1080
J. Phys. Chem. B 2009, 113, 1080–1084
Determining the Highly Anisotropic Cell Structures of Pinus sylWestris in Three Orthogonal Directions by PGSTE NMR of Absorbed Water and Methane Pa¨ivi M. Kekkonen, Ville-Veikko Telkki,* and Jukka Jokisaari Department of Physical Sciences, P.O.Box 3000, 90014 UniVersity of Oulu, Finland ReceiVed: September 4, 2008; ReVised Manuscript ReceiVed: NoVember 11, 2008
The walls of solid matrix restrict the self-diffusion of a fluid absorbed in the matrix, and this is reflected in the echo amplitudes measured by PGSTE NMR. Hence, the pore size distribution of the matrix can be extracted from the echo amplitudes. We demonstrate that, when both liquids and gases (water and methane in this case) are used as probe fluids, the scale of the dimensions observable by PGSTE NMR may be over 4 orders of magnitude. This enables determining the dimensions of highly anisotropic pores. In the present case, the wood cell structures of Pinus sylVestris in three orthogonal directions were studied. Introduction Pulsed-field-gradient spin-echo (PGSE)1 and its variant pulsed-field-gradient stimulated-echo (PGSTE)2 nuclear magnetic resonance (NMR) are standard methods for measuring selfdiffusion of fluids, because the labeling of spin coherences does not affect the diffusion of molecules and radio waves used in NMR can penetrate also inside opaque samples. In the methods, the amplitude of observed echo is the smaller the larger the average distance traveled by the molecules during the period between two gradient pulses (diffusion delay). The most important difference between these methods is that the relaxation attenuation of the signal is dominated by T2 in the former case whereas it is T1 in the latter case. If the fluid is confined to a solid matrix, the matrix restricts the self-diffusion, and this is reflected in the echo amplitude3 and in the effective, timedependent diffusion coefficient.4 Hence, the measurements may reveal the dimensions of the voids (pores) of the matrix.5 Usually, liquids (especially water) have been used for determining the pore sizes of host materials. However, when gases are used as probe fluids, much larger dimensions can be studied because of their larger diffusion coefficient.6 This work demonstrates that the combined use of liquids and gases expands the scale of the dimensions observable by PGSTE NMR to over 4 orders of magnitude. In this study, the wood cell structures of Pinus sylVestris are studied by PGSTE NMR of absorbed water and methane. According to Kettunen,7 Pinus sylVestris consists of three different cell structures (see Figure 1). Longitudinal tracheid cells constitute 93% of the volume of Pinus sylVestris. The hollow interior of traceids is called lumen, and the cross section of both tracheid cells and lumens is rectangular. The length of tracheids is 2.78-2.86 mm (standard deviation 0.63-1.08 mm). In early wood, the average width of tracheids is 25.3 and 30.2 µm in tangential and radial directions, respectively, whereas in late wood the corresponding values are 23.5 and 20.8 µm. The walls of tracheid cells in late wood are much wider than in early wood (∼5 and 1.5 µm, respectively), and therefore lumens are smaller in the former part than in the latter part. Radial rays comprise 6.4% of the wood. Some rays do not contain resin canal but some others do. The average width of rays in tangential and longitudinal directions are about 20 and 200 µm in the * Corresponding author. E-mail:
[email protected].
