Water-vapour sorption of welded bond-line of European beech and Scots pine

The wood–water interactions of welded bondlines of European beech (Fagus sylvatica L.) and Scots pine (Pinus sylvestris L.) were in this paper studied for the first time with dynamic vapour sorption equipment. The aim of this study was to characterize the water sorption in the welded bond-line and to define to which extent it deviates from water sorption of the unwelded wood. The objective was to provide deepened knowledge about water sorption of the welded bond-line, which could be used to improve the moisture resistance of welded wood in the future. The welded wood generally had lower equilibrium moisture contents than the unwelded wood. The welded bond-lines of beech and pine showed greater hysteresis than the unwelded wood from 0 to 55 % relative humidity. All specimens showed faster adsorption than desorption. However, the welded wood showed slower adsorption but faster desorption than unwelded wood. The time to complete half of the fractional change inmoisture content (E(t) = 0.5) increased as the moisture content increased. The adsorption diffusion coefficients of beech and welded beech were higher than those of pine and welded pine up to 50 % and 40 % RH, respectively. In desorption, pine had a higher diffusion coefficient than beech in the whole range of 85–0 % RH. Analogously, welded pine had a higher diffusion coefficient than welded beech in the range of 85–5 % RH. In contrast to the desorption, the welded wood always had lower adsorption diffusion coefficients than the corresponding unwelded wood. The diffusion coefficients showed irregular patterns in some ranges of the RH. Therefore, it was hard to make a clear conclusion about the water-sorption behaviour of the specimens based on the defined diffusion coefficients.


