. Hagan EWS, Charalambides MN, Young CRT, Learner TJS, Hackney S. properties of early artists’ acrylic paints. In: Materials issues in art and Viscoelastic properties of latex paint flms in tension: infuence of the archaeology VII. vol. 852. Boston: Materials Research Society; 2004. p. inorganic phase and surfactants. Prog Org Coat. 2010;69(1):73–81. 41–47. http://www.sciencedirect.com/science/article/pii/S0300944010001566. dePolo et al. Herit Sci (2021) 9:68 Page 22 of 24

38. Erhardt D, Tumosa CS, Mecklenburg MF. Long-term chemical and physi- 2016;16(4):182–195. https://content.sciendo.com/view/journals/aut/ cal processes in oil paint flms. Stud Conserv. 2005;50(2):143–50. https:// 16/4/article-p182.xml. doi.org/10.1179/sic.2005.50.2.143. 54. Hagan EWS. Thermo-mechanical properties of white oil and acrylic 39. Tumosa C, Erhardt D, Mecklenburg M, Su X. Linseed oil paint as artist paints. Prog Org Coat. 2017 Mar;104:28–33. http://www.sciencedir ionomer: synthesis and characterization. In: Materials issues in art and ect.com/science/article/pii/S0300944016302363. archaeology VII. vol. 852. Boston: Materials Research Society; 2005. p. 55. Fuster-López L, Mecklenburg M. A look into some factors infuencing 25–31. the flm forming properties of oil paint flms in copper paintings and 40. Young C. interfacial interactions of modern paint layers. In: Modern the efects of environment in their structural behavior. In: Fuster-López paints uncovered: proceedings from the modern paints uncovered L, Chulia Blanco I, Sarrio Martin MF, Vasquez de Agredos Pascual ML, symposium. Los Angeles: Getty Conservation Institute; 2007. p. Carlyle L, Wadum J, editors. Paintings on copper and other metal plates: 247–256. production, degradation, and conservation issues. Valencia: Universidad 41. Young C, Hagan E. Cold temperature efects of modern paints used Politecnica de Valencia; 2017. p. 95–102. for priming fexible supports. In: Preparation for painting: the artists’ 56. Doutre M, Murray A, Fuster-López L. Efects of humidity on gessoes for choice and its consequences. London: Archetype Publications; 2008. p. easel paintings. MRS Proc. 2017;1656:167–171. http://link.springer.com/ 172–179. 10.1557/opl.2014.828. 42. Fuesers O, Zumbühl S. the infuence of organic solvents on the 57. Roche A, Soldano A. The efect of changes in environmental conditions mechanical properties of alkyd and oil paint. In: IR, NIR, VIS UV Raman. on the mechanical behaviour of selected paint systems. Stud Conserv. Jerusalem, Israel; 2008. p. 1–14. 2018;63(sup1):216–21. https://doi.org/10.1080/00393630.2018.1504434. 43. Ormsby B, Hagan E, Smithen P, Learner TJS. Comparing contemporary 58. Fuster-López L, Izzo FC, Damato V, Yusà-Marco DJ, Zendri E. An insight titanium white-based acrylic emulsion grounds and paints: characteri- into the mechanical properties of selected commercial oil and alkyd sation, properties and conservation. In: preparation for painting: the paint flms containing cobalt blue. J Cult Herit. 2019;35:225–234. artists’ choice and its consequences. London: Archetype Publications; https://www.sciencedirect.com/science/article/pii/S12962074183010 2008. p. 163–171. 31. 44. Fuster-López L, Mecklenburg M, Castell-Agusti M, Guerola-Blay V. Filling 59. Bridarolli A, Nualart-Torroja A, Chevalier A, Odlyha M, Bozec L. System- materials for easel paintings: when the ground reintegration becomes a atic mechanical assessment of consolidants for canvas reinforcement structural concern. In: Preparation for painting: the artists’ choice and its under controlled environment. Herit Sci. 2020;8(1):52. https://doi.org/ consequences. London: Archetype Publications; 2008. p. 180–186. 