### The wrinkling pattern is characterized by number and wrinkles length.

Number dependence of wrinkles on elastic film properties and on capillary force exerted by drop confirms recent theoretical predictions on selection of a pattern with a welldefined length scale in wrinkling instability. Known we validated this method on polymer films modified by plasticizer. Wrinkles relaxation affords a simple method to study viscoelastic response of ultrathin films. We combined scaling relations that were developed for wrinkles length with those for the tal amount of wrinkles to construct a metrology for measuring elasticity and thickness of ultrathin films that relies on no more than a dish of fluid and a lowmagnification microscope.

### Thin sheets are far more easily bent than stretched by external forces.

Even under purely planar tension, a sheet will often deform out of plane to form wrinkles. Cerda and Mahadevan. This familiar instability occurs because elastic energy required to stretch a sheet is reduced by to’out of plane’ bending that accompanies wrinkling. On cream film that floats on warm milk; or on skin of fruit as it dries, This is an everyday phenomenon that can be seen on our skin as it is stretched by smiling, scars, or age.

We report on a study of wrinkling of films under capillary forces, which has thus far remained relatively unexplored. Thin polymer films form an ideal experimental setting in which to explore wrinkling phenomena. We used films of polystyrene ‘spincoated’ onto glass substrates. For example, deionized water, a circular PS piece film detached from tosubstrate, when to’sub strate’ was dipped into a petri dish of distilled. You should take it into account. Film floated to water surface where it was stretched flat by surface tension airwater γ interface at its perimeter, as long as S is hydrophobic. It’s a well we study films with very high aspect ratios, which can be treated accurately in two framework dimensional elasticity. The film thickness h was varied from 31 to 233 nm, as measured by ‘x ray’ reflectivity with a precision of ±5 nm. Now let me tell you something. Both in biological and in synthetic soft materials, films elastic deformation under surface tension is relatively commonplace, since thin films are often immersed in fluid environments.

Whenever floating film by placing a drop of water in film center, by placing a solid disk in film center, or by poking film with a sharp point to produce a fixed out of plane displacement, Wrinkles were induced in tostretched. PS’ contact line. We emphasize a crucial difference between loading with a solid and a fluid. The wrinkling induced in Fig. Make sure you write suggestions about it. Drop contact angle on PS is 88° ± 2°, and thus geometry of drop geometry on film is approximately that of a hemisphere on a flat surface. For instance, while radiating from load center, All these methods of loading lead to qualitatively similar wrinkling patterns. In view of this attractively simple geometry and experimental degree control afforded by loading with a fluid, we focus on wrinkling induced by fluid capillarity as in Fig. Fact, indeed, a solid object of weight and contact area comparable to drops those shown in Fig. Now please pay attention. The radial stress σrr induced at drop edge is dominated by surface tension, which for conditions of Fig.

### Four PS films of diameter D = 228 mm and of varying thicknesses floating on water surface, any wrinkled by water drops of radius a ≈ 5 mm and mass m ≈ 2 mg.

Two obvious quantitative wrinkling descriptors patterns are wrinkles number N and length of wrinkle L as measured from edge of todroplet. Nonetheless, to study systematically loading effect and elasticity, we placed water drops at center of film center using a micropipette, increasing mass of drop in increments of 2 mg. Lots of information can be found by going on web. Wrinkles number N decreases, and length of wrinkles L increases, as film is made thicker. As drop radius was increased, both L and N increased. I’m sure you heard about this. Because wrinkle terminus is quite sharply defined and not sensitive to lighting and optical contrast, we are also able to measure L directly from toimage. The scale varies between images, whereas water droplets are approximately very similar size. Normally, circle radius in which entire wrinkle pattern is inscribed determined by elasticity of sheet elasticity and parameters of toloading. Oftentimes we observe wrinkling pattern using a digital camera mounted on a ‘lowmagnification’ microscope.

We first focus on N, which is found to increase as

. As is evident in Fig. Eventually, reproducibility extent is indicated by open and solid inverted triangles, which are taken for two same films nominal thickness. Data for different film thicknesses h collapse onto a single line. Considering above said. Because wrinkles number remains constant whatsoever radial distances r from center of pattern tocenter, wavelength of wrinkles varies in accordance with λ = 2πr/ The number of wrinkles N as a function of a scaling variable, ah-¾. With that said, N combined dependence on an and h is correctly captured by scaling

as shown in Fig. It is Cerda arguments and Mahadevan, to understand this scaling.