Figure 1. Structure of Pinus sylVestris (modified after Kettunen7 and Howard et al.).8
former case and 52 and 406 µm in the latter case. The pores inside rays are approximately cylindrical, as can be seen from Figure 1. The portion of longitudinal resin canals is 0.6%. Their cross section is circular, and the average diameter and length are about 80 µm and 50 cm, respectively. Hereafter, longitudinal resin canals are shortly referred to as resin canals. There are only a few publications in the literature in which PGSTE NMR has been used for observing wood structures: Wycoff et al.9 determined the average cell dimensions of four different softwoods in tangential direction by measuring the time-dependent diffusion coefficient of water as a function of diffusion time. In addition, they were able to extract the cell size distributions in the same direction from the echo amplitudes measured as a function of gradient amplitude using a fixed diffusion time. Hietala et al.10 measured the average cell sizes of thermally modified Pinus sylVestris in horizontal and longitudinal directions by means of time-dependent diffusion coefficient of water. Johannessen et al.11 determined the average cell dimensions of Pinus sylVestris in the radial direction from time-dependent diffusion coefficients of water and toluene, and their simulations showed that the exchange of fluid between
10.1021/jp807848d CCC: $40.75 2009 American Chemical Society Published on Web 12/23/2008
Cell Structures of Pinus sylVestris
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1081
different wood cells was negligible during the NMR experiment. Meder et al.12 used PGSTE measurements of water diffusing in wood for determining pore alignment. The method introduced in this article enables more thorough characterization of structure of wood than the previous techniques, because it makes it possible to determine the full size distributions of cell structures of wood in three orthogonal directions, even though the dimensions differ from each other several orders of magnitude. Experimental Methods Two cylindrical sample pieces were drilled from a pine wood plank with a plug drill. The diameter and length of the pieces were approximately 8 mm and 25 mm, respectively. One piece of wood was immersed in distilled water for 2 weeks and after that it was mounted in a 10 mm NMR tube. Perfect fit of the piece inside the sample tube was ensured by wrapping Teflon tape around the sample. This was done in order to prevent the sample from rotating in consequence of shaking caused by the gradients during the experiments. Excess water was added into the tube to keep the sample piece immersed. The tube was closed with a plastic cap to prevent evaporation. Another piece of wood was inserted in an NMR tube without immersing it in water. Moisture and gases were removed from the sample by keeping it in the vacuum line for 2 h. Methane gas was condensed into the sample by immersing the sample tube into liquid nitrogen, and the tube was closed by melting it with a flame. The amount of the added methane corresponded to the pressure of 1.7 atm in an empty sample tube. 1 H NMR experiments were performed on a Bruker Avance DSX300 spectrometer equipped with a microimaging unit with x, y, and z gradients. The sample inside the spectrometer was oriented so that x, y, and z direction of the gradient system were parallel with the tangential, radial, and longitudinal direction of wood, respectively. Correct orientation was ensured by measuring axial spin-echo MRI images from the sample and by checking that the annual rings are parallel with x direction. MRI images were obtained using Bruker Paravision imaging program. In PGSTE experiments of water samples, the echo amplitude was measured as a function of gradient amplitude, which was increased from 0 to 71 G/cm using 16 steps. The width of gradient pulse and the diffusion delay were 1 and 200 ms, respectively. The diffusion delay was fixed in the experiments in order to keep the effect of relaxation on the observed echo amplitude constant. In PGSTE experiments of methane samples, the gradient amplitude was increased from 0 to 50 G/cm using 64 steps. The width of gradient pulse and the diffusion delay were 200 µs and 100 ms, respectively. Theory PGSTE pulse sequence is shown in Figure 2. If the fluid molecules are confined within a rectangular box with perfectly reflecting walls, and diffusion is studied in the direction parallel to one side of the box of length a, the amplitude of the echo observed in PGSTE experiment is3
E(q, a) )
2[1 - cos(2πqa)] + (2πqa)2 ∞
4(2πqa)2
(
2 2
∑ exp - n πa2D∆
n)1
)
1 - (-1)n cos(2πqa) (1) [(2πqa)2 - (nπ)2]2
Figure 2. PGSTE pulse sequence.
Here, q ) γδg/2π, where γ is the gyromagnetic ratio of the nucleus, δ is the gradient pulse length, and g is the amplitude of the gradient. D is the molecular self-diffusion coefficient and ∆ is the diffusion delay. If the sample contains a large amount of rectangular pores with different sizes, and if the pore size distribution is the sum of n Gaussian functions, the observed echo amplitude is n
Eobs )
∑ i)1
pi
1 √ σi 2π
∫0
∞
(
exp
-(a - ai)2 2σi2
)
E(q, a) da (2)
where pi, ai, and σi are the portion, mean value and standard deviation of the ith component, respectively. We used the experimentally determined D values of bulk water and methane at 1.7 atm pressure (2.04 × 10-9 m2/s and 9.83 × 10-6 m2/s, respectively) in the fits of eq 2 to data points shown later. Narrow gradient pulse approximation used in the derivation of eq 1 restricts the pore sizes observable by the method. In this case the approximation means that the root-mean-square distance traveled by the fluid molecules during the gradient pulse is assumed to be much smaller than the size of the box: (2Dδ) , a. Using experimentally determined values of diffusion coefficients, it can be estimated that a . 2 µm for water (D ) 2.04 × 10-9 m2/s) and a . 60 µm for methane (D ) 9.83 × 10-6 m2/s). On the other hand, in order to observe the effect of the walls on the echo amplitude, the box size cannot be much larger than the root-mean-square distance traveled by the molecules during the diffusion delay. Based on experimental experience, it is reasonable to assume that the maximum pore size observable is about 10 times larger than the root-meansquare distance traveled by the molecules: a e 10(2D∆). In the case of water measurements, a e 300 µm, and for methane measurements, a e 10 mm. The range of q values restricts also the pore sizes observable by the method. It is safe to assume that the smallest observable pore size is the inverse of the maximum q value, qmax: a g 1/qmax. In water measurements, qmax was 60 455 1/m, giving a g 17 µm, whereas in methane measurements, qmax was 4257 1/m, giving a g 230 µm. Previous values show that, when both water and methane are used as probe fluids, the range of dimensions measurable by current setup is approximately from 10 µm to 10 mm, covering all the interesting length scales in the structure of Pinus sylVestris. Water is an optimal probe for measuring the dimensions in the transverse direction whereas methane is best suited for determining longitudinal dimensions. Results MRI images. An MRI image measured from the methane sample is shown in Figure 3a. The intensity of the methane
1082 J. Phys. Chem. B, Vol. 113, No. 4, 2009
Kekkonen et al. TABLE 1: Parameters Resulting from Least-Squares Fits of Eq 2 to the Echo Amplitudes Measured from Methane and Water Samplesa al long tan, 2w tan, 2m rad, 2w rad, 2m
2.88 18.9 20.5 22.7 25.7
mm µm µm µm µm
σl
pl
ar
σr
pr
0.78 mm 4.9 µm 5.2 µm 7.4 µm 7.8 µm
87% 77% 80% 73% 83%
0.29 mm 54 µm 50 µm 53 µm 54 µm
0.13 mm 21 µm 17 µm 17 µm 15 µm
13% 23% 20% 27% 17%
Figure 3. MRI images of the methane sample (a) and the water sample after 2 weeks (b) and 2 months (c) immersion. Early and late wood areas are indicated in the MRI images.
a Subsript l refers to lumens and subscript r refers to rays in the longitudinal direction and resin canals in the transverse directions.
Figure 4. Echo amplitude as a function of q measured in the longitudinal direction using methane as a probe fluid, and the fit of eq 2 to the data points. The lumen and ray components are shown as dashed lines in the figure.
Figure 5. Pore size distribution measured in the longitudinal direction using methane as a probe fluid.
signal is substantially larger in early wood areas than in late wood areas indicating that absorption of methane in the former part is much larger than in the latter part. An image taken from the sample immersed in water for 2 weeks is shown in Figure 3b. Contrary to the methane sample, water is mainly absorbed into late wood. However, the absorption of water into early wood can be seen in the fringe of the sample. After 2 months immersion, water has absorbed much deeper into the early wood, as seen in Figure 3c. The images show that absorption of water in wood is very slow, and the wood piece is saturated by water only after several months immersion. Methane Measurements. The measured echo amplitudes in the longitudinal direction as a function of q are shown in Figure 4. A least-squares adjustment of eq 2 to the data points is also shown in the figure. The pore size distribution was assumed to be composed of two Gaussian components (n ) 2 in eq 2). When calculating E(q,a) (eq 1), only 10 first terms were taken into account from the infinite summation, because the other terms appeared negligible. The resulting values of the least-squares adjustment are shown in Table 1. Because the mean value, standard deviation, and portion of the first component are very close to the corresponding values measured for lumens inside longitudinal tracheids (see Introduction), the component was interpreted to represent the lengths of lumens, and therefore subscript l was used in the parameter symbols. The second component was interpreted to represent the heights of the pores inside radial rays, and subscript r was added to the symbols. Pore size distribution obtained by using the parameters is presented in Figure 5. Water Measurements. Water measurements were conducted in radial and tangential directions after immersion times of 2 weeks and 2 months. Measured echo amplitudes and fits of eq 2 to the data points are shown in Figure 6. Parameters obtained from the fits are shown in Table 1.
