Quantitative Nuclear Magnetic Resonance Imaging of
Liquids in Swelling Polymers
THOMAS M. HYDE,’ LYNN F. GLADDEN,‘* MALCOLM
R. MACKLEY,’ and PING GAO’
’Department of Chemical Engineering, University of Cambridge, Pernbroke Street, Cambridge, CB2 3RA, United
Kingdom and ’The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
SYNOPSIS
The variation of nuclear magnetic resonance (NMR) relaxation parameters (T,, T2)within
a polymer during swelling, limits the absolute accuracy with which liquid concentration
profiles can be obtained using NMR imaging. In this article a study of the diffusion of
decalin into ultra-high molecular weight polyethylene (UHMWPE) is reported. The study
illustrates the use of a method of analysis whereby quantitative solvent profiles can be
obtained from data influenced by both T , and T2 contrast effects. A T , and Tz map are
obtained a t a point in the uptake of liquid where the greatest range in liquid concentration
is observed. The intensity of signal corresponding to liquid in the polymer is compared to
that of pure liquid in a reference sample, and correlations for T I and T2values versus signal
intensity are used to deconvolve relaxation contrast, to yield the true liquid concentration.
The technique was used to study the effect of degree of crosslinking of UHMWPE on the
swelling kinetics and decalin transport within the polymer. A spin-echo imaging technique
was used with a recycle delay approximately equal to the average spin-lattice relaxation
time of the liquid, and an echo time approximately half the average spin-spin relaxation
time. Under these conditions the relaxation contrast was significant, yet the mass uptake
data derived from the concentration profiles obtained, using the method of analysis described,
agreed well with gravimetric data. 0 1995 John Wiley & Sons, Inc.
Keywords: NMR imaging NMR relaxation ultra-high molecular weight polyethylene
Fickian diffusion
I NTRODUCTlON
The transport of liquids in polymers is of importance
in both the manufacture and end application of
polymers. The former may be concerned with the
motion of monomer, solvent, or plasticizer molecules
in the polymer; the latter is increasingly important
in the field of controlled drug release and in other
applications such as microlithography, membrane
separation, and ultrafiltration.
The nonequilibrium transport of small molecules
in polymers has been studied for many years and
reviewed by a number of
The observed
behavior ranges from classical Fickian diffusion to
more complicated “non-Fickian” or ‘‘anomalous’’
* To whom all correspondence should be addressed.
Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 33,1795-1806 (1995)
0 1995 John Wiley & Sons, Inc.
CCC 0887-624X/95/111795- 12
transport. It is now widely believed that molecular
transport is associated with a concentration gradient-controlled diffusion process, as well as a relaxation process, which is in turn controlled by the
time-dependent response of the polymer to a swelling stress. The transport behavior observed depends
on the relative contributions of these two processes.
Based on these concepts Alfrey et al.5 proposed the
following classes of diffusion behavior:
1. Case I or Fickian diffusion where the rate of
diffusion is much slower than the relaxation
rate;
2. Case I1 diffusion where the rate of diffusion
is much faster than the relaxation rate;
3. non-Fickian (anomalous) diffusion where the
rates of diffusion and relaxation are comparable.
1795
HYDE ET AL
Case I and Case I1 diffusion are the limiting types
of transport, with various regimes of non-Fickian
diffusion in the range between. An often used semiempirical treatment of this is Mt = kt“, where Mt is
the amount of penetrant absorbed a t time t, and k
is a constant. For Case I systems n = i, for Case I1
systems n = 1, and for non-Fickian systems f < n
< 1.
Gravimetric techniques such as direct weighinFl4
are most commonly used to follow liquid transport
in polymers. Although these techniques can measure
absorption and desorption rates, they give only indirect information on structural changes and polymer and liquid interactions. Techniques that yield
more detailed information, and in some cases liquid
concentration profiles, include: electron spin resonance (ESR);I5-l7optical microscopy;*8-20refractive
index measurement^;'^-'^ X-ray mi~roradiography;’~
0-particle emission;25 Rutherford backscattering
spectrometry ( RBS);26-28and Fourier transform infrared-attenuated total reflection (FTIR-ATR)
s p e c t r o s ~ o p yMost
. ~ ~ of these techniques are invasive
or destructive. Further, the diffusion process is often
studied indirectly, requiring the use of doping or
contrasting agents and, in some cases, the polymer
can only be studied in the form of a thin film, such
that it is transparent to a probe “beam.”
