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Polymer 54 (2013) 4669e4674

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Polymer

journal homepage: www.elsevier .com/locate/polymer

Power law in swelling of ultra-thin polymer films

M. Mukherjee a,*, M. Souheib Chebil b, Nicolas Delorme b, Alain Gibaud b

a Surface Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, Indiab LUNAM Universite, IMMM, Faculté de Sciences, Universite du Maine, UMR 6283 CNRS, Le Mans Cedex 9 72000, France

a r t i c l e i n f o

Article history:Received 11 February 2013Received in revised form17 May 2013Accepted 12 June 2013Available online 20 June 2013

Keywords:PolymerSwellingPower law

* Corresponding author.E-mail addresses: manabendra.mukherjee@saha.

(M. Mukherjee).

0032-3861/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.polymer.2013.06.025

a b s t r a c t

Steady state and dynamic behaviour of swelling of spin coated polyacrylamide films have been studied atroom temperature in a precisely controlled environment of 12e99% relative humidity (RH). Swelling ofthe films was monitored by measuring the thickness of the films using X-ray reflectivity and AtomicForce Microscopy. Swellibility of the films was observed to be independent of thickness of the filmsindicating no significant influence of substrate polymer interaction or confinement effect in swelling. Thewater content of the films swelled at different humidity conditions was calculated comparing theelectron density of the dry and the swelled films. The volume fraction of water in the swelled films andtheir swellibility were found to follow double power law behaviour as a function of relative humidity andthe transition from one regime to the other was observed around 75% RH value. The behaviour wasexplained in terms of transition from short to long diffusing channels in the films. Comparison of timeevolution of relative humidity of the experimental chamber with that of the dynamics of swellings of thefilms shows that diffusion of water into the environment was several orders of magnitude faster than theswelling dynamics. The observed values of the diffusion coefficients for the films at different humiditywere same whereas the excluded volume parameter, that determine the saturated thickness of the films,was found to have dependence on relative humidity and film thickness.

� 2013 Elsevier Ltd. All rights reserved.

́

1. Introduction In our previous studies [13e17] we have presented the swelling

In recent years ultra-thin polymeric films have drawn tremen-dous application in the fields of coating, membrane, sensors etc.Confinement of the polymer leads to the changes in the equilibriumstructural and dynamical behaviours of the polymer chains close tothe substrate [1e5] due to energetic interactions between polymerchains and the substrate. When a dry polymer is exposed to asolvent, the solvent molecules enter through the porous structureof the polymer. If the solvent is a good solvent for the polymer thereis a strong attractive interaction between the polymer and thesolvent and the net interaction between the polymer segments isrepulsive. As a result, the polymer molecule starts to swell. Theunderstanding of the mobility of the polymer chains and theirequilibrium structure close to the substrate or interfaces in pres-ence of solvent vapour are of technological importance in manyareas like emulsion, coating and adhesion [6]. The phenomenon ofsolvent absorption into the pores of polymer has been exploited byseveral authors to study the diffusion of solvent into the pores [7,8],pore size distribution [9,10], viscoelastic properties [11,12] etc.

ac.in, manabsinp@gmail.com

All rights reserved.

dynamics of water soluble polymer films where the effect ofvarious interactions on swelling dynamics have been studiedextensively. Those results in general show that swelling dynamics issensitive to the minute changes in polymeric system or on polymersolvent interaction. It may be noted that all our previous in-vestigations were performed with uncontrolled humidity with anassumption that the saturated humidity condition was achievedvery quickly in the chamber thus the process of saturation does notaffect the swelling dynamics.

The present investigation was performed under variable hu-midity condition. Here the relative humidity (RH) of the chambercan be stabilize at a desired value with the application of saturatedsolution of different inorganic salts and simultaneous control of drynitrogen flow in the sample chamber. The relative humidity and thetemperature of the swelling environment can be monitored whilethe x-reflectivity measurements can be performed with the sam-ples. As the temperature of the environment strongly influence thehumidity, the temperature was always recorded along with hu-midity and the actual humidity was calculated using the calibrationequation supplied with the humidity sensor (HIH-3610, Honey-well). The schematic diagram of the experimental setup is shown inFig. 1. Here we study the swelling behaviour of polyacrylamide thinfilms at large number of stable humidity conditions leading to thenovel result that are not available in the existing literature.

Fig. 1. Schematic representation of the humidity cell and the X-ray reflectometer.Saturated solution of K2SO4 was used as the source of humidity.

