A clue to the deformation mechanism came from a passage from Porter and Easterling's “Phase Transformations in Metals and Alloys” and the accompanying illustration:

“Note that the vertical component of γ_SL remains unbalanced. Given time this force would pull the mould surface upwards until the surface tension forces balance in all directions. Therefore Equation 4.14 only gives the optimum embryo shape on the condition that the mould walls remain planar.”

In this case, the substrate, the membrane, wasn't strong enough to remain planar. Thus, the features (compared below in visual and optical profilometric micrographs) seem to be caused by the out-of-plane component of the surface tension of drying droplets. Our attempts to reproduce the phenomenon in the lab were only partly successful; experiments with drying fluids led to features, but never those as varied as the examples shown above. We therefore still don’t fully understand the details of the mechanism. Fortunately, the features do not affect the operation of the films. If necessary, they could be eliminated by engineering the membrane for higher stiffness or by incorporating a preexisting tensile stress to offset the buckling.

Since first observing the features, I've collected other examples of thin film patterns in the literature. The variety is fantastic, but I haven't found any that perfectly match the original features. Most buckled films display very regular, periodic patterns that do not resemble the blotchy, irregular arrangement of features shown in optical and AFM micrographs above. The closest patterns are those of drying liquids as they dewet substrates. The random arrangement of droplets bears a much stronger resemblance to the original features than the folded films. It may simply be that nobody has combined dewetting experiments with extremely compliant free-standing films before and published the results. (Until 2007, shortly after I drafted the first version of this note: see From Science to Engineering at the bottom of this page.)

This note summarizes these findings for the interest of others. Mounds, bumps, wrinkles, dimples… There are as many descriptions as images. The original nomenclature of the authors is the best accompaniment.

Thin film buckling

We begin with the compressive buckling of thin films. Suspended square membranes undergo at least two buckling transitions. The first is characterized by a domed shape that continues into an X, or saltire, under higher stress. The second resembles an augmented tetraskelion whose folded features become more prominent with increasing stress or membrane area. I've often seen these patterns on ceramic and metal membranes and can usually distinguish them from the random bumps that seem to be related to drying fluids.

(Ziebert et al., “Strongly buckled square micromachined membranes,” J MEMS 8 423-432, 1999)

Back in 1989, Ali Argon at MIT published some photos of SiC deposited on (and subsequently delaminating from) silicon by plasma-assisted (now termed plasma-enhanced) chemical vapor deposition; these look quite similar to the features I characterized:

(Argon et al. “Intrinsic toughness of interfaces between SiC coatings and substrates of Si or C fibre” J Materials Science 24 1207-1218 1989)

Toyoichi Tanaka, also at MIT, studied gels of acrylamide and the effect of osmotic swelling in water. As the outer portion of the gel swells due to a phase transition, the unaffected interior region transmits a compressive stress to the surface. Now we start getting into some elegant evocative descriptions:

When a polymer gel undergoes an extensive swelling, a beautiful, regular pattern appears on the surface... At the beginning, the pattern is extremely fine, having a texture similar to that of a frosted glass. As time goes on, the units of pattern coalesce, doubling their characteristic size. When the unit size becomes comparable to the size of the gel, the pattern gradually disappears.”

Tanaka also describes the patterns as having “cusps” and “thorns.”

(Tanaka et al. “Mechanical instability of gels at the phase transition” Nature 325 396-398 1987)

Annie Viallet at Joseph Fourier University investigated the shapes created in lipid vesicles during osmotic deswelling of the interior.

When the reduced volume of partially deflated vesicles varies, a great variety of shapes (pears, peanuts, starfish…) is observed.”

A great variety of vesicle shapes were obtained in the chamber at the end of the shrinkage process: ellipsoids, dumbbells, stomatocytes, discocytes, pears, stars, etc.”

As in the case for slow shrinkage, we observed various shapes…the formation of multiple small invaginations of the membrane pointed toward the interior of the vesicles, which looked like raspberries…the formation of lipid pearl necklaces.”

