Viscoelastic Properties of the Chinese Fir (Cunninghamia lanceolata) during Moisture Sorption Processes Determined by Harmonic Tests

Measured by harmonic tests, the viscoelastic properties of Chinese fir during moisture sorption processes were examined under three relative humidity (RH) modes: RHramp, RHisohume, and RHstep. The stiffness decreased and damping increased as a function of the moisture content (MC), which is presumed to be the effect of plasticization and an unstable state. The increasing damping was associated with the breaking of hydrogen bonds and the formation of free volume within polymer networks. The changes of loss modulus ratio at 1 and 20 Hz, E″1Hz/E″20Hz, proved the changing trend of the unstable state. Higher ramping rates aggravated the unstable state at the RHramp period, and higher constant RH levels provided more recovery of the unstable state at the RHisohume period. Changes of viscoelastic properties were associated with RH (varied or remained constant), and the application of Boltzmann’s superposition principle is a good approach to simulate viscoelasticity development.


Introduction
Thermo-hydro-mechanical (THM) treatment of wood, including compression, welding, molding, etc., is a promising eco-friendly method of wood processing technology [1,2] based on the combined treatments of wood by elevated temperature, moisture, and applied mechanical loading (static or dynamic loading). Under the static or dynamic loading, wood exhibits different viscoelastic behaviors. The viscoelasticity of wood is highly dependent on the organization or properties of wood polymers [3,4]. The dynamic mechanical analysis (DMA) is a well-established rheological test that offers insight into the viscoelastic behavior of wood. The improved understanding of viscoelasticity could increase the efficiency of THM treatment and the quality of THM-treated wood. In addition, the development of new processes and products that are in relation to the viscoelastic nature of wood will be achieved [5].
The mechanical properties of wood, from linearly elastic to viscous, are dependent on the temperature, moisture content (MC), and time scale of the test [6][7][8][9]. MC influences nearly all the physical and mechanical properties of wood, as water plays a role of plasticizer, and it forms hydrogen bonds (HBs) to lignin, hemicelluloses, and paracrystalline cellulose. Thus the existing HBs within the polymers are substituted and decrease the wood's stiffness [10]. The plasticization effect of moisture

Measurements of the Viscoelasticity
The dynamic mechanical analysis was performed with the instrument (TA Instruments, DMA Q800) equipped with a DMA-RH accessory, which is able to control the specimen environment in the range of 0% to 90% RH between 5 and 90 °C by modulating the flow rates of the dry nitrogen and saturated moisture. When the flow rate was completely dry nitrogen, the RH in the chamber was zero theoretically. In our previous studies, the actual lowest RH value cloud was close to zero. Therefore, the lowest RH value in this study was pre-set to zero with the neglected deviation. The viscoelasticity was determined at frequencies of 1 and 20 Hz. A dual-cantilever clamp with a distance of 35 mm was applied ( Figure 2). The displacement amplitude created by the oscillated force was 15 μm. Specimens were clamped on the radial surfaces and bending occurred in the tangential direction. After being mounted on the clamp in the testing chamber, the specimens were kept under isohume conditions (30 °C, 0% RH) for 30 min prior to the actual viscoelastic measurements. For investigating the viscoelasticity during the sorption process, three operating modes (RHramp, RHisohume, and RHstep) were conducted. During the DMA test, a storage modulus E′, a loss modulus E″, and a loss factor tanδ (tanδ = E″/E′) were automatically calculated. E′ is the ability of the material to store energy, and represents the elastic part of the material. E″ is the viscous response of the material and is proportional to its dissipated energy.

