Comparison of dissolution and mutual diffusioncoefficients during dissolution of poly(methylmethacrylate) films †

S Ugur and O Pekcan*Istanbul Technical University, Department of Physics, 80626, Maslak Istanbul, Turkey

Abstract: Steady state ¯uorescence measurements have been used for studying the dissolution of

polymer ®lms. These ®lms are formed by free radical polymerization of methyl methacrylate (MMA)

in which pyrene (Py) was introduced as a ¯uorescence probe. Dissolution of poly(methyl methacrylate)

(PMMA) ®lms in chloroform±heptane mixtures were monitored in real-time by the Py ¯uorescence

intensity change. Dissolution coef®cients Dd of Py molecules were measured during dissolution of

PMMA ®lms, and found to be about 10ÿ6cm2sÿ1. After dissolution, ¯uorescence quenching

measurements were performed and the Stern±Volmer equation was employed to measure the mutual

diffusion coef®cients of heptane (Dh) and Py (DPy) molecules; these were found to be about 10ÿ5cm2sÿ1.

# 1999 Society of Chemical Industry

Keywords: ¯uorescence; dissolution; diffusion; Stern±Volmer

INTRODUCTIONDiffusion mechanisms and the determination of diffu-

sion coef®cients (D) of small molecules in polymeric

systems have been of interest over the last two decades.

Veksli and Miller1 investigated non-solvent penetra-

tion into poly(methyl methacrylate) (PMMA) and

polystrene (PS) latex particles using ESR. MacCallum

and Rudkin2 studied the quenching of naphthalene

¯uorescence in PMMA by diffusing oxygen molecules

in thin ®lm samples. Winnik and co-workers3

measured D values in phenanthrene labelled, non-

aqueous dispersions (AND) of poly(vinly acetate)

(PVAc) latex particles, stabilized by poly(2-ethyl-hexyl

methacrylate) PEHMA, using both steady-state and

transient ¯uorescence methods. D =1.91�10ÿ5cm2sÿ1 was obtained for oxygen diffusing in

cyclohexane swollen PEHMA phase by employing

¯uorescence quenching. The ESR method, based on

the scavenging of radicals produced by high energy

g-irradiation of PMMA by oxygen was used for

measurement of the diffusion coef®cient in PMMA.4

D =3.4�10ÿ8cm2sÿ1 was determined for diffusing

oxygen into irradiated PMMA spheres. The oxygen

uptake of g-irradiated spherical PVAc particles was

investigated from changes in the intensity of ESR

signal5 and the value of D for diffusing oxygen so

obtained was 4.5�10ÿ8cm2sÿ1. Diffusion of solvent

molecules into AND of PMMA sterically stabilized by

polyisobutylene (PIB) was studied by ESR, employing

the spin-probe technique.6 Fickian type diffusion of

solvent molecules into PMMA latex particles was

observed and D values were found to be around

10ÿ15cm2sÿ1 in various solvents. Similar D values

were observed when the above technique was applied

to AND of PVAc latex particles sterically stabilized by

PEHMA in various solvents.7

Fluorescence quenching and depolarization

methods have been used for penetration and dissolu-

tion studies in solid polymers.8,9 In situ ¯uoresence

quenching in conjunction with laser interferometry

was used to investigate the dissolution of PMMA ®lms

in various solvents.10 A real-time, non-destructive

method for monitoring small molecule diffusion in

polymer ®lms was developed.11,12 This method is

based on the detection of excited ¯uorescence mol-

ecules desorbing from a polymer ®lm into a solution in

which the ®lm is placed.11±14 Recently, we have

reported a steady state ¯uorescence (SSF) study on

the dissolution of annealed latex ®lms using realtime

monitoring of ¯uorescence probes.15

The penetration of solvent molecules into glassy

polymers often does not proceed according to the

Fickian diffusion model.16,17 Penetration not

described by the Fickian model is called anomalous

diffusion, where the rate of transport is entirely

controlled by polymer relaxation. This transport

mechanism is termed case II, in contrast to Fickian

diffusion which is called case I. In the case II diffusion

model, the second step is the rate limiting step which

predicts a linear dependence of the change in ®lm

thickness with time. The ®rst and third steps, however,

follow a case I diffusion model, where the ®rst one is

Polymer International Polym Int 48:485±490 (1999)

* Correspondence to: O Pekcan, Istanbul Technical University, Department of Physics, 80626, Maslak Istanbul Turkey† This article is dedicated to the 225th anniversary of Istanbul Technical University(Received 19 August 1998; revised version 22 December 1998; accepted 4 February 1998)

# 1999 Society of Chemical Industry. Polym Int 0959±8103/99/$17.50 485

the absorption of solvent molecules by the glassy ®lm

and the third is the dissolution of polymer chains from

the gel layer. The fouth and ®nal step of polymer

dissolution involves diffusion of polymer molecules

throughout the liquid phase. In this work we are

mainly interested in the third and fourth steps of the

dissolution phenomenon.