Nuclear magnetic resonance (NMR) imaging is
becoming a n increasingly popular probe of diffusion
in polymers, because it avoids the experimental limitations of the aforementioned techniques. Rothwell
et al.30examined the penetration of water into glassreinforced epoxy resin composites. Blackband and
Mansfield31 studied water uptake in nylon 6,6 and
were able to obtain the concentration dependence
of the diffusivity of water in this system. Weisenberger and K ~ e n i g ~ ’ -studied
~’
the absorption and
desorption of solvents such as acetone and methanol
in poly(methy1 methacrylate) (PMMA), and have
observed Case I1 diffusion. Webb and Hal136-3sapplied various NMR imaging techniques to examine
single- and bicomponent diffusion of several organic
solvents in vulcanized rubber. The mobility of polymer chains during the swelling of PMMA and polystyrene (PS)was studied by Tabak and C ~ r t i ; Maf~’
fei et aL4’ examined the penetration of toluene in
poly(viny1 chloride) (PVC), of acetic acid in cellulose, and n-pentane in PS. A further study of diffusion of water in nylon 6,6 was conducted by Fyfe
et aL41
From the above it is obvious that NMR imaging
is able to follow the transport of liquid molecules in
a variety of polymer systems, where the transport
can obey Fickian, non-Fickian, or Case I1 kinetics.
T h e main advantages of NMR imaging can be summarized as follows:
1. T h e technique is noninvasive and it is possible to conduct experiments in situ, depending on the system under study.
2. Several chemical-selective techniques exist
such that specific species in a system can be
selectively imaged.
3. The liquid distribution in any region of a system can be spatially resolved; the technique
is not limited by sample geometry.
Although several NMR imaging techniques were
applied in the above studies, the listed advantages
are universal. At the same time, however, there are
inherent limitations associated with most of these
techniques. In particular, the spin-spin (T2)and
spin-lattice ( T I )relaxation processes that characterize the return of the spin system to equilibrium
following perturbation by a radio frequency (RF)
pulse, can cause attenuation of the NMR signal. The
T I and T2 characteristics of a liquid are influenced
by the surrounding environment, and hence the signal intensity corresponding to a given liquid-containing voxel will depend on the TI and T2characteristics of the liquid within the voxel. It follows
that the NMR relaxation properties of a liquid in a
solid can be used as a physicochemical probe of the
liquid-solid environment. This phenomenon has
been exploited t o determine pore structure in brinesoaked oil field sandstones4’ and to obtain the poresize distributions of porous material^.^^-^^ “Contrast” in images due to NMR relaxation is not desirable, however, if a quantitative image of the liquid
distribution in a solid is to be obtained. T o avoid
the attenuation of signal intensity by NMR relaxation contrast, Weisenberger and K ~ e n i specified
g~~
three requirements for the accurate use of NMR imaging of liquids in polymers when using spin-echo
imaging techniques:
1. The echo time of the experiment must be less
than 10% of the shortest T2of the system.
2. The recycle time of the experiment must be
a t least five times longer than the longest Tl
of the system.
3. The experiment time must be less than the
time of the inverse of the front velocity.
Imaging techniques such as the fast low-angle shot
(FLASH) imaging technique47 have been used in
past s t ~ d i e s ~ in
~ .an
~~
attempt
, ~ ’ to avoid constraints
1 and 2; this work is concerned primarily with spin-
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1796
echo imaging.48 Reasons for this are that gradientreversal imaging techniques (such a s FLASH) are
subject to magnetic susceptibility effects, and the
dephasing effects of magnetic field inhomogeneity
are not reversed a s they are in spin-echo imaging.
T h e images are therefore subject to Tg relaxation,
the effects of which are difficult to quantify. A further restriction with FLASH is that it cannot be
used on very small samples, where the spin-density
is low. The relationship between image pixel intensity, I , and relaxation parameters for spin-echo imaging is given by Callaghan47as:
I(r)=
11 - 2 exp(-(TR - TE/2)/Tl)
exp(- TR/Tl)]exp(-TE/T,)
dr)
sin 0
1 + cos 0 exp(-TRIT,)
+
where: T1and T2refer to the NMR relaxation properties of the liquid in the image voxel (as described
below); TR and TE are the recycle delay and echotime, respectively; and 0 is the angle of the first R F
pulse in the imaging sequence. It is clearly seen that
if the conditions specified by Weisenberger and Koenig (and stated above) are satisfied, I ( r ) z p ( r ) .