RHramp Mode
RH in the chamber ramped up from 0% to 90% RH with ramping rates of 0.5%, 1.0%, or 2.0% RH/min, respectively. MC was determined by weighing specimens before and after each RHramp conditioning. To obtain the MC changing trend, some other specimens were also tested under the same RHramp condition, but only until the time points marked as symbols in Figure 3a. Three replicates

Measurements of the Viscoelasticity
The dynamic mechanical analysis was performed with the instrument (TA Instruments, DMA Q800) equipped with a DMA-RH accessory, which is able to control the specimen environment in the range of 0% to 90% RH between 5 and 90 • C by modulating the flow rates of the dry nitrogen and saturated moisture. When the flow rate was completely dry nitrogen, the RH in the chamber was zero theoretically. In our previous studies, the actual lowest RH value cloud was close to zero. Therefore, the lowest RH value in this study was pre-set to zero with the neglected deviation. The viscoelasticity was determined at frequencies of 1 and 20 Hz. A dual-cantilever clamp with a distance of 35 mm was applied ( Figure 2). The displacement amplitude created by the oscillated force was 15 µm. Specimens were clamped on the radial surfaces and bending occurred in the tangential direction. After being mounted on the clamp in the testing chamber, the specimens were kept under isohume conditions (30 • C, 0% RH) for 30 min prior to the actual viscoelastic measurements. For investigating the viscoelasticity during the sorption process, three operating modes (RH ramp , RH isohume , and RH step ) were conducted. During the DMA test, a storage modulus E , a loss modulus E", and a loss factor tanδ (tanδ = E"/E ) were automatically calculated. E is the ability of the material to store energy, and represents the elastic part of the material. E" is the viscous response of the material and is proportional to its dissipated energy.

Measurements of the Viscoelasticity
The dynamic mechanical analysis was performed with the instrument (TA Instruments, DMA Q800) equipped with a DMA-RH accessory, which is able to control the specimen environment in the range of 0% to 90% RH between 5 and 90 °C by modulating the flow rates of the dry nitrogen and saturated moisture. When the flow rate was completely dry nitrogen, the RH in the chamber was zero theoretically. In our previous studies, the actual lowest RH value cloud was close to zero. Therefore, the lowest RH value in this study was pre-set to zero with the neglected deviation. The viscoelasticity was determined at frequencies of 1 and 20 Hz. A dual-cantilever clamp with a distance of 35 mm was applied ( Figure 2). The displacement amplitude created by the oscillated force was 15 μm. Specimens were clamped on the radial surfaces and bending occurred in the tangential direction. After being mounted on the clamp in the testing chamber, the specimens were kept under isohume conditions (30 °C, 0% RH) for 30 min prior to the actual viscoelastic measurements. For investigating the viscoelasticity during the sorption process, three operating modes (RHramp, RHisohume, and RHstep) were conducted. During the DMA test, a storage modulus E′, a loss modulus E″, and a loss factor tanδ (tanδ = E″/E′) were automatically calculated. E′ is the ability of the material to store energy, and represents the elastic part of the material. E″ is the viscous response of the material and is proportional to its dissipated energy.

RHramp Mode
RH in the chamber ramped up from 0% to 90% RH with ramping rates of 0.5%, 1.0%, or 2.0% RH/min, respectively. MC was determined by weighing specimens before and after each RHramp conditioning. To obtain the MC changing trend, some other specimens were also tested under the same RHramp condition, but only until the time points marked as symbols in Figure 3a. Three replicates  RH in the chamber ramped up from 0% to 90% RH with ramping rates of 0.5%, 1.0%, or 2.0% RH/min, respectively. MC was determined by weighing specimens before and after each RH ramp conditioning. To obtain the MC changing trend, some other specimens were also tested under the same RH ramp condition, but only until the time points marked as symbols in Figure 3a. Three replicates for each test were performed and the results plotted in the figures are the average values of the three replicates.

RHisohume Mode
RH in the chamber was firstly adjusted from 0% to 30%, 60%, or 90% RH, with the ramping rate of 2.0% RH/min. Then, the isohume condition was kept for 240 min. MC was determined by weighing, as indicated above. Some specimens were also tested under the same RHisohume condition, but only until the time points marked as symbols in Figure 3b. Three replicates for each test were performed and the results plotted in the figures are the average values of the three replicates.

