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Official Journal of the Japan Wood Research Society

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Determination of nuclear magnetic resonance surface relaxivity for the macropore system from wood cell lumen


To determine the surface relaxivity of pores plays a vital role in the application of time-domain nuclear magnetic resonance (TD-NMR) technology to porous structure characterization for wood. Currently, the surface relaxivity of pores is calibrated using a standard sample with a pore size of the same order as the wood pore system. However, the uniformly distributed pore size of standard sample is unfit to accurately indicate the complexity of porous structure of wood, which significantly affects the accuracy of test results. By integrating the TD-NMR technology with mercury intrusion porosimetry (MIP), the surface relaxivity of macropores in the lumen of wood cells is calibrated in this study using the tested sample, so as to avoid the error in measurement as caused by existing method. Data processing is performed using several mathematical methods including interpolation arithmetic and least square principle. Notably, the node segmentation method is applied to identify the T2 boundary of pores in cell lumen and to classify the porous structure of cell lumen into different pore systems. The approach proposed in this study is demonstrated to be effective in improving the accuracy of TD-NMR technology for characterizing the porous structure of wood. Also, it contributes a potential solution to accounting for the porous structure of wood based on the phenomenon of pore relaxation, which can improve the understanding of wood pore conformation.


As a renewable type of biomass material with the highest yield and most extensive range of applications in nature, wood possesses a series of advantages in environmental protection, such as high degradability, excellent biocompatibility and low carbon emissions [1, 2]. In general, the hierarchical porous structure of wood can be divided into macropores, mesopores and micropores in the order from large to small. Macropores are derived mainly from the vessel, tracheid, wood fiber and resin canal, while micropores are dominated by the cell wall pores with the magnitude order of molecular chain section as the largest starting point, such as the space in inter-cellulose molecular chain [3]. Mesopores are smaller than macropores but larger than micropores, such as the pit membranes and inter-microfibril space in cell walls [4,5,6]. Figure 1 illustrates the pores of different sizes in the hierarchical structure of wood [7,8,9,10], and Table 1 lists the sizes of pores in the wood of some specific structures [11, 12]. The porous structure of wood is essential for its practical application for two reasons. On the one hand, it affects the quality of wood processed through traditional methods including wood drying, wood impregnation and wood modification [13, 14]. On the other hand, it serves as a crucial carbon skeleton precursor needed to construct biological templates for extensive applications in various innovative fields like oil absorbent [15, 16], sensor [17,18,19], solar energy evaporator [20,21,22] and electrochemical catalysis [23,24,25,26]. Therefore, it is necessary to collect the information about pore structure thoroughly and accurately for the further development of high-performance wood-based product.

Fig. 1
figure 1

Pores of different scales in the wood hierarchical structure [7,8,9,10]

Table 1 The pore sizes of some specific structural elements in wood [11,12,13]

The time-domain nuclear magnetic resonance (TD-NMR) technology provides an advanced and powerful tool for the comprehensive analysis of pores in wood [27, 28]. When radiofrequency pulse is applied to the nuclei in a static magnetic field, the nuclei shift from low energy level to high energy level by absorbing energy from the radiofrequency pulse. After the equilibrium state is reached, the external radiofrequency pulses are removed, and the nuclei release the absorbed energy to restore the low energy level. During this process, the spin–lattice relaxation, which occurs due to the release of energy from the spinning nuclei to the surroundings, and the spin–spin relaxation, which is caused by energy conversion among the spinning nuclei, complete the relaxation phenomenon. Since the occurrence of relaxation is caused by the interaction among the nuclear spin, the fluid and the pore wall, the TD-NMR signal generated during relaxation carries the information about porous structures. In the TD-NMR method, the relaxation properties of water molecules with 1H protons as probe are measured for the test samples saturated with water, so as to collect the T2 data of spin–spin relaxation time (i.e., transverse relaxation time) that can be used to reveal the pattern of pore size distribution (PSD). Compared with other commonly used techniques of pore structure characterization, such as gas adsorption isotherms, mercury intrusion porosimetry (MIP), thermoporometry, cryoporometry, microscopic imaging and computed tomography [29], the TD-NMR method shows such advantages as rapidity, non-toxicity and the recyclability of samples. Moreover, there is an extremely wide range of pore sizes that can be detected due to the full penetration of water molecules into various pore systems of different sizes in wood [6, 30].