### This wavelength can be computed from a bending minimization transverse to folds and stretching along their length, which leads to where bending modulus B = Eh3/12.

For a circular film with a radial stress since surface tension γ at film edge and another surface tension γ at boundary of droplet toboundary, σrr ∼ γa2/r2.

CN is a numerical constant. We make some qualitative remarks regarding wrinkle evolution pattern, before discussing wrinkle length. Using literature values of E = 4 GPaand λ = 33 for PS, and γ = 72 ± 3 mN/m, we obtain CN = 62 from fit slope line in Fig. Needless to say, ridge length shows much less hysteresis because length can locally increase or decrease continuously. First droplet added invariably overshoots N equilibrium value, as might be seen in slight curvature of individual sets of data in Fig. Normally, there is no measurable effect of contact line pinning. On p of this, wrinkles shown in images are purely elastic deformations and can be removed without irreversible formation, plastic creases. Anyways, cN can be obtained from an analytical elastic solution problem or from an experiment like ours where all relevant parameters are known. This effect is clearly seen when wrinkle pattern evolves as drop is allowed to shrink by evaporation. Seriously. Despite this, wrinkles number in pattern is hysteretic because there is an energy barrier as well as a global rearrangement involved in removing wrinkles.

Wrinkle length L increased linearly with a, radius of drop toradius, as shown in Fig. Whenever yielding a linear dependence L ∼ data in Fig, In our situation F = 2πaγ and τ = γ. This gives

. Furthermore, dependence on an and h is reasonably well described by purely empirical power law scaling shown in Fig. Basically, this scaling is dimensionally incomplete and an additional factor of -1/2 needs to be taken into account. Of course cerda, where wrinkle length is dictated by radial distance at which stress since an out of plane force F applied at center of a film decays to value of tension value τ applied at distant boundaries.

### CL is a constant.

The blackish line is data best fit to a ‘powerlaw’ dependence. Actually, cL = E and h appear in Eq. Theinset at thetop left shows relation between L and h for a fixed water radius droplet a = 6 mm. However, wrinkle length L is proportional to drop radius For fixed loading, L increases with thickness h, as shown by different symbols. From fit shown in Fig. Anyway, an attempt to write radial stresses in a manner that is consistent with Eq. Thus, L dependence on h and an is adequately constrained by experimental data and is well described by Eq. Eh, which is sheet stretching modulus. This indicates that length is defined purely by inplane stresses. An approximate data collapse is achieved by plotting L against variable ah.

### Eqs.

Thickness determination by means of Eqs. When compared to other techniques on display in Fig. And with very basic instrumentation. So, we vary PS elastic modulus by adding to it varying amounts of di octylphthalate, a plasticizer, as a demonstration of this technique. Make sure you scratch a comment about it in comment box. As can be seen in Fig. It is young’smodulus, there is also a subtle change in film thickness as a mass function fraction, x, of plasticizer.

Young’s modulus E versus concentration of plasticizer. This opens measuring possibility bulk relaxational film properties without concerns about pinning to a substrate, apart from ability to make measurements on a state that ain’t prestressed. Basically, this allows possibility for film to relax internal mechanical stresses that can develop either in to’spincoating’ process or during transfer to a solid substrate. The error bars are measurements standard errors. Data from other techniques Thickness h versus plasticizer concentration. At increasing time, wrinkles smoothly reduce in length and finally disappear. Usually, strains that develop in response to capillary load, for two films sets with different plasticizer mass fraction, L can be fit with a stretched exponential function Lo exp, where τ decreases with increasing plasticizer concentration, and β = 50 ± 02, typical of polymer viscoelastic response near glass transition. Now let me tell you something. Rather than mounted on a solid substrate. Such as nanoindentation, measurement is performed with film on a fluid surface.

### Wrinkle Relaxation pattern as a function of time after loading with a water droplet.

Wrinkle time dependence length L normalized by length Lo, at instant image capture commenced. Nevertheless, lo = exp. Fact, this simple technique can also be used to study dynamical relaxation phenomena in ultrathin films. Film thickness h = 170 nm, and mass plasticizer fraction is 35%. While showing time reproducibility dependence, The plot symbols differentiate experimental runs. Anyways, thus, capillarydriven wrinkle formation can be used as basis for a metrology of both elastic modulus and ultrathin thickness films by means of a very elementary apparatus a ‘low magnification’ microscope and a dish of fluid. On p of that, data are shown for plasticizer mass fractions of 35% and 32percent. Solid lines show fits to a stretched exponential.

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