Introduction

A precise description of the complex interaction between wood and moisture is one of the great fundamental challenges in wood science. Advancement in this subject is expected to generate progress in specialised research fields of wood science, for example in long-term mechanical creep, mechanosorption, dimensional stabilisation, wood decay and service-life prediction. This notion has intensified the wood–moisture interaction research in recent years. The review of Engelund et al. (2013) provides a comprehensive discussion on current theories and experimental findings of wood moisture interaction. Recently, hydrogen/deuterium exchange (HDX) has been used to measure the accessible number of hydroxyl (OH) groups as potential moisture sorption sites in natural and modified woods (Rautkari et al. 2013; Popescu et al. 2014; Beck et al. 2018). Quasi-elastic and inelastic small angle neutron scattering (SANS) experiments are being used to study the dynamics of water adsorption onto cellulose (Thibault 2012; Plaza et al. 2016; O’Neill et al. 2017). Numerical molecular dynamics calculations have simulated the behaviour of water molecules in a polysaccharide matrix (Kulasinski et al. 2015; Shi and Avramidis 2017). Finally, spatially resolved spectroscopic techniques have been used to study the wood–moisture interaction simultaneously in adjacent cells or cell wall layers (Fackler and Schwanninger 2012; Passarini et al. 2015; Gezici-Koç et al. 2017).

While these advanced methods provide direct fundamental information on the molecular state of adsorbed water in wood, there is still unexplored potential for important knowledge gain from analysis of experimental wood sorption isotherms. The author has developed novel theoretical tools for this purpose (Willems 2014a, b, 2016). In this research, these tools and a complementary water cluster integral calculation are applied to the moisture adsorption isotherms of natural as well as modified woods (Hill 2006).

Moisture adsorption isotherm analysis

The wood moisture adsorption isotherm is the relation between the equilibrium moisture content (EMC, per cent kg water per kg dry wood) at constant temperature T (K) and ascending relative humidity (RH, ratio of partial water vapour pressure p to saturated water vapour pressure psat, percentage or fraction h). This characteristic has typically a sigmoid shape (IUPAC class II type adsorption), for which many theoretical explanations and empirical models have been published (Skaar 1988; Engelund et al. 2013). Some of these models were specifically developed to analyse the nature of the molecular association with the host matrix. However, since experimental EMC data can be fitted to either of these models, this provides no direct means to discriminate between different models. To obtain scientific confirmation, an independent experimental verification of the state of water in wood is required, which has been unsuccessful, to the best knowledge and judgment of the author.

Hartley et al. (1996) found no correspondence between the relative amounts of high- and low-mobility water from time-domain proton nuclear magnetic resonance (1H NMR) measurements, compared to the relative amounts of hydration water and monolayer water as calculated from the Hailwood–Horrobin sorption isotherm decomposition (Skaar 1988). The obtained monolayer water contents in natural woods systematically underestimate the accessible OH content (Taniguchi et al. 1978; Berthold et al. 1996; Zaihan et al. 2009; Willems 2015). Olsson and Salmén (2004) observed with FTIR (Fourier transform infrared) spectroscopy that all types of sorption sites on cellulose and hemicellulose in paper respond to an equal relative extent and with equal kinetic rates to humidity changes. Up to 80% RH, these authors did not find a spectroscopic band that could be assigned to the steep increase in wood moisture adsorption above 60% RH.

Another theoretical approach towards wood moisture adsorption is based on the statistical polymer solution thermodynamics according to Flory–Huggins, expanded with excess free volume concepts of glassy polymers (Rosenbaum 1970; Hancock and Zografi 1993; Vrentas and Vrentas 1996). One of the attractive features of this “Vrentas theory” is the incorporation of the plasticising effect of water on the glassy polymer matrix, providing an explanation for the steep increase in moisture adsorption with increasing RH above 60%, as well as a mechanism for moisture sorption hysteresis (Engelund et al. 2013). Hill and Beck (2017) applied this theory to the wood–water system with satisfactory fitting results of adsorption as well as desorption isotherm data. The Vrentas theory essentially states that the adsorption is distinctly different above versus below the glass transition temperature of the wood matrix and its associated critical RH (Engelund et al. 2013). However, the present paper provides evidence that there is no such transition in the wood moisture adsorption isotherm, illustrating the need for improved concepts of the association of water to the wood matrix.

