The Kinetics of Swelling of Hydrogel Polymers …NMR imaging has been extensively applied by us to...

The Kinetics of Swelling of Hydrogel Polymers studied using NMR Imaging

Mohammad Chowdhury, Karina George, David J.T. Hill, Katia Strounina, Andrew K. Whittaker and Zainuddin

Centre for High Performance Polymers, University of Queensland, QLD 4072, Australia.

[email protected] This paper presents a detailed discussion of the use of NMR imaging to study the swelling of hydrogel polymers and the range of methods available for determination of the kinetic parameters. NMR imaging provides the most detailed description of the concentration of water through swelling hydrogel devices. The analysis of the kinetics of diffusion is greatly facilitated by such information.

NMR imaging has been extensively applied by us to the problem of swelling of polymers in contact with a solvent [1-5]. Some care must be exercised to ensure that the profiles obtained using this method reflects accurately the solvent concentration in the swelling polymer. The most robust imaging sequence is based on the spin-echo method; images should be collected with a range of echo times to ensure that differences in T2 relaxation times of water molecules in different environments are taken account of. In addition the experiment should be repeated sufficiently slowly to allow full relaxation of the 1H spins. This last condition necessitates in some cases long experiment times. The spin-lattice relaxation times of the protons of water molecules (which are imaged in these experiments) increase in proportion to the water content, so that water in hydrogels which absorb large concentrations of water tend to have long relaxation times, approaching the relaxation time of pure water. Thus the imaging experiment time for this class of hydrogel may be quite long. This point is significant as the rate of swelling of these hydrogels is often very rapid, and thus it may be difficult to obtain more than one image before equilibrium has been reached. Two approaches to circumvent this problem can be envisaged. Firstly a small concentration of paramagnetic relaxation agent, usually a transition metal ion, can be added to the solvent. This has the effect of reducing the spin-lattice relaxation time of the water protons and hence decreases experiment time, however, care must be taken to ensure that the kinetics of swelling are not perturbed by the presence of the dissolved ions. A second method is to use a rapid imaging method which measures a parameter which can be related to solvent concentration, for example the spin-spin relaxation time. Examples of the use of such methodology will be given in this talk. The materials we have investigated [1-11] span the full range of behaviour reported in the literature. As is well known, when the extent of swelling is relatively small, or the matrix has the ability to relax during the swelling process, the rate of diffusion of the solvent is proportional to the concentration gradient of that solvent in the hydrogel. This is the case in general for materials which absorb less than approximately 30-40% of their initial mass in solvent. In our case we have investigated the swelling of copolymers of HEMA with hydrophilic monomers where the equilibrium water content range from zero to 1 wt. %. All of these systems display Fickian diffusion kinetics. Materials which absorb higher concentrations of water, for example copolymers of HEMA with the hydrophilic monomer MOEP, tend on the other hand, to show anomalous diffusion profiles. During free radical copolymerization with HEMA, MOEP initiates crosslinking, possibly through chain transfer to the monomer. Thus at high MOEP contents the materials are very brittle, and shatter

pcp

pcp

II IL 11

through swelling stresses on exposure to water. At low MOEP contents the water profiles obtained by NMR imaging are strongly non-Fickian (see Figure 1). This behaviour can be described using a number of different models, and we have found that having the diffusion coefficient dependent on the exponential water concentration results in good fits to the profiles. Figure 1. Profile of water concentration in a copolymer containing 3 wt.% MOEP after 24 hours immersion in distilled water. The upper curve was calculated assuming a concentration-dependent diffusion coefficient. There is some evidence of loss of water at the surface of the hydogels. An attempt will be made in this talk to present a unified approach to the analysis of such data based on the finite-difference methods described some years ago by Crank [12] and others. Systems discussed included copolymers of HEMA, blends of PVP and PVA and copolymers of NIPAM. References

1. Ghi, P. Y.; Hill, D. J. T.; Maillet, D.; Whittaker, A. K Polymer (1997), 38(15), 3985-3989. 2. Hill, David J. T.; Lim, McKenzie C. H.; Whittaker, Andrew K. Polym. Int. (1999), 48(10),

1046-1052. 3. Hill, D. J. T.; Moss, N. G.; Pomery, P. J.; Whittaker, A. K.. Polymer (1999), Volume Date

