Wood Microstructure Explored by Anisotropic 1H NMR Line Broadening

Article pubs.acs.org/JPCB

Wood Microstructure Explored by Anisotropic 1H NMR Line Broadening: Experiments and Numerical Simulations Camilla Terenzi,†,‡ Sergey V. Dvinskikh,†,§ and István Furó*,†,§ †

Division of Applied Physical Chemistry, Department of Chemistry, KTH Royal Institute of Technology, Stockholm, Sweden Wallenberg Wood Science Centre, KTH Royal Institute of Technology, Stockholm, Sweden § Industrial NMR Centre, KTH Royal Institute of Technology, Stockholm, Sweden ‡

ABSTRACT: The cellular structure of wood, which is highly anisotropic along its main growth directions, is responsible for the observed anisotropy in its physical and mechanical properties that depend in a complex manner on the moisture content. Here, we demonstrate that the 1H NMR spectra of wood from Norway spruce exhibit a strong and characteristic dependence on the direction of the sample relative to the applied magnetic field. By comparing spectra recorded at different magnetic-field strengths, we show that this variation is caused by the magnetic-field distribution created by the anisotropic and inhomogeneous distribution of matter and thereby magnetic susceptibility. On the basis of the observations that (i) the recorded spectral peak predominantly arises from translationally mobile water molecules and (ii) the spectral broadening is large if the long axis of the wood tracheid cells is perpendicular to the magnetic field, we set out to test the hypothesis that it is the susceptibility variation on the tracheid length scale that is responsible for the observed spectral features. To verify this, we numerically calculate in a discrete grid approximation the NMR line shapes obtained in realistic tracheid models, and we find that the calculated NMR line shapes are in good agreement with the corresponding experimental ones. We envisage the application of these findings for revealing the inhomogeneous distribution of water and its molecular properties in wood and wood-based materials at varying degrees of humidity.

1. INTRODUCTION Wood presents a renewable alternative for many applications, such as for building materials.1,2 One limiting factor for its use is that water content variation is known to modify its physical and mechanical properties, such as the tensile strength.3 Therefore, a detailed understanding of the wood-moisture relationship as well as their dependence on the multiscale heterogeneity of the wood matrix is of great importance. The degree of complexity is further raised by the obvious anisotropy of wood that arises from its anisotropic and inhomogeneous cellular structure. In the Norway spruce (Picea abies) that is the subject of the present study, the wood predominantly (>90%) consists of long tracheid cells with an average length typically of around 3 mm, a crosssectional average dimension of about 30 μm, and a cell-wall thickness of a few micrometers.3 The geometry of the lumens (i.e., the hollow cavities within the wood cells) typically follows that of the tracheids. Other wood types exhibit comparable structural anisotropies. © 2013 American Chemical Society

Perpendicular to the longitudinal tracheid axis along the directions that are either radial (R) or tangential (T) to the growth rings in the cross section of the stem, microstructural features such as the cell-size distribution and its variation across the earlywood−latewood transition are also anisotropic. In Norway spruce, where the tracheid cross section is approximately rectangular (Figure 1), the radial tracheid width significantly decreases from 30 to 40 μm to about 15 μm from earlywood to latewood, whereas the tangential tracheid width remains almost unchanged (∼25−28 μm).4−7 The polymer components are intricately structured in the cell walls. Potentially sorptive hydroxyl groups are present in the cellulose fibrils and the hemicellulose of the cell walls, where they form strong inter- and intrachain hydrogen bonds under oven-dried conditions.8 At the Received: May 3, 2013 Revised: June 17, 2013 Published: June 17, 2013 8620

dx.doi.org/10.1021/jp4043733 | J. Phys. Chem. B 2013, 117, 8620−8632

The Journal of Physical Chemistry B

Article

Figure 1. SEM image of Norway spruce tracheid cell cross sections over a region containing earlywood (ew) and latewood (lw) cells (left), and the schematic representation of the variation in the cellulose microfibril arrangement across the tracheid cell wall. Copyright J. Brändström, reproduced with permission.4,5

such studies of water in wood, in particular using 1H NMR.12−28 Because the 1H NMR features of water are very dependent on molecular dynamics, the studies of wood with its lumen filled by water (greenwood of waterlogged wood) give results that significantly differ in character from those obtained in wood samples in (apparent) equilibrium with a given ambient humidity and that are typically, with an exception for the highest relative humidities, below the FSP. Our studies presented here belong in this latter class. In particular, we show that the 1H NMR peak shape of water adsorbed in the cell walls of the Norway spruce is strongly dependent on the orientation of the wood sample in the magnetic field, a finding that surprisingly has not yet been reported in the literature even though other NMR observables, like diffusion coefficients,19 were shown to be anisotropic. Besides the experimental findings, in this Article we also present evidence that the anisotropic line broadening is caused by an inhomogeneous distribution of the magnetic field, which in turn is caused by the inhomogeneous distribution of matter and thereby the diamagnetic susceptibility within the wood. Specifically, we show that the defining structural feature is the tracheid, and we present numerical simulations of the magneticfield distribution and the resulting line shapes that are in good agreement with the experimental spectra. The simulation procedure is based on discretizing the magnetization in which we also correct an apparent error that seems to have pervaded the previous applications of the same method.

