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

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

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

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

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

Sublimation in 3D t=50 t=0 t=5,000 t=10,000 Notice larger change from 50 to 5000 as opposed to 5000 -10000 This particular system xi=0.1, phi_p=.221 E=3kT, np=5688 t=5,000 t=10,000

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

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

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)

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

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

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

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

Real World Applications

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. 314. 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, 3424-3433 Programs provided by Amit Chakrabarti and Siddique Khan Funded by National Science Foundation Grant 0855159