Pattern Formation in a Thin Solid Film with Interactions

Shenoy, Vijay B.; Sharma, Ashutosh

doi:10.1103/physrevlett.86.119

Cited by 162 publications

(263 citation statements)

References 17 publications

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“…Slip BC at the bottom: The solution of the elastostatic problem with the slip BC at the bottom, Eqs. (10,11), is the Airy stress function Eq. (A1) given in appendix A.…”

Section: Grinfeld Instability -Classical Way Of Calculation; Effementioning

confidence: 99%

“…In polymer films, however, this coupling should be present and important. Moreover this term establishes the connection to other elastic instabilities, namely to a buckling-like instability under compressive stress and, in the case of an externally applied field, to the elasto-electric instability investigated by Sharma et al [11][12][13][14]. Finally the growth rate of the height of the polymer film is derived in case of simultaneous action of stress and external field.…”

Section: Introductionmentioning

confidence: 99%

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Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

2011

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We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and second due to an externally applied electric field normal to the film's free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes as e.g. spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films: when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and the free surface.

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“…Slip BC at the bottom: The solution of the elastostatic problem with the slip BC at the bottom, Eqs. (10,11), is the Airy stress function Eq. (A1) given in appendix A.…”

Section: Grinfeld Instability -Classical Way Of Calculation; Effementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

2011

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“…In their works on solid elastic films with a contactor, Mönch and Herminghaus (2001) and Shenoy and Sharma (2001) showed that a surface instability is manifested in the absence of residual stress. As mentioned in the Introduction, we are interested in how the addition of a superficial residual stress affects the stability of the surface with a proximate contactor.…”

Section: Linearizationmentioning

confidence: 99%

“…Considering such material to inhabit a half-space, we impose force balance both in the bulk and on the surface. The interaction of a rigid contactor with a surface is accounted for by a potential (Mönch and Herminghaus 2001; Podio-Guidugli 1988; Podio-Guidugli and Caffarelli 1990; Shenoy and Sharma 2001). From the resulting linearized bulk and superficial equations, we derive a dispersion relation and find parameter values for which stable or unstable behavior of the film surface is manifested.…”

Section: Introductionmentioning

confidence: 99%

“…Since this stability is a surface phenomenon, it is as if we are dealing with a thin film. Also, because the films which Mönch and Herminghaus (2001) and Shenoy and Sharma (2001) investigated had thicknesses three orders of magnitude greater than the gap distance between the film surface and contactor, treating the film as semi-infinite is reasonable. Although we do not consider a film of finite depth, we extend the aforementioned work in solid elastic films in that, like Andreussi and Gurtin (1977), we account for the presence of a residual surface stress in the film.…”

Section: Introductionmentioning

confidence: 99%

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Mind the Gap: The Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

Fried

Todres

2005

J Elasticity

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Abstract. Extending Andreussi and Gurtin's (1977) pioneering work on the wrinkling of a free surface, we investigate the wrinkling stability of an incompressible elastic-like half-space whose surface is proximate to a contactor. Assuming a plane-strain deformation and accounting for both surface prestress and curvature-dependence of the surface free-energy density, we impose balances of forces and torques both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when stable or unstable behavior of the free surface is manifested. In contrast to the quadratic dispersion relation of Andreussi and Gurtin (1977), we obtain a quintic dispersion relation. An anlysis of this dispersion relation shows that the combined effects associated with surface pre-stress, curvature-dependence of the surface free-energy density, and the interactions between the surface and the proximate contactor lead always to an increased number linearly stable wrinkled configurations.

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Contact Instability of Elastic Bilayers: Miniaturization of Instability Patterns

Mukherjee

Pangule

Sharma

et al. 2007

Adv Funct Materials

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We show, both experimentally and theoretically, that the free surface of an elastic bilayer becomes spontaneously rough when brought in contact with another rigid surface. The lateral length scales of these self‐organized structures were found to scale as: λ = RF h, where h is the total bilayer thickness. The scale factor, RF could be modulated by the ratios of the individual film thicknesses and shear moduli. This is unlike the case of a single elastic film where the scale factor is independent of all material properties, RF ∼ 3. A linear stability analysis shows that the instability patterns in the bilayer can be tuned from the short waves (∼ 0.5 h) to long waves (∼ 8 h). Experiments show good agreement with the theoretical predictions regarding the existence of short wave deformations. Further, a rather catastrophic change in the wavelength from its minimum value, ∼h/2, to a limiting value of ∼ 3 h occurs by very small changes in the film thicknesses. This effect is explained by a switching of states in the bilayer energy curve which displays two minima at different wave numbers. Thus, the contact instability of elastic bilayers suggests novel strategies for the control of adhesion and engineering of feature sizes in a wide range. In particular, these findings have implications for further pattern miniaturization in the elastic contact lithography using pre‐patterned stamps.

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Pattern Formation in a Thin Solid Film with Interactions

Cited by 162 publications

References 17 publications

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Interplay of internal stresses, electric stresses, and surface diffusion in polymer films

Mind the Gap: The Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

Contact Instability of Elastic Bilayers: Miniaturization of Instability Patterns

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