so-called ultrastructure level, the wood polymers are arranged as a multilayered composite that is heterogeneous in the respective amounts of cellulose, hemicelluloses, and lignin as well as in the microfibril orientations with respect to the tracheid axis.3 In particular, the individual cellulose microfibrils have a shape that approximates long twisted rectangular rods a few nanometers across, and they form microfibril aggregates of about 15−25 nm in diameter.9 In coniferous tracheids,4 the average orientation of the cellulose microfibrils changes across the cell wall. In the inner part (called the secondary wall, S1−S3 in Figure 1), the orientation changes from being nearly transverse to the tracheid axis close to the lumen to close to parallel to the axis for the largest part of the secondary wall and then back to close to transverse. Within the primary wall (marked P in Figure 1) that wraps around the secondary wall from the outside, the fibril orientation is essentially random. All of the layers constituting the tracheid cell wall become thicker upon the earlywood− latewood transition, with the greatest width variation occurring in the large secondary layer (from about 1−2 to 3−8 μm). Resulting from both cell-shape and wall-width changes, the wallto-tracheid volume fraction increases at the earlywood−latewood transition from about 30% to 50−70%, and at 65% relative humidity (RH) the mass density of the wood is reported to increase correspondingly from about 400 kg/m3 up to about 800 kg/m3.10 In the presence of water vapor, the chains in the amorphous and paracrystalline regions in cellulose rearrange via the scission of hydrogen bonds so that adjacent fibrils are pushed apart, causing the anisotropic swelling of the cell wall with the largest expansion occurring along the R direction. Water also affects the hemicellulosic and lignin components. Beyond the so-called fiber-saturation point (FSP), which corresponds to the hydration level where all of the accessible sorption sites are saturated, water also condenses as a separate phase within the lumen.3 The general form of the tracheid is retained during swelling. However, to date there remain many open questions concerning the state of water in wood.11 Because water is very suitable for observation by nuclear magnetic resonance (NMR) spectroscopy, there have been many

2. MATERIALS AND METHODS 2.1. Wood Sample Preparation. Two cubic wood pieces of approximately 6 × 6 × 6 mm3 in size, labeled samples 1 and 2, were cut from Norway spruce grown in northern Sweden and delivered by Martinsons Trä, Sweden. The cutting planes were parallel to the main tree axes, namely, the radial (R), tangential (T), and longitudinal (L) directions. The wood samples were oven-dried at 102 °C for 4 days until they reached an apparent mass stabilization. Next, they were kept at constant RH by storage for 1 week in closed desiccators at 24 °C over saturated water solutions of either MgCl2, Mg(NO3)2, 8621



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spectral width and 256 scans. The receiver dead time was set to 5 μs, leading to some loss of the signal arising from macromolecular protons. We estimated the longest T1 component (by inversion recovery) in the examined wood samples to be about 400 ms, so the recycle delay was set to 5 s (≫5 T1). Transverse relaxation measurements were carried out at the highest RH using the spin−echo pulse sequence with an interpulse delay that varied logarithmically from 10 μs to 6 ms in 20 steps. A nonexponential signal decay of the integral intensity of the full spectrum was observed, and after having it processed by inverse Laplace transformation (ILT) with the UPEN algorithm30 about half of the total signal was found to decay with a relaxation time T2 on the order of 300−700 μs and was associated with cell-wall water, whereas the remaining signal was characterized by a broad range of short T2 values (∼20−100 μs and possibly below) and, in the absence of clear evidence to the contrary, was assigned to protons both in the wood polymers and in any adsorbed water in slow exchange with water population exhibiting the longer T2 values. In any case, protons with any of the obtained T2 values contributed to the detected spectra. We note here that the shape of the T2 distribution obtained by ILT is very sensitive to spectral noise and to limiting conditions set at the outset (e.g., for the range of T2 values sought). The magnetic-field dependence of the detected spectra was explored by performing analogous experiments at a lower field with wood samples equilibrated at 85% RH. Using a Bruker Avance II spectrometer with a proton resonance frequency of 300 MHz, the spectra were recorded under the same conditions as those at 500 MHz, except that the 90° pulse length was set to 12.7 μs.