0.05 0.10 0.15 0.20 0.2510-36

10-26

10-16

10-6

104

1014

Re

fle

ctiv

ity

qz

(-1

)

13% RH 27% RH 58% RH 75% RH 80% RH 83% RH 86% RH 89% RH 93% RH 99% RH

0 100 200 300 400 5000.00.10.20.30.40.50.60.7

Ele

ctro

n d

en

sity

(Å

-3

)

z ( )

13% RH

99% RH

Fig. 2. Measured (symbol) and calculated (line) X-ray reflectivity curves of a film withinitial thickness 322 �A at different RH. The inset shows the electron density profiles atlow and high RH of 13% and 99% respectively.

M. Mukherjee et al. / Polymer 54 (2013) 4669e46744670

2. Experimental details

2.1. Sample preparation

A powder of high molecular weight polyacrylamide (Molecularweight 5e6 � 106, supplied by Polysciences, USA) was taken asstarting material for the experiment. Three aqueous solutions withconcentration 2, 4 and 6 mg/ml were prepared from the powdersource. Films from the three solutions were prepared on siliconsubstrates by spin coating method. Before coating, silicon waferswere cleaned by RCA cleaning method, where the wafers wereboiled at 100 �C for about 15 min in a solution of H2O, NH4OH andH2O2 (volume ratio, 2:1:1). The wafers were then rinsed with Mil-lipore water. Apart from cleaning, this treatment enhances the hy-drophilicity of the silicon surface by introducing eOH danglingbonds on the surface which helps better attachment of the watersoluble polymers. Films of different thicknesses were preparedapplying different spinning speeds ranging from1000 to 3000 r.p.m.

2.2. X-ray reflectivity (XRR)

X-ray reflectivity is one of the best nondestructive methods tomeasure the structural aspects of thin polymeric films; here wehave used this technique to study the thickness and electron den-sity of polyacrylamide films prepared from the three solutions. X-ray reflectivity data were collected in horizontal geometry with ourlaboratory setup (Empyrean, PANalytical) with CuKa radiation ob-tained from copper sealed tube anode (1.2 kW), followed by amirror for focussing. The samples were placed in a chamber asdescribed in the introduction section. Specular scans with identicalincoming and outgoing angles for X-rayswere taken as a function ofmomentum transfer vector q normal to the surface (q ¼ (4p/l) sinq,with q the incident and the reflected angles of the X-ray andl ¼ 1.54 �A, the wavelength of the radiation). By using a Pixcel de-tector which has a very high dynamical range, it was possible tocollect full XRR curves in about 3 min. This is a major breakthroughin such measurements which allows us to carry out kinetics studiesof materials within this time scale.

To obtain information about the thickness and electron densityof the films, the reflectivity data were analyzed using the matrix

technique [18] including interfacial roughness. For the analysis ofthe XRR data, the input electron density profiles were divided intoseveral boxes of thickness equal or more than 2p/qmax and theinterfacial roughness were kept within 2e8 �A. During the analysis,the roughness of the polymer surface, the electron density, thethickness of the films and the roughness of the substrate were usedas fitting parameters.

2.3. Atomic force microscopy (AFM)

Room temperature AFM topographic images were obtained inintermittent-contact mode (Nanosensor PPP-NCHR-W tip) with anAgilent 5500 AFM equipped with an integrated environmentalchamber. Similar to XRR measurements, relative humidity wascontrolled by the use of a saturated aqueous K2SO4 solution andcirculation of dry N2. For film thickness determination, wemeasured the difference between the two maxima of the heightdistribution data across a scratch made on the polymer film [19].Height distribution and roughness calculations were performedusing Gwyddion freeware.

2.4. Steady state measurements

A set of four films in the thickness range of 60e322�A have beeninvestigated in the present study. X-ray reflectivity experimentswere performed at room temperature (w25 �C) at different stablehumidity conditions in the range of 13e99% relative humidity. Aswe have noticed that films can de-swell almost instantaneously,whereas, swelling takes several hours to stabilize, we first took thedata at highest humidity (w99%) and then stepwise reduced thehumidity of the chamber for taking the data at other RH values. Forattaining highest humidity we used K2SO4 saturated solution as thesource of water vapour in the closed chamber keeping the dry ni-trogen flowat off condition. After humidity in the chamber attainedits highest value (w99%) in about 2 h, XRR measurements werecarried out. For attaining lower humidity we flew dry nitrogen in acontrolled manner to attain a desired value. Adding nitrogen at anoptimum rate did not disturb the experimental condition by tur-bulence or vibration and RH ¼ 12e13% as minimum was achieved.

