Measurement of the diffusion of liquids into dental restorative resins

by stray-field nuclear magnetic resonance imaging (STRAFI)

Geoffrey Huntera,1, Deirdre M. Laneb, Sheelagh N. Scrimgeoura,c, Peter J. McDonaldb,Charles H. Lloydc,*

aDivision of Physical and Inorganic Chemistry, School of Life Sciences, University of Dundee, Dundee DD1 4HN, Scotland UKbDepartment of Physics, University of Surrey, Guildford GR2 5XH, Surrey, England UK

cDental School, University of Dundee, Dundee DD1 4HN, Scotland UK

Received 6 August 2002; received in revised form 29 August 2002; accepted 8 October 2002

In memory of our good friend and colleague Geoff who died after this research had been completed

Abstract

Objectives. The purpose of this investigation was to determine the diffusion mechanism for water/ethanol mixtures in a diacrylate dental

resin by direct observation of the absorbed liquid profiles using NMR microimaging.

Methods. Frequency-swept stray-field magnetic resonance imaging (STRAFI) was used. Solutions containing 25–65% by volume ethanol

remained in contact with visible light cured 54% TEGDMA: 46% modified TUDMA sheets while measurements were made. The diffusion

profiles were recorded periodically for diffusion times up to 10 h, to a depth of 360 mm and with readings taken at 24 mm intervals.

Results. For all liquid mixtures, diffusion was found to be Fickian with coefficients that increased progressively and smoothly with alcohol

content in the diffusing mixture, from 2.4 £ 10213 to 150 £ 10213 m2 s21. A rule of mixtures approach, as suggested by Kwei and Zupko,

gave a satisfactory description of the ethanol fraction dependence of the diffusivity.

Significance. Frequency-swept STRAFI offers a new and unique opportunity to produce spatially resolved measurements of the liquids in

dental resins to high resolution. In this study, absorption was investigated since an understanding of its mechanism is fundamental to limiting

consequent environmental degradation. STRAFI has great potential for other applications, for example drying, liquid exchange, etc. Since

STRAFI can discriminate 1H in the liquid from those in softened polymer additional applications are envisaged.

2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Keywords: Dentistry; Dental material; Diffusion; Composite; Magnetic resonance; Stray-field; NMR; STRAFI

1. Introduction

It is well established that the resin matrix in composite

restorative materials absorbs liquids from saliva and food,

and that this affects some of the properties that influence

clinical performance [1–5]. As a consequence, the kinetics

of the process are important. Diffusion of a liquid into a

glassy polymer which consequently swells to a rubber has

two (extreme) conditions. Fick’s Law is obeyed if the

diffusion rate in the swollen polymer is slow in relation to

the polymer segmental relaxation rate at the solvent induced

glass/rubber transition. The liquid concentration in the

polymer falls smoothly to zero with increasing depth into

the polymer and the diffusion front advances with the square

root of time, t0:5: Case II diffusion can be expected when the

diffusion rate is fast in relation to the polymer segmental

relaxation rate. The boundary between liquid invaded and

uninvaded polymer is sharp and advances at a constant rate,

t1: Recently published research describes how a second

mode of Case II diffusion can occur when the surface flux is

severely limited. A transition from one diffusion process to

the other is possible with intermediate anomalous Case II

diffusion [6]. Ingress of water into the dental diacrylate

composite resin matrix has been reported as consistent with

Fickian diffusion [4,5,7–11], though there has been a

suggestion that Case II diffusion takes place with food

simulating liquids (e.g. ethanol/water mixtures) [1].

Dental Materials 19 (2003) 632–638

www.elsevier.com/locate/dental

0109-5641/03/$ - see front matter 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/S0109-5641(03)00006-X

1 Deceased.

* Corresponding author. Tel.: þ44-1382-635979; fax: þ44-1382-

225163.

E-mail address: c.h.lloyd@dundee.ac.uk (C.H. Lloyd).

Measurement of the weight gained by thin disc samples over

time provides the evidence that diffusion is Fickian [4,5,

7–9]. By immersing composite in silver nitrate solution

Mair [10,11] measured the position of the diffusion front

directly and found that it advanced in agreement with

Fickian behavior.

