Water vapour sorption of wood modified by acetylation and formalisation – analysed by a sorption kinetics model and thermodynamic considerations

Experimental details

Scots pine wood blocks (P. sylvestris L.) were modified as previously described (Himmel and Mai 2014). Four sets of specimens were obtained: (i) Control samples only treated with the Lewis acid catalyst zinc chloride (ZnCl₂) (Ctrl. W_FA); (ii) samples modified with FA in presence of ZnCl₂ (W_FA); (iii) untreated control samples as reference for acetylated specimens (Ctrl. W_ac) and (iv) acetylated samples (W_ac). Weight percent gain (WPG), cell wall bulking, maximum swelling (Sw_max) and reduced maximum swelling (Sw_{max, red}) are depicted in Table 1 and discussed in Himmel and Mai (2014). Sorption isotherm analyses were performed using a DVS Intrinsic device (DVS, Surface Measurement Systems, London, UK) as described previously (Himmel and Mai 2014). The DVS apparatus provides very accurate isotherm data and sorption kinetics (Hill et al. 2009; 2010b). Hill et al. (2009) concluded that differences in sorption and desorption isotherms of different fibre types recorded in a DVS apparatus can be reliably determined below 70% RH, while differences were discernible up to 90% RH. Randomised single measurements, however, confirmed that the DVS data are very precise and reproducible (own results). Therefore, one representative sample of ca. 20 mg wood powder was used for each measurement. The calculated MC of modified wood is influenced by the additional weight of the modification chemical (Hill 2008; Dieste et al. 2010). To eliminate this influence, the reduced MC (MC_R) and the EMC_R were calculated based on the dry mass of treated samples before modification (Akitsu et al. 1993) according to Popescu et al. (2014):

The following analysis with numeric models is based on sorption isotherm data, which were previously discussed by Himmel and Mai (2014).

Theory of the PEK model

Kohler et al. (2003) reported that sorption of water vapour in natural cellulose structures can be understood as a 1^st order reaction of two sorbates by two independent, parallel processes characterised by their characteristic times. The underlying assumption is that two types of sorption sites exist for cellulosic material each with a limited sorption capacity for storage of equilibrium mass and that the driving force of adsorption and desorption of the sorptive in the vapour phase and of the sorbate at and inside the material is the difference in chemical potential. Temperature changes caused by the heat of sorption were not considered in their model. Thus, the PEK model provides two distinct mechanisms, each defined by its characteristic time and equilibrium mass value, which allows the calculation of two theoretical sorption components and the whole sorption curve for each RH interval. A slow and a fast kinetics process are related to corresponding slow and fast sorption sites (Kohler et al. 2003). The PEK model introduced by Kohler et al. (2003) and adapted to the sorption of wood by Hill et al. (2010b) is as follows:

and for the MC decrement in desorption, respectively

where MC (or MC_R) is the moisture content at time t of exposure of the sample to a constant RH, MC₀ is the moisture content or reduced moisture content of the sample at time zero or at the time at which the RH is constant after a change of RH, respectively. The two independent fast and slow sorption processes are represented by two exponential terms having characteristic times of t₁ and t₂. MC₁ and MC₂ are the moisture content or reduced moisture content increments or decrements of the sample exposed to a constant RH associated with the two independent processes.

PEK model fitting

The kinetics curve of each RH interval was obtained by plotting MC_R of the sample vs. time; MC_R is equal to MC for W_untr, and time zero corresponds to the point, at which a RH step change occurs. As reported previously (Kohler et al. 2003; Hill et al. 2010a,b,c, 2012), there is a finite time needed to stabilise the RH after moving from one set value to the next, which influences the MC of the sample and thus the precision of the fit. Hill et al. (2010a,b,c, 2012) concluded that the MC data points of the 1^st min should be removed from the fit to ensure that the characteristic times (t₁ and t₂) of any fit are representative of the material. However, as the time needed to stabilise the RH varies between the RH intervals, all data points of each experimental kinetics curve were removed from the fit, when the measured RH would differ from the target RH by absolutely more than 4% and/or relatively more than 25%.

Additionally, the results of the fit considerably depend on the start values selected for iteration; thus recalculating the same model with changed start values can give different results (Kohler et al. 2003). Due to the limitation mentioned, a two-step procedure was used to fit the non-linear PEK model (Eq. 2 for adsorption and Eq. 3 for desorption) to the experimental kinetics data for each RH interval using the “nls2” library (Grothendieck 2014) of the statistical software R (R Development Core Team 2008). In a 1^st step, a grid search (brute-force algorithm) was performed to fit the PEK model for each RH interval. In the 2^nd step, the estimated model parameters from step one served as start values for the iterative model fitting by means of the NL2SOL algorithm.