The linear relationship between T2 relaxation time and pore diameter is expressed [31,32,33,34,35] as Eq. (1):

$$d = {2}\rho_{{2}} F_{{\text{s}}} T_{{2}} ,$$

where d represents the pore diameter, ρ2 indicates the pore surface relaxivity, Fs denotes the pore geometric shape factor, and T2 stands for the transverse relaxation time. Apparently, to determine the surface relaxivity of pores plays a critical role in the conversion between T2 distribution and PSD. In the existing studies, the surface relaxivity of pores is calibrated using a standard sample with the pore size of the same order as the wood pore system to be measured for determining the PSD. However, the uniformly distributed pore size of standard samples is unsuited to indicating the complexity of porous structures in wood accurately, which affects the accuracy of test results significantly.

In the present study, a novel approach is developed to determine the NMR surface relaxivity of macropores derived from wood cell lumen. Using the tested wood sample, the surface relaxivity is calibrated, which prevents the measurement error caused by the standardized sample calibration as suggested in the existing methods. Also, the accuracy in characterizing the porous structure of wood is effectively improved by applying the TD-NMR technology.

Materials and methods


The fir (Cunninghamia lanceolata) was obtained from Anhui Province, and the cuboid samples with an approximate size of 10 mm (Tangential) × 10 mm (Radial) × 18 mm (Longitudinal) were obtained by cutting the discs longitudinally and then air dried.

TD-NMR measurement

After being boiled in water bath for 30–60 min, the wood specimens were taken out and immersed in distilled water for 20 days of saturation at room temperature. Afterward, the samples were weighed every 10 days until the difference in water absorption rate between the two adjacent locations fell below 5%. To ensure the smooth saturation of wood, the samples immersed in distilled water were stored in vacuum for 24 h. The final mass m1 and size (length, width and height) of saturated specimens were recorded, whose accuracy reached 0.001 g and 0.01 mm, respectively. After the excess water left on the surface was removed, the water-saturated specimen was transferred into the test tube, with T2 measured by the TD-NMR (Niumag NMRC12-010 V instrument, Suzhou Niumag Analytical Instrument Corporation, Suzhou, China) with Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, 90-degree pulse value of 7.4 µs, 180-degree pulse value of 14.8 µs, 16 times of scanning, cycle delay time of 2 s, echo time of 0.15 ms, and echo number of 6000. Finally, it was inversed by SIRT arithmetic [36].

MIP measurement

After TD-NMR test, the above wood specimen was fully dried in an oven at 105 ℃, with the mass m2 of completely dry specimen recorded. Then, the dried wood specimen was measured using an automatic mercury intrusion porosimeter (AutoPore IV 9500 Version 2.03.00, Micromeritics Instrument Corporation, USA) under the pressure ranging from 0.1 to 61000 PSI at room temperature to determine the porosity and PSD values.

Results and discussion

T 2 distribution analysis

Figure 2 shows the T2 distribution of the tested wood sample. It can be observed that three peaks denoted as P1 (at 126.04 ms), P2 (at 18.04 ms) and P3 (at 1.70 ms) respectively appear with the extension of T2 time. The occurrence of relaxation is caused by the relaxation of 1H protons from the water filled with wood pores and the relaxation time is prolonged with the increase of pore size. According to literature [37, 38], the P1 and P2 with a longer relaxation time than 10 ms are assigned to the free water contained in macroscopic and mesoscopic pores, such as cell lumen pores, pit and inter-microfibril space. It is also suspected that the water component from P2 is more likely attributed to the water from pits, because the P2 appears to have association with P1 and a shorter relaxation time, suggesting that its water component is connected to the water component derived from P1 and subjected to a tighter restriction in the smaller porous structure [38, 39]. Representing the bound water in the microscopic pores located mainly in the cell wall, P3 is classified into two components, i.e., the water molecules adsorbed through hydrogen bonds to cell wall polymers and the water clusters trapped in small voids [40,41,42]. In general, the relaxation time of bound water is less than 10 ms, despite some literature indicating that the bound water content as calculated using T2 data only within 10 ms is unduly low [43]. Thus, it remains necessary to determine the relaxation time boundary between free water and bound water, which is also affected by the boundary of different pore scale systems of water-saturated wood specimens.

