Report

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 APS March Meeting Dallas, March 22, 2011 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? APS March Meeting Dallas, March 22, 2011 Coarse-graining +1,+2,+3 wc e -1 tail-tail interaction potential Cooke, et al., PRE, 2005 unstable liquid gel Electrostatic effects treated within linearized Debye-Hueckel theory: V D H rij exp rij qi q j V D H rc e rij 0 for r rc for r rc Cooke, et al., PRE, 2005 APS March Meeting Dallas, March 22, 2011 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) APS March Meeting 1:2 (liquid) 1:3 (“almost” ordered) Dallas, March 22, 2011 Estimate of the bending rigidity Use results of linearized Helfrich theory: 2 L 2 hq h x, y k BT q q 4 h(x,y) vertical position at (x,y) qx ,q y hq x , q y e i qx x q y y 2 – lateral tension Electrostatic interactions significantly increase . T=0.7, wc=1.15 APS March Meeting Dallas, March 22, 2011 Estimate of the Young’s modulus Y Regular two-dimensional ionic crystals: square triangular 1:1 triangular triangular 1:2 1:3 Total energy: E N cell E cell 1 2 i, j qi q j ' 4e rij rij 12 r ij 6 extract Y E cell c (0) 1 2 c ijkl u ij u kl O ( u ij ) 3 Estimate: Y3:1/Y2:11.8 APS March Meeting Dallas, March 22, 2011 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) Segregation leads to an onset of effective line tension between differently charged regions. APS March Meeting In continuum representation: Ft dl C Dallas, March 22, 2011 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: discrete Eb i 1 n i , t n i , t 1 . Es i ,t line tension: Ft discrete 1 2 i, j APS March Meeting ti ,t j . discrete 1 2 k ij l l 0 2 i, j We used simulated annealing Metropolis Monte Carlo simulations to find optimal shapes. Dallas, March 22, 2011 Optimal faceted structures hard/soft=10 Yhard/Ysoft=5 line tension =0.1 =0.3 =0.6 hard component fraction 20% APS March Meeting 40% 60% 80% Dallas, March 22, 2011 Optimal faceted structures hard/soft=30 Yhard/Ysoft=10 line tension =0.1 =0.3 =0.6 hard component fraction 20% APS March Meeting 40% 60% 80% Dallas, March 22, 2011 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 Funding provided by the U.S. Department of Energy APS March Meeting Northwestern High Performance Computing System Quest Dallas, March 22, 2011