Evaluating the environmental response of Rembrandt’s The Night Watch (1642) using water sorption experiments and diffusion modelling

Abstract

Rembrandt’s The Night Watch (1642) has been wax-resin lined, which involved attaching a new canvas to its reverse using a beeswax-resin mixture to achieve structural stabilisation and shielding against environmental humidity. We investigated the effect of wax-resin lining on water transport in The Night Watch using a one-dimensional, multi-layered water transport model based on ideal diffusion. Model input parameters were estimated using dynamic vapour sorption experiments. The paint layer response in the environmental conditions of the BIZOT Green Protocol was evaluated. During the fastest allowed RH fluctuation in BIZOT, water concentration in the paint layer of wax-resin lined paintings only reached 30% of the maximum concentration at static RH conditions (60% RH). Furthermore, we show that the water sorption capacity of the wax-resin adhesive of The Night Watch increased after ca. 50 years of natural ageing. Modelling results indicated that the effect of this increase on the overall response is minor.

Introduction

Wax-resin lining was a popular stabilisation and consolidation treatment for canvas paintings in the Netherlands in the 19th and 20th century¹. In this treatment, a new canvas was attached to the back of an original canvas painting using a mixture of beeswax and a natural resin (often colophony) as adhesive. A wax-resin lining treatment served three important functions: consolidation (re-adhesion), stabilisation, and protection against moisture¹. Flaking and blistering paint layers were re-adhered through impregnation of the painting with the wax-resin mixture. Structural stabilisation was achieved through the attachment of the lining canvas to strengthen the original aged canvas. Since the nature of the wax-resin used for the consolidation and stabilisation was highly hydrophobic, it was deemed a good protection against moisture entering the painting from the environment. Although wax-resin lining is not practiced widely anymore for several decades due to aesthetic and ethical concerns, an estimated 90% of 17th-century Netherlandish paintings on canvas in Dutch collections are currently wax-resin lined². This large group includes Rembrandt’s The Night Watch (1642), the subject of extensive research and conservation efforts within Operation Night Watch at the Rijksmuseum. As a consequence, questions were put forward in this project regarding the current state and long-term performance of the wax-resin lining of The Night Watch and of collections of lined paintings in general. Thus far, the adhesive properties of the lining of The Night Watch were investigated using shearography³, which is an optical technique that can detect surface deformation. Furthermore, the lining practice has been researched from a conservation history perspective⁴.

In this study, we dive deeper into the protective properties of a wax-resin lining against moisture from the environment. This is particularly relevant in light of the implementation of the BIZOT guidelines for museum indoor climate (Group BIZOT, The BIZOT Green Protocol. https://www.cimam.org/sustainability-and-ecology-museum-practice/bizot-green-protocol/ (2023)). These new guidelines were proclaimed in view of the urgency felt in the heritage sector to reduce energy consumption related to indoor climate control. In this new BIZOT regime, the relative humidity (RH) will be allowed to fluctuate between 40 and 60% RH with a maximum change of 10% RH per 24 hours and the temperature (T) between 16 and 25 °C. The regime in the Rijksmuseum main building (comparable to many other museums) is more strict and allows the RH to fluctuate between 50 ± 5% RH and T between 20 ± 2 °C in winter and 54 ± 5% RH and 23 ± 2 °C in summer with a maximum change of the average humidity of 1% RH and 0.5 °C per month. Currently, however, the Rijksmuseum is implementing BIZOT in a controlled step-by-step manner. In this study, our objective is to address two fundamental questions relevant to preventive conservation:

• 1. What is the environmental response of The Night Watch and lined paintings in general to the more varying climatic conditions according to the BIZOT guidelines?

• 2. How does ageing of the wax-resin adhesive mixture affect the future protective performance of the lining against humidity fluctuations?

Elaborating on the moisture barrier function of linings, it is well known that all layers in a painting stratigraphy can absorb and desorb moisture in response to RH changes in its environment, albeit to different degrees and with different rates. Figure 1 displays a schematic representation of the build-up of a traditional oil painting. When the mechanical response to RH in the different layers does not match, stress build-up can occur with deformations and cracks as a result^5,6,7.

Fig. 1: Schematic of the stratigraphy of a wax-resin-lined oil painting on canvas.

Traditional lining practice involved the attachment of a new canvas to the reverse of a painting using a glue-based adhesive. In the 19th century in the Netherlands, the water-based adhesive was replaced with wax-resin to be more suitable in a humid climate. Hence, the lining practice using wax-resin is commonly known as ‘The Dutch Method’¹. A wax-resin lining was thought to slow down moisture penetration, which would minimise the risk of a differential response of the layers of a painting to RH fluctuations. In other words, the wax-resin lining increases the response time of a painting. This response time is a measure of the time required for a material to reach a new equilibrium after a change in RH, usually expressed as hygrometric half time (t₅₀)⁷. Several studies into the environmental response of wax-resin lined paintings show the retarding effect of the wax-resin³⁵. For example, Gregers-Høegh et al. found that a fresh wax-resin impregnation slows down the response time of canvas by a factor 200–400. While wax-resin linings hamper moisture diffusion, wax-resin linings are not impenetrable and do take up water. This fact was emphasised in the work by Krarup Andersen et al., who detected tension in wax-resin lined paintings due to swelling of the canvas fibres after 18-hour equilibration at high humidity^20,36,37. They showed that the wax-resin adhesive mixture prevents the canvas threads from expanding as they take up moisture, which causes tension in the canvas that could lead to buckling and deformation. In this respect, a wax-resin lining does not protect a painting from moisture-related damage; it can, in fact, exacerbate it. Therefore, we will avoid using the term protective but instead use the term shielding to describe the function of wax-resin lining aimed to slow down moisture transport. The studies by Krarup Andersen et al. highlight that, beyond the moisture transport properties of the wax-resin impregnation, the timescale of RH fluctuations is an important factor in determining the shielding capacity of wax-resin linings. Consequently, an essential first step towards answering questions about the long-term shielding performance of wax-resin linings is to disentangle the factors that determine the environmental response of a painting.

The current study is based on a multi-layered ideal diffusion model that was recently developed by our group to calculate moisture transport through the stratigraphy of a canvas painting in response to RH fluctuations⁸. The model is based on a one-dimensional version of Fick’s second law of diffusion, which describes the transport of a penetrant (in this case, water) through a material due to a concentration gradient. The input for the model consists of three parameters for each layer in the stratigraphy: a water diffusion coefficient D (m²/s) that indicates the rate of the water diffusion process; a water sorption isotherm, which describes the equilibrium water concentration (kg/m³) at a given environmental RH between 0 and 95% RH; and layer thickness d (m). Often, we refer to the water concentration at 95% RH as c₉₅, which serves as an indicator for the maximum sorption. While this model is rather simple and obviously does not accurately reflect the material complexity of a real painting, a more refined model is only possible and useful if it is guided by detailed information on the physical structure and moisture transport properties of individual layers or layer components. Lacking such information, we demonstrate that even for a simple water transport model, the unavailability of reliable parameter values is a significant bottleneck for carrying out useful calculations, not only the simplicity of the model. Water diffusion coefficients and sorption isotherms can be found in literature for many common materials, but data about artist materials such as aged paint, ground, and canvas are far more scarce. For that reason, we focus in this study on generating new experimental sorption data that we acquired with dynamic vapour sorption (DVS) experiments. In a DVS experiment, the weight of a sample is recorded as the RH is increased or decreased stepwise, which yields water sorption isotherms. We present a methodology to obtain values for the input parameters of the model based on the DVS data of samples of reconstructions and historical lining materials. Furthermore, we use the time-based gravimetric data obtained with DVS to estimate effective diffusion coefficients in our samples. The model calculates water concentrations throughout the painting stratigraphy as a function of time, from which the response time of the paint layers can be calculated. As such, the model represents a first-order approximation of a highly complex system. By tackling the lack of relevant sorption data first, this study aims to provide a foundational step towards more advanced modelling.