The breaking of axial symmetry in the glassy skin of drying polysaccharide dextran leads to a pentagonal arrangement of radial wrinkles:

(Pauchard et al. “Stable and unstable surface evolution during the drying of a polymer solution drop” Phys Rev E 68 052801 2003)

Drying droplets of colloidal polystyrene become buckled and folded (photographs are on top, simulated shapes below):

(Tsapis et al. “Onset of buckling in drying droplets of colloidal suspensions” Phys Rev Lett 94 018302 2005)

...and “blisters” appear as a polymer film swells in water:

(Sharp et al. “Swelling-induced morphology in ultrathin supported films of poly(d,l-lactide)” Phys Rev E 66 011801 2002)

Simulations of tethered membranes produce a “wavelike pattern of mounds”:

(Moldovan et al. “Tethered membranes far from equilibrium: buckling dynamics” Phys Rev E 60 4377 1999)

Another group's analysis predicts “ridges,” “cones,” “mounds,” and “basins”:

(Uchida “Orientation order in buckling elastic membranes” Physica D 205 267-274 2005)

Some of these simulated shapes have been observed in a different context. A elastomer substrate whose top layer undergoes volumetric expansion from oxygen plasma exposure displays “complex yet periodic wavy structures”:

(Chua et al. “Spontaneous formation of complex and ordered structures on oxygen-plasma-treated elastomeric polydimethylsiloxane” Applied Physics Letters 76 721-723 2000)

Chan and Crosby made a phase map of these features as influenced by the oxidation time and region size:

(Chan et al. “Fabricating microlens arrays by surface wrinkling” Advanced Materials 18 3238-3242 2006)

At this point it's probably time for a shar pei (“sand [i.e., rippled] skin”):

(Instagram 2016)

“Skeletal wrinkles” appear when the hexamine solvent is evaporated during zinc oxide sol-gel preparation:

(Kwon et al. “Wrinkling of a sol-gel-derived thin film” Physical Review E 71 011604 2005)

...and ridges of deflated PDMS are shown in these micrographs of the canonical buckling model—a film that's too big for its environment:

(Jin et al. “Mechanical instabilities of soft materials: creases, wrinkles, folds, and ridges” PhD thesis, Harvard 2014)

Straight-sided wrinkles evolve into “worm-like” buckling patterns in a sub-100 nm sputter-deposited stainless steel layer atop polycarbonate:

(Claymand et al. “Experimental investigation of the instability of buckling patterns: From straight-sided to wormlike structures” Scripta Materialia 44 2623-2627 2001)

Similar features have also been described as “telephone cord buckles”:

(Moon et al. “An experimental study of the influence of imperfections on the buckling of compressed thin films” Acta Materialia 50 1219-1227 2002)

Claymand et al. called their row of buckled gold film features a “quasiperiodic varicose” pattern:

(Claymand et al. “Atomic force microscopy investigation of buckling patterns of nickel thin films on polycarbonate substrates” Philosophical Letters 82 477-482 2002)

“Herringbone” shapes appear when a gold film is cooled after deposition on PDMS:

(Chen et al. “A family of herringbone patterns in thin films” Scripta Materialia 50 797-801 2004)

...and a disorganized array of herringbones is termed a “segmented labyrinth”:

(Cai et al. “Periodic patterns and energy states of buckled films on compliant substrates” J Mech Phys Solids 59 1094-1114 2011)

Separated segments are described as exhibiting a “peanut” morphology:

(Yang et al. “Harnessing surface wrinkle patterns in soft matter” Adv Funct Materials 20 2550-2564 2010)

Under other conditions, the same report by Yang et al. presents “ripples”:

Permanent wrinkles are seen in a free-standing boron nitride film after its salt support is dissolved away:

(Coupeau et al. “Evidence of plastic damage in thin films around buckling structures” Thin Solid Films 469-470 221-226 2004)

...and casein gels exhibit still more features similar to what I saw in suspended metal films:

(Leocmach et al. “Hierarchical wrinkling in a confined permeable biogel” Science Advances 1 e1500608 2015)

“Creases” and wrinkles appear when an elastomer is affixed to a relatively rigid substrate using an electric field:

(Wang et al. “Creasing-wrinkling transition in elastomer films under electric fields” Phys Rev E 88 042403 2013)

Finally, “undulations” and “cracks” are fabricated:

(Guvendiren et al. “Solvent induced transition from wrinkles to creases in thin film gels with depth-wise crosslinking gradients” Soft Matter 6 5795-5801 2010)

Thin Film Dewetting

We now turn to the dewetting of liquids, sometimes modeled as a decomposition into wet and dry phases. Anshutosh Sharma of the Indian Institute of Technology describes dewetting morphology:

As the film thickness is increased, the initial pathway of evolution changes from the formation of small spherical droplets, to long mesas (parapets) and islands, to circular holes, all of which eventually resolve by ripening into a collection of round pancakes at equilibrium. However, beyond a certain transition thickness, a novel metastable honeycombed morphology, resembling a membrane or a slice of Swiss cheese, is uncovered, which is produced by an abrupt “freezing” of the evolution during hole growth.