10.1186/s40494-020-00396-x. 45. Carlyle L, Young C, Jardine S. The mechanical response of four-paste 60. Mecklenburg MF, Institute CC, Institution S, National Gallery of Art (U S grounds. In: Preparation for painting: the artist’s choice and its conse- ), Gallery T, editors. Art in transit: studies in the transport of paintings. quences. London: Archetype Publications; 2008. p. 123–131. Washington: National Gallery of Art; 1991. 46. Hagan EWS, Charalambides MN, Young CT, Learner TJS, Hackney 61. Mecklenburg MF, McCormick-Goodhart M, Tumosa CS. Investiga- S. Tensile properties of latex paint flms with TiO2 pigment. Mech tion into the deterioration of paintings and photographs using Time Depend Mater. 2009;13(2):149–61. https://doi.org/10.1007/ computerized modeling of stress development. J Am Inst Conserv. s11043-009-9076-y. 1994;33(2):153–170. https://www.jstor.org/stable/3179424. 47. Tumosa CS, Mecklenburg MF. Oil paints: the chemistry of drying oils 62. Zumbuhl S, Attanasio F, Scherrer NC, Muller W, Fenners N, Caseri W. and the potential for solvent disruption. In: New insights into the clean- Solvent action on dispersion paint systems and the infuence on the ing of paintings: proceedings from the cleaning 2010 international con- morphology—changes and destruction of the latex microstructure. ference, Universidad Politecnica de Valencia and Museum Conservation In: Modern paints uncovered: proceedings from the modern paints Institute. No. 3 in Smithsonian Contributions to Museum Conservation. uncovered symposium. Los Angeles: Getty Conservation Institute; 2007. Washington, D.C.: Smithsonian Scholarly Press; 2013. p. 51–58. p. 257–268. 48. Mecklenburg M, Tumosa CS, Vicenzi E. The infuence of pigments and 63. Erhardt D, Tumosa CS, Mecklenburg MF. Natural and accelerated ther- ion migration on the durability of drying oil and alkyd paints. In: New mal aging of oil paint flms. Stud Conserv 2000;45(sup1):65–69. http:// insights into the cleaning of paintings: proceedings from the cleaning www.tandfonline.com/doi/full/10.1179/sic.2000.45.Supplement-1.65. 2010 international conference, Universidad Politecnica de Valencia and 64. Rogala D, DePriest P, Charola AE, Koestler R. The mechanics of art mate- Museum Conservation Institute. No. 3 in Smithsonian Contributions to rials and its future in heritage science. No. 10 in Smithsonian contribu- Museum Conservation. Washington, D.C.: Smithsonian Scholarly Press; tions to museum conservation. Washington D.C.: Smithsonian Scholarly 2013. p. 59–67. Press; 2019. 49. Doménech-Carbó MT, Silva MF, Aura-Castro E, Doménech-Carbó A, 65. Young CRT, Hibberd RD. Biaxial tensile testing of paintings on canvas. Fuster-López L, Gimeno-Adelantado JV, et al. Multitechnique approach Stud Conserv. 1999;44(2):129–141. https://www.jstor.org/stable/15067 to evaluate cleaning treatments for acrylic and polyvinyl acetate paints. 25. In: New insights into the cleaning of paintings: proceedings from the 66. Young C. Measurement of the biaxial properties of nineteenth century cleaning 2010 international conference, Universidad Politecnica de canvas primings using electronic speckle pattern interferometry. Opt Valencia and Museum Conservation Institute. No. 3 in Smithsonian Lasers Eng 1999;31(2):163–170. http://www.sciencedirect.com/science/ Contributions to Museum Conservation. Washington, D.C.: Smithsonian article/pii/S014381669900007X. Scholarly Press; 2013. p. 125–134. 67. Young C, Ackroyd P, Hibberd R, Gritt S. The mechanical behaviour of 50. Hagan EWS, Charalambides MN, Young CRT, Learner TJS. The efects of adhesives and gap fllers for re-joining panel paintings. In: National strain rate and temperature on commercial acrylic artist paints aged gallery technical bulletin. vol. 23. London: National Gallery Publications; one year to decades. Appl Phys A. 2015;121(3):823–35. https://doi.org/ 2002. p. 23–96. 