Since we are also interested in the future protective performance of the lining against humidity fluctuations, it is essential to understand how the water sorption and transport properties of the wax-resin materials change over time due to ageing. Different recipes for the wax-resin adhesive mixture exist, but the majority contain beeswax and natural resins such as colophony or mastic². Beeswax without resin does not have enough adhesive power for lining. In addition, the resin increases the melting temperature of the mixture, without which the adhesive would be very sensitive to temperature fluctuations. The proportion of beeswax to resin would vary according to the practice of the restorer and/or the condition of the painting. The latest of three wax-resin linings that The Night Watch received (in 1851, 1945-7, and 1975-6) was a mixture of beeswax and colophony resin in a 5:2 ratio^1,4,9. Beeswax is a complex natural material with crystalline and amorphous phases, containing long-chain hydrocarbons, fatty acids, fatty alcohols, and their esters. Beeswax is well-known for its superhydrophobic properties, particularly in the food industry¹⁰. The diffusion coefficient of water in beeswax is in the order of 10^-14 m²/s¹¹, a factor 10 lower than lead white oil paint, which exhibits the slowest water diffusion of all the layers commonly found in an oil painting on canvas⁸. Mixing beeswax with colophony, a hydrophobic tree resin mainly composed of diterpenoid acids with pimarane, abietane and labdane structures, yields a very slight increase in water diffusion coefficient (from 0.391 to 0.626·10⁻¹³ m²/s in a 5:2 ratio)¹¹. Both beeswax and colophony are found to experience chemical change as they age. The diterpenoid resin acids in colophony are known to undergo oxidation and cleavage reactions^12,13,14,15. Artificial ageing of beeswax and analysis of archaeological samples showed that beeswax can undergo hydrolysis and oxidation reactions that lead to the formation of low molecular weight components^12,16,17. Subsequent loss of these small, volatile molecules that act as plasticizers leads to embrittlement and formation of cracks¹⁸. Both the oxidation of the resinous fraction and the formation of cracks in the wax fraction of wax-resin have been hypothesised to affect the moisture-shielding function of wax-resin linings^19,20.

In this paper, the focus is placed on The Night Watch and answering the two preventive conservation questions – impact of BIZOT guidelines and ageing effects - related to its wax-resin lining. In order to model the layers of The Night Watch, the model input parameters were estimated based on DVS experiments. The parameter estimation process is divided into separate, smaller research topics. We will discuss the ideal laminate and the ideal diffusion assumptions of the model in more detail using experimental data. Secondly, the effect of wax-resin impregnation on the water diffusion and sorption properties of the system is evaluated. Subsequently, the ageing of wax-resin is explored to understand the potential effect of ageing on the shielding function of wax-resin linings. Finally, the layer properties of The Night Watch are used as input for the model to calculate the effect of the wax-resin lining on the environmental response time of the paint layers under various external RH conditions. These calculations provide insights into the long-term performance of the wax-resin lining of The Night Watch and wax-resin-lined paintings in general. Overall, we aim to show how a simple model with experimentally derived input parameters can contribute to our understanding of complex multi-layered systems and provide a scientific basis for preventive conservation decision-making.

Methods

Samples of conservation materials

Three samples of lining canvas from the 1970s were collected. The first sample was from the tacking edge of the current lining canvas of The Night Watch (SK-C-5_032). During the structural treatment of the painting in 2022, the wax-resin on the tacking edges of the lining canvas was reduced to make them flexible enough to create casings for the new spring tensioning system. The wax-resin reduction was done using a heated spatula and a small iron (max. ca. 90 °C) and blotting paper to absorb the molten wax-resin mixture. From these tacking edges, circles (1.2 cm in diameter) were punched using a wood punch to create holes for attaching the canvas to the new aluminium strainer. One of these circles was analysed in this study. The other two lining canvas samples were punched (1.2 cm diameter) from the tacking edge of the lining canvas of two other paintings, SK-A-3802 (Portrait of Jan Jacob Rochussen (1797–1871), Gouverneur-generaal (1845–51) by Nicolaas Pieneman, 1845, Rijksmuseum) and SK-A-807 (Portrait van Elisabeth van Oosten (1660–1714), as a child by Willem Jansz. Ploy (attributed to), 1663, Rijksmuseum). In addition to the lining canvas samples, samples of wax-resin (granules) that were collected from the tacking edge of The Night Watch during the treatment (before the reduction) were analysed.

Reconstructions

Reconstructions on canvas (Set 1 and 2) were previously prepared as part of Operation Night Watch to reconstruct the ground used by Rembrandt in The Night Watch. In this painting, Rembrandt used for the first time a natural earth ground rich in quartz and clay minerals. This type of ground was unique for Rembrandt and his studio²¹. Moreover, recent findings have indicated that Rembrandt appears to have prepared his canvas using a lead-containing oil²². For this study, we did not have access to reconstructions of canvas prepared with a lead-containing oil. Round samples (1.2 cm diameter) were taken using a wood punch from these reconstructions for DVS analysis. The thickness of all samples was measured using a digital calliper.

Set 1 consists of reconstructions on canvas that were previously prepared in 2021 to reconstruct the ground layer and a paint layer of The Night Watch and to investigate a possible darkening effect of wax-resin impregnation²³. The reconstructions were composed of a glue-sized canvas and a kaolin-based ground layer. Parts of the canvas were subsequently impregnated with a wax-resin mixture, consisting of 6 g colophony, 12 g unbleached beeswax, and 9 g larch turpentine. More details about the preparation can be found in Supplementary Note 1. The reconstructions were naturally aged for approximately 1.5 years in lab conditions before round samples were punched from the sized canvas (sample SC1), sized canvas with ground (SC1-G), and wax-resin impregnated sized canvas with ground (WR-SC1-G).

Set 2 consists of reconstructions on canvas that were previously prepared in 2023 to reconstruct the recipe of the clay-quartz ground used by Rembrandt in The Night Watch²⁴. These reconstructions were composed of an oil-based clay ground applied on Melinex and on prepared canvas. More details about the preparation of these reconstructions can be found in Supplementary Note 1. After approximately 2 years of natural ageing in lab conditions, a piece of Melinex with the ground layer was cut (sample G) together with a piece of bare Melinex as a reference. In addition, two round samples were punched from the sized canvas (SC2) and the sized canvas with a ground layer (SC2-G).