Fig. 2 shows the XRR data for a typical sample at different hu-midity. At stable humidity conditions, the data could be collectedfor a long acquisition time. Therefore these data can be used fordetailed analysis of the electron density profiles of the films in

0 20 40 60 80 100

0

20

40

60

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.61.62.02.42.83.23.64.04.4

Swel

libilit

y(%

)

Relative Humidity(%)

XRR data AFM data

slope 0.49 ± 0.07

slope 4.60 ± 0.73

slope 0.68 ± 0.05

Ln(s

wel

libilit

y)

Ln(RH)

slope 4.81 ± 0.31

Fig. 4. Swellibility of the films as a function of relative humidity measured by XRR(solid symbol) and AFM (open symbols) techniques. The straight line fits in the insetshows power law behaviour of film swelling.

M. Mukherjee et al. / Polymer 54 (2013) 4669e4674 4671

presence of different amount of water in the film structure. Theinset of Fig. 2 shows the electron density profiles corresponding totwo different humidity RH ¼ 13% and RH ¼ 99% of a particular film.

The swellibility Dt/t (Dt is the change in thickness and t is theinitial thickness of the films) of different films were measured bytaking quick scans in a quasi steady state while the humidity of thechamber was slowly increasing. The advantage of this method isthat a large number of data for intermediate humidity can be takenin a relatively short time. In Fig. 3 we have compared the swelli-bility of the films as a function of relative humidity. We find that thevariation of swellibility or relative change in thickness as a functionof RH was non-linear in nature and it was nearly identical for thefilms of different thicknesses. This indicates that swellibility of thefilms is thickness independent phenomenon. The result may beinterpreted in terms of the fact that the substrate polymer inter-action does not play any significant role in swelling of the films. Ifthere is strong interaction between the substrate and the polymermolecules, the swellibility is likely to change with thickness. As forthinner films larger fraction of monomer units would be directlyattached to the substrate compared to the thicker ones, the influ-ence of the interaction would be stronger for thinner films leadingto thickness dependent swellibility. The result also suggests thatphysical confinement of the polymer chains does not significantlyinfluence the equilibrium absorption of water molecules.

To measure the swellibility of the films more correctly the hu-midity of the chamber was stabilized at different values usingabove mentioned technique and both AFM and XRR data werecollected in steady state. In Fig. 4 we have plotted the swellibility ofa particular film (initial thickness 322 �A) at different stabilizedhumidity. One can observe very good agreement between AFM andXRR results despite some differences in operating conditions suchas sensor position, cell volume, etc. for the two instruments.Although the variation of data in Fig. 4 appears to be linear withtwo slopes in two regions, the quasi steady state data (Fig. 3) clearlyindicate the non-linearity. To take a closer look, we plot of the samedata in logarithmic scale in the inset of Fig. 4.

It can be observed from the inset that two straight lines withtwo different slopes can be fitted with two regions of the data. Thisindicates that the swellibility follows a double power law behaviouras a function of relative humidity and there is a sharp cross overfrom one behaviour to the other around relative humidity value of75% (70% for AFM and 80% for XRR). In the lower humidity regionthe power obtained from the straight line fit was 0.68 � 0.05 for

0 20 40 60 80 100

0

10

20

30

40

50

60

Relative Humidity (%)

Swel

libilit

y (%

)

Initial thickness: 60 ÅInitial thickness: 173ÅInitial thickness: 322Å

Fig. 3. Swellibility of the films as a function of relative humidity. Solid and hollowsymbols represent static and quasi-static data respectively.

XRR and 0.49 � 0.07 for AFM, whereas, at higher humidity regionthese values were 4.81 � 0.31 and 4.60 � 0.73 respectively. It maybe noted that comparison between XRR and AFM data is stronglydependent on the measurement of exact humidity value on thesample surface. Therefore the difference in the values obtained bythe two techniques may be attributed to the inherent limitations ofthe techniques such as chamber size or proximity of the humiditysensor to the sample surface. However, the clear change of theswelling behaviour at certain humidity observed from both tech-niques indicates that some new phenomenon starts to take placearound this value.