Polymer dissolution can be affected by various

parameters, including solvent quality, polymer mol-

ecular weight, solvent thermodynamic compatibility,

agitation and temperature. In this work, the effect of

solvent quality on polymer dissolution has been

studied using the SSF method by real-time monitoring

of the (Py) intensity change. Chloroform and heptane

mixtures were used as dissolution agents. In situ SSF

experiments were performed to observe the dissolution

processes. Dissolution experiments were designed so

that Py molecules, dissolving from ®lms, were detected

in real-time monitoring of SSF intensity. Dissolution

coef®cients, Dd were measured using curves of

intensity versus time. Direct illumination of the ®lm

sample was avoided, during the in situ dissolution

experiments. After dissolution experiments were per-

formed, the quenching effect on Py molecules was

detected to measure the mutual diffusion coef®cient,

Dm, using the Stern±Volmer model.

THEORETICAL CONSIDERATIONSFickian DissolutionWe employ the classical diffusion model to interpret

the results of polymer dissolution experiments. This

model includes only case I diffusion kinetics, because

gelation during dissolution was eliminated using

continuous agitation. The case I or Fickian diffusion

model includes the solution of a unidirectional

diffusion equation for a set of boundary conditions

set by Crank and Park.18 For a constant diffusion

coef®cient D and ®xed boundary conditions, the

absorption and dissolution transport in and out of a

thin slab is given by the relation

M1

M1� 1ÿ 8

�2

X1n�0

1

�2n� 1�2 exp�ÿ�2n� 1�2D�2t

d2�

�1�Here, Mt represents the amount of materials absorbed

or dissolved at time t, M? is the equilbrium amount of

material, and d is the thickness of the slab; n comes

from the solution of the diffusion equation in the form

of a trigonometrical series.

Finite concentration fluorescence quenchingThe theories of ¯uorescence quenching with and with-

out diffusion are well established.19 A chromophore A

in its ground state is converted to an electronically

excited state A* by absorption of a photon hnex, i.e.

h�ex � Aÿ!A�

The excited state A* decays to A by producing a

¯uorescence with a lifetime t0, through

A�ÿ!A� h�fl

or the excited state A* can be quenched by collision

with quencher Q at a rate k, described by

A� �Qÿ!A�Q

and, even in the absence of excitation, A and Q are

assumed capable of reacting to form a complex AQ

with a rate kf

A�Q ÿÿ! AQ

and AQ decays with rate kb.

The related rate equations governing the above

processes are solved neglecting diffusion, and the

following equation is obtained:20

I0

I� 1� �k�0 �K��Q� � k�0K �Q�2 �2�

which is known as Stern±Volmer law in the absence of

diffusion control. Here I0 and I present the intensities

of a chromophore with and without quencher and

K =kf/kb.

The Stern±Volmer law in the presence of diffusion

at in®nite concentration can be obtained by solving the

many particle diffusion equation with reactive terms;

Figure 1. Dissolution cell as used in LS-50 Perkin Elmer spectrofluorimeter(a) before and (b) after dissolution. (I0 and Ip are the excitation and emissionintensities at 345nm and 375nm, respectively).

486 Polym Int 48:485±490 (1999)

SË UgÆur, OÈ Pekcan

for the probability densities of A* and Q and equation

(2) it is reproduced20 with

k � 4�NADmpR

1000�Mÿ1sÿ1� �3�

where Dm=DPy�Dh is the sum of the mutual diffusion

coef®cients of chromophore (Py) and quencher (hep-

tane), respectively, R =RPy�Rh is the sum of their

interaction radii, NA is Avagadro's number, and p is a

factor describing the reaction probability per collision.

Here DPy and Dh are the mutual diffusion coef®-

cients and RPy and Rh are the radii of Py and heptane

molecules, respectively. At ®nite concentration, ie

quenchers present in suf®ciently large concentrations

(typically [Q]=0.1M while [A]=10ÿ4M), the com-

plex formation can be neglected and eqn (2) reduces to

the form

I0

I� 1� k�0�Q� �4�

EXPERIMENTALMonomer MMA (Merck) was freed from inhibitor by

shaking with a 1.79M aqueous KOH solution,

washing with water and drying over sodium sulphate.