10.1007/s00339-015-9423-6. 68. Brinson HF, Brinson LC. Polymer engineering science and viscoelasticity: 51. Fuster-López L, Izzo FC, Piovesan M, Yusá-Marco DJ, Sperni L, Zendri an introduction. 2nd ed. New York: Springer; 2015. E. Study of the chemical composition and the mechanical behaviour 69. Sturdy LF, Yee A, Casadio F, Shull KR. Quantitative characterization of of 20th century commercial artists’ oil paints containing manganese- alkyd cure kinetics with the quartz crystal microbalance. Polymer. based pigments. Microchem J. 2016;124:962–973. http://www.scien 2016;103:387–396. http://www.sciencedirect.com/science/article/pii/ cedirect.com/science/article/pii/S0026265X15001964. S0032386116308631. 52. Krzemień L, Łukomski M, Bratasz Ł, Kozłowski R, Mecklenburg MF. 70. Hedley G, Odlyha M, Burnstock A, Tillinghast J, Husband C. A study of Mechanism of craquelure pattern formation on panel paintings. Stud the mechanical and surface properties of oil paint flms treated with Conserv. 2016;61(6):324–30. https://doi.org/10.1080/00393630.2016. organic solvents and water. J Therm Anal. 1991;37(9):2067–88. https:// 1140428. doi.org/10.1007/BF01905579. 53. Penava Ž, Penava DŠ, Tkalec M. Experimental analysis of the tensile properties of painting canvas. Autex Research Journal. dePolo et al. Herit Sci (2021) 9:68 Page 23 of 24

71. Odlyha M, Chan TYA, Pages O. Evaluation of relative humidity efects 87. Blayo A, Gandini A, Le Nest JF. Chemical and rheological characteriza- on fabric-supported paintings by dynamic mechanical and dielectric tions of some vegetable oils derivatives commonly used in printing analysis. Thermochimica Acta. 1995;263:7–21. http://www.sciencedir inks. Ind Crops Products. 2001;14(2):155–167. http://www.sciencedirect. ect.com/science/article/pii/0040603194023874. com/science/article/pii/S0926669001000796. 72. Foster GM, Ritchie S, Lowe C. Controlled temperature and relative 88. Belgacem MN, Blayo A, Gandini A. organosolv lignin as a fller in inks, humidity dynamic mechanical analysis of paint flms. J Therm Anal varnishes and paints. Ind Crops Products. 2003;18(2):145–153. http:// Calorim. 2003;73(1):119–26. https://doi.org/10.1023/A:1025133508109. www.sciencedirect.com/science/article/pii/S0926669003000426. 73. Ormsby B, Learner TJS, Foster GM, Druzik JR, Schilling M. Wet cleaning 89. Cimino D, Chiantore O, de La Rie ER, McGlinchey CW, Ploeger R, Poli acrylic emulsion paint flms: an evaluation of physical, chemical, and T, et al. Binary mixtures of ethylene containing copolymers and low optical changes. In: Modern paints uncovered: proceedings from the molecular weight resins: a new approach towards specifcally tuned art modern paints uncovered symposium. Los Angeles: Getty Conserva- conservation products. Int J Adhes Adhes. 2016;67:54–62. http://www. tion Institute; 2007. p. 189–200. sciencedirect.com/science/article/pii/S0143749615002298. 74. Ormsby B, Foster G, Learner T, Ritchie S, Schilling M. Improved con- 90. Marx KA. Quartz crystal microbalance: a useful tool for studying thin trolled relative humidity dynamic mechanical analysis of artists’ acrylic polymer flms and complex biomolecular systems at the solution- emulsion paints: Part II. General properties and accelerated ageing. J surface interface. Biomacromolecules. 2003;4(5):1099–120. https://doi. Therm Anal Calorim. 2007;90(2):503–508. http://link.springer.com/10. org/10.1021/bm020116i. 1007/s10973-006-7725-9. 