Wax-resin model systems (set 3) were prepared by mixing beeswax and colophony in a 5:2 ratio, according to the recipe of the third wax-resin lining of The Night Watch by Kuiper. 100 g of colophony (Kremer Pigmente) was heated to 90 °C on a hot plate, after which 250 g beeswax (Kremer Pigmente) was added to the molten resin and stirred to form a homogeneous mixture. Small pieces of the cooled mixture were re-heated using au-bain-marie to be applied on glass microscope slides using a drawdown bar with an approximate thickness of 500 µm.

Dynamic vapour sorption

Dynamic vapour sorption (DVS) was performed using an automatic multi-sample moisture sorption analyser (SPSx-11m, Project Messtechnik). The RH inside the climatic chamber was conditioned by mixing a gas flow saturated with water with a dry nitrogen gas flow. The increase in mass of the samples was measured with a 10-minute interval on a microbalance (WXS206SDU, Mettler Toledo). Two separate DVS experiments were undertaken. The samples of the lining canvas, wax-resin of The Night Watch and reconstruction sets 1, 2 and 3 were subjected to an initial drying step (0% RH) for 300 h in the first experiment and 80 h in the second before the sorption experiment started. The RH was varied in 10% steps every 50 h up to 90%, with a final step between 90 and 95% RH at a constant temperature of 22 °C. Time steps of 50 h were chosen so that most samples would reach equilibrium sorption. Equilibrium sorption was assumed to have been reached when there was no mass change of >0.001% over a period of 60 min or a maximum step time of 50 h. In the second experiment, the RH steps 0 to 10%, 50 to 60% and 70 to 80% were shortened due to an error in the software (ca. 37 h instead of 50 h). The canvas samples were placed in aluminium pans with ground and/or paint layers facing up.

Fickian diffusion modelling

A one-dimensional moisture transport model was used to calculate water diffusion through a painting stratigraphy in the direction perpendicular to the paint surface. Ideal diffusion was assumed and given the low concentrations of water in the painting stratigraphy, material swelling was not taken into account. Each layer in the stratigraphy was considered as a continuous solid medium with a constant thickness (i.e., ideal laminate assumption). The diffusion coefficients were assumed to be constant within the experimental domain. Fick’s second law, expressed as a second-order partial differential equation, was evaluated using a method-of-lines approach. The transport model was implemented in MATLAB using a standard ODE solver. Details about the model are published elsewhere⁸.

Model parameter estimation based on experimental DVS data

A method was developed to estimate the input parameters for the water diffusion model on the basis of the DVS results. The DVS analysis yields gravimetric data over time under static RH conditions that are stepwise increased from 0 to 95% RH in 50-hour steps of 10% RH and a final one of 5% RH. The final twenty datapoints of each RH step were averaged to find the equilibrium weight, which together form the sorption isotherm of that particular sample. The weight increase was divided by the sample volume to calculate the water concentration in kg/m³. Water concentration, as opposed to relative weight increase, is independent of the density of the samples and allows for a more insightful comparison between different samples. Using the sorption isotherm, the water concentration at 95% RH (referred to as c₉₅) and the thickness of the sample (d) as input parameters for the diffusion model, a diffusion coefficient (D) could be estimated that best matched the gravimetric data. This estimation was done by systematically trialling values for the diffusion coefficient and evaluating them according to a least-squares fit criterion. D was estimated for each RH step between 30 and 70% RH and then averaged. This averaged value represents the effective diffusion coefficient (D_eff) of the sample. The limit of 70% RH was chosen to avoid possible effects such as significant swelling of hygroscopic materials, dissolution of water-soluble materials, and water clustering at high RH values, which may affect the diffusion process^25,26. Furthermore, 30-70% RH represents the limits of a typical museum climate that is relevant for this study. For the D_eff estimation, one-sided diffusion of water from the top into the sample in the DVS pan was assumed, unless specified differently.

Light microscopy

Unembedded canvas samples were examined and photographed using a Zeiss Axio Imager A2m microscope equipped with a Zeiss AxioCam Mrc5 digital camera. White light was provided by a light-emitting diode (LED) lamp with a colour temperature of 5600 K for bright field photography. Ultraviolet-induced luminescence images were obtained with a colibri.7 controller with an LED light source at 385 nm, a filter cube composed of a 385 nm excitation filter (EX G 385), a beamsplitter at 395 nm (BS FT 395), and an emission long-pass filter at 420 nm (EM LP 420).

Attenuated total reflection Fourier-transform infrared spectroscopy

Attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectra were collected on a Frontier spectrometer (Perkin Elmer) with a diamond GladiATR module (Pike Technologies). Individual spectra were collected as a single scan and at 4 cm⁻¹ resolution.

Portable microscopy

A digital microscope (Dino-Lite) was used to capture images in situ of the lining canvas of The Night Watch.

Thermally assisted hydrolysis and methylation pyrolysis chromatography

For thermally assisted hydrolysis and methylation pyrolysis chromatography (THM-Py-GC/MS) analysis, samples of wax-resin (~0.2 mg) were placed in an Eco Cup SF (Frontier Laboratories, Japan) and 3 μL of 25% tetramethylammonium hydroxide (TMAH) in methanol was added to the cup. Then the cup was placed with the sampler in the pyrolyzer. Sample material was divided and run in triplicate, partly following the procedure developed previously²⁷, here adjusted. The samples were analysed with a multi-shot pyrolyzer PY-3030D (Frontier Laboratories, Japan) that was coupled to a Thermo Trace 1310 GC system and interfaced to an ISQ 7000 single quadrupole mass spectrometer (Thermo Fisher Scientific, USA). The pyrolyzer was heated after the sample introduction from 350 °C to 660 °C at 500 °C/min, for a total time of 1 min. The pyrolyzer interface was set at 290 °C, the temperature of the SSL injector was 200 °C and the split ratio was 1:23. The purge flow of the septum was set at 0.5 ml/min. Using a Supelco SLB5 MS (20 m x 0.18 mm × 0.18 m) capillary column, the GC separation was achieved. The chromatographic conditions were as follows: 35 °C for 1.5 min, 60 °C /min to 100 °C, 14 °C/min to 250 °C, 6 °C/min to 315 °C for 2.5 min at a constant helium flow rate (0.9 mL/min). The MS parameters were set as follows: ion source temperature was kept at 240 °C; electron impact ionization (EI, 70 eV) in positive mode; transfer line temperature was 270 °C; scan range 29-600 amu with a dwell of 0.2. The Py-GC/MS data were processed with Xcalibur software (Thermo Fisher Scientific, USA) and AMDIS software (Automated Mass spectral Deconvolution and Identification System, v.2.70). The NIST 14 mass spectral library and the ESCAPE user library²⁸ were used for the mass spectral identification.