RHstep Mode
RH in the chamber was adjusted by a ramping rate of 2% RH/min from 0% to 30%, 60%, and 90% RH, successively. The isohume conditions were kept for 60 min. To acquire the MC changing trend,

RH isohume Mode
RH in the chamber was firstly adjusted from 0% to 30%, 60%, or 90% RH, with the ramping rate of 2.0% RH/min. Then, the isohume condition was kept for 240 min. MC was determined by weighing, as indicated above. Some specimens were also tested under the same RH isohume condition, but only

RH step Mode
RH in the chamber was adjusted by a ramping rate of 2% RH/min from 0% to 30%, 60%, and 90% RH, successively. The isohume conditions were kept for 60 min. To acquire the MC changing trend, some specimens were also tested until reaching the RH ramp or RH isohume stages marked as symbols in Figure 3c [28]. Three replicates for each test were performed and the results plotted in the figures are the average values of the three replicates.

Measurement of the Equilibrium Moisture Content (EMC)
Equilibrium moisture contents (EMCs) were reached under constant RH conditions (30%, 60%, and 90% RH) during the isothermal sorption tests, which was determined by means of a dynamic vapor sorption (DVS) Intrinsic apparatus (Surface Measurement Systems Ltd., London, UK). Specimens were prepared from wood chips (ca. 15 mg) after the samples were dried over P 2 O 5 . The preset RH was increased in steps in the preprogrammed sequence (0%, 30%, 60%, and 90% RH). The sorption processes were performed at a constant temperature of 30 • C in the whole RH range. Before moving to the next RH level, the instrument maintained the specimen at the constant RH until the weight changes per minute (dm/dt) were less than 0.002% per minute. Three replicates for the test were performed and the results plotted in the figures are the average values of the three replicates. Figure 4 shows the time dependence of moisture sorption (Figure 4a), which is related to the normalized (n) data concerning nE ( Figure 4b) and nE" (Figure 4c) during the RH ramp period (0% → 90% RH) with different ramping rates measured at 1 Hz. The normalized data are calculated:

