Polymer International Polym Int 49:1641±1647 (2000)

Effect of molar size and solubility parameter ofsolvent molecules on swelling of a gel: afluorescence studyO Pekcan* and M ErdoganDepartment of Physics, Istanbul Technical University, Maslak 80626, Istanbul, Turkey

(Rec* Co

# 2

Abstract: Gels were swollen in various solvents with different molar volume V and solubility parameter

d. In situ steady state ¯uorescence (SSF) measurements were performed for swelling experiments in

gels formed by free radical crosslinking copolymerization (FCC) of methyl methacrylate (MMA) and

ethylene glycol dimethacrylate (EGDM). Gels were prepared at 75°C with pyrene (Py) as a ¯uor-

escence probe. After drying these gels, swelling and slow release experiments were performed in

various solvents with different V and d at room temperature by time monitoring of the Py ¯uorescence

intensity. The Li±Tanaka equation was used to produce time constant t1 values. Cooperative diffusion

coef®cients (Dc) were measured and found to be strongly correlated to the molar volume of the solvents

used. Solvent uptake and degree of swelling were found to be dependent on the solubility parameter of

the solvent.

# 2000 Society of Chemical Industry

Keywords: ¯uorescence; gel; solubility; molar volume; swelling

INTRODUCTIONThe equilibrium swelling of gels in solvents has been

extensively studied.1±3 The swelling kinetics of

chemically crosslinked gels can be understood by

considering the osmotic pressure versus the restraining

force.4±8 The total free energy of a chemical gel

consists of bulk and shear energies. In fact, in a swollen

gel, bulk energy can be characterized by the osmotic

bulk modulus K de®ned in terms of the swelling

pressure and the volume fraction of polymer at given

temperature, whilst the shear energy which keeps the

gel in shape can be characterized by shear modulus G.

Here shear energy minimizes the non-isotropic defor-

mations in gel. The theory of kinetics of swelling for a

spherical chemical gel was ®rst developed by Tanaka

and Filmore9 where the assumption was made that the

shear modulus G is negligible compared with the

osmotic bulk modulus. Later, Peters and Candau10

derived a model for the kinetics of swelling in spherical

and cylindrical gels by assuming non-negligible shear

modulus. Recently, Li and Tanaka4 have developed a

model where the shear modulus plays an important

role which keeps the gel in shape due to coupling of

any change in different directions. This model predicts

that the geometry of the gel is an important factor, and

swelling is not a pure diffusion process.

Several experimental techniques have been em-

ployed to study the kinetics of swelling, shrinking and

drying of chemical and physical gels, among which are

neutron scattering,11 quasielastic light-scattering,10

eived 4 February 2000; revised version received 6 June 2000; acceprrespondence to: O Pekcan, Department of Physics, Istanbul Technic

000 Society of Chemical Industry. Polym Int 0959±8103/2000/$3

macroscopic experiments12 and in situ interfero-

metric13 measurements. Recently, we reported in situobservations of sol±gel phase transition in free-radical

crosslinking copolymerization, using the ¯uorescence

technique.12,14,15 The same technique was also

applied for studying swelling and drying kinetics in

disc-shaped gels.16±18

In this work, swelling and slow release processes of

gels formed by solution free radical crosslinking

copolymerization (FCC) of methyl methacrylate

(MMA) and ethylene glycol dimethacrylate (EGDM)

have been studied. Pyrene (Py) is used as a ¯uor-

escence probe to monitor swelling and slow release

processes during in situ ¯uorescence experiments in

various solvents with different molecular sizes and

solubility parameters. In situ steady state ¯uorescence

(SSF) experiments were performed for real-time

monitoring of swelling and slow release processes.

Our goal in the present work is to study the swelling

process in various solvents to determine the relation

between diffusion and solvent quality Cooperative

diffusion coef®cients Dc are determined and found to

increase from 3.6�10ÿ5 to 6.9�10ÿ5cm2sÿ1, de-

pending on the molar volume V of the solvent

molecule, indicating that the molar size of the solvent

molecule is strongly correlated to the diffusion in gels.

THEORETICAL CONSIDERATIONSIt is known that the kinetics of swelling of a polymer

ted 4 July 2000)al University, Maslak 80626, Istanbul, Turkey

0.00 1641

1

OÈ Pekcan, M ErdogÆan

network or gel should obey the following relation:4

W �t�W1

� 1ÿX1n�1

Bneÿt=tn �1�

where W(t) and W? are the swelling or solvent uptake

at time t and at equilibrium, respectively. W(t) can also

be considered as a volume difference of the gel

between the time t and zero. Each component of the

displacement vector of a point in the network from its

®nal equilibrium location after the gel is fully swollen,

decays exponentially with a time constant tn which is

independent of time t.Here Bn is given by the relation4

Bn � 2�3ÿ 4R��2

n ÿ �4Rÿ 1��3ÿ 4R� �2�

where R is de®ned as the ratio of the shear and the

longitudinal osmotic modulus, R =G/M. The long-

itudinal osmotic modulus M is a combination of shear

modulus G and osmotic bulk modulus K (M =K�4G/3) and an is given as a function of R as

R � 1� �nJ0��n�J1��n�

� ��3�

where J0 and J1 are the Bessel functions.

