VOLUME 80, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 30 MARCH 1998
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Dewetting of an Evaporating Thin Liquid Film: Heterogeneous Nucleationand Surface Instability
Uwe Thiele, Michael Mertig, and Wolfgang PompeInstitut für Werkstoffwissenschaft, Technische Universität Dresden, D-01062 Dresden, Germany
(Received 13 November 1997)
Film rupture as the initial stage of dewetting is investigated for a volatile, spin-coated nonwetting filmDuring structure formation in the liquid film the film thickness is continuously reduced via evaporationThe dynamical character of the experiment allows the study of hole formation caused by distinct ruptumechanisms occurring at different film thicknesses. Both heterogeneous nucleation for thick filmswell as spinodal dewetting for film thickness below 10 nm have been observed. The balance betwboth processes can be shifted by controlling the ambient humidity. The structures resulting from firupture are quantified with respect to their different geometrical properties. For the first time we finthat spinodal dewetting is caused by destabilizing polar interactions. [S0031-9007(98)05676-2]
PACS numbers: 68.15.+e, 68.45.–v, 68.55.–a
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The wetting behavior of films is of central importancefor thin film technology since it determines the homogeneity of thin films and coatings [1–3]. Controlled dewettingcan be employed to pattern thin films on the nanometscale as was recently demonstrated by the productionbiomolecular coatings with a defined structure for medicapplications via spin coating of protein solutions [4].
Investigations of thin nonvolatile liquid films on non-wetting substrates have shown that dewetting takes plain three successive phases: rupture of the film, growththe holes resulting in the formation of a polygonal nework of straight liquid rims, and the decay of rims viaa Rayleigh instability. The growth dynamics of singleholes is well understood [5], whereas the understandingfilm rupture as the initial stage of dewetting remains insufficient. From theoretical considerations, two possibrupture mechanisms have been discussed [6]: first, herogeneous hole nucleation due to defects in the liqufilm [7], and, second, spontaneous rupture under the inflence of long range molecular forces [8], known as spinodal dewetting. These forces can destabilize a thin fil(thickness,h , 100 nm) by causing surface fluctuationsto grow exponentially. Rupture takes place on a lengscale corresponding to the wavelength of the surface udulation whose amplitude increases most rapidly. In thcase of an apolar Lifshitz–van der Waals interaction, thwavelength scales with the square of the film thickne[8]. In addition, polar interactions may become significant for systems such as aqueous solutions at the smalfilm thickness (h , 10 nm), either stabilizing or destabi-lizing the film [9].
Up to now, experimental investigations of film ruptureexist only for apolar films. The system studied in mosdetail is polystyrene (PS) on silicon [1,10]. Howeverwith regard to the two rupture mechanisms mentioneabove the experimental observations hitherto presentconflicting picture. An observedh24 dependence ofthe density of initially formed holes has been take
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as evidence for film surface instability [1]. However,recent investigations on PS films show that the spatiseparation of the holes is not correlated as would bexpected for spontaneous rupture at the wavelengththe fastest growing mode [10]. A novel approach tgain insight into film rupture is to realize experimentaconditions which assist the simultaneous occurrenceboth rupture mechanisms, as reported recently for thmetal films on fused silica substrates after melting bylaser pulse [3]. In this case, the liquid metal dewets fromthe substrate within a small time window before the filmresolidifies. In addition to large circular holes assigneto heterogeneous nucleation, the appearance of smholes with a characteristic wavelength proportional toh2
has been observed, giving strong evidence of spinoddewetting. The investigations of both PS and metal filmhave been carried out at a constant film thickness ofh .
10 nm, whereby this lower thickness limit arises from therequirement that the film should be homogeneous.
In this Letter, we report on a novel dynamical dewettinprocedure whereby a spin-coated, nonwetting thin film oa volatile liquid on a solid substrate is continuously reduced in thickness by evaporation. Under the conditiothat the characteristic time constant for viscous processis much smaller than that of evaporation, structure fomation in the liquid film is dominated by dewetting andnot by the evaporation itself. Here, while the general scnario of dewetting is the same as that mentioned abovthe dewetting process competes with the ongoing thinninof the film, which is accompanied by a continuing holeformation.