Magnetic resonance imaging (MRI) can reveal the

distribution of liquid molecules within a polymeric solid.

Hydrogen nuclei are caused to resonate and those in the

liquid can be differentiated from those in the solid by virtue

of the difference in their nuclear spin relaxation rates. For

conventional spin-echo MRI, spatial resolution is produced

by applying time-dependent magnetic field gradients in 3D

to change the 1H resonance frequency with position in the

specimen. The rate of the free induction decay of the

resonance (created by applying a RF energy pulse) is

determined by structure and molecular mobility, and

reflected in a time parameter T2:1H in liquid molecules

has sufficient mobility to enable magnetization to be

retained and give a long T2; whereas 1H mobility in a

glassy polymer is restricted and results in a short T2: When

liquid molecules are within a polymer their mobility is more

restricted (than is the case in the free liquid) and as a

consequence T2 is much reduced, relative to the free liquid

value. Even so, conventional spin-echo MRI can in principle

discriminate between 1H in the diffusing liquid and that in

the polymer. The use of instruments that have a high static

magnetic field and high magnetic field gradients has

produced high-resolution MRI, which has become known

as magnetic resonance microimaging (MRM). Although this

technique has been used in a significant number of studies

on the diffusion of liquid into polymers, for example see

references [6,12–14], only three dental applications have

been reported [14–16]. The use of MRM in diffusion studies

does have limitations. There are practical limits to the

switching of magnetic field gradients and increasing the

resolution incurs a time penalty since an increased number

of acquisitions are necessary to produce an acceptable signal

to noise ratio.

An alternative approach is used in stray-field magnetic

resonance imaging (STRAFI). Very high magnetic field

gradients exist in the fringe-field (also referred to as the

stray-field) of superconducting magnets that are used in

NMR spectrometers. In its normal operating mode, STRAFI

utilizes this static gradient together with movement of the

specimen in place of applied, switched gradients. In the

fringe-field gradient, a RF pulse excites resonances in a very

narrow slice orthogonal to this gradient. Since the gradient

cannot be switched off, the specimen must be moved

mechanically (stepwise) to obtain resonances from material

in slices away from the first. To produce full 3D STRAFI,

two rotational movements of the specimen are added (in

addition to the stepping movement) as pulses are applied

and echoes recorded. Obviously, these movements consume

time, though at each position the pulse application and echo

recording are rapid. To investigate the diffusion of liquids

into polymers, measurement in one dimension alone is

required, given a specimen with appropriate geometry. Thus,

rotation of the specimen is not necessary. If a one-dimen-

sional profile is to be produced, mechanical movement can be

eliminated altogether by use of the frequency-swept

technique [17,18]. Altering the frequency of the RF pulse

changes the position of the excited slice. It is possible to

frequency sweep and select slices over a distance of a few

hundred micrometers. By dispensing with movement,

STRAFI profiles may be recorded in a time determined

only by the time to apply pulses and acquire the echoes.

While STRAFI has been used to study the diffusion of

liquids in polymers in general [6,12,17–21], it has not yet

been applied to the absorption of liquids by dental polymers.

STRAFI has, however, found application in imaging teeth

[22–25], fluoride profiling [26] and the polymerization of

dental resins [26–28]. The objective of this research was to

investigate the diffusion of water and water/ethanol

mixtures into a polymer that has been used in a commercial

dental composite restorative material by using frequency-

swept STRAFI. This liquid mixture is used to simulate

exposure to food [2] and has been shown to produce a

composition dependent effect in related dental diacrylate

resins [1–3].

2. Materials and methods

The resin, 54% TEGDMA: 46% modified TUDMA with

1.0 wt% camphorquinone initiator and 0.86 wt%

DMAEMA activator, contained no filler. Polymerized

sheets approximately 500 mm thick were produced by

sandwiching this monomer between two (160 mm thick)

glass microscope slides, separated by other slides and light

curing. A 2 min exposure from a Luxorw light curing unit

(ICI Dental Plc, Macclesfield, England) was followed by a

second 2 min cure after the slides had been removed. In both

cases the light guide was passed across the greater surface

area of the specimen to produce a uniform cure. This source

has a nominal light output of 110 mW cm22 between 462

and 478 nm. All cured sheets were inspected and found to be

defect free. The edges were trimmed to produce a sample

with an area 22 mm £ 22 mm.