2000, 41(4), 1287-1296. 4. Goodwin, A. A.; Whittaker, A. K.; Jack, K. S.; Hay, J. N.; Forsythe, J. Polymer (2000),

41(19), 7263-7271. 5. Ghi, P.Y.; Hill, D.J.T.; Whittaker, A.K.. Biomacromolecules, (2001), 2, 504-510. 6. Ghi, Phuong Y.; Hill, David J. T.; O'Donnell, James H.; Pomery, Peter J.; Whittaker, Andrew K

Polym. Gels Networks (1996), 4(3), 253-267. 7. Hodge, R. M.; Simon, G. P.; Whittaker, M. R.; Hill, D. J. T.; Whittaker, A. K. J. Polym. Sci.,

Part B: Polym. Phys. (1998), 36(3), 463-472. 8. Ghi, P.Y.; Hill, D.J.T.; Whittaker, A.K. J. Polym. Sci., Part A: Polym. Chem. (1999),

37(19), 3730-3737. 9. Faragalla, M.M.; Hill, D.J.T.; Pomery, P.J.; Whittaker, A.K.. Polym. Bull, (2002), 47, 421-427. 10. Ghi, P.Y.; Hill, D.J.T.; Whittaker, A.K. Biomacromolecules (2002), 3(3), 554-559. 11. Ghi, P.Y.; Hill, D.J.T.; Whittaker, A.K. Biomacromolecules (2002), 3(5), 991-997. 12. Crank, J.. “The Mathematics of Diffusion”, 2nd Ed. Oxford, Clarendon Press, 1975.

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Distance across diameter

Rel

ativ

e co

ncen

trat

ion

Experimental Profile

Calculated Profile

D0 = 4.5 × 10^-8 cm^2/sA = 2

pcp

II IL 11

Diffusion in Polymeric Hydrogels studied using NMR ImagingAndrew K. Whittaker,Centre for Magnetic Resonance,The University of Queensland,Australia.

Acknowledgements

David HillPhuong Yen GhiNaomi MossLucy BakerJames BeckMagdy FaragallaMohammad ChowdhuryKatia StrouninaZainuddin

Members of the Department of Chemistryand the Centre for High Performance Polymers

Outline of this talkThe problem definedMeasurement of swelling of polymersNMR imaging methodologyExperimental examples

PHEMA hydrogelsPVP/PNVP hydrogelsPHEMA-MOEP hydrogelsPNIPAM-DMA hydrogels

Do we have a unified approach?

The problem defined

Say an equilibrium is perturbed by addition of a solvent or a change in concentration

Diffusion of solvent into

surface of object

The end result?

At equilibrium, the degree of swelling will depend on a number of factors:

Chemistry (hydrophilicity)Crosslink densityCracking GeometryAdditives, for e.g. drugsActivity of solution

Kinetics of swelling

What affects rate of initial diffusion?What about subsequent molecules?

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

Other methods

Gravimetry

Diffusion Time (mins)0 4000 8000 12000

M(t)

-M(0

)/M(0

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PHEMA

PHEMA + 10% B12PHEMA + 5% B12

PHEMA + 5% Aspirin

PHEMA + 10% Aspirin

Analysis of gravimetric data

In the case of relatively small weight gains we use classical solutions to Fick’s laws

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0

PHEMA

22 2

1

41 exp( )tn

n n

M D tM a

αα

∞

=∞

= − −∑

Need for imaging data

Many solutions to the previous dataRequire more detailed information:

Optical densityRutherford backscatteringMicrointerferometryFluorescence techniquesESR imagingFT-IR imagingNMR imaging

Analysis of swelling hydrogels

Require numerical methodsFinite difference methods

• Planar sheet divided into layers of thickness h

• Initial concentrations at interfaces = C0, C1, C2..