Viscoelasticity under RH ramp Mode
where the lower case '0' designates the corresponding data at the beginning of the RH ramp period.
Higher MC values were achieved as a function of time, regardless of the ramping rate ( Figure 4a). At the end of the RH ramp period, MC increased by 7.5%, 4.9% and 3.6% at 0.5%, 1.0%, and 2.0% RH/min, respectively. The higher the RH ramping rate was, the lower the final MC value was obtained. Wood is a hygroscopic material. Moisture is attracted to the surfaces of the test specimen and pores, and absorbed within the wood cell walls. The moisture sorption quantity is determined by the number of polar groups (hydroxyl) in wood's main chemical components, while the sorption rate is influenced by the moisture diffusion rate in the specimen. The moisture diffusion rate is closely related to the structural anatomy of the wood. When moisture penetrates from the specimen shell to the core, the diffusion rate lags behind the RH changes due to the large resistance donated by the lumen-cell wall interface and the interior of the cell wall [29]. In addition, the kinetic sorption was linked to the glass transition of hemicellulose, which allowed for accommodation of more water molecules within the wood cell walls [10]. Lower ramping rate meant longer sorption time within the same RH region, i.e., the longer the sorption time, the higher the final MC was during the transient stage.
During the whole RH ramp period, quasi-linear decrement of nE and increment of nE" were observed in Figure 4b,c. At the end of the RH ramp period, nE were 0.89, 0.91, and 0.93 at 0.5%, 1.0%, and 2.0% RH/min ramping rates, respectively. nE" were 2.00, 2.00, and 1.86 at 0.5%, 1.0%, and 2.0% RH/min ramping rates, respectively. The decreasing normalized E and the increasing normalized E" are attributed to the increase in MC. Water acts as a plasticizer to affect the wood stiffness and soften Materials 2016, 9, 1020 6 of 17 hemicellulose [10,30]. When penetrating into the wood cell wall, water molecules break HBs within the polymers and form HBs between water molecular and amorphous components (hemicellulose, lignin, and paracrystalline cellulose). The plasticization of the amorphous polymers enhances the flexibility of the polymer network [31]. The increasing degree of nE" was obviously higher than the decreasing degree of nE , regardless of the ramping rate. Takahashi et al. confirmed that the decrease in elasticity is not as great as the increase in damping during the sorption process [32]. Since cellulose, hemicellulose, and lignin have different absorbability, the extents of hygro-expansion vary within the wood cell walls, providing the shear slip between cellulose and matrix, and leading to a large energy dissipation [21,24].  The constant ramping rates of RH made it possible to establish the relationships between RH and viscoelasticity. In Figure 5, the MC and viscoelasticity as a function of RH are presented with various RH ramping rates. Not only MC, but also the higher increasing rate of MC was observed at a higher RH level, regardless of the ramping rate (Figure 5a). This is because the new adsorptive sites produce and further increase the amounts of sorption water.
Changes of nE″ were almost the same with increasing RH when the ramping rates were 0.5% and 1.0% RH/min (Figure 5c), although MC and nE′ showed discrepancies of behavior at these two ramping rates (Figure 5a,b). This result may be associated with the existence of an unstable state in the cell wall. The unstable state is the representation of the moisture gradient and stress gradient The constant ramping rates of RH made it possible to establish the relationships between RH and viscoelasticity. In Figure 5, the MC and viscoelasticity as a function of RH are presented with various RH ramping rates. Not only MC, but also the higher increasing rate of MC was observed at a higher RH level, regardless of the ramping rate (Figure 5a). This is because the new adsorptive sites produce and further increase the amounts of sorption water.