The structure of the diffusion cell and frequency-sweep

STRAFI surface coil are shown in Fig. 1. The resin

samples were glued to a 160 mm glass slide with a thin film

of epoxy adhesive resin. A PTFE ring (20 mm o.d., 16 mm

i.d. £ 25 mm high) was bonded to this with cyanoacrylate

adhesive to form the solvent well. The glass dome sealed the

cell to prevent evaporation during the experiment. The small

excitation coil, about 3 mm diameter, is below the sample.

The small coil ensures that only a small central area of the

sample is interrogated so limiting edge effects.

The ingress of ethanol/water mixtures with 25, 35, 45, 55

and 65% by volume ethanol was measured at 22 8C for

diffusion times up to 10.24 h. One specimen was used for

G. Hunter et al. / Dental Materials 19 (2003) 632–638 633

each diffusing mixture. The solvent remained in the well, in

contact with the resin throughout this period. Pure water was

included in the planned programme but its use was

suspended when no echo was obtained. Samples were

stored in water at 22 8C for an extended period (nine

months) to investigate whether this was simply due a slower

diffusion rate. At the end of this time no signal was obtained

and the decision taken to discontinue studies with pure

water.

The STRAFI stage was mounted in the fringe-field below

an 89 mm vertical bore 9.4 T superconducting magnet. The

magnet had a 58 Tm21 stray-field gradient and a 5.3 T static

field strength at the plane at which 1H resonance (227 1H

MHz) was excited. When frequency-sweeping, the RF

excitation from the surface coil penetrates the sample to a

depth of about 800 mm. However, in the present experiment,

measurements were restricted to a depth of 360 mm (from

the liquid/polymer interface). A quadrature pulse sequence

was used to excite resonance in a thin slice and produce a

train of echoes:

900x 2 t2 ð900

y 2 t2 echo 2 t2Þn

where 900x and 900

y are two orthogonal pulses, t is the pulse

gap and n the number of echoes in the train. A train of eight

echoes was recorded. The amplitude of the echo decreases

with each successive echo in the train, reflecting the T2

weighting of the decay. The 20 ms pulse excites a slice

nominally 20 mm thick. By sweeping with 60 kHz incre-

ments the specimen was sampled in spatial steps of 24 mm.

A full profile (one average) was acquired in approximately

4.0 s. It is desirable to accumulate a number of averages for

two reasons: (i) A very high gradient is in use and the signal

to noise ratio reduces as the magnetic field gradient

increases [19]; (ii) The echoes that are used are the lower

intensity fifth to eighth. Five hundred and twelve averages

were recorded to produce profiles for the three lower ethanol

concentrations. Solutions containing 55 and 65% ethanol

diffuse more rapidly, which necessitates reducing the time

to complete a profile. Therefore, 64 averages were collected

for the two higher concentrations.

3. Results

Absorbed liquids plasticize glassy polymers. Greater

mobility is given to segments of the polymer chain and as

a consequence the value for 1H spin-spin relaxation time,

T2; increases. Since resonances are produced by all 1H

nuclei, the initial echoes in the train will contain

contributions from the unaffected glassy polymer and the

liquid affected polymer, as well as the liquid. Short T2

signals from rigid (unaffected) polymer are lost rapidly and

do not contribute to any significant degree to the echo signal

after the initial echoes. The increased T2 in softened

polymer causes this contribution to persist for more echoes.

The final echoes are effectively the result of liquid

resonances alone. This has been demonstrated using the

absorption of acetone by PVC [20]. In the present

investigation, profiles of the liquid were produced by

summing the fifth to eighth echoes.

Fig. 2 shows the series of profiles recorded for the

diffusion of a solution containing 35% ethanol.

