Outline • • • • • •

Introduction Model Theory Simulation methods Results and comparison to theory Summary

Outline • • • • • •

Introduction Model Theory Simulation methods Results and comparison to theory Summary

Self-assembly: the spontaneous organization of matter into reversibly bound aggregates due to minimization of free energy. Attractive site

Self-assembly

Preisler Z. et. al., Soft Matter, 2014, 10, 5121

Why study self-assembly: • Fundamental science: Key to understand living structures

• Technology: Create new materials, new methods in fabricating materials (1) Life: The Science of Biology, 8th edtion, W. H. Freeman, 2007 (2) Q. Chen, S.C. Bae and S. Granick, Nature 469, 381 (2011)

(1)

Simplified plot of cell membrane, a selfassembling phospholipid bilayer. (2)

Patchy particles self-assemble into an open Kagome lattice, not closed-packed crystal as usually observed with spheres.

A particular case of self-assembly: interactions between monomers favour the formation of linear chains Nematic phase: The system has orienatational order but no positional order

Liquid crystals formed by short DNA duplexes (6-20) base pairs (1) (1): M. Nakata et al., Science 318, 1276 (2007)

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Introduction Model Theory Simulation methods Results and comparison to theory Summary

1) Sticky hard cylinders Experiments: self-assembing short DNA duplexes form nematic phase, unexpectedly due to low anisotropy Short DNA duplexes: 6-20 base pairs

M. Nakata et al., Science 318, 1276 (2007)

1) Sticky hard cylinders • Hard cylinders of elongation X0 = 2 • Two opposite sticky points on ends • Site-site potential:

u0 VW ( x) 0

Base stacking

Sugar-phosphat backbon

12 bp ~ 4 nm

Base pairing

~ 2 nm

if if

x x

2) Bent hard cylinders Experiments: sequence dependence of nematic critical nematic concentration in DNA duplexes 12 base pairs G. Zanchetta, T. Bellini, M. Nakata and N. A. Clark, J. Am. Chem. Soc., 2008, 130 , 12864 – 12865

Hypothesis: They are bent core of different bending angles Perform all-atom molecular dynamic simulations to (i) confirm and (ii) estimate bending angles

2) Bent hard cylinders Snapshot from all-atom molecular dynamic simulations

Nematic concentration at coexistence(1) (1)G.

500 mg/ml

620 mg/ml

850 mg/ml

Zanchetta, F. Giavazzi, M. Nakata, M. Buscaglia, R. Cerbino, N. A. Clark and T. Bellini, Proc. Natl. Acad. Sci. U. S. A. , 2010, 107 , 17497 – 17502

2) Bent hard cylinders 2 alike hard cylinders

Estimates of bending angles only slightly different between SYBC and ASBC => Go for symmetry model

2 hard cylinders, different length

3) Sticky hard spheres

Kern-Frenkel VKF model:

if R12 D D R12 D and u0 if cos( R12 r1 ) cos and cos( R12 r2 ) cos 0 otherwise /2

r1

D/2

2

r2

R12

Outline • • • • • •

Introduction Model Theory Simulation methods Results and comparison to theory Summary

Some proposed theories for isotropic, nematic phases and self-assembly: • Wertheim theory for self-assembly in isotropic phase

(1984)

• Onsager and Parsons-Lee theory of isotropic-nematic phase transition in rigid, monodisperse particles (1949) • Lü and Kindt semi-phenomenological theory of linear self-assembly of bi-functional spheres (2004) • Kuriabova theoretical framework of linear selfassembly of hard cylinders (2010)

Some proposed theories for isotropic, nematic phases and self-assembly: • De Michele et. al., Macromolecules, 2012, 45 , 1090 –

1106

M: average number of monomers in a chain : packing fraction

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Introduction Model Theory Simulation methods Results and comparison to theory Summary

Simulation techniques used Coexistence lines • Locate one point of coexistence: Successive umbrella sampling (SUS) to compute probability distribution P[N](1) • Using Kofke method to obtain coexistence line from the point(2) (1) P. Virnau, M. Muller, J. Chem. Phys., Vol. 120, No. 23, 15 June 2004 (2) D. A. Kofke, J. Chem. Phys., Vol. 98, No.5, 1 March 1993

SUS • Perform grand canonical simulation simultaneously on many systems, the number of particle of each is limited in a window of size w = 2, and consecutive windows overlap. • Hk [N]: the frequency that state N of kth windows is visited Hkl and Hkr: histogram of its left and right boundary, respectively. H1r H 2 r H k [ N ] P[ N ] P[ N min ] H1l H 2l H kl

SUS • Reweight P[N] so that it has 2 peaks, the areas below them are equal: zSim ( N , zRe w ) zRe w Re w

P P

Sim

( N , zSim )

N

Kofke • Integrate Clausius-Clapeyron equation: d ln P h Pv d

h,v : computed by NPT simulation

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Introduction Model Theory Simulation methods Results and comparison to theory Summary

1) Hard cylinders Isotropic-nematic oexistent lines

Nguyen KT, Sciortino F, De Michele C, Langmuir. 2014; 30(16):4814-9.

1) Hard cylinders Average aspect ratio of chains

Nguyen KT, Sciortino F, De Michele C, Langmuir. 2014; 30(16):4814-9.

1) Hard cylinders Average aspect ratio of chains: compare with other theory

Nguyen KT, Sciortino F, De Michele C, Langmuir. 2014; 30(16):4814-9.

2) Bent hard cylinders Isotropic-nematic phase coexistence lines

Nguyen KT, Battisti A, Ancora D, Sciortino F, De Michele C, Soft Matter, 2014; DOI: 10.1039/C4SM01571A

2) Bent hard cylinders Root of the bending angle-dependence of phase coexistence lines

Nguyen KT, Battisti A, Ancora D, Sciortino F, De Michele C, Soft Matter, 2014; DOI: 10.1039/C4SM01571A

2) Bent hard cylinders Root of the bending angle-dependence of phase coexistence lines

Nguyen KT, Battisti A, Ancora D, Sciortino F, De Michele C, Soft Matter, 2014; DOI: 10.1039/C4SM01571A

2) Bent hard cylinders Nematic coexistent concentration: Comparison between theory and experiment(1)

GST : stacking free energy, estimated by experiments(2)

(1) G.

Zanchetta, F. Giavazzi, M. Nakata, M. Buscaglia, R. Cerbino, N. A. Clark and T. Bellini, Proc. Natl. Acad. Sci. U. S. A. , 2010, 107 , 17497 – 17502 (2) C. De Michele, L. Rovigatti, T. Bellini and F. Sciortino, Soft Matter, 2012, 8, 8388 –8398 Nguyen KT, Battisti A, Ancora D, Sciortino F, De Michele C, Soft Matter, 2014; DOI: 10.1039/C4SM01571A

2) Bent hard cylinders Theoretical prediction: cN insensitive to GST for highly bent particles

Nguyen KT, Battisti A, Ancora D, Sciortino F, De Michele C, Soft Matter, 2014; DOI: 10.1039/C4SM01571A

3) Hard spheres Isotropic-nematic coexistent lines

3) Hard spheres Average aspect ratio of chains

3) Hard spheres Chain length distribution Lü, X. et. al. (1) for chains of low flexibility (persistence length ~ 100 -1000) in nematic phase:

(1)

Lü, X.; Kindt, J. Chem. Phys. 2004 , 120, 10328-10338.

3) Hard spheres Chain length distribution

Outline • • • • • •

Introduction Model Theory Simulation methods Results and comparison to theory Summary

Summary • Introduced a procedure to compute phase coexistent lines (not only for isotropic-nematic transition) with high precision • Provided some sets of highly accurate data of isotropic-nematic coexistent lines in selfassembling systems for different models to compare with theory • Therefore showed the potential of the theory as a framework to study coupling of selfassembly and nematization