1. Wrinkles/Folds and the Role of Interfacial Thermodynamics
Luka Pocivavsek
James Franck Institute and Department of Chemistry,
The University of Chicago, Chicago IL, USA

2. Motivation: Stress Focusing in Elastic Manifolds
Unsupported membranes (e.g. paper) crumple:
flat piece
of paper
confine
un-confine
Confien a flat piece of paper by crumpling it into a ball and it packs by bending and stretching along certain lines while remaining flat along others. By uncrumpling the paper the lines along which all the stress was concentrated during compaction remain since the paper was stretched in this region, however the surface between the ridges is flat. The interesting phenomenon here is the focusing of mechanical stresses only into particular parts of the paper and not a distribution of this stress across the entire paper. Now take a similar membrane and place it on top a fluid. Compress along one direction and you get wrinkles. Compress more and the now purely bending stresses are focused into only one part of the surface, the fold.
How would this behavior change if the membrane was resting on a substrate?

3. Wrinkle to fold transition in thin elastic film
Polyester (t = 10 m) on water
 ~ 2cm A1 A0
Start with a wrinkled surface: continuous, distributed stress across the surface -> folds: focused, localized stress and displacement.

4. Numerical study of thin elastic films resting on fluids (with E. Cerda)
equation for
membrane curvature
kinematic equations
Boundary conditions:
Imposed horizontal displacement:

5. Quantifying the Wrinkle to Fold Transition
amplitude order parameter
dimensionless displacement (/)
A wrinkled surface should be stable against further confinement by a third of its initial wavelength, beyond this the surface geometry becomes unstable toward the new localized folded state.

6. Analytical work - scaling relations
inextensibility
Wrinkles - linear case
Fold - non-linear case

7. Critical Compression - predictive power of scaling energies
dimensionless energy
dimensionless displacement (/)
Analytical predictions in agreement with experiments and numerics.

8. Generality of wrinkle to fold in thin films
Collaboration with Binhua Lin (UChicago)
Gold nano-particle trilayer ~ 15nm thick
Full angstrom level characterization of film:
D. Schultz et al. Structure, Wrinkling, and Reversibility of Langmuir
Monolayers of Gold Nanoparticles, J. Phys. Chem. B, (2006), 110,

9. Coexisting states also seen in model systems studied:
Wrinkle to Fold Model Explains Instabilities in Molecular Films
Condensed lipid monolayer (thickness = 2nm) has coexisting parts: a flat interfacial layer and deep buckles.
Coexisting states also seen in model systems studied:
system: DPPC:POPG 7:3 monolayer at 25oC compressed at 0.1mm/sec
“grid structure” - dark crystalline domains (DPPC) in a disordered bright matrix (POPG), monolayer is rigid.
“folds” - bright lines running up/down perpendicular to compression correspond to large out-of-plane buckles
“jerks” - lateral displacements of monolayer as folds form.
bilateral compression axis

10. Non-intuitive response with small changes in subphase composition
system: DPPC:POPG 7:3 monolayer at 25oC compressed at 0.1mm/sec
0% glycerol (1 mPa•sec)
40% glycerol (3 mPa•sec)
small amplitude folds
large amplitude folds
Large folds seen for >10% glycerol.
Non-intuitive at first why a small perturbation would give rise to an order of magnitude change in fold size.

11. Connection between interface structure and folding?
Quantifying different folding behavior of water and glycerol solutions:
0% glycerol
40% glycerol
lipid
glycerol rich boundary layer
bulk fluid
Structural/Mechanical Sugar Hypothesis:
Increased thickness gives rise to larger folds
Need an understanding of relaxation times and viscosities of bound glycerol layer
XR, neutron reflectivity, and GID show glycerol enriched layer that stabilizes lipids  cross-linked hydrogen bond network induced by glycerol
Q : Phase Separation of Water/Glycerol Binary Mixtures Next to Lipid Monolayers --
An X-ray and Neutron Reflectivity Study Wednesday 2:03-2:15 PM

12. compress a thin solid film on a fluid:
Wrinkle to fold transition holds over 3 decades in thickness
compress a thin solid film on a fluid:
linear response  wrinkling
non-linear response  fold
simply considering the monolayer a homogenous elastic membrane the wrinkle to fold model explains:
(1) fold size
(2) fold directionality
(3) folding in non-biphasic monolayers
Pocivavsek L., R. Dellsy, A. Kern, S. Johnson, B. Lin, KYC Lee, E. Cerda, Stress and Fold Localization in Thin Elastic Membranes, Science 320, 912 (2008)

13. Acknowledgments Ka Yee Lee, Binhua Lin, Enrique Cerda
University of Chicago
USACH/UdeC
SPEAR, Lujan, LANL
Tom Witten
Kseniya Gavrilov
Eva Chi
Kathleen Cao
Shelli Frey
Dongxu Li
Brian Leahy
Sebastian Johnson
Nico Rivas
Jarek Majewski
Eric Watkins
ChemMatCARS, ANL/UChicago
Mati Meron
Tim Graber
Jim Viccaro