Introduction
First pioneered in the 1980s, wood-welding technology marked a new epoch in the wood joining industry, and welded wood raised interest mainly in the furniture industry. In this energy-efficient process, joints are produced by rubbing two timber surfaces under an external pressure at a high frequency . Welded wood as an all-wood assembly, with neither adhesive nor metal fasteners, offers the opportunity to improve the building materials' environmental performance and increase their reusability and recyclability. However, to date, there have been few studies related to structural applications of the welded wood, in part due to the vulnerability of the welded bond-line to damage from moisture (Vaziri 2011).
Examination of the weld interface and of the adjacent areas shows structural and chemical changes in the wood material due to friction welding. These changes are important for the mechanical and moisture-related properties of welded wood . Welding involves destruction of the cellular structure of the wood, creating a dense amorphous mass containing portions of the cell walls. Under the influence of mechanical pressure and high temperature, the bond-line is densified, and the cell walls collapse (Stamm et al. 2005), but the densification is less pronounced in latewood.
The microstructural and mechanical properties of the welded bond-line are highly related to heat generation in the weld interface which is associated with welding parameters and wood properties. A study on welded Norway spruce (Picea abies (L.) Karst.) showed that the welded bond-line consists of a molten zone and a heat-affected zone (Figure 1). Ganne-Chédeville et al. (2006) measured the thicknesses of the different bond-line zones in welded radial surfaces. In the middle of the bond line, 155 µm of wood material was totally melted (molten zone), and a zone with a thickness of 1.076 µm outside it was only heat affected.
An effective indicator of the quality of the welded bondline is the density. Wood is a porous material that can be compressed until the density reaches that of the cell wall material, i.e., about 1500 kg/m 3 . The density of the welded bond-line of European beech (Fagus sylvatica L.) (750 kg/m 3 ) is about 1000 kg/m 3 , but in rotary friction welding, the bond-line density may reach values between 1350 kg/m 3 and 1500 kg/m 3 (Pizzi et al. 2004). Vaziri et al. (2015) studied the bond-line density profile of welded European beech using nano X-ray computed tomography (CT). The bulk density of wood in the welded bond-line was increased to approximately 1000 kg/m 3 , whereas the cell-wall density was decreased to about 1100 kg/m 3 due to degradation of the cell-wall material.
Wood is a hygroscopic material, meaning that it adsorbs and desorbs water vapour at different vapour pressures of the ambient air (Siau 1995). The adsorption and desorption of water vapour by wood until reaching the equilibrium moisture content (EMC) generally result in dimensional instability due to swelling and shrinkage and a reduction in strength (Skaar 1988). Repeated dimensional changes by frequent variations in wood moisture content (MC) will eventually lead to crack formation in wood and/or bondline and joint failure Hoadley 2000;Vaziri and Sandberg 2021;Vaziri et al. 2020).
At least two different mechanisms govern the moisture movement in the wood below the fibre-saturation point: water-vapour diffusion in the cell lumen and pit openings and bound-water diffusion in the cell-wall substance (Avramidis 2007;Siau 1995;Skaar 1958). To separate the diffusion of bound water from the diffusion of water vapour, very thin wood specimens must be used as described in a range of sorption experiments by Christensen and Kelsey (1959), and Kelly and Hart (1970) using a vacuum apparatus.
Direct measurements of bound-water diffusion in the cell wall are difficult to perform. This is because of cellwall geometry and the very slow diffusion of bound water compared to vapour diffusion in the porous structure (Hozjan and Svensson 2011). Hence, mathematical models are usually used to estimate it by inverse analysis. An overview of the wood drying modelling during the past 30 years shows that Fick's equations have been a classical way of explaining sorption kinetics in thin specimens of adhesive and wood (Engelund et al. 2013).
The methods for sorption assessment of wood are not standardised and can vary a lot. Thybring et al. (2019) presented the state-of-the-art measurements that are used to advance our understanding of water-vapour sorption in wood. The dynamic vapour sorption (DVS) technique has shown its ability to measure water sorption in wood with much less labour and potentially higher accuracy than the conventional gravimetric methods (Altgen et al. 2020;Glass et al. 2018;Grönquist et al. 2019;Humar et al. 2020;Williams 1995). The DVS equipment provides fast and precisely an abundance of highly reproducible data based on the rate of change of the specimen's mass over time as the specimen adsorbs or desorbs moisture until it approaches an equilibrium state. These data can be used to supply sorption isotherms over a wide range of relative humidity (RH), to determine sorption kinetics, and thereby provide further insights into the phenomenon of hysteresis and diffusion (Popescu et al. 2014).
Several studies have used DVS to examine wood and related cellulosic materials (Glass et al. 2018;Grönquist et al. 2019;Hill et al. 2013;Humar et al. 2020;Vetter et al. 2010). Nevertheless, presenting a complete overview of adsorption and desorption of water in wood in the hygroscopic range of 0-95 % RH are few (Fredriksson and Thybring 2018;Venkateswaran 1970;Xie et al. 2010). In addition, results of DVS experiments made on welded and unwelded wood have not been compared in the literature. To the best of the authors' knowledge, there are no publications regarding DVS experiments on welded wood. This work presents the first application of DVS for water-sorption analysis of welded wood. The objective is to find out how water sorption in the welded bond-line deviates from that in unwelded wood.  (Stamm et al. 2005).
In this study, some aspects of the water sorption in the hygroscopic range of 0-95 % RH are presented, such as kinetics of mass exchanges (i.e., sorption kinetics), vapoursorption isotherms, and hysteresis analysis. Additionally, the diffusion coefficients of welded and unwelded European beech and Scots pine (Pinus sylvestris L.) are compared.
The characterisation of the water sorption phenomena can improve our understanding of the wood-water relations and thus, allow researchers to develop drying schedules and improve the quality of timbers. This knowledge is necessary to develop welded wood into an engineering material and to introduce it into the market. The present work needs continuous research in the future.

