Mechanically driven wrinkling instability in thin film polymer bilayers

J. S. Sharp, K. R. Thomas, and M. P. Weir

Phys. Rev. E 75, 011601 – Published 3 January 2007

Abstract

Optical microscopy and atomic force microscopy were used to study a mechanically induced wrinkling instability in thin film poly(caprolactone)/polystyrene and poly(ethylene oxide)/poly(methyl methacrylate) bilayers. The instability in these samples was shown to be driven by changes in the interfacial area between a semicrystalline polymer underlayer and a glassy polymer capping layer that occurred when the underlayers were melted. The wrinkling instability resulted in the formation of one-dimensional corrugations at the surface of the bilayer samples that had a well-defined wavelength on the micrometer length scale. A linear stability analysis was used to derive a simple model of the wrinkling process in these samples. This model considered the flow and deformation of material in the molten underlayer as well as the balance of stresses in the glassy polymer capping layers. Rheological data were also obtained from polymers similar to those used to form the bilayers. These data were used to show that the model is capable of quantitatively predicting the capping layer and underlayer thickness dependencies of the characteristic wrinkling wavelengths, if the mechanical properties of the two layers and the strain in the capping layers can be determined.

Received 20 July 2006

DOI:https://doi.org/10.1103/PhysRevE.75.011601

Authors & Affiliations

J. S. Sharp^*, K. R. Thomas, and M. P. Weir

School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

^*Email address: james.sharp@nottingham.ac.uk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 75, Iss. 1 — January 2007

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic diagram showing how the thin film bilayer samples are prepared. Thin film membranes of a glassy polymer are transferred onto the surface of a semicrystalline polymer film supported on a Si substrate (a). As the films are brought together, surface forces pull the two films into intimate contact [(b) and (c)]. When the bilayers are heated above the melting temperature of the underlayer, the interface between the two films is pulled flat by interfacial tension and the capping layer is left in a state of compressive stress (d). Thermal fluctuations at the surface of the bilayer then cause the capping layer to buckle (e).Reuse & Permissions
Figure 2
Optical micrographs of PCap/PS and PEO/PMMA bilayers taken before and immediately after (within $1 s$ ) heating above the melting temperature of the semicrystalline underlayers. Panels (a) and (b) show the surface of PCap/PS bilayer comprising a $107 nm$ thick PCap underlayer and a $115 nm$ thick PS capping layer. Panel (a) shows the surface of the bilayer at $25 ° C$ prior to heating and panel (b) shows an image of the same region taken within $1 s$ of heating the bilayer to $65 ° C$ $[T_{m} (PCap) = 58 ° C]$ . Panels (c) and (d) show the surface of PEO/PMMA bilayer comprising a $371 nm$ thick PEO underlayer and a $118 nm$ thick PMMA capping layer. Panel (c) shows the surface of this bilayer at $25 ° C$ prior to heating and panel (d) shows an image of the same region taken within $1 s$ of heating the bilayer to $70 ° C$ $[T_{m} (PEO) = 63 ° C]$ . The bottom panel shows a line profile of the radial intensity distribution that was taken from the 2D Fourier transform (FT, see inset in bottom panel) of the image shown in panel (b). This line profile was taken along a line joining the center of the FT and the two dominant peaks on either side of the center of the FT. These line profiles were used to determine the position of the dominant peak in wave-vector space, $q_{\max}$ .Reuse & Permissions
Figure 3
Atomic force microscope images of PCap and PEO films and PCap/PS and PEO/PMMA bilayers taken before and after heating. Panel (a) shows the surface of a $67 nm$ thick PCap film prior to bilayer formation. Panel (b) shows the surface of a PCap/PS bilayer that was formed by placing a $47 nm$ PS capping layer on top of the film shown in panel (a). This image was taken at $25 ° C$ and prior to heating. Panel (c) shows the surface of the same PCap/PS bilayer after heating to $65 ° C$ for $\sim 1 s$ , followed by a rapid quench $(\sim 50 ° C \min^{- 1})$ to room temperature. Panel (d) shows the surface of a $174 nm$ thick PEO film prior to bilayer formation. Panel (e) shows the surface of a PEO/PMMA bilayer that was formed by placing a $70 nm$ thick PMMA capping layer on top of the film shown in panel (d). This image was taken at $25 ° C$ and prior to heating. Panel (f) shows the surface of the same PEO/PMMA bilayer after heating to $70 ° C$ for $\sim 1 s$ , followed by a rapid quench $(\sim 50 ° C \min^{- 1})$ to room temperature. All AFM images were collected in tapping mode and were taken using a $20 μ m \times 20 μ m$ scan area. The insets in all of the panels show a height profile of the surface of the samples that was taken along one of the main diagonals of each image.Reuse & Permissions
Figure 4
Characteristic wavelength of the wrinkling morphology for each of the bilayer samples studied. Data are shown as function of the capping layer thickness $(L)$ for different values of the underlayer thickness $(h_{o})$ . The experimental data were obtained from values of $q_{\max}$ that were determined from FT line profiles (similar to those shown in Fig. 2), using the relation $λ = 2 π ∕ q_{\max}$ . Panel (a) shows data that were collected from thin film PCap/PS bilayer samples where the thickness $(h_{o})$ of the underlying PCap film was $67 nm$ (엯), $107 nm$ (◻), and $462 nm$ (Δ), respectively. Panel (b) shows data that were collected from thin film PEO/PMMA bilayer samples where the thickness $(h_{o})$ of the underlying PEO film was $174 nm$ (엯), $371 nm$ (◻), and $650 nm$ (Δ) respectively. The solid lines in this figure represent values of the fastest growing wavelength that were calculated from simulations of the amplitude growth rate, $s (q)$ , that were determined using Eq. (9). The values of $E$ , $G$ , $ν_{L}$ , and $ϵ$ that were used to generate these lines are given in Table .Reuse & Permissions
Figure 5
Frequency dependence of the shear modulus of a $10 000 {gmol}^{- 1}$ poly(caprolactone) sample taken at $60 ° C$ (top panel) and a $35 000 {gmol}^{- 1}$ poly(ethylene oxide) sample (bottom panel) taken at $65 ° C$ . Hollow and filled symbols are used to represent the real and imaginary parts [ $G^{'} (ω)$ and $G^{″} (ω)$ ] of the frequency-dependent modulus, respectively. The arrows point to the axis that is related to each data set. The solid lines shown on these plots are the results of polynomial fits to the $G^{'} (ω)$ and $G^{″} (ω)$ data. The insets in each panel show the time-dependent stress relaxation modulus of the polymers. These plots were obtained by Fourier transformation of the frequency-dependent modulus $[G (ω) = G^{'} (ω) + i G^{″} (ω)]$ of the polymers that were constructed using the polynomial fits to the frequency-dependent rheology data.Reuse & Permissions
Figure 6
Calculations of the q-dependant growth rate $[3 η s (q)]$ for sinusoidal perturbations at the surface of the bilayers studied. The main panel shows calculations of the reduced growth rate for a fixed value of the capping layer thickness $(L = 150 nm)$ using values of $h_{o} = 174$ , 371, and $650 nm$ , respectively. The inset shows the results of similar calculations that were performed for a fixed value of the underlayer thickness $(h_{o} = 371 nm)$ using different values of $L = 50$ , 150, and $300 nm$ , respectively. All of the curves shown are calculated using Eq. (9) with values of $E = 3.7 GPa$ , $ν_{L} = 0.325$ , $ϵ = 0.1 \times 10^{- 3}$ , and $G = 24 kPa$ , respectively.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics