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One- and Two-Dimensional NMR in Studying Wood–Water Interaction at Moisturizing Spruce. Anisotropy of Water Self-Diffusion

Authors:

Abstract

This paper examines how wetting the surface of wood affects characteristics of wood materials. An important question is how moisturizing wood has an effect on diffusion parameters of water, which will change conditions of the technological treatment of material. A fibrous structure of wood can result in different diffusivities of water in the perpendicular direction and along the wood fibers. The work explores how 1- and 2-dimensional NMR with pulsed field gradients (PFG) highlights an anisotropic diffusion of water when moisturizing spruce wood. The methods applied: T2-relaxation (CPMG) measurements with the application of inverse Laplace transform (ILT), cross-relaxation experiments (Goldman–Shen pulse sequence), 1D PFG NMR on oriented wood pieces or applying gradients in various orientation, and 2D diffusion-diffusion correlation spectroscopy (DDCOSY) with two pairs of colinear gradient pulses. The results showed anisotropic restricted diffusion correlating the size of tracheid cells. The experimental 2D diffusion-diffusion correlation maps were compared with model calculations based on parameters of 2D experiment on spruce and the theory of 2D DDCOSY with ILT. Moisturizing spruce wood resulted in anisotropic diffusion coefficient which can be monitored in 2D NMR to discover different diffusion coefficients of water along the axis of wood fibers and in orthogonal direction.
colloids
and interfaces
Article
One- and Two-Dimensional NMR in Studying
Wood–Water Interaction at Moisturizing Spruce.
Anisotropy of Water Self-Diusion
Victor V. Rodin
Institute of Organic Chemistry, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria;
victor.rodin@jku.at
Current Address: Glasgow Experimental MRI Centre, Institute of Neuroscience and Psychology,
College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow G61 1QH, UK.
Received: 6 June 2019; Accepted: 29 July 2019; Published: 2 August 2019


Abstract:
This paper examines how wetting the surface of wood aects characteristics of wood
materials. An important question is how moisturizing wood has an eect on diusion parameters of
water, which will change conditions of the technological treatment of material. A fibrous structure of
wood can result in dierent diusivities of water in the perpendicular direction and along the wood
fibers. The work explores how 1- and 2-dimensional NMR with pulsed field gradients (PFG) highlights
an anisotropic diusion of water when moisturizing spruce wood. The methods applied: T
2
-relaxation
(CPMG) measurements with the application of inverse Laplace transform (ILT), cross-relaxation
experiments (Goldman–Shen pulse sequence), 1D PFG NMR on oriented wood pieces or applying
gradients in various orientation, and 2D diusion-diusion correlation spectroscopy (DDCOSY) with
two pairs of colinear gradient pulses. The results showed anisotropic restricted diusion correlating
the size of tracheid cells. The experimental 2D diusion-diusion correlation maps were compared
with model calculations based on parameters of 2D experiment on spruce and the theory of 2D
DDCOSY with ILT. Moisturizing spruce wood resulted in anisotropic diusion coecient which can
be monitored in 2D NMR to discover dierent diusion coecients of water along the axis of wood
fibers and in orthogonal direction.
Keywords:
PFG NMR; moisturizing wood; restricted diusion; DDCOSY; Inverse Laplace Transform
1. Introduction
Wood is a natural fibrous material with porous structure which allows a transfer of water through
the pores [
1
,
2
]. This water transport corresponds to the wettability of the wood material, which changes
for dierent kinds of wood and various surface and inner microstructures [
3
,
4
]. It can result in various
moisture of wood and change in the properties of material [
5
8
]. Wood is anisotropic composite
material [
8
,
9
]. Therefore, the properties of wood can be dierent in longitudinal (along the fiber
direction), radial (across the grown rings) and tangential (at a tangent to the rings) orientations [
6
10
].
Moisture of wood is the critical parameter aecting technological regimes of treatment of wood
materials [
2
6
]. It is important to know how wetting the wood aects porous microstructure and how
to find suitable methods for estimation of pore-water interactions and water transport during changing
moisture of wood [
3
9
]. Dierent methods including those based on the phenomenon of nuclear
magnetic resonance (NMR spectroscopy and NMR Imaging) have been applied and developed to
monitor wettability and saturation of dierent porous materials with water [
1
,
4
,
11
14
]. For instance,
dierent NMR techniques (spin-spin relaxation time (T
2
) as a function of saturation, spin-lattice
relaxation time (T
1
) NMR dispersion, T
2
shift, NMR diusion and T
1
/T
2
ratio) have been probed for
Colloids Interfaces 2019,3, 54; doi:10.3390/colloids3030054 www.mdpi.com/journal/colloids
Colloids Interfaces 2019,3, 54 2 of 14
wettability measurements on chalk, rock, sandstone, coal [
14
17
]. Because NMR signal is sensitive to
the interaction of liquid with solid surface, it is considered to be a suitable candidate for determination
of wettability [
11
,
12
,
14
16
]. Advantages of magnetic resonance methods are associated with quickness
of measurement, and the result of the measurement (diusion coecient Dand T
1
and T
2
relaxation
times) can be obtained in real time [
16
]. A correlation between these NMR parameters is also important
in such experiments because wettability aects all those parameters [
14
,
15
]. NMR signal can be
sensitive also to other dierent properties of a material. Therefore, in practice, information about
wettability from NMR data obtained can be extracted if the NMR parameters (T
1
,T
2
or D) have been
already obtained and treated for proper analysis [
14
16
]. Considering the wettability as the interaction
between the molecules of liquid and a solid surface, an intensity of these solid-water interactions
can be clarified from the value of the T
1
/T
2
ratio [
11
,
12
,
16
]. The ratio of spin-lattice relaxation time
to spin-spin relaxation time is supposed to test the local wettability. Using the eective relaxivity,
the authors of Reference [12] consider the T2Ddata for obtaining the wetting surface coverage.
As for moisturizing wood materials, these considered NMR parameters have not been studied
properly to obtain the details on wood–water interaction in pieces of felled mature spruce in a wide range
of water contents. However, some published data on spruce [
7
,
8
,
18
] showed that a cross-relaxation
process between protons of solid surface and the ones of water can aect the behaviour of T
1
relaxation and should be considered for correct estimation of self-diusion coecients at various
diusion times with stimulated-echo pulse sequence [
19
,
20
]. Additionally, it was shown [
18
,
21
] that
2D correlation experiments with two pairs of gradient pulses applied in orthogonal directions to
wood pieces can be valuable means to define an anisotropy of water self-diusion. The current
work is going further to study an interaction between water and spruce wood surface applying for
one- and two-dimensional pulsed field gradients (PFG) NMR experiments. This is to show how
cross-relaxation eect and diusion-diusion correlations should be considered in analysisof the results
on water anisotropic diusion at wetting the spruce wood. The work is looking for the details of
wood–water interaction also at higher water amount than fiber saturation point (FSP). This point does
mean such an amount of water in wood when only bound water is present in the spruce material,
i.e., at FSP, there is no free water in the wood [
8
,
21
]. From the other side, if added water results in
the range of moisture above the FSP, three T
2
components (two are between 0.1 and 10 ms, and third
one is in a slow relaxing range of 20–140 ms) can be observed [7,8].
