Surface fractal analysis of the pore structure in natural and heat-treated spruce wood cell walls using nitrogen adsorption/desorption test

doi:10.21203/rs.3.rs-1991981/v1

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Surface fractal analysis of the pore structure in natural and heat-treated spruce wood cell walls using nitrogen adsorption/desorption test

https://doi.org/10.21203/rs.3.rs-1991981/v1

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Surface fractal dimension evaluates the internal surface complexity of pores in a wide range of materials. Unfortunately, the scale-dependent property of surface fractal in the pore structure of natural and heat-treated wood remains unclear. In this study, derived from the Frenkel-Halsey-Hill (FHH) fractal model and the Neimark fractal model, a comprehensive surface fractal analysis of the pore structure of natural and heat-treated wood was carried out based on nitrogen adsorption/desorption data. The results showed that two regions were identified as surface fractal, i.e., the pores with diameters less than 10 nm (Region 1) and the pores with diameters larger than 10 nm (Region 2). The scale-dependent property of two fractal regions was not affected by the different heat treatment atmospheres. The FHH and Neimark surface fractal dimensions of the pores in Region 1 were 2.079–2.155 and 2.780–2.940, respectively, and showed an obvious difference. The FHH and Neimark surface fractal dimensions of the pores in Region 2 were 2.481–2.536 and 2.413–2.551, respectively, and showed a slight difference. In addition, the FHH surface fractal dimensions of the pores in Region 2 had a positive relationship with the rate of early-stage moisture absorption. These findings are expected to evaluate the relationship between the transport properties and the pore structure in wood cell walls through the surface fractal dimension.

Heat treatment

nitrogen adsorption/desorption test

pore structure

spruce wood

surface fractal dimension

The pores in wood cell walls significantly affect the properties of wood such as moisture diffusion, sound adsorption, gas permeability, heat conductivity, and strength (Eitelberger and Hofstetter 2011a, 2011b; Yuan et al. 2013; Wang et al. 2017; Jang and Kang 2019; Jang et al. 2020; Zhao, Guo, et al. 2021). Unfortunately, wood has a more heterogeneous pore structure than most porous materials (Fahlén and Salmén 2005; Eitelberger and Hofstetter 2011b). For example, the classification of pore size defined by the IUPAC does not quite fit with the complex anatomy of wood (Rouquerol et al. 1994). Several experimental methods have been applied to examine the complex pore structure in wood cell walls, including scanning electron microscopy (SEM), nuclear magnetic resonance (NMR), differential scanning calorimetry (DSC), mercury intrusion porosimetry (MIP), and gas adsorption analysis (Papadopoulos et al. 2003; Kojiro et al. 2008; Grigsby et al. 2013; Zauer et al. 2014; Peng et al. 2015; Shi and Avramidis 2018; Li and Zhao 2020; Shen et al. 2021). However, the SEM test has a small field of vision and needs high-quality slices of wood samples, which is time-consuming; NMR and DSC are extremely expensive tests; and the MIP test lacks accuracy for small pores due to the fact that pores in cell walls collapse under high intrusion pressure. Among the above techniques, the nitrogen adsorption/desorption (NAD) test is an effective and much cheaper method to examine the pore structure in wood cell walls.

At first, fractal geometry was proposed to describe the grossly irregular of nature (Mandelbrot 1982). In recent years, fractal geometry has widely been regarded as an important approach to describe the complex pore structure of many natural and artificial porous materials, such as soils, rocks, coals, and cement pastes (Xu 2004; Lai and Wang 2015; Liu and Nie 2016; Tang et al. 2017). The fractal dimension is a measure of the ability of a fractal object to “fill” its space and should be determined first before fractal geometry can be used to characterize the structure of pores in wood cell walls. There are pieces of research on the calculation of the fractal dimension of wood using light microscopic and digital camera images, X-ray computed tomography scanning images, two-dimensional images obtained by scanning electron microscopy (SEM) imaging, or three-dimensional topographical images obtained by atomic force microscopy (AFM) imaging (Koňas et al. 2009; Yu and Qi 2011; Li et al. 2016; da Conceição et al. 2021). However, these calculation methods only included an image analysis, which is limited by the resolution and therefore not suitable for the pore structure in wood cell walls. The MIP test has been used to determine the fractal dimension of pores ranging from 2 nm to 350 µm in wood, and to predict the equivalent thermal conductivity of wood (Zhao, Guo, et al. 2021; Zhao, Yang, et al. 2021). However, the calculation of fractal dimensions of pores ranging from 2 nm to 100 nm is questionable since the MIP test lacks accuracy for the nano-scale pores of wood. Besides, the fractal type of this calculation method can be regarded as volume fractal since it examines the relationship between the volumes of non-wetting pore phase and applied intrusion pressure. The fractal type of the pore structure of wood could also be surface fractal since the surfaces of most materials are fractal (Avnir et al. 1984). As a popular method, the Frenkel-Halsey-Hill (FHH) fractal model has been used to calculate the surface fractal dimensions of the internal surface of pores using the relationship between the relative pressure and the amount of N₂ adsorption from the NAD test (Liu and Nie 2016; Peng et al. 2017). On the other hand, the Neimark fractal model is an effective approach to determine the surface fractality of the pores in many materials using the relationship between the internal surface area of pores and the pore diameter from the NAD test (Neimark 1992; Zeng et al. 2010; Mahamud and García 2018; Xu 2018). Both the FHH fractal model and the Neimark fractal model may be reasonable to determine the surface fractal dimensions of pores in wood. However, so far, there has been little discussion about the surface fractal dimensions of the pore structure in wood cell walls (Chi et al. 2017).

