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Zhao, Z., Zhang, M., Liu, W., and Li, Q. (2020). "Measurement of pore sized microporous-mesoporous materials by time-domain nuclear magnetic resonance," BioRes. 15(1), 1407-1418.


Time-domain nuclear magnetic resonance (TD NMR) technology has been used for pore detection in porous materials for a long time, but there are few pore detection methods for microporous-mesoporous materials. The surface of different materials is obtained by pore detection of known pore materials. Relaxation rate, which obtains aperture information, has an important practical significance for the application of time-domain NMR technology in the characterization of porous materials. In this study, the T2 peaks of pores of known pore size materials, namely zeolite molecular sieves (0.3 nm and 1 nm) and anodized aluminum porous membranes (30 nm and 90 nm), were used to calculate the pore surface relaxation of zeolite molecular sieve with 0.3 nm pore size and 1 nm pore size. The ratio of the rate of the surface is 3.379; the ratio of the pore surface relaxation ratio of the 30 nm and 90 nm apertures of the anodized aluminum porous film is 3.031. This result is very close to the pore size ratio, indicating that the surface relaxation rate of the same material is directly related to the pore size, while the T2 peak can qualitatively measure the pore size.

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Measurement of Pore Sized Microporous-Mesoporous Materials by Time-Domain Nuclear Magnetic Resonance

Zhi-hong Zhao, Ming-hui Zhang,* Wen-Jing Liu,* and Quan-teng Li

Time-domain nuclear magnetic resonance (TD NMR) technology has been used for pore detection in porous materials for a long time, but there are few pore detection methods for microporous-mesoporous materials. The surface of different materials is obtained by pore detection of known pore materials. Relaxation rate, which obtains aperture information, has an important practical significance for the application of time-domain NMR technology in the characterization of porous materials. In this study, the T2 peaks of pores of known pore size materials, namely zeolite molecular sieves (0.3 nm and 1 nm) and anodized aluminum porous membranes (30 nm and 90 nm), were used to calculate the pore surface relaxation of zeolite molecular sieve with 0.3 nm pore size and 1 nm pore size. The ratio of the rate of the surface is 3.379; the ratio of the pore surface relaxation ratio of the 30 nm and 90 nm apertures of the anodized aluminum porous film is 3.031. This result is very close to the pore size ratio, indicating that the surface relaxation rate of the same material is directly related to the pore size, while the T2 peak can qualitatively measure the pore size.

Keywords: Nuclear magnetic resonance; Porous materials; microporous; CPMG (Carr-Purcell-Meiboom-Gill); Surface relaxation rate

Contact information: School of Materials Science and Art Design, Inner Mongolia Agricultural University, 306 Zhaowuda Road, Saihan District, Hohhot, Inner Mongolia, China;

*Corresponding author:


Porous materials are advantageous in terms of physical and chemical properties such as high specific surface area, high porosity, strong adsorption, and easy assembly. Their uses include medical, chemical, energy storage, environmental protection, functional materials, and other fields along with being an important research object of modern material science (Ajayan et al. 2006; Levitz 2007; Song 2007; Stein et al. 2008). According to porous material aperture size (diameter, d), the porous materials are divided into three categories by IUPAC, namely, microporous (d < 2 nm), mesoporous (2 nm < d < 50 nm), and macroporous (d > 50 nm) (Everett 1972). However, the study of porous materials is inseparable from the characterization and analysis of pores. The main parameters of porous materials include pore size, distribution, morphology, and channel characteristics (Kubik 1992). There are many pore characterization methods, such as mercury intrusion porosimetry (MIP), scanning electron microscopy (SEM), gas adsorption, solute exclusion, and small-angle X-ray scattering. The emerging characterization methods in recent years are atomic force microscopy (AFM), DSC thermoporosimetry (DSCT), and NMR cryoporometry (NMRC) (Yamamoto et al. 2005; Zhu et al. 2006).

Mercury intrusion porosimetry (MIP) is applied to detect the pores of porous materials, and its operation is simple. However, the pores measured by it are generally macropores, and for natural polymer porous materials such as wood, it is easy to destroy some thin-wall cell pores in the process of mercury intrusion, resulting in inaccurate detection results (Roels et al. 2001; Moura et al.2005; Plötze and Niemz 2011).