91. Johannsmann D. Viscoelastic, mechanical, and dielectric measurements 75. Phenix A. Thermal mechanical transitions in artists’ oil paints and on complex samples with the quartz crystal microbalance. Phys Chem selected conservation materials: a study by dynamic mechanical analy- Chem Phys. 2008;10(31):4516. http://xlink.rsc.org/?DOI b803960g. sis (DMA). In: The AIC paintings specialty group. vol. 22. Los Angeles: 92. Johannsmann D. The quartz crystal microbalance in soft= matter American Institute for Conservation and Historic Works; 2009. p. 72–89. research. Soft Biol Matter. Cham: Springer International Publishing; 76. Baij L, Hermans JJ, Keune K, Iedema PD. Time-dependent ATR-FTIR 2015. http://link.springer.com/10.1007/978-3-319-07836-6. spectroscopic studies on solvent difusion and flm swelling in oil paint 93. Shull KR, Taghon M, Wang Q. Investigations of the high-frequency model systems. Macromolecules. 2018;51(18):7134–7144. http://pubs. dynamic properties of polymeric systems with quartz crystal resona- acs.org/doi/10.1021/acs.macromol.8b00890. tors. Biointerphases. 2020;QCM2020(1):021012. https://avs.scitation.org/ 77. Andersen CK, Freeman A, Mortensen MN, Beltran V, Łukomski M, Phenix doi/full/10.1116/1.5142762%40bip.2020.QCM2020.issue-1. A. Mechanical and moisture sorption properties of commercial artists’ 94. dePolo GE, Schafer E, Sadman K, Rivnay J, Shull KR. Sample preparation oil paint by dynamic mechanical thermal analysis (DMA), nanoin- in quartz crystal microbalance measurements of protein adsorption dentation, and dynamic vapour sorption (DVS). In: van den Berg KJ, and polymer mechanics. JoVE J Vis Exp. 2020;(155):e60584. https:// Bonaduce I, Burnstock A, Ormsby B, Scharf M, Carlyle L, et al., editors. www.jove.com/video/60584. Conservation of modern oil paintings. Cham: Springer International 95. Sturdy L, Casadio F, Kokkori M, Muir K, Shull KR. Quartz Crystal Rheom- Publishing; 2019. p. 403–418. https://doi.org/10.1007/978-3-030-19254- etry: A quantitative technique for studying curing and aging in artists’ 9_32. paints. Polym Degrad Stabil. 2014;107:348–355. http://linkinghub.elsev 78. Freeman AA, Lee J, Andersen CK, Fujisawa N, Łukomski M, Ormsby B. A ier.com/retrieve/pii/S0141391014000573. pilot study of solvent-based cleaning of yellow ochre oil paint: efect on 96. Oliver WC, Pharr GM. An improved technique for determining hardness mechanical properties. Herit Sci. 2021;9(1):28. https://doi.org/10.1186/ and elastic modulus using load and displacement sensing indentation s40494-021-00501-8. experiments. J Mater Res. 1992;7(06):1564–1583. http://www.journals. 79. Fischer EK. Rheological properties of commercial paints. J Colloid Sci. cambridge.org/abstract_S0884291400017039. 1950;5(3):271–281. http://www.sciencedirect.com/science/article/pii/ 97. Oyen ML, Cook RF. A practical guide for analysis of nanoindentation 0095852250900304. data. J Mech Behav Biomed Mater. 2009;2(4):396–407. http://www.scien 80. Eley RR. Applied rheology and architectural coating performance. cedirect.com/science/article/pii/S1751616108000805. J Coat Technol Res. 2019;16(2):263–305. https://doi.org/10.1007/ 98. Chiantore O, Scalarone D. The macro- and microassessment of physical s11998-019-00187-5. and aging properties in modern paints. In: Modern paints uncovered: 81. Groen K. Investigation of the use of the binding medium by rembrandt. proceedings from the modern paints uncovered symposium. Los Zeitschrift fur Kunsttechnologie und Konservierung. 