However, it is not always possible to satisfy these
three requirements. Condition 1 is to some extent a
hardware restriction, as the echo time is limited by
delays that must be allowed for such as the rise time
of gradient pulses and the length of the selective 90”
R F pulse. Unfortunately T2 constants of liquids in
polymers, particularly those of water, often approach
the value of TE, which makes the resulting spinecho images nonquantitative. T h e effect of Tl contrast can always be negated by applying condition
2. However, in practice, when the longest Tl is of
the order of 2-3 s, this approach can be prohibitive
with respect to spectrometer time. Condition 3 is
usually satisfied a t room temperature.
The purpose of this work has been t o examine
the feasibility of using NMR imaging quantitatively
when: the Tls of the liquid in the polymer are long;
the liquid T2sapproach the experimental echo time;
and the sample is small. In this study it is important
t o note that the TI and T, of the solvent will change
during penetration into the polymer, as a result of
the increasing concentration of solvent a s the polymer network swells. Thus a rigorous quantitative
study of solvent uptake would require acquisition of
Tl and T2 maps for the solvent within the polymer
a t each time point in the study, thereby making the
experiment prohibitively long. In this work a n alternative method for quantitative analysis of the
1797
solvent concentration during the uptake process is
presented. A correlation has been observed between
the relaxation times and the pixel intensity in the
images recorded. Having identified this correlation,
i t follows that the intensity of any given pixel taken
from a relaxation-contrasted image can be directly
correlated with the Tl and T2of the solvent molecules associated with that pixel. T h e analysis presented in the following section indicates how these
data can be used t o estimate, quantitatively, the solvent concentration within that image voxel. The
system chosen to demonstrate the application of this
approach was the diffusion of decalin (dehydronaphthalene) into crosslinked ultra-high molecular
weight polyethylene (UHMWPE) a t 130°C. For this
system the diffusion regime is known t o be that of
generalized Fickian d i f f ~ s i o n , ~which
’
in the onedimensional (1-D) case can be described by Fick’s
second law with the addition of a concentrationdependent diffusivity term:50
and for which the absorption curves are initially linear against t1/2over the majority of the uptake process. T h e effect of degree of crosslinking on decalin
transport within UHMWPE has also been investigated.
METHOD FOR DECONVOLVING
RELAXAT I 0N CONTRAST
T o obtain quantitative images of a penetrant-polymer system exhibiting the features described above,
a technique has been developed where spin-echo
imaging is applied in combination with a method
that explicitly corrects for the effects of T1 and T2
relaxation. T h e polymer (containing the penetrating
liquid) is imaged along with a reference sample of
free liquid. Figure 1( a ) contains a spin-echo image
of a sample of decalin-loaded UHMWPE and a reference sample of decalin ( t h e bright circle). T h e
images shown have been rotated, and the ends of
the samples excluded, using image analysis software,
for ease of comparison. T h e image in Figure 1( a ) is
a map of the decalin distribution only, because no
signal is detected from the polymer. Although it can
be said qualitatively that the brighter the intensity
of a pixel in the image the more liquid there is in
the voxel, the image is subject t o relaxation contrast
t h a t must be deconvolved if the image data are t o
be used quantitatively. Accordingly, the concentra-
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N M R OF LIQUIDS IN SWELLING POLYMERS
HYDE ET AL.
Figure 1. (a) Spin-echo image and (b) T,map of decalin in a sample of UHMWPE
crosslinked with 2.02 w t ?4 lupersol. Data were acquired after 15-min solvent uptake. Higher
intensities (white) indicate (a) greater solvent concentrations and (b) longer relaxation
times. The range of intensities in (b) correspond to relaxation times in the range of 6.625.0 ms. The ends of the samples have been excluded in the images shown. The image in
(a) was acquired with TE = 7.4 ms and TR = 1 s.
tion ( C ) of the liquid in a given voxel in the polymer
is determined using:
(3)
where Co is the concentration of the free liquid in
the reference sample, p(r)pis the spin density of
the liquid in the polymer, and j5( r ) r ,is the average
spin density of liquid in the reference sample. Equation (1)is used to determine p( r)p,and j5( r ) r ,and
a n RF pulse angle of 0 = 90" is used. With the assumption that TE < TR, and the substitution of 0
and the expressions for p( r ) p and P ( r ) r , into eq.