In this study, a detailed analysis of the surface fractal of the pore structure in natural and heat-treated wood cell walls was carried out based on the data of the NAD test. The data from the NAD tests revealed that surface fractal geometry is one of the possible fractal types in spruce wood. The surface fractal dimensions derived from two models were compared and used to characterize the heterogeneity of a specific surface area. In addition, the FHH surface fractal dimensions of the pores with diameters larger than 10 nm had a positive relationship with the rate of early-stage moisture absorption but not with the amount of moisture absorption. This study provides an overview of the surface fractal geometry of pores in natural and heat-treated wood cell walls, which is expected to characterize the relationship between the pore structure in wood cell walls and the microscopic moisture transport properties.

2.1. Materials and sample treatment

Samples facing north were cut from the sapwood of Balfour spruce (Picea likiangensis var. balfouriana) wood, which was harvested in Sichuan Province in southwest China. Wood samples with dimensions of 70 mm × 20 mm × 20 mm (L × T × R) were cut with a circular saw. Heat treatment of wood samples was carried out under air, nitrogen, saturated steam, or ammonia atmospheres, respectively. The heat treatments lasted 3 h at 180°C. These four kinds of heat-treated wood were named HT-air, HT-N₂, HT-steam, and HT-NH₃, respectively. Natural spruce wood was named C (the control).

2.2. Fractal model of N₂ adsorption/desorption test

In order to remove moisture, wood samples were ground into wood powder (120–200 mesh) and dried at 103°C for 20 h. NAD isotherms were obtained using an Autosorb-iQ2-MP (Quantachrome, USA) at 77 K. The FHH fractal method assumes that capillary condensation adsorption is dominant. Based on this assumption, a straight-line relationship between the amount of N₂ adsorption ($V$) and the adsorption potential () can be determined by considering the recorded isotherm data on a log-log basis. This relationship can be expressed as Eq. (1):

$$\begin{array}{c}lnV\propto \left({D}_{F}-3\right)\text{ln}\left(1\right)\end{array}$$

where ${D}_{F}$ is the surface fractal dimension calculated using the FHH fractal model. The adsorption potential can be calculated using Eq. (2):

$$\begin{array}{c}\mu=-RTln\left(P/{P}_{0}\right)\left(2\right)\end{array}$$

where $R$ is the universal gas constant (8.314 J mol^− 1 K^− 1), $T$ is temperature in K units, $P$ is the gas equilibrium pressure in MPa, ${P}_{0}$ is the gas saturation pressure in MPa, and $P/{P}_{0}$ is the relative pressure. Therefore, ${D}_{F}$ can be determined using Eq. (3):

$$\begin{array}{c}lnV\propto \left({D}_{F}-3\right)ln\left(-\text{l}\text{n}(P/{P}_{0})\right)\left(3\right)\end{array}$$

Hence, ${D}_{F}$ can be calculated using the slope of $\text{l}\text{n}V$ versus $\text{l}\text{n}\left(-\text{l}\text{n}(P/{P}_{0})\right)$ linear fitting plots.

