1
KJM

MEF4010

Eksperimentelle metoder
Module: Diffusion of fluids within porous materials, NMR part II.
(
Water confined between glass beads)
Eddy W. Hansen
UiO, February 2005
Introduction
Nuclear Magnetic Resonance (NMR) represents a notab
le tool to characterize molecular
dynamics within both solid and liquid samples. In this project we will concentrate on
spin

spin relaxation time (T
2
), spin

lattice relaxation time (T
1
) and diffusion (D)
measurements of water confined within small glass be
ads with the object to characterize
the molecular dynamics of pore

confined water. In general, NMR is capable of pinning
down details regarding motional characteristics of any fluid confined in porous materials
like; catalytic materials (zeolites and mesop
orous materials), sandstone, clay, wood,
plants and biological materials (like the human body). Also, the interaction between the
fluid molecules and the molecules belonging to the solid surface may be probed by this
spectroscopic.
Although a large fract
ion of the nuclei in the periodic table are NMR active, only the
proton nucleus will be amenable for detection in this project. The outlined theory will,
however, be of general validity.
Activities
Lectures (approximately 2

3 hours) and laboratory work (
under supervision)
Teaching material
Distributed at the first lecture
Time schedule
2 weeks (31.03
–
13.04)
Objects
To understand the concept of
relaxation
and
diffusion
from a phenomenological
point of view (Bloch equations)
To be able to perform relax
ation and diffusion measurements
To derive information on diffusivity, surface

to

volume

ratio and surface

fluid
interaction by model fitting (using PC)
To understand the additional complexity involved in analyzing NMR data from
pore

confined fluids, as co
mpared to bulk fluids.
To recognize the applicability of NMR in varies aspects of material science.
2
Introduction
Nuclear Magnetic Resonance (NMR) represents a notable tool in characterizing
molecular dynamics within both solids and liquids. In this pro
ject we will concentrate on
the measurement of relaxation times (T
1
and T
2
) and diffusivity (D) of water confined
between small glass beads aiming at elucidating the molecular dynamics of pore

confined
water. In general, NMR is capable of detailing the mot
ional characteristics of any fluid
confined in porous materials like; catalytic materials (zeolites and mesoporous materials),
sandstone, clay, wood, plants and biological materials (“human body”). Also, the strength
of the molecular interaction between fl
uid molecules and pore surface molecules of the
matrix can be probed, as well.
A second object with the project is to present a brief outline of the NMR theory, via the
Bloch equation concept, and to give the student some practical NMR experience.
Hopeful
ly, the student will realize the potential of the NMR spectroscopic technique in
various areas of material science research.
Although a large fraction of the nuclei in the periodic table are NMR active, the proton
nucleus will be the only probe molecule co
nsidered in this project. The theoretical outline
will, however, be of general validity.
Theory
As pointed out in the introductory section, most of the nuclei in the periodic table possess
a magnetic moment (
). For a proton nucleus, its magnetic moment
will orient either
parallel or anti

parallel to an external magnetic field B
0
. At thermal equilibrium, a surplus
of the proton nuclei within a sample will have their magnetic moments oriented parallel
to the static magnetic field B
0
and hence generate a m
acroscopic magnetic moment M
0
aligned parallel to the static field B
0
, as illustrated in Fig.1A.
Figure 1A
. At equilibrium the macroscopic magnetization M
0
is aligned parallel to the
static magnetic field B
0
.
B)
If applying an rf

pulse B
1
of duration t
p
along the x

axis, the
macroscopic magnetization will rotate by an angle
=
B
1
t
p
around this axis.
Since the detector coil is aligned normal (y

axis) to the external magnetic field B
0
, no
signal will be detected (Figure 1A), since the macroscopic magne
tization has no
component along this axis. In order to detect a signal the macroscopic magnetization
must be tilted away from the z

axis, as illustrated in Figure 1B. Such a re

orientation, or
rotation of the magnetization is performed by irradiating the s
ample with a radio
3
frequency (rf) pulse of duration t
p
and magnitude B
1
. The single pulse sequence and the
resulting time signal are illustrated in Figure 2.
Figure 2
. NMR signal intensity against time (along the y

axis) after application of an rf

puls
e
Fig.3 shows the actual signal response from bulk water after application of an rf

pulse of
duration 2.15
s, which corresponds to a tip

angle of 90
0
,i.e., the macroscopic
magnetization is rotated 90
0

relative to the z

axis

and onto the y

axis.
Figure 3.
Proton NMR signal (Free Induction Decay) of bulk water after applying a
/2
rf

