The vibrational properties of native and thermally modified wood in dependence on its moisture content

The vibrational properties of spruce (Picea abies Karst.) and European beech (Fagus sylvatica L.) were investigated in this study in dependence on the relative humidity (RH). The RH was measured at 20 °C ranging from oven-dried to 85%. For the evaluation of the vibrational properties the dynamic modulus of elasticity E’ and the damping coefficient tan δ were measured at 7 climate steps. The same samples used for the vibrational tests were afterwards mildly thermally modified at 180 °C and measured at the same climate steps. Both wood species were compared and evaluated considering the property changes (E’, tan δ, sorption isotherms and volume swelling) due to the thermal modification. The chosen modification resulted in a marginal change in the vibrational properties of spruce, whereas the properties of beech were clearly changed. The vibrational properties of beech could be improved in the usual RH range (35–85%) due to this thermal modification. For spruce, it was concluded that a mild modification, conducted in this study, is not suitable for improving the vibrational properties. Further conclusions concerning the underlying causes as well as the use in musical instruments were drawn.


Introduction
Wood is an important material for the manufacturing of musical instruments. Usually the vibrational properties are parameters for the evaluation of the acoustic properties of wood (e.g. Ahmed and Adamopoulos 2018;Brémaud 2012;Sproßmann et al. 2017). Besides the relevance for the making of musical instruments, the vibrational properties are a good way of understanding the physical material behavior of wood with regard to its structure and components (Brémaud and Gril 2020). Regarding the cell wall components, the cellulose microfibrils are responsible for the elastic properties of wood and the cell-wall-matrix (hemicelluloses and lignin) is held responsible for the viscoelasticity and the hygroscopicity. The examination of the vibrational properties offer information on both the elastic behavior, described by the dynamic modulus of elasticity E', and on the viscoelastic behavior, described by the damping coefficient tan δ (Brémaud and Gril 2020) and thus allow conclusions to be drawn on the behavior of the wood structure and its components.
In dependence on the equilibrium moisture content (EMC) or the relative humidity (RH), the damping coefficent tan δ shows different behavior than the known behavior of other mechanichal properties, such as the dynamic modulus of elasticity E'. Obataya et al. (1998) have found non-linear correlations for spruce as shown in Fig. 1. Whereas the dynamic modulus of elasticity has a local maximum point at about 8% EMC followed by a continious decrease, the damping coefficient has a wave-shaped trend with two peaks. The graph has the first maximum at a very low EMC (1 … 2%) followed by a second minimum point at about 5 … 7% EMC, followed by a continuous increase up to about 20% EMC and then a flattening. The behaviors of the funcion of E' and tan δ depending on EMC were confirmed by a number of scientists, for both hardwood and softwood. Brémaud and Gril (2020) give a comprising literature review with a number of wood species and characteristic values in their study. For the usage in musical instrument manufacturing a low damping coefficient and a high dynamic modulus of elasticity is preferred (e.g. Bucur 2006;Wengst 2006).
The thermal modification of wood was designed to improve its hygroscopic properties. A thermal modification leads to an EMC reduction, which improves a number of physical properties of wood. There are various methods of thermal modification processes, for example using a steam, vacuum or nitrogen atmosphere. The chemical 1 3 alterations of wood resulting from the thermal modification are strongly dependent on the process parameters (Candelier et al. 2013;Bal 2018), which means a comparison of results of thermally modified wood is always difficult.