The present work shows how the relaxation spectra of water components at moisturizing spruce
wood and apparent diusion coecients measured in one dimensional PFG NMR experiments on
wood with dierent orientation of the samples to the magnetic field or dierent direction of gradients
produce valuable information about microstructure giving an estimation of cell sizes in conditions of
restricted diusion and anisotropic properties of water in spruce pieces. In addition to this, for model
of water diusion anisotropy with two dierent diusion coecients in two orthogonal directions,
it was shown that 2D diusion-diusion correlation experiment with collinear pairs of gradients
and the use of Inverse Laplace Transform result in 2D diusion map with two spots on a diagonal
as a reflection of two dierent diusion coecients. The results of 2D experiments were in line with
theoretical calculations. That gave an opportunity to follow a change in diusional anisotropy with
moisturizing spruce wood. As this capacity is governed by moisture transport, the data obtained
would clarify water–wood interaction and highlight more details about diusivity and NMR relaxation
parameters used in characterization of wettability properties.
2. Materials, Methods and Theory
Preparation of samples. Felled mature Sitka spruce (Picea sitchensis) pieces were used. The samples
for NMR studies were cut from original pieces of wood, and they had a roughly shape of a cube
(size 6
×
6
×
6 mm
3
=longitudinal, radial and transverse) or a parallelepiped (size 6
×
6
×
10 mm
3
).
Prepared samples were covered by the polymer film and kept in the fridge before the start of
the experiment. They could be tested in an NMR probe at dierent moisture conditions including drying
Colloids Interfaces 2019,3, 54 3 of 14
in oven until constant weight. Dried samples were used in wetting experiments. After moisturizing
the samples, each of the pieces was then placed in a 10 mm NMR tube and sealed. A stopper was used
on the top of each sample to prevent an evaporation of water from the sample during NMR experiment.
A 400 MHz Chemagnetics Infinity spectrometer equipped with a 10 mm Fraunhofer Institute
1
H probe
and a vertical wide-bore (89 mm) Magnex superconducting magnet was used for measurements of free
induction decay (FID), T1,T2and cross relaxations, and PFG NMR diusion [2225].
Water content in the samples was made in opened supported system under atmosphere of relative
water humidity (in desiccator) and measured in g H
2
O/g dry matter [
20
]. The samples were weighed
before and after hydration. In wettability experiments, a placement of water drops on the surface of
wood pieces was realised following equilibrium distribution of water inside the sample. The samples of
both kinds were compared by FID and/T
2
peaks distribution analysis for 6–36 h to monitor establishing
equilibrium of water distribution across the sample.
NMR methods. The spin-lattice relaxation times were measured using the inversion recovery pulse
sequence (180
τ
–90
) whereas T
2
measurements have been carried out using Carr–Purcell–Meiboom–Gill
(CPMG) pulse sequence [
7
,
22
,
25
]. The sample was placed within the volume of the probe coil to ensure
RF field homogeneity. All measurements were performed at proton resonance frequency of 400 MHz
and at room temperature. The 90
pulse length was 8–10
µ
s. The dead time was 6–8
µ
s. Time for
repetition of pulse sequence was typically 1 s., and 1024 averages were acquired per spectrum. A signal
from the probe with empty NMR tube was small. It was routinely subtracted from the total signal in
the experiment. After measurements wood samples were kept in the fridge (5 C).
FID. The FID signals measured in hydrated wood samples were also converted from the time
domain to the frequency domain using the Fourier transform (for additional analysis of frequency
spectra). The result of this transformation presented a spectral line of proton resonance signal.
The signal of total time domain in hydrated wood sample is the sum of the signals of the water protons
and the protons of macromolecules of wood. Figure 1shows FID data from
1
H NMR experiments on
wood samples with dierent moisture content (one FID is for dry sample, and other FID is for the sample
with big amount of added water). For hydrated wood sample (Figure 1), FID is characterized by
the total amplitude of the protons of wood and the water protons, i.e., A =A
wat
+A
wood
. Gaussian-sinc
function is normally fitted to the proton signal of the wood part of FID, whereas the water part can be
described by exponential or Voigt functions [7,8,22].
CPMG. When measuring T
2
in the wood with the CPMG pulse sequence, a time interval of
0.025 ms between pulses is commonly used. Normally, 8000 echoes are applied to cover the full range
for CPMG decay in wet wood. For dry wood samples, about 1000–2000 echoes (or fewer) were often
enough to perform correct CPMG experiment. For very wet spruce samples, the pulse gap interval
in the CPMG experiment was increased up to 0.5 ms. Echo decays were inverted using the Inverse
Laplace Transform algorithm. Alternatively, to get NMR relaxation times, the analysis of raw data
sets were also conducted by performing the non-linear least squares fit (a sum of several exponential
functions) to the data (using in-house MatLab®codes).
Figure 2gives an example of CPMG measurement on wet wood sample and following treatment
of findings to result in T
2
distribution. This is a case with wettability higher FSP, when all T
2
peaks are
observed in the range from 2–3 ms to 80 ms testifying that a huge amount of water is still in mobile
state, and no observable bound water with spin-spin relaxation times less than 1 ms. The Inverse
Laplace Transform is used for extraction of f(T
2
) from the CPMG echo train [
8
,
21
], i.e., the data can be
modelled applying ILT in one direction. The probability density f(T
2
) is calculated from the spin-echo
signal Mtpresented elsewhere [7,20,22].
PFG. The PFG NMR was applied in one and two dimensions [
7
,
8
,
21
26
]. In one-dimension PFG
experiments, in order to cover a long range of diusion times, spin-echo pulse sequence (SE) with
two RF pulses (90
and 180
) and stimulated-echo (STE) pulse sequence with three 90
RF pulses
were applied. After application of a pair of gradient pulses [
8
,
22
,
23
,
27
], the amplitudes of echo were
Colloids Interfaces 2019,3, 54 4 of 14
monitored. The gradient pulses had a duration 2 ms and maximum amplitude Gmax =1.2 T/m.
Typically, 1024 averages with a repetition time of 1 s were recorded per echo spectrum.
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 4 of 14
Figure 1. FID signals of protons in two wood samples: dry (blue line) and wet (black line) with
moisture > FSP. T = 298K, and the frequency is 400 MHz. The fast relaxing component of the FID
characterized wood protons and could be fitted by the Gaussian-sinc function [21,25]. The shape of
FID was sensitive to water content in the wood pieces. FID-based method provided the possibility
to quantitatively estimate the waterwood interactions on the base of proton populations of the
components with different T2 relaxation times.
PFG. The PFG NMR was applied in one and two dimensions [7,8,2126]. In one-dimension PFG
experiments, in order to cover a long range of diffusion times, spin-echo pulse sequence (SE) with
two RF pulses (90° and 180°) and stimulated-echo (STE) pulse sequence with three 90° RF pulses
were applied. After application of a pair of gradient pulses [8,22,23,27], the amplitudes of echo were
monitored. The gradient pulses had a duration 2 ms and maximum amplitude Gmax = 1.2 T/m.
Typically, 1024 averages with a repetition time of 1 s were recorded per echo spectrum.
In order to carry out experiments with the correct orientation of wood samples (longitudinal,
transverse or radial) to direction of X- (Y-) gradients, it was necessary to detect the orientations of the
gradient with respect to the sample in the coil. These correct directions of the gradients in relation to
faces of the sample should be found before placement of NMR tube with wood sample into the coil
for measurement. The wood samples were prepared in the manner of a cube with flat face. 1D
Imaging (profile) experiments on two narrow glass capillaries with doped water were applied for
finding the gradient orientation (Figure 3). At rotation of the sample with 2 vertical capillary tubes
around Z-direction (magnetic field B0), the profile spectra were dependent on rotation angle and
changed from 2 peaks to 1 peak. The targeted case in this rotation imaging experiment was a
coalescence of two peaks into one peak that occurs at the orientation of the X- (Y-) gradient in the
plane of 2 capillaries (Figure 3).