pulse. The red curve represents a single

exponential fit to the data.
Bloch equations
How the macroscopic magnetization (
k
M
j
M
i
M
M
z
y
x
) depends on tim
e can be
described phenomenological by the following vector equation (Bloch equation);
M
D
k
T
M
M
j
T
M
i
T
M
B
x
M
t
M
z
y
x
2
1
0
2
2
(1a)
4
where
B
represents external magnetic fields as well as rf

pulses, D i
s the self

diffusion
coefficient and
z
y
x
/
/
/
2
2
2
2
. These equations reveal two
independent signals to appear in an NMR experiment; a transversal magnetization M
x(y)
decaying with rate constant 1/T
2
and a longitudinal magnetization M
z
(t) which in
creases
asymptotically with time at a rate constant 1/T
1
. T
1
and T
2
define the spin

lattice
relaxation time and the spin

spin relaxation time, respectively.
Free Induction Decay (FID)
If excluding the diffusion term (D = 0) a
/2 rf

pulse (B
1
) along the x

axis will rotate the
magnetization into the y

axis (M
y
), after which it must obey the Bloch equation under the
constraint that
B
= 0 i.e.;
'
2
y y
dM M
dt
T
(1b)
showing that M
y
will decay with a rate constant 1/T
’
2.
. T
he explicit solution to Eq. 1b
reads;
'
0 2
exp/
y
M M t T
(2)
The solid (red) curve in Figure 3 represents a non

linear least squares fit to Eq 2 with
T’
2
= 1.5s. As will become clearer later T’
2
does not necessarily reflect the true spin

spin
relaxation time T
2
.
T
1

measurement
If applying an rf

pulse which inverts the longitudinal magnetization (

pulse), i.e., M
z
=

M
0
, the time behavior of this longitudinal magnetization M
z
(t) can easily be determined
by simple integration of Eq. 1a with r
espect to time;
1
0
/
0
1
0
0
2
1
'
'
T
t
z
t
z
z
M
M
e
M
M
T
dt
M
M
dM
z
(3)
The experimental approach to determine T
1
is thus to apply the following pulse sequence;
Figure 4
. Schematic view of the inversion recovery pulse sequence used to measure T
1
.
5
in which the longitudinal m
agnetization is measured at various times t = t
1
. For a given t
1
,
the pulse sequence is repeated a finite number of times (number of scans) in order to
improve the signal

to

noise ratio (Figure 5). The time delay t
R
between each inversion
sequence should b
e chosen so that t
R
> 5*T
1
.
Figure 5
. A series of inversion recovery pulse sequences, with a time delay t
R
between the
read pulse (
/2

pulse) in one sequence and the inversion pulse in the next sequence.
Figure 6 shows the results of an inversion reco
very experiment (T
1
experiment) applied
to bulk water. The circles represent the longitudinal magnetization at different times, t
1
.
Figure 6
. Inversion recovery data of bulk water recorded at different inversion times t
1
(Figure 5) with t
R
set equal
to 15s. The red curve represents a non linear least squares fit
to Eq 3 with T
1
= (3315
+
50) ms. The blue curve represents the residuals.
Exercise 1; Measure T
1
of water confined in glass beads and discuss the results with
respect to a “two

phases in fa
st exchange”

model (see appendix A). Determine F
1
=
T
1,pore

water
/T
1,bulk

water
. What does this parameter tell you about the fluid

surface
interaction?
T
2

measurement
As can be inferred from the data shown in Figures 3 and 6, T
1
is significantly larger t
han
T’
2
. For distilled water containing no oxygen these relaxation times are expected to be
identical. The reason for T’
2
being smaller than T
1
originates from a combined effect of
magnetic field inhomogeneities within the sample and molecular diffusion. T
he effect of
the former can be circumvented by applying a train of

pulses, as illustrated in Figure 7.
6
Figure 7
. A train of spin

echo pulses illustrating the Carr

Purcell

Meiboom

Gill

pulse
sequence (CPMG).
The expression for the n’th echo intensity
(at time t = n
.
2
) can be calculated and reads
(Appendix B);
3 2
2 2 2 2
0 0 0
2 2
2 2 1
exp exp ( )
3 3
n
n n
M M D G D G t
T T
(4a)
Figure 8A shows the echo envelope of bulk water as derived from a CPMG pulse
sequence (Figure 7) for different times
. If no diffusive motion occurs (D = 0) the
di
fferent echo