It was then distilled under reduced pressure over

copper chloride. The initiator, 2,2'-azobisisobutyro-

nitrile (AIBN) (Merck, Detroit), was recrystallized

twice from methanol. The solvents chloroform and

heptane (Merck) were used as received.

The radical polymerization of MMA was performed

in bulk in the presence of AIBN as an initiator. AIBN

(1.59�10ÿ2 M) and Py (4�10ÿ4M) were dissolved in

MMA and this solution was poured into round glass

tubes of 15mm internal diameter. Before polymeriza-

tion, each solution was deoxygenated by bubbling

nitrogen for 10min. Radical polymerization of MMA

was performed at 65�3°C. After polymerization was

complete, the tube was broken. Disc shaped, thin

samples (around 0.2cm) were cut for the swelling and

dissolution experiments.

In situ ¯uorescence experiments were performed

using a Perkin Elmer (London) LS-50 spectro¯uori-

meter. All measurements were made at the 90° posi-

tion and the slit width was kept at 2.5mm. Dissolution

experiments were performed in a 1cm�1cm quartz

cell which was placed in the spectro¯uorimeter. The

¯uorescence emission was monitored so that ®lm

samples were not illuminated by the excitation light.

Disc shaped samples were placed on one side of a

quartz cell ®lled with chloroform±heptane mixture; the

cell was then illuminated with 345nm excitation light.

The pyrene ¯uorescence intensity, IP, was monitored

at 375nm during dissolution using the `time drive'

mode of the spectro¯uorimeter. Py emission was

Figure 2. Pyrene intensity Ip versusdissolution time for film samples dissolvedin various chloroform–heptane mixtures athigh stirring speed. Samples a–g are listedin Table 1.

Polym Int 48:485±490 (1999) 487

Dissolution of poly(methyl methacrylate) ®lms

recorded continuously at 375nm as a function of time.

The cell and the sample position are presented in Fig

1. Here the 1cm�1cm quartz cell was equipped with

a magnetic stirrer at the bottom. The Py ¯uorescence

emission was monitored at a 90° angle as shown in

Fig 1.

RESULTS AND DISCUSSIONDissolution coefficientsPlots of Py intensity Ip versus dissolution time for

various chloroform±heptane mixtures at high stirring

speed are shown in Fig 2. Samples are listed in Table

1. It is seen that as the heptane content increases,

curves reach a plateau at longer times. In other words,

PMMA ®lms dissolve more slowly in solutions with

higher heptane content. After dissolution was com-

plete SSF spectra of Py were taken in various chloro-

form±heptane mixtures. Figure 3 presents the results

for the samples having 10, 30 and 70% heptane

content (mixtures b, d andg, respectively). No shift is

observed at the maximum Py intensity. Smaller

intensity values in Py spectra for high heptane content

mixtures may be explained by collisional quenching in

the low viscous environment (3.8�10ÿ4 Pas) of

heptane, in which excited Py can be quenched more

easily than in a high chloroform content mixture,21

which has relatively high viscosity (5.8�10ÿ4 Pas).

The curves in Fig 2 seem to follow a case I (Fickian)

diffusion model. In processing the dissolution data, it

is assumed that Ip is proportional to the number of Py

molecules dissolving from the PMMA ®lm. The

logarithmic form of eqn (1) is written for n =0, with

Ad=Ddp2/d2 and Bd=ln;(8/p2) as follows

ln�1ÿ Ip

Ip1� � Bd ÿ Adt �5�

Here, Ip? represents the number of Py molecules at

equilibrium, Dd is the dissolution coef®cient and d is

the thickness of the PMMA disc. Figure 4b, d andg

shows the dissolution curves for mixtures having 10,

Figure 3. Emission spectra of pyrene (Py)in 10, 30 and 70% heptane mixtures withchloroform.

Table 1. Film thickness and dissolution coefficients for samples in variouschloroform–heptane mixtures

Samples Heptane (%) Dd�10ÿ6 (cm2/sÿ1) d (cm)

a 0 3.73 0.196

b 10 2.81 0.182

c 20 3.48 0.191

d 30 1.93 0.169

e 40 2.81 0.206

f 50 2.25 0.185

g 70 1.59 0.233

a Dd values were obtained by ®tting eqn (5) to the data in Fig 2. Here,

chloroform±heptane mixtures are used as dissolution agents, and high

speed stirring was employed during experiments; d is the ®lm thickness for

each sample.

488 Polym Int 48:485±490 (1999)

SË UgÆur, OÈ Pekcan

30 and 70% heptane content (b, d andg, respectively)

digitized for numerical treatment according to eqn (5).