Results

The first part of the results discusses the estimation of input parameters for each layer in a wax-resin lined painting stratigraphy, i.e., varnish, paint, ground, canvas, and wax-resin lining. The input parameters are the thickness of each layer in the stratigraphy, the effective diffusion coefficient (D_eff), water concentration at 95% RH (c₉₅) and the sorption isotherm. In the second part of the results, these input parameters are used to construct four scenarios representing The Night Watch and to model the scenarios’ response to the BIZOT environmental conditions.

Parameter estimation of oil paint and varnish

For the input parameters of oil paint and varnish, data from the literature is available. In our previous work, we collected information on the sorption behaviour of oil paints⁸. Based on this, we know that the moisture sorption properties of different oil paints are comparable. The diffusion coefficient of oil paints falls in the range of 10⁻¹³ to 10⁻¹² m²/s. The equilibrium moisture content at 95% RH varies somewhat depending on the composition. In this study, values representing a typical oil paint were chosen (D_eff = 5*10⁻¹³ m²/s and c₉₅ = 50 kg/m³). Furthermore, in our previous work, we have shown that the outcome of the modelling is not very sensitive to the shape of the isotherm. Therefore, we can safely assume the shape of lead white oil paint as input, even though the paint layers in the background of The Night Watch may not be composed of lead white oil paint.

A dammar varnish was applied to The Night Watch during the restoration campaign in the 1970s. The D_eff of the dammar varnish was based on water diffusion measurements using ATR-FTIR spectroscopy (D_eff = 1*10⁻¹³ m²/s)²⁹ and the isotherm and c₉₅ were based on a gravimetric study (c₉₅ = 10 kg/m³) ³⁰.

Parameter estimation canvas and ground

Model parameters for the canvas support and ground layer were estimated based on experimental DVS data. Figure 2 shows an example of a sized canvas sample from sample set 1 (SC1). With one-sided diffusion from the top assumed, the D_eff found to best match the experimental data was 1.5*10⁻¹¹ m²/s. A photograph of this sample can be found in Supplementary Fig. 1, as well as more details on the D_eff estimation in Supplementary Table 1. DVS data of a similarly sized canvas sample from sample set 2 (SC2) was also analysed. The obtained parameters can be found in Table 1. Additional information about this sample is presented in Supplementary Figs. 2, 11, 12 and Supplementary Table 2.

Fig. 2: Parameter estimation based on DVS sample for SC1.

a Sorption isotherm of SC1 with c₉₅ indicated in the figure. The cylinder represents the sample volume, represented as an ideal laminate. b Time-based gravimetric data converted to water concentration (kg/m³) as a result of stepwise increase of the RH between 30 and 70%. The last 20 data points represent the equilibrium water concentration per RH step. The D_eff value indicated in the figure is the average of the D_eff values per RH step.

Table 1 Comparison of model input parameters of sized canvas

It is noticeable that the modelled Fickian diffusion profiles in Fig. 2b (black curves) do not precisely follow the experimental values (beige points), particularly within the first 10 hours of sorption. We present two hypotheses why Fickian diffusion does not capture the sorption behaviour of sized canvas accurately. Firstly, the experimental data exhibit a two-phase diffusion behaviour: rapid initial sorption followed by a slower sorption process on long timescales, indicative of two different sorption processes occurring at the same time. It is likely that the different materials present in the sized canvas sample, i.e., glue and linen threads, are causing these two sorption processes. In the diffusion model, this sample is assumed to be one homogeneous material with ideal sorption properties. Treating a composite material like sized canvas as a homogeneous material is a simplification. Secondly, it is possible that this sample does not obey the boundary conditions included in the model, where moisture sorption at the air-sample interface is assumed to be faster than the redistribution of moisture inside the sample. If this boundary condition is met, an emission coefficient can be dropped from the diffusion equation. A linear relation between moisture content and the square root of time would indicate that the diffusion process is diffusion-controlled, rather than emission-controlled³¹. Supplementary Fig. 22 shows indeed that only on a very short timescale this relation is linear for sized canvas. Similarly, Long & Thompson (1955) show that a linear relation between the logarithm of the water concentration difference and time indicates an ideal diffusion process. Supplementary Fig. 23 indicates that this is not the case for sized canvas. Therefore, it is likely that the sorption process is (partly) emission-controlled in this case, which our simple model does not accommodate.

The effects of these simplifications that the current model introduces are mostly limited to the short time immediately after an RH change, while the overall timescale of material response is well-described by the model. This can be seen in Table 1, where the hygrometric halftime of SC1 and SC2 are compared to values in literature. In Table 1 some variation is observed in the values for the water concentration at 95% RH (c₉₅) and effective diffusion coefficient (D_eff). Nevertheless, the values of all four samples are in the same order of magnitude. The study by Daly & Michalski reports the hygrometric halftime, t₅₀, when the RH was increased from 2 to 44%³². For comparison, the halftime under the same RH conditions was calculated for sized canvas samples 1 and 2 using the model with the input parameters stated in Table 1. It should be noted that the halftime is a function of sample thickness, which is not uniform for all four samples. Nevertheless, the hygrometric halftime can be a useful metric to facilitate comparison of diffusion and sorption properties of different samples.

To understand the input parameters of an oil-based clay ground, the water sorption of this ground applied on a Melinex sheet (G) and the Melinex sheet itself were measured using DVS. The water sorption of the Melinex was found to be negligible (Supplementary Fig. 15). For the oil-based clay ground, a c₉₅ of 97 kg/m³ and a D_eff of 4·10^-13 m²/s were found, see also Supplementary Figs. 3, 13, 14 and Supplementary Table 3. This value for the effective diffusion coefficient is in agreement with values reported for oil-based paints⁸.

Next, a two-layer system of a sized canvas with the oil-based clay ground applied on top (SC2-G) was analysed using DVS. This was done to validate the ideal laminate assumption of the model, which states that the properties of the canvas and the ground layer do not change when they are combined in a stacked system, and that their interface is perfectly straight.

However, an issue arises when ideal laminates are assumed. Firstly, the two-layer system absorbed more water than a simple stacking of the two individual layers with their corresponding c₉₅ could account for. The two-layer system absorbed 4.2 mg more water than the sized canvas alone. If all this extra water had to be absorbed into the added ground layer, the c₉₅ of the ground layer had to be raised by a factor 4. Instead, we explain this additional sorption of the two-layer system by considering that some of the applied ground layer sank between the canvas threads and fibres, rather than sitting strictly on top of the canvas. This is also visible in the cross-sections in Fig. 3c,d. As such, if we increase the sorption capacity of the sized canvas in the two-layer system from 135 kg/m³ to 183 cm kg/m³ we can account for the additional water sorption. We refer to this approach as the ‘hybrid approach’ where the sorption capacity of the canvas layer is increased, but the values for the other model input parameters are the same as those found for the individual layers, i.e., D_eff of the canvas, D_eff and c₉₅ of the ground and the sorption isotherms of canvas and the ground.