Preparation of specimens
The specimens were prepared from defect-free European beech (F. sylvatica L.) and Scots pine sapwood (P. sylvestris L.) with planed surfaces and dimensions of 20 mm × 20 mm × 230 mm (radial (R) × tangential (T) × longitudinal (L)), grown outside Skellefteå in the north of Sweden. All specimens were made of the same tree.
The specimens were conditioned for two weeks at 20°C and 65 % RH in an environmental chamber to 12 % MC. They were welded together in pairs to dimensions of 20 mm × 40 mm × 230 mm (longitudinal welding of two radial faces) using a linear vibration welding machine, Branson model M-624 (Branson Ultraschall, Dietzenbach, Germany) with a frequency of 240 Hz and settings according to Table 1. The most influential welding parameters were selected based on earlier studies (Vaziri et al. , 2012. The appropriate ranges of the parameters that could result in the maximum shear strength of the welded joints were defined by screening tests. The non-welded wood specimens were used as references. Specimens can be cut into small pieces or be grounded for DVS measurement. Glass et al. 2017 state that differences in specimen preparation may not have a large effect on the EMC but may affect the time to reach equilibrium (Glass et al. 2017). Grinding of the specimens and the size of the particles influence the hygroscopic properties of not only wood but also other bio-based materials (Hebrard et al. 2003;Hill et al. 2009;Murrieta-Pazos et al. 2014;Murr and Lackner 2018).
To make thin specimens of welded wood, the welded bond-line should be opened to get access to their welded interface. The welded bond-lines of the specimens were opened with a steel chisel and carefully cleaned with hexane before each use ( Figure 2C). Welded bondlines are generally thin and brittle and cutting them into thin strips to eliminate the non-welded wood adjacent to the welded areas is difficult. The welded areas were cut into thin strips with dimensions of 20 mm length and 6 mm width with a sliding microtome. It was attempted to cut all the specimens with identical dimensions, but due to the rigidity of welded wood, some of them got irregular edges that could be one of the error sources in the DVS experiment. After cutting, the final thicknesses of the strips were on average 0.6 mm throughout and weighed in average approximately 4 mg ( Figure 2D).
The unwelded wood specimens (references) were cut in the longitudinal direction from the outer surface of the same welded wood pieces. They were made in the same sizes as the welded specimens and weighed in average approximately 3 mg.

Sorption experiment
Dynamic vapour sorption measurements were performed using an automated sorption balance device (DVS Advantage ET 85, Surface Measurement Systems Ltd.). This equipment allows the determination of sorption isotherms at a constant temperature using a range of pre-set RH levels. The instrument has a microbalance with a resolution of 0.1 µg, and the specimen is placed in a stainless-steel mesh basket suspended from the balance. Specimen holders were connected to the microbalance by hanging wires on two arms in a chamber, both being thermostatically controlled.
In each DVS run one pair of the specimens consisting of welded wood and corresponding unwelded wood, as a reference, were tested. The specimens were pre-dried before measurement for 10 h at 40°C and 0 % RH. The specimens were exposed to a series of RH steps, from 0 % to 95 % in increments of 5 % and 10 % RH, followed by the same steps in reverse order. The dry mass m 0 of each specimen, which was used as reference mass is listed in Table 2. The specimens were exposed to a nitrogen carrier gas of grade 5.0 with a flow rate of 200 sccm.
Glass and co-workers have highlighted that the most common mass stability criterion used as a stop criterion for determining equilibrium in DVS experiments mischaracterizes the EMC. They observed that changes in moisture content at long hold times affected EMC more than 0.1 % MC. Hence, most prior DVS data that were taken with hold times of either 60 min or until the change in moisture content was <0.002 % min −1 over a 10-min period could not capture the actual form of the sorption curves (Glass et al. 2017(Glass et al. , 2018. Considering Glass' and co-workers' recommendation (Glass et al. 2017), the stop criterion (d m /d t ) used in this study was more straightened than the usual standard and identical to the stop criterion used by Grönquist et al. (2019). Equilibrium in each step was defined to be reached at a mass change per time (d m /d t ) of less than 0.0005 % min −1 over a 10 min window or a maximal time of 1000 min per step.
Data on mass change was acquired every 20 s. The running time, target and actual RH, target and actual temperature, and specimen weight were recorded throughout the isotherm run. Figure 3A shows the relative humidity and temperature stability as a function of time during hold time. The temperature and RH in the chamber were almost stable throughout the long hold time. Figure 3B shows that the error in holding the target RH constant was larger in desorption than that in adsorption. Figure 3C shows that it took some minutes for RH to commence proceeding into the next step. This can also be seen in Figure 4A. At the Table : Welding procedure and classification of the specimens.
The initial welding pressure, p w , was applied during the first welding time, t w ; followed by the second welding pressure, p w , during the second welding time, t w ; and finalising with the holding pressure, p h , during the holding time, t h . NOS denotes the number of specimens.
beginning of this finite time of RH transition, the corresponding MC was not initially moving towards a static equilibrium point. That might be explained by how the measurement data was acquired. The data was not acquired instantaneously but was acquired as a moving average through the running time of the experiment for making the signal more stable. The actual steady-state RH value differed from the target value. The actual RH of 87 % corresponded to the target RH of 85 %, whereas the actual and target RH of 90 % are almost at the same level. Figure 3D shows an example of the calibration of the DVS device at the beginning of the measurement which in this case took 40 min.