Neimark (1992) determined surface fractal dimension using the relationship between the internal surface area $S$ and the pore size $r$, which can be expressed as Eq. (4):

$$\begin{array}{c}lnS\propto \left(2-{D}_{N}\right)lnr\left(4\right)\end{array}$$

where ${D}_{N}$ is the surface fractal dimension calculated using the Neimark fractal model. The pore size $r$ can be calculated using the Kelvin equation, which can be expressed as Eq. (5):

$$\begin{array}{c}r=\frac{2}{RT\left(-\text{l}\text{n}(P/{P}_{0})\right)}\left(5\right)\end{array}$$

where is surface tensor of the interface between liquid and gas of nitrogen and is the molar volume of liquid nitrogen. From the balance between the formation work of the interface and the adsorption work, the surface area at a given adsorption, $V\left(X\right)$, can be calculated through Eq. (6):

$$\begin{array}{c}S\left(X\right)=-{\int }_{V\left(X\right)}^{{V}_{s}}dV=\frac{RT}{}{\int }_{V\left(X\right)}^{{V}_{s}}(-\text{l}\text{n}(P/{P}_{0}))dV\left(6\right)\end{array}$$

where ${V}_{s}$ is the adsorption volume when the relative pressure tends to 1. As presented later, the FHH and Neimark surface fractal dimensions are determined using Eq. (3) and Eq. (4), respectively.

2.3. Moisture adsorption analysis

According to Shi et al. (2021), about 0.2 g of 120–200 mesh wood powder samples (8 replicates) were placed into 2 ml plastic tubes and oven-dried for 4 h at 103 ℃. Then, their oven-dried masses were weighted. All wood powder samples were exposed to a wet condition (75.3% relative humidity) formed by the saturated analytical grade NaCl solution. The temperature was controlled at 25°C using the conditioning chamber. Wood powder samples were weighed every 1 h until their weights had not changed. The plastic tubes with caps can provide a closed space during the weighing processes and hence reduce the errors. The moisture content of the samples was calculated using Eq. (7):

$$\begin{array}{c}MC\left(\%\right)=\frac{{M}_{i}-{M}_{0}}{{M}_{0}}\times 100\left(7\right)\end{array}$$

where ${M}_{i}$ is the mass of wood powder samples after moisture adsorption and ${M}_{0}$ is the oven-dried mass of wood powder samples.

3.1. Pore structure characteristics and N₂ adsorption/desorption isotherms

Based on the classification proposed by IUPAC, the hysteresis loop in all of the adsorption/desorption isotherms of wood samples was type H3, which means the desorption curves are extremely consistent with the adsorption curves (Fig. 1) (Sing 1985). These results suggest that the pores that can be determined by the NAD test in all wood samples are mainly open pores. The adsorption curves of type H3 increased slowly when the relative pressure was less than 0.9 and increased rapidly when the relative pressure was higher than 0.9. According to Eq. (5), the pore diameter is 10 nm when the relative pressure is 0.9. The adsorption volumes of the wood samples before and after heat treatment in different atmospheres were obviously different. This result can be attributed to the fact that heat treatment atmospheres had different effects on the degradation of the chemical components of wood.

As shown in Table 2, the pore volume, the specific surface area, and the average pore diameter of the wood samples before and after heat treatment in different atmospheres were calculated using the BJH method. The data varied between 10.1×10^− 3 to 13.5×10^− 3 cm³ g^− 1, 2.08 to 3.16 cm² g^− 1, and 3.429 to 3.847 nm, respectively. These pore parameters of the wood samples before and after heat treatment in different atmospheres showed a strong difference, and the trends were similar to those of adsorption volume. The pore volume and the specific surface area of HT-air, HT-N₂, HT-steam, and HT-NH₃ were higher than those of C. These results can be attributed to the degradation of hemicellulose and amorphous cellulose during heat treatment. However, the pore volume and the specific surface area of HT-NH₃ were most consistent with those of C. This result suggests that ammonia neutralized the acid produced during heat treatment and inhibited the degradation of hemicellulose and amorphous cellulose. The pore volume and the specific surface area of wood samples were mainly determined by the pores with a range of 2–10 nm and then by pores with a range of 10–80 nm, as shown in Fig. 2b and d. The average pore diameter of HT-air, HT-N₂, HT-steam, and HT-NH₃ was bigger than that of C (Table 1). This result suggests that the degradation of hemicellulose and amorphous cellulose increased the distance between cellulose fibers in wood cell walls.