NaNO2, KCl, or K2SO4, resulting in RH values of 34, 54, 65, 85, and 97%, respectively. The wood pieces were exposed to a given RH in an increasing order of water activity, and after each hydration step at a given RH the NMR measurements were recorded. The moisture contents that were reached after each equilibration step are reported in Table 1. At 97% RH, we Table 1. Moisture Contents (MC) and 1H NMR Line Widthsa for the Narrow Peak with the Magnetic Field Oriented along the Longitudinal (ΔνL), Radial (ΔνR), and Tangential (ΔνT) Directions Obtained in the Two Wood Pieces after Having Equilibrated Them at Different Relative Humidities (RH) sample 1

sample 2

RH (%)

MC (%)

ΔνL

ΔνR

ΔνT

MC (%)

ΔνL

ΔνR

ΔνT

34 54 65 85 97

3.9 7.1 8.2 17.1 22.0

1.5 1.2 1.3 1.1 1.1

6.1 6.3 6.0 6.0 5.9

6.3 6.2 6.2 6.0 5.9

4.3 6.3 7.9 17.1 22.6

1.5 1.6 1.5 1.6 1.3

6.0 6.2 6.2 6.0 5.9

6.1 6.1 6.2 6.0 5.8

a

In kHz, as obtained at 500 MHz and as defined in Figure 2.

reached 22% moisture content (MC), which is far below the FSP for spruce that is typically given29 as ∼35−37%. Hence, no capillary condensation is expected to occur, which is also evident from the absence of any spectral component with long transverse relaxation times typically identified as capillary condensed water.15,28 Each wood sample was positioned in a 10 mm NMR tube on a cylindrical Teflon plug that provided reliable and reproducible sample orientation with respect to the static magnetic field of the NMR spectrometer. During the NMR measurements, whose duration was about 20 min, the NMR tube was sealed with a plastic cap and Parafilm to avoid changes in moisture content, which was also checked by weighing the sample before and after the measurements. 2.2. 1H NMR Measurements. The 1H NMR spectra were obtained using a Bruker Avance III 500 MHz NMR spectrometer. During the experiments, the temperature was kept constant at 24 °C to within 0.2 °C, and the samples were allowed to equilibrate in the NMR probe for 30 min before starting the measurements. The data were acquired by single-pulse experiments with 7 μs 90° radio-frequency pulses with a 500 kHz

3. EXPERIMENTAL RESULTS In Figure 2, we present the general characteristics of the 1H NMR spectra that were obtained. The broad spectral component with a line width of about 50 kHz is assigned to macromolecular protons. The line width indicates a corresponding T2 < 10 μs; hence, this spectral component was not detected in the spin−echo experiments described above. It is the narrower spectral component that has yielded a broad T2 distribution, and we assign this to adsorbed water, exchangeable hydroxyl protons in the cellulose and hemicellulose molecules within the cell walls, and presumably some more mobile macromolecular

Figure 2. (a) 1H NMR spectrum of sample 1 equilibrated at 97% RH and measured with the magnetic field along the tangential (T) direction. (b) Frequency derivative of the NMR spectrum with the line width defined as the frequency difference, ΔνT, between the peaks of the derivative (indicated by dots in panels a and b). 8622



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components.31 Although the broad spectral component does not significantly change with the sample orientation or with the moisture content, the narrower 1H NMR peak exhibits strong changes with both variables. Even though the narrow peak is probably of composite character, it seems that its most significant contribution arises from water. This is supported by the often observed linear correlation between the 1H NMR intensity and the gravimetric water content (although one should note that in many studies the acquisition delay times were longer, thus having cut away broader spectral components).13,16,17,21,25,27,28,32,33 Aside from the spectral shape of the narrow line, we also seek to quantify its line width, Δν, which we define as the peak−peak distance in the frequency derivative of the NMR spectrum, as shown in Figure 2b. This line width definition is more suitable for irregular peak shapes than the full-width at half-maximum that, for a single Lorentzian peak, is equal to 31/2Δν. As can be seen in Table 1, the line width shows small specimen variability between samples 1 and 2, which is an important and encouraging feature for our biological sample. Within the same sample, the line width was reproducible to within 10−12 m2/s.35 Hence, on the characteristic time scale set from the inverse line width to T2* = 1/πΔν, 8623



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scale. Below, we investigate whether the line shapes can verify this hypothesis. 4.2. Simulating the Magnetic-Field Distribution. The local magnetic field induced within structures composed of weakly magnetic materials36,37 and placed in an otherwise uniform magnetic field has been calculated using both analytical and numerical methods. Analytical mathematical models are available for simple geometries, such as spherical and cylindrical objects, where the Maxwell equations can be solved exactly.38 Durney et al.39 introduced a procedure that is valid for small susceptibilities and is based on the first-order surface integral expression of the magnetic field for rectangular surfaces, which allowed the calculation, without numerical integration, of the magnetic-field distribution for simple geometries, such as spheres, spherical shells, cubes, cubical shells, and rectangular parallelepipeds.39,40 Any shapes, regular or irregular, can be investigated using numerical finite-difference methods41−44 to solve the field equations for arbitrary 2D and 3D magneticsusceptibility distributions. Hence, the NMR line shape for liquids imbibed in real porous media was evaluated.45 As an alternative numerical method,46 a simple algorithm was presented that did not require finite element analysis. On the basis of subdividing the volume into discrete spherical volume elements, the magnetic-flux density at any given point (field point) was calculated as the linear superposition of the dipole fields from the surrounding volume elements. In addition to the effect of those volume elements, a uniform field shift47 of