In this way a superposition of structures is arrived awhose evolution is initiated at different film thicknessesThis dynamical dewetting scheme therefore possesses tadvantages: first, it allows the simultaneous observatioof both rupture mechanisms on one and the same sampand, second, it enables for the first time the study othe structure development for films ath , 10 nm not
VOLUME 80, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 30 MARCH 1998
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accessible before by any other technique. The evaporaspeed of the solvent, controlled by its partial pressuallows control of the rate of film thinning in comparison tthe characteristic times of both rupture and hole growIn this way the balance between the different ruptumechanisms can be altered. The resulting film structuare visualized by a small quantity of macromoleculesthe solvent that dry-in on the substrate and thus decorthe finally developed film structure.
The dewetting experiments were performed withmonomeric collagen solution (protein concentratio0.2 mgyml) in 0.1 M acetic acid (pH 3). In some casesthe collagen monomers were denatured by warmingprecursor solution to 50±C for 30 min. Freshly cleavedhighly oriented pyrolytic graphite (HOPG) has been usas the substrate (contact angle of the precursor,u 75±).Collagen films with an initial thickness of about10 mmwere prepared by spin coating under controlled relatihumidity between 0% and 90% at room temperatuThe films dry within tens of seconds. The final filmstructures were examined by scanning force microsco(SFM) operating in tapping mode using a NanoScope I(Digital Instruments). In comparable experiments wia very low protein concentration on mica, immobilizesingle collagen molecules with a diameter of 1.5 nm andlength of 300 nm could be imaged [4], indicating that thmonomers are not damaged during sample preparation
Figure 1 (left part) shows a series of SFM imagescollagen films prepared under different ambient humiity conditions. A transition from structures consisting osome large, quasicircular holes embedded in a homoneous pattern of very small holes [Fig. 1(a)] towards fuldeveloped homogeneous polygonal networks [Fig. 1(is observed with increasing humidity. To quantify the paterns, the distribution functions corresponding to the aroccupied by holes belonging to a certain class of holeameters (HDF) have been calculated and plotted inright part of Fig. 1. We have chosen this particular reresentation, where the distribution function correspondsthe product of number of holes per class multiplied by taverage area of the class, in order to evaluate the retive contributions of a limited number of larger holes ia background of numerous small holes. At 15% humiity the HDF exhibits two well separated peaks at 50 a400 nm. The position of the second peak shifts steadto larger diameters with increasing humidity. At the samtime the height of the rims around the larger holes icreases from about 3 to about 8 nm (not shown). Bothe increasing diameter of the holes and the heightenof the accumulated material along their perimeter indicathat the time the large holes have to grow increases wincreasing humidity. In contrast, the position of the firpeak at 50 nm does not depend on humidity. Howeverdoes vanish with increasing humidity.
The pronounced bimodality of the HDF at low humidity clearly indicates the occurrence of two distinct ho
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FIG. 1. Series of images of collagen films prepared at different humidities: (a) 15%, (b) 60%, (c) 82%, and (d) 88%. Left:SFM images (5 mm 3 5 mm) in height mode. Right: Corre-sponding area weighted diameter distribution functions (in arbtrary units).
formation mechanisms. In particular, the completely different dependencies of the distributions of the larger ansmaller holes on humidity, as well as the entire suppression of smaller holes at higher humidity suggest that thtwo hole types emerge at different film thicknesses. Wassign the larger holes to film rupture due to heterogeneous nucleation at defects. Step lines between neighboing monolayer terraces of the HOPG are a probable defesource. This is supported by the observation that largeholes accumulate in the vicinity of these step lines whethe step height is of the order of a few monolayer distances. On the contrary, we assign the 50 nm diametholes to spinodal dewetting caused by destabilizing polar interactions. These interactions control the structurformation at film thicknesses below 10 nm. As is analyzed later on in more detail, in the present case the apol
VOLUME 80, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 30 MARCH 1998
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interactions stabilize the film, which would lead to the observed deep minimum between the two peaks in the HDat low humidity.