Table 1

Pore parameters of different wood samples.
Sample	Pore volume (10^− 3×cm³/g)	Specific surface area (cm²/g)	Average pore diameter (nm)	Hysteresis loop types
C	10.1	2.08	3.429	H3
HT-air	13.5	3.16	3.847	H3
HT-N₂	12.8	2.84	3.430	H3
HT-steam	12.6	2.63	3.847	H3
HT-NH₃	10.2	2.41	3.432	H3

3.2. The surface fractal dimensions of adsorption pores

According to the FHH fractal model, the surface fractal property of the wood samples before and after heat treatment in different atmospheres was examined using the relationship between $\text{l}\text{n}V$ and $\text{l}\text{n}\left(-\text{l}\text{n}(P/{P}_{0})\right)$ (Fig. 3). Hence, two distinct pore ranges (pore diameter < 10 nm and pore diameter > 10 nm) with the linearity of $\text{l}\text{n}V$ versus $\text{l}\text{n}\left(-\text{l}\text{n}(P/{P}_{0})\right)$ were easily identified in all samples. As shown in Table 2, the ${D}_{F1}$ values of the wood samples varied from 2.079 to 2.155, while the ${D}_{F2}$ values of the wood samples varied from 2.481 to 2.536. All the liner fitting curves showed good fits (R² ≥ 0.976). These results suggest that the pore structures in wood cell walls can be determined as the surface fractal using the FHH fractal model. An obvious inflection point was detected at about 10 nm in all samples, and thus the scale-dependent property of the surface fractal determined by the FHH fractal model did not change after heat treatment. The ${D}_{F1}$ values are clearly lower than the ${D}_{F2}$ values, which suggest that the internal surface complexity of pores in Region 2 is clearly higher than that of pores in Region 1. This difference between ${D}_{F1}$ values and ${D}_{F2}$ values could be attributed to the complex anatomy of wood cell walls.

Table 2

Surface fractal dimensions calculated through the FHH fractal model.
Sample	Pore diameter < 10 nm (Region 1)				Pore diameter > 10 nm (Region 2)
Sample	Slope	Intercept	R²	${D}_{F1}$	Slope	Intercept	R²	${D}_{F2}$
C	-0.881	-0.850	0.987	2.119	-0.497	-0.455	0.996	2.503
HT-air	-0.891	-0.375	0.976	2.109	-0.464	0.077	0.997	2.536
HT-N₂	-0.857	-0.476	0.984	2.143	-0.490	-0.099	0.999	2.510
HT-steam	-0.845	-0.500	0.977	2.155	-0.519	-0.238	0.996	2.481
HT-NH₃	-0.921	-0.771	0.984	2.079	-0.486	-0.325	0.995	2.514

According to the Neimark fractal model, the surface fractal property of the wood samples before and after heat treatment in different atmospheres was examined using the relationship between $\text{l}\text{n}S$ and $\text{l}\text{n}r$ (Fig. 4). All curves can also be divided into two distinct regions. Two distinct pore ranges (pore diameter < 10 nm and pore diameter > 10 nm) with the linearity of $\text{l}\text{n}S$ versus $\text{l}\text{n}r$ were easily identified in all samples. As shown in Table 3, the ${D}_{N1}$ values of five samples varied from 2.780 to 2.940, while the ${D}_{N2}$ values of five samples varied from 2.413 to 2.551. All the liner fitting curves also showed good fits (R² ≥ 0.917). These results suggest that the pore structures in wood cell walls can also be determined as the surface fractal using the Neimark fractal model. An obvious inflection point was also detected at about 10 nm in all samples, and thus the scale-dependent property of the surface fractal determined by the Neimark fractal model did not change after heat treatment. Hence, the surface fractal determined by the Neimark fractal model is consistent with that of the surface fractal determined by the FHH fractal model. The ${D}_{N1}$ values are clearly larger than the ${D}_{N2}$ values, which suggest that the internal surface complexity of pores in Region 1 is clearly higher than that of pores in Region 2. As shown in Fig. 5a, the pointes of five samples are far away from the line of $y=x$, which suggests that the ${D}_{F1}$ values were clearly lower than the ${D}_{N1}$ values. As shown in Fig. 5b, the points of C, HT-air, and HT-N₂ are extremely near the line of $y=x$, while the points of HT-steam and HT-NH₃ are slightly under the line. These results suggest that the ${D}_{F2}$ values and the ${D}_{N2}$ values are nearly equal. Although the ${D}_{F2}$ values are similar to the ${D}_{N2}$ values, the ${D}_{F1}$ values are totally different from the ${D}_{N1}$ values. Jaroniec (1995) proposed that these two models are essentially equivalent, but the Neimark fractal model has limited validity and robustness. Hence, the surface fractal dimensions evaluated by the FHH fractal model were mainly used for the analysis below.

