Controlled mud-crack patterning and self-organized cracking of polydimethylsiloxane elastomer surfaces

Exploiting pattern formation – such as that observed in nature – in the context of micro/nanotechnology could have great benefits if coupled with the traditional top-down lithographic approach. Here, we demonstrate an original and simple method to produce unique, localized and controllable self-organised patterns on elastomeric films. A thin, brittle silica-like crust is formed on the surface of polydimethylsiloxane (PDMS) using oxygen plasma. This crust is subsequently cracked via the deposition of a thin metal film – having residual tensile stress. The density of the mud-crack patterns depends on the plasma dose and on the metal thickness. The mud-crack patterning can be controlled depending on the thickness and shape of the metallization – ultimately leading to regularly spaced cracks and/or metal mesa structures. Such patterning of the cracks indicates a level of self-organization in the structuring and layout of the features – arrived at simply by imposing metallization boundaries in proximity to each other, separated by a distance of the order of the critical dimension of the pattern size apparent in the large surface mud-crack patterns.


Thermal expansion of the PDMS during the plasma treatment
In order to evaluate the role of thermal expansion of the PDMS in the process, the temperature rise of the PDMS -during oxygen plasma -exposure was evaluated. This was achieved ex situ for every plasma dose (1.8 kJ -180 kJ) after 35 seconds venting with N 2 using a piece of PDMS resting on a glass slide exposed to the plasma and using a FI622TI laser thermometer (Française d'Instrumentation, France). Supplementary Fig. 2  3. Spontaneous cracking of PDMS elastomer exposed to high dose, high pressure oxygen plasma Supplementary Figure 3 shows optical microscope images of the surfaces of PDMS samples which were exposed to high pressure 5

Wetting contact angle on PDMS as a function of plasma dose: the influence of cracking
The impact of the plasma dose on the surface energy of the PDMS was assessed using contact angle measurements. Supplementary Fig. 5 shows When the CA is measured 3 weeks later, the measured values are much nearer to the value of untreated PDMS. However, the data indicates that there is a minimum for the PDMS exposed to a plasma dose of 1.8 kJ. Supplementary Fig. 5 shows photographs of the cracking caused by the plasma treatment -taken using a DM4000M optical microscope (Leica AG, Germany). As the plasma dose is increased, the transition from no cracking <1.

Atomic force microscopy (AFM) measurements of the PDMS surfaces
Tapping mode atomic force microscopy (AFM) measurements were conducted on the PDMS surfaces using a Dimension D3100 (Bruker-Veeco USA). Over the plasma dose range and oxygen pressure studied here, the AFM did not reveal the presence of organized winkles 1,10 known to form on PDMS surfaces following exposure to low dose O 2 plasmas. No spontaneous cracking of the PDMS surfaces is observed following exposure to oxygen plasma doses less than 1.8 kJ. Indeed, the PDMS surfaces exposed to a 40 Pa pressure oxygen plasma over the dose range 360 J to 1.5 kJ are flat -as observed using AFM. Our experiments indicate that PDMS surfaces exposed to oxygen plasma in the dose range < 1. cracks. b, a crack generated using an oxygen plasma dose of 24 kJ.

Modelling of the residual stress in the chromium film
This section describes the analytical model used here to estimate the level of residual stress in an evaporated chromium layer of thickness h deposited on an oxygen plasma exposed PDMS sample.
As detailed in the text, the evaporated gold layer does not affect the mesa radius λ but only contributes to increasing the crack width by providing additional stresses on pre-cracked mesas. Evaporated gold films are known to have residual tensile stresses much less than that of evaporated chromium films on polymeric substrates 11 For layers (l) in series, the force is the same in individual parts; for layers in parallel, the strain is the same in the individual parts. Thus, it follows that: We can denote = ε to be the ratio between the critical mesa strain and the global strain and = ∑ ℎ =0 ℎ to be the ratio between the equivalent mesa stiffness and the crack region stiffness. One obtains: In the following expression, we see that the characteristic length λ is function of three physical quantities: (1) the ratio between the strain (or stress) amplitude and the critical mesa strain (or stress), (2) the ratio between the equivalent stiffness of the metallized mesas and of the crack domains, (3) the metallization and crack dimensions. Let us consider the case, where L tends toward infinity, i.e. large metallization or infinite metallized lines. In this case equation 1 becomes: where is a geometrical parameter, i.e. the crack spacing-to-crack width ratio.
If we now focus on the specific practical case presented in the paper, i.e. the PDMS/SiO x /Cr system, this general equation can be rewritten to explicitly relate the chromium stress loading, the crack spacing and the mechanical properties of the materials to give: One should note that the mechanical properties of thin films can be affected by their uniformity. It is well known that metal-insulator percolation transition for very thin evaporated films is about 2 nm for chromium 18 and between 6 nm and 20 nm for gold 19 depending on processing conditions, e.g. vacuum pressure, deposition rate and substrate temperature. 20 This is the reason why we chose the chromium thickness to be in the range 2-100 nm and the gold thickness to be fixed at 100 nm.