Capillary Wrinkling of Floating Thin Polymer Films
Jiangshui Huang1,2,
Megan Juszkiewicz1,
Wim H. de Jeu2,3,
Enrique Cerda4,
Todd Emrick2,
Narayanan Menon1* and
Thomas P. Russell2*
1 Department of Physics, University of Massachusetts, Amherst, MA 31003, USA.
2 Polymer Science and Engineering Department, University of Massachusetts, Amherst, MA 31003, USA.
3 FOM Institute for Atomic and Molecular Physics, Amsterdam, Netherlands.
4 Departamento de Física, Universidad de Santiago de Chile, Santiago, Chile.
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Fig. 1. Four PS films of diameter D = 22.8 mm and of varying thicknesses floating on the surface of water, each wrinkled by water drops of radius a  0.5 mm and mass m 0.2 mg. As the film is made thicker, the number of wrinkles N decreases (there are 111, 68, 49, and 31 wrinkles in these images), and the length of wrinkles L increases. L is defined as shown at top left, measured from the edge of thewater droplettothe whitecircle. The scale varies between images, whereas the water droplets are approximately the same size.
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Fig. 2. The number of wrinkles N as a function of a scaling variable, a h– . Data for different film thicknesses h (indicated by symbols in the legend) collapse onto a single line (the solid line is a fit: N = 2.50 x 103ah–). The extent of reproducibility is indicated by the open and solid inverted triangles, which are taken for two films of the same nominal thickness.
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Fig. 3. (A) Wrinkle length L is proportional to the drop radius a. For fixed loading, L increases with thickness h, as shown by the different symbols. (B) An approximate data collapse is achieved by plotting L against the variable ah. Theinset at thetop left shows the relation between L and h for a fixed radius of the water droplet a = 0.6 mm. The black line is the best fit of the data to a power-law dependence: L = 0.0872 h0.58; the red line is the best fit to a square root: L = 0.129 h.
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Fig. 4. (A) Young's modulus E versus concentration (by weight %) of plasticizer (dioctyl phthalate). E is computed from the wrinkling pattern (solid black symbols) by means of Eqs. 2 and 3. Data from other techniques (12) are shown for comparison. (B) Thickness h versus plasticizer concentration. h is computed from Eqs. 2 and 3; compare with data from x-ray reflectivity measurements (7). The error bars are the standard errors of the measurements.
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Fig. 5. (A) Relaxation of the wrinkle pattern as a function of time after loading with a water droplet. The thickness of the film h = 170 nm, and the mass fraction of the plasticizer is 35%. (B) The time dependence of wrinkle length L normalized by the length Lo, at the instant image capture commenced. Data are shown for plasticizer mass fractions of 35% (blue symbols) and 32% (red symbols). The plot symbols differentiate experimental runs, showing reproducibility of the time dependence. Solid lines show fits to a stretched exponential: L(t)/Lo = exp[–(t/ )ß].
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