period. As seen in Figure 6, higher |∆nE′/∆MC| and |∆nE″/∆MC| were found at lower RH regardless of the ramping rate. On the one hand, these results are related to the varied plasticization effect among different water layers (monomolecular or polymolecular water layer) within the wood cell wall [33]. The plasticization effect on chain segments of wood polymers is likely to be much greater for the monomolecular water layer, and subsequently less for each additional polymolecular water layer [5]. On the other hand, the influence of FV reduces with the increasing MC, i.e., the unstable state diminishes as a function of sorption time [24]. In addition, higher |∆nE′/∆MC| and |∆nE″/∆MC| were obtained at higher ramping rates, which confirms that higher ramping rates produce greater destabilization during the sorption process [24,27,34,35].  Changes of nE" were almost the same with increasing RH when the ramping rates were 0.5% and 1.0% RH/min (Figure 5c), although MC and nE showed discrepancies of behavior at these two ramping rates (Figure 5a,b). This result may be associated with the existence of an unstable state in the cell wall. The unstable state is the representation of the moisture gradient and stress gradient when RH varies. When penetrating into the wood cell wall, moisture molecules not only break HBs within wood polymer, but also associate with the promotion of FV in the wood cell wall for the motions of surrounding polymer substances. The FV in the wood cell wall forms localized stress and disturbs the equilibrium packing of polymer molecules, resulting in more energy dissipation [17,23]. The changes of nE" could be explained by the double-effect of plasticization effect and unstable state. The parameters of |∆nE /∆MC| and |∆nE"/∆MC| were used to evaluate the double-effect and calculated as where the subscript 'i' designates the corresponding data when a predefined RH of 30%, 60%, or 90% is reached, and the subscript '0' designates the corresponding data at the beginning of the RH ramp period. As seen in Figure 6, higher |∆nE /∆MC| and |∆nE"/∆MC| were found at lower RH regardless of the ramping rate. On the one hand, these results are related to the varied plasticization effect among different water layers (monomolecular or polymolecular water layer) within the wood cell wall [33]. The plasticization effect on chain segments of wood polymers is likely to be much greater for the monomolecular water layer, and subsequently less for each additional polymolecular water layer [5]. On the other hand, the influence of FV reduces with the increasing MC, i.e., the unstable state diminishes as a function of sorption time [24]. In addition, higher |∆nE /∆MC| and |∆nE"/∆MC| were obtained at higher ramping rates, which confirms that higher ramping rates produce greater destabilization during the sorption process [24,27,34,35]. In our previous study, it was proposed that changes in the E″ ratio at different frequencies were proposed as an effective method for directly evaluating the unstable state induced by the varying MC [27]. The ratios of E″ at 1 and 20 Hz (E″1Hz/E″20Hz) during the whole RHramp period were calculated and are presented in Figure 7b, combined with the E′ ratios at 1 and 20 Hz (E′1Hz/E′20Hz) in Figure 7a. E′1Hz/E′20Hz ranged at 0.98 without any obvious variation, proving that the stiffness is not influenced by the unstable state at different frequencies. When the stiffness of wood is determined, especially along the longitudinal direction, the most attention is given to cellulose. The rationale is that the cellulose with its highly arranged crystalline structure is the stiff, reinforcing material in the wood cell wall [36]. The most recent analysis estimated that the elastic modulus in the longitudinal direction (Ex) for the cellulose crystalline region ranged between 120 and 170 GPa [37]. It is found that Ex basically does not vary with the increasing MC because the moisture is only absorbed on the microfibril surfaces and does not penetrate into the interior spaces. Therefore, the stiffness is not In our previous study, it was proposed that changes in the E" ratio at different frequencies were proposed as an effective method for directly evaluating the unstable state induced by the varying MC [27]. The ratios of E" at 1 and 20 Hz (E" 1Hz /E" 20Hz ) during the whole RH ramp period were calculated and are presented in Figure 7b, combined with the E ratios at 1 and 20 Hz (E 1Hz /E 20Hz ) in Figure 7a. E 1Hz /E 20Hz ranged at 0.98 without any obvious variation, proving that the stiffness is not influenced by the unstable state at different frequencies. When the stiffness of wood is determined, especially along the longitudinal direction, the most attention is given to cellulose. The rationale is that the cellulose with its highly arranged crystalline structure is the stiff, reinforcing material in the wood cell wall [36]. The most recent analysis estimated that the elastic modulus in the longitudinal direction (Ex) for the cellulose crystalline region ranged between 120 and 170 GPa [37]. It is found that Ex basically does not vary with the increasing MC because the moisture is only absorbed on the microfibril surfaces and does not penetrate into the interior spaces. Therefore, the stiffness is not affected by the unstable state.

