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FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS

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. 100 nm. Motivation. Experiments find faceted structures in the 100nm size range. -1. PCDA-OH.

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FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS

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  1. FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS RastkoSknepnek, Cheuk-Yui Leung, Liam C. Palmer GrazianoVernizzi, Samuel I. Stupp, Michael J. Bedzyk, Monica Olvera de la Cruz

  2. 100 nm Motivation Experiments find faceted structures in the 100nm size range. -1 PCDA-OH PCDA-KKK +3 Greenfield, M., et al., JACS (2009) Minimization of electrostatic energy on fixed geometry reveals that in certain cases faceted structures are energetically favorable. Vernizzi & Olvera de la Cruz, PNAS (2007) Can electrostatic interactions lead to faceting?

  3. Coarse-graining +1,+2,+3 wc e -1 tail-tail interaction potential Cooke, et al., PRE, 2005 unstable Electrostatic effects treated within linearized Debye-Hueckel theory: liquid gel Cooke, et al., PRE, 2005

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

  5. Estimate of the bending rigidity k Use results of linearized Helfrich theory: h(x,y) vertical position at (x,y) s – lateral tension Electrostatic interactions significantly increase k. T=0.7, wc=1.15

  6. Estimate of the Young’s modulus Y Regular two-dimensional ionic crystals: square triangular triangular triangular 1:1 1:2 1:3 Total energy: extract Y Estimate: Y3:1/Y2:1»1.8

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

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

  9. Optimal faceted structures khard/ksoft=10 Yhard/Ysoft=5 line tension g=0.1 g=0.3 g=0.6 hard component fraction 40% 60% 80% 20%

  10. 100 nm Optimal faceted structures khard/ksoft=30 Yhard/Ysoft=10 line tension g=0.1 g=0.3 g=0.6 hard component fraction 40% 60% 80% 20%

  11. Summary • 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 Experimental collaborators: Dr. Megan Greenfield Cheuk Leung Prof. Michael Bedzyk Prof. Samuel Stupp Northwestern High Performance Computing System - Quest Funding provided by the U.S. Department of Energy

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