The EMC_R values of the slow and fast component adsorption isotherm are the sum of the estimated MC_R (MC₁, MC₂) value of each RH step and the calculated EMC_R value of the former RH step (Kohler et al. 2003). The EMC_R values of the slow and fast component desorption isotherm are obtained by subtracting the estimated MC_R (MC₁, MC₂) value of each RH step from the calculated EMC_R value of the former RH step. The starting point was the calculated EMC_R maximum at 95% RH from the corresponding adsorption isotherm. The total modelled adsorption and desorption branches are the sum of slow and fast components.

Theory of the ESW

Adsorption systems might be regarded as an open system in mechanical and thermal equilibrium (Adolphs and Setzer 1996; Adolphs 2007). Based on this assumption, the notion ESW was introduced by Adolphs and Setzer (1996) as a new thermodynamic function, defined as the sum of surface free energy and isothermal isobaric work of sorption (Churaev et al. 1998). Thus, each adsorbed molecule decreases the surface energy and simultaneously increases the work of sorption. Plotting the ESW vs. the number of sorbate molecules, the volume or the mass of adsorbate results in a minimum, if both, the free sorption energy and work of sorption are balanced (Adolphs and Setzer 1996; Adolphs 2007). This implies that the ESW minimum (ESW_min) defines a completed monolayer, that is, the sum of the areas of adsorbed molecules at the maximum of interaction with the adsorbent (Adolphs and Setzer 1996; Adolphs 2007). Below ESW_min, the surface free energy dominates; in contrast, the work of sorption is prevalent at higher sorption capacities, meaning that after completion of a monolayer the surface-adsorbate interaction changes to an adsorbate-adsorbate interaction (Adolphs 2007). This enables calculation of the specific surface area of an adsorbent related to its dry mass as well as of the surface energy directly from the sorption isotherm by considering the monolayer capacity (number of adsorbed molecules at ESW_min) and the specific surface occupied by an adsorbed molecule in the monolayer (Adolphs and Setzer 1996). As wood behaves like a swelling gel, the surface area increases with increasing vapour sorption and swelling. Thus, the specific surface area determined from ESW_min is defined as the area, where a minimum of swelling has occurred and all sorption sites form a monolayer of sorbed water molecules.

Calculation of the ESW and the specific surface area

The ESW Φ was calculated based on the EMC of W_untr and EMC_R of W_tr according to Kohler et al. (2003) (Eq. 4) based on the thermodynamic function of Adolphs and Setzer (1996).

where n_ads is the number of sorbate molecules (surface excess amount), Δμ change in chemical potential, M_∞ sorbate mass in equilibrium or MC in equilibrium, M_mol molar mass of the sorbate, R gas constant with 8.31447(15) J mol^-1 K^-1 (Mohr et al. 2008), T absolute temperature in Kelvin and (p/p₀)=(RH/100) equilibrium partial pressure of the sorptive vapour.

The specific surface area A of an adsorbent related to its dry mass is defined as (Adolphs and Setzer 1996):

where n_mono is the monolayer capacity (number of adsorbed molecules at ESW_min), N_A is the Avogadro constant with 6.02214179(30) 10²³ mol^-1 (Mohr et al. 2008), and A_mol is the specific surface occupied by an adsorbed water molecule with approximately 18 Ų (=1.8 10^-19 m²) (Butenuth et al. 2004).

PEK model

Kinetics curve fitting

As in this work the limitations of the PEK model are considered, a high goodness of fit was achieved in most cases for fitting the non-linear PEK model equations (Eqs. 2 and 3) to the sorption data of W_untr and W_tr. This is in accordance to previous studies (Hill et al. 2010a,b; Xie et al. 2010; Zaihan et al. 2010a,b; Popescu et al. 2014). In contrast to these previous studies, however, it was impossible to estimate MC_R increments and decrements (MC₁ or MC₂) and the characteristic times (t₁ or t₂) associated with the slow sorption process for all RH intervals for W_untr and W_tr (Figures 1a–d and 2a–d); in those cases, one of the two exponential terms were approaching zero and thus give unrealistic and non-significant estimations. The latter was the case, either if the estimation of the characteristic time (t₁ or t₂) became very high or if the corresponding estimated MC_R increment or decrement (MC₁ or MC₂) was approaching zero. From these results, however, it cannot be concluded that the slow (relaxation limited, Popescu et al. 2014) sorption process did not occur in these RH intervals. Apparently, the kinetics curves of W_untr and W_tr for low and high RH showed a less pronounced double exponential form; thus, the calculation of two theoretical sorption components was impossible with the PEK model. Therefore, the authors decided to exclude those non-significant estimations from the calculation of the slow adsorption and desorption branch as well as from the total modelled adsorption and desorption isotherm (Figures 1a–d and 2a–d).