AFM was also used to characterize surface morphology evolu-tion as function of the swelling of the polymer film. In Fig. 5 wehave presented the surface roughness of a film as a function ofrelative humidity which clearly shows the invariance of the filmmorphology during swelling. It is interesting to note that the sur-face roughness does not show any change even around 75% RHwhere the scaling law shows a different behaviour. This indicatesthat the effect of swelling is limited only to the interior of the films.Similar surface roughness values were also observed from XRRmeasurements as can be observed from the inset of Fig. 2.

10 20 30 40 50 60 70 80 900.00

0.06

0.12

0.18

0.24

0.30

0.36

0.42

0.48

RM

S ro

ughn

ess

[nm

]

Relative Humidity [%]

Fig. 5. RMS surface roughness as a function of the relative humidity during swelling,measured on 5 � 5 mm images.

M. Mukherjee et al. / Polymer 54 (2013) 4669e46744672

From a quantitative analysis of the XRR curves it is possible todetermine the electron density profile of the film at any RH. Theelectron density of the film exposed to the lowest humidity was0.464 e/�A3 while it becomes 0.420 e/�A3 at RH ¼ 99%. Correlatively,the change in the thickness of the film goes from 322�A at RH¼ 13%to 482�A at RH ¼ 99%. One can thus observe that the film swells byabout 50% while the electron density decreases by about 9.5%. Onecan calculate the amount of water molecules entering the films bycomparing the electron density of the dry and the swollen films. Ifno water intake or addition of solvent mass is considered then thenumber of electrons per unit area of the film is constant at anythickness of the film. The electron density per unit area can beexpressed as the product of the electron density of the film and itsthickness rA ¼ rt, This quantity remains constant for the polymerat all thickness, or in other words when the films expand (notincluding the addition of water) from state 1 to state 2 the productr1t1 ¼ r2t2. Therefore if one knows the electron density r1 of thedry film (polymer only), it is possible to estimate the electrondensity r2 of the polymer (only), at any swollen condition asr2 ¼ r1t1=t2. Here we assume the electron density of the filmsmeasured at the lowest RH (13%) to be equal to that of the dry film.This concept of surface electron density was recently introduced toevidence the trapping of CO2 molecules inside ultra-thin films ofpolystyrene [20].

At swollen conditions the electron density of the film includingwater may be expressed as rpþw ¼ np þ nw=Ats, where np and nware the total number of electrons in polymer andwater respectively,A is the area of the film and ts is the swelled thickness. Using aboverelations one can express the effective electron density of water inthe film as rw ¼ rpþw � r1t1=ts. Knowing the electron density ofbulk water as rbw ¼ 0.334 e/�A3, one can obtain the volume fractionof water in the film as F ¼ rw=rbw.

In Fig. 6, we have plotted the volume fraction of water forsaturated swelling at different RH conditions for the same filmwhose data is shown in Fig. 4. It is interesting to note that volumefraction of water also shows a similar nature that of swellibility as afunction of RH. In this case also there are two power laws with asharp cross over from one to the other around RH value of 75%. Thevalues of the powers were close to those observed for swellibility.In the lower humidity region the power was 0.58 � 0.03 and athigher humidity region this value was 5.01 � 0.47. However, com-parison between Figs. 4 and 6 shows that at all humidity the

0 10 20 30 40 50 60 70 80 90 100

0

10

20

30

40

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.61.6

2.0

2.4

2.8

3.2

3.6

Wat

er v

olum

e fr

actio

n (%

)

Relative Humidity (%)

slope 0.58 0.03Ln(w

ater

frac

tion)

Ln(RH)

slope 5.01 0.47

Fig. 6. Variation of volume fraction of water in a completely swelled film at variousrelative humidity. The straight line fits in the inset shows power law behaviour ofwater volume fraction.

