John M. Maloney – Analysis Curiosity: Skinny Movie Patterns

are
often unnoticeable—the partitions of a home don’t buckle as
paint dries. If a drying fluid contacts a comparatively compliant
assist, nevertheless, the stress might be sufficient to trigger native or
common buckling of the assist.

A clue to the deformation mechanism got here from a passage from Porter and Easterling’s “Part Transformations
in Metals and Alloys” and the accompanying illustration:

“Observe that the vertical element of γ_SL stays unbalanced.
Given time this power would pull the mould floor upwards till the
floor stress forces steadiness in all instructions. Due to this fact Equation
4.14 solely provides the optimum embryo form on the situation that the
mould partitions stay planar.”

On this case, the substrate, the membrane, wasn’t sturdy sufficient to
stay planar. Thus, the options (in contrast beneath in visible and optical profilometric
micrographs) appear to be attributable to the out-of-plane element of the floor stress of drying droplets. Our makes an attempt to breed the phenomenon within the lab had been solely partly profitable; experiments with drying fluids led to options, however by no means these as diversified because the examples proven above. We due to this fact nonetheless don’t totally perceive the main points of the mechanism. Luckily, the options don’t have an effect on the operation of the
movies. If needed, they could possibly be eradicated by engineering
the membrane for greater stiffness or by incorporating a preexisting
tensile stress to offset the buckling.

Since first observing the
options, I’ve collected different examples of skinny movie patterns in
the literature. The variability is unbelievable, however I have never discovered any
that completely match the unique options. Most buckled movies
show very common, periodic patterns that don’t resemble the
blotchy, irregular association of options proven in optical and AFM
micrographs above. The closest patterns are these of drying liquids
as they dewet substrates. The
random association of droplets bears a a lot stronger resemblance to
the unique options than the folded movies. It might merely be that
no one has mixed dewetting experiments
with extraordinarily compliant free-standing movies earlier than and revealed the
outcomes. (Till 2007, shortly after I drafted the primary model of this be aware: see From Science to Engineering on the backside of this web page.)

This be aware summarizes these
findings for the curiosity of others. Mounds, bumps, wrinkles,
dimples… There are as many descriptions as photos. The unique
nomenclature of the authors is the very best accompaniment.

Skinny movie buckling

We start with the compressive buckling of skinny
movies. Suspended sq. membranes bear at the very least two buckling
transitions. The primary is characterised by a domed form that
continues into an X, or
saltire, below greater stress.
The second resembles an augmented tetraskelion
whose folded options grow to be extra distinguished with rising stress or
membrane space. I’ve usually seen these patterns on
ceramic and steel membranes and may often distinguish them from
the random bumps that appear to be associated to drying fluids.

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

Again in 1989, Ali Argon at MIT revealed some pictures of SiC deposited on (and subsequently delaminating from) silicon by plasma-assisted (now termed plasma-enhanced) chemical vapor deposition; these look fairly much like the options I characterised:

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

Toyoichi Tanaka, additionally at MIT, studied gels of
acrylamide and the impact of osmotic
swelling in water. Because the outer portion of the gel swells on account of a
part transition, the unaffected inside area transmits a
compressive stress to the floor. Now we begin moving into some elegant evocative descriptions:

When a polymer
gel undergoes an in depth swelling, a stupendous, common sample
seems on the floor… Firstly,
the sample is extraordinarily effective, having a texture much like that of a
frosted glass. As time goes on, the models of sample coalesce,
doubling their attribute measurement. When
the unit measurement turns into similar to the dimensions of the gel, the sample
step by step disappears.”

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

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

Annie Viallet at
Joseph Fourier College investigated the shapes created in lipid
vesicles throughout osmotic deswelling of the inside.

When the
decreased quantity of partially deflated vesicles varies, an excellent selection
of shapes (pears, peanuts, starfish…) is noticed.”

An incredible
number of vesicle shapes had been obtained within the chamber on the finish of
the shrinkage course of: ellipsoids, dumbbells, stomatocytes,
discocytes, pears, stars, and so forth.”

As within the
case for gradual shrinkage, we noticed numerous shapes…the formation
of a number of small invaginations of the membrane pointed towards the
inside of the vesicles, which seemed like raspberries…the
formation of lipid pearl necklaces.”

(Viallat
et al. “Large lipid vesicles full of a gel: form
instability induced by osmotic shrinkage” Biophys J 86
2179-2187 2004)

The breaking of axial symmetry within the
glassy pores and skin of drying polysaccharide dextran results in a pentagonal
association of radial wrinkles:

(Pauchard
et al. “Steady and unstable floor evolution throughout the drying
of a polymer resolution drop” Phys Rev E 68 052801
2003)

Drying droplets of colloidal polystyrene grow to be buckled and folded (images are on high, simulated shapes beneath):

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

…and “blisters” seem as a polymer movie swells in water:

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

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

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

One other group’s evaluation predicts “ridges,” “cones,”
“mounds,” and “basins”:

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

A few of these simulated shapes have been noticed in a special
context. A elastomer substrate whose high layer undergoes volumetric
enlargement from oxygen plasma publicity shows “advanced but
periodic wavy buildings”:

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

Chan and Crosby made a part map of those options as influenced by the oxidation time and area measurement:

(Chan et al. “Fabricating microlens arrays by floor wrinkling” Superior Supplies 18
3238-3242 2006)

At this level it is most likely time for a shar pei (“sand [i.e., rippled] pores and skin”):

(Instagram 2016)

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

(Kwon et al. “Wrinkling
of a sol-gel-derived skinny movie” Bodily Evaluate E 71
011604 2005)

…and ridges of deflated PDMS are proven in these micrographs of the canonical buckling mannequin—a movie that is too huge for its surroundings:

