The ABC of pattern evolution in self-destruction of thin polymer films

DOI 10.1007/s1010500e0002EPJdirect E2, 1–9 (2000) EPJdirect

electronic onlyc© EDP Sciences 2000c© Societa Italiana di Fisica (SIF) 2000c© Springer-Verlag 2000

The ABC of pattern evolution in self-destructionof thin polymer films

Rajesh Khanna1∗, Ashutosh Sharma2, Gunter Reiter1†

1 Institut de Chimie des Surfaces et Interfaces, CNRS, 15, rue Jean Starcky, B.P. 2488,68057 MULHOUSE Cedex, FRANCE

2 Department of Chemical Engineering, Indian Institute of Technology at Kanpur,INDIA–208 016

Received: 17 Apr 2000 / Accepted: 6 Sep 2000 / Published online: 22 Sep 2000

Abstract. We present the first real time observation of the pattern evolution in self-destruction of thin polymer films based on experiments with polydimethylsiloxane filmssandwiched between silicon wafers and aqueous surfactant solutions. Four distinctstages of pattern evolution have been identified: (A) amplification of surface fluctu-ations, (B) breakup of the film and formation of holes, (C) growth and coalescence ofholes and, (D) droplet formation and ripening. Only one of these stages, A, is uniqueto self-destruction of thin films as stages B, C and D are also present in nucleation in-duced dewetting of the film. As similar looking undulating patterns characterize stagesA and C, it becomes imperative to have a full temporal evolution of the pattern toidentify different stages and the likely mechanism of film breakup.

PACS: 47.20.-k, 68.15.+e, 68.10.-m

The destruction and pattern formation in thin fluid films is of central impor-tance in many technological applications (e.g., wetting, adhesion, heterogenousnucleation, colloids, membrane-morphology, dry eye syndromes, opto-electronicdevices) as well as in a variety of physical and biological thin film phenomena(e.g., polymeric and metal coatings, foams, emulsions, flotation). The generalcontours of the mechanics and thermodynamics of thin film instability haveemerged during the last fifty years [1, 2, 3, 4, 5]. Initial surface fluctuations atthe free surface of an initially rather uniform thin film get amplified sponta-neously whenever the second derivative of the excess intermolecular free energy(per unit area) with respect to the local film thickness is negative and theirwavelength is larger than a critical wavelength. This amplification eventuallyleads to the dewetting of the underlying substrate in the form of dry patches[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. Dewetting can also beinitiated by formation of isolated circular holes due to nucleation by defects, dust

∗Present address: Department of Chemical Engineering, Indian Institute of Technology atDelhi, India

†e-mail: [email protected]

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EPJdirect E2, 1–9 (2000) Springer-Verlag 2

particles, heterogeneities etc [13, 11, 12, 21, 22]. Identifying the correct mech-anism of film breakup becomes of enormous significance when stable films aredesired or needed. Obviously, efforts to minimize nucleating factors such as usingcleaner environments will not help if the films under examination are inherentlyunstable. Although the theory to explain the intrinsic amplification of surfacefluctuations and resulting dewetting is firmly in place now [1, 2, 3, 4, 5, 6], theexperimental understanding of the processes, especially the former, lags far be-hind. This disparity between the theoretical and experimental advances has beenmostly due to absence of any realtime direct observation of the initial amplifi-cation despite introduction of sophisticated measuring techniques such as AFMover the years [9, 10, 11, 15]. The current work aims at presenting the completepicture of the film self-destruction including the initial amplification and subse-quent dewetting in order to provide the much needed experimental input to thecurrent understanding of the thin film breakup. In particular it seeks to provideanswers to the following questions:

1. How does the film morphology evolve during different stages of film self-destruction?

2. Can these morphological patterns help in deciding the likely mechanism offilm self-destruction?

The experiments were done on thin (< 200 nm) polydimethylsiloxane (PDMS)films sandwiched between variously PDMS coated silicon wafers and aqueous sur-factant solutions. This system is a suitable candidate to study the self-destructionof thin polymer films as it provides excellent control over intermolecular in-teractions and kinetics [14, 20, 23]. Two types of coatings were used (1) amonolayer of reactive (Si-H terminated) long chain PDMS (molecular weight,Mw,= 78kg/mol; and polydispersity, I, < 1.1) and (2) a bimodal PDMS layercomprising of long chain reactive PDMS (Mw = 122kg/mol, I < 1.1) connec-tors attached to a underlying monolayer of short chain reactive PDMS (Mw =8.8kg/mol, I < 1.1). Both coatings provided a short range stabilizing force due tolong chain molecules chemically endgrafted on previously cleaned and smooth sil-icon wafers. The thickness of the 78k and 8.8k monolayers was found to be about15 and 6 nm, respectively, by ellipsometric measurements [14]. Adding connec-tors increased the thickness of the second coating to about 12 nm. Thin PDMSfilms of various molecular weight PDMS (Mw ranging from 3 to 308kg/mol) wereput on the coated silicon wafers by spincasting dilute solutions of nonreactivePDMS in heptane. Again ellipsometery was used to measure the thickness of thePDMS film. The system was stable in air as the film’s surface stayed smootheven after months of storage but became unstable when air was replaced bywater [14, 17, 20, 23]. It should be noted that the overlying PDMS film wettedthe PDMS coating (wet brush regime). Even as the film surface evolved underthe influence of destructive long range forces, the stabilizing short range forcesguaranteed that a thin film of PDMS remained attached to the coating andtrue-dewetting of the substrate, characterized by a real triple phase contact line,did not occur. In actual experiments the instability was initiated by putting asmall drop (∼ 10µl) of aqueous solution containing surfactant L77 (polyalkenox-ide modified heptamethyltrisiloxane) on the PDMS film. It should be stressed



that adding surfactants changed only the interfacial tension, thereby changingthe length– and time–scales of the evolution, without bringing any qualitativechange in different stages of evolution as compared to films under pure water[23]. Aqueous L77 solutions were used in place of pure water to have convenienttime and lengthscales for the breakup of about 100 nm thick films which wererequired to have sufficient optical contrast especially during the early stages.L77 reduced the interfacial tension by about hundred times to a very low valueof about 0.4 mN/m from about 39 mN/m which is the value for pure water[24].The lowering of the interfacial tension led to a faster amplification of the surfacewaves and smaller lengthscales allowing for good statistical analysis. The surfac-tant concentration was kept at about 5 times the critical miceller concentrationto avoid any Marangoni flow induced complications [25, 26]. The spatio-temporalevolution of the instability and the resulting breakup of the film was observedin real time by optical microscopy and video recorded for later analysis.

Fig. 1 presents the typical evolution of the morphological pattern during theself-destruction of a PDMS film with the help of a time-series of optical micro-graphs. This visual information is complemented by presentation of structuralmeasures of these patterns in Figs. 2 and 3. A “waterfall presentation” of theradially averaged intensities of 2D FFT of the micrographs is presented in Fig. 2to highlight the lateral regularity of the pattern. The position of the peak (qmax)in the curves of Fig. 2 is presented in Fig. 3 to show the evolution of the domi-nant wavelength of the pattern. Fig. 3 also includes the number of isolated holes(n), as a function of time. We now combine the information contained in thesefigures to discuss the evolution of pattern in self-destruction of thin polymerfilms. Four different time regimes viz., A, B, C and D have been identified inthese figures to mark the different patterns and to facilitate the correspondencebetween the figures. Though, the results are presented only for the first kind ofcoating (78k) for illustration purposes, the films on the second type of coating(bimodal brush) also evolved in the same manner indicating the generality ofthe process.

An undulating pattern (image A1 of Fig. 1) emerges from an initially rathersmooth film. This low amplitude pattern amplifies and becomes more pronounced(images A2 to A4 of Fig. 1) as evolution continues. The increasing prominenceof the peak in Fig. 2 during this period shows a clear preference for a distinctwavelength. It should be noted that the dominant wavelength stays constantduring the first phase of evolution (region A in Figs. 2 and 3). While the lateralregularity of the structure is maintained during this period, the amplification isnonhomogeneous with different depressions thinning at different rates as indi-cated by different levels of gray at different depressions (image A4 of Fig. 1).This feature is expected due to the fact that the local rate of thinning at thesethicknesses is mostly governed by the long range interactions whose strengthincreases nonlinearly as the film thins (e.g., the strength of omnipresent vander Waals forces varies inversly as third power of film thickness) whereby anysmall difference in the local thickness results in self-reinforcing vastly differentrates of thinning. It may be noted that most of the amplification has occured inthe last 30 seconds of this stage which is only about 10% of the total durationof the stage. This also confirms the theoretical predictions [2, 3, 4, 5, 6] that



E: Extra

D: Droplets

C: Coalescence

B: Breakup

A: Amplification

1 2 3 4

Fig. 1. Optical micrographs of evolution of morphological pattern during theself-destruction of a 85 nm thick and highly viscous (1000 Pa.s) PDMS film ona silicon wafer coated with a 15 nm thick monolayer of endgrafted PDMS (78k)molecules. The levels of gray indicate the local thickness of the film with darkerregions representing thicker portions. Different micrographs (from left to rightand top to bottom) correspond to times (in sec.) 200, 230, 245, 260, 275, 300,315, 330, 420, 435, 500, 570, 660, 840, 1110 and 1680, respectively. The last stripE shows results for another film of a different thickness (110 nm) and viscosity(100 Pa.s) at times 150, 170, 190 and 220 seconds, respectively. The area shownin each image is 25 × 25µm2

the amplification is slow in the beginning whereby the surface fluctuations getarranged on a dominant wavelength but later on enters a nonlinear explosivephase of growth.