swellibility is larger in magnitude compared to water volumefraction. This indicates that in addition to the contribution of watermolecules there is extra expansion of the polymer films in presenceof solvent. The gradual increase of this difference with humidityalso suggests that this additional expansion is RH dependent. Thedouble power law may be explained in terms of the followingmodel. It is known that there is isolated free volume in all glassysystems. In our earlier study using Positron Annihilation Spec-troscopy we have observed that the dimension of these free vol-umes arew0.5 nm [21]. When films are exposed to humidity, watermolecules adsorb onto the surface and subsequently penetrate intothe free volume or pores of the films and during swelling of thefilms these pores are also swelled. It may be possible that at theinitial stage up to around 75% humidity the individual pores areexpanded/elongated separately. At higher humidity these poresmay be sufficiently elongated to get interconnected and createlarger channels for diffusion of water molecules into the films. Suchabrupt change of pore size or channel lengths may explain theobserved change of power law behaviour in the water intake andswellibility around RH 75% value. In the present method volume ofwater is an indirect measure of the pore volume. Sudden increase inthis volume therefore can be correlatedwith sudden change in porevolume. The justification of our model is based on this logic. It maybe mentioned here that the AFM measurements are unable toobserve any substantial change in the surface roughness at higherhumidity (see Fig. 5). This indicates that either the pores are notresolvable by the technique or they are embedded into the bulk ofthe films.

2.5. Kinetics measurement

To study the swelling dynamics, XRR data were collected as afunction of swelling time allowing acquisition time of about 3 minfor each scan. The counting of swelling time was started as soon asthe flow of dry nitrogen to the chamber (containing K2SO4) wasstopped. The reflectivity data as a function of swelling time for atypical film is shown in Fig. 7. It can be observed from the data thatthe number of oscillations in the same angular range is increasingwith time clearly indicating increase in thickness due to swelling.

In Fig. 8 we have plotted the evolution of humidity and corre-sponding film thickness as a function of swelling time. From thedata, it appears at a first glance that the change of film thicknesssomewhat follows change of humidity. However, to have a correct

0.02 0.04 0.06 0.08 0.10

10-15

10-13

10-11

10-9

10-7

10-5

10-3

10-1

96% RH

90% RH

85% RH

75% RH

66% RH

48% RH

Ref

lect

ivity

qz (Å-1)

14% RH

Fig. 7. X-ray reflectivity data for a typical film at different relative humidity. Each scanwas measured in 3 min.

0 20 40 60 80 100 120

20

40

60

80

100

60

70

80

90

Film

Thi

ckne

ss (

)

Time (min)

Rel

ativ

e H

umid

ity (%

)

RH (%) Film Thickness

Fig. 8. Comparative evolution of relative humidity in the experimental cell togetherwith change of film thickness.

50 100 150 200 250 300 350 4001E-16

1E-15

1E-11

1E-10

1E-9

1E-16

1E-15

1E-11

1E-10

1E-9

v/(film thickness)

norm

alis

ed e

xclu

ded

volu

me

diffu

sion

coe

ffici

ent D

p (cm

2 /sec

)

Thickness (Å)

1.19x10

Fig. 10. Diffusion coefficient and normalized excluded volume parameters as a func-tion of initial film thickness.

M. Mukherjee et al. / Polymer 54 (2013) 4669e4674 4673

understanding about the situation one needs to quantify the dy-namics of humidity and swelling.

It can be assumed that in the beginning of the experiment theenvironment was dry as the relative humidity inside the chamberwas very low. As time progress, the water molecules diffuse fromthe K2SO4 saturated solution container into the atmosphere.Therefore, the increase of humidity as a function of time may betreated as the mass uptake by the environment. IfMt represents themass of water in the atmosphere at time t (or relative humidity attime t) andMsat the same at saturation, then the facts that (a) plot ofMt/Msat vs. t½/L (L is chamber dimension, 5 cm) is linear in the initialphase and (b) the linearity holds for at least up to Mt/Msat ¼ 0.6 thediffusion processes can be considered as Fickian [22]. This kind ofdiffusion can be described by Fick’s second law of diffusion, whichcan be solved considering appropriate boundary conditions fordiffusion into a semi infinite [23] volume exposed to an infinitebath of penetrant for the short time (initial phase of uptake) to read,Mt=Msat ¼ ð2=LÞð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Dwt=pp Þ, where Dw is the diffusion coefficient of

water vapor in the atmosphere. In Fig. 9 we have plotted normal-ized mass uptake, Mt/Msat against square root of time scaled by thecell dimension, t½/L and from the slope of the curve we determinethe diffusion coefficient of water, Dw ¼ 2.3 � 10�2 cm2/s, for thediffusion of water into the dry environment. As there is attractiveinteraction between the polymer and the water molecules, it is

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

DataLinear Fit of CN

orm

alis

ed R

elat

ive

Hum

idity

t1/2/L (sec1/2cm-1)

Dw=2.3x10-2cm2/sec

Fig. 9. Evolution of relative humidity inside the experimental cell as a function ofnormalized time.

likely that oncewatermolecules enter into the pores of the polymerfilms they would be trapped inside. Therefore the humidity insidethe pores of the films would attain the saturated humidity at a ratecomparable to the diffusion coefficient of water molecules in theexperimental chamber.