1997;2:207–227. Angeles: Getty Conservation Institute; 2007. p. 96–104. https://pure.tue.nl/ws/fles/1370067/617823.pdf. 99. Salvant J, Barthel E, Menu M. Nanoindentation and the micromechanics 82. de Viguerie L, Ducouret G, Cotte M, Lequeux F, Walter P. New insights on of van gogh oil paints. Appl Phys A. 2011;104(2):509–515. http://link. the glaze technique through reconstruction of old glaze medium for- springer.com/10.1007/s00339-011-6486-x. mulations. Colloids Surf A: Physicochem Eng Aspects. 2008;331(1):119– 100. Andersen CK, Freeman A, Mortensen MN, Beltran V, Łukomski M, Phenix 125. http://www.sciencedirect.com/science/article/pii/S092777570 A. Mechanical and moisture sorption properties of commercial artists’ 8004809. oil paints by dynamic mechanical thermal analysis (DMA), nanoinden- 83. de Viguerie L, Ducouret G, Lequeux F, Moutard-Martin T, Walter P. tation, and dynamic vapour sorption (DVS). In: Conservation of modern Historical evolution of oil painting media: a rheological study. Comptes oil paintings. Springer; 2019. p. 403–417. Rendus Physique. 2009;10(7):612–621. http://www.sciencedirect.com/ 101. Fujisawa N, Łukomski M. Nanoindentation near the Edge of a science/article/pii/S163107050900111X. Viscoelastic Solid with a Rough Surface. Materials & Design. 2019 84. Tirat S, Echard JP, Lattuati-Derieux A, Le Huerou JY, Serfaty S. Recon- Dec;184:108174. Available from: https://www.sciencedirect.com/scien structing historical recipes of linseed oil/colophony varnishes: infuence ce/article/pii/S0264127519306124. of preparation processes on application properties. J Cult Herit. 2017;27, 102. Freeman A, Łukomski M, Beltran V. Mechanical characterization of a Supplement(Wooden Musical Instruments):S34–S43. https://reader. cross-sectional TiO2 acrylic-based paint by nano-indentation. J Am Inst elsevier.com/reader/sd/pii/S1296207417305654. Conserv. 2020;59(1):27–39. https://doi.org/10.1080/01971360.2019. 85. de Viguerie L, Jaber M, Pasco H, Lalevée J, Morlet-Savary F, Ducouret 1603062. G, et al. A 19th century “ideal” oil paint medium: a complex hybrid 103. Tiennot M, Paardekam E, Iannuzzi D, Hermens E. Mapping the mechani- organic–inorganic gel. Angewandte Chemie Int Edn. 2017;56(6):1619– cal properties of paintings via nanoindentation: a new approach for 1623. https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201611136. cultural heritage studies. Sci Rep. 2020;10(1):7924. https://www.nature. 86. de Viguerie L, Glanville H, Ducouret G, Jacquemot P, Dang PA, Walter com/articles/s41598-020-64892-7. P. Re-interpretation of the old masters’ practices through optical and 104. Chyasnavichyus M, Young SL, Tsukruk VV. Probing of polymer surfaces rheological investigation: the presence of calcite. Comptes Rendus in the viscoelastic regime. Langmuir. 2014;30(35):10566–82. https://doi. Physique. 2018;19(7):543–552. http://www.sciencedirect.com/science/ org/10.1021/la404925h. article/pii/S1631070518301142. dePolo et al. Herit Sci (2021) 9:68 Page 24 of 24

105. Kolluru PV, Eaton MD, Collinson DW, Cheng X, Delgado DE, Shull KR, 120. Eumelen GJAM, Bosco E, Suiker ASJ, van Loon A, Iedema PD. A et al. AFM-based dynamic scanning indentation (DSI) method for fast, computational model for chemo-mechanical degradation of histori- high-resolution spatial mapping of local viscoelastic properties in soft cal oil paintings due to metal soap formation. J Mech Phys Solids. materials. Macromolecules. 2018;51(21):8964–8978. https://pubs.acs. 2019;132:103683. http://www.sciencedirect.com/science/article/pii/ org/doi/10.1021/acs.macromol.8b01426. S0022509619302182. 106. Collinson DW, Eaton MD, Shull KR, Brinson LC. Deconvolution of 121. Bosco E, Suiker ASJ, Fleck NA. Crack channelling mechanisms in brittle stress interaction efects from atomic force spectroscopy data across coating systems under moisture or temperature gradients. Int J Fract. polymer-particle interfaces. Macromolecules. 