Measurements of sorption kinetics
Sorption kinetics describes the change in mass and (thus MC) over time in the approach to equilibrium. The MC could be calculated using where MC(t) denotes moisture content (%) at time t (s), M(t) (g) denotes the mass at time t (s), and M 0 (g) denotes the initial mass. A typical example of sorption kinetics is shown in Figure 4.

Fractional change of moisture content
A convenient way of expressing the rate of water vapour sorption is plotting the fraction of the total change in MC, E(t) as a function of time or the square root of time. The E(t) is calculated as where, M(∞) (g) is the mass at equilibrium. The correct values of E(t) require that the equilibrium has been reached.

Determination of a constant diffusion coefficient (D)
2.5.1 Short background: Diffusion coefficients of water in wood changes over time, but assuming the coefficient to be constant makes solving the diffusion problem easier. Hence, the value of D should be as representable as possible for the entire range of E(t) = 0 to E(t) = 1. There are a few different methods for doing this in the literature, some of which use the E(t) = 0.5 relation.
In this paper the "initial rates of sorption and desorption" method (IROSAD) is used as it is described in Section 10.6.7, Crank (1975). Note that the term "sorption" in Crank (1975) corresponds to the term "adsorption" in this paper. The terminology varies somewhat in the literature, and this topic is to some extent discussed by Thybring et al. (2019). The IROSAD method should under the right circumstances give similar results to the other methods (Crank 1975). This method is based on E(t) for small values of t, which is why the "small time" solution to the diffusion problem is used.
2.5.2 "Short-time" solution to the diffusion problem: The specimens used in this study were plane thin sheets of wood and welded bond-line. The thicknesses of the sheets were much smaller than their lengths and widths to enable neglection of the edges' diffusion interaction with the surroundings. Hence, almost all diffusion interaction took place through the plane faces of the specimen. The MC was constant and equal at the surfaces of the specimens like the RH of the ambient air was constant after a stepwise change. Moreover, the distance between centre of the specimen and the surfaces were assumed to be symmetrical (−L ≤ x ≤ L).
The short-time solution of the diffusion problem constrained by the above given description is Equation (3) where D (m 2 /s) is the diffusion coefficient with MC as driving potential and L (m) is half of the specimen thickness (corresponding to distance from the centre of the cell wall to the lumen surface).

2.5.3
Derivation of the computation of the diffusion coefficient: For a thin plate with a thickness of 2L, Equation (3) for t ≈ 0 can be approximated to

Specimens Replicates
Moreover, according to p. 245 Crank (1975), the sorption curve is in practice approximately linear when plotted against up to E(t) = ½. Applying the linearity assumption,

RH Target [%]
) as a function of the square-root of time.
which together with Equation (5) gives and solving Equation (8) for D gives The main reason for choosing the IROSAD method was twofold, (1) With this approach one does not have to bother for how many terms in the series the approximation is acceptable, since the series vanish for x ≈ 0, (2) The fractional change of MC in Appendix Figures A1-A3 indicates that most of the curves are linear up to t ½ which is making the chosen method valid.

Sorption isotherm
The sorption isotherms of the specimens and their hysteresis (obtained by subtracting the adsorption from the desorption-isotherm loop for EMC) are presented in Figures 5 and 6. The isotherms were plotted for individual RH steps in which the EMC was approached. The welded specimens showed similar isotherm curves to the unwelded specimens, the typical sigmoidal shape which is commonly observed for wood.
The welded specimens generally had lower EMC than the unwelded specimens in the whole studied range of RH.
The maximum EMC values at 95 % RH were 21 % for beech, 15 % for welded beech, 22 % for pine, and 16 % for welded pine ( Figure 5). Since welded wood is to some extent comparable to thermally modified wood, this result is consistent with a similar DVS study by Humar et al. (2020), where the thermally modified Norway spruce showed lower EMC values than the untreated wood.
The lower EMC values for the welded wood should be related to heat and friction altering of wood cell wall components. Hemicellulose is the most degradable among the wood constituents, and lignin is the most stable polymer during thermal treatment (Stamm 1956). A longstanding explanation for decreasing water adsorption of thermally modified wood, introduced by Urquhart and Williams (1924), is related to sorption site availability in thermally modified wood (Stamm 1964). Based on this