Viscoelasticity under RHisohume Mode
The time-dependent nature of wood moisture sorption, nE′ and nE″, during the RHisohume period (30%, 60%, and 90% RH) is shown in Figure 8. During the RHisohume period, a lower increasing rate of MC was found as a function of time, showing that the wood is approaching EMC during the isohume exposure period. The higher the RH level, the higher and faster increase in MC was found. After the RHisohume period of 240 min, the final values of MC were 3.4%, 7.1%, and 12.1% at 30%, 60%, and 90% RH, respectively (Figure 8a). Wood gains moisture from the surrounding atmosphere and approaches EMC. Through the DVS tests, EMC at 30%, 60%, and 90% RH is 8.0%, 13.7%, and 23.2%, respectively. In Figure 9, MCd (the difference value of MC during the RHisohume period and EMC at 30%, 60%, and 90% RH) was calculated as where the subscript 'a' represents the EMC value at 30%, 60%, or 90% RH, by DVS tests, and the subscript 'i' designates the corresponding MC at each RHisohume time point (60, 120, or 240 min). Regardless of the RHisohume level, MCd decreased as a function of time. Within the same isohume time, the higher the RH level, the more pronounced decreasing rate was obtained, i.e., the higher the sorption rate. The sorption rate is controlled by the external resistance from the boundary layer and the internal resistance from the wood cell walls. Avramidis and Siau found that the external resistance decreases with the increasing RH, confirming that quicker sorption rates could be observed at higher RH levels [39]. nE′ (Figure 8b) decreased and nE″ (Figure 8c) increased during all three RHisohume periods (30%, 60%, and 90% RH). The higher the RH level, the lower the nE′ and the higher the nE″ observed. These Figure 7. Influence of RH on E 1Hz /E 20Hz (a) and E" 1Hz /E" 20Hz (b) during the RH ramp period (0% → 90% RH) with different RH ramping rates. E" 1Hz /E" 20Hz ( Figure 7b) increased with the increase in RH, indicating the presence of an unstable state and the energy dissipation with the RH increment. The changes of E" ratios at 1 and 20 Hz could be caused by that lower frequency, which allows a more complete evolution of the unstable state [38]. Hence the increase in E" 1Hz /E" 20Hz would be observed when the unstable state is more pronounced. Furthermore, at the end of the RH ramp period, E" 1Hz /E" 20Hz was 1.21, 1.25, and 1.28 at ramping rates of 0.5%, 1.0%, and 2.0% RH/min, respectively. Greater values of E" 1Hz /E" 20Hz were found at higher ramping rates, which confirmed the increasing destabilization effect and more energy dissipation.

