APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko...
-
Upload
claude-long -
Category
Documents
-
view
218 -
download
0
Transcript of APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko...
![Page 1: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/1.jpg)
APS March Meeting Dallas, March 22, 2011
FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS
Rastko Sknepnek, Cheuk-Yui Leung, Liam C. PalmerGraziano Vernizzi, Samuel I. Stupp, Michael J. Bedzyk, Monica Olvera de la Cruz
![Page 2: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/2.jpg)
APS March Meeting Dallas, March 22, 2011
Motivation
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
-1
+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.
![Page 3: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/3.jpg)
APS March Meeting Dallas, March 22, 2011
Coarse-graining
Cooke, et al., PRE, 2005tail-tail interaction potential
wc
Cooke, et al., PRE, 2005
+1,+2,+3
-1
gel
liquid
unstable
e
exp
0
ij
i j DH c cDH ij ij
c
rq q V r for r r
V r r
for r r
Electrostatic effects treated within linearized Debye-Hueckel theory:
![Page 4: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/4.jpg)
APS March Meeting Dallas, 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, 0.7wc=1.15
1:1 (liquid) 1:2 (ordered) 1:3 (ordered)T=0.7
1:1 (liquid) 1:2 (liquid) 1:3 (“almost” ordered)
![Page 5: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/5.jpg)
APS March Meeting Dallas, March 22, 2011
224 2B
q
k TL h
q q
Use results of linearized Helfrich theory:
,,
, x y
x yx y
i q x q y
q qq qh x y h e
h(x,y) vertical position at (x,y)
s – lateral tension
T=0.7, wc=1.15
Electrostatic interactions significantly increase k.
Estimate of the bending rigidity k
![Page 6: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/6.jpg)
APS March Meeting Dallas, March 22, 2011
Estimate of the Young’s modulus Y
Regular two-dimensional ionic crystals:
square triangular triangular triangular
1:1 1:2 1:3
12 6
'
,
14
2i j
cell celli j ij ij ij
q qE N E
r r r
Total energy:
(0) 31( )
2cell ijkl ij kl ijE c c u u O u extract Y
Estimate: Y3:1/Y2:1»1.8
![Page 7: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/7.jpg)
APS March Meeting Dallas, 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
-1
Segregation leads to an onset of effective line tension between differently charged regions.
In continuum representation:
t CF dl
![Page 8: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/8.jpg)
APS March Meeting Dallas, 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)
, , 1,
1 .discreteb i i t i t
i t
E n n
bending energy:
All effects of charge are encoded in the elastic properties.
stretching energy:
20,
1
2discretes ij
i j
E k l l
line tension: ,,
1 .2 i j
discretet t t
i j
F We used simulated annealing
Metropolis Monte Carlo simulations to find optimal shapes.
![Page 9: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/9.jpg)
APS March Meeting Dallas, March 22, 2011
Optimal faceted structures khard/ksoft=10 Yhard/Ysoft=5
g=0.1
g=0.3
g=0.6
linetension
hard component
fraction 20% 40% 60% 80%
![Page 10: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/10.jpg)
APS March Meeting Dallas, March 22, 2011
Optimal faceted structures khard/ksoft=30 Yhard/Ysoft=10
g=0.1
g=0.3
g=0.6
linetension
hard component
fraction 20% 40% 60% 80%
100 nm
![Page 11: APS March MeetingDallas, March 22, 2011 FACETING OF MULTICOMPONENT CHARGED ELASTIC SHELLS Rastko Sknepnek, Cheuk-Yui Leung, Liam C. Palmer Graziano Vernizzi,](https://reader036.fdocuments.net/reader036/viewer/2022062409/56649d015503460f949d3f0c/html5/thumbnails/11.jpg)
APS March Meeting Dallas, March 22, 2011
Summary
Funding provided bythe U.S. Department of Energy
Experimental collaborators:
Dr. Megan GreenfieldCheuk LeungProf. Michael BedzykProf. Samuel Stupp
Northwestern High PerformanceComputing 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