Figure 1:

Comparison of measured adsorption isotherms and calculated isotherms produced from the PEK model fits for the untreated controls (a) Ctrl. W_ac and (b) Ctrl. W_FA as well as the modified wood samples (c) W_ac and (d) W_FA.

Figure 2:

Comparison of measured desorption isotherms and calculated isotherms produced from the PEK model fits for the untreated controls (a) Ctrl. W_ac and (b) Ctrl. W_FA as well as the modified wood samples (c) W_ac and (d) W_FA.

Desorption

It has previously been shown that the desorption curve measured with a DVS apparatus differs from the desorption boundary curve obtained from water saturated wood; the DVS curve was therefore denoted “scanning curve” (Engelund et al. 2010). Furthermore, according to Kohler et al. (2003) it is difficult to select the accurate point from which the calculation of desorption starts. They suggested to calculate the weight loss (desorption branch) beginning at the maximum point of the whole isotherm which is the maximum point of adsorption. This should be considered for the following discussion.

For W_untr, the slow desorption process, also referred to as desorption from the slow sites (Kohler et al. (2003), proceeded less rapid than the slow adsorption, which resulted in a noticeable amount of retaining water at 0% RH (Figures 2a and b, 3a and b). In contrast, more water was obviously desorbed by the fast process than adsorbed. Kohler et al. (2003) assumed that some of the water, primarily adsorbed by the slow process, is stored at newly generated fast sites (called extra water) which might have been created upon swelling (Runkel and Lüthgens 1956; Malmquist and Söderström 1996). This extra water can be desorbed by the fast process. Regarding the extra water (Figure 3a and b), however, it seems that the higher amount of water adsorbed at high RH by the slow process was somewhat compensated by a higher moisture decrement at low RH. Thus, the extra water from the adsorption process was mainly but not totally desorbed by the fast process. Ctrl. W_FA (pretreated with ZnCl₂) indicated less extra water compared to the untreated control, probably due to the degraded hemicelluloses. At 80% RH both controls showed an unexpected sudden change in their difference of MC increment and decrement for the slow and fast process. This effect could not be explained for the time being. For W_ac, the described effect was also observed but to a lesser extent (Figures 2c and 3c). Less new sorption sites were generated by swelling of W_ac, because of the diminished relaxation in the volumetric margin between cell wall bulking and maximum water swelling. Still, it cannot be assumed that extra water was completely desorbed by the fast process because EMC_R values could not be estimated for the slow process in adsorption and desorption for the RH range below 20%.

Figure 3:

Difference (Δ) of moisture increment and decrement at given RH level during the sorption run associated with the “fast” and “slow” kinetic processes. Untreated controls (a) Ctrl. W_ac and (b) Ctrl. W_FA as well as the modified wood samples (c) W_ac and (d) W_FA.

For desorption of W_FA, however, formation of extra water hardly occurs (Figure 2d). Up to 20% RH, W_FA behaves like its control and at higher RH range W_FA showed a somewhat higher adsorption than desorption in the slow process (Figure 3c and d).

Assuming that the slow and fast sorption process estimated with the PEK model represent different forms of sorbate-sorbent or sorbate-sorbate interaction (Kohler et al. 2003, Xie et al. 2010), it seems that the form of interaction represented by both processes is different in adsorption and desorption. Thus, further investigations of the dynamic water vapour sorption in combination with, for example, spectrometric methods are needed to explain the effect of extra water.

Hysteresis

The hysteresis of wood has previously been interpreted in terms of sorption into and out of nanopores embedded in a glassy solid matrix below the glass transition temperature (T_g) (Hill et al. 2010b). According to the model of Lu and Pignatello (2002), the matrix is kinetically hindered, attaining thermodynamically stable configurations during desorption and adsorption, which may occur in different physically environment.

In W_untr, swelling occurs due to relatively high flexibility of the cell wall matrix, and the differences between the physical state at adsorption and desorption are large (Himmel and Mai 2014). The course of the hysteresis associated with the fast sorption process for the control specimens was almost equal to that of W_ac. These were strongly negative at low RH and increased almost linear to zero at high RH (Figure 4a–c). It is assumed that cross-linking by FA significantly reduces swelling (Table 1) because it increased the resistance of the cell wall to deformation at high RH and reduces the time lag due to matrix relaxation and, thus, hysteresis. The smaller hysteresis of W_FA was dominated by the hysteresis of the slow process (Figure 4d), while the one attributed to the fast process was almost constant and close to zero over the whole RH range; the latter indicates that extra water was hardly formed.