Fig. 3: Overview of hybrid approach.

a Schematic representation of the isolated samples SC2 and oil-based clay ground on Melinex (G), the two-layer system where the layers are stacked (SC2-G) and the “hybrid approach” where the c₉₅ of the sized canvas layer is increased. b Photograph of the two-layer system in the DVS pan. c Cross-section of sized canvas SC2. d Cross-section of the oil-based clay ground applied on the sized canvas. The dashed line indicates the interface between the two layers. e Experimental sorption profiles between 30 and 70% RH of the two-layer system in brown with the simulated sorption profile according to the hybrid approach in black, assuming one-sided diffusion from the bottom of the sample.

Secondly, if one-sided diffusion from the top of the two-layered sample is assumed, it appears impossible to simulate the experimental sorption data. Instead, it seems more likely that the water sorption primarily occurred through the underlying canvas, rather than through the barrier-like oil-based top layer. This is a consequence of how the samples were placed in the aluminium pans, with unsealed circumference and undersides. Looking at the photograph of the sample in the pan in Fig. 3b, it becomes clear that there is some air access to the lower canvas layer. If, instead, one-sided diffusion is assumed through the bottom canvas layer, we are able to simulate the experimental data quite well (Fig. 3e). Also, in this sample, it appears that the sorption curves are the result of two diffusion processes, a slow and a rapid one.

Impact wax-resin impregnation of diffusion rate canvas

The effect of wax-resin impregnation on the moisture sorption behaviour of canvas was investigated by comparing two samples from sample set 1: sized canvas with an oil-based kaolin ground (SC1-G) and its wax-resin impregnated counterpart (WR-SC1-G) (Supplementary Figs. 4 and 5). Figure 4 shows the normalised sorption profiles for an RH increase from 30 to 40%. Several observations can be made from these measurements. First of all, the c₉₅ of these two samples is very comparable, with 204 kg/m³ for the sized canvas with the oil-based kaolin ground and 195 kg/m³ for the wax-resin counterpart (see Supplementary Fig. 16). The thickness of the sample increased slightly with wax-resin impregnation, from 778 to 791 μm. These values suggest that the wax-resin, which probably mostly occupies free volume in the stratigraphy, absorbed very little water.

The shape of the sorption profile did significantly change (Fig. 4). The sorption profile of the impregnated system exhibits a shape more in line with one ideal diffusion process, whereas the system before impregnation showed signs of multiple diffusion processes occurring simultaneously, as we have seen before. The water concentration also showed an almost linear relationship with the square root of time as opposed to the non-impregnated counterpart (Supplementary Figs. 24–27). This indicates that the water sorption process becomes more diffusion-controlled after impregnation and agrees better with the boundary conditions of the model. This transition to diffusion-controlled transport is caused by a decreasing sorption rate after impregnation, showing that the water transport behaviour is dominated by the wax-resin. The decrease in the rate of sorption could be quantified by estimating D for the wax-resin impregnated canvas layer. To do so, the sorption of the two-layer system was simulated using the D and c₉₅ found for the oil-based clay ground from sample set 2. To focus specifically on quantifying the difference in D and to circumvent any difference in absolute sorption between the samples from the two different sample sets, the profiles are normalised in Fig. 4. The non-impregnated bilayer is simulated well assuming one-sided diffusion from the bottom and using a D_30-40%RH for sized canvas of 1.5*10⁻¹¹ m²/s and c₉₅ of 195 kg/m³, somewhat higher than the 151 kg/m³ found for the isolated SC1, in line with the ‘hybrid approach’. For the oil-based clay ground, a D_30-40%RH of 4*10⁻¹³ m²/s and a c₉₅ of 97 kg/m³ was used. Even though this ground contains kaolin instead of Rhine clay, the input parameters found in the section ‘Parameter estimation canvas and ground’ were a good fit. Figure 4 shows that for the impregnated system, the experimental data could be approximated by reducing the D_30-40%RH of the canvas by a factor 6 to 2*10⁻¹² m²/s. Per RH step, this factor varied slightly, between 6 (30 to 40% and 60 to 70% RH) and 7.5 (40 to 50% and 50 to 60% RH).

Fig. 4: Normalised sorption profiles of wax-resin impregnated and non-impregnated bilayer for RH step 30 to 40%.

The brown data points correspond to the experimental sorption profile of a bilayer of sized canvas (d = 585 μm) and oil-based kaolin ground (d = 193 μm) (SC1-G). The yellow datapoints correspond to the experimental sorption profile of the same bilayer that was wax-resin impregnated (WR-SC1-G) (d_{impregnated canvas} = 588 μm). The black lines are the simulated sorption profiles.

Parameter estimation for wax-resin lining canvas

A piece of the lining canvas from the tacking edge of The Night Watch was analysed with DVS. The wax-resin in this area was reduced using heat and absorbent tissue as part of the structural treatment of the painting in 2022. Therefore, this piece of lining canvas may not be representative of the lining canvas behind the pictorial layers of the painting. For that reason, two additional pieces of non-reduced lining canvas were analysed that originate from two paintings that received a wax-resin lining around the same time as The Night Watch in the painting conservation studio of the Rijksmuseum. The samples came from the tacking edge of Portrait of Jan Jacob Rochussen by Nicolaas Pieneman from 1845 (accession number SK-A-3802) and Portrait of Elisabeth van Oosten by Willem Jansz. Ploy from 1663 (accession number SK-A-807). Supplementary Table 7 contains more information about the paintings and their conservation history. Figure 5 show the water sorption isotherms of the three lining samples. Their sorption isotherms are very similar in shape and c₉₅ value. Table 2 shows that the D_eff of the lining canvas of The Night Watch was considerably higher (factor >10) than the other two samples, likely a result of the reduction of the wax-resin. The details of the D_eff estimation can be found in Supplementary Figs. 6–9, 17–19 and Supplementary Tables 4–6. Similar to the wax-resin impregnated canvas in the previous section (WR-SC1-G), the sorption profile of the pieces of lining canvas exhibits a shape in line with one ideal diffusion process.

Fig. 5: Water sorption isotherms of lining canvas samples of The Night Watch (NW), SK-A-3802 and SK-A-807.

The gravimetric data are converted to water concentration using the estimated density of the samples (dry weight/volume).

Fig. 6: Effects of ageing on wax-resin properties.

a Water sorption isotherms of the samples of the wax-resin of The Night Watch (in yellow) and the fresh wax-resin model system (in green). The images of the samples in the DVS pans are inserted. b ATR-FTIR spectrum of the wax-resin of The Night Watch in yellow, compared to the spectra of fresh wax-resin. The ATR-FTIR spectra are normalised on their maximum absorbance and baseline corrected at 4000 cm⁻¹.

Fig. 7: Sorption profiles resulting from an RH increase from 30% to 70% at t = 0 h indicating the four scenarios of The Night Watch.

a Global water concentration refers to the water concentration averaged over all laminates. b Local water concentration corresponds to the centre of the paint layer. The inserts show a schematic of the simulated stratigraphy. The numbers of the laminates correspond to Table 3.