ΔB⃗ =

2 χ B0⃗ 3 vol

(1)

where χvol is the volume magnetic susceptibility48 and B⃗ 0 is the applied static magnetic-flux density, accounted for the effect of the material within the actual spherical volume element at the field point. Recently, this approach has been adapted by Mayer and Terheiden,49 who proposed using a grid of space-filling cubic volume elements and, by including the exchange of molecules among volume elements, provided a pathway to simulations50 that can easily include the effect of molecular displacements on the NMR-detected magnetic-field distributions. We note here that, curiously, the contribution from the local field within the actual cubic volume element at the field point was not taken into account in these latter works.49,50 This omission leads to an erroneous field shift, as is evident from simulations of finite cylindrical volumes,49 that differs from the analytical result exactly by the local magnetization term in eq 1.39 Here, we represent the material distribution by a grid of cubic volume elements;49,50 however, at the field point we add to the sum of the surrounding dipolar fields the local field within the actual volume element. We do this by noting that the average local field within a cubic volume element is equal to the value of the uniform field within a homogeneous spherical volume element;51 hence, this procedure is exact in the limit of an infinitely small volume element (or, for NMR purposes, for volume elements within which the field inhomogeneity is motionally averaged). We chose this method instead of the more familiar finite element-based solutions because we consider it to be more intuitive and more conducive to studying the effect of diffusion, which we intend to investigate in the future. 4.3. Simulation Procedure and Verification. The simulation procedure starts by (i) defining the shape that represents the distribution of matter and (ii) discretizing the volume within that shape into N3 cubic elements indexed along the three Cartesian directions by ijk (all within 1, ..., N), with their

Figure 4. Comparison of 1H NMR spectra of Norway spruce wood equilibrated at RH = 85%, acquired at Larmor frequencies of 300 MHz (dashed line) and 500 MHz (solid line), and with the magnetic field oriented along the L (a), T (b), and R (c) directions of the wood. The ratio of the line widths obtained at the two frequencies is given (500)

as Δν /Δν(300).

we can derive an estimate for the average displacement d from ⟨d2⟩ = 2DT2*. By considering that at 300 MHz the line width was still predominantly inhomogeneous, we get, via T2*(300 MHz) ≈ 100 μs, d ≳ 15 nm. This means that inhomogeneity on the microfibril aggregate length scale (∼20 nm aggregate diameter) does not contribute to the observed inhomogeneous broadening and that we should seek the source for our detected line shapes on the length scale >100 nm. This makes it plausible that the detected line broadening is caused by field distribution arising from the microstructural heterogeneities on the tracheid length 8624



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centers defined as being at xi, yj, and zk. The volume ΔVel of the element scales linearly with N3. At this stage, we assume that space is sharply divided into two regions: one with 0 and one with a small finite magnetic susceptibility that are assumed to be distributed uniformly. Note that the simulation results do not depend on absolute dimensions, just on the shape.39 The presence of a homogeneous external magnetic field H⃗ with its associated free-space magnetic-flux density B⃗ 0 = μ0H⃗ , where μ0 = 4π × 10−7 m−1 H is the vacuum permeability, induces a magnetization density in each volume element ΔVel. The presence of this induced magnetization is represented by a magnetic moment at the center of the volume element given by m⃗ = M⃗ ΔV el = k volB0⃗ ΔV el

(2)

where M⃗ 0 = χvolH⃗ is the magnetization density and χvol = μ0kvol is the dimensionless scalar volume magnetic susceptibility that is assumed to be isotropic. The volume magnetic susceptibility, kvol = M/B0, is expressed in units H−1 m.48 For weakly magnetic materials, such as our water/wood system, the local magnetic-flux density perturbation can be approximated by a linear superposition of the magnetic-flux densities caused by the magnetic moments m⃗ within the individual grid volume elements.40 Hence, the local net magnetic-flux density, ΔB⃗ ijk, at each grid point ijk can be calculated as the linear superposition of two terms: the magnetic-flux density, ΔB⃗ cube, generated by the magnetic material within the cubic volume element at which the field is calculated and given by eq 1, and the magnetic-flux density caused by the magnetic dipoles within all of the other cubic volume elements i′j′k′ located at a distance ri⃗ i′,jj′,kk′ from ijk: ⃗ = ΔBijk