envelopes will be identical and independent of
. However, as can be
inferred from Figure 8A the slope (1/T
'
2
) of the echo

envelope increases with increasing
(Figure 8B) and is emphasized by the apparent spin

spin relaxation rate 1/T’
2
being
a
function of
2
(Figure 8B).
Figure 8A)
The echo signal intensity of bulk water as obtained from a CPMG pulse train
with different time distances (2
) between successive

pulses (see Figure 7). The solid
curves represent non

linear least squares fit
s to Eq.4a.
B)
The apparent spin

spin relaxation rate (1/T`
2
) versus
. The true spin

spin relaxation
rate (1/T
2
) was determined from the intercept (
= 0) of a second order polynomial fit in
2
(Eq. 4b), resulting in T
2
= (3156
+
50) ms.
7
This behavior i
s indicative of a diffusive motion in an inhomogeneous magnetic field. If
assuming the magnetic field experienced by the water molecules to be approximated by a
constant gradient field G
0
, i.e., B = B
0
+ G
0
z, it is possible to show that the observed rate
(
1/T’
2
) of the decay of the echo

envelope can be expressed by the following formula (see
appendix 2);
2
0
2
2
2
'
2
3
1
1
DG
T
T
(4b)
where D represents the self

diffusion coefficient of bulk water. The dotted (red) curve in
Figure 8B represents a non

linear least squares fit to a second order polynomial in
2
and
explains semi

quantitatively the experimental data. The true T
2
was derived from the
intercept of this curve with
= 0 (Figure 8B) and reads T
2
= (3156
+
50) ms, showing
that T
1
≈ T
2
, as exp
ected for bulk water.
Exercise 2; Measure T
2
of water confined in glass beads and discuss the results with
respect to T
2
of bulk water. What is F
2
= T
2,pore

water
/T
2,bulk

water
? Is F
1
= F
2
? What
can you say about the homogeneity of the magnetic field w
ithin the pores? Is it
different from the homogeneity observed in bulk water?
Diffusion
In the previous section we noted that diffusion of molecules within an inhomogenios
magnetic field might have a significant effect on the slope of the echo envelope w
hen
applying a CPMG pulse sequence. In this section we will see how to take advantage of
this effect by designing a controlled inhomogeneity along the static magnetic field by
generating gradient pulses for a certain time duration (pulsed gradient fields)
along the z

axis. The simplest pulse sequence to consider in this case is illustrated in Figure 9.
Figure 9
. Illustration of the simplest pulsed field gradient scheme used to measure
diffusivity. g represents the strength of the gradient field of dura
tion
. The timing of both
rf

pulses and gradient pulses are illustrated along the time axis.
8
From basic NMR theory the following relation between magnetization (M), gradient field
strength (g), diffusivity and the time distance
between the
/2

pulse a
nd the

pulse can
be derived, ;
D
)
/
(
g
exp
T
exp
M
M
3
2
2
2
2
2
0
(5)
where
is a constant denoted the gyromagnetic ratio (= 2.675
.
10
8
rads

1
). When
measuring the diffusivity of fluid molecules confined in porous materials the effect of
internal gradients (E
xercise 2), eddy currents (caused by strong gradient pulses),
unwanted echoes (when applying more than a single rf

pulse) and the observation that T
2
is frequently much shorter than T
1
must be considered. This calls for designing a pulse
sequence of a sign
ificant more complexity, denoted the “13

interval pulse sequence”, as
illustrated in Figure 10. It is beyond the scope of this project to detail the derivation of a
formula relating M, D and g. However, the approach is the same as for deriving Eqs 4a
and 5
(Appendix B and C). We simply present the result (Eq 6) without further
discussion;
Figure 10
. Illustration of the “13 interval pulse gradient stimulated echo sequence”
using bipolar gradients with g representing the strength of the gradient field of d
uration
. The timing of both rf

pulses and gradient pulses are illustrated along the time axis.
6
/
2
/
3
)
(
4
exp
exp
2
exp
2
2
2
1
2
0
t
t
t
D
g
T
T
M
M
(6)
Eq 6 shows that D of a confined fluid depends on the diffusion time t. In contrast, for
bulk solutions D is independent of t
D
. Due to t
he spatially restricted diffusion of a pore
confined fluid, an increasing fraction of the fluid molecules will sense this restriction
with increasing diffusion time. Hence, we expect the effective diffusivity D to decrease
with increasing diffusion time. F
or long diffusion times, the diffusivity will approach a
limiting value, corresponding to the long