Fig. 8: Water concentration difference probed at the centre of the paint layer, normalised to the equilibrium water concentration of the paint layer at 60% RH.

The four scenarios representing The Night Watch are subjected to a fluctuating RH between 40 and 60% RH in 96 h with 50% RH as the initial condition. The RH is indicated as the dotted line, corresponding to the secondary y-axis.

Fig. 9: Relation between dampening inside the paint layer of the four scenarios representing The Night Watch and the frequency of the RH fluctuation.

Dampening is relative to the equilibrium water concentration in the paint layer at 60% RH, as indicated in Fig. 8. The dashed line corresponds to the maximum frequency allowed by the BIZOT guidelines (10% RH change in 24 h; one full fluctuation between 40 and 60% RH in 96 hours, starting condition 50% RH). The grey area indicates slower fluctuations that are allowed in the BIZOT regime.

Table 2 Results of the parameter estimation and Py-GC/MS analysis of the three lining canvas samples

To confirm that the lining samples were comparable in terms of their chemical composition and level of ageing, Py-GC/MS analysis of the wax-resin was performed. Table 2 shows that the ratio of beeswax to colophony is consistent for all three lining samples. The fraction of beeswax is higher than expected based on the recipe that was used (71% beeswax would be expected in a mixture with a 5:2 ratio). We hypothesise that the resin markers are more difficult to track by Py-GC/MS analysis. Alternatively, another explanation for the high beeswax fraction could be that the beeswax and colophony in the wax-resin mixture are heterogeneously distributed. Besides composition, the py-GC/MS analysis allowed the calculation of the IDOX, an index for the degree of oxidation of the abietic acids in the resin³³, which was performed according to the method reported by Van den Berg and co-authors. The IDOX of all three lining canvas samples is around 0.50, which corresponds well to the value reported by Van den Berg et al. for a >50-year-old wax-resin sample. Importantly, all three samples show very similar IDOX values, which indicates that the wax-resin linings fall within a comparable age range and chemical oxidation state of the abietic acid derivatives used to calculate the IDOX. For that reason, we can safely use the input parameters found for the non-reduced lining samples to inform further diffusion modelling of The Night Watch.

Ageing of wax-resin

To develop our understanding of the long-term shielding performance of wax-resin linings, we performed preliminary investigations into the effect of ageing on the sorption and diffusion properties of the wax-resin adhesive mixture. Figure 6a shows the sorption isotherm of the sample of the wax-resin adhesive mixture coming from the tacking edge of The Night Watch (‘WR NW’) in yellow. The gravimetric data was converted to water concentration using the density of wax-resin in a 5:2 ratio of beeswax to colophony. The c₉₅ of the wax-resin samples reaches 20 kg/m³ (which corresponds to 2 wt%). To put this result in context, a wax-resin model system was prepared using the same ratio of beeswax to colophony, which was kept in the dark for several weeks at lab conditions (fresh WR). Figure 6a shows that the sorption capacity of fresh WR does not come close to the sorption capacity of the wax-resin of The Night Watch. To help explain this difference, ATR-FTIR spectra were recorded of the samples. In contrast to fresh WR, the ATR-FTIR spectrum of wax-resin of The Night Watch (Fig. 6b in yellow) indicates the presence of products of oxidation and hydrolysis, ageing reactions that lead to more polar groups in the material. This is particularly visible in the OH stretching region between 3000 and 3500 cm⁻¹ that exhibits a broad band for the sample of The Night Watch, indicative for the presence of alcohols. The spectrum of fresh WR shows no band in this region. Furthermore, distinct broadening of the two bands in the C=O stretching region of ester and acid groups at 1740 cm⁻¹ and 1710 cm⁻¹, respectively, is visible in the sample of The Night Watch. In addition, the relative intensity of the acid band compared to the ester band increased in the sample of The Night Watch, which is indicative of hydrolysis of the ester bond. Finally, the region around 1200 cm⁻¹ shows a broad increase in intensity in the sample of The Night Watch, which suggests the presence of various oxidation products containing C–O bonds³⁴, which is less pronounced in the fresh WR sample.

It was not possible to reliably determine the diffusion coefficient of the wax-resin samples because of their low water sorption. Therefore, no insights were gained about a possible accelerating effect of ageing on water transport. Furthermore, it is important to note that the sample of the wax-resin model system is not expected to reach full equilibrium sorption in 50 hours, the duration of each RH step in the DVS experiment. Reaching equilibrium sorption would take longer, considering the thickness of the sample (600–1000 µm) and the reported diffusion coefficient for beeswax in literature (~10⁻¹⁴ m²/s). Therefore, the true equilibrium sorption of the wax-resin model system must be slightly higher (Supplementary Fig. 20). The wax-resin sample of The Night Watch consists of samples with a larger surface area (granules) and its sorption profiles indicate that the sample nearly reached equilibrium at each RH step (Supplementary Fig. 21) For these reasons, the observations made above remain valid.

Scenario description and parameter estimation for The Night Watch

The gained insights about sorption and diffusion properties of a lined painting stratigraphy are now applied to select the most sensible input parameters for modelling the environmental response of The Night Watch. The aim of the environmental response modelling is to understand the effect of the layer build-up on the response to RH fluctuations inside the paint of The Night Watch and lined paintings in general. The choice to focus on the paint is related to the goal of future research to connect chemical deterioration in the paint to RH exposure. However, using the modelling approach, it is possible to report the water concentration anywhere else in the stratigraphy.

Here, we aim to present a complete image of the environmental response of the paint and to account for the inevitable uncertainty associated with the parameter estimation for a complex system like a historical painting. To achieve that, four layered systems are simulated to reflect different scenarios of The Night Watch (wax-resin lined and unlined) and different areas of the painting (thin and thick paint layers in the back- and foreground). The four scenarios are described below, and their associated input parameters are listed in Table 3. This table also shows the estimated thickness of layers of The Night Watch, based on observations made by the research and conservation team of Operation Night Watch. The varnish, ground and canvas layers were kept constant in thickness in all four scenarios. In all scenarios, the hybrid approach is followed to properly account for the non-ideal laminate stacking of the ground layer on the canvas support. As discussed before, we did not have access to reconstructions of canvas prepared with a lead-containing oil for this study, even though Rembrandt used this type of preparation for The Night Watch as opposed to glue sizing. Instead, the parameters are estimated based on reconstructions with a glue sizing. As the glue size has a much higher D_eff compared to lead-containing oil, the input parameters used for the canvas support reflect a worst-case scenario.

Table 3 Input parameters for environmental response modelling of The Night Watch

The first scenario reflects a stratigraphy of The Night Watch with typical layer thicknesses that includes a lining canvas and a layer of wax-resin covering the lining canvas (‘benchmark scenario’). The retarding effect of the wax-resin impregnation on the original canvas (decrease of D_eff by factor 6) was implemented. The paint layer was chosen to be 50 µm in thickness, which could be indicative of relatively thin paint layers in the background of the painting. The properties of the lining canvas are based on the findings of the lining canvas sample of SK-A-3802, which reflect a lining canvas with wax-resin impregnation after ca. 50 years of natural aging. In the absence of a value for D_eff of naturally aged wax-resin, this parameter was based on the study by Cruces et al. of a fresh beeswax and colophony mixture¹¹. The isotherm and c₉₅ of the wax-resin layer were based on the DVS measurements of the wax-resin samples of The Night Watch.

