We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.
REFERENCES
1.
2.
K.
Matyjaszewski
and J.
Xia
, Chem. Rev.
101
, 2921
–2990
(2001
).3.
V. C.
Gibson
and S. K.
Spitzmesser
, Chem. Rev.
103
, 283
–316
(2003
).4.
N. M. G.
Franssen
, J. N. H.
Reek
, and B.
de Bruin
, Chem. Soc. Rev.
42
, 5809
–5832
(2013
).5.
R.
Saito
, G.
Dresselhaus
, and M. S.
Dresselhaus
, Physical Properties of Carbon Nanotubes
(Imperial College Press
, London
, 1998
), Vol. 4
.6.
M. M.
Shulaker
, G.
Hills
, N.
Patil
, H.
Wei
, H.-Y.
Chen
, H.-S.
Philip Wong
, and S.
Mitra
, Nature (London)
501
, 526
–530
(2013
).7.
T.
Scheibel
, R.
Parthasarathy
, G.
Sawicki
, X.-M.
Lin
, H.
Jaeger
, and S. L.
Lindquist
, Proc. Natl. Acad. Sci. U.S.A.
100
, 4527
–4532
(2003
).8.
W.-F.
Xue
, S. W.
Homans
, and S. E.
Radford
, Proc. Natl. Acad. Sci. U.S.A.
105
, 8926
–8931
(2008
).9.
Q.
Meng
, Y.
Kou
, X.
Ma
, Y.
Liang
, L.
Guo
, C.
Ni
, and K.
Liu
, Langmuir
28
, 5017
(2012
).10.
A. G.
Daful
, J. B.
Avalos
, and A. D.
Mackie
, Langmuir
28
, 3730
(2012
).11.
Y. A.
Berlin
, A. L.
Burin
, and M. A.
Ratner
, Superlatt. Microstruct.
28
, 241
–252
(2000
).12.
C.
De Michele
, T.
Bellini
, and F.
Sciortino
, Macromolecules
45
, 1090
–1106
(2012
).13.
H. R.
Vutukuri
, A. F.
Demirörs
, B.
Peng
, P. D. J.
van Oostrum
, A.
Imhof
, and A.
van Blaaderen
, Ang. Chem.
124
, 11411
–11415
(2012
).14.
F.
Smallenburg
, H. R.
Vutukuri
, A.
Imhof
, A.
van Blaaderen
, and M.
Dijkstra
, J. Phys.: Condens. Matter
24
, 464113
(2012
).15.
S. C.
Greer
, Ann. Rev. Phys. Chem.
53
, 173
(2002
).16.
S. C.
Greer
, J. Phys. Chem. B
102
, 5413
–5422
(1998
).17.
T. F.
De Greef
, M. M.
Smulders
, M.
Wolffs
, A. P.
Schenning
, R. P.
Sijbesma
, and E.
Meijer
, Chem. Rev.
109
, 5687
–5754
(2009
).18.
F.
Sciortino
, E.
Bianchi
, J. F.
Douglas
, and P.
Tartaglia
, J. Chem. Phys.
126
, 194903
(2007
).19.
K.
Liu
, Z.
Nie
, N.
Zhao
, W.
Li
, M.
Rubinstein
, and E.
Kumacheva
, Science
329
, 197
–200
(2010
).20.
M. E.
Cates
and S. J.
Candau
, J. Phys.: Condens. Matter
2
, 6869
(1990
).21.
R.
Goldstein
and L.
Stryer
, Biophys. J.
50
, 583
–599
(1986
).22.
M. M.
Smulders
, M. M.
Nieuwenhuizen
, T. F.
de Greef
, P.
van der Schoot
, A. P.
Schenning
, and E.
Meijer
, Chem-Eur. J.
16
, 362
–367
(2010
).23.
J.
van Jaarsveld
and P.
van der Schoot
, Macromolecules
40
, 2177
–2185
(2007
).24.
J. F.
Douglas
, J.
Dudowicz
, and K. F.
Freed
, J. Chem. Phys.
128
, 224901
(2008
).25.
J.
Stambaugh
, K. V.
Workum
, J. F.
Douglas
, and W.
Losert
, Phys. Rev. E
72
, 031301
(2005
).26.
W.
Knoben
, N. A. M.
Besseling
, and M. A.
Cohen Stuart
, Macromolecules
39
, 2643
–2653
(2006
).27.
G.
Jackson
, W. G.
Chapman
, and K.
Gubbins
, Mol. Phys.
65
, 1
(1988
).28.
K. V.
Workum
and J. F.
Douglas
, Phys. Rev. E
71
, 031502
(2005
).29.
K.
Van Workum
and J. F.
Douglas
, Phys. Rev. E
73
, 031502
(2006
).30.
J.
Dudowicz
, K. F.
Freed
, and J. F.
Douglas
, Phys. Rev. Lett.
92
, 045502
(2004
).31.
J.
Dudowicz
, K. F.
Freed
, and J. F.
Douglas
, J. Chem. Phys.
111
, 7116
(1999
).32.
J.
Dudowicz
, K. F.
Freed
, and J. F.
Douglas
, J. Chem. Phys.
119
, 12645
–12666
(2003
).33.
I. G.
Economou
and M. D.
Donohue
, AIChE J.
37
, 1875
–1894
(1991
).34.
J.
Dudowicz
, K. F.
Freed
, and J. F.
Douglas
, J. Chem. Phys.
113
, 434
–446
(2000
).35.
B.
Huisman
, P.
Bolhuis
, and A.
Fasolino
, Phys. Rev. Lett.
100
, 188301
(2008
).36.
