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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
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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.
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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:
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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)
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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
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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
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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:
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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.
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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%
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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
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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
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