0 5 10 15 20 25 30 35 40 45 50
0
2
4
6
8
10
12
x 105
time (ms)
Intensity/ (a.u.)
CPMG decay/Re-data/number of echos =200; pe63;wood N;dw8
Figure 1.
FID signals of protons in two wood samples: dry (blue line) and wet (black line) with moisture
>FSP. T=298K, and the frequency is 400 MHz. The fast relaxing component of the FID characterized
wood protons and could be fitted by the Gaussian-sinc function [
21
,
25
]. The shape of FID was sensitive
to water content in the wood pieces. FID-based method provided the possibility to quantitatively
estimate the water–wood interactions on the base of proton populations of the components with
dierent T2relaxation times.
In order to carry out experiments with the correct orientation of wood samples (longitudinal,
transverse or radial) to direction of X- (Y-) gradients, it was necessary to detect the orientations of
the gradient with respect to the sample in the coil. These correct directions of the gradients in relation
to faces of the sample should be found before placement of NMR tube with wood sample into the coil
for measurement. The wood samples were prepared in the manner of a cube with flat face. 1D Imaging
(profile) experiments on two narrow glass capillaries with doped water were applied for finding
the gradient orientation (Figure 3). At rotation of the sample with 2 vertical capillary tubes around
Z-direction (magnetic field B
0
), the profile spectra were dependent on rotation angle and changed from
2 peaks to 1 peak. The targeted case in this rotation imaging experiment was a coalescence of two peaks
into one peak that occurs at the orientation of the X- (Y-) gradient in the plane of 2 capillaries (Figure 3).
The PFG NMR methods (SE and STE) measure self-diusion when the nuclear spins are labelled
by their frequencies of Larmor precession in a varying magnetic field after applying a field gradient
(with strength Gand duration
δ
). NMR signal of echo is registered during increasing the gradient
value. Echo intensity is smaller than that in absence of gradients. The measured signal is presented
according to Equation (1) [2224]:
I(G)
I(0)=exp[(γGδ)2(δ
3)D](1)
Here,
γ
is the (
1
H) nuclear gyromagnetic ratio.
is the time interval between front edges of
gradient pulses. I(0) is the echo intensity in absence of gradients. For free diusion, this equation
can be applied to calculate the diusion coecient from the dependence of expression 1 on G
2
.
I(0) ~ exp(
τ1
/T
2
) for SE pulse sequence (
τ1
is the gap between 90
and 180
RF pulses), and I(0)
~ exp(
2
τ1
/T
2
)
.
exp(
τ2
/T
1
) for STE pulse sequence. In the case of STE,
τ1
is the time gap between
first 90
and second 90
RF pulses whereas
τ2
is the time interval between second 90
and third 90
RF pulses). The stimulated echo is less sensitive to T
2
relaxation. NMR STE diusion experiment is
sensitive to T1relaxation.
Colloids Interfaces 2019,3, 54 5 of 14
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 4 of 14
Figure 1. FID signals of protons in two wood samples: dry (blue line) and wet (black line) with
moisture > FSP. T = 298K, and the frequency is 400 MHz. The fast relaxing component of the FID
characterized wood protons and could be fitted by the Gaussian-sinc function [21,25]. The shape of
FID was sensitive to water content in the wood pieces. FID-based method provided the possibility
to quantitatively estimate the waterwood interactions on the base of proton populations of the
components with different T2 relaxation times.
PFG. The PFG NMR was applied in one and two dimensions [7,8,2126]. In one-dimension PFG
experiments, in order to cover a long range of diffusion times, spin-echo pulse sequence (SE) with
two RF pulses (90° and 180°) and stimulated-echo (STE) pulse sequence with three 90° RF pulses
were applied. After application of a pair of gradient pulses [8,22,23,27], the amplitudes of echo were
monitored. The gradient pulses had a duration 2 ms and maximum amplitude Gmax = 1.2 T/m.
Typically, 1024 averages with a repetition time of 1 s were recorded per echo spectrum.
In order to carry out experiments with the correct orientation of wood samples (longitudinal,
transverse or radial) to direction of X- (Y-) gradients, it was necessary to detect the orientations of the
gradient with respect to the sample in the coil. These correct directions of the gradients in relation to
faces of the sample should be found before placement of NMR tube with wood sample into the coil
for measurement. The wood samples were prepared in the manner of a cube with flat face. 1D
Imaging (profile) experiments on two narrow glass capillaries with doped water were applied for
finding the gradient orientation (Figure 3). At rotation of the sample with 2 vertical capillary tubes
around Z-direction (magnetic field B0), the profile spectra were dependent on rotation angle and
changed from 2 peaks to 1 peak. The targeted case in this rotation imaging experiment was a
coalescence of two peaks into one peak that occurs at the orientation of the X- (Y-) gradient in the
plane of 2 capillaries (Figure 3).
0 5 10 15 20 25 30 35 40 45 50
0
2
4
6
8
10
12
x 105
time (ms)
Intensity/ (a.u.)
CPMG decay/Re-data/number of echos =200; pe63;wood N;dw8
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 5 of 14
Figure 2. The plots presenting the data from CPMG (T2) experiment on wood sample with moisture
higher than FSP (T=298K, proton resonance frequency is 400 MHz). Top: the experimental CPMG
decay measured after moisturizing the piece of wood. The intensities in the top plot were normalized
per 103. Bottom: T2 distribution obtained from CPMG echo train with the aid of inverse Laplace
transformation.
The PFG NMR methods (SE and STE) measure self-diffusion when the nuclear spins are
labelled by their frequencies of Larmor precession in a varying magnetic field after applying a field
gradient (with strength G and duration
). NMR signal of echo is registered during increasing the
gradient value. Echo intensity is smaller than that in absence of gradients. The measured signal is
presented according to Equation (1) [2224]:
 
])
3
(exp[
)0( )( 2DG
IGI
Here,
is the (1H) nuclear gyromagnetic ratio. Δ is the time interval between front edges of
gradient pulses. I(0) is the echo intensity in absence of gradients. For free diffusion, this equation can
be applied to calculate the diffusion coefficient from the dependence of expression 1 on G2. I(0) ~
exp(-2
1/T2) for SE pulse sequence (
1 is the gap between 90° and 180° RF pulses), and I(0) ~
exp(-2
1/T2).exp(-
2/T1) for STE pulse sequence. In the case of STE,
1 is the time gap between first 90°
and second 90° RF pulses whereas
2 is the time interval between second 90° and third 90° RF
pulses). The stimulated echo is less sensitive to T2 relaxation. NMR STE diffusion experiment is
sensitive to T1 relaxation.
Figure 2.
The plots presenting the data from CPMG (T
2
) experiment on wood sample with moisture
higher than FSP (T=298K, proton resonance frequency is 400 MHz). Top: the experimental CPMG decay
measured after moisturizing the piece of wood. The intensities in the top plot were normalized per 10
3
.
Bottom:T
2
distribution obtained from CPMG echo train with the aid of inverse Laplace transformation.