This amplification of surface fluctuations is followed by the process of “pseudo-dewetting” initiated by the “touch-down” of the depressions at the minimum



1 2 3 4 51.0

2.0

2.5

time

D

C

B

A

Inte

nsity

[a

.u.]

wave vector, q [µm-1]

Fig. 2. A “waterfall presentation” of the average radial intensity of 2D-FFT ofthe images (stripes A to D) shown in Fig. 1. The different curves correspond toincreasing times (in sec) 200, 215, 230, 245, 260, 275, 300, 315, 330, 360, 390,420, 435, 500, 570, 660, 840 and 1110, respectively. The dotted line roughly goingthrough the peaks of different curves is to guide the eye

thickness (determined by the grafted layer) to form isolated circular holes (whiteportions), with the relatively deeper depressions touching earlier (images B1 andB2 in Fig. 1) and others following later (image B3 in Fig. 1). The variation ofnumber of holes with time is also presented in Fig. 3 to highlight the existenceof a finite time window for the formation of holes. This phenomenon is moreclearly shown in the stripe E, of images in Fig. 1 which show results for a 25nm thicker film. It should be remembered that a thin film of polymer alwaysremains attached to the coating at the bottom of these holes due to short rangestabilization by the polymer brush. This asynchronous formation of holes is animportant phenomenon as it opens up the possibility of a growing hole disturb-ing the depressions around it and dictating the local pattern, a phenomenon towhich not much attention has been directed at until now [22]. It is also possiblethat the growing hole fills up some of the lagging depressions. This is more likelyto happen in the case of an additional attractive force at shorter range whichcan significantly increase the contact angle and the velocity of the hole growthwithout much effect on the timescale for the formation of holes, which is mostly(if not entirely) governed by the long range forces[1, 2, 3, 4, 5]. In the present ex-periments, the short range repulsion provided by the coating makes this scenarioless likely and indeed, visual tracking of depressions as well as a rather constant



200 1000 20001.0

2.0

2.4DCBA

n(t)

[µ

m-2]

q max

[µ

m-1]

time [sec]

0.00

0.04

0.08

0.12

Fig. 3. The evolution of the position of the peak (qmax, filled circles) of thecurves shown in Fig. 2 and number of isolated circular holes (n, open squares)with time

qmax during this time window (region B of Fig. 3) show that there is a one toone correspondence between initial depressions and circular holes. It should bestressed again that this equivalence may not hold for other systems with strongshort range attractive forces.

The above presented morphological evolution is now supplemented by a com-parison of the length and timescales with theoretical estimates [1, 2, 3, 4, 5, 6].To this end the data is put through a very stringent length and timescale con-sistency test as introduced in one of our recent works[23]. For a general form ofpotential, the wavevector (qmax) of the undulating pattern (regime A) and thetime of formation of isolated holes (τ) are given by [2, 5, 6]

q2max = P/2γ (1)

τ ≈ 12ηγ/(h3P 2) (2)

P is the force per unit volume at the initial film thickness (h), γ is the interfacialtension at the film bounding medium interface and η is the viscosity of the filmliquid. The relevant values for the above experiment are, h = 100 ± 1 nm, γ =0.4±0.1 mN/m, η = 1000 Pa.s, qmax = 2.2±0.03 µm−1 and τ = 300±15 seconds.On substituting these values, the two equations (1) and (2) independently givethe following similar values of the force, P : 3.8± 0.08× 109N.m−3 and 4± 0.4×109N.m−3, respectively. The larger error in the value obtained from Eq. (2) is apropogation of the error in the value of τ which reflects the existence of a finitetime window for formation of holes. This represents a strong support for thevalidity of the theory of self-destruction of thin liquid films [1, 2, 3, 4, 5, 6].