The resolution is limited by levelling of the sample (i.e.

the positioning the sample surface orthogonal to the

magnetic field gradient), by the finite size of the pixel

(24 mm) and by a broadening effect. In this case the true

resolution was somewhat more than 24 mm. As in other

investigations [12,21,29], the distance to the diffusion front

was measured directly from profiles, such as those in Fig. 2,

Fig. 1. The diffusion cell mounted on the frequency-swept STRAFI stage. The structure is drawn to scale. Note the central 500 mm £ 3 mm sensitive region

from which readings were taken.

G. Hunter et al. / Dental Materials 19 (2003) 632–638634

from the nominal sample surface to the point where the

intensity level fell to half its surface value. A problem was

encountered with the specimen used to study the diffusion of

the 45% ethanol solution 3.5 h into the experiment.

Unreliable results were produced after that time. As a

consequence analyzed data has been restricted to results

recorded before this time for this sample. Fig. 3 shows plots

of front-position vs. time graphs. For all samples they have a

distinct curvature suggestive of a t0:5 ingress behavior and

hence Fickian diffusion.

Accordingly, the data points have been fit to

x ¼ At1=2 þ x0 ð1Þ

where x is the front position and x0 is a small offset to take

account of the difficulty in identifying the exact position of

the liquid—polymer interface and A is a constant. This

interface is poorly defined in the profiles because: (i) of

the finite resolution of the imaging experiment (ii) of the

difficulty of ensuring that the sample plane is exactly

orthogonal to the field gradient and (iii) of the finite time

over which profiles are recorded. At the start, the liquid

rapidly swells the surface. The front position inclusive of the

offset has been plotted a second time as a function of t0:5 in

Fig. 4 along with the resultant least squares fit line. In no

case did the required offset exceed 2 pixels and in most it

was substantially less than 1 pixel. It is thus seen that the

distance to the front as a function of the square root of time

is a good approximation to linear, as is required when a

Fickian mechanism is operating.

Since the 512 averages used to obtain the absorption

profiles for solutions containing 25, 35 and 45% ethanol

were recorded over 34.13 min intervals and the 64

averages for solutions containing 55, 65 ethanol were

recorded over 4.27 min intervals, the profiles are averaged

for these collection periods. Consequently, allowing a

small time offset further improves the fit to the data.

However, such an action carries a risk of over-interpreting

the data. In practice, adding the time offset does not

significantly alter the result and it was not applied during

processing of the data.

Fig. 2. The diffusion profiles for the 35% ethanol/65% water mixture recorded and averaged at 0.57 h intervals up to a total of 5.12 h diffusion time. The

magnetization from the absorbed liquid is recorded by summing the fifth to eighth echoes in the echo train. However, a small residual signal from the polymer

persists and results in the offset on the y-axis.

Fig. 3. The distance to the diffusion front as a function of diffusion time for: (a) 25% V, for 35% B and 45% O ethanol in water mixtures. (b) 55% W and 65% X

ethanol in water mixtures.

G. Hunter et al. / Dental Materials 19 (2003) 632–638 635

Diffusion coefficients have been calculated from the

gradients to the fits in Fig. 4 using expressions given by

Crank [30] for solutions to Fick’s second law of diffusion:

x ¼ 0:95ffiffiffiffiffiffiðD:tÞ

pwhen Cx=C0 ¼ 0:5 ð2Þ

in which C0 is the equilibrium concentration of the solvent

in the polymer here taken as the surface concentration, Cx is

the concentration at distance x;D is the diffusion coefficient

(assumed constant) and t the time. Calculated values of D as

a function of ethanol fraction are listed in Table 1 and are

seen to increase progressively and smoothly with ethanol

content (Fig. 5).