Equilibrium occupancy of water adsorption sites in wood

Normalised wood moisture adsorption isotherms

The use of normalised wood moisture sorption isotherms was introduced by the author in the analysis of the T-dependence of the sorption isotherm shape (Willems 2014a). It was found that the T-dependence of the standard EMC curves of the Wood Handbook (Glass and Zelinka 2010) has a reversible and a non-reversible part. The non-reversible part is contained in the extrapolated EMCmax(T) at RH = 100% (h = 1), whereas the reversible part is in the normalised moisture content ω(μ) ≡ EMC(h,T)/EMCmax(T), which is entirely described by the water chemical potential μ (Willems 2016):

$$\mu = - RT \ln h,$$
(1)

adopting a positive-sign convention, where RT (kJ mol−1) has the usual meaning of the unit molar thermal energy. In this representation, sigmoid EMC versus RH isotherms are transformed into a monotonously decreasing function ω(μ). The ω(μ) correlation as found by Willems (2016) is drawn in Fig. 1a against klinki pine data of Kelsey (1957), in Fig. 1b, c against beech and spruce data of Weichert (1963), showing that the humidity and temperature dependence of EMC/EMCmax indeed only depend on µ. This result gives credits to the Wood Handbook EMC data, after Glass et al. (2014) assessed that these data are not scientifically assured.

Fig. 1
figure 1

Universality in ω(μ) = EMC/EMCmax, the normalised equilibrium moisture adsorption versus water chemical potential μ, a for klinki pine (Kelsey 1957), b beech and c spruce (Weichert 1963) and d sitka spruce (Wood Handbook: Glass and Zelinka 2010) and three pine chemical modifications, heat treatment (Chaouch et al. 2013), DMDHEU-resin-treatment (Papadopoulos and Mantanis 2012) and acetylation (Papadopoulos and Hill 2003)

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Figure 1d reproduces the plots of Sitka spruce data of the Wood Handbook for two temperatures 26.7 and 98.9 °C, fitting other EMC/EMCmax data for chemically modified pine by 230 °C heat treatment (mass loss (ML) = 15%) (Chaouch et al. 2013), a cured cross-linking resin treatment (weight gain (WPG) = 17%) (Papadopoulos and Mantanis 2012) and reaction with acetic anhydride (WPG = 19.6%) (Papadopoulos and Hill 2003). Note that the three wood modification treatments are very different in their nature how they change the wood chemistry and structure. In heat-treated wood, the dry mass and the total number of OH groups decrease significantly (Seborg et al. 1953; Phuong et al. 2007; Mitsui et al. 2008; Chaouch et al. 2013) and there is some cross-linking in the wood matrix (Salmén et al. 2008; Altgen et al. 2018). DMDHEU is a cross-linking resin, adding mass and new OH groups to the wood structure (Dieste et al. 2010). Acetic anhydride reacts almost exclusively inside the wood matrix, substituting wood-OH groups by bulky acetyl groups, increasing the dry mass and dry volume without cross-linking (Hill 2006).

The ω(μ) curve was found similarly applicable (not shown) to other wood species, other heat treatments and wood modifications using different types of anhydrides (Papadopoulos and Hill 2003) and glutaraldehyde (Xie et al. 2011). On the other hand, there are examples of sorption data that do not fit into the correlation of Fig. 1, notably for formaldehyde-treated pine (Himmel and Mai 2016) and natural African wood species wengé and doussié in the data of Popper et al. (2009). These anomalous adsorption isotherms either (1) belong to wood specimens lacking a fast cell wall relaxation capability (Willems 2015) and/or the equilibration time may have been chosen too short (Glass et al. 2017) or (2) are subject to a stress interaction σ from swelling/shrinkage constraints in the wood matrix.