Figure 6. Echo amplitude of absorbed water as a function of q measured in radial (Rad) and tangential (Tan) directions after 2 weeks (2w) and two months (2m) immersion. Fits of eq 2 to the data points are also shown in the figure.
Again, the pore size distribution was assumed to be composed of two Gaussian functions, and the first component was associated with the widths of longitudinal tracheids and the second component with the widths of longitudinal resin canals. Corresponding pore size distributions are presented in Figure 7. The results imply that the average lumen size in the radial direction is larger than in the tangential direction. In addition, the measured lumen dimensions in both directions increase with increasing immersion time, which is mainly a consequence of increased absorption of water in early wood (see Figure 3b,c): the size of lumens in early wood is larger than in late wood (see Introduction), and therefore the increase of the relative amount of water in early wood increases the average size of lumens observed by this method. The actual lumen size may also increase slightly, as was speculated by Hietala et al.10 The size of resin canals is independent of the measurement direction because of the cylindrical geometry
Cell Structures of Pinus sylVestris
Figure 7. Pore size distribution measured in radial and tangential directions measured by means of absorbed water after 2 weeks (a) and 2 months (b) immersion.
of the canals, and different immersion time does not change it either. The resin canal component is much larger than the portion of the canals in wood. Probably long and large resin canals are easily accessible for water, and therefore they are saturated by water in both experiments. However, because the other wood structures are not fully saturated by water, the relative portion of resin canals observed by this method is large. The portion decreases with increasing immersion time because of increased absorption of water in the other wood structures. Discussion Pore size distributions were assumed to consist of two Gaussian components in the fits shown in this article. Oneand three-component fits were also performed (not shown here). One-component fits were significantly worse than the two-component fits in every cases. Three-component fits were not much better than the two-component fits, and in those fits, all the components did not have physical meaning; i.e., they could not be associated with the known structure of Pinus sylVestris. Hence, it was reasoned to present twocomponent fits as results. The diffusion of methane inside resin canals in the longitudinal direction should be free diffusion like, producing a component to very large pore sizes in the pore size distribution. However, that kind of component was not observed. Resin canals constitute only 0.6% of the volume of Pinus sylVestris, and possibly the present method is not sensitive enough for observing such a small component. The component may have coalesced into tracheid component, whose distribution extends to relatively large pore sizes.