Cross relaxation. The studies of wood samples showed that there is a proton exchange
between the water and exchangeable protons of wood fibers. That is why spin-lattice relaxation
shows two components, and the changes in the intensity of relaxing components are associated
with this exchange [
7
,
19
,
20
]. Many macromolecular systems with low moisture content showed
this cross-relaxation eect (CR) [
8
,
19
]. We implemented cross-relaxation experiments on wood
pieces with dierent moisture content with the aid of Goldman–Shen (GS) pulse sequence
(90
x
τo
–90
x
t–90
x
) [
19
,
20
,
28
]. The sequence applies first two pulses to separate longitudinal
magnetizations of macromolecular protons and water protons. After first
π
/2 RF pulse, i.e., when
τ0
is varied, the wood signal disappears very fast whereas the water magnetization practically
does not change. An application of the second RF pulse (90
x
) rotates the magnetization of water
proton back to the steady magnetic field. In order to analyze the CR eect properly, we assume
that wood with water can be described as two-phase system which consists from protons of water
phase and protons of macromolecules (wood). According to accepted wisdom in the literature view
on hydrated macromolecular systems, the equations describing the longitudinal relaxation of both
phases in the presence of cross relaxation includes exchange terms in the Bloch equations for the Z
magnetization of both phases [
7
,
19
]. Then, m
w
(t) and m
m
(t) can be defined as time-dependent Z
magnetizations of the water protons and the protons of macromolecules (wood phase) with equilibrium
values m
we
and m
me
.R
1w
and R
1m
can be considered as intrinsic longitudinal relaxation rates, and k
w
Colloids Interfaces 2019,3, 54 6 of 14
and k
m
are the exchange rate constants. p
w
=k
m
/(k
w
+k
m
) and p
m
=k
w
/(k
w
+k
m
) are the fractions of
the protons belonging to these two phases. The equations for the longitudinal relaxation of protons
in these two phases in presence of cross relaxation are presented and discussed anywhere [
8
,
19
21
].
Reference [
19
] presents the complete expression for stimulated-echo attenuation in the presence of
cross relaxation. The authors showed that when the combined parameter C=k
w
+R
1w
k
m
R
1m
and the product k
w
k
m
are found, the diusion coecient can be determined by analysis of
the echo-attenuation curve with the cross-relaxation factor [7,19].
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 6 of 14
050 100
0
100
200
300
400
500
050 100
0
50
100
150
200
250
050 100
0
50
100
150
200
250
050 100
0
50
100
150
200
250
050 100
0
50
100
150
200
250
050 100
0
100
200
300
400
500
Figure 3. Dependence of 1D imaging profile for 2 capillary tubes with doped (paramagnetic Mn2+)
water on the position of the sample in the bore of magnet. The direction of X-(Y-) gradient was fixed.
The data for 6 positions of the sample after the rotation around B0 are presented. When X-(Y-)
gradient was orthogonal to the flat of the capillaries, maximal distance between two peaks of equal
intensity has been observed in imaging profile. When the direction of the gradient was in the flat of
two capillaries, the only one peak has been registered. 400 MHz. T=298 K. The intensity (Y-axis) scale
is in arbitrary units. X-axis scale is in points.
Cross relaxation. The studies of wood samples showed that there is a proton exchange between
the water and exchangeable protons of wood fibers. That is why spin-lattice relaxation shows two
components, and the changes in the intensity of relaxing components are associated with this
exchange [7,19,20]. Many macromolecular systems with low moisture content showed this
cross-relaxation effect (CR) [8,19]. We implemented cross-relaxation experiments on wood pieces
with different moisture content with the aid of GoldmanShen (GS) pulse sequence
(90°xτo‒90°-xt‒90°x) [19,20,28]. The sequence applies first two pulses to separate longitudinal
magnetizations of macromolecular protons and water protons. After first π/2 RF pulse, i.e., when
0
is varied, the wood signal disappears very fast whereas the water magnetization practically does
not change. An application of the second RF pulse (90°-x) rotates the magnetization of water proton
back to the steady magnetic field. In order to analyze the CR effect properly, we assume that wood
with water can be described as two-phase system which consists from protons of water phase and
protons of macromolecules (wood). According to accepted wisdom in the literature view on
hydrated macromolecular systems, the equations describing the longitudinal relaxation of both
phases in the presence of cross relaxation includes exchange terms in the Bloch equations for the Z
magnetization of both phases [7,19]. Then, mw(t) and mm(t) can be defined as time-dependent Z
magnetizations of the water protons and the protons of macromolecules (wood phase) with
equilibrium values mwe and mme. R1w and R1m can be considered as intrinsic longitudinal relaxation
rates, and kw and km are the exchange rate constants. pw=km/(kw+km) and pm=kw/(kw+km) are the
fractions of the protons belonging to these two phases. The equations for the longitudinal relaxation
of protons in these two phases in presence of cross relaxation are presented and discussed anywhere
[8,1921]. Reference [19] presents the complete expression for stimulated-echo attenuation in the
presence of cross relaxation. The authors showed that when the combined parameter
C=kw+R1w-km-R1m and the product kwkm are found, the diffusion coefficient can be determined by
analysis of the echo-attenuation curve with the cross-relaxation factor [7,19].
2D DDCOSY. 2D diffusion-diffusion correlation NMR studies were carried out with combined
two SE pulse sequences and two pairs of collinear gradients according previous description in
Figure 3.
Dependence of 1D imaging profile for 2 capillary tubes with doped (paramagnetic Mn
2+
)
water on the position of the sample in the bore of magnet. The direction of X-(Y-) gradient was fixed.
The data for 6 positions of the sample after the rotation around B
0
are presented. When X-(Y-) gradient
was orthogonal to the flat of the capillaries, maximal distance between two peaks of equal intensity has
been observed in imaging profile. When the direction of the gradient was in the flat of two capillaries,
the only one peak has been registered. 400 MHz. T=298 K. The intensity (Y-axis) scale is in arbitrary
units. X-axis scale is in points.
2D DDCOSY. 2D diusion-diusion correlation NMR studies were carried out with combined
two SE pulse sequences and two pairs of collinear gradients according previous description in
References [
7
,
18
,
24
28
]. 2D ILT with algorithm from References [
29
32
] has been used to invert echo
decays and produce 2D maps. Additionally, the parameters from 2D experiments on wood were used
in simulations based on the theory of DDCOSY studies with collinear gradients [
7
,
20
,
24
,
25
,
29
]. In 2D
studies, the signal is recorded as function of two variables. In common 2D spectroscopy, fast Fourier
transform is used to produce 2D data. In Reference [
31
], the authors presented 2D T
1
T
2
correlation
experiment and described how to use 2D ILT to analyze the data acquired as two-dimensional
array and to get 2D maps with T
1
and T
2
. In [
30
], the authors solved the class of the 2D Fredholm
integrals. These approaches have been developed further in studying diusion-diusion correlations
in 2D experiments on dierent materials [
25
,
29
,
33
]. For the case of echo-attenuation in 2D diusion
experiment, the expressions for signals can be found in References [
24
,
26
,
29
]. In the works on
diusion-diusion correlations in materials with anisotropic properties [
24
,
29
], the scheme with axial
symmetry was assumed in order to apply the equations to the locally anisotropic diusion domains
which could be randomly oriented.
In wood pieces, the tracheid cells can be characterized by molecular frame with diffusion
anisotropy [
7
,
8
,
18
]. The algorithm of the works [
30
,
31
] gives an opportunity to carry out two-dimensional
Colloids Interfaces 2019,3, 54 7 of 14
numerical ILT for the 2D data measured on anisotropic samples. Targeting the echo signal, the algorithm
solves the double integral equation for signal as a function of two variables q
1
=(
γ
G
δ
)
1
and q
2
=(
γ
G
δ
)
2
which can be varied independently. Therefore, based on the DDCOSY theory and published data on
different anisotropic materials, it is reasonable to suggest that diffusion behavior in wood is characterized
by the diffusion tensor with axial symmetry, i.e., by two diffusivities D
1
and D
2
along the local axes in
molecular frame. The echo attenuation in 2D diffusion-diffusion correlation experiment can be described
by Equation (2) [29,34]:
Iq12,q22
I(0)=exp(q12D1)exp(q22D2)(2)
With this model approach, a distribution of the diusion tensor elements in 2D (SE and STE)
experiments has been calculated [
7
,
25
,
33
]. 2D ILT results in D
1
and D
2
as diusion tensor elements [
18
].
When the matrices of echo signals are numerically calculated, then 2D ILT transforms them into
spectral 2D maps. In simulation study, the matrices I(q
12
,q
22
) for various D
1
and D
2
with given ratios
of D
1
/D
2
=1; 5; 10 have been calculated using such experimental parameters as values of gradients,
diusion times and gradient pulse length. Therefore, the parameters from two-dimensional DDCOSY
experiments with two pairs of collinear gradients have been introduced into variables q
1
and q
2
(the wave vectors q
1
and q
2
were oriented in one direction) to produce the matrices of the echo signals.
Next, a signal analysis applied 2D ILT to produce 2D map for diusion tensor elements.
3. Results and Discussion
Figure 4(top) presents intensity of the normalized deviation
m
w
=(M
w
(t)
M
weq
)/M
weq
from
the equilibrium value of longitudinal magnetization of the water phase (M
weq
) in spruce wood
according to considered cross-relaxation model [8,18,20] in series of Equations (3)–(7):
mw=Mw(t)Mweq
Meq
w
=c+eR+t+ceRt(3)
c+= +mw(τ0)kw+R1wR
R+Rmm(τ0)kw
R+R(4)
2R+=kw+R1w+km+R1m+ [(kw+R1wkmR1m)2+4kwkm]1/2(5)
c=mw(τ0)kw+R1wR+
R+R+mm(τ0)kw
R+R(6)
2R=kw+R1w+km+R1m[(kw+R1wkmR1m)2+4kwkm]1/2(7)
From fitting the data to Equations (3)–(7), the values of c
+
,c
,R
+
, and R
are found. According to
the Reference [
19
], the equations presented above may be rewritten as: (R
+
R
)(c
+
c
)=C
m
w
(0)
– 2k
w
m
m
(0) and (c
+
+c
)=
m
w
(0). It is easier to analyse CR equations when
m
m
(0) will be
the value of
1 (at chosen long time interval
τ0
between 1st and 2nd 90
pulses). Then, this expression
consists of a part (term C
m
w
(0)) with linear dependence on
m
w
(0) (Figure 4, bottom) and a term
which approaches to constant value 2kwvery fast [19].
Cross-relaxation eect was depending on the water content in the wood spruce. When wettability
of the wood sample was very low, e.g., 0.03 g H
2
O/g dry matter, there was no any mobile component
in T
2
distribution. All observable water signals characterizing bound water had T
2
about 1 ms
or less. In these conditions, the cross-relaxation rate was estimated as k
w
~39 s
1
. The value of
cross-relaxation rate was decreasing when water content was increasing. For instance, at wettability
corresponding to ~0.55 g H
2
O/g dry matter, the GS experiment resulted in the cross-relaxation rate k
w
~ 15 s
1
. The CR was a reason for bi-exponential behavior of the longitudinal magnetization [
7
,
20
,
34
].
When the spin-lattice relaxation rate of water on the water-macromolecule boundary was less than
the exchange rate of spin energy through the interface, the CR eect was significant [
8
,
28
]. With CR
Colloids Interfaces 2019,3, 54 8 of 14
data obtained, apparent diusion coecient in spruce with dierent water content could be corrected
using CR factor [8,19,21,34].
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 8 of 14
RR k
m
RR RRk
mc w
m
ww
w)()( 0
1
0
(6)
2/12
1111 ]4)[(2mwmmwwmmww kkRkRkRkRkR
(7)
From fitting the data to Equations 37, the values of c+, c-, R+, and R- are found. According to the
Reference [19], the equations presented above may be rewritten as: (R+ R-)(c+ c-) = C Δmw(0)
2kwΔmm(0) and (c+ + c-) = Δmw(0). It is easier to analyse CR equations when Δmm(0) will be the value of
−1 (at chosen long time interval τ0 between 1st and 2nd 90° pulses). Then, this expression consists of
a part (term CΔmw(0)) with linear dependence on Δmw(0) (Figure 4, bottom) and a term which
approaches to constant value 2kw very fast [19].
Figure 4. top: The intensity of water protons as a function of spacing t between the 2nd and 3rd 90
pulses in GS sequence 90°x
090°-xt90°x for the spruce sample with water content of 0.03 g H2O
per g dry matter at
0 = 65 s. Solid line is fitting the data to Equations 3 characterizing CR effect
[7,19,20]. T=298 K, frequency = 400 MHz. bottom: Determination of C and kw using the function (R+ -
R)(c+ - c-) in GS experiment.
Cross-relaxation effect was depending on the water content in the wood spruce. When
wettability of the wood sample was very low, e.g., 0.03 g H2O / g dry matter, there was no any
mobile component in T2 distribution. All observable water signals characterizing bound water had
T2 about 1 ms or less. In these conditions, the cross-relaxation rate was estimated as kw ~39 s-1. The
value of cross-relaxation rate was decreasing when water content was increasing. For instance, at
wettability corresponding to ~0.55 g H2O / g dry matter, the GS experiment resulted in the
cross-relaxation rate kw ~ 15 s-1. The CR was a reason for bi-exponential behavior of the longitudinal
magnetization [7,20,34]. When the spin-lattice relaxation rate of water on the water-macromolecule
boundary was less than the exchange rate of spin energy through the interface, the CR effect was
significant [8,28]. With CR data obtained, apparent diffusion coefficient in spruce with different
water content could be corrected using CR factor [8,19,21,34].
The raw data in 1D PFG NMR experiment have been measured and presented as the echo
signals in the frequency domain. Figure 5 (left) shows how the echo intensities changed with
increasing value of gradient. Further, the intensities of echoes were collected for all gradient steps
and presented as echo attenuation vs G2. Figure 5 (right) shows the intensities of echoes as
Figure 4. top
: The intensity of water protons as a function of spacing tbetween the 2nd and 3rd 90
pulses in GS sequence 90
x
τ0
–90
x
t–90
x
for the spruce sample with water content of 0.03 g H
2
O
per g dry matter at
τ0
=65
µ
s. Solid line is fitting the data to Equations (3) characterizing CR
eect [
7
,
19
,
20
]. T=298 K, frequency =400 MHz.
bottom
: Determination of Cand k
w
using the function
(R+R)(c+c) in GS experiment.
The raw data in 1D PFG NMR experiment have been measured and presented as the echo signals
in the frequency domain. Figure 5(left) shows how the echo intensities changed with increasing value
of gradient. Further, the intensities of echoes were collected for all gradient steps and presented as echo
attenuation vs G
2
. Figure 5(right) shows the intensities of echoes as dependence on G
2
. Fitting linear
part of echo-attenuation experimental curves by Equation (1) results in calculation of apparent diusion
coecients D. With CR factor, the diusion coecients could be presented as a dependence on eective
diusion time (Figure 6).