( 3 ) , the following is obtained:
1 - exp(-TR/Tlr)
1 - exp(-TR/TlP)
where Ip and 1,are the voxel intensity of the signal
from the liquid in the polymer and the average signal
intensity from the liquid in the reference sample
respectively. plrand TZrare the relaxation constants
for the pure, bulk, reference liquid, that can be determined either by a standard nonresolved NMR
technique, or by averaging the values of the reference
pixels on a T, or T z map, respectively. T l pand Tzp
are the spatially resolved relaxation constants for
the liquid in the polymer. Equation (4)therefore
enables the conversion of pixel intensity to a quan-
titative measurement of solvent concentration in
any given voxel, provided that Tlpand TZpare known
for that pixel. T h e method used to determine the
required values of T I Pand TZpis now described.
Relaxation Time/ Pixel Intensity Correlation
The procedure for determining the relaxation time /
pixel intensity correlation is outlined here using the
Tz/intensity correlation as a n example. An analogous procedure using a TI map produces the TI/
intensity correlation. The T2map for the sample in
Figure 1( a ) is shown in Figure 1( b ) . The T2 map
values for the reference sample are higher than those
corresponding to the decalin within the polymer, indicating that the free liquid has a longer T2 relaxation time. This is as would be expected because the
polymer-liquid interaction enhances spin-spin energy transfer, thereby reducing T2for the decalin in
the polymer.
Using Figure 1(a,b) the T2relaxation time/pixel
intensity correlations can be obtained for any pixel
within the image. In practice, each point in the correlation, shown in Figure 2, was obtained by averaging the intensity, or T 2values, of each image over
20 columns within each row of data. It is noted that
the pixel intensity is approximately constant along
each row of data in the image; this averaging process
therefore reduced the influence of noise in the data
on the relaxation time / intensity correlations presented here. In this approach relaxation maps are
only obtained a t one time point in the uptake process, but a t such a time when there is the widest
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1798
0.9
,
0.1
118
0.2
0.4
0.3
0.5
11
0.6
lP/C
1799
Fig. 3 ( a )1, by the molar density of the free decalin
in the reference sample, Co (6.43 mol/L) .
The transport kinetics of a liquid in a polymer
are often followed by plotting the swelling ratio (the
mass of penetrant over the mass of polymer, W,/
W,) versus time. It is possible to determine the
swelling ratio from the relaxation-corrected NMR
concentration profiles because the volume fraction
of the liquid in the polymer is directly proportional
to the spin density of the liquid within each image
pixel. For the case where no polymer is present, the
maximum liquid spin density ( p (
is obtained,
Figure 2. TIPand Ta versus uncorrected pixel intensity
(normalized to the intensity of the reference sample) for
decalin in UHMWPE crosslinked with 2.02 wt % lupersol.
0.6 -
range of liquid concentrations within the polymer.
It is also noted that the pixel intensity value used
in Figure 2 is expressed as the ratio I p / I r ,therby
normalizing the sample pixel intensity to that of the
reference sample and allowing comparison between
images acquired at different times. The same procedure using a T , map, produces the T I versus I,/
1,correlation also shown in Figure 2. Thus having
obtained these two correlations for a given
UHMWPE sample, any pixel intensity taken from
an image of the same decalin/UHMWPE system
(of the same degree of crosslinking) can be converted
to an estimate of absolute decalin concentration
within the voxel using eq. (4).The technique also
allows for changes in imaging parameters as different
values of TE and TR need only be entered in eq.
(4).This analysis requires the assumption that for
a given degree of polymer crosslinking the NMR
relaxation properties of the liquid in the polymer
depend only on solvent concentration.
