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Letter Cite This: ACS Macro Lett. 2017, 6, 1296-1300

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Time Allowed for Equilibration Quantifies the Preparation Induced Nonequilibrium Behavior of Polymer Films Sivasurender Chandran,*,† Rishab Handa,† Marwa Kchaou,‡ Samer Al Akhrass,‡ Alexander N Semenov,¶ and Günter Reiter†,§,∥ †

Institute of Physics, University of Freiburg, Herman Herder Str. 3, Freiburg, 79104, Germany Ingénierie des Matériaux Polyméres IMP - UMR CNRS 5223, Université Claude Bernard Lyon 1, Villeurbanne Cedex 69622, France ¶ Institut Charles Sadron CNRS, UPR 22, rue du Loess - BP 84047, F-67034, Strasbourg Cedex 2, France § Freiburg Center of Interactive Materials and Bioinspired Technologies, University of Freiburg, 79110 Freiburg, Germany ∥ Freiburg Materials Research Center, University of Freiburg, 79104 Freiburg, Germany ‡

S Supporting Information *

ABSTRACT: Performance and properties of materials may strongly depend on processing conditions. This is particularly so for polymers, which often have relaxation times much longer than the processing times and therefore may adopt preparation dependent nonequilibrated molecular conformations that potentially cause novel properties. However, so far it was not possible to predictably and quantitatively relate processing steps and resulting properties of polymer films. Here, we demonstrate that the behavior of polymer films, probed through dewetting, can be tuned by controlling preparation pathways, defined through a dimensionless parameter W , which is the appropriate preparation time normalized with the characteristic relaxation time of the polymer. We revealed scaling relations between W and the amount of preparation-induced residual stresses, the corresponding relaxation time, and the probability of film rupture. Intriguingly, films of the same thickness exhibited hole nucleation densities and subsequent dewetting kinetics differing by up to an order of magnitude, indicating possibilities to adjust the desired properties of polymer films by preparing them in appropriate ways.

T

conformations and the resulting properties of polymers are still missing. Here, we present a systematic study that allows to quantify changes in macroscopic behavior of polymers induced by a controlled variation of preparation pathways. To this end, we have employed spin coating, an often used and highly versatile film preparation technique, and varied the operation parameters. For a quantification of processing-induced changes in properties, we relied on dewetting, a rheological approach allowing the determination of the viscoelastic behavior of polymer films.12,20 Dewetting of the polymer fluid is initiated by the stress-driven nucleation of circular holes whose growth rate is controlled by the balance of viscoelastic and capillary stresses. It has been demonstrated previously that variations in dewetting velocity genuinely and sensitively report preparation-induced differences in rheological properties of polymer films.12,21−25 We have performed experiments on films of atactic polystyrene (Mw = 524 kg/mol, Đ = 1.04), spin coated onto silicon wafers coated with a layer of adsorbed polydimethylsiloxane (PDMS), which assured slippery substrates.22,23 We have performed dewetting experiments at a temperature Tdew = 190 °C on films of thickness ≈ 90 nm, obtained by spin coating at

he art of enhancing performance and stability of large scale structures via appropriate processing conditions is being developed since antiquity, with an enhanced interest in recent times.1−7 For example, strength and hardness of the mighty swords of Merovingian Franks and Vikings have been related to the presence of fine carbon nanopatterns at their edges, introduced by spinodal decomposition during ingeniously conducted quenching of martensitic steel with high carbon content.1 Thus, processing can generate nonequilibrium features on various length scales, which may control properties and performance of materials.1−7 However, nonequilibrium smallscale structures often have short life times, causing temporal changes in properties and thus limit the usability of such materials. In this context, the enormously long intrinsic relaxation times of polymers may be considered as an advantage, as they may allow for long-lasting metastability of processinginduced nonequilibrium structures,5−10,12−15 which may control macroscopic properties of polymers. Accordingly, correlations between processing conditions and resulting properties of polymers have received enormous attention.5−11,16,17 For example, employing (fast) processing technologies like gelspinning or extrusion are known to improve material properties.16,17 Moreover, some intriguing behavior of polymer films are often qualitatively linked with preparation-induced nonequilibrium conformational states.12,18,19 However, quantitative correlations between preparation-induced variations in chain © XXXX American Chemical Society