The circular holes formed in regime B continue to expand laterally andquickly loose their axisymmetric shape due to coalescence with other growingneighbors (image C1 of Fig. 1). The repeated coalescence of holes results in longpseudo-dewetted channels which together with the long ridges of polymers givethe appearance of a secondary undulating pattern (images C2 to C4 of Fig. 1).The appearance of the second undulating pattern is a very likely source of con-fusion in experiments involving breakup of thin polymer films especially if thepreceding stages of the evolution could not be resolved properly. This can possi-bly happen due to extremely fast kinetics and/or insufficient contrast in relationto the observation technique which was employed. In that case, the evolutionmay be erronously thought to follow the pathway of undulating pattern directlygoing to drops. This, among other false conclusions, may also lead to a wrongestimate of the the form and magnitude of excess intermolecular force field inthe vicinity of the initial film thickness [6].

More importantly, any such confusion may also lead to wrong conclusionsabout the mechanism of initial film breakup as to whether the breakup is anintrinsic feature (self-destruction) of the system or is it induced by externalfactors (nucleation). It is clear now, that an undulating pattern can result fromdifferent causes and thus cannot be taken as a sufficient proof for spontaneousbreakup [10]. An undulating structure (the second) can very well be caused bygrowth and coalescence of nucleated holes. So, how can one differentiate betweenthe two undulating patterns? The fact that the second undulating pattern hasa larger amplitude and wavelength when compared to the first (region C inFigs. 2 and 3) and the wavelength of the first is directly related to the excessintermolecular force per unit volume does not help for the lack of appropriatereference values. However, one absolute criterion for differentiating is that thewavelength of the second undulating pattern increases continuously with timewhereas it stays constant in the case of the first.

The long cylindrical ridges of this structure then undergo fragmentation (se-ries D of Fig. 1) possibly due to Rayleigh instability of long cylinders, and breakup in small droplets which become increasingly spherical as time progresses (im-age D4 of Fig. 1). The structure now resembles an array of spherical dropletsarranged on a thin near equilibrium thickness intervening film. Ripening of thesedroplets occurs by material transport via the intervening film until a thermo-dynamic equilibrium state of a single drop is reached, a scenario similar to thecollapse of a smaller bubble if connected to a bigger bubble. Of course, in thecase of true-dewetting where the droplets are separated by dry substrate, ripen-ing of drops can not occur for the lack of any connection to transfer polymeramong them.

It is now clear that self-destruction of a thin polymer film is a combinationof two serial processes viz., amplification of initial surface fluctuations and sub-sequent dewetting of the underlying substrate. There is a finite time windowduring which the holes are formed and both processes overlap. The evolution ofmorphological pattern during the whole process can be summarized as follows

A Initial largely uncorrelated surface fluctuations (NOT visible) organize intoa shallow undulating pattern on a distinct characteristic wavelength whichis consistent with the linear theory. The pattern amplifies without change in



its lengthscale. The amplification is not homogeneous and some depressionsare amplified faster than others.

B The depressions of the undulating pattern develop into isolated circularholes. The propogation of the nonhomogeneity in amplification results indifferent depressions developing into holes at different times. The length-scale of the pattern still remains the same with a one to one correspondencebetween the depressions and the holes.

C The holes expand laterally and coalesce to form a second undulating pat-tern which coarsens in time. When compared to the first undulating pat-tern, this pattern has a much larger amplitude and larger characteristicwavelength which continuously increases in time.

D The long and high ridges of this pattern fragment into a collection ofspherical droplets arranged on an almost equilibrium thickness film. Thesedrops may ripen to the final state of a single drop or may remain frozenin time depending on whether they are interconnected or not.

Of all these stages only the stage A is an exclusive feature of the self destruc-tion of the film as all other stages (B, C and D) appear also during nucleationinduced destruction of the film. As similar looking undulating patterns whichcharacterize stages A and C can be contrasted to each other only by a time-varying wavelength, a temporal evolution of the pattern is necessary to identifythe various stages and to be sure that the film is self-destructing. Once the self-destructive nature of the film is established, then valuable information about thestrength of breakup causing excess intermolecular forces can also be gatheredby matching experimental results and theoretical predictions. The present workprovides a comprehensive experimental support in form of matched morpho-logical pattern evolution, length– and time–scales to the theory of intrinsicallyunstable thin liquid films and thus helps in a better interpretation of experimentsinvolving breakup of thin films.

Acknowledgements

We are indebted to Philippe Auroy for providing us with the endfunctionalizedPDMS-molecules. This work was supported by the Indo-French Centre for thePromotion of Advanced Research/Centre Franco-Indien Pour la Promotion dela Recherche.

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The ABC of pattern evolution in self-destruction of thin polymer films

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