∑ i′j′k′

⎞ μ0 ⎛ 3(m⃗ · rii⃗ ′, jj ′ , kk ′) rii⃗ ′ , jj ′ , kk ′ m⃗ ⎜ ⎟ − ⎜ 5 3⎟ 4π ⎝ | rii⃗ ′ , jj ′ , kk ′| | rii⃗ ′ , jj ′ , kk ′| ⎠

+ ΔB⃗

cube

(3)

In NMR spectroscopy, the observed inhomogeneous broadening ultimately depends on the magnitude of the resulting flux density. Hence, for weak magnetic susceptibilities one can neglect field components perpendicular to B⃗ 0 because they contribute on second order only.46 Customarily, by defining ẑij//B⃗ 0, where ẑ is the unit vector along the z axis, computations can be limited to calculate the z component of the magnetic-flux ⃗ density in eq 3, which is defined as ΔB(z) ijk = ΔBijkẑ. In the MATLAB routine we use, this calculation is performed in a parallel manner for all points on the grid, yielding the variation of ΔB(z) ijk over the investigated object. A convenient way of representing the resulting magnetic-field distribution within the explored volumes and shapes is in terms of a histogram, where the number of sampling points having a local normalized field shift, ΔB(z) ijk /(|χvol|B0), within each small interval is plotted versus ΔB(z) ijk (|χvol|B0). The performance of our simulation procedure has been tested by computing the field distributions for simple homogeneous structures, such as the sphere and a finite cylinder, using the −6 diamagnetic susceptibility of water (χwater vol ≈ −9.04 × 10 ). The histograms for a sphere were obtained by increasing the grid density and, correspondingly, the number of volume elements from 0.9 × 104 in Figure 5a to 2.2 × 105 in Figure 5b, which corresponds to reducing the linear size ε of the volume elements by roughly a factor of 3 (from 0.1 to 0.033 times the radius). With respective computation times of ca. 3 s and 10 min on a conventional personal computer, both histograms provide the

Figure 5. Histograms of the normalized field shift, ΔB(z) ijk /(|χvol|B0), obtained for the simple geometric objects. (a, b) Distribution of the magnetic field in a homogeneous sphere obtained with 0.9 × 104 (a) to 2.2 × 105 (b) cubic volume elements within the simulation grid occupying the spherical volume. (c) Using the latter grid resolution, the distribution obtained for a homogeneous long cylinder with a length/ diameter ratio equal to 10 and with its long axis parallel to B⃗ 0.

expected (recall eq 1) negative normalized field shift of −2/3, and at the higher grid density, the field distribution approaches well the single-spike shape expected for the homogeneous field within the sphere. Figure 5c shows the field shift histogram obtained by the same grid resolution as in Figure 5b for a solid cylinder having a length/diameter ratio equal to 10 and oriented with its long axis parallel to B⃗ 0. It exhibits a peak around −1, and 8625



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Figure 6. Rectangular parallelepiped-shell model of cell walls used for simulating the 1H NMR spectra of adsorbed water in Norway spruce wood. The radial-to-tangential aspect ratio, τ = b/a, and the volume fraction of the cell wall were independently set to earlywood or latewood. To account for the effect from neighboring cells, the final line-shape simulations were performed for the middle cell within the groups of 3 × 3 identical adjacent parallelepipedic shells.

fraction of the cell walls, αtot, becomes dependent on the amount of adsorbed water as

its shape resembles the analytically derived expression for a long finite rectangular parallelepiped.39 4.4. Wood-Tracheid Model and Simulated Field Distributions. Within wood tracheids, three sources of magnetic susceptibility contrast are present: wood, water, and −6 air. The paramagnetic susceptibility of air is χair vol = 0.4 × 10 . It is the difference diff wall air χvol = χvol − χvol

⎛ ρ wall ⎞ α tot = αdry ⎜1 + MC water ⎟ ρ ⎠ ⎝

yielding αtot = 0.35 at MC = 22%. However, in the opposite limit of negligible swelling and constant α (equivalent to the assumption that water merely occupies holes in the cell-wall structure) we would instead obtain

(4)

wall air between the susceptibility of the cell wall, χvol , and χvol that controls the magnetic-field inhomogeneity. The mass susceptibility of dry wood52 (in vacuum, the average of the data for the four different wood sorts) has been given as wood wood ≈ −6.1 × 10−9 m3/kg, which provides χdry = χdry mass vol dry wood dry wood −6 dry wood ρ × χmass ≈ −2.4 × 10 , where ρ in Norway spruce was set to 0.4 × 103 kg/m3.53 From this, one can obtain the corresponding susceptibility of the dry cell wall by first establishing the volume fraction of the cell wall

αdry =

wet wall dry wood χvol = χvol + MC wall χwet vol

(5)

where the typical figure for the density of the cell wall is ρwall = 1.5 × 103 kg/m3,54 yielding αdry = 0.27. Hence, one obtains dry wall χvol =

dry wood χvol

αdry

ρ wall water χ ρ water vol −6

= −9.1 × 10−6 (6)