Figure 3 ( a ) shows the effect of the individual T I
and T 2corrections, described by the two bracketed
terms in eq. (4),on an intensity profile taken from
the image shown in Figure 1( a ) . Figure 3 ( b ) shows
the sample orientation with respect to the profiles
given in Figure 3 (a). It is apparent from Figure 3 ( a )
that the two relaxation corrections act in opposite
directions, and it is possible that for certain values
of TE and TR, the fully corrected profile may indeed
be very similar to the profile obtained without such
corrections. However, any change in the relative
values of T I and T 2 during the experiment would
clearly lead to errors in interpretation of the data.
The decalin concentration profile for the sample
shown in Figure 1( a ) is obtained by multiplying the
values of I,/ fr for the intensity profile, corrected
for both T , and T 2relaxation contrast [as given in
0.5 -
0.4
-
l i
.
s'. 0.3
-
\
0.2
:
t
O.'
0'
'
-I
"
-0.5
'
I
0
.
'
0.5
"
I
'
Distance (mm)
Figure 3. (a) The effect of T Iand T2relaxation contrast
on the intensity profile. The following profiles are shown:
uncorrected (-);
T I corrected (---); T2 corrected
( - -); and both TI and T2corrected ( - * - -). (b)
The geometry of the as-prepared UHMWPE samples.
Image profiles are taken in the y-direction and are averaged
over 20 image pixels in the x-direction. Distances in (a)
are measured from t h e y = 0 line drawn through the center
of the sample.
-
+
--
-
-
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NMR OF LIQUIDS IN SWELLING POLYMERS
HYDE ET AL.
corresponding to the concentration of the bulk liquid
( Co). The volume fraction of liquid in the polymer
can therefore be written as
where V, is the volume of liquid, VTis the total volume of the liquid and polymer, and is defined as
c
e =xl-JorXC d x
I t follows that the volume fraction of the polymer
is given by
and the swelling ratio is simply obtained by the ratio
of expressions for V , and V, with a mass density
correction:
where ps and pp are not to be confused with spin
density, and are the mass densities of the liquid and
polymer, respectively. Hence, W,/ W, can be calculated from a n NMR image by integrating the corrected concentration profile to obtain (?
. and substituting this value into eq. ( 8 ) .
The technique outlined for determining concentration profiles and swelling data could also be used
with 1-D imaging, which would reduce the imaging
time significantly. However, the advantage of 2-D
imaging over 1-D imaging (and gravimetric) techniques is that data from damaged or heterogeneous
regions of a sample can be excluded.
EXPERIMENTAL
T h e U H M W P E was crosslinked using lupersol
(2,5 dimethyl-2,5 d i ( t-butylperoxy) hexyne 3 ) )
and samples were manufactured a t eight degrees of
crosslinking. T h e samples were 25 mm in diameter
with a thickness of 1.8 mm ( l o ) . T h e maximum degree of crosslinking was achieved with a lupersol
level of 2 wt 5% above which the equilibrium swelling
ratio did not change. The samples were impregnated
with decalin a t 130°C for varying lengths of time
ranging from 30 s to 1h. The high temperature and
speed of diffusion prohibited in situ experiments.
Therefore, after a specified impregnation time the
polymer was removed from the decalin and quenched
to room temperature, thereby completely halting the
diffusion process. T h e center of each sample was
excised to give a 6 X 6 mm2 specimen approximately
2-5 mm thick, and was then imaged using a Bruker
MSL 200 NMR spectrometer equipped with a microimaging probehead tuned to 200.13 MHz for the
proton resonance. A spin-echo imaging pulse sequence was used. A T , and T 2map were obtained
(using a preconditioning pulse sequence before the
imaging pulse sequence47)for a sample of each degree of crosslinking, typically after 15-min impregnation a t which time the maximum range in liquid
distribution was observed. All the images shown here
were obtained with four scans and contain 128 X 128
pixels. Gradients in the read (G,) and phase-encode
(G,,) directions were set a t 46.7 G/cm giving a n inplane resolution (pixel width) of 76.6 pm; the image
slice thickness was 0.9 mm. An echo time ( T E ) of
7.4 ms and a recycle delay ( T R )of 1s were employed.