Scanning electron microscopy can be used comprehensively to detect the porosity, pore size, morphology, and other information of porous materials. However, for the naturally formed polymer in porous substances, the preparation stage of the test sample may also destroy the original pore structure, and the sampling process may have rendered the detection information incomplete due to natural polymers pore inhomogeneity (Bolton et al. 1988; Wallström and Lindberg 1999).

Gas adsorption is the most commonly used characterization method for pore detection at this stage. It detects the pore size and distribution, pore morphology, and specific surface area of the material. This method usually uses nitrogen adsorption. For smaller pores, argon or krypton is also used. The slow detection speed of the sample usually takes dozens of hours and the material needs to be dry, while moisture is an important component or medium of many natural polymer materials. The gas adsorption method usually characterizes only the open pores. Wood-based porous materials and biomass porous media produce closed pores during the process of absolute drying, which can lead to a decrease in the accuracy of the characterization of porous materials by gas adsorption. Hence, it is not easily applied to biological porous materials because water is an essential part of the porous structure (Westermarck 2000; Topgaard and Söderman 2002; Papadopoulos et al. 2003; Jia et al. 2007).

The solute exclusion method involves water-saturated porous materials immersed in a solution of probe molecules that can reach equilibrium with the solution. Probe molecules enter the macropores of the porous materials and if they are small enough, they can penetrate the mesoporous. When probes enter the pores of probe molecules, they replace the water in them, which then dilutes the bulk probe solution remaining outside of the materials. The decrease in concentration of the probe solution is a measure of the pore volume of the porous materials (Telkki et al. 2013). However, the probe objects penetrate the porous materials in the manner of diffusion and cannot enter the micropores, which are smaller than the probe objects. Using probe molecules of different sizes, it is possible to obtain data for the pore size distribution of the materials (Hill 2006; Walker 2006). Most of these studies report a maximum size for swollen cell wall micropores in the region of approximately 2 to 4 nm (Hill 2006; Walker 2006).

Small-angle X-ray scattering (SAXS) is commonly used to characterize microporous materials, which is the degree of regularity of pore arrangement of mesoporous materials. The detection range for pores is 2 to 200 nm. However, because this method is greatly affected by the structure of the sample, the characterization of pore size and distribution, pore structure, and specific surface area is not completely accurate (Gindl et al. 2003; Furuno et al. 2004; Gierling et al. 2005; Jeremic and Cooper 2009; Xu et al. 2013).

Atomic force microscopy (AFM) is a new pore characterization method, which can reflect microscopic information such as the pore size and morphology of the sample. It provides the three-dimensional morphology of the sample and does not require special treatment. It is recommended for testing in a variety of environments. However, atomic force microscopy has higher requirements for the flatness of the sample and the needle tip of the instrument. The imaging range is small, which still has limitations in the detection of porous materials with uneven pores (Notley and Wagberg 2005; Wang and Liu 2006).

DSC thermoporosimetry (DSCT) uses water as the medium and is based on the principle that the lower pressure at the inner surface of the pore bending in the porous material leads to the lower melting temperature of the ice crystal in the capillary. The relationship between the temperature reduction and the pore diameter is calculated by the Gibbs-Thomson equation. This method can obtain the porosity, pore size and distribution, pore morphology, pore volume, and other information of the material as well as achieve the measurement of the closed pore (Jiang et al. 2012a, 2012b, 2013). The sample preparation method is simple, and the degree of pore damage is small (Cavallaro et al. 2013). However, this method has higher requirements for temperature control equipment and measurement accuracy when studying water status in wood pores by DSC, which is expressed by the percentage of water content (Nakamura et al. 1981; Park et al. 2006). The pore characterization methods mentioned above have high requirements in sample preparation, detection conditions, etc., and there are still many deficiencies in the detection of natural polymers in porous materials.

Nuclear magnetic resonance is a non-destructive and fast pore characterization method in the study of porous media. In other words, the determination of pore structure by NMR is widely used in oil field exploration, finding underground water resources, crude oil structure analysis, three-dimensional structure analysis, and measurement of protein in food. Great progress has been made especially in the study of solid porous media such as soil and rock. NMR reflects pore information by measuring the NMR signal of a fluid in a porous medium. NMR signals mainly include relaxation time and free induction decay signals (Pauli et al. 2005). The signal attenuation rate is different when T2 is measured by NMR, because the fluid in porous material is affected by external binding conditions such as pore, pore surface, capillary, etc. A smaller pore diameter results in faster signal attenuation. The use of NMR T2 signal to study the pore structure of porous materials has begun to be applied in many fields such as geology, materials, food, and biomaterials. Li Haibo et al. (2008) compared and analyzed the mercury intrusion data and T2 distribution of the core. The distribution of the core pore radius obtained by the T2 distribution spectrum correlated with the pore throat radius distribution obtained by the mercury intrusion method. Halperin (1994) used a time-domain NMR to observe the microstructure evolution of mud hydration. The total surface area and pore size distribution during mud hydration was obtained through the T2 distribution. Wang and Wang (2013) determined the pore size distribution of the gel filtration medium by the time-domain NMR, which confirmed the feasibility of the method. Teng et al. (2014) studied the development of the water state in lignite by low temperature drying and an obtained time domain NMR to continuously monitor the change of water and pore size distribution in lignite without damage. Zhao et al. (2006) studied the conversion method and corresponding relationship between the nuclear magnetic resonance T2 distribution of tight sandstone reservoirs and the pore-throat distribution obtained by the capillary pressure curve from mercury intrusion. Zhao obtained a close correlation between them. It is effective to use the T2 distribution to evaluate the pore throat radius distribution of tight sandstone reservoirs (Zhao et al. 2006).

Magnetic resonance imaging (MRI) is representative of modern three-dimensional characterization technology. Its advantage lies in its ability to quantify the internal space of the measured substance, but its technical bottleneck has two aspects. First, the resolution of MRI imaging cannot achieve the standard that can be effectively utilized by image analysis software at this stage. This disadvantage affects the application of MRI in the characterization of porous materials. Second, the water content of the substance to be tested has certain requirements, and there are limitations in dynamically monitoring the change of material moisture. These constraints affect the application of MRI in the characterization of porous pores (Akoka et al. 1999; Bucur 2003; Telkki 2012).

Nuclear magnetic resonance cryoporometry (NMRC) establishes the relationship between the pore size and the freezing point of the water based on the Gibbs-Thomson equation. In other words, it reflects the pore information of the substance by measuring the different freezing points of the water in different pores. The NMRC method measures the signal returned by the freezed substance in the pore, while the DSC method measures the transient heat flow in phase transitions. The nuclear magnetic resonance technique is very sensitive in distinguishing solids from the liquids, so the measurement result has a high precision (Wang et al. 2012, 2013). This method has been used to study the saturation point and pore size distribution of wood fibers in nanoscale porous materials including pulp, membrane materials, and wood after thermal modification (Mitchell et al. 2008). It is currently unknown whether the expansion coefficient after water freezes in the pore in NMRC affects the testing results (Jackson and Makenna 1990).

In this study, nuclear magnetic resonance was used to study the pores of porous materials. The goal was to achieve a non-destructive and rapid method to determine the pore information of porous materials. A standard sample simulation method was used to determine the surface relaxivity of micropores, mesopores, and other pores. The calculation was used to simulate the pore information. The detection method is convenient and rapid because it does not require special treatment of the sample and can accurately describe pores such as micropores.


Materials and Equipment


There are two kinds of hydrophilic substances to be tested for measuring the surface

relaxation rate. The first one is zeolite molecular sieve. The zeolite molecular sieve has a

single pore size and is hydrophilic (the zeolite molecular sieve with two pore sizes is selected). The pore diameters are 0.3 nm and 1 nm, respectively, labeled 3A and 13X, The selected zeolite molecular sieve is produced by China Henan Zhongbang Environmental Protection Technology Co., Ltd.; the second measured substance is anodized aluminum porous membrane (AAO). The aluminum porous membrane has a single pore size and the

surface is lyophilic (selecting an anodized aluminum porous membrane of two pore sizes, pore diameters of 30 nm and 90 nm, respectively, depth of 60 μm, labeled AAO30 and AAO90, respectively).


T2 measurements for each sample were performed using a Bruker Minispec MQ20NMR spectrometer (Bruker, Karlsruhe, Germany). The console operates at 19.95 MHz inside the magnet with a probe dead-time of 4.5 s. T2 measurements were performed using a CPMG (Carr-Purcell-Meiboom-Gill) sequence with 16 scans. The echo time of 0.2 ms was always used, and 300 echoes for the initial measurement were set. Depending on the specific data, data was analyzed using an Origin Pro 9.1 (version 91E, Origin Lab Corporation, Northampton, MA, USA). T2 decay curves were fitted using a third/second/first order exponential decay function.