The thickness of the paint layers in The Night Watch varies considerably, particularly when considering the impasto painting technique of Rembrandt. In the second scenario (‘thick paint scenario’), all input parameters and layer thicknesses are the same as the benchmark scenario, apart from the thickness of the paint layer. Here, a paint layer of 500 µm is modelled with the same properties as the benchmark scenario, to understand the effect of painting technique on the environmental response inside the paint layer.

To learn more about the future performance of the shielding capacity of wax-resin linings, a scenario was selected that represents a worst-case ageing scenario of the wax-resin lining (‘aged lining scenario’). Currently in The Night Watch, the layer of wax-resin at the reverse is very heterogenous in thickness. In some areas, the lining canvas is completely covered in wax-resin, whereas in other areas the lining canvas is exposed (Supplementary Fig. 10). If cracks appear in the wax-resin due to further ageing and subsequent embrittlement, the lining canvas becomes exposed in more areas. To understand this effect on the environmental response in the paint layer, the wax-resin layer is omitted completely in this scenario. Furthermore, to simulate a scenario where the diffusion rate of water in the wax-resin has increased significantly due to ageing, we select the D_eff found for the reduced wax-resin lining sample described in section ‘Parameter estimation for wax-resin lining canvas’. Whether the diffusion coefficient of wax-resin would increase to that extent due to ageing, we have not been able to confirm with our preliminary ageing experiments.

To contribute to our understanding of the general effect of wax-resin lining on the sorption and diffusion properties of the total system and the response of the paint layer, we selected a scenario without lining (‘no lining scenario’). Here, the entire lining canvas is omitted, and the input parameters of the canvas are based on SC1. We have just seen in the previous sections that the sorption behaviour of sized canvas that is not wax-resin impregnated is not well captured with our simple model. Therefore, the no lining scenario serves solely as a rough comparison to the more accurately modelled lined scenarios.

Response of The Night Watch scenarios to RH increase

With the input parameters for the four scenarios established, it is now possible to calculate the response of the layered systems to different RH conditions. First, a situation was simulated where the RH is increased from 30% to 70% at time = 0 h. Figure 7a shows the water concentration averaged over all laminates in the stratigraphy in response to the RH increase. We refer to this as the global water concentration, which is comparable to gravimetric data. The retarding effect of the wax-resin lining is clearly visible when comparing the no lining scenario to the other three scenarios. The aged lining scenario is approaching the no lining scenario, but still exhibits slower sorption thanks to the presence of the lining canvas (layer 5). Much slower sorption is visible in the benchmark scenario with an intact layer of wax-resin at the bottom of the stratigraphy (layer 6). The thick paint layer scenario, with a paint layer that is 10 times thicker compared to the benchmark scenario exhibits the slowest response of all. Both the benchmark and the thick paint layer scenario have an intact layer of wax-resin at the bottom of the stratigraphy, and a paint and varnish layer on the top. The large amount of water that can be absorbed into these systems, particularly in the two canvas layers, has to travel through these barrier-like layers on either end of the stratigraphy. This is the reason why these two systems take such a long time to reach their equilibrium sorption.

The advantage of a computational approach is that the water concentration at any location in the stratigraphy can be probed. Figure 7b shows the local water concentration probed in the centre of the paint layer (layer 2). Again, it can be seen that the paint layer in the no lining scenario and the thick paint layer scenario respond the fastest and slowest of all scenarios, respectively. It is important to note that the paint layer in all four scenarios will eventually reach the same equilibrium water concentration at 70% RH (23.6 kg/m³). Looking at the aged lining and the benchmark situation, a different picture emerges in the local sorption compared to the global sorption, particularly in the short term. We observe that below 30 hours the response in the paint layer of the benchmark and the aged lining scenario is roughly the same. This is in contrast to the global sorption, where the benchmark situation always exhibits much slower sorption than the aged lining situation. The shape of the local sorption curves can be explained as follows. Sorption in the benchmark scenario happens predominantly from the top of the stratigraphy (through the varnish). In fact, the depth profile in Supplementary Fig. 28 shows that there is very little water travelling beyond the ground layer into the impregnated canvas and lining layers due to their low D_eff. In contrast, water sorption in the aged lining scenario occurs much more gradually, through both the top and the bottom of the stratigraphy (Supplementary Fig. 30). This means that, in the aged lining scenario, water absorbed through the varnish layer is able to cross through the paint layer towards the underlying canvas layers. This process results in a temporarily low water concentration in the paint layer. After ~30 hours in the aged lining scenario, water starts building up in the paint as well, resulting in an increase in sorption rate, visible in Fig. 7b. To investigate the shape of the aged lining sorption profile further, two scenarios were simulated where no diffusion was allowed via either the bottom or the top of the stratigraphy (Supplementary Fig. 32). These simulations confirm that the water concentration profile of the aged lining scenario is a combination of sorption through the top and the bottom of the stratigraphy, leading to a sorption process that starts fast, slows down between approximately 10 and 30 hours, and accelerates again after 30 hours. These results indicate that the canvas and lining canvas in the aged lining scenario act as a water reservoir, effectively slowing down the response of the paint layer.

Response of The Night Watch scenarios to RH fluctuation

Next, the response of the multi-layered systems to a fluctuating RH was investigated. The four scenarios were subjected to an RH that fluctuates between 40 and 60% with a change of 10% RH per 24 h. This is the maximum frequency allowed by the BIZOT climate guidelines. Figure 8 shows the RH fluctuation as the dotted line, corresponding to the secondary y-axis. For each scenario, the water concentration at the centre of the paint layer is probed and presented as normalised water concentration difference. This means that 0 on the primary y-axis corresponds to the paint layer equilibrium water concentration at 50% RH and 1 to the paint layer equilibrium water concentration at 60% RH. The corresponding depth profiles are found in Supplementary Figs. 33–36.

It can be observed that the amplitude of the fluctuating water concentration in the paint layer is dampened and delayed when the paint layer is part of a layered system. The dampening and delay in each scenario are summarised in Table 4. A slight downward sloping trend is visible in the sorption curves. When running a longer simulation, the trend stabilises. The same observation was found in our previous study, and it seems to be an effect of the isotherm shape⁸. The values in Table 4 are therefore based on the second peak in the sorption profiles. It is noticeable that the sorption profile of the paint layers is not symmetric in absorption and desorption, which is due to the shape of the lead white oil paint isotherm. The no lining scenario provides the least amount of dampening and the thick paint layer scenario the most, as expected. Also, the longest delay is visible in the thick paint layer scenario. Surprisingly, the aged lining scenario provides very similar dampening as the benchmark scenario. This effect is related to the reservoir function of the underlying layers in the aged lining scenario that buffers the response of the paint layer in the short term. The no lining, aged lining and benchmark scenario all exhibit a similar delay.