(Jin et al. “Mechanical instabilities of soppy supplies: 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 buildings” Scripta Materialia 44
2623-2627 2001)

Related options have additionally been described as “phone twine buckles”:

(Moon et al. “An experimental research of the affect of imperfections on
the buckling of compressed skinny movies” Acta Materialia 50
1219-1227 2002)

Claymand et al. referred to as their row of buckled gold movie includes a “quasiperiodic varicose” sample:

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

“Herringbone” shapes seem when a gold movie is cooled
after deposition on PDMS:

(Chen et al. “A household of
herringbone patterns in skinny movies” Scripta Materialia 50
797-801 2004)

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

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

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

(Yang et al. “Harnessing floor wrinkle patterns in mushy matter” Adv Funct Supplies 20
2550-2564 2010)

Below different situations, the identical report by Yang et al. presents “ripples”:

Everlasting wrinkles are seen in a free-standing boron nitride
movie after its salt assist is dissolved away:

(Coupeau et al. “Proof
of plastic harm in skinny movies round buckling buildings”
Skinny Stable Movies 469-470 221-226
2004)

…and casein gels exhibit nonetheless extra options much like what I noticed in suspended steel movies:

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

“Creases” and wrinkles seem when an elastomer is affixed to a comparatively inflexible substrate utilizing an electrical discipline:

(Wang et al. “Creasing-wrinkling transition in elastomer movies below electrical fields” Phys Rev E 88
042403 2013)

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

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

Skinny Movie Dewetting

We now flip to the
dewetting of liquids, generally modeled as a decomposition into moist
and dry phases. Anshutosh Sharma of the Indian Institute of
Know-how describes dewetting morphology:

As
the movie thickness is elevated, the preliminary pathway of
evolution modifications from the formation of small spherical droplets, to
lengthy mesas (parapets) and islands, to round holes, all of which
ultimately resolve by ripening into a group of spherical pancakes at
equilibrium. Nevertheless, past a sure 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 throughout gap development.

(Sharma et al. “Sample
formation and dewetting in skinny movies of liquids displaying full
macroscale wetting: from ‘pancakes’ to ‘swiss
cheese’” Langmuir 20 10337-10345
2004)

Leonard Schwarz on the College of Delaware dried a thermosetting polymer on an inked aluminum sheet. His group noticed “specific
patterns of holes, ridges, filaments, and, in the end, droplets”
each in experiments and in simulations:

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

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

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

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

(Reiter,
“Unstable skinny polymer movies: rupture and dewetting course of,”
Langmuir 9 1344-1351,
1993)

A lot later, Manoj Chaudhury carried out an in depth research of fingering instabilities, together with the “debonding, sliding, peeling and the therapeutic of a blister,” producing spectacular
photos resembling the next:

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

Skinny Movie Deposition

When silver is sputtered onto a layer of silicone oil, the preliminary
sputtered atoms are pushed into the highest layer of the oil. At some
percolation threshold, a “branched construction” 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. “Development
habits and floor morphology of Ag tough movies deposited on
silicone oil surfaces” Skinny Stable Movies 342 30-34
1999)

I’ve
included these silver options due to their visible enchantment;
nevertheless, it’s essential to notice that their origins are extra
advanced than the opposite patterns proven beforehand. The entire earlier
patterns are attributable to imposed or inside compressive stress (within the
case of the buckled movies) or surface-volume vitality tradeoffs (within the
case of the dewetting movies). In distinction, the sputtered silver movie
morphology is attributed to mixing of the
silver atoms with the silicone oil layer.

From Science to Engineering

Scientists essentially use instruments to study extra about nature; engineers essentially find out about nature to develop higher instruments.
Beginning round 2007, reviews of skinny movie deformation by liquids, the phenomenon that so mystified me, exploded within the literature. It began with Huang et al.’s report of “Capillary wrinkling of floating skinny polymer movies” in Science:

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

Immediately, a brand new discipline—elastocapillarity—was rising. Enrique Cerda, one of many coauthors, had achieved his postdoc with Mahadevan at Harvard with a heavy focus on wrinkling; in reality, Adam Zeiger and I cited one among their papers within the
context of cell-contraction-induced wrinkling of a thin silicone film.
Right here, I used to be circling again to skinny movie patterns from a special route—animate actomyosin-generated buckling through stay cells:

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

Floor instabilities had been a sizzling matter ( you have made it when your discipline will get surveyed in MRS Bulletin):

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

…and Wang and Zhao offered a part map of morphologies:

(Wang et al. “A 3-dimensional part diagram of
growth-induced floor instabilities”
Scientific Experiences 5 8887
2015)

With this explosion of latest analysis, I discovered some extra shut matches to the localized floral patterns I noticed in my sub-micron-thick suspended Ti/Au/Ti membranes 50 μm on a aspect:

(Yan et al. “Spontaneous wrinkling sample of a constrained skinny movie
membrane”
Utilized Physics A 107 761-767
2012)

Nonetheless different reviews have described tents, branches, tubes, sawteeth, shrivels, wavy leaves, ruga, furrows, curtains, and—one among
my favorites to this point—wrinklons! Positive, let’s coin one other phrase, given the apparent paucity of the language to explain these options.

The
massive variety of reviews within the literature and the frequency of
rediscovery of those patterns proven above (and there are various extra,
related, patterns not included right here) recommend that an atlas of
patterns could be useful to researchers. Due to the evocative
descriptions discovered to this point, I’m awaiting the invention of extra
reviews of crinkles,
nodules, buttons, indents, grooves, puckers, scabs, scales, depressions, notches, slashes, serrations, channels…scallops…corrugations…crenulations…