The hypothesis that the film rupture mechanisms dicussed above take place at different film thicknessesstrongly supported by the observation that the balanbetween the different predominant mechanisms canvaried by altering the ambient humidity. At high hu-midity the evaporation rate of the precursor solution ilow. Thus, early in the process of film rupture nucleated holes have time to grow until neighboring holes meand form common rims of polygonal networks as seenFig. 1(d). With decreasing humidity the time being available for hole growth reduces whereby the film structuryields to holes with smaller diameters. Consequently, thholes become increasingly isolated, and the area occupby these holes decreases. That is, at high humidity heerogeneously nucleated holes may conquer the whole abefore the remaining film gets thinner than 10 nm. Inthis case the formation of additional holes by spinodadewetting cannot take place. If, however, nonrupturearea remains when the thickness reaches the range whthe destabilizing polar interactions become dominant, thfilm ruptures at once due to spinodal dewetting leadingthe bimodal film patterns as observed at humidity belo70% [see Figs. 1(a) and 1(b)].
In the case, in which the thin film undergoes spinodadewetting at the wavelength of the fastest growing modone expects a well developed short range order in thspatial hole distribution. To prove this, we have calculatethe pair correlation function of the mass centers of all hole(PCF). Figure 2 shows the PCF of a sample prepared15% humidity. The PCF exhibits a pronounced maximumatr0 50 nm. Further peaks are obtained at about2 3 r0and 3 3 r0. This result is in agreement with the valuederived from the first maximum of the HDF [see Fig. 1(a)]
FIG. 2. Pair correlation functions of the mass centers of thholes of the same sample as shown in Fig. 1(a) (solid line) anof denatured collagen (dashed line). In the inset the correlatiofunctions of the sample shown in Fig. 1(c) (solid line) and oa model hard-core Poisson distribution (dash-dotted line) aplotted. The correspondingr0 values are given in the text.
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Again, to make the difference between smaller and largholes evident, we have calculated the PCF for the samshown in Fig. 1(c) (82% humidity), where hole formatiois dominated by heterogeneous nucleation. The resulplotted in the inset of Fig. 2. Here, the PCF exhibits onone less pronounced peak atr 0
0 156 nm. It decreasescontinuously forr . r 0
0, quickly approachinggsrd 1.This behavior can be reproduced by modeling the PCof a hard-core Poisson distribution of points [11], drawas a dotted line in the inset. The observed discrepanat r , r 0
0 can be explained by the fact that a “soft-core[12] rather than a hard-core hole distribution is obtainein a dynamical dewetting experiment, resulting fromdecrease of the critical hole nucleation radius causedthe decreasing thickness of the evaporating film.
Since the characteristic sizes of the observed film pterns have been found to be of the same order as the lenof the collagen molecule used to decorate the developfilm structures, it seems possible that the film structure fomation itself might be influenced by the presence of colagen in the precursor. If this were the case, one wouexpect the largest effects for the surface instability becauthe observed wavelength for this process is much smathan 300 nm. To investigate this, all of the above expements have been repeated with denatured collagen.size of the macromolecule decreases due to the changthe conformation into a random coil accompanied by a rduction of the mechanical stiffness of the molecule. Wdid not observe general differences in the experimentstween the two collagen specimens, indicating that the oserved structure formation is an intrinsic property of thsolvent (water) HOPG system. The first peak of the PCof denatured collagen prepared at 15% humidity (Fig.dashed line) is observed at 53 nm. Thus, rupture of tfilms due to the surface instability takes place at very simlar characteristic wavelengths in both collagen specimeproving that the size of the molecules does not directly ifluence the hole formation process. However, as indicaby a larger ratio of the amplitude of the first maximum tthe amplitude of the first minimum in the PCF, the structuof the denatured films appears more developed, as laramplitude ratios are usually taken as a sign for a more pnounced pair correlation [12]. This result follows as a drect consequence of the reduced mechanical stiffnessthe denatured collagen molecule—allowing the molecuto follow movements of the solvent on the substrate duing structure formation more easily. However, we nevobserved coalescence of holes, which is a result of the sbilization of the rims by the collagen molecules. Structustabilization is one of the advantages of the method of dnamical dewetting described here, since it allows the oservation of features generated in the early stages of fiformation.