• The flux of fluid passing through R is given by qR = -Dτ(C1-C0)/h

• Simple extension to plane S

• More stable solutions available, e.g. Crank-Nicholson method

Swelling of a gel matrix

Li and Tanaka, 1990Derive a collective diffusion constant

Solutions provided for all geometriesFor cylinders define an apparent De

De depends on time and position

0 ( 4 / 3) /D K fµ= + K = compressional modulusµ = zero shear modulusf = friction coefficient

Swelling of a glassy matrix

Thomas and Windle have provided most successful description of so-called Case-II diffusionCouples viscoelastic response of glassy polymer to osmotic swelling stress, and Fickian diffusion

/Ptφ η∂ =

∂( / ) ln( )eBP k T φ

φ= Ω 0 exp( )mη η φ= −

Linear viscous response

Osmotic swelling pressure

Viscosity

Magnetic resonance imagingConventional spin-echo sequence

• Frequency-selective 90˚ RF pulse is applied in the presence of a gradient Gslice to excite a slice within the sample

• The MR signal is refocused with a 180˚ pulse

• FID signal is collected after echo time TE in the presence of the gradient Gread to encode frequency as a function of a spatial position in the direction of Gread

• The sequence is repeated and increasing Gphaseis applied perpendicular to slice and read gradients, thus providing spatial resolution in the direction of Gphase

Time resolution in MRI experiment

In polymers with slower equilibration in water, imaging time brings small uncertainty into the water content measured

In polymers with faster equilibration the uncertainty becomes significant, so there is need to reduce imaging time

Imaging time depends on the rate of spin relaxation

0102030405060708090

100

t

Wat

er C

onte

nt, %

∆WC

Timag

0102030405060708090

100

t

Wat

er C

onte

nt, %

∆WC

Timag

Relaxation of nuclear spins

Two kinds of spin relaxation: spin-lattice (T1) and spin-spin (T2)Both depend on the “state of water”

HEMA hydrogels (equilibrium over 48 hours)• Water content 5- 40 %• T1 (spin- lattice relaxation time) ca. 600ms.• Trepetition in imaging pulse sequence is ca. 2 sec.• Total imaging time 25- 30 min

Relaxation of nuclear spins

Two kinds of spin relaxation: spin-lattice (T1) and spin-spin (T2)Both depend on the “state of water”

PVA/PVP hydrogels (equilibrium over 12 hours)• Water content ~ 80- 95 %.• T1 is ca. 1- 2 sec• Trepetition ~ 5- 10 sec• Total imaging time ca. 2 hrs.

NMR contrast – gift or curse?

Differences in T1, T2 are used in medical imaging to create contrastExamples of parameter-weighted images

Goal of medical imaging is

contrast, not quantitative intensities

How to overcome this problem?

Addition of paramagnetic relaxation agentBut these salts can affect diffusion kinetics

Measure a property proportional to proton density

T1 relaxation time – but experiment very longT2 relaxation time – need to cope with diffusion attenuation

Pulse sequences for T2 map

RF

Gphase

Gslice

Gread

90x

180y90-x

180y90x

0* TE* 0 TE

Increasing echo time, TE*

Diffusion profilesT2 depends on water contentCalculated for each point according to:

Known values: before swelling 0.879 mol water, at equilibrium 0.983 mol.

2 2 2

1 w p

w p

n nT T T

= +

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

R, cm

WC

, mol 1

5.7

72.1

100.7

227.5

Time, h

0.920.930.940.950.960.970.980.99

11.01

0 5 10 15 20pixels

Imag

e in

tens

ity

29 h

Profile from TProfile from T22 map after 29 hmap after 29 h

Calculated water content profilesCalculated water content profiles

HEMA copolymersApplication is drug delivery

We aim for a fundamental understanding

Copolymerized to control diffusion kinetics

C

CH3

CH2

C

O

O

CH2

CH2OH

CH2 C

CH3

C O

O

CH2

O

x y

Hydrophilic Hydrophobic

Mass uptake

High HEMA content

f HEMA

0 50 100 150 200 250 300 350

Wat

er U

ptak

e (g

H2O

/ g

dry

poly

mer

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6PHEMAT10H90T20H80T30H70T40H60T50H50

D, EWC depend on composition

Slight overshoot at high HEMA

content

Mass uptake

Low HEMA content

f HEMA

0 50 100 150 200 250 300 350

Wat

er U

ptak

e (g

H2O

/ g

dry

poly

mer

)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

T60H40T70H30T80H20T90H10PTHFMA

Slow second stage at low

HEMA contents

NMR imaging

Contour plot of MRI image, central slice, of PHEMA-co-THFMA (90:10),

2 hrs diffusion time, 37 oC

Profile along this plane

Initial stages

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0

Distance Across Diameter (mm)