2019. https://pubs.acs. 2020;225(1):1–30. https://doi.org/10.1007/s10704-020-00461-3. org/doi/10.1021/acs.macromol.9b01378. 122. Bosco E, Suiker ASJ, Fleck NA. Moisture-induced cracking in a fexural 107. Klausmeyer P, Cushman M, Dobrev I, Khaleghi M, Harrington EJ, Chen bilayer with application to historical paintings. Theor Appl Fract Mech. X, et al. Quantifying and mapping induced strain in canvas paintings 2021;112:102779. https://www.sciencedirect.com/science/article/pii/ uising laser shearography. In: The noninvasive analysis of painted sur- S0167844220303554. faces: scientifc impact and conservation practice. No. 5 in Smithsonian 123. Tantideeravit S, Charalambides MN, Balint DS, Young CRT. Prediction of Contributions to Museum Conservation. Washington D.C.: Smithsonian Delamination in multilayer artist paints under low amplitude fatigue Scholarly Press; 2016. p. 1–13. loading. Eng Fract Mech. 2013;112-113:41–57. http://www.sciencedir 108. Kalms MK, Osten W, Jueptner WPO. Advanced shearographic system for ect.com/science/article/pii/S0013794413003172. nondestructive testing of industrial and artwork components. In: Deng 124. Johnson AP, Robert Hannen W, Zuccari F. Vibration control during S, Okada T, Behler K, Wang X, editors. Photonics Asia 2002. Shanghai, museum construction projects. J Am Inst Conserv. 2013;52(1):30–47. China; 2002. p. 34. http://proceedings.spiedigitallibrary.org/proceeding. http://search.ebscohost.com/login.aspx?direct true&db asu&AN aspx?doi 10.1117/12.482923. 86141021&site ehost-live. = = = 109. Kalms MK,= Jueptner WPO. A mobile shearography system for non- 125. Wei W, Sauvage= L, Wölk J. Baseline limits for allowable vibrations for destructive testing of industrial and artwork components. Key Energy objects. In: Preventive conservation. vol. 1516. Paris: International Coun- Mater. 2005;295–296:165–70. cil of Museums; 2014. p. 7. 110. Groves RM, Osten W, Doulgeridis M, Kouloumpi E, Green T, Hackney S, 126. Sauvage L, Wei WB, Martinez M. When conservation meets engineer- et al. Shearography as part of a multi-functional sensor for the detec- ing: predicting the damaging efects of vibrations on pastel paintings. tion of signature features in movable cultural heritaged. In: Fotakis C, Stud Conserv. 2018;63(sup1):418–20. https://doi.org/10.1080/00393630. Pezzati L, Salimbeni R, editors. Optical metrology. Munich, Germany; 2018.1504444. 2007. p. 661810. http://proceedings.spiedigitallibrary.org/proceeding. 127. Sauvage L, Stratis H, Harrison L. Pastel roundtable. J Paper Conserv. aspx?doi 10.1117/12.727497. 2018;19(1):33–5. https://doi.org/10.1080/18680860.2019.1580005. 111. Groves RM,= Li A, Liu X, Hackney S, Peng X, Osten W. 2.5D Virtual reality 128. Baij L, Hermans J, Ormsby B, Noble P, Iedema P, Keune K. A review of visualisation of shearography strain data from a canvas painting. In: solvent action on oil paint. Herit Sci. 2020;8(1):43. https://doi.org/10. Pezzati L, Salimbeni R, editors. SPIE Europe Optical Metrology. Munich, 1186/s40494-020-00388-x. Germany; 2009. p. 739109. http://proceedings.spiedigitallibrary.org/ 129. Udell NA, Hodgkins RE, Berrie BH, Meldrum T. Physical and chemical proceeding.aspx?doi 10.1117/12.827519. properties of traditional and water-mixable oil paints assessed using 112. Groves RM, Pradarutti= B, Kouloumpi E, Osten W, Notni G. 2D and 3D single-sided NMR. Microchem J. 2017;133:31–36. https://www.scien non-destructive evaluation of a wooden panel painting using shear- cedirect.com/science/article/pii/S0026265X16306038. ography and terahertz imaging. NDT & E International. 