In attempting to reduce the size of functional devices, the thickness of polymer films has reached values even smaller than the diameter of the unperturbed molecule. However, despite enormous efforts for more than a decade, our understanding of the origin of some puzzling properties of such thin films is still not satisfactory and several peculiar observations remain mysterious. For example, under certain conditions, such films show negative expansion coefficients or show undesirable rupture although energetically they are expected to be stable. Here, we demonstrate that many of these extraordinary effects can be related to residual stresses within the film, resulting from the preparation of these films from solution by fast evaporation of the solvent. Consequently, depending on thermal history and ageing time, such films show significant changes even in the glassy state, which we quantify by dewetting experiments and corresponding theoretical studies. Identifying the relevance of frozen-in polymer conformations gives us a handle for manipulating and controlling properties of nanometric thin polymer films.

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy 1 , whereas compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy [2][3][4][5][6][7][8] . Here, we study the energy distribution for highly confined membranes and show the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic selforganized focalization of the deformation energy is observed provided that an up-down symmetry breaking, induced by the intrinsic nonlinearity of the elasticity equations, occurs. The physical model, exhibiting an analogy with parametric resonance in a nonlinear oscillator, is a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues, for example wrinkled skin Several theoretical approaches have been proposed to describe the wrinkling instability for very small compression ratio, that is, near the instability threshold 2,3,7 . However, the large-compression domain remains largely unexplored, with the notable exception of the wrinkle-to-fold transition observed in ref. 8 for an elastic membrane on liquid and the self-similar wrinkling patterns in skins 14 . In the former case, the deformation of the membrane is progressively focalized into a single fold, concentrating all the bending energy. In contrast, for thin rigid membranes on elastomers, large compression induces perturbations of the initial wrinkles but the elasticity of the soft foundation maintains a regular periodic pattern whose complexity increases with the compression ratio.A polydimethylsiloxane (PDMS) film, stretched and then cured with ultraviolet radiation-ozone, or a thin polymer film bound to an elastomer foundation, remains initially flat. Under a slight compression, δ = (L 0 − L)/L 0 , these systems instantaneously form regular (sinusoidal) wrinkles with a well-defined wavelength, λ 0 . Increasing δ generates a continuous increase of the amplitude of the wrinkles and a continuous shift to lower wavelength (λ = λ 0 (1 − δ); see Fig. 1g). By further compression of the sheet, more complex patterns emerge. Above some threshold, δ > δ 2 0.2, we observe a dramatic change in the morphology leading to a pitchfork bifurcation: one wrinkle grows in amplitude at the expense of its neighbours (Fig. 1). The profile of the membrane is no longer described by a single cosinusoid but requires a combination of two periodic functions, cos(2π x/λ) and cos(2π x/2λ). The amplitude of the 2λ mode increases with the compression ratio, whereas the λ mode vanishes. This effect is similar to period-doubling bifurcations in dynamical systems 15,16 observed in Rayleigh-Bernard convections 17 , dynamics of the heart tissue 18-20 , oscillated granular matter 21,22 or bouncing droplets on soap film 23 . In contrast to previous works, we describe here a sp...

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We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles. The drive towards miniaturization in technology is demanding for increasingly thinner components, raising new mechanical challenges [1]. Thin films are, however, unstable to boundary or substrate-induced compressive loads: moderate compression results in regular wrinkling [2][3][4][5][6] while further confinement can lead to crumpling [7,8]. Regions of stress focusing can be a hindrance, acting as nucleation points for mechanical failure. Conversely, these deformations can be exploited constructively for tunable thin structures. For example, singular points of deformation dramatically affect the electronic properties of graphene [9].Here, we show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles, from strained suspended graphene to ordinary hanging curtains. We develop a formalism based on wrinklons, a localized transition zone in the merging of two wrinkles, as building blocks to describe these wrinkled patterns.To illustrate this hierarchical pattern, in Fig. 1(a), we show a wrinkled graphene sheet along with an ordinary hanged curtain. These patterns are also similar to the selfsimilar circular patterns first reported by Argon et al. for the blistering of thin films adhering on a thick substrate [10]. The diversity and complexity of those systems, characterized by various chemical and physical conditions, could suggest, a priori, that the underlying mechanisms governing the formation of these patterns are unrelated. However, these systems can be depicted, independently from the details of the experiments, as a thin sheet constrained at one edge while the others are free to adapt their morphology. These constraints can take the form of an imposed wavelength at one edge or just the requirement that it should remain flat.

Performing detailed studies of viscoelastic dewetting of thin polystyrene films on solid substrates, we demonstrate the existence of residual stress due to strongly out of equilibrium chain conformations and a reduced entanglement density resulting from film preparation by spin coating. The ratio of stress over elastic modulus was found to increase strongly with decreasing film thickness and increasing chain length. Full equilibration of chain conformations required long times comparable to bulk reptation times. However, for chains longer than about 3000 monomers, the residual stress relaxed faster, at a rate independent of chain length.