In eqn (1), tn is inversely proportional to the

collective cooperative diffusion coef®cient Dc of a gel

disk at the surface and is given by the relation5

tn � 3a2

Dc�2n

�4�

Here the diffusion coef®cient Dc is given by Dc=

M/f =(K�4G/3)/f, f being the friction coef®cient

describing the viscous interaction between the poly-

mer and the solvent, and a representing half of the disc

thickness in the ®nal in®nite equilibrium which can be

experimentally determined.

The series given by eqn (1) is convergent. The ®rst

term of the series expansion is dominant at large t,which corresponds to the last stage of the swelling. As

seen from eqn (4) tn is inversely proportional to the

square of an, where an values are the roots of the Bessel

functions. If n>1, an increases and tn decreases very

rapidly. Therefore, for kinetics of swelling in the limit

of large t or if t1 is much larger than the rest of tn (ref

4), all high-order terms (n�2) in eqn (1) can be

Table 1. Characteristics of solventsemployed

Parameter Acetone (AC)

a0 (cm) 0.130

a? (cm) 0.160

W? (g) 0.168

t1 (s) 4700

d (MPa1/2) 20.3

V (cm3 molÿ1) 73.53

Dc (cm2 sÿ1) 6.04�10ÿ

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dropped, so that the swelling and shrinking can be

represented by the ®rst-order kinetics.13 In this case

eqn (1) can be written as

W �t�W1

� 1ÿ B1eÿt=t1 �5�

Equation (5) allows us to determine the parameters B1

and t .

EXPERIMENTSEGDM has been commonly used as crosslinker in the

synthesis of polymeric networks. Here, for our use, the

monomers MMA (Merck) and EGDM (Merck) were

freed from the inhibitor by shaking with a 10%

aqueous KOH solution, washing with water and

drying over sodium sulfate. They were then distilled

under reduced pressure over copper chloride.

The radical copolymerization of MMA (80%v/v)

and EGDM (1%v/v) was performed in toluene

(20%v/v) at 75°C in the presence of 2,2'-azobisiso-

butyronitrile (AIBN) an initiator. AIBN (0.26wt%)

was dissolved in MMA and transferred into round

glass tubes of 9.5mm internal diameter. Py was added

as a ¯uorescence probe before the gelation process

during sample preparation. Here the Py concentration

was 4�10ÿ4M. All samples were deoxygenated by

bubbling nitrogen for 10min, and then radical

copolymerization of MMA and EGDM was per-

formed. The reaction time was 35min. The monomer

(MMA), crosslinker agent (EGDM) and toluene were

purchased from Merck. The gels were not pre-soaked

in toluene to remove unreacted monomers, and up to

5% monomers may have been present in the gels at the

beginning of the swelling experiments. After the gels

had been formed and dried in vacuum for 1h at room

temperature, they were cut into discs to use in swelling

and slow release experiments. Four different solvents

with different molar volume and solubility parameters

were chosen for swelling experiments. Spectroscopi-

cally pure grade ethyl acetate (EA), chloroform (CH),

dichloromethane (DM) and acetone (AC) were

purchased from Merck and used as received. Charac-

teristics of solvents are listed in Table 1.

Steady state ¯uorescence measurements were

carried out using a Perkin Elmer model LS-50

spectro¯uorimeter. All measurements were made at

the 90° position, and slit widths were kept at 10nm. In

Solvent

Chloroform (CH) Dichloromethane (DM) Ethyl acetate (EA)

0.185 0.070 0.135

0.250 0.095 0.165

0.312 0.110 0.166

9799 1168 9942

19.0 19.8 18.6

80.17 64.00 97.895 4.02�10ÿ5 6.90�10ÿ5 3.57�10ÿ5

Polym Int 49:1641±1647 (2000)

Fluorescence study of gel swelling

situ swelling and slow release experiments were both

performed in a 1�1cm2 quartz cell at room tempera-

ture. Gel samples were attached to one side of the

quartz cell by pressing the disc with thin steel wire.

The quartz cell was ®lled with AC, CH, DM and EA

for separate swelling and slow-release experiments.

