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colloids

and interfaces

Article

One- and Two-Dimensional NMR in Studying

Wood–Water Interaction at Moisturizing Spruce.

Anisotropy of Water Self-Diﬀusion

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 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: 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 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.

Keywords:

PFG NMR; moisturizing wood; restricted diﬀusion; 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 diﬀerent 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 diﬀerent 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 aﬀecting technological regimes of treatment of wood

materials [

2

–

6

]. It is important to know how wetting the wood aﬀects porous microstructure and how

to ﬁnd suitable methods for estimation of pore-water interactions and water transport during changing

moisture of wood [

3

–

9

]. Diﬀerent 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 diﬀerent porous materials with water [

1

,

4

,

11

–

14

]. For instance,

diﬀerent 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 diﬀusion 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 (diﬀusion coeﬃcient 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 aﬀects all those parameters [

14

,

15

]. NMR signal can be

sensitive also to other diﬀerent 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 eﬀective relaxivity,

the authors of Reference [12] consider the T2–Ddata 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 aﬀect the behaviour of T

1

relaxation and should be considered for correct estimation of self-diﬀusion coeﬃcients at various

diﬀusion 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-diﬀusion. 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 eﬀect and diﬀusion-diﬀusion correlations should be considered in analysisof the results

on water anisotropic diﬀusion 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 diﬀusion coeﬃcients measured in one dimensional PFG NMR experiments on

wood with diﬀerent orientation of the samples to the magnetic ﬁeld or diﬀerent direction of gradients

produce valuable information about microstructure giving an estimation of cell sizes in conditions of

restricted diﬀusion and anisotropic properties of water in spruce pieces. In addition to this, for model

of water diﬀusion anisotropy with two diﬀerent diﬀusion coeﬃcients in two orthogonal directions,

it was shown that 2D diﬀusion-diﬀusion correlation experiment with collinear pairs of gradients

and the use of Inverse Laplace Transform result in 2D diﬀusion map with two spots on a diagonal

as a reﬂection of two diﬀerent diﬀusion coeﬃcients. The results of 2D experiments were in line with

theoretical calculations. That gave an opportunity to follow a change in diﬀusional 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 diﬀusivity 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 diﬀerent 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 diﬀusion [22–25].

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 diﬀerent 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 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

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 water–wood 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 [7,8,21–26]. 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

diﬀerent 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-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 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) [22–24]:

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 diﬀusion, this equation

can be applied to calculate the diﬀusion coeﬃcient 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 diﬀusion 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 water–wood 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 [7,8,21–26]. 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) [22–24]:

])

3

(exp[

)0( )( 2DG

IGI

(1)

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 eﬀect (CR) [

8

,

19

]. We implemented cross-relaxation experiments on wood

pieces with diﬀerent 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 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, 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 diﬀusion coeﬃcient 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 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

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

[8,19–21]. 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=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 diﬀusion-diﬀusion 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 diﬀusion-diﬀusion correlations

in 2D experiments on diﬀerent materials [

25

,

29

,

33

]. For the case of echo-attenuation in 2D diﬀusion

experiment, the expressions for signals can be found in References [

24

,

26

,

29

]. In the works on

diﬀusion-diﬀusion 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 diﬀusion 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 diﬀusion tensor elements in 2D (SE and STE)

experiments has been calculated [

7

,

25

,

33

]. 2D ILT results in D

1

and D

2

as diﬀusion 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,

diﬀusion 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 diﬀusion 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+e−R+t+c−e−R−t(3)

c+= +∆mw(τ0)kw+R1w−R−

R+−R−−∆mm(τ0)kw

R+−R−(4)

2R+=kw+R1w+km+R1m+ [(kw+R1w−km−R1m)2+4kwkm]1/2(5)

c−=−∆mw(τ0)kw+R1w−R+

R+−R−+∆mm(τ0)kw

R+−R−(6)

2R−=kw+R1w+km+R1m−[(kw+R1w−km−R1m)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 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 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 eﬀect was signiﬁcant [

8

,

28

]. With CR

Colloids Interfaces 2019,3, 54 8 of 14

data obtained, apparent diﬀusion coeﬃcient in spruce with diﬀerent 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 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 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–

0–90°-x–t–90°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

eﬀect [

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 diﬀusion

coeﬃcients D. With CR factor, the diﬀusion coeﬃcients could be presented as a dependence on eﬀective

diﬀusion 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., diﬀerence in diﬀusion coeﬃcients (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 diﬀusional anisotropy decreased,

i.e., became equal to 1.6 (at

∆

=17 ms). At the same measurable conditions, the sample of bulk water

showed the diﬀusion coeﬃcient of 2.37

×

10

−9

m

2

/s which was not changing with increasing

∆

value

within error of measurements. Therefore, this discovered anisotropic self-diﬀusion of water in spruce

wood (self-diﬀusion coeﬃcient 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 diﬀusional anisotropy in

ﬁbrous materials, e.g., in collagenous tissues and natural silk [8,34–37].