range diffusivity limit.
9
Using general physical arguments it can be shown that for short diffusion times the
following Eq can be derived (P.P.Mitra, P.N.Sen
, L.M.Schwartz,
Phys. Rev. B
,
1993
, 47,
8565)
t
V
S
t
t
D
R
V
S
t
t
D
V
S
D
t
D
D
6
)
(
1
6
)
(
9
4
1
)
0
(
)
(
0
(7a)
where 1/R
0
represents the curvature of the restricting geometry and
defines the surface
relaxation strength. For shorter diffusion times, Eq 7a simplifies to;
t
t
D
V
S
D
t
D
)
(
9
4
1
)
0
(
)
(
(7b)
Figure 11 (left) shows the signal intensity of bulk water for different diffusion times t
D
as
a function of the gradient field strength squared (g
2
) using the 13

interval pulse sequence
depicted in Figure 10. The dotted curves represen
t non linear least squares fit to Eq 6.
The derived diffusivity as a function of diffusion time is plotted in Figure 11 (right) and
confirms that (for a bulk solution) the diffusivity is independent of diffusion time and
equals (2.58
+
0.08)
.
10

9
m
2
/s.
Figure 11.
Observed echo intensity (normalized) of bulk water as a function of diffusion
time (t
D
) and gradient field strength squared (left) and the corresponding bulk water
diffusivity as a function of diffusion time (right)
.
Exercise 3; Measure the d
iffusivity of water confined in glass beads and plot the
diffusivity against diffusion time. Estimate the diffusivity for short and long
diffusion times. Determine the surface

to

volume ratio (S/V) of the pores from the
slope of the D(t
D
)

curve for short d
iffusion times (Eq 7b).
10
11
Appendix A. Spin

lattice relaxation time of fluid molecules undergoing fast
exchange (on an NMR time scale) between two different regions in space.
Assume fluid molecules to be conf
ined in a pore of volume V and surface area A (Figure
A1). The fluid molecules sensing the pore matrix surface is defined by a relaxation rate
1/T
1s
while the bulk fluid molecules within the pore have a relaxation rate identical to the
bulk fluid, 1/T
1b
.
Figure A1
. Illustration of a random pore geometry with volume V and surface area S.
The thickness of the fluid at the surface is d.
If we assume that the molecules at the surface (dark region) exchange with molecules
within the pore (light area) on a
time scale which is fast compared with the NMR time
scale, we expect that the observed relaxation rate of the fluid molecules to be expressed
by (when assuming the density within the two regions to be the same).
;
s
T
V
s
V
b
T
V
b
V
T
1
1
1
1
1
1
(A1)
Si
nce V
S
≈ d
.
S and V = V
b
+ V
s
we can write Eq A1 in the form;
)
b
T
s
T
(
V
S
d
b
T
T
1
1
1
1
1
1
1
1
(A2)
If T
1s
<< T
1b
(which is often the case when the interaction between the matrix and the
surface molecules is significant), Eq A2 simplifies to;
V
S
b
T
s
T
V
S
d
b
T
T
1
1
1
1
1
1
1
1
(A3)
The parameter
(= d/T
1s
) defines the relaxivity parameter.
12
Appendix B. Spin

echo intensity observed in a constant magnetic field gradient.
It can be shown that for fluids undergoing diffusion in a gradient field (g), the Bloch
equation takes the form;
y
iM
x
M
M
with
M
T
M
zgM
i
t
M
;
2
2
(B1)
After some complex and elaborate calculations (R.F. Karlicek and I.J. Lowe,
J. Magn.
Res
.,
1980
, 37, 75 and R.M. Cotts, M.J.R. Hoch, T. Sun and J.T. Markert,
J. Magn. Res
.,
1989
, 83, 252) the so
lution to Eq B1 can be written;
t
t
dt
dt
t
g
D
T
t
M
M
0
'
0
'
2
)
'
'
)
'
'
(
(
2
2
/
1
exp
0
(B2)
where D is the diffusion coefficient, g(t’’) is the total magnetic field gradient, T
2
is the
spin

spin relaxation time and t
1
represents the duration when the NMR signal is
influenced by tr
ansverse relaxation processes. In practical use,
0
M
and
M
can be
replaced by I and I
0
.
We will apply Eq B1 to the following situation;
Figure B1A) A spin