Received: October 16, 2017 Accepted: October 30, 2017

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DOI: 10.1021/acsmacrolett.7b00815 ACS Macro Lett. 2017, 6, 1296−1300

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ACS Macro Letters

Figure 1. Films of similar thickness exhibit systematic differences in behavior: Optical micrographs (648 × 484 μm2), taken at tann = 400 s, showing the difference in rupture probability of films of thickness h ≈ 90 nm, obtained by spin coating at (a) ω = 500 rpm and (b) ω = 12000 rpm. Nucleation of the holes is a random process and (c) exhibits the radius (R) of the holes as a function of dewetting time (tdew) for different holes that are nucleated after different delay times (tdelay). (d) Semilogarithmic representation of the corresponding early stage dewetting velocities (vi(tdelay)) vs tdelay. Continuous lines in (d) are fits to the data based on eq 1. The horizontal dashed line indicates the limiting value vi(∞) measured for holes nucleated at times much larger than the relaxation times (τres), while the horizontal dotted lines indicate the dewetting velocities of the holes nucleated in the corresponding films at tdelay = 0. The residual stresses σres, derived from (vi(0) − vi(∞))/vi(∞) (depicted by the double-sided dashed arrows) and τres (deduced from eq 1) are also indicated.

rotation speeds ω = 500 and 12000 rotations per minute (rpm) with appropriately adjusted concentrations of the toluene solutions (Supporting Information (SI): Figure S1). Figure 1a,b shows representative optical micrographs (SI: Figure S2), taken after an annealing time tann = 400 s at Tdew. Clearly, the number of holes formed in the film prepared at ω = 12000 rpm was far higher than for the film prepared at ω = 500 rpm, suggesting that the probability of film rupture (nucleation of holes) increases with ω. We note that equilibrated or aged films of similar thickness do not show any holes.21 Further, as captured in Figure 1c, radius (R) of the holes nucleated after longer delay times (tdelay) increased more slowly with dewetting time tdew = tann − tdelay. Surprisingly, the early stage dewetting velocity (tdew → 0) of the initial holes (i.e., tdelay → 0) in the film prepared at ω = 12000 rpm was much larger than for the initial holes in the film prepared at ω = 500 rpm. For both films, the early stage dewetting velocity vi(tdelay) (determined at tdew = 10 s) decreased exponentially with increasing tdelay (Figure 1d), reflecting the relaxation of preparation-induced residual stresses (σres).12,22,23 During rapid evaporation of the solvent in the course of spin coating, (highly) nonequilibrated conformations of the polymer chains got frozen-in. The thereby generated force (per unit area) σres can be viewed as molecular springs under tension. It is shown22−24,26 that describing the data in Figure 1d with a simple exponential function allows to quantify σres and the time taken for its relaxation (τres), parameters characterizing the impact of processing conditions: ⎛ tdelay ⎞ vi(tdelay ) = (vi(0) − vi(∞)) ·exp⎜ − ⎟ + vi(∞) ⎝ τres ⎠

stresses with respect to capillary stresses.24,26 The here presented dewetting studies allowed for a time resolution of about 1 s. Hence, we only could detect residual stresses that remained for times longer than 1 s. We cannot exclude that higher stresses may have existed at tdelay < 1 s. We note, however, that the order of magnitude of values of σres deduced in Figure 1d is well corroborated by complementary experiments.28−30 Since the thickness of the films used in Figure 1 were similar, the observed differences are attributed to nonequilibrated polymer chains in the spin-coated films varying with the chosen preparation pathways (SI: Supplementary text and Figure S4). To clearly demonstrate the importance of preparation pathways, systematic dewetting experiments were performed on films of various thicknesses (h = 80−300 nm) obtained by two complementary preparation methods: (1) Varying the initial concentration (c) of the solution used for spin coating at ω = 500 rpm and (2) spin coating solutions of a given c at different ω (≥500 rpm), yielding thinner films for higher ω. Results from dewetting experiments performed at Tdew = 190 °C are summarized in Figure 2. All raw data used for obtaining Figure 2 are shown in SI (Figures S1−S13). Figure 2 clearly shows that for a given thickness σres and τres can take up widely different values. While films prepared along method (1) covered only a rather small range of σres and τres with h, significantly stronger variations of σres and τres were found for films prepared by method (2). Generally, σres decreased and τres increased with increasing h, consistent with previous observations,23 but in contradiction to some other reports.29,30 Even for films of similar h (indicated by vertical dashed lines in Figure 2), σres and τres may vary by orders of magnitude. In addition, the maximum number of nucleated dewetting holes Nmax (measured at tann = 400 s) showed a similarly strong variation, also depending on the chosen preparation pathway (see Figure 2c). In general, Nmax increased with decreasing h, in accordance with published data.31 Thus, the experiments shown in Figures 1 and 2 clearly demonstrate that the behavior of polymer films is not governed by film thickness only, reflecting that films of similar thicknesses can be prepared along widely varying pathways. Here, we explore the possibility to integrate all factors influencing the properties of polymer films into a single preparation parameter characterizing and ultimately predicting the resulting behavior.