Fig. 2
figure 2

The T2 distribution of the tested wood sample

MIP PSD analysis

Based on the non-infiltrating properties of liquid mercury, the MIP method is applied to the characterization of porous structure in wood by injecting liquid mercury into wood specimens. Then, the PSD is evaluated according to Washburn equation [44] as shown in Eq. (2):

$$r = - {2}\gamma {\text{cos}}\theta /p,$$

where r represents the pore radius, γ indicates the surface tension of mercury (0.48 N/m), θ denotes the wetting angle of mercury (140°), and p stands for the pressure. Figure 3 shows the PSD of tested wood sample as obtained by MIP. As can be seen from the figure, the PSD ranges from 0.03 µm to 282.88 µm with a distinct peak observed at 0.83 µm and a moderate peak discovered at 17.25 µm, which is ascribed mainly to the macroscopic and mesoscopic pore systems in wood. For the characterization of micropores by MIP, the high pressure makes it inevitable to destroy the micropore structure and affect the accuracy of measurement [45].

Fig. 3
figure 3

The PSD of tested wood sample obtained by MIP

Determination of ρ 2 for wood cell lumen macropore system

This study aims to determine the relationship between the T2 relaxation time and MIP pore diameter (dm) in the cell lumen macropores. Due to the limitation of the MIP method, it is impossible to detect those micropores whose dm < 3 nm, which is not the case for the TD-NMR method. To ensure the consistency and comparability between these two methods, the range of cumulative distribution percentage as used for calculation is supposed to be within the percentage of mercury saturation (Ps), which is calculated using Eq. (3):

$$P_{{\text{s}}} = P_{{\text{m}}} /P_{{\text{n}}} \times {1}00\% = P_{{\text{m}}} /[(m_{{1}} - m_{{2}} )/(\rho_{{\text{w}}} \times V)] \times {1}00\% ,$$

where Pm represents the porosity measured using the MIP method, Pn indicates the porosity of water-saturated sample, m1 denotes the water-saturated sample mass; m2 refers to the dry sample mass; ρw indicates the density of water at room temperature (1 g/cm3); and V denotes the volume of the saturated sample [46]. According to the experimental data obtained in this study, Ps is 91.01%, which means the range of calculation as required to determine the linear relationship between T2 relaxation time and dm is the range in which the cumulative distribution percentage does not exceed 91.01%, as shown in Fig. 4. Within the above range, the values of T2 and dm are obtained by means of interpolation arithmetic and the correlation between T2 and dm is shown in Fig. 5 (Curve I).

Fig. 4
figure 4

The cumulative distribution curves of T2 and dm

Fig. 5
figure 5

The correlation between T2 and dm (Curve I) and the dm cumulative distribution (Curve II). The determined nodes of Curve II and their corresponding locations in Curve I pointed by red arrows were shown as filled dots and squares, respectively

The dm cumulative distribution as shown in Fig. 5 (Curve II) can be treated as a series of straight lines with different slopes, and the data of each consistent slope are obtained from the same pore system with a similar porous structure [47]. Thus, nodes are introduced to locate these multiple pore systems and calculate the transverse coefficients of T2 and dm for each cell lumen macropore system separately. Since the wood sample used in this study is classed into the softwood with a greater tracheid diameter than 10 µm [6, 48], the lower limit of the cell lumen pore diameter (dmin) is set to the same as the dm at the end node of the last pore system through the dm data point which is the closest to 10 µm. Herein, dmin = 6.03 µm, and the T2 is 151.48 ms accordingly. This is consistent with the argument that the T2 boundary between free water and bound water should be no less than 10 ms [43]. As shown in Fig. 5, the starting and ending nodes of each consistent slope part on Curve II are taken as the nodes for segmentation by filled dots, and the determined nodes are indicated by filled squares on Curve I. The values of these nodes are listed in Table 2.