4. Discussion

A STRAFI signal was detected from the absorbed ethanol/

water mixtures in a dental diacrylate resin but not from pure

water. The failure to measure the ingress of pure water, even

after immersion for up to nine months could be the result of

an insufficient mobility of the water on its own in this

polymer, even for STRAFI. While this is not a unique effect

to be associated with dental diacrylate resin, since a similar

result was found for epoxy resin (Aralditew, Vantico AG,

Basel, Switzerland) after immersion in pure water [31], it

should not be taken as a general effect. The results that were

obtained with the liquid mixtures show that their distri-

bution can be measured at a 24 mm separation between

readings by frequency-swept STRAFI. Because there is a

nuclear spin-spin relaxation time, T2; dependence of

magnetization with concentration, the profile shape is not

a liquid concentration map. In other studies [32] calibration

curves have been determined and hence a concentration

map has been inferred, but this is beyond the need of the

present work. Profiles for a diffusing liquid can be recorded

periodically to determine the rate at which the diffusion

front progresses into the polymer.

STRAFI produces direct evidence that diffusion in this

case is Fickian in nature. It supports reports that the

weight gained by composites absorbing water is consistent

with gains predicted when Fickian diffusion is assumed

Fig. 4. The distance to the diffusion front as a function of the square root of the diffusion time for: (a) 25% V, 35% B and 45% O ethanol in water mixtures. (b)

55% W and 65% X ethanol in water mixtures. The position offsets found from best fits to data in Fig. 3 (which never exceed more than two pixels) are included.

Table 1

The diffusion coefficients for ethanol/water mixtures in a dental light cured

diacrylate resin (54% TEGDMA: 46% modified TUDMA) at 22 8C

Ethanol in the diffusing

mixture

Diffusion rate coefficient (m2 s21)

Volume (%) Mole fraction Observed, D Fit by Kwei Zupko analysis

25 0.093 2.4 £ 10213 5.4 £ 10213

35 0.142 9.7 £ 10213 12 £ 10213

45 0.201 27 £ 10213 25 £ 10213

55 0.273 61 £ 10213 47 £ 10213

65 0.364 150 £ 10213 82 £ 10213

Fig. 5. The diffusion coefficient for ethanol/water mixtures in a dental light

cured diacrylate resin (54% TEGDMA: 46% modified TUDMA) at 22 8C as

a function of the ethanol mole fraction. The points are for the measurement

of the diffusion coefficient ðDÞ and the line for the values calculated using

the Kwei Zupko analysis ðkÞ:

G. Hunter et al. / Dental Materials 19 (2003) 632–638636

[4,5,7–10]. Case II diffusion was not evident and we must

conclude that the segmental relaxation rate is rapid even

in the presence of the fastest diffusing mixture. Further-

more, the direct contact between the solvent and the

polymer favors Fickian rather than the surface flux limited

Case II diffusion.

The presence of ethanol in the liquid enables water to

diffuse more easily into the polymer and both species

ingress together, at a rate that increases as the fraction of

‘more effective solvent’ increases. Though in principle, the

results could be due to ethanol diffusion alone, on the

balance of previous evidence [13,14,17,21] it is likely that

the water and the ethanol diffuse together. A detailed

exploration of how each component diffuses and the ratio of

the components behind the front are outside the scope of this

paper. Such information could be obtained by the selective

and systematic use of deuterated liquids, as for example, has

been done in a study of the diffusion acetone/ethanol

mixtures into pmma [17]. Moreover under those conditions,

STRAFI (uniquely) will allow the recording of not only the

liquid profile but also that of the polymer (relative to the

liquid) [17].

The consequence of exposure of the polymer to a liquid

upon clinical performance is of over-riding importance. The

composition of the diffusing solutions used in this study

place them within the range of values for the Solubility

Parameter of food-simulating liquids [1–3]. (The Solubility

Parameter was defined originally by Heldebrand using

thermodynamics to predict the solubility of polymers in

liquids and is the square root of the cohesive energy density

in the polymer or in the liquid [33]. Solubility is expected

when the difference between the values for polymer and

liquid are small). The maximum softening effect occurs

when the solubility parameters of the polymer and solution

are equal [2]. The polymer used in this study is one that has

been used previously in a composite product, Occlusinw

(ICI Dental Plc, Macclesfield, England). Kao [3] found that

the greatest surface softening of this product occurred after

exposure to a solution of 50% ethanol, which was

interpreted as meaning that that the polymer has a Solubility

Parameter approximately 3.7 £ 104 J0.5 m21.5. However,

McKinney and Wu [2] note that diffusion is as important

as the solubility parameter in determining softening. Given

that a solution has a potential to soften by virtue of its

Solubility Parameter, the extent of the damage produced

will depend on its diffusion rate into the polymer. There is a

clear implication that diffusion of the solution into the

polymer is an important rate-controlling factor when

environmentally induced surface softening occurs.