In addition, the volume magnetic susceptibility of the dry cell wall is contributed to by the water adsorbed there. wall Coincidentally, χdry is very close to χwater vol vol . Hence, under the assumption that wood cells swell during moisture uptake in exact proportion to the volume of adsorbed water, the volume susceptibility of the wall remains practically constant and we −6 obtain χdiff vol = −9.5 × 10 via eq 4. In this limit, the total volume

χdiff vol

(8) −6

that yields = −12.0 × 10 , = −12.4 × 10 , and volume fraction αtot = αdry for the cell wall. The former assumption is the valid one for Norway spruce,3 where the lumen area remains approximately constant under moisture content variation, and the change in the wall volume of the wood tracheids is equal to the change in the volume of adsorbed water. Therefore, the field simulations have been performed using −6 χdiff vol = −9.5 × 10 . The geometry in our model of the wood-tracheid microstructure is a long rectangular parallelepiped shell (Figure 1) whose aspect ratio is defined by the edge lengths a, b, and c (with a set to 1), as shown in Figure 6. Because the results are shape (and not absolute size) dependent, the control parameters are the aspect ratios

ρdry wood ρ wall

(7)

λ = c /a

(9a)

τ = b/a

(9b)

and the cell-wall volume fraction for individual tracheids α (that is, the relative thickness of the shells) that can be varied independently. The linear dimension ε of the cubic volume element is now relative to a. 8626



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To test the simulation procedure, we calculated the field shift histograms for single (that is, without adjacent shells) cubic (τ = 1 and λ = 1) shells with volume fractions α = 0.10, 0.58, and 1 (similar to those calculated analytically in the literature 39) and with the axis of the cavity perpendicular to B⃗ 0. With a higher grid resolution than that used for Figure 5 and with a computation time less than 2 min, we obtained the results presented in Figure 7, which are in very good agreement with the corresponding analytical field distributions.39 One

particular feature of this is that the thicker the shell the narrower the field-shift histogram. To account better for the actual wood structure, in the final simulations the field histograms were calculated for the middle cell within a group of 3 × 3 identical adjacent parallelepipedic shells, shown in Figure 6, having aspect ratios of λ = 10. In Norway spruce, the proportion X of earlywood (ew) and latewood (lw) section volumes is roughly 4.10 Although the volume fractions of the cell walls in the earlywood and latewood can be set freely, they have to satisfy the condition set by the total cell-wall volume fraction as α tot =

αlw + αewX 1+X

(10)

Taking into account the limitations imposed by the grid discretization and by eq 10, the α and τ ranges for the earlywood and latewood tracheids were chosen according to the SEM images of Norway spruce wood reported by Brändström.4 A Gaussian distribution of αtot to within 0.33−0.40 with the average value set to 0.38 has thus been considered to account in part for the variation in wood microstructure. Correspondingly, the volume fraction of the individual cell walls, α, has been varied to within 0.29−0.35 for earlywood and within 0.59−0.70 for latewood. Within the limits imposed by the chosen grid resolution, this variation was achieved by changing in discrete steps of integer multiples of ε the thickness of the cell walls, and the following geometries were obtained: (αew, τew) = (0.29, 1.7); (0.30, 1.6); (0.31, 1.4); (0.32, 1.3); (0.33, 1.2); and (0.35, 1.1) and (αlw, τlw) = (0.59, 0.6); (0.66, 0.5); and (0.70, 0.6). With the exception of (αew, αlw) = (0.35, 0.66) and (0.35, 0.70), the other 16 combinations of earlywood and latewood cells satisfy eq 10, thus they will be considered in the present simulations. All numerical calculations were performed at a moisture content of 22%, which corresponds to the hydration level reached by the investigated wood samples after 1 week of equilibration at 97% RH. For each simulation, the results have been checked for convergence (within 0.1 kHz of line width, see below) with an increasing grid density number. We have similarly tested that line width results obtained by λ = 100 (a more realistic value for the longitudinal aspect ratio of wood tracheids) are within 0.1 kHz of those obtained by λ = 10. 4.5. Simulated 1H NMR Spectra of Wood Tracheids. To simulate the actual 1H NMR line shapes measured at 500 MHz, B0 has been set to 11.7 T, and the site-dependent shift of the Larmor frequency ωijk (in units of Hz) has been obtained as (z) ωijk = γ ΔBijk

(11)

where γ = 42.57 MHz/T is the H gyromagnetic ratio. In addition, the homogeneous line broadening was accounted for by Lorentzian broadening of the frequency-shift histogram as 1

S(ω) =

∑ k

n(k) T2 1+

T22(2π (ω

− ωok))2

(12)

where ωok and n(k) are the Larmor frequency and the number of counts corresponding to the kth interval of the histogram, respectively, which yields the spectrum S(ω). To illustrate the results, Figure 7a and e display the field histograms obtained for the middle cell within a group of 3 × 3 identical earlywood tracheids (αew = 0.31, τew = 1.4) and for the middle cell within a group of 3 × 3 identical latewood tracheids (αlw = 0.66, τlw = 0.5), respectively. This combination of αew