EMC [%]
Beech Welded Beech Pine Welded Pine Figure 6: Hysteresis plotted as a function of relative humidity of the welded and unwelded beech and pine.
theory, the presence of moisture and suitable heat during the welding can result in auto-condensation reactions and cross-linking in wood components that decrease the number of free hydroxyl groups. Altgen et al. (2018) showed that the further reduction in EMC of heat-treated wood at 93 % RH could be a result of cross-links in the cell wall matrix and thermally removal of polar sites in wood. The cross-linking leads to a reduction in the number of simultaneously active OH groups, but not a further reduction in the hydroxyl accessibility. Figure 6 shows sorption hysteresis of the wood specimens as a result of higher EMC in desorption than in adsorption at equal ambient climate conditions. The sorption data of the specimens are presented in Table 3.
From 0 % up to 50 % RH, the welded specimens showed greater hysteresis than their respective references (unwelded), and the greatest hysteresis belonged to welded beech. This trend was changed for beech above the given RH (from 60 % RH) so that the hysteresis of beech became greater than of welded beech. Hill et al. (2010) explained hysteresis from the time lag in reaching thermodynamic equilibrium states for the cell wall molecular configurations, which are disturbed by incoming and departing water molecules in the adsorption and desorption process. An interesting part of the Hill et al. (2010) theory is that the time lag can be related to the rigidity of the cell wall, and the rigidity can be further related to the lignin composition due to its cross-linking structure. According to this theory, more lignin content would cause more hysteresis. Gfeller et al. (2003) showed that the temperature during welding exceeds the glasstransition point of lignin and hemicelluloses. The presence of moisture and suitable heat during the welding and thermal modification can lead to softening and concentration of more lignin in the weld interface.
The isotherms show that there is an unequal moisture distribution in the intersection area between the welded bondline and the adjacent wood. This can lead to restrained swelling and shrinkage and consequently to internal stresses and cracking in the bond-line.

Sorption kinetics
To provide further insights into the phenomenon of water sorption, the kinetics of the mass change in time was monitored for the entire sorption process, and the results were presented in Figures 7 and 8. All specimens exhibited faster adsorption than desorption.
In comparison, the welded specimens showed slower adsorption but faster desorption than their respective reference specimens. The structural change induced by welding can explain the change in sorption kinetics.
The fractional changes in moisture content E( t) for a sequence of adsorption and desorption steps in the hygroscopic range of 0-95 % RH were measured for pine and beech (see "Appendix").
The time to reach E(t)=0.5 increases as the moisture content increases. The rate of adsorption for successive moisture increments over different RH ranges decreased as the value of the initial moisture content increased. The non-Fickian features, cf. Figure 11.1 in Crank (1975), at high RH values in Figure 9, and A1-A6 give a strong indication for the presence of latent heat transfer effect (Crank 1975;Willems 2022). According to this theory the involved heat exchange of MC-changes limits the sorption rates. Therefore, the Fickian diffusion problem with a stepwise RH change in the ambient must be solved with special boundary conditions. This appears to be generally the case for DVS at high RH where Equations (3) and (9) are no longer valid (Willems 2022). For more illustrations of this phenomenon, see This result is to some extent consistent with the diffusion coefficients estimations in Figure 10 and Table 3, where the diffusion coefficients decreased with increasing RH target from about 20 to 85 % (increasing MC, shown in Figure 8). Similar study on ash (Eucalyptus regnans F. Muell.), oak (Quercus alba L.), and yellow poplar (Liriodendron tulipifera L.) in a vacuum sorption balance showed that diffusion coefficients decreased during adsorption (Christensen 1960;Kelly and Hart 1970). However, the temperature changes in the vacuum sorption method could affect the rate of sorption and thus the resulting diffusion coefficient. The effect of temperature on sorption rates is not only present in vacuum, but also evident under condition of room temperature and atmospheric pressure (Willems 2022).
The direct (experimentally) measurement of the diffusion coefficient of the cell walls in similar materials to wood such as wood-derived polymers showed that the diffusion coefficient increased with increasing RH (Heikkilä et al. 2012;Stamm 1956). Therefore, the diffusion coefficient of the wood cell wall was expected to increase during adsorption and decrease during desorption.
However, the estimation of the diffusion coefficients in Figure 10 shows the discrepancy between the directly measured diffusion coefficents in the literature and the in this paper determined coefficients using a Fickian model. The discrepancy between the RH dependence of steadystate versus unsteady-state diffusion coefficients has been reported by Christensen and Kelsey (1959), Wadsö (1993), and Zhan et al. (2019).