(Sharma et al. “Pattern formation and dewetting in thin films of liquids showing complete macroscale wetting: from ‘pancakes’ to ‘swiss cheese’” Langmuir 20 10337-10345 2004)

Leonard Schwarz at the University of Delaware dried a thermosetting polymer on an inked aluminum sheet. His group observed “particular patterns of holes, ridges, filaments, and, ultimately, droplets” both in experiments and in simulations:

(Schwartz et al. “Dewetting patterns in a drying liquid film” J Colloid Interface Sci 234 363-374 2001)

Observers of drying water films report the appearance of “star-like formations” and “parabolic dendrites” as dry patches nucleate:

(Samid-Merzel et al. “Pattern formation in drying water films” Physica A 257 413-418 1998)

...and “fingering instabilities” are seen as viscous polystyrene dewets from an octadecyltrichlorosilane-coated silicon wafer during annealing:

(Reiter, “Unstable thin polymer films: rupture and dewetting process,” Langmuir 9 1344-1351, 1993)

Much later, Manoj Chaudhury performed an extensive study of fingering instabilities, including the “debonding, sliding, peeling and the healing of a blister,” producing spectacular images such as the following:

(Chaudhury et al. “Adhesion-induced instabilities and pattern formation in thin films of elastomers and gels” Eur Phys J E38 82 2015)

Thin Film Deposition

When silver is sputtered onto a layer of silicone oil, the initial sputtered atoms are driven into the top layer of the oil. At some percolation threshold, a “branched structure” consisting of silver clusters nucleates:

(Ye et al. “Structural and electrical properties of a metallic rough-thin-film system deposited on liquid substrates” Phys Rev B 54 14754-14757 1996; Feng et al. “Growth behavior and surface morphology of Ag rough films deposited on silicone oil surfaces” Thin Solid Films 342 30-34 1999)

I’ve included these silver features because of their visual appeal; however, it’s important to note that their origins are more complex than the other patterns shown previously. All of the earlier patterns are caused by imposed or internal compressive stress (in the case of the buckled films) or surface-volume energy tradeoffs (in the case of the dewetting films). In contrast, the sputtered silver film morphology is attributed to mixing of the silver atoms with the silicone oil layer.

From Science to Engineering

Scientists necessarily use tools to learn more about nature; engineers necessarily learn about nature to develop better tools. Starting around 2007, reports of thin film deformation by liquids, the phenomenon that so mystified me, exploded in the literature. It started with Huang et al.'s report of "Capillary wrinkling of floating thin polymer films" in Science:

(Huang et al. “Capillary wrinkling of floating thin polymer films” Science 317 650-653 2007)

Suddenly, a new field—elastocapillarity—was emerging. Enrique Cerda, one of the coauthors, had done his postdoc with Mahadevan at Harvard with a heavy concentration on wrinkling; in fact, Adam Zeiger and I cited one of their papers in the context of cell-contraction-induced wrinkling of a thin silicone film. Here, I was circling back to thin film patterns from a different direction—animate actomyosin-generated buckling via live cells:

(Burton et al. “Keratocytes generate traction forces in two phases” Mol Biol Cell 10 3745 1999)

Surface instabilities were a hot topic (you know you've made it when your field gets surveyed in MRS Bulletin):

(Wang et al. “Beyond wrinkles: Multimodal surface instabilities for multifunctional patterning” MRS Bulletin 41 115-121 2016)

(Wang et al. “A three-dimensional phase diagram of growth-induced surface instabilities” Scientific Reports 5 8887 2015)

With this explosion of new research, I found some more close matches to the localized floral patterns I saw in my sub-micron-thick suspended Ti/Au/Ti membranes 50 μm on a side:

(Yan et al. “Spontaneous wrinkling pattern of a constrained thin film membrane” Applied Physics A 107 761-767 2012)

Still other reports have described tents, branches, tubes, sawteeth, shrivels, wavy leaves, ruga, furrows, curtains, and—one of my favorites so far—wrinklons! Sure, let's coin another word, given the obvious paucity of the language to describe these features.