Comparative diffusion coefficient values for the uptake of

ethanol/water mixtures by dental diacrylate resins do not

exist in the published literature. However, values for water

absorption at 37 8C have been reported. Braden’s group

measured ranges of 0.3–3.2 £ 10 213 m2 s21 (absorption,

first cycle) for early composite products [7], 1.6 –

8.2 £ 10 213 m2 s21 for commercial microfilled products

[8] and 9–17 £ 10 213 m2 s21 for experimental microfilled

composites [9]. However, a lower value, 2 £ 10 214 m2 s21,

for a microfine filled composite has been published more

recently by Oshida et al. [4]. Also, Oshida et al. [4] have

given values for modern hybrid filled composites, 1–

4 £ 10 214 m2 s21. Kalachandra and Wilson [5] measured

somewhat higher diffusion coefficients for first generation

hybrid filled products, 1.7–3.2 £ 10 212 m2 s21. A single

diffusion coefficient for water into an unfilled diacrylate resin

(75% Bis-GMA/25% TEGDMA copolymer) has been

published [5], 7 £ 10 213 m2 s21. Though it is lower than

values that this group produced for composite, it must be

considered as representing a value at the upper limit for

measurements reported by research groups active in this

field. Extrapolation of the curve in Fig. 5 to 0% ethanol

results in a diffusion coefficient in the order of 10 214 m2 s21.

This value can be considered to be in good agreement with

the value that might be expected after considering the

literature.

The observed diffusion coefficient values increase on a

smooth curve with respect to ethanol content of the

diffusing liquid (Fig. 5). Kwei and Zupko [34] have

suggested that a rule of mixtures approach can be applied

to liquid mixtures diffusing into cross-linked glassy

polymers. They suggest that

x ¼ ðN1k1 þ N2k2Þt1=2 ð3Þ

where Ni is the mole fraction of one of the ith liquid

components and ki is a constant related to the diffusion

coefficient of the single component liquid in the polymer

according toEq. (2). Values for these pure component

coefficients do not exist, so it is possible only to assess

whether this rule is obeyed in this case, based upon

reasonable assumptions. It is clear from the observed values

that the diffusion coefficient of ethanol into the dental resin

is substantially greater than that of water, that is the value

for water can be considered zero by comparison. Good

agreement with data is found for values, k1 ¼ 7:9 £ 1026

(ethanol) and k2 ¼ 0 (water) ms20.5. The corresponding fit

curve is shown in Fig. 5. These values for k imply that the

value for the diffusion coefficient of ethanol into the

polymer is 6.8 £ 10211 m2 s21.

5. Conclusions

It is possible to produce liquid concentration profiles for

water/ethanol mixtures diffusing into a dental diacrylate

resin by frequency-swept STRAFI. These profiles have a

high spatial resolution, 24 mm, and the depth to which

recordings can be made is adequate. The results show that

the diffusion mechanism is Fickian with a coefficient that

increases with ethanol content (over the range 25–65%) and

that the observed diffusivity obeys a law of mixtures for the

components of the liquid in the measured range. STRAFI

G. Hunter et al. / Dental Materials 19 (2003) 632–638 637

has considerable potential for use in research on the

distribution, movement or change in ‘liquid’ content in

dental resin and ionomeric materials.

Acknowledgements

This research was supported by the UK Engineering and

Physical Science Research Council (Grant GR/K 12397),

for which we are grateful. We would like to thank ICI

Dental Plc (Astra-Zeneca) for their generous donation of

materials and Mr TA Roberts for his generosity and very

helpful discussions.

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