Viscoelasticity under RH isohume Mode
The time-dependent nature of wood moisture sorption, nE and nE", during the RH isohume period (30%, 60%, and 90% RH) is shown in Figure 8. During the RH isohume period, a lower increasing rate of MC was found as a function of time, showing that the wood is approaching EMC during the isohume exposure period. The higher the RH level, the higher and faster increase in MC was found. After the RH isohume period of 240 min, the final values of MC were 3.4%, 7.1%, and 12.1% at 30%, 60%, and 90% RH, respectively (Figure 8a). Wood gains moisture from the surrounding atmosphere and approaches EMC. Through the DVS tests, EMC at 30%, 60%, and 90% RH is 8.0%, 13.7%, and 23.2%, respectively.
In Figure 9, MC d (the difference value of MC during the RH isohume period and EMC at 30%, 60%, and 90% RH) was calculated as where the subscript 'a' represents the EMC value at 30%, 60%, or 90% RH, by DVS tests, and the subscript 'i' designates the corresponding MC at each RH isohume time point (60, 120, or 240 min). Regardless of the RH isohume level, MC d decreased as a function of time. Within the same isohume time, the higher the RH level, the more pronounced decreasing rate was obtained, i.e., the higher the sorption rate. The sorption rate is controlled by the external resistance from the boundary layer and the internal resistance from the wood cell walls. Avramidis and Siau found that the external resistance decreases with the increasing RH, confirming that quicker sorption rates could be observed at higher RH levels [39].
where the subscript 'i' designates the corresponding data at each RHisohume time point (60, 120, or 240 min) while the subscript '0' is for the data obtained at the beginning of the RHisohume period.  These values are plotted as a function of time in Figure 10. The values of |∆nE′/∆MC| (Figure 10a) were basically constant, and ranged by about 0.01 at all three RHisohume levels. The basically constant values of |∆nE′/∆MC| explain why the wood stiffness has a linear relationship with MC under RHisohume conditions [41,42]. A linear decrease of |∆nE″/∆MC| (Figure 10b) was observed regardless of RHisohume level. The lower values of |∆nE″/∆MC| could be observed as a function of sorption time, illustrating that |∆nE″/∆MC| decreased with the increasing MC. These results can probably be attributed to two aspects: (1) more rapid sorption is associated with greater changes in damping, especially early in the RHisohume period; and (2) during the RHisohume period, the unstable state of wood cell wall is mitigated and polymers can be stabilized because of the reorientation of molecular chains [24,27,34,35].  nE (Figure 8b) decreased and nE" (Figure 8c) increased during all three RH isohume periods (30%, 60%, and 90% RH). The higher the RH level, the lower the nE and the higher the nE" observed. These results confirm the plasticization effect of water, which enhanced the flexibility of the polymer network [31]. Compared to nE , greater changes of nE" were found at all three RH isohume levels, which is proved by the large change in energy dissipation owing to the shear slip between the cellulose and matrix [21,24,40]. The changes of |∆nE /∆MC| and |∆nE"/∆MC| were calculated as where the subscript 'i' designates the corresponding data at each RH isohume time point (60, 120, or 240 min) while the subscript '0' is for the data obtained at the beginning of the RH isohume period. These values are plotted as a function of time in Figure 10. The values of |∆nE /∆MC| (Figure 10a) were basically constant, and ranged by about 0.01 at all three RH isohume levels. The basically constant values of |∆nE /∆MC| explain why the wood stiffness has a linear relationship with MC under RH isohume conditions [41,42]. A linear decrease of |∆nE"/∆MC| (Figure 10b) was observed regardless of RH isohume level. The lower values of |∆nE"/∆MC| could be observed as a function of sorption time, illustrating that |∆nE"/∆MC| decreased with the increasing MC. These results can probably be attributed to two aspects: (1) more rapid sorption is associated with greater changes in damping, especially early in the RH isohume period; and (2) during the RH isohume period, the unstable state of wood cell wall is mitigated and polymers can be stabilized because of the reorientation of molecular chains [24,27,34,35].
In order to analyze the unstable state during the RH isohume period, the values of E 1Hz /E 20Hz and E" 1Hz /E" 20Hz were also calculated and are presented in Figure 11. E 1Hz /E 20Hz (Figure 11a) remained at 0.98 with no obvious variation, which is consistent with the results during the RH ramp period. E" 1Hz /E" 20Hz ( Figure 11b) decreased with the RH isohume time regardless of RH level, indicating the diminishing energy dissipation and mitigating the unstable state. At the end of the RH isohume period, E" 1Hz /E" 20Hz decreased by 7.2%, 9.5%, and 10.3% at the RH isohume level of 30%, 60%, and 90% RH, respectively. Much reduction in E" 1Hz /E" 20Hz at higher RH isohume indicates a rapid recovery of the unstable state. To investigate the relationships between unstable state and MC d , the values of E" 1Hz /E" 20Hz at RH isohume time points (60, 120, and 240 min) were plotted as a function of MC d , as shown in Figure 12. E" 1Hz /E" 20Hz quasi-linearly decreased with the decreasing MC d at all three RH isohume levels. The decreasing in E" 1Hz /E" 20Hz represents that the unstable state diminishes when MC approaches the equilibrium value, i.e., the EMC value. In addition, the higher the isohume RH level, the greater the reduction in E" 1Hz /E" 20Hz observed, showing that a higher RH level provides more mitigation of the unstable state during the RH isohume period.
were basically constant, and ranged by about 0.01 at all three RHisohume levels. The basically constant values of |∆nE′/∆MC| explain why the wood stiffness has a linear relationship with MC under RHisohume conditions [41,42]. A linear decrease of |∆nE″/∆MC| (Figure 10b) was observed regardless of RHisohume level. The lower values of |∆nE″/∆MC| could be observed as a function of sorption time, illustrating that |∆nE″/∆MC| decreased with the increasing MC. These results can probably be attributed to two aspects: (1) more rapid sorption is associated with greater changes in damping, especially early in the RHisohume period; and (2) during the RHisohume period, the unstable state of wood cell wall is mitigated and polymers can be stabilized because of the reorientation of molecular chains [24,27,34,35].  In order to analyze the unstable state during the RHisohume period, the values of E′1Hz/E′20Hz and E″1Hz/E″20Hz were also calculated and are presented in Figure 11. E′1Hz/E′20Hz (Figure 11a) remained at 0.98 with no obvious variation, which is consistent with the results during the RHramp period. E″1Hz/E″20Hz (Figure 11b) decreased with the RHisohume time regardless of RH level, indicating the diminishing energy dissipation and mitigating the unstable state. At the end of the RHisohume period, E″1Hz/E″20Hz decreased by 7.2%, 9.5%, and 10.3% at the RHisohume level of 30%, 60%, and 90% RH, respectively. Much reduction in E″1Hz/E″20Hz at higher RHisohume indicates a rapid recovery of the unstable state. To investigate the relationships between unstable state and MCd, the values of E″1Hz/E″20Hz at RHisohume time points (60, 120, and 240 min) were plotted as a function of MCd, as shown in Figure 12. E″1Hz/E″20Hz quasi-linearly decreased with the decreasing MCd at all three RHisohume levels. The decreasing in E″1Hz/E″20Hz represents that the unstable state diminishes when MC approaches the equilibrium value, i.e., the EMC value. In addition, the higher the isohume RH level, the greater the reduction in E″1Hz/E″20Hz observed, showing that a higher RH level provides more mitigation of the unstable state during the RHisohume period.