The appearance of a surface instability in thin filmcan be described by hydrodynamics within the lubricatioapproximation of the Stokes equation under considerat
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VOLUME 80, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 30 MARCH 1998
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of long range molecular interactions [8]. The timeevolution of the film thickness can be derived fromthe partial differential equation,ht 2sh3y3hsssghxx 1
Pshddddxdx, where subscriptsx andt denote spatial and timederivatives, respectively,h is the effective viscosity,g isthe surface tension, andPshd is the thickness-dependentdisjoining pressure [7,13]. A linear stability analysisyields the wavelength of the fastest growing model 2p
p2gsdPydhd21, and its typical rupture time,
t 6hgyh3sdPydhd22. l only exhibits nonimaginaryvalues if the argument of the square root is positiveThat is, the film is unstable fordPydh $ 0 and stableotherwise. The disjoining pressure containing the polaand apolar interaction contributions is given by [9]
Pshd 2SAPd2
0
h31
SP
lefsd02hdylg. (1)
Here d0 0.158 nm is the Born repulsion length, andl is the correlation length of a polar fluid. For wa-ter, l is approximately 0.6 nm [9]. SP and SAP arethe polar and apolar components of the total spreading coefficient,S SAP 1 SP gscosu 2 1d, whereu
is the macroscopic contact angle. From Eq. (1) it cabe seen that film rupture due to surface instability maonly occur if at least one component ofS is negative.The apolar componentSAP is derived from the effectiveHamaker constantA of the air–thin film–substrate sys-tem,SAP 2Ay12pd2
0 , whereA can be calculated fromthe individual constants of water (W) and graphite (G)by the sum rules:A AWW 2 AGW ø
pAWW s
pAWW 2p
AGG d [13,14]. Applying this formalism to the systemwater on graphite studied here (u 75±, g 72.2 3
1023 Nym, AWW 4.38 3 10220 N m, AGG 47.0 3
10220 N m [15]) yields S 253 3 1023 Nym, SAP 106 3 1023 Nym, andSP 2159 3 1023 Nym. Con-sequently, the apolar part of the interaction acts stabilizing, whereas the polar contribution destabilizes the filmThe polar interaction becomes dominating forh , hC,wherehC can be calculated from Eq. (1) under the condition dPydh 0. For l between 0.5 and 0.8 nmhC isbetween 5 and 10 nm.
The driving force grows exponentially with decreasingfilm thicknessh , hC, leading to exponential decrease ofbotht andl. Thus,t may become much smaller than thetypical evaporation time, yielding to spontaneous rupturof the remaining film. However, to give an estimate ofthe rupture time, one has to make a realistic assumptiofor the viscosity of the solution, which might become veryhigh for the last stages of solvent evaporation and caunfortunately, not be directly measured for those highcollagen concentrations. On the other hand, due to thexponential dependency of Eq. (1), a realistic estimate o
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the lower bound of viscosity will already yield a goodassessment of the rupture time. Assumingh ø 1000 Pa s(derived by an extrapolation from low concentration dat[16]), t becomes smaller than the evaporation time of thremaining liquid, which is typically of the order of tenthsof a second, at a film thickness between 2 and 6 nmWith these values the corresponding wavelength of thinstability can be estimated to be between 20 and 80 nmrespectively. This is in good agreement with the observevalue of 50 nm.
In conclusion, in dynamical dewetting experiments whave observed two coexisting film rupture mechanismoccurring at different film thicknesses down to below10 nm. The film structures exhibit distinct spatial orderholes initiated by heterogeneous nucleation at defecare randomly distributed, whereas holes resulting fromspinodal dewetting exhibit a well developed short rangorder with a periodicity that corresponds to the calculatevalue taking polar interactions into consideration.
We wish to thank J. Bradt, D. Klemm, and H. Wen-drock for assistance in the experiments and geometricanalysis of film structures. We thank P. Leiderer for valuable discussions and M. S. Golden for a critical reading othe manuscript.
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