-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.18D = 1.5 * 10-7 cm2s-1


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0 Mt / Minf = 0.33

A

B

AB

Water concentration profiles

Prior to fronts meeting

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

-3 -2 -1 0 1 2 3

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.43

Mt / Minf = 0.62


C /

C0

A

B

B

A

Diffusion fronts have met

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.75D = 1.5*10-7 cm2s-1

Mt / Minf = 0.72A

B

AB

Close to overshoot

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.83D = 2.1*10-7 cm2s-1


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.79D = 1.5*10-7 cm2s-1

A

B

BA

Final stages

Time1/2 (min1/2)

0 50 100 150 200 250

Mt /

Min

f

0.0

0.2

0.4

0.6

0.8

1.0


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0Mt / Minf = 0.84


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0 Mt / Minf = 1.00

A

B

A

B

PVP-PVA hydrogels

Application is wound dressingCrosslinked in swollen state in waterInitial WC = 85 %Final equilibrium swelling depends on crosslink density (90-97%)

H2C CH

OHn

H2C CH

N

CO

n

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

T 1/2,sec 1/2

Ct/C

inf

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250

T, h

Ct/C

inf

At intermediate times obeys Fickian diffusion

Kinetics over full range not fully understood

Require higher- order model

Acquire T2 maps as described earlier

Mass uptake

ImagesTime, h

0 2.9 12.6 24.3 43.2 100.7 142.3 225.6

Incr

ease

T2

Numerical modelling of water concentration profiles

Water content profiles were modelled using equations based on Fick’s second law

Diffusion coefficients were determined numerically

20

21 1

( / )1 2 exp( )

t n n

n n n

C J r R D tC J R

β ββ β

∞

=∞

= − −

∑

r – radius of the voxel(point), 0<r<RR – radius of the sampleβn – roots of the Bessel function of order nD – diffusion coefficient

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

-0.8 -0.3 0.2 0.7R, cm

WC

1

5.7

72.1

100.7

227.5

Time, h

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

R, cm

WC

T = 73h

Diffusion coefficients

Diffusion coefficient is time- dependent due to:

Increased resistance to deformation as the polymer approaches equilibrium swelling ratioResult broadly consistent with Li and Tanaka

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

6.00E+05

7.00E+05

8.00E+05

9.00E+05

T, sec

D, m

2 sm-1

Swelling time

Copolymers of HEMA and MOEP

Application is controlled calcificationRandom copolymers grafted onto surfacesMOEP enhances rate of calcification

O

OOH

O

OO P

O

OH

OH

HEMA

MOEP

Effect of crosslinking on EWC

454749515355575961

0 10 20 30 40mol % MOEP

EWC

Increasing EWC due to hydrophilicity

of MOEPDecreasing EWC due to crosslinking

through MOEP

Mass uptake

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 200 400 600 800 1000 1200 1400 1600

Time^0.5 (s^0.5)

Wat

er C

onte

nt

PHEMA

3MOEP

6MOEP

10MOEP

20MOEP

30MOEP

MRI of 3% MOEP copolymer

PHEMA-co-MOEP (97:3), 12 hrs diffusion time, 37 oC

Water concentration profiles

0

0.2

0.4

0.6

0.8

1

-0.4 -0.2 0 0.2 0.4Distance Across Diameter (cm)

Rel

ativ

e C

once

ntra

tion

6%MOEP

20% MOEP

Fickian Profile

Full time course

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion

Experimental ProfileCalculated Profile

D0 = 3×10^-8 cm^2/sA = 3

00

CCA

eDD =

Do = 3.0 x 10-8 cm2/s

A = 3

Time = 1 hr

3% MOEP

Full time course 00

CCA

eDD =

Do = 3.0 x 10-8 cm2/s

A = 3

Time = 3.5 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 3×10^-8 cm^2/s A = 3

3% MOEP

Full time course 00

CCA

eDD =

Do = 3.0 x 10-8 cm2/s

A = 1.6

Time = 7 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 3 × 10^8 cm^2/sA = 1.6

3% MOEP

Full time course 00

CCA

eDD =

Do = 2.5 x 10-8 cm2/s

A = 2

Time = 8.7 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 2.5 × 10^-8 cm^2/sA = 2

3% MOEP

Full time course 00

CCA

eDD =

Do = 2.6 x 10-8 cm2/s

A = 2

Time = 12 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e C

once

ntra

tion


D0 = 2.6 × 10^-8 cm^2/sA = 2

3% MOEP

Full time course 00

CCA

eDD =

Do = 3.0 x 10-8 cm2/s

A = 1.6

Time = 18 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 3 × 10^-8 cm^2/sA = 1.6