Table 4 Delay and dampening of the water concentration in the centre of the paint layer in each scenario in BIZOT conditions

Response of The Night Watch scenarios to RH fluctuations with varying frequency

The dampening and delay observed in Fig. 8 are caused by the relatively slow diffusion of water inside a layered painting, causing slow equilibration with its surroundings. The magnitude of the dampening and delay are not only influenced by the properties of the layers, but also by the frequency of the RH fluctuations. Figure 9 provides further insight into the relationship between frequency of the RH fluctuations and dampening inside the paint layer. From this figure, we learn that fast fluctuations have a limited impact on the water concentration in the paint layer in the layered systems. Interestingly, the four scenarios seem to converge at high frequencies. A 1/24 h frequency corresponds to a full fluctuation between 40 and 60% RH in 24 h, or to a 10% RH change in 6 hours. At this frequency, the dampening of water concentration in the paint layer in all scenarios is >80% compared to the equilibrium water concentration at 60% RH. At the maximum frequency as allowed by BIZOT, the dampening in the paint layer in the scenarios representing The Night Watch with wax-resin lining is between 60 and 95%. Here, the no lining scenario is already providing much less dampening on the paint layer (only 25% dampening compared to the equilibrium sorption at 60% RH). At a slow fluctuation of 1/384 h, the no lining scenario provides almost no protection for the paint layer anymore against influences from the environment. Finally, it can be observed that the curves of the benchmark and aged lining are very similar at the maximum BIZOT frequency (1/96 h) and faster. This is because the reservoir-effect of the underlying layers in the aged lining situation only occurs in the short term (Fig. 7b). These findings indicate that, contrary to our first intuition, the aged lining scenario provides similar shielding as the benchmark situation at the fastest allowed frequency in the BIZOT regime, as a result of the combined behaviour of the multi-layered system.

Discussion

The transport behaviour of water in complex wax-resin-lined painting stratigraphies could be approximated by ideal diffusion and an ideal laminate assumption. The challenge of finding reliable parameter values was addressed by acquiring DVS data on reconstructions and historical samples. We have shown that putting together our first estimates generated valuable insights into the response of layered systems to fluctuating environments. Particularly when simulating complex multi-layered systems in the scenarios representing The Night Watch, the insights generated in this computational approach surpassed our intuition. This became apparent when comparing the sorption behaviour of the aged lining scenario to a scenario corresponding to a typical intact lined painting. The observations of the reservoir function of the support layers in the aged lining scenario show the added benefit of a computational approach. In future research, it would be interesting to explore experimental ways to validate this finding.

There are several ways in which the current model can be improved, for example, by extending it to two or three dimensions, incorporating swelling, allowing multiple diffusion coefficients to simulate composite materials or variable diffusion coefficients that are dependent on water concentration or temperature. However, also with a more sophisticated model, significant uncertainty remains associated with the parameter estimation of painting materials, as they are not standardised materials and often undergo significant ageing. More refined values for the model parameters can be obtained by sealing the samples in the DVS pans, which would lead to more certainty on the direction of water diffusion. Furthermore, the next step in this research would be to investigate how sensitive painting materials are to changes in their sorption and diffusion properties as a result of ageing. Preliminary experiments to understand the sensitivity of wax-resin to ageing have shown that ageing of this material can lead to increased water sorption capacity. In future research, it would be relevant to include backing boards in future investigations into the environmental response of lined paintings, as they are often installed with the aim to further reduce environmental exposure.

The long-term goal of this research is to couple the water concentration in the paint layer and other layers in the painting stratigraphy to chemical reactivity and to mechanical response. A quantitative understanding of the influence of water on chemical and mechanical change is required to inform conservation decisions. This work provides a first step towards this goal.

Based on the results presented in this study, it is possible to formulate answers to the two preventive conservation questions posed in the introduction.

What is the environmental response of The Night Watch and lined paintings in general to the climatic conditions according to the BIZOT guidelines?

The environmental response of a complex multi-layered system is influenced by the water sorption and diffusion properties of each layer, the thickness of the layers, the stacking order of the layers, and the amplitude and frequency of the RH fluctuation. Our computational approach, based on experimentally derived input parameters, allows us to explore the environmental response in different hypothetical scenarios of The Night Watch. In this work, we focussed on water concentration in the paint layer, although the computational approach allows calculating the water concentration in any layer of a painting stratigraphy.

We have shown that the layers surrounding the paint layer provide dampening of the paint’s environmental response. During the fastest RH fluctuation allowed by the BIZOT guidelines (RH fluctuation between 40-60% RH, max. 10% RH change per 24 h), the maximum water concentration inside a paint layer is dampened by 25% by the surrounding layers (varnish, ground and canvas support). The dampening effect on the paint layer response is increased to 70% by the presence of a wax-resin lining in these RH conditions. Furthermore, the paint layer itself also has a shielding effect on its own response. In a stratigraphy with a thick paint layer (500 µm) in BIZOT conditions, the response at the centre of this paint layer is dampened 10% more than in a stratigraphy with a thin paint layer of 50 µm. This result highlights that the environmental response in the stratigraphy can vary in different parts of the painting.

Moreover, this study indicates that the paint layer experiences more dampening at higher frequency RH fluctuations. If a 10% RH change occurs in 6 hour or less, almost no variation in water concentration in the centre of the paint layer is expected. The dampening in the paint layer in a typical wax-resin-lined painting at this frequency is more than 90%. Even in an unlined painting, the dampening in the paint layer is in that same order. Thus, at this frequency, the effect of the lining on the environmental response in the paint layer is minimal, instead time is the dominating factor. At lower frequencies, which are allowed in the BIZOT indoor climate, the dampening on the paint layer response overall becomes less and the effect of the lining becomes more important. At an RH change of 10% per 96 hours, the paint layer in an unlined painting experiences almost no shielding from the environment by the surrounding layers. In lined paintings, approximately 20-60% dampening still occurs.

How does ageing of the wax-resin adhesive mixture affect the future shielding capacity of the lining against humidity fluctuations?

This study indicates that ca. 50 years of natural ageing of the wax-resin mixture in a museum environment can lead to an increased water sorption capacity of the wax-resin. The effect of ageing on the water diffusion properties of the wax-resin could not be established. If it is assumed that ageing of the wax-resin leads to an increased water diffusion rate and to the formation of cracks in the wax-resin layer covering the lining canvas, we observe that the rate of water sorption into the painting stratigraphy as a whole increases significantly. However, the computational results also suggest that more gradual water sorption in an aged lining scenario leads to an additional shielding effect on the paint layer response in the short term. This is why the effect of ageing on the shielding capacity of the lining seems more moderate in fluctuating RH conditions than first expected.

Overall, this study enhances our general understanding of the behaviour of complex multi-layered systems in fluctuating environmental conditions and by doing so, aims to contribute to a scientific foundation for preventive conservation decision-making.