1. Sublimation in Colloidal Crystals
Kevin Schoelz
Mentor: Amit Chakrabarti
Thanks to Siddique Khan

2. Asakura-Oosawa Potential
Entropic “Force”
Bringing the colloidal particles together reduces the depletion zone of the polymers
Colloids are hard spheres--Polymers and Colloids cannot overlap
Depletion Zone

3. Asakura-Oosawa Potential
Energy
Main paramerters are well depth-- determined by the volume fraction
And the range of interaction, determined by the diameter of the polymer(Distances are normalized to the diameter of the colloid)
Interaction range

4. Phase Diagram
Graph shows three parameters--Temperature, volume fraction and interaction range,
We are in the second graph--Protein Limit

5. Sublimation in 2D 2006 paper by Savage et. al. “Transient Liquid”
Measures Order
y6=ei6ø
Check order parameter: Solids have higher values than liquids (Is this really an order parameter?)
In 3D system, order parameter is Spherical Harmonics

6. Sublimation in 3D t=50 t=0 t=5,000 t=10,000
Notice larger change from 50 to 5000 as opposed to
This particular system xi=0.1, phi_p=.221 E=3kT, np=5688
t=5,000
t=10,000

7. Geometry of a melting sphere
Assume crystal is spherical
Assume even particle loss
Then, Nm~3R0 ∆R~ ∆V R0
For a sphere, Nm and Nc are volume terms
Uses mostly simple geometry ∆R

8. Geometry of a melting sphere
Linear Regime
Assumptions from previous slide don’t universally hold, but we can see a linear regime where these assumptions seem to be true.
(Geometry points are model generated from assumptions. Slope of linear regime and geometry line approx. the same)
Assumptions seem to be universally true for 3.5kT data points
Problem occurs at the beginning of other data sets

9. Sublimation Crystals were formed at 4kT
Crystals melted at at 2kT, 2.5kT, 3kT and 3.5kT
At 2kT, sublimation was too quick: exponential behavior?
Other energy levels exhibited scaling
Scaling meaning Nm~t^(alpha) where alpha=2/3
Really not crystals--lacking in structure (if time mention that if much below 4kT, gel structures form)

10. Monomers Early Behavior ~t^1
In other systems early behavior always around 1, total behavior usually around 2/3 (ranges from .6 to .7071)

11. Kinetics of 3D Sublimation
Looked at several possible sublimation mechanisms
Particles come from
Surface?
Entire volume?
Edges and boundaries?
dN/dt=aR^2-bR^3
Right now still too many undetermined constants: Needs further work

12. Kinetics of 3D Sublimation
Adding an interaction term to the equation provides promising results

13. Real World Applications
The AO potential is useful in studies of insulin
Insulin in gel form
Breaks up into droplets

14. Real World Applications

15. Sources
Imaging the Sublimation Dynamics of Colloidal Crystallites. J. R. Savage, D. W. Blair, A. J. Levine, R. A. Guyer, A. D. Dinsmore Science 3 November 2006: Vol no. 5800
Insulin Particle Formation in Supersaturated Aqueous Solutions of Poly(Ethylene Glycol). Bromberg L., Rashba-Step J., Scott T. Biophysical Journal Vol 89, Nov 2005,
Programs provided by Amit Chakrabarti and Siddique Khan
Funded by National Science Foundation Grant