For quantitative analysis of swelling dynamics we assume thatin presence of solvent vapor all the coiled chains swell indepen-dently. This allows us to study the swelling dynamics in terms ofthe dissipative equation of motion for the end-to-end distance ofthe polymer R, combined with Flory approximation for the freeenergy F(R) in d-dimensions as [24,25],

vRvt

¼ �mvFðRÞvR

¼ �mkBTv

vR

�R2

b2Nþ v

N2

Rd

�(1)

The first and the second terms in the bracket give entropic andexcluded volume contributions to the free energy respectivelywhere b is the monomer length and n (d dimensional volume) is theexcluded volume parameter. The diffusion coefficient for thepolymer chains can be described in terms of chain mobility m usingEinstein’s relation as Dp ¼ mkBT .

The general solution of the above differential equation reads,

RðtÞ ¼ e�2mkBT

Nb2t�Rdþ20 þ vdN3b2

2

�e2ðdþ2ÞmkBT

Nb2t � 1

�� 1dþ2

(2)

with initial condition R(t ¼ 0) ¼ R0, describes the change of the sizeof a polymer coil on swelling as a function of time.

In case of thermal expansion of ultra-thin polymer films, themovements of the polymer chains were observed mainly in thedirection perpendicular to the film surface, other two directionsbeing restricted by the physical boundary of the substrate size [26].In the present swelling study of the polymer films, no spill over ofthe polymer was observed on swelling, indicates that in this casealso the expansion of the film can be considered to be one-dimensional and occurs in the direction perpendicular to the sur-face similar to that of thermal expansion. For one-dimensional caseand considering monomer length b to be 1 �A, Equation (2) reads,

RðtÞ ¼ e�2DpN t

�R30 þ

vN3

2

�e6DpN t � 1

��13

(3)

where N is the degree of polymerization, the ratio of polymer tomonomer molecular weight.

The two parameters obtained by fitting the film thickness vs.swelling time data using Eq. (3) (Fig. 11) for different films are

Fig. 11. Evolution of the film thickness for two environments of relative humidity in thecell, using pure water and saturated solution of K2SO4 as the source of water vapour.

M. Mukherjee et al. / Polymer 54 (2013) 4669e46744674

shown in Fig. 10. It can be observed from the figure that thediffusion coefficients are nearly same for all the films, whereas, theexcluded volume parameters are found to be dependent on filmthickness as.

To study the effect of humidity on the swelling dynamicswehaveperformed dynamical experiments on the same film with twodifferent humidity conditions produced by using pure water andK2SO4 saturated solutions as humidity source respectively. In case ofwater the saturated humidity in the experimental cell was 85.5%,whereas, this valuewas98.5% forK2SO4 saturated solutions. In Fig.11we have shown the swelling dynamics of the film at two differenthumidity. It may be noted that saturated humidity in the cell as wellas the rate of change of humidity or the diffusion coefficients ofwater into the cell Dwwere different for the two cases. The values ofDw calculated using Fick’s law (as shown above) in case of water andK2SO4 were 1.1 �10�2 and 2.3 � 10�2 cm2/s respectively.

It is interesting to note that the diffusion coefficients of polymerchains in the film Dp at two different RH are identical as shown inthe figure. This indicates that the diffusion coefficients of thepolymer chains are independent of the value of RH. Also the dif-ference in the rate of change of humidity (or humidity dynamics) inthe cell does not affect the diffusion dynamics of the chains as Dw

and Dp are different by several orders of magnitude. The result maybe interpreted in terms of the fact that water molecules saturatesthe pores of the polymer very quickly (since the diffusion coeffi-cient of water in the atmosphere is very large as compared to that ofpolymer swelling) and creates nearly identical environment forswelling at all humidity. Whereas the saturation thickness of thefilm at two conditions are widely different. This is attributed to thedifferent values of excluded volume parameter (v/(initial filmthickness), see Figs. 10 and 11) at two different humidity conditions.Since the excluded volume parameter is the measure of separationbetween two neighbouring segments, this will be reflected in thehigher value of this parameter for swelling at a larger humidity.