In the first case, the data cannot be used for accurate sorption isotherm analysis, because there is no equilibrium. In the second case, the entire correlation of Fig. 1 is left-shifted by v w σ along the μ-axis for compressive stress on the wood matrix (Willems 2014a), with v w the molar volume of water. The discussion of these stress interactions will be postponed to a future paper for didactical reasons. It is practically justified for most wood specimens to ignore stress interactions, when one is interested in moisture adsorption in the hygroscopic range (roughly < 95% RH). Taking note of this limitation, one may postulate from Fig. 1 that for RH < 95%:

  • EMCmax represents the number of active sorption sites in (modified) wood, since EMCmax corresponds to the calculated moisture content when each active OH group is occupied by one water molecule (Berthold et al. 1996; Willems 2014b).

  • Each active sorption site has the same equilibrium occupancy probability determined by μ.

Through different modes of action (degradation, substitution, bulking, cross-linking, lumen-filling) wood modification thus primarily changes the active number of sorption sites, rather than the occupancy of these sites. In other words, the sigmoid sorption isotherm seems associated with each individual active sorption site.

Sorption site occupancy (SSO) model

Based on an indirect analysis, allowing the determination of the water occupancy of sorption sites in thermally modified wood as a function of h, Willems (2014b) found a h0.7 (Freundlich) type of occupancy, instead of a sigmoid one. This inconsistency can be fixed by considering an apparent increase in the number of sorption sites with increasing RH, responsible for the increase in EMC at high RH: the sorption site occupancy (SSO) model states that the momentary moisture content u(h) [mol water/kg dry wood] can be factored into a part c(h) [mol/kg] that is proportional to the density of sorption sites and a part θ(h) = hn that describes the statistical occupancy of a sorption site:

$$u\left( h \right) = c\left( h \right)h^{n}$$
(2)

It was shown (Willems 2014b, 2015) that the occupancy function θ(h) = hn is generally valid for wood moisture adsorption (increasing h) and desorption (decreasing h). The exponent n is found from the adsorption isotherm ueq(h) as the slope of the double logarithmic relation ln(ueq) versus ln(h) in the range 0 < h < 0.5, where c(h) appears nearly constant. Peleg (1993) proposed an empirical sigmoid adsorption isotherm equation that complies with Eq. 2:

$$u_{\text{eq}} \left( h \right) = u_{1} h^{n} + u_{2} h^{n + m} = \left( {u_{1} + u_{2} h^{m} } \right)h^{n}$$
(3)

Krupińska et al. (2007) found that wood sorption isotherms fit to the Peleg Eq. 3 with the same accuracy as the standard Hailwood–Horrobin isotherm (Skaar 1988; Glass and Zelinka 2010). The room temperature (T0 = 293 K) moisture adsorption isotherm from Glass and Zelinka (2010) is fitted accurately with u1 = u2 = umax/2, n0 = 0.71 and m0 = 6.28 (curve drawn in Fig. 1):

$$\omega \left( h \right) = \frac{{u_{\text{eq}} }}{{u_{\rm{max} } }} = \left( {\frac{{1 + h^{6.28} }}{2}} \right)h^{0.71}$$
(4)

The factor outside parentheses of Eq. 4, θ = h0.71 at T0, or more generally θ(µ) = exp(− 0.29µ), are the occupancy of the accessible sorption sites and

$$c_{\text{eq}} \left( h \right) = \frac{{1 + h^{6.28} }}{2}u_{\rm{max} }$$
(5)

is the apparent sorption site density at T0, or more generally ceq(μ) = ½(1 + exp(− 2.57μ)), drawn in Fig. 2.

Fig. 2
figure 2

Density of sorption sites c(h) as calculated according to the SSO theory (Eq. 5). The correspondence between h and μ is for 25 °C

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An interesting observation from Eq. 5 is that at low RH (μ → ∞), ceq approaches c L  = umax/2, while the limiting value of ceq is c H  = umax at h = 1 (μ = 0). In view of the universality in Fig. 1, the apparent number of accessible sorption sites at h = 1 then always becomes twice the number at low h. The author failed finding any viable explanation of this property in the Vrentas theory. Qualitatively, at low RH, the number of accessible sorption sites is nearly constant, consistent with the considerations that wood at low humidity is in a glassy state (Hill and Beck 2017). At high RH, mechanical softening might be considered responsible for an increased number of accessible OH groups; however, ω is hardly affected by neither cross-linking (DMDHEU and heat treatment), nor thermal softening of the wood matrix as evidenced from the similarity in Sitka spruce normalised ω(μ) data at 98.9 and 26.7 °C (Fig. 1).

