Evolution of a Stress-Driven Pattern in Thin Bilayer Films: Spinodal Wrinkling

We report the full spectrum of the evolution of the wrinkle pattern formation in a thin bilayer film of an elastic metal on a viscoelastic polymer. Although the origin is different, the transition of an initial islandlike pattern to a labyrinthine structure without any change in the wavelength ($q\sim t^0$) and the overall evolutionary process is strikingly similar to that in the spinodal system but the process is robust and takes place on a long time scale (about 10 days). The change into a mountainous topography in the late stages is accompanied by an increase in the length scale from an initial wavelength to another. This change, due to the relaxation of the confined polymer that results in a transition from elastic- to viscouslike behavior, induces wave coarsening ($q\sim t^{-1.04\pm 0.08}$) and macroscopic roughening.

Figure 1

AFM images of the temporal evolution of stress-driven surface wavy patterns ($80\mathrm{\mu }\mathrm{m}\times 80\mathrm{\mu }\mathrm{m}$). Set I (a)–(f) is for smaller waves that result in a thin metal layer (40 nm) and a relatively thin polymer layer (350 nm) and set II (g)–(l) is for larger waves that result when the polymer layer is made thicker (580 nm). Insets show the FFT images for given textured patterns. (a) Set I data after 3 min. (b) Set I data after 12 h. (c) Set I data after 36 h. (d) Set I data after 72 h. (e) Set I data after 100 h. (f) Set I data after 170 h. (g) Set II data after 3 min. (h) Set II data after 36 h. (i) Set II data after 72 h. (j) Set II data after 96 h. (k) Set II data after 120 h. (l) Set II data after 195 h.

Figure 2

AFM images of initial stage of wave development ($40\mathrm{\mu }\mathrm{m}\times 40\mathrm{\mu }\mathrm{m}$). The upper inset shows FFT for a given pattern and the lower inset gives sectional data and mean roughness value (RMS). (a) Islandlike pattern of set I data after 3 min of annealing. (b) Textured pattern of set I data after 20 min. (c) Weak labyrinthine pattern of set I data after 6 h. (d) Fully developed labyrinthine pattern of set I data after 24 h.

Figure 3

(a) Power spectra intensity of evolving patterns as a function of wave number. Arbitrary unit is used for simultaneous representation of both sets I and II. Arrows indicate the maximum intensity peak of the pattern that formed on the surface initially. The second peak emerges with time and then become dominant in time. (b) Strain-time relation of metal layer. Strain-growth region corresponds to the early stage (stage I). The slope simply depends on material properties. In stage II, the strain is constant.

Figure 4

(a) SEM micrograph for verification of “pinned” wave after 280 h of annealing in set II. The inset is a magnified image of the “pinned” region. One can observe that one half of one large wave (viscosity-induced wave) is composed of four small waves (elasticity-induced wave) as seen in Fig. 1l. (b) Dominant wave number-time relation in stages I and II. The wavelength is constant during stage I but increases almost linearly with time in stage II.