In comparison with isotropic diﬀusion (e.g., in solutions, when all directions of motion are

equivalent), water diﬀusion 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 aﬀect

an anisotropy [

8

,

34

,

36

]. Therefore, it is not obvious how to quantify a diﬀusion anisotropy in spruce

pieces correctly. The nature of the wood sample and alignment of the tracheid cells are responsible

for the barriers to diﬀusion. 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 diﬀusion rates are not equal in diﬀerent directions. Therefore, structural

morphology in wood can result in diﬀusion 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

-0.7

-0.6

-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. 10−9 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 [8,34–37].

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 diﬀusion 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 diﬀusion in tangential direction. The diﬀusion

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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Magnitude spectra

050 100 150 200 250 300

-0.7

-0.6

-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. 10−9 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 [8,34–37].

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 diﬀusion coeﬃcient in spruce wood on eﬀective diﬀusion 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 diﬀusion. Water diﬀusion along the length of the cell is less restricted than

diﬀusion motion of water in tangential (radial) directions. Therefore, the orientation of the gradient to

the wood cells eﬀected on the dependence of echo intensity on gradient values. For direction of applied

gradient along magnetic ﬁeld B

0

and in perpendicular one, diﬀerent 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

diﬀusion 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

Diﬀusion coeﬃcients were dependent on diﬀusion time (Figure 6): they were decreasing from

5.12

×

10

−10

m

2

/s (at

∆

=7 ms) with increasing diﬀusion 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 diﬀusion. Reference [

38

] showed also that apparent diﬀusion coeﬃcient

of water in eastern white pine was decreasing with increasing

∆

. The authors of Reference [

38

]

considered also that small decrease of the diﬀusion coeﬃcient 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 diﬀusion coeﬃcient with increased diﬀusion 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 diﬀusion times >200 ms have not been carried out in that study [

40

].

The apparent diﬀusion coeﬃcient ~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 diﬀusion coeﬃcient 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 diﬀusion coeﬃcient 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 diﬀusion 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 diﬀusion 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 diﬀusion data could be ﬁtted by two structural components with

mean lengths of 2.88 mm and 0.29 mm.

Water diﬀusivity in wood samples can follow to the dependence D~

∆k−1

where kvalue is less than

1 [

28

,

34

,

41

]. Therefore, the water diﬀusion in the spruce wood could be considered as quasi-restricted [

8

].

For clarifying the water diﬀusion 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

,

34,39,41–43]. The apparent diﬀusion coeﬃcient measured for the small ∆values could be considered

as a free diﬀusion coeﬃcient D

0

[

7

,

39

,

42

,

43

]. When diﬀusion time is increasing to big

∆

values,

the diﬀusion coeﬃcient approaches asymptotic value D

asym

. The free diﬀusion coeﬃcient 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 diﬀusion coeﬃcient D

app

/D

0

vs reduced diﬀusion

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 diﬀusion time where D

app

is equal to its average value is used. This is in

order to obtain diﬀusion time t1/2and 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 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 diﬀusion-diﬀusion correlations [24–26,33].

Figure 7shows 2D diﬀusion-diﬀusion correlation maps obtained with 2D ILT on the numerically

calculated 2D array at modelling anisotropic diﬀusion (simulation for D

2

=5D

1

=10

−9

m

2

/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 D

1

and D

2

. 2D map

of isotropic diﬀusion 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 diﬀusion 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 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 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. 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.

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 diﬀusivities

D

1

and D

2

are parallel and perpendicular to the local principal axis in molecular frame, and they

characterize the diﬀusion tensor with an axial symmetry. Diﬀusion-diﬀusion correlation pulse sequence

with two collinear pairs of gradients is another 2D method studying diﬀusion 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

eﬀects of wettability/moisturizing wood. This work shows how the methods of NMR relaxation

and NMR diﬀusion (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 eﬀects on wood. The results obtained

clarify how NMR parameters (relaxation times and apparent diﬀusion coeﬃcients) 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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