Theory and Methods


According to the analysis of the relaxation mechanism of T2 NMR spectroscopy, the internal water relaxation mechanism of porous materials is mainly composed of three parts: a bulk relaxation rate, a surface relaxation rate, and a diffusion relaxation rate (Xiao 1998; Toumelin et al. 2007). Equation 1 is the formula for calculating the surface relaxation rate,

1 ÷ T2 = (1 ÷ T2B) + (1 ÷ T2s) + (D(γGTE)2 ÷ 12) (1)

where T2 is the total relaxation time; T2B is the relaxation time for water in the pores that is not in contact with the inner wall surface of the pores; and T2s is the relaxation time of water in the pores in contact with the inner surface of the pores. D(γGTE)2 is the relaxivity of water at the pore surface.

Under normal conditions, the solid-liquid interface interaction near the pore surface can significantly accelerate the relaxation process of water in the pore, while the relaxation efficacy of bulk water in the pore is much lower so the pore surface water provides the main T2 relaxation contribution. T2B is negligible (Deng 2010; Li et al. 2015). In addition, D is the water diffusivity in air strikes. Usually, the diffusivity of freely moving water at room temperature is approximately 210 to 3 cm2 / s (Zhao 2010), and the water diffusivity in the pores is much smaller. The parameter γ is the proton gyromagnetic ratio 267.52 MHz/T, G is the external magnetic field gradient, and TE is the callback time. When the external magnetic field is relatively uniform (G ≈ 0 G s/cm), D(γGTE)2 is negligible. Eq. 1 can therefore be simplified to Eq. 2.

1 ÷ T2 ≈ 1 ÷ T2(2)

Equation 3 describes surface relaxation,

1 ÷ T2s = ρ (S ÷ V) (3)

where ρ is the pore surface relaxivity, is the pore surface area, and V is the pore volume.

Equation 4 describes T2 of the moisture in the pore,

1 ÷ T2 ρ (S ÷ V) = ρ (Fs ÷ r) (4)

where r is the pore radius and FS is the form factor, which is generally for spherical pores (FS = 3). For cylindrical pores, F= 2 (Mao et al. 2005). Both the zeolite and AAO porous membranes in this study are cylindrical pores, resulting in Eq. 5,

T2 = d ÷ 4ρ (5)

where is the pore diameter.

Generally, the surface relaxation occurs on the solid-liquid contact surface and under the ideal fast diffusion limit conditions, i.e., the pores are very small and the surface relaxation is very slow, so that the molecules can travel to and from the pores several times during relaxation (Bin 2014). According to the formula, the surface relaxation rate of the sample can be calculated.

Provencher (1982) developed a linear integral equation inversion software (CONTIN). In this paper, CONTIN software was used with the Bruker time domain NMR analyzer to invert the T2 data. Among them, peaks represent states of water, and the sum of the signal amplitudes covered by the peaks represent the relative content of water in this state. The abscissa of the highest point of the peak corresponds to the mean relaxation time of water in this state.


The molecular sieve was put into a beaker to absorb water for 24 h to confirm its water saturation, and the molecular sieve was taken out of the water. The molecular sieve was wiped dry of surface moisture, put it into the test tube, and the time domain nuclear magnetic resonance spectrometer was used to determine T2. The scan times of the time CPMG pulse sequence used for the T2 measurement was 8, cycle delay time was 2 s, τ (half echo time) was 0.2 ms, and the echo number was 300.

AAO porous membrane was immersed into distilled water, to allow the surface to bubble for 1 h. The surface moisture was removed, and the membrane was placed at the bottom of test tube. T2 was collected and the parameter setting in the test was the same as the test parameter of the molecular sieve sample.

The natural mica sheet was placed in a beaker to absorb water for 24 h to determine its water absorption saturation. The mica sheet was taken out from the water to wipe dry the surface moisture, put it into a test tube, and T2 was determined with a time-domain nuclear magnetic resonance spectrometer. The parameter setting in the test was the same as the test parameters of the molecular sieve and the AAO porous membrane sample. After the detection, the T2 distribution of moisture was obtained by the inversion of the T2 data collected using the CONTIN algorithm, and then the pore size analysis can be performed.

The zeolite samples (0.3 nm versus 1 nm), AAO porous membranes (30 nm versus 90 nm), and natural mica sheets in the previous step were subjected to an absolute drying treatment, respectively. The pore size of the dried sample was measured by nitrogen adsorption and the BET analysis result was obtained. The T2 results measured by the time-domain NMR were compared with those by nitrogen adsorption.