J. Phys. Chem. B, Vol. 113, No. 4, 2009 1083 In the transverse directions, we were not able to observe separate components from tracheids in early and late wood. Probably the pore sizes in these regions are so close to each other that it is not possible to separate them in the fits. Radial rays (6.4%) did not produce their own component to the fits either. The component may have coalesced into tracheid component in tangential direction, because the diameter of the pore inside the ray is close to the width of the lumen inside tracheid cells, and it may have coalesced into resin canal component in the radial direction, because the axis of the pores is in the radial direction, and the resin canal distribution extends to relatively large pore sizes. The geometry of the pores was assumed to be rectangular in the fits, which is a very good approximation in the case of longitudinal tracheids constituting 93% of Pinus sylVestris. The cross sections of pores inside rays and resin canals are cylindrical, and this may cause some inaccuracy in the results. However, on the basis of conclusions of Wycoff et al.,9 we assume that the results of the fits obtained by using rectangular and cylindrical geometry would be close to each other. Diffusion of fluid molecules between different cells or cell structures was not taken into account in the model used here, even though water molecules can travel between different tracheid cells through small pits connecting the cells in fresh wood. However, the pits are closed in dry wood,7 and hence the diffusion between tracheid cells is very slow, making the use of the current model reasonable. Slow absorption of water in wood (see Figure 3) and the results of Johannessen et al.11 confirm also that the diffusion between cells is insignificant during the time scale of PGSTE experiment. The experimentally determined D values of bulk water and methane were used in the fits of eq 2 to the data points. One can consider that, if the collisions of molecules on the walls parallel to gradient direction are not perfectly elastic, the effective D is reduced slightly, causing inaccuracy in the pore size distributions obtained from the fits. However, the agreement of the pore size distributions given by the fits with the known structure of wood implies that this effect is minor. Conclusions We showed that the combined use of water and methane as probe fluids and current experimental parameters allows the measurement of dimensions of porous solid ranging from 10 µm to 10 mm by PGSTE NMR. If liquid with smaller or gas with larger diffusion coefficient were used, the scale would be even larger. It was demonstrated that the method makes it possible to determine the dimensions of all the important cell structures of Pinus sylVestris in three orthogonal directions, even though the length scales vary by several orders of magnitudes. The results are in good agreement with the known structure of wood. This method is applicable for investigating many kinds of biological and technological porous materials with pore dimensions within the abovementioned range, and, relating to wood research, it can be used for determining how technological processes, such as thermal modification, affect the structure of wood. Acknowledgment. The authors are grateful to Academy of Finland for financial support (grants no. 116824 and 123847). References and Notes (1) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (2) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523.
1084 J. Phys. Chem. B, Vol. 113, No. 4, 2009 (3) Tanner, J. E.; Stejskal, E. O. J. Chem. Phys. 1968, 49, 1768. (4) Latour, L. L.; Mitra, P. P.; Kleinberg, R. L.; Sotak, C. H. J. Magn. Reson. 1993, 101, 342. (5) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Oxford University Press: New York, 1991. (6) Mair, R. W.; Wong, G. P.; Hoffman, D.; Hu¨rlimann, M. D.; Patz, S.; Schwartz, L. M.; Walsworth, R. L. Phys. ReV. Lett. 1999, 83, 3324. (7) Kettunen, P. O. Puun rakenne ja ominaisuudet (Structure and Properties of Wood); Trans Tech Publications: Tampere, Finland, 2001. (8) Howard, E. T.; Manwiller, F. G. Wood Sci. 1969, 2, 77. (9) Wycoff, W.; Pickup, S.; Cutter, B.; Miller, W.; Wong, T. C. Wood Fiber Sci. 2000, 32, 72. (10) Hietala, S.; Maunu, S. L.; Sundholm, F. J. S.; Viitaniemi, P. Holzforschung 2002, 56, 522.
Kekkonen et al. (11) Johannessen, E. H.; Hansen, E. W.; Rosenholm, J. B. J. Phys. Chem. B 2006, 110, 2427. (12) Meder, R.; Codd, S. L.; Franich, R. A.; Callaghan, P. T.; Pope, J. M. Holz Roh- Werkstoff 2003, 61, 251. (13) Mitra, P. P.; Sen, P. N.; Schwartz, L. M.; Le Doussal, P. Phys. ReV. Lett. 1992, 68, 3555. (14) Fengel, D. Wood Sci. Technol. 1970, 4, 176. (15) Mitra, P. P.; Sen, P. N.; Schwartz, L. M. Phys. ReV. B 1993, 47, 8565. ¨ dberg, L. Langmuir 1997, 13, 3570. (16) Li, T.-Q.; Ha¨ggkvist, M.; O (17) Codd, S. L.; Altobelli, S. A. J. Magn. Reson. 2003, 163, 16. (18) Ka¨rkka¨inen, M. Puutiede (Wood Science); Sallisen Kustannus Oy: Sotkamo, Finland, 1985.
JP807848D