The implications of the penetrant concentration
and structure-dependent NMR relaxation behavior
for practical and quantitative imaging are important,
and the effect of T1and T2contrast on intensity
profiles has already been illustrated in Figure 3. The
T I and T 2of pure decalin were 1.53 s and 28.6 ms,
respectively; for decalin in the polymer T , and T 2
ranged from 0.6 to 1.4 s and 12 to 20 ms, respectively.
Considering these values, and those of T E and TR
used, it is obvious that significant relaxation contrast
is present in images acquired under these conditions.
RESULTS AND DISCUSSION
Figure 4 contains a selection of images of samples
a t extremes of degree of crosslinking and at various
impregnation times; these images, like those shown
in Figure 1( a ) , have not been corrected for NMR
relaxation contrast. The identical intensities of the
reference in each set of images allows qualitative
observations to be made. It is obvious from the samples that have undergone swelling for 60 min that
the degree of swelling is significantly reduced by increasing the degree of crosslinking. The resulting
decrease in solvent loading is also clearly seen. The
images in Figure 4 illustrate the ability of NMR imaging to provide direct qualitative information of
liquid distribution and sample structure.
Figure 5 shows maps of the T 1constants in a
lightly and a heavily crosslinked sample after 15 min.
The fits of voxel intensities toward the center of the
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1800
4 min; (b) 8 min; ( c ) 15 min; and (d) 60 min. “Lightly crosslinked” = 0.12 wt % lupersol.
“Heavily crosslinked” = 2.02 wt % lupersol.
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NMR spin-echo images of decalin in UHMWPE after immersion times of (a)
Figure 4.
Decalin in heavily
crosslinked UHMWPE
Decalin in lightly
crosslinked UHMWPE
1801
NMR OF LIQUIDS IN SWELLING POLYMERS
HYDE ET AL.
Figure 5. TImaps of decalin in (a) lightly and (b) heavily crosslinked UHMWPE. Data
were acquired after 15-min solvent uptake. The range of' intensities in (a) and (b) correspond
to Tlrelaxation times in the ranges 0.55-1.40 s and 0.46-1.15 s, respectively. White corresponds to long relaxation times.
samples, where low signal intensity is evident in the
images, to the saturation-recovery T1 relaxation
equation4' were good. Th e fact that the T 1of the
liquid reduces as the center of the sample is approached, indicates that the liquid molecules are interacting with the polymer to a greater degree. The
same trend was observed in the T 2 maps for the
same samples.
Figures 6 and 7 show plots of T,and T 2 versus
decalin concentration values as a function of degree
of crosslinking. Th e relaxation-corrected concentration data were obtained using the method described in the previous section. I t is apparent that
increasing the degree of crosslinking significantly
and consistently reduces the T1of the solvent within
1.4
the polymer matrix. The range in spin-lattice relaxation behavior as a function of decalin concentration
is significant and is indicative of a short range liquidpolymer interaction; this interaction becomes
greater as the free volume in the polymer becomes
smaller. The fact that T1 reduces overall as the degree of crosslinking increases indicates that the network becomes more rigid and the molecular mobility
of decalin is reduced. The variation in spin-spin relaxation behavior is also strongly dependent on solvent concentration and, as opposed to the spin-lattice behavior that exhibits approximate linearity,
follows a slight exponential trend. I t is also noted
that the T 2 behavior is less affected by the degree
of crosslinking, suggesting that there is a long range
i
1.2
20 18
-
h
- 1
v1
v
16
G
G
0.8
0.6
0.4
2
3
4
5
Concentration (mom)
Figure 6. Decalin Tlversus concentration for a range
of degrees of UHMWPE crosslinking. Data are shown for
the following lupersol contents: (A) 0 wt %; (0)
0.25 wt %;
( 0 )0.82 wt%; and (0)2.02 wt %. The lines drawn through
the data represent fits of simple polynomial equations to
illustrate trends.
14
-
12
-
."0
1
2
3
4
5
6
Concentration (mom)
Figure 7. Decalin T2versus concentration for a range
of degrees of UHMWPE crosslinking. Data are shown for
the following lupersol contents: (A) 0 wt %; (0)0.54 wt
%; and (0)
2.02 wt %. The dashed line represents the data
for the uncrosslinked UHMWPE; the solid line represents
the general trend for crosslinked UHMWPE.