Analysis of the diffusion coefficients
Surprisingly few studies report the differences in adsorption and desorption of thin specimens of wood. Figure 10 shows that in desorption, pine had a higher diffusion coefficient than beech in the whole range of 85-0 % RH. Analogously, welded pine had a higher diffusion coefficient than welded beech in the range of 85-5 % RH.

Desorption
The results were less consistent in comparing welded beech to beech, and welded pine to pine. From 85 % to 60 % RH the coefficients were larger for unwelded wood, and conversely from 40 % to 0 % RH smaller for unwelded wood. The results were irregular for pine and beech in 50 % and 90% RH.
There was a general trend of decreasing diffusion coefficients for all specimens from 90 % to 70 % RH accompanied by an increase from 60 % down to 25 % RH, after which the trend was decreasing again.

Adsorption
The adsorption diffusion coefficients of beech and welded beech were higher than those of the pine and welded pine up to 50 % and 40 % RH, respectively. From there up to 95 % RH the coefficients became smaller for beech and welded beech than those of the pine and welded pine.
In contrast to the desorption, the welded wood always had lower diffusion coefficients than the corresponding unwelded wood.
There was a general trend of increasing diffusion coefficients for all specimens from 0 % to 20 % RH accompanied by a decrease to 85 % RH, after which some flattening took place.

Summary
The irregularities of the diffusion coefficient in some ranges of relative humidity illustrated that a Fickian diffusion model cannot explain the sorption process in the entire range of 0-95-0 % RH.

The reaching of equilibria
The stop criterion used in this study was stricter than the usual standard. However, Figure 9 and A1-A6 show that welded wood and beech typically needed longer hold times to reach equilibrium. Moreover, the specimens generally  The fact that some of the samples did not fully reach their equilibrium moisture contents does indeed affect the results of the study. It is recommended for future studies, especially for welded wood, to use stricter stop criteria to ensure that equilibria have been attained for all specimens and RH levels in adsorption as well as desorption. 3.5 The approximate linearity for E(t 1/2 ) ≤ 0.5 Appendix Figures A1-A6 show that the fractional sorption curves for most of the RH levels behaved linearly up to E(t 1/2 ) = 0.5. For adsorption, the relations were linear up to 70 % RH for pine and welded pine, whereas beech and welded beech deviated from linearity before t ½ at 60 % RH (Appendix Figures A1-A3).
Apart from some exceptions, the desorption curves were generally linear for E(t) ≤ 0.5. Nonlinearities could be noticed down to 50 % RH, more for beech and welded beech than for pine and welded pine. As is shown in Appendix Figure A4, the 90 % RH curves were, peculiarly, often more linear than the 50 % and 75 % RH curves.

Conclusions
In this first study of water sorption of welded wood with DVS a few observations were made. The water adsorption of welded wood is lower and slower than that of the unwelded wood. However, the water desorption of welded wood is higher and faster than that of the unwelded wood. This means that welded wood in general is more reluctant to keep water, c.f. Figure 5. The hysteresis is however in general larger for the welded wood, c.f. Figure 6. The time to reach E(t) = 0.5 increases as the moisture content increases.
The DVS study showed that there is an unequal moisture distribution between the welded bond-line and the adjacent wood. This can lead to restrained swelling and shrinkage and consequently to internal stresses and eventually cracking in the bond-line.
Examination of the diffusion coefficients shows irregular patterns in some ranges of the RH. Therefore, it is hard to make a clear conclusion whether the Fickian model can explain the whole observed sorption process. Non-Fickian models might provide further information from which obvious trends of the diffusion coefficient can be seen in the whole range of the water sorption process. Continuative studies should be encouraged.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding: None declared. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.