In the PFG experiments on spruce wood (e.g., in Figure 6), the orientation of the gradient in
longitudinal (along magnetic field B
0
) or tangential (radial) direction to face of wood piece discovered
anisotropy, i.e., dierence in diusion coecients (1.82 times at
=10 ms). When a wettability was
increasing, e.g., exceeded 0.8 g H
2
O/g dry mass of wood sample, a diusional anisotropy decreased,
i.e., became equal to 1.6 (at
=17 ms). At the same measurable conditions, the sample of bulk water
showed the diusion coecient of 2.37
×
10
9
m
2
/s which was not changing with increasing
value
within error of measurements. Therefore, this discovered anisotropic self-diusion of water in spruce
wood (self-diusion coecient D
1
in direction of wood fibers oriented along the static magnetic field
B
0
and D
2
in perpendicular direction) was in line with published data on diusional anisotropy in
fibrous materials, e.g., in collagenous tissues and natural silk [8,3437].
In comparison with isotropic diusion (e.g., in solutions, when all directions of motion are
equivalent), water diusion in spruce wood is with preferred direction along the wood fibers.
Many factors, e.g., permeability of cell membranes, pore size and pore size distribution can aect
an anisotropy [
8
,
34
,
36
]. Therefore, it is not obvious how to quantify a diusion anisotropy in spruce
pieces correctly. The nature of the wood sample and alignment of the tracheid cells are responsible
for the barriers to diusion. In the natural environment of wood cells, there is water transport along
Colloids Interfaces 2019,3, 54 9 of 14
the length of the tracheid cell. Additionally, there are barriers to water movement in transverse
direction. In the wood, the diusion rates are not equal in dierent directions. Therefore, structural
morphology in wood can result in diusion anisotropy.
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 9 of 14
dependence on G2. Fitting linear part of echo-attenuation experimental curves by Equation 1 results
in calculation of apparent diffusion coefficients D. With CR factor, the diffusion coefficients could be
presented as a dependence on effective diffusion time Δ (Figure 6).
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050 100 150 200 250 300
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-0.5
-0.4
-0.3
-0.2
-0.1
0
grad (G/cm)2
Ln(I/Io) for PFG
BDelta (ms)=200
Figure 5. Dependence of echo signals on gradient value in 1D NMR diffusion experiment on spruce
piece with water content of 0.8 g H2O/g dry matter. MATLAB code was developed (Matrix 7 × 5) to
get echo-attenuation value (magnitude with following calculation of integral area) for each gradient
step. Wood sample was oriented along X-direction testing for diffusion in tangential direction. The
diffusion time Δ = 200 ms. Frequency is 400 MHz, T = 298 K. For left Figure: The intensity (Y-axis)
scale is in arbitrary units. X-axis scale is in points.
In the PFG experiments on spruce wood (e.g., in Figure 6), the orientation of the gradient in
longitudinal (along magnetic field B0) or tangential (radial) direction to face of wood piece
discovered anisotropy, i.e., difference in diffusion coefficients (1.82 times at Δ = 10 ms). When a
wettability was increasing, e.g., exceeded 0.8 g H2O /g dry mass of wood sample, a diffusional
anisotropy decreased, i.e., became equal to 1.6 (at Δ = 17 ms). At the same measurable conditions,
the sample of bulk water showed the diffusion coefficient of 2.37. 109 m2/s which was not changing
with increasing Δ value within error of measurements. Therefore, this discovered anisotropic
self-diffusion of water in spruce wood (self-diffusion coefficient D1 in direction of wood fibers
oriented along the static magnetic field B0 and D2 in perpendicular direction) was in line with
published data on diffusional anisotropy in fibrous materials, e.g., in collagenous tissues and
natural silk [8,3437].
Figure 6. A dependence of the apparent diffusion coefficient in spruce wood on effective diffusion
time Δ at orientation of the gradient in the tangential direction. Frequency is 400 MHz. Water content
in the spruce wood is 0.62 g H2O / g dry mass. T=298 K. Δ is presented in logarithmic scale.
Figure 5.
Dependence of echo signals on gradient value in 1D NMR diusion experiment on spruce
piece with water content of 0.8 g H
2
O/g dry matter. MATLAB code was developed (Matrix 7
×
5) to get
echo-attenuation value (magnitude with following calculation of integral area) for each gradient step.
Wood sample was oriented along X-direction testing for diusion in tangential direction. The diusion
time
=200 ms. Frequency is 400 MHz, T=298 K. For left Figure: The intensity (Y-axis) scale is in
arbitrary units. X-axis scale is in points.
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 9 of 14
dependence on G2. Fitting linear part of echo-attenuation experimental curves by Equation 1 results
in calculation of apparent diffusion coefficients D. With CR factor, the diffusion coefficients could be
presented as a dependence on effective diffusion time Δ (Figure 6).
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-0.4
-0.3
-0.2
-0.1
0
grad (G/cm)2
Ln(I/Io) for PFG
BDelta (ms)=200
Figure 5. Dependence of echo signals on gradient value in 1D NMR diffusion experiment on spruce
piece with water content of 0.8 g H2O/g dry matter. MATLAB code was developed (Matrix 7 × 5) to
get echo-attenuation value (magnitude with following calculation of integral area) for each gradient
step. Wood sample was oriented along X-direction testing for diffusion in tangential direction. The
diffusion time Δ = 200 ms. Frequency is 400 MHz, T = 298 K. For left Figure: The intensity (Y-axis)
scale is in arbitrary units. X-axis scale is in points.
In the PFG experiments on spruce wood (e.g., in Figure 6), the orientation of the gradient in
longitudinal (along magnetic field B0) or tangential (radial) direction to face of wood piece
discovered anisotropy, i.e., difference in diffusion coefficients (1.82 times at Δ = 10 ms). When a
wettability was increasing, e.g., exceeded 0.8 g H2O /g dry mass of wood sample, a diffusional
anisotropy decreased, i.e., became equal to 1.6 (at Δ = 17 ms). At the same measurable conditions,
the sample of bulk water showed the diffusion coefficient of 2.37. 109 m2/s which was not changing
with increasing Δ value within error of measurements. Therefore, this discovered anisotropic
self-diffusion of water in spruce wood (self-diffusion coefficient D1 in direction of wood fibers
oriented along the static magnetic field B0 and D2 in perpendicular direction) was in line with
published data on diffusional anisotropy in fibrous materials, e.g., in collagenous tissues and
natural silk [8,3437].
Figure 6. A dependence of the apparent diffusion coefficient in spruce wood on effective diffusion
time Δ at orientation of the gradient in the tangential direction. Frequency is 400 MHz. Water content
in the spruce wood is 0.62 g H2O / g dry mass. T=298 K. Δ is presented in logarithmic scale.
Figure 6.
A dependence of the apparent diusion coecient in spruce wood on eective diusion time
at orientation of the gradient in the tangential direction. Frequency is 400 MHz. Water content in
the spruce wood is 0.62 g H2O/g dry mass. T=298 K. is presented in logarithmic scale.
In the spruce wood, the tracheid cells are mostly vertical narrow ones. The length of the cells is
circa ~2 mm whereas cell diameters are in the range of 20 to 40
µ
m. The walls of the tracheid cells cause
the restrictions for water diusion. Water diusion along the length of the cell is less restricted than
diusion motion of water in tangential (radial) directions. Therefore, the orientation of the gradient to
the wood cells eected on the dependence of echo intensity on gradient values. For direction of applied
gradient along magnetic field B
0
and in perpendicular one, dierent values of Dhave been measured.
In comparative PFG experiments, when the gradient was applied in radial or tangential directions to
faces of wood pieces, there was no discovered systematic variation in Dvalues. Therefore, anisotropic
diusion motion has been found in spruce samples only at comparison of longitudinal (along tracheid
cells) and perpendicular directions.
Colloids Interfaces 2019,3, 54 10 of 14
Diusion coecients were dependent on diusion time (Figure 6): they were decreasing from
5.12
×
10
10
m
2
/s (at
=7 ms) with increasing diusion time to
=1100 ms (D=0.145
×
10
10
m
2
/s).
References [
8
,
28
,
34
40
] showed also that barriers of macromolecular arrangement produce a restriction
phenomenon for water diusion. Reference [
38
] showed also that apparent diusion coecient
of water in eastern white pine was decreasing with increasing
. The authors of Reference [
38
]
considered also that small decrease of the diusion coecient in longitudinal direction with increasing
may indicate that a degree of restriction is small, i.e., this is less than that in tangential direction.
A reduction of the diusion coecient with increased diusion time (longitudinal direction) was
dependent on the kind/type of wood and water content in wood sample [
6
,
9
,
38
]. In References [
8
,
40
],
the findings on the sitca spruce wood with variation of
from 60 ms to maximum =200 ms have been
considered. The experiments for the diusion times >200 ms have not been carried out in that study [
40
].
The apparent diusion coecient ~1.75
×
10
9
m
2
/s (at 60 ms) measured on sitca spruce at water
content of 0.7 g H
2
O/g dry mass (60 MHz) [
40
] was lower than diusion coecient of free bulk water.
From PFG STE findings (400 MHz) on the spruce wood with moisture of 0.84 g H
2
O/g dry matter [
8
],
for longitudinal direction, apparent diusion coecient was about ~2.1
×
10
9
m
2
/s at
=20 ms
(this Dvalue was decreasing with increasing
although not in such an extent, as it was obtained for
tangential direction) showing that water diusion experiences much less restriction than that in radial
or tangential orientations. The tracheid cells in wood can have the length exceeding the width up to
100 times [
6
,
9
,
38
,
40
]. This can explain anisotropic diusion dependence for water in the spruce wood.
Some published works [
6
,
9
] studied the longitudinal wood cell structure using methane and absorbed
water as a probe. They found that the diusion data could be fitted by two structural components with
mean lengths of 2.88 mm and 0.29 mm.
Water diusivity in wood samples can follow to the dependence D~
k1
where kvalue is less than
1 [
28
,
34
,
41
]. Therefore, the water diusion in the spruce wood could be considered as quasi-restricted [
8
].
For clarifying the water diusion in wood, it is possible to consider a material medium with barrier
spacing aand arbitrary permeability p. This approach has been applied in the publications before [
23
,
34,39,4143]. The apparent diusion coecient measured for the small values could be considered
as a free diusion coecient D
0
[
7
,
39
,
42
,
43
]. When diusion time is increasing to big
values,
the diusion coecient approaches asymptotic value D
asym
. The free diusion coecient D
0
,D
asym
,
barrier spacing a, and permeability pare combined by Equation (8) [8,35,42,43]:
Dasym =D0ap
D0+ap (8)
D
asym
,D
0
,ap can be estimated from the experiment using the approach suggested by
Tanner
[7,23,39].
Tanner considered relative apparent diusion coecient D
app
/D
0
vs reduced diusion
time D
0.
t/a
2
. Within the approach, D
app
/D
0
became equal to 1 at zero time. Additionally, the point in
the dependency of D
app
on diusion time where D
app
is equal to its average value is used. This is in
order to obtain diusion time t1/2and to calculate further restriction size a, and permeability p.
The 1D PFG data on anisotropic diusion of water in spruce wood have been confirmed in 2D
PFG studies. 2D spectra are calculated for the local domain. It is considered that the diusion
tensor has axial symmetry in this domain. Two diusivities D
1
and D
2
characterize parallel
and perpendicular movement to the local principal axis in molecular frame. This is in line with
the theory of two-dimensional diusion-diusion correlations [2426,33].
Figure 7shows 2D diusion-diusion correlation maps obtained with 2D ILT on the numerically
calculated 2D array at modelling anisotropic diusion (simulation for D
2
=5D
1
=10
9
m
2
/s: left 2D
spectrum) and for 2D diusion-diusion correlation experiments on spruce wood (right: three 2D
spectra). Two diagonal peaks reflect diusion anisotropy with diusion constants D
1
and D
2
. 2D map
of isotropic diusion with D
1
=D
2
=10
9
m
2
/s showed one round spot on the diagonal. The 2D
simulated spectra for the case of isotropic diusion also showed one spot on the diagonal.
Colloids Interfaces 2019,3, 54 11 of 14
Colloids Interfaces 2018, 2, x FOR PEER REVIEW 11 of 14
apD
apD
Dasym
0
0 (8)
Dasym, D0, ap can be estimated from the experiment using the approach suggested by Tanner
[7,23,39]. Tanner considered relative apparent diffusion coefficient Dapp/D0 vs reduced diffusion time
D0.t/a2. Within the approach, Dapp/D0 became equal to 1 at zero time. Additionally, the point in the
dependency of Dapp on diffusion time where Dapp is equal to its average value is used. This is in order
to obtain diffusion time t1/2 and to calculate further restriction size a, and permeability p.
The 1D PFG data on anisotropic diffusion of water in spruce wood have been confirmed in 2D
PFG studies. 2D spectra are calculated for the local domain. It is considered that the diffusion tensor
has axial symmetry in this domain. Two diffusivities D1 and D2 characterize parallel and
perpendicular movement to the local principal axis in molecular frame. This is in line with the
theory of two-dimensional diffusion-diffusion correlations [24–26,33].
Figure 7 shows 2D diffusion-diffusion correlation maps obtained with 2D ILT on the
numerically calculated 2D array at modelling anisotropic diffusion (simulation for D2 = 5D1 = 10−9
m2/s: left 2D spectrum) and for 2D diffusion-diffusion correlation experiments on spruce wood
(right: three 2D spectra). Two diagonal peaks reflect diffusion anisotropy with diffusion constants
D1 and D2. 2D map of isotropic diffusion with D1 = D2 = 10−9 m2/s showed one round spot on the
diagonal. The 2D simulated spectra for the case of isotropic diffusion also showed one spot on the
diagonal.
Dx (m2/s * 1011)
Dy (m2/s * 1011)
10-2 10- 1 100101102103
10-2
10-1
100
101
102
103
Dx (m2/s * 1010)
Dy (m2/s * 1010)
10-2 10-1 1001 01102103
10-2
10-1
100
101
102
103
Dx (m2/s * 1010)
Dy (m2/s * 1010)
10-2 10-1 10010110 2103
10-2
10-1
100
101
102
103
Dx (m2/s * 1010)
Dy (m2/s * 1010)
10-2 10-1 1001011021 03
10-2
10-1
100
101
102
103
Figure 7. 2D diffusion-diffusion correlation maps obtained in simulated two-dimensional
experiment (top, left) and 2D DDCOSY NMR experiments on three spruce samples (with variable
moisture: 0.60 (top, right); 0.58 (bottom, left); 0.57 g H2O /g dry mass (bottom, right)) with the
collinear pairs of the magnetic field gradient pulses. Simulation (top, left) has been done at D1 =2 ×
10−10 m2/s, D2 = 10−9 m2/s. Diffusion anisotropy is characterized by two stretched spots on the diagonal
whereas in the case of isotropic diffusion one spot on the diagonal is observed.
Figure 7.
2D diusion-diusion correlation maps obtained in simulated two-dimensional experiment
(top, left) and 2D DDCOSY NMR experiments on three spruce samples (with variable moisture: 0.60
(top, right); 0.58 (bottom, left); 0.57 g H
2
O/g dry mass (bottom, right)) with the collinear pairs of
the magnetic field gradient pulses. Simulation (top, left) has been done at D
1
=2
×
10
10
m
2
/s,
D
2
=10
9
m
2
/s. Diusion anisotropy is characterized by two stretched spots on the diagonal whereas
in the case of isotropic diusion one spot on the diagonal is observed.
In previous publications on studying anisotropy in wood [
7
,
18
,
21
], it was shown that if the pairs of
gradient pulses are oriented in perpendicular directions to each other, 2D DDCOSY experiment results
in one peak (spot) on the diagonal and two long spots (wings) outside diagonal. Two diusivities
D
1
and D
2
are parallel and perpendicular to the local principal axis in molecular frame, and they
characterize the diusion tensor with an axial symmetry. Diusion-diusion correlation pulse sequence
with two collinear pairs of gradients is another 2D method studying diusion anisotropy that resulted
in 2D maps with two spots on a diagonal. Moisturizing wood sample resulted in changes of distance
between the diagonal peaks (Figure 7). A very wet sample could be characterized by only one spot on
the diagonal.
Both DDCOSY methods have a target to look for anisotropy and local order in molecular frame
whereas Diffusion-diffusion correlation experiment has a place in laboratory frame. According to these
methods, the echo-attenuation function with D
1
and D
2
tensor elements (in molecular frame) is transferred
into laboratory frame using relevant rotations. All possible orientations of local directors of molecular
coordinate system are used to produce the total summary of echo attenuations. In diffusion-diffusion
correlation experiments, two pairs of gradient pulses can be applied independently in different directions.
4. Conclusions
Water is the most important fluid that exists naturally in wood and reveals anisotropic properties.
Moreover, wettability of wood materials changes these properties. Because of the importance of NMR
Colloids Interfaces 2019,3, 54 12 of 14
parameters in characterization of wood–water interactions, there is need to clarify more details on
eects of wettability/moisturizing wood. This work shows how the methods of NMR relaxation
and NMR diusion (1D and 2D) can be applied correctly in order to investigate wood–water interactions
in the porous structure of spruce wood. The findings and discussion suggest new possibilities in
developing NMR methods for characterization of wettability eects on wood. The results obtained
clarify how NMR parameters (relaxation times and apparent diusion coecients) should be applied
in studying and analysing wood.
Funding: This research received no external funding.
Acknowledgments: The author thanks Peter McDonald and Marc Jones.
Conflicts of Interest: The author declares no conflict of interest.
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©
2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
... MQF NMR has been applied for the study of the tissueengineered cartilage and showed that collagen molecules in such a cartilage have no order in orientation (Kotecha 2013b, c). Twodimensional correlation NMR spectroscopy discovers the distributions of diffusion coefficients in two orthogonal directions in the anisotropic materials (Callaghan and Furó 2004;Callaghan et al. 2007;Callaghan 2011;Rodin 2017;Rodin 2019). The 2D diffusion maps can be used in studying tissues with anisotropic structure and a local anisotropy (on microscopic scale) in the presence of isotropy (Rodin et al. , 2014Rodin 2017Rodin , 2018bCallaghan 2005Callaghan , 2011. ...
... In the two-dimensional PFG SE NMR experiment, spin echo attenuation is a function of independent variables q 1 2 and q 2 2 (the wave vectors q 1 and q 2 characterize two independently applied gradients G 1 and G 2 , respectively). Therefore, the signal of spin echo is presented by Eq. (7) as a product of two exponential functions (Callaghan 2005(Callaghan , 2011Rodin 2019): ...
... A 2D diffusion map, as a representation of 2D DDCOSY NMR data, discovered the two peaks on the diagonal (Rodin and Nikerov 2014). So, these 2D NMR spectra were in line with 2D ILT simulations (Rodin 2017(Rodin , 2019 which showed a correlation of two diffusion constants D 1 and D 2 (characterizing self-diffusion in two perpendicular directions in the molecular frame) and resulted in two spots on the diagonal (Fig. 5). The two registered peaks on the diagonal in the 2D map reflect an anisotropy in water self-diffusion in collagen samples. ...
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Thermal modification is an environmentally friendly process that enhances the lifetime and properties of timber. In this work, the absorption of water in pine wood (Pinus sylvestris) samples, which were modified by the ThermoWood process, was studied by magnetic resonance imaging (MRI) and gravimetric analysis. The modification temperatures were varied between 180 ° C and 240 ° C. The data shows that the modification at 240 ° C and at 230 ° C decreases the water absorption rate significantly and slightly, respectively, while lower temperatures do not have a noticeable effect. MR images reveal that free water absorption in latewood (LW) is faster than in earlywood (EW), but in the saturated sample, the amount of water is greater in EW. Individual resin channels can be resolved in the high-resolution images, especially in LW regions of the modified samples, and their density was estimated to be (2.7 ± 0.6) mm-2. The T 2 relaxation time of water is longer in the modified wood than in the reference samples due to the removal of resin and extractives in the course of the modification process.
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The quantification of moisture transport in heated wood is relevant to several fields, e.g. for lumber drying and processing and for fire safety risk assessment. We present non-destructive and simultaneous measurements of the moisture content and temperature distributions in pine wood during unilateral exposure to a heat source. The moisture content is measured by a nuclear magnetic resonance setup specifically built for the evaluation of moisture transport in porous materials at elevated temperatures. Temperature profiles are obtained by thermocouples placed at different distances from the exposed surface. While the temperature rises, a peak in the moisture content is formed, which travels towards the unexposed surface. The velocity of the moisture content peak depends on the principal direction in which transport occurs, as confirmed by experiments. Numerical simulations of moisture transport are performed which can qualitatively reproduce the behavior observed in experiments. Moreover, several characteristics, such as the timescale and non-linearity of the moisture peak position, are well captured. The influence of several input parameters, such as the permeability and diffusion coefficient, on the moisture peak dynamics is elaborately explored.
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Two nuclear magnetic resonance (NMR) pulsed field gradient diffusion approaches have been applied to the measurement of the magnitude and the distribution of the tangential dimension of cells in a number of wood samples. The results thus obtained were compared with the results from microscopy. The results from these two approaches agree with each other and they also give excellent agreement with the microscopy results. The results of this work demonstrate that NMR diffusion is an accurate and convenient method for the measurement of cell sizes in wood and in similar porous systems.
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The wetting, dimensional stability and sorption properties of a range of modified wood samples obtained either by acetylation or furfurylation were compared with those of unmodified samples of the same wood species via a multicycle Wilhelmy plate method. Wettability measurements were performed with water and octane as the swelling and non-swelling liquids, respectively. It was found that acetylation reduces water uptake mainly by reducing the swelling. In comparison, furfurylation reduces both swelling and the void volume in the sample. To quantify the effect of the modification process of the wood properties, the parameters “liquid up-take reduction” and the “perimeter change reduction” were introduced, which were determined from multicycle Wilhelmy plate measurements. Compared with the acetylated wood, the furfurylated wood with a higher level of weight percent gain exhibited larger property changes on the surface and in terms of swelling and sorption properties.