Reflections on bound wood moisture in a polysaccharide hydrogen bond network

Bulk water requires a saturated water vapour environment to prevent its evaporation. Equilibrium wood moisture is maintained in unsaturated water vapour by adhesion forces that exceed the cohesion forces in bulk water. It was shown by Willems (2016) that ωeq is an explicit function of µ (Fig. 1), the differential heat of adsorption hads is necessarily equal to µ. hads is the extra enthalpy needed for the evaporation of 1 mol of adsorbed water in comparison with that of 1 mol of bulk water (h v  = 44/kJ mol−1 at 25 °C). The heat required for evaporation is then given by the sum of h v and hads which ranges typically from 44 kJ mol−1 (at h = 1) to 50 kJ mol−1 (at h = 0.05).

Water may form up to 4 hydrogen bonds (H-bonds), having two hydrogens for donation and an oxygen atom with two hydrogen-accepting orbitals (Jeffrey and Saenger 1994). However, water has effectively only 2 full-strength H-bonds, each of which can bifurcate into two H-bonds of half-strength (Keutsch and Saykally 2001). Hence, each water molecule in wood is effectively bound by two H-bonds of 22–25 kJ mol−1 each, consistent with the accepted range of H···OH hydrogen bond energies between 20 and 25 kJ mol−1 (Steiner 2002). At low RH, wood moisture is then considered dispersed in isolated water molecules, firmly bound by two relatively strong H-bonds with a pair of nearby OH groups of the amorphous polysaccharide polymers of the wood matrix (Fig. 3a). With increasing moisture concentration, the water-polysaccharide H-bonds may become weakened under strain in the swelling matrix. Meanwhile, the cooperativity in the H-bond network increases with increasing moisture content (Jeffrey and Saenger 1994), gradually allowing the coalescence of water vapour molecules with already adsorbed water molecules to form water dimers. These dimers are thought to be bound by relatively weak H-bonds with a OH group pair (Fig. 3b), thermodynamically stabilised by the small μ at RH > 50% (Willems 2016).

Fig. 3
figure 3

Proposed configurations of adsorbed water at hydroxyl (OH) pair sites: a monomer water bridge. b Dimer water bridge. Large black spheres: C(sp3) atoms. Medium, dark grey spheres: O atoms. Small white spheres: H atoms. Sticks: covalent bonds. Dotted lines: H-bonds

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The arrangement of atoms in Fig. 3 is neither verified by quantum chemical calculation nor by experiment, merely providing a visualisation of the H-bond interactions between the hydroxyl groups and water molecules. The geometries of the hydroxyl group and the water monomer are taken from textbook values for isolated methanol and water molecules, respectively. The geometry of the water dimer is taken from Keutsch and Saykally (2001) for the isolated dimer. The used H-bond length of 1.8 Å and O–H···O bond angle of 177° are typical values as catalogued by Jeffrey and Saenger (1994).

Monomer–dimer decomposition of wood moisture

The two configurations in Fig. 3 would fit into the humidity dependence of the sorption site density (Fig. 2). At high RH, each active pair of OH groups may be saturated with 1 dimer molecule, i.e. c H  = umax. At low RH, the water “monomer” between two OH groups is consistent with c L  = umax/2.

Since the occupancy function θ = hn in Eq. 2 applies to the entire h-range, where the relative amounts of monomer and dimer water would vary significantly, it is considered applicable to monomeric (u M ) as well as the dimeric (u D ) contributions in u = u M  + u D . Consequently, u M and u D can be calculated from u. The density of sorption sites (2 OH groups per site) is umax/2. The total number of occupied sorption sites is then (umax/2) θ = u M  + (u D /2). Solving for u M and u D :

$$\begin{aligned} u_{M} & = u_{\rm{max} } \theta - u \\ u_{D} & = 2u - u_{\rm{max} } \theta \\ \end{aligned}$$
(6)

Note that Eq. 6 is considered locally valid in a small wood volume element, without necessity for a true moisture content equilibrium. The calculated monomer and dimer contributions of the sigmoid EMC curve u = ueq(h) are drawn in Fig. 4, showing an exponential increase in water dimers for RH > 50%. Water cluster formation in this RH range has been earlier suggested conceptually (Hartley et al. 1992), experimentally (Olsson and Salmén 2004; Cox et al. 2010; Gezici-Koç et al. 2017) and emerged in molecular dynamics calculations (Kulasinski et al. 2015; Shi and Avramidis 2017).