echo pulse sequence performed in a static magnetic gradient field
G
0
. B) Due to t
he

pulse, the effective gradient magnetic field is inverted.
To apply Eq B1, we set up the following Table.
Table B1. Effective gradients and integrals
1)
13
Time
interval
nr. (i)
Time
interval
Gradient
g(t’’)
'
0
'
'
)
'
'
(
)
'
(
t
dt
t
g
t
i
g
'
0
2
)
'
'
)
'
'
(
(
t
dt
t
g
'
dt
)
'
'
dt
)
'
'
t
(
g
(
'
t
t
0
2
0
1
t
1
=0, t
2
=
G
0
'
t
G
)
'
t
(
g
0
1
2
2
0
'
t
G
3
/
3
2
0
t
G
2
t
2
=
,
t
3
=2

G
0
)
'
t
(
G
)
'
t
(
g
2
0
2
2
2
0
2
)
'
t
(
G
)
3
/
2
4
(
3
2
2
2
0
t
t
t
G
1)
Note, since g(t’’) is constant, it follows that
g
i
(t’) must be a linear function in t’, i.e., g
i
(t’) = g(t’’)t’+
i
.
Also, since we inquire g
i
to be continuous throughout the time region t’ we must have; g
i
(t
i+1
) = g
i+1
(t
i+1
) for
all possible i, which makes it possible to determine each
i
. For simplici
ty and without loss of generality we
can choose
1
= 0
We can now easily calculate the last exponential term in Eq B2 by insertion, i.e.;
3
/
2
)
3
/
2
4
(
3
/
'
)
'
'
)
'
'
(
(
3
2
0
2
3
2
2
0
3
'
2
0
'
0
2
0
G
t
t
t
t
G
dt
dt
t
g
t
t
(B2)
The first echo intensity will thus have the intensity;
)
3
/
2
/
2
exp(
)
0
(
)
2
(
3
2
2
0
2
DG
T
I
I
(B3)
Likewise, the second echo at t = 4
will be;
)
3
/
2
/
2
exp(
)
3
/
2
/
2
exp(
)
0
(
)
4
(
)
3
/
2
/
2
exp(
)
2
(
)
4
(
3
2
2
0
2
3
2
2
0
2
3
2
2
0
2
DG
T
DG
T
I
I
DG
T
I
I
(B4)
We can thus easily find the echo intensity at t = n
.
2
to read;
3
/
/
1
(
exp
)
3
/
2
/
2
exp(
)
3
/
2
/
2
exp(
)
0
(
)
(
)
0
(
)
2
(
2
2
2
0
2
3
2
2
0
2
3
2
2
0
2
DG
T
t
n
DG
T
n
DG
T
I
t
I
I
n
I
n
(B5)
Eq B5 is equivalent to Eq 4a in the main text.
14
Appendix C. Spin

echo in
tensity obtained by applying pulsed gradient fields.
Let us calculate the echo intensity from the pulse sequens shown in Figure C1
Figure C1.
Illustration of the simplest pulsed field gradient pulse sequence used to
measure diffusivity. g represents th
e strength of the gradient field of duration
. The
timing of both rf

pulses and gradient pulses is shown along the time axis.
We use the same approach as discussed in appendix B
Table C1. Effective gradients and integrals
1)
Time
interval
nr. (i)
Time
interval
Gradient
g(t’’)
'
0
'
'
)
'
'
(
)
'
(
t
dt
t
g
t
i
g
'
0
2
)
'
'
)
'
'
(
(
t
dt
t
g
'
'
0
2
)
'
'
)
'
'
(
(
0
dt
t
dt
t
g
t
1
t
1
=0,
t
2
=
0
0
0
2
t
2
=
,
t
3
=
g
2
/
)
(
)
'
(
2
g
gt
t
g
)
4
/
)
(
'
)
(
(
2
2
'
2
t
t
g
)
8
/
)
(
2
/
)
(
3
/
(
2
2
3
2
t
t
t
g
3
t
3
t
4
=3
/
0
g
)
'
t
(
g
3
2
2
g
2
2
g
t
4
t
4
t
5
=3
/

