1. APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi, Samuel I. Stupp, Michael J. Bedzyk, Monica Olvera de la Cruz

2. APS March MeetingDallas, March 22, 2011 MotivationMotivation Can electrostatic interactions lead to faceting? 100 nm Greenfield, M., et al., JACS (2009) Vernizzi & Olvera de la Cruz, PNAS (2007) PCDA-OH PCDA-KKK +3 Experiments find faceted structures in the 100nm size range. Minimization of electrostatic energy on fixed geometry reveals that in certain cases faceted structures are energetically favorable.

3. APS March MeetingDallas, March 22, 2011 Coarse-grainingCoarse-graining Cooke, et al., PRE, 2005 tail-tail interaction potential wcwc Cooke, et al., PRE, 2005 +1,+2,+3 gel liquid unstable  Electrostatic effects treated within linearized Debye-Hueckel theory:

4. APS March MeetingDallas, March 22, 2011 Molecular dynamics of a bilayer patch with 4000 lipids. T=0.6 Focus on a small region of phase diagram T=0.6, 0.7 w c =1.15 1:1 (liquid)1:2 (ordered)1:3 (ordered) T=0.7 1:1 (liquid)1:2 (liquid)1:3 (“almost” ordered)

5. APS March MeetingDallas, March 22, 2011 Use results of linearized Helfrich theory: h(x,y) vertical position at (x,y)  – lateral tension T=0.7, w c =1.15 Electrostatic interactions significantly increase . Estimate of the bending rigidity 

6. APS March MeetingDallas, March 22, 2011 Estimate of the Young’s modulus Y Regular two-dimensional ionic crystals: squaretriangular 1:11:21:3 Total energy: extract Y Estimate: Y 3:1 /Y 2:1  1.8

7. APS March MeetingDallas, March 22, 2011 In addition, different valence charges are expected to segregate. MD simulation of a three component system (1:2 and 1:3) in liquid phase (T=0.9) +3 +2 Segregation leads to an onset of effective line tension between differently charged regions. In continuum representation:

8. APS March MeetingDallas, March 22, 2011 We find shaped using a discretized version of the continuum theory of elasticity. Regions with different charge ratios have different elastic properties. (Seung and Nelson, PRA 1988) bending energy: All effects of charge are encoded in the elastic properties. stretching energy: line tension: We used simulated annealing Metropolis Monte Carlo simulations to find optimal shapes.

9. APS March MeetingDallas, March 22, 2011 Optimal faceted structures  hard /  soft =10 Y hard /Y soft =5  =0.1  =0.3  =0.6 line tension hard component fraction 20% 40%60%80%

10. APS March MeetingDallas, March 22, 2011 Optimal faceted structures  hard /  soft =30 Y hard /Y soft =10  =0.1  =0.3  =0.6 line tension hard component fraction 20% 40%60%80% 100 nm

11. APS March MeetingDallas, March 22, 2011 SummarySummary Funding provided by the U.S. Department of Energy Experimental collaborators: Dr. Megan Greenfield Cheuk Leung Prof. Michael Bedzyk Prof. Samuel Stupp Northwestern High Performance Computing System - Quest We show that electrostatic interaction can lead to lipid crystallization Charge significantly renormalizes elastic properties Different regions segregate – effective line tension Resulting shapes are faceted