It was previously assumed that an association of the two sorption components with hysteresis may only be found for the slow process (Hill et al. 2012; Popescu et al. 2014). Kohler et al. (2003) presumed, however, that hysteresis cannot exclusively been explained by one process. This was confirmed for the control specimens and W_ac. As compared to the controls, acetylation did not hinder the relaxation of the cell wall matrix; swelling created new fast sorption sites relatively to the same extent like in the controls. For W_FA, however, it is assumed that the hysteresis was mainly attributed to the slow process.

Figure 4:

Comparison of hysteresis of sorption isotherms produced from the PEK model fits; the graphs show the total hysteresis and the hysteresis associated with the “fast” and “slow” kinetic processes for the untreated controls (a) Ctrl. W_ac and (b) Ctrl. W_FA as well as the modified wood samples (c) W_ac and (d) W_FA.

Excess surface work

ESW_min defines a completed monolayer, that is, the sum of the areas of adsorbed molecules at the maximum of interaction with the adsorbent (Adolphs and Setzer 1996; Adolphs 2007). For Ctrl. W_ac, the ESW values were almost equal in the range of RH 30%–40% (Figure 5a). However, the ESW_min (i.e., completion of the monolayer or the maximum of interaction of incoming water molecules with the OH groups) was reached at RH 40% (Table 2). Ctrl. W_FA also showed similar ESW values around its ESW_min in the range of RH 15%–30% (Figure 5a). Both controls exhibited similar ESW_min (Figure 5a, Table 2), but Ctrl. W_FA reached the completion of the monolayer at lower EMC and corresponding RH than Ctrl. W_ac. This resulted in a lower monolayer capacity (n_mono) and thus in a lower specific surface area (A) for Ctrl. W_FA (Table 2). These findings are attributed to the degradation of hemicelluloses by ZnCl₂. Above EMC of approximately 6% and 40% RH, however, both controls displayed almost equal courses of ESW.

Figure 5:

Comparison of the excess surface work (ESW) of untreated controls (Ctrl. W_ac and Ctrl. W_FA), acetylated wood (W_ac) and formaldehyde-modified wood (W_FA) specimens as a function of the adsorbed mass of water (a). The ESW ratios (b) of modified wood specimens related to their untreated controls were calculated from the ESW values at each given RH during the adsorption run.

W_FA showed similar value of ESW_min and reached the completion of the monolayer at 15% RH, that is, in the same RH range as its control (Figure 5a). Based on ESW_min, however, W_FA reached the completion of the monolayer at somewhat lower EMC_R and corresponding RH than its control (Table 2). Up to 20% RH, the measured adsorption isotherms as well as the fast adsorption isotherm components of W_FA and its control were almost equal (Figure 1b and d). Still, Ctrl. W_FA and W_FA revealed differences. Specific surface area (A) and n_mono of W_FA were somewhat lower than those of Ctrl. W_FA (Table 2). After establishing a completed monolayer, the ESW of W_FA deceased much more strongly with increasing adsorbed water and corresponding RH than both controls and W_ac (Figure 5a). This resulted in a decreasing course of the ESW ratio of W_FA above 15%–20% RH (Figure 5b), which is equivalent to a decreasing EMC ratio of W_FA reported previously (Himmel and Mai 2014). These effects are caused by the inflexible cross-linking of cell wall polymers by formalisation; the extension of the cell wall matrix is confined (Burmester 1971; Yasuda et al. 1995; Rowell 2006). Hence, the swelling is hindered and thus monomolecular adsorption of water molecules on the new created sorption sites during swelling as well as the polymolecular adsorption is reduced. W_ac, in contrast, exhibited considerably lower ESW values over the whole hygroscopic range compared to Ctrl. W_ac (Figure 5a). Monolayer capacity (n_mono) and, with it, the corresponding EMC_R were reduced due to acetylation. As for W_FA, W_ac reached the completion of the monolayer with RH of 30% in the same RH range as its control (Figure 5a), even if W_ac reached the absolute minimum of ESW at lower RH as compared to its control (Table 2). In contrast to W_FA, however, the slope of the ESW curve of W_ac is less steep and runs parallel to both controls. Thus, the ESW (i.e., the work of sorption after completion of monolayer) was only reduced by a constant factor which is the bulking coefficient. As a consequence, the ESW ratio was constant above 15%–20% RH as previously observed for the EMC ratio (Himmel and Mai 2014).