Table 2 Calculation results of different pore systems

After the calculation interval is subdivided as above, Eq. 4 is used to quantify the linear relationship between T2 and the dm for each cell lumen pore system using the least square method. This is purposed to determine the conversion coefficient Ki for the ith pore system when the error δi between the pore size value as calculated by Ki × T2j and the dmj reaches its minimal. In addition, the pore size distribution percentage wj is introduced as the weight for calculation, so as to reduce the impact of PSD inhomogeneity on the fitting error [49]. The residual in regression calculation is ignored.

$$\delta _{i} = {\mkern 1mu} \left( {\sum\nolimits_{{(j = 1)}}^{n} {w_{j} (d_{{mj}} - K_{i} {\mkern 1mu} \times {\mkern 1mu} T_{{2j}} )2/} \sum\nolimits_{{(j = 1)}}^{n} {w_{j} } } \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}$$

where n represents the number of data points between two adjacent nodes in Curve I; wj indicates the distribution percentage of the jth dm data point between two adjacent nodes, and dmj denotes the dm value of the jth data point between two adjacent nodes; T2j refers to the T2 value of the jth data point between two adjacent nodes. Based on this, “XIAOXIAOMU WOOD FAIRY” software is developed to calculate the Ki value of different pore systems, the results of which are shown in Table 2. Compared with manual calculation, the software reduces the calculation time for each sample from 3 to 5 h to 5 min, while eliminating the error caused by manual calculation. This significantly improves the efficiency of calculation, and facilitates the large-scale calculation as required for future research.

To verify the above method for its accuracy, Fig. 6 compares the PSD experimentally given by the MIP method (PSD-0) with the PSDs estimated from T2 value using Ki values in Table 2 (PSD-1), K value calculated without introducing nodes (PSD-2), and K value calculated by method mentioned in existing studies (PSD-3). It can be found out that the PSD-1 is more consistent with PSD-0 than both PSD-2 and PSD-3. This confirms the reliability of the approach proposed in this study.

Fig. 6
figure 6

The comparison in the PSD calculated by different methods

Finally, the surface transverse relaxivity ρ2i is calculated by substituting the Ki values into Eq. (5) as follows:

$$\rho_{{{\text{2i}}}} = K_{{\text{i}}} /({2} \times F_{{\text{s}}} ),$$

where Fs = 2 since the pore shape is assumed as cylindrical in accordance with the MIP method. Table 2 lists the ρ2i values of different macropore systems derived from wood cell lumen. It can be found out that the calculated ρ2i values are of the same magnitude order with an average of 0.0877 µm/ms obtained through the existing method and standardized sample calibration (ρ2 = 0.064 µm/ms for cell lumen pores and 0.0027 µm/ms for cell wall pores). Meanwhile, the ρ2i value is also calculated to show a decreasing trend with the reduction in pore size. This substantiates the feasibility and effectiveness of the proposed approach.


In the present study, a novel approach is developed to determine the TD-NMR transverse surface relaxivity of the macropore system derived from wood cell lumen. The surface relaxivity of the tested sample is calibrated by integrating TD-NMR with MIP. Also, data processing is conducted according to interpolation arithmetic and least square principle. Then, the node segmentation method is introduced to significantly improve the accuracy of TD-NMR technology for PSD characterization of wood. To sum up, this study contributes a potential solution to accounting for the porous structure of wood based on pore relaxation for the full understanding of wood pore conformation.

Availability of data and materials

All data generated or analyzed during this study are included in this published article.



Time-domain nuclear magnetic resonance


Pore size distribution


Mercury intrusion porosimetry


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This work was supported by the National Natural Science Foundation for Youth (32001254).


This study was funded by the National Natural Science Foundation for Youth (32001254).

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ZJ: funding acquisition, conceptualization, methodology, validation, investigation, writing—original draft. YF: conceptualization, methodology, supervision. QC: methodology, writing—review and editing. ZZ: conceptualization, methodology, validation, investigation, writing—review and editing.

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Correspondence to Zhen Zeng.

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Jin, Z., Fu, Y., Chen, Q. et al. Determination of nuclear magnetic resonance surface relaxivity for the macropore system from wood cell lumen. J Wood Sci 70, 5 (2024).

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