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1802
1803
a recycle delay of 2 s. Considering the T I and T ,
parameters determined above, the profiles would be
subject to severe T , contrast, and this might explain
why the profiles determine by Webb and Hall are
much sharper toward the center of the sample where
the T 2constants are shortest.
The data shown in Figure 8 were also compared
with gravimetric mass uptake data. Equation (8)
was used where the average decalin concentration,
was found by numerical integration of the concentration profiles; ps and p p were taken to be 0.89 g/
cm3 and 0.95 g/cm3, respectively. Figure 9 contains
the mass uptake data for 2.02 wt % lupersol samples
with W,/W,, plotted against t1/'/Zo, where lo is the
original thickness of the sample. The mass uptake
calculated from NMR data, both corrected and not
corrected for T I and T 2 relaxation, is also given.
The uncorrected NMR data do not agree well with
measured mass uptake data, particularly at short
impregnation times. The error in the NMR data is
difficult to assess but considering the deconvolution
process, and the signal-to-noise ratio, the error is
estimated a t between 10 and 20%. The error in the
gravimetric measurement a t room temperature relative to the actual uptake a t 130°C is also estimated
a t 10-20% .49 When comparing the gravimetric and
NMR-derived mass uptake data a t room temperature, the error in the gravimetric measurements is
taken as that due to the microbalance used ( < 1%) .
The NMR data corrected for relaxation behavior
are shown in Figure 9 with an error of 5~15%and
these agree very well with gravimetric mass uptake
data.
Figure 1 0 ( a ) contains a plot of the gravimetric
mass uptake for a range of degrees of crosslinking.
Here the mass uptake is plotted using the more
c,
?I!,
'
-;
'
-015
'
0
'
0;s
Distance (mm)
'
1'
'
'
I .5
I
6,
Distance (mm)
Figure 8. (a) Decalin concentration profiles for
UHMWPE crosslinked with 0.12 wt % lupersol after decalin uptake for: (-) 45 min; (---) 20 min; ( . ) 10 min;
(- - -) 6 min; ( .-) 4 min; and ( .- .- .-) 1 min.
(b) Decalin concentration profiles for UHMWPE crosslinked with 1.02 wt % lupersol after decalin uptake for:
(-) 45 min; (---) 30 min; ( * * . ) 20 min; (- - -) 10 min;
(.-.
* -) 6 min; and ( * - * - * -) 4 min.
- -1-
._.
I
liquid-polymer interaction that is concentration
dependent, but is, to a large degree, independent of
the network structure. Weisenberger and K ~ e n i g ~ ~
1.o
have observed varying trends in the T , and T 2behavior of acetone and methanol in PMMA and re0.8 lated the behavior to short- and long-range liquid3" .0.6
polymer interactions.
3" .
Figure 8 shows the time evolution of relaxation0.4 corrected concentration profiles a t two degrees of
0.2 crosslinking; these data provide a quantitative meaAA
surement of the swelling and diffusion process,
0.01
0
I
2
3
showing the reduction in swelling and solvent load*l12
/lo
(min"2/mm)
ing as the degree of crosslinking is increased. Interestingly, the profiles shown in Figure 8 are much
Figure 9. A comparison between (0)gravimetric mass
broader than the 1-D images Webb and Hall3' obuptake data and NMR data, recorded for UHMWPE
tained by volume imaging of decalin in UHMWPE.
crosslinked with 2.02 wt % lupersol, (A) before and (0)
after correction for NMR relaxation contrast.
In their study an echo time of 14.2 ms was used with
I
*ipHX
f
P
I
"
"
'
1
.
"
10990518, 1995, 11, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/pola.1995.080331106 by University Of California - Berkeley, Wiley Online Library on [31/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
NMR OF LIQUIDS IN SWELLING POLYMERS
HYDE ET AL.
(a)
1.0,
I
i
/-I
I
T
0.8
0.00
0.2
I
2
3
4
data sets are plotted with a n error of +15%. I t is
apparent that over the full range of crosslinking
studied here, acquisition of NMR data yields the
same conclusions and quantitative results on the
solvent uptake kinetics as is obtained from gravimetric measurements, within experimental error.