(1)

Holes nucleated after complete relaxation of σres, that is, at tdelay ≫ τres, dewetted at a constant velocity vi(∞), reflecting the behavior of equilibrated polymeric melts (Newtonian fluids).22 Under such conditions, dewetting is purely driven by capillary stresses (σcap), given by the ratio of spreading coefficient (|S|) over film thickness (h) (σcap = |S|/h, with |S| = γf(1 − cos θ)).12,22−24,26 In the following, we have used values of the surface tension of PS with air (γf) from literature22,27 and a contact angle θ ≈ 0.5 rad, as obtained from atomic force microscopy measurements (SI: Supplementary text and Figure S3). Accordingly, the ratio vi(0)/vi(∞) = (σres + σcap)/σcap is a measure of total driving 1297

DOI: 10.1021/acsmacrolett.7b00815 ACS Macro Lett. 2017, 6, 1296−1300

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until complete evaporation of the solvent, defined by ttr, should be considered. An alternative possibility assumes that at initially low concentrations polymers are equilibrated. However, in the course of solvent evaporation, concentration, and the corresponding relaxation time increase. When the time tev for evaporating the remaining solvent becomes shorter than the polymer relaxation time, nonequilibrium polymer conformations are frozen in. Accounting for both possibilities, we define dimensionless preparation parameters, ⎧ 2·ρ ·E2 ·ω 2 ⎫1/3 τref ⎬ ≈ τref ·⎨ Wtr = t tr ⎩ 3·ηs(c) ⎭

Wev =

⎪

⎪

⎪

⎪

ϕ τref ≈ τref · o2 ·D tev h

(2)

(3)

where ρ is the density of the solution, ηs(c) is the concentration dependent viscosity of the solution, ϕo is the volume fraction of polymers corresponding to the initial concentration c and D characterizes the diffusion coefficient of the polymers (details of derivation of W tr and W ev, and the parameters used to calculate them are given in SI: Supplementary text, Table S1, and Figure S14). Interestingly, we found that W tr can be related to W ev by W ev = n·W tr = W , with the multiplying factor (n).34 This preparation parameter W , like the Weissenberg number in rheology experiments, represents the ratio of the time required over the time allowed for equilibration. Equilibrium can only be reached if W is much less than 1, that is, the preparation time is much larger than the characteristic relaxation time of the polymers. Thus, we anticipate that by increasing W we introduce larger deviations from equilibrium conformations, causing an increase of σres and Nmax. In Figure 3a−c, we show the variation of σres, τres, and Nmax with W in a double logarithmic representation. As can be seen, all data sets superimpose on master curves, indicating welldefined scaling relations with W . The existence of master curves suggest that W is appropriately taking into account variations of c and ω. Via the determination of W , we are able to establish a quantitative correlation between preparation pathways and macroscopic behavior of polymer films. We believe that variations in τres and Nmax are caused by changes in σres with W . To explicitly highlight this causality, in Figure 4a,b we have shown τres and Nmax with respect to an increase in σres. It is clear that an increase in σres accelerates stress relaxation and increases the rupture probability of polymer films.

Figure 2. The behavior of polymer films does not depend on film thickness only: Double logarithmic representation of (a) residual stresses, σres, (b) stress relaxation time, τres, and (c) maximum number of dewetting holes Nmax (determined at tann = 400 s) as a function of film thickness, h. Squares indicate the films prepared by method 1. All the other symbols indicate the films prepared by method 2.