Vibrational properties of thermally modified wood were investigated in various studies (e.g. Zauer et al. 2016;Sproßmann et al. 2017;Karami et al. 2020;Mania and Skrodzka 2020). The aim of most investigations was the use of thermally modified wood in musical instruments because some relevant properties can be improved with a mild thermal modification. The concerning properties for most investigations on thermally modified wood were conducted in the standard climate at 20 °C and 65% RH (Zauer et al. 2016, Sproßmann et al. 2017, Karami et al. 2020. Karami et al. (2020), for example, have investigated the vibrational properties of mildly thermally modified spruce wood under five different modification conditions. They varied the RH, the temperature and the duration of the process. All investigated properties were determined at 20 °C/65% RH. Mania and Skrodzka (2020) also did their investigations in one climate, but they did not declare the conditions. Ahmed and Adamopoulos (2018) have investigated the vibrational properties of different types of modified wood at 20 °C and 35%, 65% and 85% RH. They regarded three types of commercially produced thermally modified wood. They found that the thermally modified wood shows a significantly lower tan δ than the other modified materials in all three humid conditions, but they did not work out a differentiation between the three humidities. The results of the studies mentioned above are different considering the vibrational properties. With regard to an evaluation of the acoustic properties of wood (used as tonewood), a thermal modification can result in improvements as well as in degradations or in no significant changes.
Wood and thermally modified wood are used in a wider range of humidity. Especially musical instruments are played in a large range of different climate conditions. Regarding this and the possible improvement of some relevant properties due to thermal modification, the following study was conducted. The aim was to clarify the following questions: 1. How do the vibrational properties of thermally modified wood behave in dependence on the RH in a range of 0-85%? Follow the parameters E' and tan δ the same non-linear behavior as described by Obataya et al. (1998)? 2. Are there differences between beech as hardwood and spruce as softwood? 3. Is an improvement of the acoustic properties for the use in musical instruments possible due to thermal modification in a RH range of 0-85%?

Base material
Spruce (Picea abies Karst.) as softwood and European beech (Fagus sylvatica L.) as hardwood were used for the investigations. Spruce is a typical tonewood used in a number of musical instruments. The spruce samples were taken from a musical instrument maker. In general, European beech is rarely used in the musical instrument making because of its poor stability. Investigations of Zauer et al. (2016) result in a clear improvement of the acoustic properties using thermal modification, which is why beech was chosen for this study. The beech samples were obtained by a commercial merchant. All samples were free from knots or other special features. 15 samples with the dimensions L × R × T: 190 mm × 28 mm × 7 mm were prepared for testing for each species. Because the testing method is nondestructive, the same samples could be tested multiple times, so, growthrelated influences could be excluded. Initially, all samples were tested in the climate steps shown in Table 1. After oven-drying, the samples were conditioned in the next climate step until the desired EMC was reached. The tests were conducted in the direction of adsorption. The conditioning for every step took 5-6 weeks. The conditioning was conducted with salts or in a climate chamber (Table 1). Table 1 shows the densities and EMCs of all samples as mean values. The coefficient of variation is given in brackets.
After the measurement of the base material, the same samples were thermally modified.

Thermal modification (TM)
Prior to the TM process, the samples were oven-dried for 24 h at 103 °C. The TM was performed in an autoclave under nitrogen atmosphere. Thereto a vacuum of 50 mbar was applied followed by filling nitrogen with 1.1 bar. The samples were preheated for 3 h at 80 °C, and then, heated with a rate of 5 K/h up to 180 °C. With the temperature of 180 °C in a nitrogen atmosphere, a mild modification was chosen. Zauer et al. (2016) have found that with such mild modification parameters, the acoustic properties as well as the dimensional stability of beech can be improved whereas the mechanical properties are not degraded. After 8 h at 180 °C, the samples were cooled down to room temperature with a rate of 5 K/h. Thus, the modification can be estimated as a dry, mild modification. The resulted mass loss m L was calculated according to (Eq. 1), where m OD is the oven-dried mass before and m TM_OD after TM.
For spruce as well as for beech the mass loss due to TM amounted to 2.5%. It should be noted that the spruce mass loss includes the volatile components (resin) whereas the beech mass loss is solely reasoned by the degradation of the cell wall components. Thus, spruce has a lower mass loss of cell wall components, although it has the same mass loss as beech. The conditioning for testing the vibrational properties was conducted in the same way as the unmodified samples were conditioned (see Table 1). Thus, the measurements took all in all nearly 90 weeks. (1)

Experimental
Vibrational tests were conducted using modal analysis with free boundary conditions as described by Sproßmann et al. (2017). Therefore, the sample was supported vertically by two rubber pieces located at the node of vibration of the first bending node. The sample was hit by an impact hammer on one end. The complex vibrations were measured by a microphone located diagonal at the other end of the sample. The analysis of the measured signal results in the estimation of the frequency f 1 and the damping from the corresponding mode shape. The dynamic modulus of elasticity E' was calculated using the Euler-Bernoullitheory (Eq. 2), where m = 4.73 is a non-dimensional constant corresponding to the first bending mode of a free flexural vibration, l is the sample length and h its height. The damping coefficient tan δ (non-dimensional) can be described by the flexural internal friction (Q −1 ) and was calculated from the peak frequency (f R ) and the half-value width of the resonance maximum point (Δf) according to Brémaud et al. (2012) The volume swelling coefficient α V was determined according to DIN 52184 (1979) (Eq. 4), where α (%) is the maximum swelling coefficient in the coresponding anatomical direction (T… tangential, R… radial, L… longitudinal) correlated to the oven-dried condition. Table 2 shows all measured results (E', tan δ and α v ) for every climate step. Note that at low RH, due to the very low changes in the dimensions, the coefficients of variation are very high for the volume swelling. This is due to the measurement accuracy, which is of the same magnitude as the dimensional changes which were measured.

Results and discussion
Following, the results are discussed for each species individually. Thereby it should be noted that softwood is basically more thermally stable than hardwood. Different chemical processes occur in both wood species under the same thermal modification conditions (Hill et al. 2021), which is the reason why the results differ for both species. Finally, the results of both species were compared.

Spruce
First of all, the sorption isotherms of spruce and spruce TM are regarded in order to see changes due to the TM. Conclusions may be drawn which can be helpful for the understanding of the changes of the vibrational properties. Figure 2 shows the sorption isotherms and the decrease in the EMC due to the TM. At about 10% RH, the difference between spruce and spruce TM starts, between 50 and 65% RH the difference is more obvious and at about 85% RH the difference in EMC is less noticeable.
Note that the curves in all diagrams are for a better visualization and are no mathematic functions.
A clear reduction in the EMC occurred due to the mild thermal modification although softwood is relatively thermally stable (Fengel and Wegener 2003). Softwood has less hemicelluloses, which can be degraded. Furthermore, there are only small chemical changes (Bächle et al. 2010;Gaff et al. 2019). Nevertheless, there is a clear reduction in the EMC. Since Rautkari et al. (2013) found that there is no direct correlation between the OH content and the EMC of thermally modified wood, it is clear that there must be additional mechanisms responsible for the reduction in EMC. Figure 3 shows the correlations between E', tan δ, α v for both RH and EMC respectively. Figure 3b) shows the correlation between tan δ and the EMC for spruce and spruce TM. The basic curve is the same as described by Obataya et al. (1998) (Fig. 1). There is only a marginal difference between the values of spruce and spruce TM. The peak at 20 °C/ 65% RH 11.2 (12.0%) 11.3 (12.0%) 13.9 (14.4%) 14.7 (14.2%) 7.36 (5.4%) 6.43 (4.3%) 9.97 (10.2%) 7.76 (8.3%) 5.52 (9.4%) 3,15 (13.8%) 6.83 (11.1%) 3.09 (15.7%) 20 °C/ 85% RH 10.4 (12.3%) 10.2 (12.1%) 12.5 (14.4%) 12.7 (14.3%) 9.50 (5.9%) 8.84 (4.4%) 11.78 (12.0%) 10.44 (11.2%) 8.13 (8.9%) 6.88 (9.2%) 11.18 (8.9%) 8. 76 (10.7%) about 2% EMC occurs at the same point where the volume swelling (Fig. 3d) starts. At this point the water molecules begin to bond to the OH-groups of the hemicelluloses and the amorphous parts of the celluloses. Thus, a first noticeable swelling occurs. The minimum at about 5 to 6% EMC is the beginning of the physical adsorption, comprehensible at the transition to the steeper and more constant slope of the volume swelling. In theory, this is the point where the water molecules start to accumulate to the first water layer, which is chemically bonded at the cell wall components.