All curves in Fig 4 present linear dependence with

time, con®rming our assumption of relationship with a

diffusion model. When these linear curves in Fig 4 are

compared to computations using eqn (5), dissolution

coef®cients Dd for Py molecules are obtained. These

are listed in Table 1 with values for other samples. Dd

values for the PMMA discs dissolved in mixtures

having high heptane content were smaller than those

obtained in low heptane mixtures. These results are

expected for PMMA dissolved in a solvent mixture

which contains a greater amount of non-solvent.

In general, Dd values obtained in these experiments

are three orders of magnitude larger than that found in

our recent work with PMMA latex ®lms.15 In this

study the PMMA discs were 200 times thicker than the

latex ®lms. Thickness effects were observed by

Enscore et al16 where 300-fold larger polystyrene

spheres caused twofold larger dissolution coef®cients

for hexane. This was explained by formation of a

spherical shell during the absorption process. In our

case, however, the gel layer is removed from the

surface of the PMMA discs by stirring. Smaller

dissolution coef®cients in latex ®lms compared to

those of PMMA discs can be explained by the

annealing effect, which resulted in the formation of

mechanically strong ®lms. Most probably, PMMA

discs used in this work have greater free volumes than

annealed latex ®lms. In fact, during latex ®lm

dissolution, a long gelation period (case II diffusion)

was observed at early times. However, the PMMA

discs used here show dissolution by following pure

Fickian (case I) behaviour, or the stirring effect may

prevent us observing case II diffusion. In other words,

the gel layer is immediately removed from the surface

of the PMMA disc by stirring, so that case I diffusion

dominates the dissolution process.

Mutual diffusion coefficientThe results in Fig 3 can be explained by heptane

quenching of excited Py molecules. The Ip of dissolved

samples decreases as the heptane content increases,

indicating effective heptane quenching of the excited

state of Py. These data can be analysed in terms of the

Stern±Volmer model (eqn (4)) by assuming that

collisional quenching of Py becomes very active in

the presence of diffusion at large concentrations of

heptane. I0/Ip is plotted as a function of heptane

(quencher) concentration in Fig 5. In a well behaved

system, such a plot yields a slope equal to kt0 and the

straight line passes through 1.0. When t0 is known, the

magnitude of the collisional quenching rate constant kcan be determined. The linearity of the plot in Fig 5

Figure 4. Plot of digitized data from Fig 2, which obey the relationln(1ÿIp/Ip?)=BdÿAdt, where t is the dissolution time. Curves b, d and grepresent the data for samples containing 10, 30 and 70% heptane,respectively.

Figure 5. Stern–Volmer plot of Io /Ip versus quencher (heptane)concentration [Q] in chloroform.

Polym Int 48:485±490 (1999) 489

Dissolution of poly(methyl methacrylate) ®lms

indicates that the Stern±Volmer law is obeyed and

suggests that unique values of k and t0 exist. When

data in Fig 5 are ®tted to eqn (4), the rate constant for

heptane quenching of Py is found to be

k =1.22�107Mÿ1sÿ1, where t0=20ns was taken as

measured in the presence of oxygen at room tempera-

ture.22 The sum of mutual diffusion coef®cients

calculated with eqn (3) from this k value is found to

be Dm=2.05�10ÿ5cm2sÿ1, where R is taken as

7.86AÊ (ie RPy=3.98AÊ and Rh=3.88 AÊ ) and p is

assumed to be unity. Here it is assumed that heptane

and Py molecules are homogeneously distributed in

chloroform. Because the radii of Py and heptane

molecules are almost equal, it is reasonable to

approximate the mutual diffusion coef®cients (DPy

and Dh) as 1.02�10ÿ5cm2sÿ1 for both molecules.

These observed diffusion coef®cients are typical for a

chromophore in an organic solvent at room tempera-

ture.23±25 If one imagines that the gel layer from the

swollen polymer ®lm is taken away rapidly due to the

effect of vigorous stirring, an order of magnitude

difference between dissolution (Dd) and mutual (DPy

and Dh) diffusion coef®cients seems to be reasonable.

Here the absorption of heptane molecules is immedi-

ately followed by dissolution of Py molecules

(Dd�10ÿ6cm2sÿ1) and it can be assumed that

dissolution of PMMA chains occurs with the same

rate as that of Py.

CONCLUSIONSThis work studied the dynamical parameters of the last

two steps of polymer dissolution, ie dissolution of

polymer chains into a liquid reservoir and diffusion in a

liquid reservoir, respectively. Further suitable work

can be achieved using dye labelled polymer chains and

the ¯uorescence technique.

ACKNOWLEDGEMENTSWe wish to thank the referees for their critical and

constructive reading of our manuscript; we gained a lot

from their comments and objections.

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SË UgÆur, OÈ Pekcan