An advantage of NMR imaging studies over
gravimetric techniques is that the motion of the
penetrant front can be followed. For a system exhibiting generalized Fickian diffusion the penetrant
front moves as a function of t ' / 2 .Figure 11 shows
a plot of front position versus t 1 l 2for uncrosslinked
polymer. Determination of the front position in the
crosslinked polymer was subject to error as the front
was not as sharp as was observed for the uncrosslinked polymer, suggesting the diffusion coefficient
for decalin in uncrosslinked UHMWPE is more
concentration dependent. Based on free-volume
theory the diffusion coefficient of decalin in the uncrosslinked polymer would be expected t o vary more
widely because of the significantly higher swelling
ratio of the polymer. The front position, d , is defined
as the distance the front has moved relative t o the
original position of the sample surface, and is calculated by measuring r , the distance from the center
of the sample to the front [as indicated in Fig. 3 ( b ) 1,
and subtracting this value from the original half
thickness of the sample, Ro. The relationship between d and t '/* is linear as expected.
CONCLUSIONS
Figure 10. (a) Mass uptake plots from gravimetric uptake data for a range of degrees of crosslinking. Data are
shown for the following lupersol contents: (A) 0 wt %; ( 0 )
0.12 wt %; (0)0.82 wt %; (A)1.25 wt %; and (0)
2.02 wt %.
(b) NMR-derived mass uptake data for samples containing
(A) 0 wt % a n d (0)
2.02 wt % lupersol. T h e gravimetric
data (solid symbols) are shown for comparison.
common convention as M t / M e q :the mass of solvent
in the polymer a t time t , over the mass of solvent
a t equilibrium. The values of M t / M e ,were calculated
as (W,/W,),/( Ws/Wp)eq.As the sorption kinetics
occurred a t 13OoC,the error in the gravimetric data
is expressed as t 1 5 % to reflect the solvent loss during quenching to room temperature. For all degrees
of crosslinking the uptake kinetics are linear with
t ' / 2 / 1 0 ,within experimental error, and hence the diffusion is Fickian in nature as expected. Figure 10( b )
compares NMR generated uptake data with gravimetric data a t the extremes of crosslinking. Both
The diffusion of decalin into UHMWPE was studied
because this system displays characteristics that
would normally prohibit the use of NMR imaging
as a quantitative probe of solvent transport. These
I .o
0.8
-
0.6
-
0.2
-
-u
0.01
0.0
"
0.5
.
'
1.0
"
1.5
"
2.0
'
'
2.5
.
'
3.0
'
,
5
Figure 11. Penetrant front position versus time for
uncrosslinked UHMWPE.
10990518, 1995, 11, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/pola.1995.080331106 by University Of California - Berkeley, Wiley Online Library on [31/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1804
characteristics are, namely: short T 2 relaxation
constants relative to echo time; long T1 constants
relative to recycle delay; and small volumes of spins
preventing the use of fast imaging techniques. The
degree of crosslinking of the UHMWPE was varied
to generate a range of T , and T 2behavior.
A novel, easy-to-use technique has been used to
spatially resolve and quantify the liquid concentration in the polymer, by considering the ratio of the
signal intensity associated with the liquid in the
polymer to that from a reference sample of pure liquid. This technique was used to study the effect of
crosslinking on the transport of decalin within samples of UHMWPE. The NMR data were used to
generate mass uptake plots and compared with actual mass uptake data. The agreement was poor
when the data were not corrected for T , and T 2contrast, yet agreement was very good when corrected
for relaxation, even though T , was approximately
equal to TR and T 2was generally only twice as large
as T E . The degree of crosslinking was found to significantly affect the dynamic and equilibrium swelling of UHMWPE by decalin.
It has been shown in this study that it is possible
to quantitatively use NMR imaging for following
liquid transport in polymers over a much broader
range of T , and T 2behavior than has been studied
previously.
T. M. Hyde is grateful to the Association of Commonwealth Universities for the award of a Commonwealth
Scholarship. The authors wish to thank Dr. P. Alexander
for providing the image analysis software used in this
study, and the Process Engineering Committee of SERC
for the award of the NMR spectrometer. L. F. Gladden
also wishes to thank ZENECA for the award of a ZENECA
Fellowship.
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Received June 20, 1994
Accepted January 16, 1995
10990518, 1995, 11, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/pola.1995.080331106 by University Of California - Berkeley, Wiley Online Library on [31/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1806