This cell was placed in the spectro¯uorimeter and

¯uorescence emission was monitored at a 90° angle.

Two different experiments were carried out for two

different positions of the gel samples for each set of

experiment (see Fig 1). In both experiments, identical

disc-shaped gels were used which were dried cut from

the cylindrical gels obtained from FCC. The thickness

of these disc shaped gels was around 0.13cm. In the

®rst position, only the gel was illuminated by the

excitation light and the total ¯uorescence emission Ip

caused by Py molecules comes from the Py molecules

immersed in the gel and desorbed from the swelling

gel. In the second position, the gel sample was shifted

slightly upwards so that only the cell with solvent was

illuminated by the excitation light. Here the ¯uor-

escence emission Id from Py molecules desorbed from

the swelling gel was monitored. Figure 1(a) and (b)

show the ®rst and second position of the gels,

respectively. These experiments were repeated for

each solvent.

During the experiments the wavelength of the

excitation light was kept at 345nm, and Py intensities

was monitored at 395nm using the time drive mode of

Figure 1. Fluorescence cell in LS-50 Perkin Elmer spectrofluorimeter.Monitoring of (a) swelling (the first position) and (b) desorption (the secondposition) processes of the gel explained in the text. I0 is the excitationintensity at 345nm, and Ip and Id are the emission intensities at 395nm.

Polym Int 49:1641±1647 (2000)

the spectro¯uorimeter. No shift was observed in the

wavelength of maximum intensity of Py and gel

samples remained transparent during the experiments.

Desorption curves of Py molecules were used to obtain

pure swelling curves by subtracting the intensities

taken from samples at the positions given in Fig 1(a,b).

In swelling experiments, continuous volume transi-

tions are expected and these should result in a con-

tinuous decrease in Ip during swelling. Here, one may

expect that as solvent uptake (W) increases, desorption

of Py molecules from the swollen gel will increases,

and as a result, Py intensity in the ®rst position (Ip) will

decrease. However, during slow release experiments

one should expect an increase in Id, due to the in-

creasing amount of Py molecules released into solvent

in the cell.

RESULTS AND DISCUSSIONPyrene intensities in the ®rst and second position of

the gel versus time are plotted in Fig 2(a, b, c and d) for

AC, CH, DM and EA solvents, respectively. The

curves in Fig 2 were obtained during in situ ¯uor-

escence experiments described in Fig 1(a, b), where at

the beginning all Py molecules are in the gel and Ios is

obtained. After solvent penetration starts, some Py

molecules are washed out from the swollen part of the

gel into the cell; as a result Py intensity Is from the

glassy gel decreases as swelling time increases. At the

equilibrium state of swelling, the Py intensity from the

glassy gel reaches the I?s value, where the solvent

uptake by swollen gel is W. A schematic representation

of these swelling stages is shown in Fig 3 where the

intensity from the desorbed Py molecules is repre-

sented by Id. The relation between solvent uptake Wand ¯uorescence intensity Is from the glass part of gel

is given by the relation

W

W1� Ios ÿ Is

Ios ÿ I1s

�6�

Because Ios�I?s, eqn (7) becomes

W

W1� 1ÿ Is

Ios

�7�

This relation predicts that as W increases Is decreases;

it is quite similar to the equation used to monitor

oxygen uptake by poly(methyl methacrylate) and

polyvinyl acetate) spheres.19,20 Combining eqns (5)

and (7), the following relation can be obtained

ln�Is=Ios� � ln B1 ÿ t=t1 �8�If one imagines that the ¯uorescence intensity curves

Ip in Fig 2 originate only from the gels, then eqn (8) has

to be obeyed by the data. However, during the swelling

experiments, desorbing Py molecules also contribute

to the ¯uorescence intensity,16 which prevents us

observing pure swelling curves as shown in Fig 3. In

fact, the Ip data in Fig 2 represent the total Py intensity,

during in situ swelling experiments; the following

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Figure 2. Total Py intensity Ip, and intensity from desorbing Py molecules Id, versus swelling and desorption time for the gel samples swollen in (a) AC, (b) CH,(c) DM and (d) EA. The gel in the cell was illuminated at 345nm (at the first position) during Ip measurements; Id intensities were measured at the second position.

OÈ Pekcan, M ErdogÆan

relations are operative at different times

t � 0 Iop � Ios � Iod

t > 0 Ip � Is � Id

t � 1 Iop � I1p � I1d �9�

where Id is the Py intensity from the desorbing Py

molecules as shown in Fig 3. Plots of Id versus time are

shown in Fig 2 below each Ip curve obtained from the

experiments performed according to Fig 1(b). In Fig

2, Id increases as the swelling and desorption time

increases for all samples. Because Id is directly

proportional to the number of Py molecules in the

solvent, the behaviour of the Id curves in Fig 2 suggests

that Py molecules are slowly released from the gels.

