Superficial wrinkles in stretched, drying gelatin films
Fall 2010 entry - Anna Wang
Superficial wrinkles in stretched, drying gelatin films R. Rizzieri, L. Mahadevan, A. Vaziri and A. Donald, Langmuir, 22, 3622, 2006
An environmental scanning electron microscope (ESEM) was used to study gelatin films as they were simultaneously dried and stretched. Unexpectedly, they were found to wrinkle on a small and large length scale and this paper focuses on characterising and explaining this.
The gelatin film was made form dissolving gelatine powder in either deionised water or ethylene glycol (less volatile than water), and cooled and pressed into a thin sheet of uniform thickness. The gelled sheets were attached to a tensometer which was placed in the ESEM. At first the sheets rested on a cooling block equilibrated at 2˚C (the ambient temperature of the ESEM chamber); upon stretching, the sheet lifted off from the block and was ~1mm above the cooling block and hence free from the effects of slipping or sticking to the cooling block. Water vapour at ~5Torr was used as the imaging gas, and kept the humidity controlled.
As gelatin sheets exhibit relatively large strain (>10%) at failure, the change in cross sectional area must be accounted for when working out the ‘true’ stress. Assuming constant volume of the sheet (V = AL = al where V is the volume, A and L are the final area and volume and a and l the initial values), we have the following corrected terms:
True stress: σ = FL/al
Corrected strain: ε = ln(L/l)
Elastic modulus = σ/ε
Results and discussion
Figure 1 shows the true stress/strain curve, and ESEM images of the film during deformation. At strains >20%, regular bands appeared quite unexpectedly. These bands were aligned in the direction of the applied strain, and had a periodicity much less than the sample thickness (~0.3mm vs ~2mm).The wrinkles first appeared around the top and bottom of the sample, where the sample was attached to the tensometer, and then spread. At larger strains, cracks revealed fresh, smooth gelatin but this quickly wrinkled too. Upon further stretching, the sheet breaks and curls in the direction of the bands. The curl is in the opposite direction, however, if the broken sheet is submerged in water suggesting that surface water content may play a critical part in the behaviour of the sheet.
The system wrinkles in a similar fashion to PDMS skin-PDMS substrate systems, which is not unexpected since the top and bottom of the gelatin sheet is expected to dehydrate and be stiffer than the interior. The skin resists short wavelengths, the substrate is less stiff and resists long wavelengths. Applying the existent theory in the PDMS studies, we have a wrinkling wavelength
λ ~ h(Es/Eb)1/3
where h is the thickness of the film and Es and Eb are the elastic moduli of the skin and bulk respectively. The secondary wrinkling can be explained as follows: after the primary short wavelength wrinkles are formed, the system continues to stretch but the skin is now effectively wrinkle + skin ie much thicker than the original skin. This new ‘skin’ wrinkles on larger length scales since it is stiffer, and the pattern in Figure 2 can be seen.
Figure 3 shows the effect of sheet thickness, and NaCl added to the gelatin solution on the wrinkling wavelength. Increasing salt content lowers the vapour pressure of the gel, so the gel dries more slowly. This means a smaller Es/Eb ratio and hence smaller wavelengths. Increasing the thickness of the sheet means that the top of the sheet is much further from the cooling block than the bottom, meaning that water will evaporate from the top of the sheet more quickly. This results in a larger Es and h.
Quantitative comparisons with the equation can also be made. At the early stages of deformation, the skin is yet to form and so the elastic modulus for the bulk Eb (35kPa) can be estimated from the start of the stress/strain curve. At late stages of the experiment, much of the sheet has dried and so Es (350kPa) is estimated from the end of the stress/strain curve. This yields λ ~ 10µm, which is in remarkable agreement with the experimental value of 9µm given the approximations made. A simple finite element computational model of a skin/substrate system also provides support for the proposed mechanism for wrinkling.