As a side note, the fact that the volume swelling in correlation to the EMC (Fig. 3d) is basically the same for both spruce and spruce TM could be considered as proof for the marginal degradation of the hemicelluloses and the amorphous areas of the cellulose due to TM.
Considering the correlation of the tan δ and the RH (Fig. 3a), a displacement of the damping coefficient graph in direction to a higher RH occurs. This behavior can only be reasoned by the reduced EMC due to the TM. Thus, tan  Fig. 3 Dynamic modulus of elasticity E ' and damping coefficient tan δ in dependence on RH (a) and EMC (b); volume swelling in dependence on RH (c) and EMC (d) for spruce and spruce TM δ of spruce TM is higher than tan δ of spruce in the range of 30 to 50% RH.
In Fig. 3b) the dynamic modulus of elasticity E' is also shown correlated to the EMC. There, the known correlation is mapped: after a slight increase till about 2-3% EMC, the modulus decreases with increasing EMC (Obataya et al. 1998). The progression of E' is nearly the same for spruce and spruce TM. All values of E' for spruce TM are lower than for spruce. Considering the correlation to the RH (Fig. 3a) the progression and the values of E' for both, spruce and spruce TM, can be rated as the same, although in the literature different results can be found. Pfriem and Wagenführ (2008) describe the correlation between the static modulus of elasticity E and the RH as a continuous enhancement of E for spruce TM compared to the values for spruce. However, related to the EMC their results show a displacement of the spruce TM values in the direction to a lower EMC. Karami et al. (2020) have found similar results for E' as well as for tan δ as shown in our study. They also show that the modification regime has a clear influence on the increase or decrease in the values. A possible explanation for a reduction of the E' values is the development of cracks and changes in the cell structure due to the thermal modification (e.g. Lin et al. 2017;Bernabei and Salvatici 2016;Zauer et al. 2014). Thus, the cohesion of the structure would be weakened and the forces could not be transmitted in the same way as in unmodified wood. The development of cracks might be extended by oven-drying the samples multiple times (measurement of the oven-dried properties for spruce, for spruce TM after modification, and ovendrying before the thermal modification). Especially in case of low RH, the cracks would be wide opened since there is less swelling. At low RH (Fig. 3c), up to 35% RH, the volume swelling is very low and there is no difference between spruce and spruce TM. In case of higher RH, there is a higher volume swelling. The cell wall swells, so that cracks could gradually come in contact again. Thus, a transmission of forces by friction might occur and the values of E' of spruce TM can reach those of unmodified spruce (Fig. 3a). A further increase in RH results in a decrease in E' due to the softening of the cell wall. The progression of E' (Fig. 3a) and of the volume swelling (Fig. 3c) confirms this thesis. The range of the maximum swelling comprises 35-85% RH. This is exactly the same range where E' of spruce and spruce TM are identical.
Thus, the main changes of the vibrational properties of spruce due to TM can be reasoned towards the changes of the EMC. The chemical structure and components seem to change very slightly. The slight changes of all properties in relation to the EMC are considered proof for this conclusion. Further, volume swelling is nearly equal for both spruce and spruce TM, in the range of 2-8% EMC the spruce TM swelling is slightly higher which could be interpreted as an indication for the crack theory. Due to the cracks, the accessibility would be better and more water molecules could reach the cell wall and increase the swelling. In this range, the damping coefficient is slightly higher what is a non-desirable effect for the acoustic properties.