Figure 7. Histograms of the normalized field shift, ΔB(z) ijk /(|χvol|B0), for cubic shells (cf. Figure 6) with volume fractions 0.10 (a) , 0.58 (b), and 1 (c) and the grid density set to ε = 0.025. The applied magnetic field is perpendicular to the axis of the cubic cavity. Each histogram is normalized to its total number of counts. 8627



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Figure 8. Numerically calculated histograms of the normalized field shift (a, e, for the middle cell of a group of 3 × 3 shells as in Figure 6) and the respective simulations of the NMR line shape with T2 = 90 (b, f) and 550 μs (c, g) and using a distribution of T2 values (d, h) for earlywood (αew = 0.31, τew = 1.4; left column) and latewood (αlw = 0.66, τlw = 0.5; right column) with B⃗ 0 oriented along the R direction. Both field histograms are normalized to their total number of counts.

and αlw values gives αtot = 0.38 using eq 10. In both cases, the rectangular parallelepipedic shells were oriented with their radial direction parallel to B⃗ 0. The calculations were found to converge,

within the experimental error, when they reach the same grid resolution as in the preliminary tests on simple geometries (Figures 4 and 6). The computation time varied from 8628



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Figure 9. Comparison of the 1H NMR line shapes along the R (left column), T (middle column), and L (right column) directions measured at MC = 22% (a−c) with the respective simulated spectra (d−i). For the middle cell of a group of 3 × 3 shells, as in Figure 6, obtained by summing the line shapes calculated using T2 = 90 μs for panels d−f (dotted line), a distribution of six earlywood sets (αew = 0.29−0.35, τew = 1.1−1.7) and one latewood set (αlw = 0.59, τlw = 0.6), a distribution of five earlywood sets (αew = 0.29−0.33, τew = 1.2−1.7), and one latewood set with αlw and τlw equal to 0.66 and 0.5 (dashed line) and to 0.70 and 0.6 (solid line), respectively. The uppercase text in the legend of the plots in d and e indicates the αlw value. For each wood direction, the last row (g−i) shows the comparison between the sum of the respective line shapes from d−f (solid line) and the line shape calculated for one earlywood (αew = 0.32, τew = 1.3) and one latewood set (αlw= 0.59, τlw = 0.6) (dashed line). The calculated spectra along the L direction were overlapping (f, i).

estimate. For comparison, in Figure 8c,g the line-shape calculation was performed by setting T2 ≈ 550 μs, which considers only the long T2 range; however, the simulated spectra deviate considerably from the experimental ones. Figure 8d,h show the results obtained with eq 12 using a weighted distribution of 16 T2 values (the result does not vary much for having the number of points in the 10−20 range) between 20 and 700 μs, representing roughly the shape of a full T2 distribution obtained by UPEN. The spectra appear to be contributed to by an apparently broader and another narrower component, where the latter is similar to the spectra obtained with the geometric average estimate of T2 and the former can appear as merged with the broad spectral component demonstrated in Figure 2. As yet, we do not have sufficiently good criteria to estimate what the valid distribution of the T2 values in wood is, and, moreover, we do not have any information on whether those distributions are different in earlywood and latewood and/or when recorded with sample directions R, T, and L. Therefore and because in this Article the primary goal is to demonstrate the origin of

approximately 3 to 8 h, depending on the aspect ratio of the rectangular parallelepipedic shells. In an attempt to account for the broad T2 dispersion, as experimentally found for wood at MC = 22%, and because of the ill-posed nature of the inverse Laplace transformation (which makes finer details in the T2 distributions derived from our spinecho data less reliable), we explored a few different regimes in the NMR line-shape calculation from the histograms in Figure 7a,e. Hence, Figure 8b,f show the respective spectral simulations obtained using eq 12 with T2 = 90 μs, which approximately corresponds to the geometric mean55 value of our obtained T2 distributions. (Similar use of an average relaxation time from multiexponential decays has already been reported for histogram convolutions.46) Obviously, such a T2 estimate falls between the short (20−100 μs) and long (300−700 μs) spin−spin relaxation components. The line widths in Figure 8b,f were 6.1 and 4.1 kHz, respectively; in the case of earlywood shells, increasing the T2 value by 10 μs gave ΔνR = 5.9 kHz, whereas for the latewood shells there was no significant difference in the line-width 8629



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the different aspect ratios of earlywood and latewood tracheids can the experimental line shapes along the R and T directions be properly described.