Table 3

Surface fractal dimensions calculated through Neimark fractal model.
Sample	Pore diameter < 10 nm (Region 1)				Pore diameter > 10 nm (Region 2)
Sample	Slope	Intercept	R²	${D}_{N1}$	Slope	Intercept	R²	${D}_{N2}$
C	-0.828	2.342	0.935	2.828	-0.491	1.218	0.956	2.491
HT-air	-0.906	2.880	0.975	2.906	-0.551	1.853	0.960	2.551
HT-N₂	-0.780	2.551	0.922	2.780	-0.511	1.623	0.981	2.511
HT-steam	-0.830	2.515	0.961	2.830	-0.413	1.254	0.946	2.413
HT-NH₃	-0.940	2.700	0.945	2.940	-0.457	1.182	0.917	2.457

3.3. Relationship between hygroscopicity of wood and surface fractal dimensions

As a porous material, wood can absorb or desorb water depending on its moisture content and the relative humidity of the space it resides in. Heat-treated wood has a lower equilibrium moisture content (EMC) and a higher dimensional stability than untreated wood due to the degradation of hemicellulose and amorphous cellulose during heat treatment. The pore structures in wood cell walls have an important effect on the hygroscopicity of wood. The fractal geometry could be used for the analysis of water transport properties in porous media. Figure 6a shows the relationship between the surface fractal dimensions of the pores in wood cell walls and the EMC of wood. Unfortunately, there was no obvious relationship between them. This result suggests that the EMC of wood samples mainly depends on the chemical composition and less on the pore structure. A positive relationship between the ${D}_{F2}$ values and the rate of moisture absorption in 0–1 h (Fig. 6b) was determined but not for the rate of moisture absorption in 1–2 h (Fig. 6c) and 2–3 h (Fig. 6d). This difference can be attributed to the irregular internal surface of pores providing more available moisture sorption sites, which can significantly increase the rate of early-stage moisture absorption. In addition, the ${D}_{F2}$ values are more relative to the rate of moisture absorption than the ${D}_{F1}$, which can be attributed to the larger pores being more effective at moisture absorption. Hence, it is easy to find that the surface fractal dimensions are relative to the rate of moisture absorption rather than the amount of moisture absorption. Although the relationship between the surface fractal dimension of pores in wood cell walls and microscopic moisture transport properties was determined in this study, it is found that the rate of early-stage moisture absorption is related to the FHH surface fractal dimension of pores in Region 2.

In this study, the fractal property of the pore structure in natural and heat-treated spruce wood cell walls was evaluated based on NAD test data. The surface fractal was determined as one of the possible fractal types of pores in wood cell walls. Two fractal regions were identified in the studied samples, i.e., the region of pores with diameters less than 10 nm (Region 1) and the region of pores with diameters larger than 10 nm (Region 2). The two fractal regions showed clear surface fractal properties and scale-dependent properties according to the FHH fractal model and the Neimark fractal model. The FHH and Neimark surface fractal dimensions of pores in Region 2 are similar, while the FHH and Neimark surface fractal dimensions of pores in Region 1 are different. In addition, the FHH surface fractal dimensions of pores in Region 2 showed a positive relationship with the rate of early-stage moisture absorption.

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No competing interests reported.

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Surface fractal analysis of the pore structure in natural and heat-treated spruce wood cell walls using nitrogen adsorption/desorption test

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials And Experiments

2.1. Materials and sample treatment

2.2. Fractal model of N₂ adsorption/desorption test

2.3. Moisture adsorption analysis

3. Results And Discussion

3.1. Pore structure characteristics and N₂ adsorption/desorption isotherms

3.2. The surface fractal dimensions of adsorption pores

3.3. Relationship between hygroscopicity of wood and surface fractal dimensions

4. Conclusions

References

Additional Declarations

Status:

Version 1

Surface fractal analysis of the pore structure in natural and heat-treated spruce wood cell walls using nitrogen adsorption/desorption test

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials And Experiments

2.1. Materials and sample treatment

2.2. Fractal model of N2 adsorption/desorption test

2.3. Moisture adsorption analysis

3. Results And Discussion

3.1. Pore structure characteristics and N2 adsorption/desorption isotherms

3.2. The surface fractal dimensions of adsorption pores

3.3. Relationship between hygroscopicity of wood and surface fractal dimensions

4. Conclusions

References

Additional Declarations

Status:

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2.2. Fractal model of N₂ adsorption/desorption test

3.1. Pore structure characteristics and N₂ adsorption/desorption isotherms