Figure 1 shows the time-domain NMR T2 spectra measured under water-absorbing saturated conditions for 3A (pore size of 0.3 nm) molecular sieve sample, 13X (pore size of 1 nm) molecular sieve sample, AAO (30) (pore size of 30 nm) anodic aluminum oxide porous membrane sample, and AAO (90) (pore size of 90 nm) anodic aluminum oxide porous membrane sample. The inversion data of the T2 spectrum was obtained through the inversion of CONTIN software. A double exponential fit was performed on the data after inversion by Origin software to obtain the T2 spectrum. Since the sample is a single pore material, there is only one peak in this T2 spectrum

The T2 spectrum of the 3A sample in Fig. 1a had a peak apex at a position of approximately 0.3 ms. The T2 spectrum of the 13X sample in Fig. 1b had a peak apex at a position of approximately 1 ms. The T2 spectrum of the AAO (30) sample had a peak apex at a position of approximately 3 ms. The T2 spectrum of the AAO (90) sample has a peak apex at a position of approximately 9 ms. Table 1 shows the data presentation of the peak apex in the 8 T2 spectra of the four test samples. The reliability of the experiment was increased by averaging the values of all 8 measurements. In Table 2 the surface relaxivity was obtained by the average calculation of the T2 peak apex of the sample in Table 2, which was calculated using Eqs. 1 through 5.

Fig. 1. The T2 spectrum after water absorption saturation of (a) 3A (0.3 nm), (b) 13x (1 nm), (c) AAO30 (30 nm), and (d) AAO90 (90 nm) molecular sieves. The spectra were inverted with CONTIN software and fitted with ORIGIN software.

The obtained surface relaxations were 3Aρ = 0.218 nm/ms, 13Xρ = 0.2159 nm/ms, AAO30ρ = 2.471 nm/ms, and AAO90ρ = 2.497 nm/ms. For 13X zeolite / 3A zeolite, the relaxation time ratio of T2 peak apex was 3.379, and for AAO90 / AAO30, the relaxation time ratio of T2 peak apex was 3.031. The actual pore ratios of the samples were 3.334 for 13X / 3A and 3.000 for AAO90 / AAO30. Comparing the pore diameter calculated from the T2 spectrum with the actual pore diameter of the sample, it can be found that the results of the two were within an acceptable range, which indicates that the pore size result reflected by the relaxation time of the T2 spectrum can be used as a pore size detection method.

Table 2 shows that the surface relaxation rates of the same type of zeolite materials were basically the same, but the surface relaxation rates of different materials are very different due to the different adsorption forces of the inner walls of the pores on the liquid. Surface relaxation between identical materials is affected by pore size; smaller pores result in larger surface relaxation rates. This shows that the T2 spectrum can reflect the pore size of the material and is related to the relaxation rate of the material.

Table 1. Peak Top Values of Spectrum

Table 2. Average Value of T2 Apex, Surface Relaxivity, Proportion of T2 Peak Apex, and Proportion of Pore Size


  1. The surface relaxivity of the material is converted from the single pore size material. The surface relaxivity of zeolite and that of AAO porous membrane are quite different, but the surface relaxivity of the same material is the same. The surface relaxivity of the substance is related to its property and the size of pore. When the pore of the substance is a micropore, the smaller the pore is, the stronger the surface bondage received by the content is, and the faster the surface relaxivity occurs.
  2. The zeolite molecular sieve material itself has strong water absorption characteristics, and the zeolite molecular sieve sample has a smaller pore size, which indicates that the pore inner surface of the zeolite molecular sieve sample has a stronger adsorption force with water, and the surface relaxation rate is related to the pore size. There is a strong relationship between adsorption strength, which is worthy of further discussion.
  3. The pore size of porous materials can be calculated by the relationship between the T2 spectrum and surface relaxivity. The proportion of the peak apex of the T2 spectrum tends to be consistent with the proportion of pore size, which contributes greatly to the characterization of pore information of porous materials using TD NMR technology. The method of calculating the surface relaxation rate by T2 spectrum calculation can be studied in depth, and thus becomes a method of pore characterization.


This research is supported by the National Natural Science Foundation of China (31860185/C160301).


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Article submitted: August 30, 2019; Peer review completed: October 19, 2019; Revised version received: December 9, 2019; Accepted: December 10, 2019; Published: January 8, 2020.

DOI: 10.15376/biores.15.1.1407-1418