the observed line shape, we resorted to the use of the simple geometric average. To account for the variation in the wood tracheid microstructure associated with earlywood−latewood transitions (aside from orientation), field-shift histograms, as in Figure 8a,e, were summed with relative weights representing the relative contributions of earlywood and latewood. As one factor, we consider the proportion of earlywood and latewood section volumes in Norway spruce10 to be X ≈ 4. However, the relative contributions to the NMR signal are also proportional to the volume fractions of the cell wall in those two regions. Hence, the two contributing field histograms were added with a relative weight of Xαew /αlw. These summed histograms have been calculated along the R, T, and L directions for the 16 chosen combinations of 3 × 3 earlywood and 3 × 3 latewood rectangular shells, as in Figure 6, with volume fractions satisfying eq 10. In Figure 9, the experimental spectra, measured at RH = 97% along the radial (a), tangential (b), and longitudinal directions (c), are compared with the calculated line shapes (d−i). Figure 9d,e report the line shapes obtained along the R and T directions, respectively, for a distribution of five or six earlywood sets and one different latewood set with αlw equal to 0.59 (dotted line), 0.66 (dashed line), and 0.70 (solid line). In Figure 9f, the corresponding calculated spectra along the L direction are overlapping. The sum of the line shapes in Figure 9d,e is shown in Figure 9g,h, respectively, in a comparison with the line-shape calculation for one earlywood and one latewood set (αew = 0.32, τew = 1.3 and αlw = 0.59, τlw = 0.6), with αew and τew chosen equal to the average values within their respective investigated ranges. Again, the simulation results for the L direction were identical (Figure 9i). In both the radial and tangential directions, the line-width estimates for all of the above combinations of earlywood and latewood tracheids are within the experimental error of the corresponding experimental line-width values. A T2 variation of 10 μs results in a change in ΔvR,T of about 0.1 kHz, whereas ΔvL changes by about 0.2 kHz, showing that, as expected, along the longitudinal direction the static magnetic-field inhomogeneity is less significant. The detailed peak features and the mutual differences between the radial and tangential spectra in Figure 9 depend on both αew and αlw; clearly, the spectrum can report on the wood structure. Along directions R and T, the spectral shape is well reproduced in the sense that the peak splitting appears slightly more pronounced in the R axis. In the longitudinal direction, the peak shape is simple, lacking the features for the R and T directions, but the simulated line broadening is larger than the experimental one and is independent of αew and αlw. This is most probably a consequence of not representing sufficiently well in our simulations the distribution of T2. This affects the L spectra the most because their field distribution is narrow. Presumably, we may be also underestimating the structural variation of the wood, which could make the spectral features in the R and T directions less sharp. Although we try to account for large-scale variation in the average geometry (cf. the variations of the ew and lw parameters in Figure 9), we do not consider any deviation of the tracheid cells from the ideal rectangular shape. The observed results suggest that with the simplified geometric model used to describe the heterogeneous wood-tracheid structure, with the uncertainty concerning the microstructural parameters and their respective distributions for the examined wood specimens notwithstanding, the 1H spectral features are well reproduced. Moreover, the comparison between Figure 8b,f and Figure 9 shows that only by simultaneously accounting for

5. CONCLUSIONS The 1H NMR spectrum of wood has been recorded for over 40 years. Surprisingly, even though the effect is strong and distinct (Figure 3) no one has so far reported that the spectrum depends on the direction of the wood piece relative to the magnetic field. Once this was detected, it was rather obvious that this is as it should be because wood is a material made anisotropic by the elongated shape of its aligned tracheid cells. The large susceptibility difference between the cell wall and the air-filled lumen makes the magnetic field inhomogeneous in a manner that is dependent on the direction that the tracheids are oriented with respect to the field. In its nature, the resulting line broadening is the same as that detected in other biological materials such as lung tissue39,40 or in technological materials such as foams.56 As we show, the line shapes can be modeled well by firstprinciples simulations with input information from microscopy (tracheid and cell-wall shapes) and basic physical measurements (mass density, volume fractions, and diamagnetic magnetic susceptibility). Using a simple discrete-grid model49 for the material and thereby susceptibility distribution, we obtained the field distribution within the cell walls that along with the information obtained from crude but robust transverse-relaxation experiments can provide the 1H NMR line shapes. Even though our model does not and cannot fully involve all aspects of the variation in real wood cell walls (i.e., in shape and in composition), we reproduce well in the three orthogonal directions the main features of the line shapes and with the exception of the longitudinal direction, the values of the line widths. Further advances will require a more accurate representation of the distribution of the T2 relaxation times. The main advantage of the discrete-grid model used here is that it is easy to include the distribution of the properties of the material as well as molecular dynamics. Hence, the method could be easily tailored to account for the self-diffusion of cell-wall water and the distribution of the different material components in wood−polymer composites. Hence, we envisage further studies in heterogeneous wood and wood-based materials.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS Financial support from the Wallenberg Wood Science Center and Swedish Research Council VR is gratefully acknowledged. REFERENCES

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Wood Microstructure Explored by Anisotropic 1H NMR Line Broadening

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