3% MOEP

Full time course 00

CCA

eDD =

Do = 4.5 x 10-8 cm2/s

A = 2

Time = 24 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 4.5 × 10^-8 cm^2/sA = 2

3% MOEP

Full time course 00

CCA

eDD =

Do = 4.0 x 10-8 cm2/s

A = 3.8

Time = 24 hr

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 4 × 10^-8 cm^2/sA = 3.8

3% MOEP

Copolymers of DMA and NIPAM

Application is thermally-responsive gelsAbsorb up to 900 % water

CH

C O

N

CH3 CH3

DMA

CH2CH

C O

N

CH

CH3 CH3

NIPAM

CH2

H

Temperature (oC)

20 40 60 80

Turb

idity

0.0

0.5

1.0

1.5

PNIPAM75:25 NIPAM:DMA50:50 NIPAM:DMA25:75 NIPAM:DMAPDMA

Mass uptake

Time (mins)0 1000 2000 3000 4000 5000 6000

Mt/M

equi

l

0.2

0.4

0.6

0.8

1.0

PDMA75:25 DMA:NIPAM50:50 DMA:NIPAM25:75 DMA:NIPAMPNIPAM

MRI of swelling hydrogels

Images of swelling cylinder in water

Image intensity ~

water content

PNIPAM, 30 minsdiffusion

time, 37 oC

Images during swelling

Imaged every nine minutesTecho = 14 msQuantitative images

Profiles of water concentrationPoly(DMA)

Radial Co-ordinate (mm)-4 -2 0 2 4

Imag

e In

t. (a

.u.)

0

50

100

150

200

250

9 minutes18 minutes28 minutes35 minutes44 minutes53 minutes61 minutes70 minutes79 minutes88 minutes

D scales with concentration

D = D0(1 + 8.[H2O])


Imag

e In

t. (a

.u.)

020406080

100120140160180200

Diffusion into PNIPAM


Imag

e In

t. (a

.u.)

0

50

100

150

200

158 Minutes316 minutes474 minutes632 minutes790 minutes948 minutes1106 minutes1264 minutes

Radial co-ordinate (mm)-4 -3 -2 -1 0 1 2 3 4

Am

plitu

de (f

ract

ion

wat

er)

0.0

0.2

0.4

0.6

0.8

1.0

Poor fit to diffusion profiles for PNIPAM

Thomas and Windle model

Radial co-ordinate (mm)-4 -3 -2 -1 0 1 2 3 4

Imag

e In

t. (a

.u.)

0

20

40

60

80

100


Imag

e In

t. (a

.u.)

0

50

100

150

200


Systematic changes seen in TW parameters seen across copolymer composition range

Model development

Approach depends on whether rate of diffusion varies with:

Concentration gradientChemistryRate of deformation of matrix


-3 -2 -1 0 1 2 3

C /

C0

0.0

0.2

0.4

0.6

0.8

1.0

Mt / Minf = 0.18D = 1.5 * 10-7 cm2s-1

Low water contents

Classical Fickian diffusion confirmedAdditional features such as cracking confirmed

Intermediate water contents

Chemistry determines the form of kineticsConcentration-dependent diffusion coefficients

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4


Rel

ativ

e co

ncen

trat

ion


D0 = 3 × 10^-8 cm^2/sA = 1.6

High water contents

Swelling from dry polymer results in Case-II diffusionDeformation of matrix determines kinetics


Imag

e In

t. (a

.u.)

0

50

100

150

200


Elastic networks

Fickian diffusion again confirmedDiffusion coefficient decreases and so evidence for swelling stressCare need with measurement techniques

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

-0.8 -0.3 0.2 0.7R, cm

WC

1

5.7

72.1

100.7

227.5

Time, h

Thanks to ..

Australian Research Council

Braden, Patel of LHMC

Chirila of Lions Eye Institute, Perth

Centre for Magnetic Resonance

Organisers of Gel Sympo 2003

Thanks to you!

The Kinetics of Swelling of Hydrogel Polymers …NMR imaging has been extensively applied by us to...

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Transcript of The Kinetics of Swelling of Hydrogel Polymers …NMR imaging has been extensively applied by us to...