2009;42(6):543– 130. Rooney M. Efect of pigment volume concentration on physical and 549. http://www.sciencedirect.com/science/article/pii/S096386950 chemical properties of acrylic emulsion paints assessed using single- 9000619. sided Nmr [Master of Science]. College of William and Mary. Virginia; 113. Morawitz M, Hein N, Alexeenko I, Wilke M, Pedrini G, Krekel C, et al. Opti- 2018. https://scholarworks.wm.edu/etd//1530192815. cal methods for the assessment of transport and age induced defects 131. Busse F, Rehorn C, Küppers M, Ruiz N, Stege H, Blümich B. NMR relax- of artwork. In: Osten W, editor., et al., Fringe 2013. Berlin, Heidelberg: ometry of oil paint binders. Magn Reson Chem. 2020;58(9):830–839. Springer; 2014. p. 951–5. https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/abs/10. 114. Meybodi MK, Dobrev I, Klausmeyer P, Harrington EJ, Furlong C. Investi- 1002/mrc.5020. gation of thermomechanical efects of lighting conditions on canvas 132. Rooney M, Meldrum T. Efect of pigment concentration on nmr paintings by laser shearography. In: Furlong C, Gorecki C, Novak EL, relaxometry in acrylic paints. Magn Reson Chem. 2020;58(9):880–888. editors. SPIE Optical Engineering Applications. San Diego, California, https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/abs/10. USA; 2012. p. 84940A. http://proce+edings.spiedigitallibrary.org/proce 1002/mrc.5053. eding.aspx?doi 10.1117/12.958089. 133. Fife GR, Stabik B, Kelley AE, King JN, Blümich B, Hoppenbrouwers R, et al. 115. Buchta D, Heinemann= C, Pedrini G, Krekel C, Osten W. Combination of Characterization of aging and solvent treatments of painted surfaces FEM simulations and shearography for defect detection on artwork. using single-sided NMR. Magn Reson Chem. 2015;53(1):58–63. https:// Strain. 2018;54(3):12269. https://onlinelibrary.wiley.com/doi/abs/10. onlinelibrary.wiley.com/doi/abs/10.1002/mrc.4164. 1111/str.12269. 134. Prati S, Sciutto G, Volpi F, Rehorn C, Vurro R, Blümich B, et al. Cleaning oil 116. Bratasz Ł, Akoglu KG, Kékichef P. Fracture saturation in paintings makes paintings: nmr relaxometry and SPME to evaluate the efects of green them less vulnerable to environmental variations in museums. Herit Sci. solvents and innovative green gels. New J Chem. 2019;43(21):8229– 2020;8(1):11. https://doi.org/10.1186/s40494-020-0352-0. 8238. https://pubs.rsc.org/en/content/articlelanding/2019/nj/c9nj0 117. Mecklenburg M, Tumosa C, McCormick-Goodhardt M. A general 0186g. method for determining the mechanical properties needed for the 135. Walter P, de Viguerie L. Materials science challenges in paintings. Nat computer analysis of polymeric structures subjected to changes in Mater. 2018;17(2):106–109. https://www.nature.com/articles/nmat5070. temperature and relative humidity. In: Materials research society sym- 136. Shull K. Future trends in studies of the mechanics of artists’ paints. In: posium. vol. 267. San Francisco, CA: Materials Research Society; 1992. p. The mechanics of art materials and its future in heritage science. No. 10 337–358. in Smithsonian Contributions to Museum Conservation. Washington 118. Chiriboga Arroyo PG. Finite element modeling of vibrations in D.C.: Smithsonian Scholarly Press; 2019. p. 87–92. canvas paintings [Doctoral]. Technische Universiteit Delft. Delft, Netherlands; 2013. https://repository.tudelft.nl/islandora/object/ uuid%3Aa30b358e-d0de-4a81-92f3-e9f255443043 Publisher’s Note 119. Bratasz Ł, Sereshk MRV. Crack saturation as a mechanism of acclima- Springer Nature remains neutral with regard to jurisdictional claims in pub- tization of panel paintings to unstable environments. Stud Conserv. lished maps and institutional afliations. 2018;63(sup1):22–7. https://doi.org/10.1080/00393630.2018.1504433.