Fig. 4
figure 4

Standard wood equilibrium moisture sorption isotherm u(h) at 25 °C, decomposed into monomer u M (h) and dimer u D (h) contributions

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The replacement of strongly bound monomers by loosely bound dimer species with increasing h (Fig. 4) is fundamentally different from multilayer or hydration sorption models, where a strongly bound monolayer remains present as a substrate for loosely bound secondary water at high RH.

Ruckenstein–Shulgin water cluster analysis

It has been argued by the author that wood moisture sorption might be best explained by considering the pool of active OH groups in wood being in a liquid mixture with the wood moisture molecules (Willems 2014b). To investigate this mixture for the likelihood of water clusters, a statistical evaluation tool is used, as put forward by RS (Ruckenstein and Shulgin 2009). The RS calculation results in a number Δn11, expressing the excess number of water molecules in a small control volume around a chosen central water molecule, compared to the expectation value, based on the average concentration and molecular sizes of the components of the solution. Other excess numbers Δn ij (where i and j are either 1 = water or 2 = wood-OH) can also be calculated. The RS calculation improves an earlier version of the theory by ZL (Zimm and Lundberg 1956), by explicitly accounting for Δn ij  = 0 in case of an ideal mixture and for the interdependency of Δn ij ’s for the local excess of one species depleting the other. In both theories (ZL and RS), the relative interaction strengths between the solution components are derived from the slope of sorption isotherm (Zimm 1953).

Defining the molar volumes (v1, v2) for liquid water molecules (1) and a unit of wood containing on average one active OH group (2), the limiting moisture content umax (mol kg−1) is supposed to be reached when all active OH groups are occupied by one water molecule. The molar volume of a OH group is then calculated as v2 = (ρ2umax)−1 with the true density of dry wood substance (ρ2 ≈ 1500 kg m−3). The molar volume of water is v1 = 1.8 × 10−5 m3 mol−1. Defining the molar volume ratio γ = v1/v2, the original RS expression for Δn11 (see Appendix in Electronic Supplementary Material) is evaluated to

$$\Delta n_{11} = \frac{{\frac{h}{\omega }\frac{\partial \omega }{\partial h} - 1 - \omega }}{{\left( {1 + \gamma \omega } \right)^{2} }}$$
(7)

for direct application to Eq. 4. Δn11 is plotted in Fig. 5 as a function of h, at T0 and EMCmax = 25%. The limiting values of Δn11 at h = 0 and h = 1 may, respectively, correspond (see Fig. 4) to the local excesses at monomer sites (Δn11,M ≈ −0.4) and dimer sites (Δn11,D ≈ 1.2). The broken line in Fig. 5 shows that these excesses remarkably fit the entire Δn11(h) curve as a weighted average, using the calculated u M and u D at each ueq(h) with Eq. 6:

Fig. 5
figure 5

Local moisture excess Δn11 from Ruckenstein–Shulgin water cluster calculation (Eq. 7) of the standard moisture adsorption isotherm (Eq. 4), compared to a fit with a weighted average of monomer and dimer contributions (Eq. 8)

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$$\left\langle {\Delta n_{11} } \right\rangle = \frac{{u_{M} \Delta n_{11,M} + u_{D} \Delta n_{11,D} }}{{u_{M} + u_{D} }} = \frac{{ - 0.4u_{M} + 1.2u_{D} }}{u}$$
(8)

The graphical comparison between Δn11 and \(\left\langle {\Delta n_{11} } \right\rangle\) is given in Fig. 5.