Beech
First of all, the sorption isotherms of beech and beech TM are observed in order to see changes in properties due to the TM. As shown in Fig. 4, a clear reduction in the EMC due to TM can be reached. The differences between beech and beech TM start at about 10% RH, increase clearly between 35 and 65% RH and are slightly reduced at about 85% RH. The reduction in EMC is greater than for spruce TM because this mild modification is more effective with beech. The hardwood hemicelluloses react more sensible to a thermal modification. They are less crosslinked and thus easier degradable. Due to the remarkable part of acetyl groups, acetic acid is formed during the modification. Thus, a hydrolysis occurs and the degradation of the hemicelluloses is catalyzed. As a result, more hemicelluloses are degraded compared to softwood (Hill et al. 2021) and the EMC reduction is higher. Figure 5 shows the correlations between E', tan δ, α v for both RH and EMC respectively. Figure 5b) shows the same progression of tan δ in correlation to the EMC as shown by Obataya et al. (1998) (Fig. 1). All values for beech TM are lower than for unmodified beech. Thus, for the same EMC a clear reduction in tan δ occurs due to the TM. Besides the reduction in the EMC, chemical changes in the wood must have occurred, otherwise this reduction is not explainable. As mentioned above, the cell-wall-matrix (hemicelluloses and lignin) is considered to be responsible for the viscoelasticity and the hygroscopicity (Brémaud and Gril 2020). The TM results in the degradation of the hemicelluloses and a re-crosslinking of both hemicelluloses and lignin, also described as condensation reactions (Hill et al. 2021). These crosslinks result in a more thermosetting character, which leads to a reduction in the viscoelastic properties. As a result, tan δ decreases. A confirmation for this explanation might be seen in Fig. 5d) where the volume swelling is correlated to the EMC. The first peak of tan δ is exactly in this range, where the volume swelling begins at about 2% EMC. In contrast to spruce TM, where this peak is also in this range, the volume swelling of beech TM between 2 and 4% EMC is lower than that of the unmodified beech. This can be interpreted as a clear indication for the chemical changes described. Considering tan δ in correlation to RH (Fig. 5a)-what is more interesting for use-a reduction in tan δ below 25% RH and above 40% RH and an overlap in the range of 25-40% RH of beech TM are noticeable. Thus, besides the reduction in tan δ, a displacement of the beech TM graph in the direction of a higher RH occurs. Due to the reduction and the displacement of the beech TM behavior, this overlap of both graphs between 25 and 40% RH occurs. Overall, tan δ can be evaluated better for beech TM than for unmodified beech. This improvement can be explained by the superposition of chemical changes and the reduction in the EMC.
In Fig. 5b), E' for beech and beech TM in correlation to the EMC is shown. Both graphs are comparable. The maximum is at about 2% EMC for the unmodified beech as well as for the beech TM. These ranges coincide with the first saddle point of the volume swelling (Fig. 5d). After this point, E' decreases because the water accumulation between the cellulose fibrils increases clearly, indicated by the increasing volume swelling, and the softening starts. The comparable progression of both graphs shows that the chemical changes (degradation of hemicelluloses and re-crosslinking of hemicelluloses and lignin) do not seem to have any influence. Either these changes are superimposed by other effects, such as cracks and changes in the  cell structure which were necessarily also occurring during beech modification, or these chemical changes do not influence the elastic properties as explained in Brémaud and Gril (2020). With this comprehension, the elastic property E' can only be changed if the cellulose is changed too. However, relevant changes in cellulose occur at higher temperatures of about 200 °C (González-Peña et al. 2009) than what was used for this thermal modification. Thus, relevant changes of E' are not to be expected. Concerning the cracks and structural changes that surely have also developed (Altgen and Militz 2016) it might be possible that the more complex structure of hardwood can withstand such damages even better than the simpler structure of a softwood. Differences between beech and beech TM are more obvious for E' correlated to RH. Until about 25% RH, the values of beech and beech TM are almost the same. In the range of 25-65% RH, the E' of beech TM is clearly higher, at 85% RH the E' decreases to a value that is comparable with unmodified beech. The reason for this behavior is well explainable: the EMC is barely reduced until 25% RH. Thus, both variants are comparable. In the range of reduced EMC and thus reduced water accumulation (25-65% RH), the effect of the TM is obvious. The level of E' is nearly held by beech TM, i.e. the water accumulation into the cell wall is so far reduced by the modification that a softening cannot occur. This procedure is also well visible because of the noticeable volume swelling (Fig. 5c). Thus, the main changes of the vibrational properties of beech due to the TM can be reasoned by a superposition of the changes of the EMC and the chemical changes. The chemical changes are the degradation of the hemicelluloses and the re-crosslinking of the hemicelluloses and the lignin (Hill et al. 2021). Thus, a higher viscoelasticity and possibly a reduction in the internal friction are reached. As a result, the vibrations in the wood can be transmitted better and the reduction in the tan δ is explainable. The change of the EMC as a result of the TM leads to a displacement of the values towards higher RH. This is especially clear for the E' and leads to a higher E' in higher RH ranges.