L.
Bouteiller
and P.
van der Schoot
, J. Am. Chem. Soc.
134
, 1363
–1366
(2012
).37.
M.
Roman
, C.
Cannizzo
, T.
Pinault
, B.
Isare
, B.
Andrioletti
, P.
van der Schoot
, and L.
Bouteiller
, J. Am. Chem. Soc.
132
, 16818
–16824
(2010
).38.
M.
Bellot
and L.
Bouteiller
, Langmuir
24
, 14176
–14182
(2008
).39.
J.
van Gestel
, P.
van der Schoot
, and M.
Michels
, Langmuir
19
, 1375
–1383
(2003
).40.
R. E.
Harris
, J. Phys. Chem.
74
, 3102
–3111
(1970
).41.
J. C.
Wheeler
, S. J.
Kennedy
, and P.
Pfeuty
, Phys. Rev. Lett.
45
, 1748
–1752
(1980
).42.
G.
Gee
, Trans. Faraday Soc.
48
, 515
–526
(1952
).43.
F.
Fairbrother
, G.
Gee
, and G. T.
Merrall
, J. Polym. Sci.
16
, 459
–469
(1955
).44.
J. A.
Cuesta
and R. P.
Sear
, Phys. Rev. E
65
, 031406
(2002
).45.
A.
Wegner
and J.
Engel
, Biophys. Chem.
3
, 215
–225
(1975
).46.
F.
Federiconi
, P.
Ausili
, G.
Fragneto
, C.
Ferrero
, and P.
Mariani
, J. Phys. Chem. B
109
, 11037
–11045
(2005
).47.
P.
Mariani
, F.
Spinozzi
, F.
Federiconi
, H.
Amenitsch
, L.
Spindler
, and I.
Drevensek-Olenik
, J. Phys. Chem. B
113
, 7934
–7944
(2009
).48.
N.
Kern
and D.
Frenkel
, J. Chem. Phys.
118
, 9882
–9889
(2003
).49.
50.
E.
Bianchi
, J.
Largo
, P.
Tartaglia
, E.
Zaccarelli
, and F.
Sciortino
, Phys. Rev. Lett.
97
, 168301
(2006
).51.
C.
Vega
, E.
Sanz
, J. L. F.
Abascal
, and E. G.
Noya
, J. Phys.: Condens. Matter
20
, 153101
(2008
).52.
F.
Romano
, P.
Tartaglia
, and F.
Sciortino
, J. Phys.: Condens. Matter
19
, 322101
(2007
).53.
Q.
Chen
, S. C.
Bae
, and S.
Granick
, Nature (London)
469
, 381
–384
(2011
).54.
F.
Romano
and F.
Sciortino
, Soft Matter
7
, 5799
–5804
(2011
).55.
E. G.
Noya
, C.
Vega
, J. P. K.
Doye
, and A. A.
Louis
, J. Chem. Phys.
132
, 234511
(2010
).56.
E. G.
Noya
, C.
Vega
, J. P. K.
Doye
, and A. A.
Louis
, J. Chem. Phys.
127
, 054501
(2007
).57.
E. G.
Noya
, M. M.
Conde
, and C.
Vega
, J. Chem. Phys.
129
, 104704
(2008
).58.
J. P. K.
Doye
, A. A.
Louis
, I.-C.
Lin
, L. R.
Allen
, E. G.
Noya
, A. W.
Wilber
, H. C.
Kok
, and R.
Lyus
, Phys. Chem. Chem. Phys.
9
, 2197
–2205
(2007
).59.
F.
Romano
, E.
Sanz
, P.
Tartaglia
, and F.
Sciortino
, J. Phys.: Condens. Matter
24
, 064113
(2012
).60.
F.
Romano
, E.
Sanz
, and F.
Sciortino
, J. Chem. Phys.
134
, 174502
(2011
).61.
T.
Vissers
, Z.
Preisler
, F.
Smallenburg
, M.
Dijkstra
, and F.
Sciortino
, J. Chem. Phys.
138
, 164505
(2013
).62.
F.
Romano
and F.
Sciortino
, Nat. Matter
10
, 171
–173
(2011
).63.
F.
Romano
and F.
Sciortino
, Nat. Commun.
3
, 975
(2012
).64.
G.
Munaó
, Z.
Preisler
, T.
Vissers
, F.
Smallenburg
, and F.
Sciortino
, Soft Matter
9
, 2652
(2013
).65.
Z.
Preisler
, T.
Vissers
, F.
Smallenburg
, G.
Munaò
, and F.
Sciortino
, J. Phys. Chem. B
117
, 9540
–9547
(2013
).66.
R.
Fantoni
, A.
Giacometti
, F.
Sciortino
, and G.
Pastore
, Soft Matter
7
, 2419
–2427
(2011
).67.
R.
Pool
and P. G.
Bolhuis
, J. Phys. Chem. B
109
, 6650
–6657
(2005
).68.
D. J.
Kraft
, R.
Ni
, F.
Smallenburg
, M.
Hermes
, K.
Yoon
, D. A.
Weitz
, A.
van Blaaderen
, J.
Groenewold
, M.
Dijkstra
, and W. K.
Kegel
, Proc. Natl. Acad. Sci. U.S.A.
109
, 10787
–10792
(2012
).69.
Z.-W.
Li
, Z.-Y.
Lu
, Z.-Y.
Sun
, and L.-J.
An
, Soft Matter
8
, 6693
–6697
(2012
).70.
L.
Leibler
, Prog. Polym. Sci.
30
, 898
–914
(2005
).© 2014 AIP Publishing LLC.
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