Viscoelasticity under RH step Mode
The changes of ambient RH (a), wood MC (b), E (c), and E" (d) are presented in Figure 13. The changes of stiffness ( Figure 13c) and damping (Figure 13d) during the RH step period are related to the plasticization and the unstable state effects [28]: The plasticization effect of moisture molecules causes decreasing stiffness and increasing damping, no matter whether RH is varied or constant. Concerning the unstable state effect, the varied RH, as a driving force, accelerates the sorption of water molecules on the specimen surface and aggravates the moisture gradient from the specimen shell to core [29]. On the other hand, localized stresses occur when external stresses are concentrated in the more moisture-sensitive load-bearing elements, such as the matrix, which would further aggravate the localized stress-driven (or heterogeneity-driven) unstable state effect [43].
In order to simulate viscoelasticity during the RH step period, Boltzmann's superposition principle was used to estimate in each RH ramp and RH isohume stage. Zhuoping confirmed that the rheology properties of wood could be simulated conveniently by the application of the generalized Boltzmann's superposition principle [44]. The summations of the viscoelasticity in each stage were expressed as: where E 0 and E" 0 are the initial values in the RH step period. ∆t equals 15 or 60 min for the time of RH ramp or RH isohume stage, respectively. When MC increased continuously, Equations (8) and (9) could be depicted by the integrals: Based on the regressions of E , E", and MC during the RH ramp and RH isohume stages, the predicted values of E and E" are presented in Figure 13c,d, together with the tested values. In Figure 13c, the discrepancy of predicted and tested value of stiffness could be obviously observed when RH was up to 60%; meanwhile, the prediction of damping was not well fitted when RH remained constant at 30% or 60% RH (Figure 13d). The deviations of stiffness and damping were probably associated with the varied unstable state effect when RH changed or remained constant, which merits further investigation.

Conclusions
The influence of RH on the viscoelastic properties of the Chinese fir during sorption processes was investigated by the RHramp, RHisohume, and RHstep modes. The conclusions of this study are as follows: Figure 13. Changes of the RH (a); MC (b); normalized E (c); and normalized E" (d) during the RH step period (0% → 30% → 60% → 90% RH).

Conclusions
The influence of RH on the viscoelastic properties of the Chinese fir during sorption processes was investigated by the RH ramp , RH isohume , and RH step modes. The conclusions of this study are as follows: (1) The changes of E and E" during moisture sorption processes are attributed to the water plasticization effect and the unstable state in wood cell walls. The unstable state is related to the breaking of hydrogen bonds within the polymer network, and the formation of free volume in cell walls. (2) Higher ramping rates aggravated the unstable state during the RH ramp period, and higher constant RH levels provided more recovery of the unstable state during the RH isohume period. During the sorption process, the more recovery of unstable state was observed when MC was approaching EMC.
Changes of viscoelasticity are associated with whether RH varied or remained constant. The varied RH, as a driving force, aggravated the internal stress gradients and accelerated the unstable state. The application of Boltzmann's superposition principle is an approach to simulate the viscoelasticity in an in-depth investigation.