Comparison of beech and spruce
Altogether, the thermal modification conducted with both wood species has caused more obvious changes in the hardwood beech than in the softwood spruce. Table 3 shows the changes due to the modification compared to the unmodified samples.
As described in the literature, spruce as softwood is basically more stable during thermal modification (Fengel and Wegener 2003;Hill et al 2021). The reduction in the EMC of spruce due to TM is in a comparable range to beech TM. Spruce as softwood has generally a higher EMC compared to beech as hardwood. Thus, the value of EMC of spruce TM is nevertheless higher than the EMC value of beech TM. All these points explain the weaker effect of the thermal modification on the properties of spruce TM compared to the properties of beech TM. Cracks, which also might have been developed at a mild thermal modification (Bernabei and Salvatici 2016;Zauer et al. 2014), certainly have more impact on the simple-structured softwood with a lower density than beech as hardwood. Due to the layered structure of the thin-walled spruce early wood and thick-walled late wood, a crack in the early wood weakens the wood and can probably barely be compensated by the cells placed around. Thus, the stiffness (E') of spruce is more influenced by cracks than this might be the case in beech wood. The authors assume that such cracks overlay other effects of the TM and are the reason for the reduced E' of spruce TM. There are more relevant chemical changes in beech TM and thus, a higher reduction in its EMC. Thus, a reduction in the tan δ on the one hand and an increase in E' on the other hand can be reached in the relevant range of RH.
In order to improve the vibrational properties for spruce compared to beech by using TM, other process parameters have to be used (such as higher temperature, duration or wet conditions). Investigations of Arnold (2010) have shown the influence of the process parameters. He has investigated beech and spruce, thermally modified under wet conditions and estimated the bending modulus of elasticity in different climate steps. The results are completely reversed to the results of this study: the modulus of elasticity of beech is reduced due to TM whereas the modulus of elasticity of spruce is increased by the TM.

Conclusion
Considering the questions asked above the following answers and conclusions can be drawn: The vibrational properties, defined as E' and tan δ, of thermally modified wood follow the same non-linear behavior as described by Obataya et al. (1998). The behavior of the functions between 0 and 85% RH is basically similar, but there are differences between spruce as softwood and beech as hardwood. The tan δ of spruce TM is higher until about 50% RH and thereafter lower than tan δ of the unmodified wood. Tan δ of the beech TM is lower or equal to the tan δ of unmodified beech over the whole range of RH. The E' of spruce TM is reduced due to the modification over the whole range of RH. Concerning beech there is another result. The E' is marginally reduced until about 25% RH and increased in the range between 25 and 85% RH compared to unmodified beech. Therefore, as a result of this thermal modification, the acoustic properties for use in musical instruments can be improved in beech, but not in spruce. Furthermore, it can be assumed that • cracks and structural damages, certainly developing during the modification process, seem to have clearly stronger influence on the properties of softwood like spruce than hardwood like beech, • the mild modification under dry conditions conducted in this study, leads to marginal changes in softwood like spruce and to more effective changes in hardwood like beech, • for an improvement of the acoustic properties of spruce for the manufacturing of musical instruments other process parameters for the TM have to be used.