g
2
/
)
3
(
)
'
(
4
g
gt
t
g
)
4
/
)
3
(
'
)
3
(
(
2
2
'
2
t
t
g
)
8
/
)
3
(
2
/
)
3
(
3
/
(
2
2
3
2
t
t
t
g
5
t
5
t
6
=2
0
0
5
)
'
t
(
g
0
0
1)
Note, since g(t’’) is constant, it follows that g
i
(t’) must be a
linear function in t’, i.e., g
i
(t’) = g(t’’)t’+
i
.
Also, since we inquire g
i
to be continuous throughout the time region t’ we must have; g
i
(t
i+1
) = g
i+1
(t
i+1
) for
all possible i, which makes it possible to determine each
i
. For simplicity and without l
oss of generality we
can choose
1
= 0
We can easily calculate the last exponential term in Eq B2 by insertion, i.e.;
15
D
g
t
t
t
t
t
t
t
g
dt
dt
t
g
t
t
)
3
/
(
)
8
/
)
3
(
)
3
(
3
/
(
)
(
)
8
/
)
(
2
/
)
(
3
/
(
'
)
'
'
)
'
'
(
(
2
2
2
/
)
3
(
2
)
3
(
2
2
3
2
/
)
3
(
2
/
)
(
2
2
/
)
(
2
/
)
(
2
2
3
2
'
0
2
0
(C1)
Hence,
D
g
I
I
)
3
/
(
2
2
exp
0
(C2)
Eq C2 is equivalent to Eq 5 in the main text.
16
A Simplified User Manual for the Maran Ultra NMR Instrument
(Non

expert User Manual)
Before initiating new experiments do the following
1.
Insert sample (10 mm height) in correct position
2.
Set RD to approximately 5*T1 (5s)
3.
Set P90 to 2.15 (
s)
and RG =1
4.
Sequence → load → FID.EXE → Open
Optimize Receiver Gain (RG), Offset (O1) and
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1.
Commands → Auto O1 (wait)
2.
Commands → Auto RG (wait)
3.
Commands Auto P90 (wait)
Acquiring an FID
1.
Sequence → load → FID.EXE → Open
2.
GO
Store the FID
1.
File → Save As → (file name)
T
1
Measurement
1.
Acquisition → Sequence → Load → INVREC.EXE → Open
2.
.T1 →

list (file name) → Open → OK→ File name..(for storing T1 data) →
save
3.
A plot will appear on the display at the end of the experiment”, press; OK.
Calc
ulating T
1
1.
Process → T1 → Enter file name (T1 data) → Yes → T1 (with uncertainty) is
calculated and presented on the display.
2.
Alternatively; WinFit → File → Open → Select file → data → Select Fit Option
→Auto Initialize → Fit → Data (Read out values), or
print, i.e.; File → Print
3.
You may also read the T1 data within an excel spread sheet; Retrieve excel →
File → Open → File name (*.INT)
T
2
measurement
1.
Acquisition → Sequence → Load → CPMG.EXE → Open
2.
Check that SI = 1
3.
TAU (Set a

value in microseconds
)
4.
NECH (number of echoes), which must be chosen according to the expected T2
and the TAU (NECH*TAU*2 ≈ 5*T2)
5.
GO
6.
File → Save As → (file name…..)
7.
Store as *.xls file (File → Export → file name)
Calculating T
2
8.
After acquisition, type; T2 (T2 based on a sing
le exponential fit).
9.
File → Save As → M:
\
........... (file name)
17
10.
Alternative; WinFit → File → Open → Select file → data → Select Fit Option →
Auto Initialize → Fit → Data (Read out values), or print, i.e.; File → Print
Initiating diffusion measurem
ents
1.
Acquisition → Sequence → Load → CPMGB13.EXE → Open
2.
Set: SI
=
512, DW
=
0.1, NS
=
8, RD
=
7000000, DEAD1
=
3, DEAD2
=
5, D1
=
100, D2
=
500, D3
=
300, D7
=
100, G1
=
100, G2
=

100, RG
=
20, C1
=
4,
C2
=
2, FW
=
1E6
, VT = 25
3.
Commands → Auto R
G
4.
Commands → Auto O1 (wait)
5.
Commands Auto P90 (wait)
Diffusion measurement
1.
. PFG_DIFF_AT_EWH
2.
Files; G1 gradient list (f) G2 gradient lists (g), Experiment starts)
1)
3.
File → Save As → File name.
4.
Change D7 (the tutor will give details about this) and repea
t the measurement by
starting from point 1 above.
Calculating the self

diffusion coefficient
1.
The tutor has prepared an Excel spreadsheet, which you will use for this purpose.
Details will be given during the course.
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