To produce the pure swelling intensity (Is) curves, Id

data are subtracted from the Ip data for each swelling

experiment according to eqn (9) for AC, EA, CH and

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DM, respectively. To con®rm the correctness of the

pure swelling curves, data were digitized according to

eqn (8) and are plotted Fig 4, where linear relations are

obtained except at long time-regions. Long time-

deviations are explained by saturation of solvent

uptake. The short time-deviation for the CH experi-

ment may correspond to fast relaxation processes in

the gel at an early swelling stage.16,18 Using eqn (8), a

linear regression of curves in Fig 4 provides us with B1

and t1 values. Taking into account the dependence of

B1 on R one obtains R values, and from the a1±Rdependence a1 values were produced.4 Then using eqn

(4) for n =1, cooperative diffusion coef®cients Dc were

determined for AC, CH, DM and EA swelling

experiments. Experimentally obtained parameters t1

and Dc, together with the solubility parameter d21 and

molar volume V,22 are listed in Table 1, where a0, a?and W? values are also presented for AC, CH, DM

and EA experiments. Here one should note that

Polym Int 49:1641±1647 (2000)

Figure 3. Schematic representation ofthe swelling processes in the gel duringsolvent uptake. Fluorescenceintensities from Py molecules are alsopresented:(a) gel before swelling whereIos is the fluorescence intensity fromglassy gel at t =0;(b) swollen gel inwhich Is and Id present the fluorescenceintensities from glassy gel anddesorbed Py molecules at t>0 and Wis the solvent uptake;(c) highly swollengel where I?s and I?d are thefluorescence intensities at t =? andW? is the solvent uptake at t =? (hereIp represents the total Py intensity).

Figure 4. Linear regression of the Is data according to eqn (8). B1 and t1 values were obtained from the intersections and slopes of the plots in (a), (b), (c) and (d)for the gels in AC, CH, DM and EA, respectively.

Polym Int 49:1641±1647 (2000) 1645

Fluorescence study of gel swelling

Figure 6. Plots of (a) (a?ÿa0) and (b) W? versus solubility parameters d ofsolvents AC, CH, DM and EA.

OÈ Pekcan, M ErdogÆan

measured t1 and Dc values are found to be strongly

dependent on the molar volume V of the solvent and

not on the solubility parameter d.

It is important to note that penetration of solvent

molecules into gel substantially depends on the

hydrocarbon employed. Now the challenge is to

determine whether kinetic effects associated with the

solvent viscosity Z or thermodynamic effects (poly-

mer±solvent interactions) are responsible for the

swelling of the gel. No correlation has been found

between Z and t1 values. Here it is convenient to test

whether the solvent quality ie polymer±solvent inter-

action, is responsible for the swelling processes or not.

Solution theory predicts that the polymer±solvent

interaction parameter w is related to solubility par-

ameter d and molar volume V via the relation23

w � V

RT�� ÿ �p�2 �10�

where R is the gas constant, T is the temperature and

dp is the solubility parameter of the polymer. It is seen

in Table 1 that there is strong correlation between t1

and V, ie it takes longer for a larger molecule to

penetrate into the gel.

When the network is swollen by absorption of

solvent, the chains between network junctions are

required to assume elongated con®gurations, and

exert a force akin to the swelling process. As swelling

proceeds, this force increases and the dilution force

decreases. Dc is the measure of the force of retraction

in a stretched network structure. Here, as the gel swells

faster (small t1), a higher force of retraction is applied;

as a result Dc values increase as in DM. However, slow

penetration of solvent molecules into the gel result in

smaller Dc values as in EA. In Fig 5, Dc is plotted

versus V, where a strong correlation between these

parameters is seen. In Fig 6(a, b), the variation in the

®nal (a ) and initial (a ) disc thickness (a ÿa ) and

? 0 ? 0

Figure 5. Plot of Dc versus molar volume V of solvents AC, CH, DM andEA.

1646

the ®nal solvent uptake (W?) are plotted versus

solubility parameter d of the solvents. It is seen that

there is correlation between these parameters, ie as

(dÿdp) approaches zero, (a?ÿa0) and W? values

present increase (where �p=18.57 MPa1/2 was taken

for PMMA). From here one can conclude that solvent

uptake is strongly correlated to the polymer±solvent

interaction parameter w. In other words, for the best

solvent (CH), the degree of swelling of the gel is

largest.

Here, the basic conclusion can be reached that the

swelling process of gels is associated with the thermo-

dynamic effects, ie polymer±solvent interactions,

where both the molar volume V and the solubility

parameter d play important roles in the process.

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