As described earlier, nonequilibrium chain conformations are inherited during the rapid evaporation of solvent in the course of spin coating. With this preparation process, two different time scales become evident: (a) time available for the polymers to relax during the preparation and (b) a reference time (τref) that characterizes the time needed for the equilibration of polymers under similar conditions. Since we had not varied the molecular weight and the nature of the polymer in our experiments, τref will be constant. For simplicity, we have set τref = 1 s. During spin coating, film thinning is shown to be described by an initial spin-off process (expulsion of solution off the substrate edges) followed by hydrodynamic thinning and evaporation (characterized by the evaporation rate E of the solvent used).32,33 It is possible that the polymers were already frozen into nonequilibrium conformations during the transition from the spin-off process to hydrodynamic thinning and evaporation. Accordingly, the duration from the end of the spin-off process

Figure 3. The characteristic preparation parameter W influences the behavior of polymer films: Double logarithmic representation of (a) σres, (b) τres and (c) Nmax as a function of W (filled symbols for W = W ev and unfilled symbols for W = n·W tr; refer to text for n). Dashed lines indicate the mean slopes defining the variation of all the experimental observables with W , whose values are indicated in the lower corners of the respective panels. The different symbols have the same meaning as in Figure 2. 1298

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future experimental and theoretical efforts, we will profoundly advance our understanding of the relevant microscopic processes, which link macroscopic behavior of polymers with W . We anticipate that the observed correlations between resulting materials properties and sample preparation remain valid over a wide range of parameters, including industrial processing conditions, allowing to tune properties of polymer for a desired performance in various applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00815. Materials and Methods, Supplementary text, Figures S1− S14, Table S1, and references (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 761 203 5856. Fax: +49 761 203 5855. ORCID Figure 4. Correlation between parameters characterizing the nonequilibrium behavior of polymer films: Double logarithmic representation of (a) τres and (b) Nmax vs σres. Dashed lines indicate the mean slopes (values are mentioned in the respective panels). The different symbols have the same meaning as in Figure 2.

Sivasurender Chandran: 0000-0003-0547-0282 Günter Reiter: 0000-0003-4578-8316 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for discussions with Dr. F. Ziebert and the members of the International Research Training Group (IRTG-1642) - Soft Matter Science, funded by the Deutsche Forschungsgemeinschaft (DFG). S.C. acknowledges funding via the Innovationsfonds Forschung of the University of Freiburg and DFG (CH 1741/2-1).

We have related the increased dewetting velocities during the initial stages of our experiment to preparation induced σres, in addition to the expected σcap. Initially, during dewetting, the increased driving stresses are balanced by the elastic stresses, that is, σcap + σres = G0·ϵ, where ϵ is the strain. We assume G0 to be the bulk modulus corresponding to the equilibrated polymer. Alternatively, we may attribute the initial accelerated dewetting to a decreased effective modulus of the freshly prepared film (Geff), that is, σcap = Geff·ϵ, where Geff = G0 − (σres/ϵ). Through crack formation, recent experiments36 revealed that the preparation induced residual stresses are tensile in nature, justifying the negative sign in the expression for Geff. Assuming strains of order unity, this simple relation predicts that an increase in σres will cause a decrease in Geff by the same order of magnitude, consistent with observations in aging experiments of bulk samples.35 For the elevated temperatures used in our experiments, G0 (≈200 kPa) is characterized by the rubbery plateau modulus of the polystyrene. Interestingly, values of σres varied around G0. Accordingly, depending on the chosen preparation pathway defined by W , polymer films can be hard and brittle or soft and malleable. Although such correlations have been discussed qualitatively for different systems, we are not aware of any quantitative description. The here presented quantitative correlations between σres and τres may be considered as a first step toward predicting such properties. To conclude, we have demonstrated that the macroscopic behavior of nonequilibrated, spin-coated, polymer films is predictable through W , which is the appropriate preparation time normalized with the characteristic relaxation time of the polymer. Through a systematic variation of the preparation pathways, we have shown that nucleation density of dewetting holes, residual stress and the corresponding relaxation time can be varied by orders of magnitude. Intriguingly, we discovered scaling relations between τres and σres and between Nmax and σres. We are optimistic that based on such detailed relations and

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DOI: 10.1021/acsmacrolett.7b00815 ACS Macro Lett. 2017, 6, 1296−1300