Discussion

By plotting ω(μ), the normalised EMC as a function of the water chemical μ, one obtains a curve that seems to describe the h- and T-dependency of the occupancy of each active sorption site in wood. An active site is always an accessible site, but not vice versa. Acetylation reduces the accessible OH group content of wood by the number of acetyl-substituted OH groups (Beck et al. 2018), while the active OH group content c H is reduced by the (larger) number of water molecules that fit within the volume of the bulky acetyl substituents (Papadopoulos and Hill 2003). EMCmax corresponds to the moisture content when all active OH groups are occupied by one water molecule. Bulking limits the number of active sites but does not determine which of the accessible sites is active. Mobile moisture molecules may dynamically move between all accessible sites and HDX accordingly deuteriates all accessed OH groups successively even if they cannot be simultaneously active. In this work, the site occupancy θ relates to the active sorption site content.

The universal ω(μ) has a fundamental significance. It was shown by Willems (2016) that in such case, the differential enthalpy of adsorption hads is equal to μ and the entropy of wood moisture is necessarily invariant at each h along the sorption isotherm. This property is speculated to originate from: (1) the local mobility of water in the wood matrix at all RH, as evidenced by time-domain 1H-NMR relaxation measurements (e.g. Cox et al. 2010; Gezici-Koç et al. 2017), and (2) the H-bond network in the polysaccharide-rich wood matrix (Jeffrey and Saenger 1994), providing an equal environment for water molecules as in capillary stressed bulk water.

It must be noted here that EMCmax is generally found T-dependent, which is related to structural changes (Skaar 1988; Willems 2014a, 2016). When this non-reversible T-dependence is included into a thermodynamic analysis with the Clausius–Clapeyron relation, the constant entropy result is erratically lost (Willems 2014a). Figure 1 confirms that a non-reversible T-dependent EMCmax is to be regarded as a modified wood case.

The constant entropy of wood moisture with h-variation is inconsistent with the localised sorption theories of Langmuir, Brunnauer–Emmet–Teller (BET) and Guggenheim–Andersson–de Boer (GAB). It is neither consistent with Flory–Huggins and Vrentas type of polymer-penetrant solution theories, where the configurational entropy of polymer segments determines the isothermal water sorption at high RH.

The sigmoid sorption isotherm has a steep slope at high RH (Fig. 4), which the sorption site occupancy (SSO) theory (Willems 2014b) attributes to a strong increase in the number of sorption sites at high RH (Fig. 2). Remarkably, the SSO analysis of the universal normalised EMC curve of Fig. 1 results in a doubling of the number of sorption sites from low h to h = 1 (Fig. 2) and the shape of c(h) curve is not influenced by different wood modifications, including a cross-linking and a softening treatment. The supposed influence of glass softening on the shape of the wood moisture adsorption isotherm in Vrentas theory (Hill and Beck 2017) does therefore not seem to hold as a generic mechanism.

Since the sigmoid sorption isotherm was found associated with each individual active sorption site, a change in the local bonding state of moisture at different h might be a more likely explanation. From the argument that a stable state in unsaturated water vapour requires each adsorbed water molecule to be H-bonded with either (1) two wood-OH groups or (2) one wood-OH and another water molecule, two bonding configurations were proposed (Fig. 3) that could account for the relative increase in the apparent number of sorption sites through the conversion of water monomers into dimers at high RH. The actual number of sorption sites (number of active pairs of OH groups) is therein considered constant at each RH. Each sorption site has a statistical hn occupancy for either a monomer or a dimer, consistent with the analysis of Willems (2014b). The hn-like dependency of all moisture-related integrated FTIR absorption bands, as determined by Olsson and Salmén (2004), suggests that these data show no sensitivity for monomer or dimer occupation of the moisture sorption sites in wood.

The relative quantities of monomer and dimer water can be calculated at any moisture content, temperature and humidity from Eq. 6. Applied to desorption isotherms, hysteresis would be attributed to an excess of dimers and a coupled depletion of monomers in comparison with adsorption. It might be speculated that dimers formed in relatively high numbers at high RH are metastable at lower RH in desorption, in which case a suitable spectroscopic technique might be able to identify the monomer/dimer species by comparison of spectra in adsorption and desorption.