3. Conclusion

We have studied the swelling behaviour of spin coated poly-acrylamide films at room temperature at different relative humidityvalues in the range of 12e99%. As the thickness of the films increase

due to swelling, the same was monitored using XRR and AFMtechnique at different humidity conditions. Swellibility of the filmswas observed to be independent of thickness of the films. This in-dicates that there was no significant influence of substrate orconfinement on swelling of the polymer. Considering the fact thatthe electron density per unit area is a conserved quantity if no ma-terial is added to a film, we have calculated the volume fraction ofwater for the swelled films at different humidity conditions. Thevolume fraction of water in the swelled films and their swellibilitywere found to follow a double power law behaviour and the tran-sition from one regime to the other was observed around 75% RH. Itis important to establish that the humidity of the chamber does notchange during swelling which was an assumption in our earlierstudy. Here we have shown that the time scale of saturation of hu-midity in the chamber was several orders of magnitude smallercompared to the swelling dynamics. As the films swell differently atdifferent humidity and the excluded volume parameter determinesthe saturated thickness of the films, this parameter was found to bedependent on relative humidity. On the other hand the values ofdiffusion coefficients for the films remains constant at different RHconditions indicating that pores of films saturates much fastercompared to the “speed” of swelling.

Acknowledgements

The work is partially supported by the India-France collabora-tive project (No. 3808-3) supported by Indo-French Centre for thePromotion of Advanced Research (IFCPAR).

References

[1] Lin EK, Kolb R, Satija SK, Wu W-L. Macromolecules 1999;32:3753e7.[2] Keddie JL, Jones RAL, Cory RA. Europhys Lett 1994;27:59e64.[3] Zheng Z, Kuang F, Zhao J. Macromolecules 2010;43:3165e316.[4] Torres JM, Stafford CM, Vogt BD. ACS Nano 2009;3:2677e85.[5] Jeon HS, Dixit PS, Yim H. J Chem Phys 2005;122:104707.[6] Sanchez IC. Physics of polymer surfaces and interfaces. Boston, MA: Butter-

worth-Heinemann; 1992.[7] van Hooy-Corstjeens CSJ, Magusin PCMM, Rastogi S, Lemstra PJ. Macromole-

cules 2002;35:6630e7.[8] Wende C, Schönhoff M. Langmuir 2010;26:8352e7.[9] Lee HJ, Soles CL, Liu DW, Bauer BJ, Wu WL. J Polym Sci Part B Polym Phys

2002;40:2170e7.[10] Silverstein MS, Shach-Caplan M, Bauer BJ, Hedden RC, Lee H-J, Lande BG.

Macromolecules 2005;38:4301e10.[11] Domack A, Johannsmann D. J Appl Phys 1996;80:2599e604.[12] Smith AL, Mulligan Sr RB, Shirazi HM. J Polym Sci Part B Polym Phys 2004;42:

3893e903.[13] Singh A, Mukherjee M. Macromolecules 2003;36:8728e31.[14] Mukherjee M, Singh A, Daillant J, Alain M, Cousin F. Macromolecules 2007;40:

1073e80.[15] Mondal MH, Mukherjee M. Macromolecules 2008;41:8753e8.[16] Singh A, Mukherjee M. Macromolecules 2005;38:8795e802.[17] Mukherjee M, Singh A. Phys Status Solidi B 2007;244:928e42.[18] Daillant J, Gibaud A. X-ray and neutron reflectivity principles and applications.

Berlin and Heidelberg, Germany: Springer; 2009.[19] Winter HT, Cerclier C, Delorme N, Bizot H, Quemener B, Cathala B. Bio-

macromolecules 2010;11:3144e51.[20] Chebil M Souheib, Vignaud G, Grohens Y, Konovalov O, Sanyal MK, Beuvier T,

et al. Macromolecules 2012;45:6611e7.[21] Mukherjee M, Chakravorty D, Nambissan PMG. Phys Rev B 1989;52:848e56.[22] Crank J, Park GS. Diffusion in polymers. London and New York: Academic

Press; 1968.[23] Shewmon Paul G. Diffusion in solids. McGraw-Hill Book Company; 1963.[24] Pitard E, Bouchaud JP. Eur Phys J E 2001;5:133e48.[25] Doi M, Edwards SF. The theory of polymer dynamics. Oxford, England: Oxford

University Press; 1986.[26] Mukherjee M, Bhattachrya M, Sanyal MK, Geue Th, Grenzer J, Pietch U. Phys

Rev E 2002;66:061801.