Verification experiments on the postulate of hydroxyl-pair nature of sorption sites are currently being conducted, whereby the EMC changes with respect to quantitative OH content variation are studied. These studies are particularly interesting in conjunction with the poorly understood effect of the partial reversibility of EMC modification in dry heat-treated wood (Obataya and Tomita 2002; Altgen and Militz 2016). In the present model, it requires the destruction of only one OH group to inactivate a OH group pair as a sorption site for water; hence, the short-term effect on EMC is the loss of 1 mol of moisture per 1 mol of removed OH groups (Willems 2014b). However, the OH group singles of the destructed sorption sites may reorganise (mechanical relaxation) to form new OH group pairs. The time required for the reorganisation process increases with the level of cross-linking in the cell wall, and reorganisation is accelerated in varying climates. In effect, the EMC reduction may ultimately attain only ½ mole of moisture per 1 mol of removed OH groups, when all OH group singles have formed new pairs. The available EMC data on dry-heated wood (Obataya and Tomita 2002; Altgen and Militz 2016) indeed show a recovery of around 50% of the thermal EMC reduction after several wet–dry cycles.

The model configurations in Fig. 3 might be extended with larger clusters than dimers, which are deemed important only for RH > 95%. Unfortunately, there are at present no measurement techniques for the determination of the water cluster size distribution in wood to directly verify this assumption. Instead, the RS calculation of Δn11 was used to analyse the likelihood of and the average size of water clusters (Fig. 5). This local excess water number may be directly probed by small angle scattering of X-rays (SAXS) or neutrons (SANS) (Sinibaldi et al. 2008). RS-calculated Δn11 are difficult to interpret in pictorial configurations as in Fig. 3, because the correlation volume of the cluster is undetermined, as pointed out by RS. Moreover, in case of a simultaneous presence of monomers and dimers, Δn11 obviously cannot refer to just one type of interaction. A linear combination of contributions from monomers Δn11,M = − 0.4 and dimers Δn11,D = 1.2 was successfully fitted to the overall excess number (Fig. 5). Naively, one might have expected the values 0 (no cluster) for a monomer and 1 for a dimer, respectively. The fitted negative value (depletion) for the monomer may result from an excess of wood-OH drawn towards the monomer by strong H-bonds. The excess water number for dimers reasonably agrees with the expected value, giving some support to the proposed water monomer/dimer model.

Conclusion

Based on the present moisture sorption isotherm shape analysis, some firm conclusions regarding wood moisture sorption can be drawn:

  1. 1.

    Wood moisture sorption is an enthalpic process

  2. 2.

    Wood moisture adsorption results from a universal occupation law of mobile water species at active sorption sites, controlled by the water chemical potential μ

  3. 3.

    Wood modification treatments primarily change the number of active water sorption sites, each giving an equal contribution to the overall water adsorption isotherm of wood

  4. 4.

    The steep increase in EMC in the sigmoid water adsorption isotherm above RH = 60% is not caused by a softening transition in the wood matrix. Conversely, the increase in EMC at high RH can be suppressed by large compressive stresses, acting on the wood matrix.

These conclusions do not rely on results from the application of the Sorption Site Occupancy theory or any of the model assumptions made in the proposed molecular bonding model of wood moisture.

The model considers a constant number of sorption sites, constituted by wood-OH pairs, binding water as isolated molecules (monomers) or dimers. This provides an alternative explanation for the steep EMC increase at high RH, by preferential occupation of sorption sites by monomers at low RH being converted to dimers at high RH. The occupation of sorption sites by water dimers at high RH is supported by a theoretical cluster calculation result.

The model allows a direct calculation (Eq. 6) of the relative amounts of monomers and dimers at any given EMC, EMCmax, RH and T, in adsorption as well as desorption isotherms. This may be used in the spectroscopic identification of water dimer and monomer species in wood and in sorption hysteresis studies. A second feature of the model, postulating the hydroxyl-pair nature of sorption sites, can be tested by investigating quantitative relationships between accessible OH groups and EMC, taking bulking and structural relaxation effects in the wood cell wall into account.