In this work, we theoretically investigate the conditions favoring the interfacial self-assembly of PbSe nanocrystals (NCs) resulting in silicene-honeycomb superstructures. Using a coarse-grained molecular dynamics model, we study the NCs’ self-assembly at the dispersion-air interface with respect to the input parameters regulating the various forces experienced by the NCs at the interface. From these results, we extrapolate detailed assembled-phase diagrams showing which ranges of the input parameters promote the formation of silicene-honeycomb superstructures and which regimes result in square geometries. Then, we use a sharp-interface numerical model to compute the energy landscape experienced by each NC at the dispersion-air interface with respect to the NC’s surface chemistry. From such an energy landscape, we fit the parameters regulating the interface-adsorption forces experienced by the NCs at the interface. Combining these findings with the results presented in our assembled-phase diagrams, we find out which surface-chemistry properties of the NCs better promote the interfacial self-assembly in silicene-honeycomb superstructures, and we speculate on some experimental strategies to reach an improved control on the synthesis of PbSe silicene-honeycomb superstructures.
REFERENCES
1.
M. A.
Boles
, M.
Engel
, and D. V.
Talapin
, “Self-assembly of colloidal nanocrystals: From intricate structures to functional materials
,” Chem. Rev.
116
(18
), 11220
–11289
(2016
).2.
A. C.
Berends
and C.
de Mello Donega
, “Ultrathin one- and two-dimensional colloidal semiconductor nanocrystals: Pushing quantum confinement to the limit
,” J. Phys. Chem. Lett.
8
(17
), 4077
–4090
(2017
).3.
F.
Reincke
, S. G.
Hickey
, W. K.
Kegel
, and D.
Vanmaekelbergh
, “Spontaneous assembly of a monolayer of charged gold nanocrystals at the water/oil interface
,” Angew. Chem., Int. Ed.
43
(4
), 458
–462
(2004
).4.
H.
Duan
, D.
Wang
, D. G.
Kurth
, and H.
Möhwald
, “Directing self-assembly of nanoparticles at water/oil interfaces
,” Angew. Chem., Int. Ed.
43
(42
), 5639
–5642
(2004
).5.
K. M.
Gattás-Asfura
, C. A.
Constantine
, M. J.
Lynn
, D. A.
Thimann
, X.
Ji
, and R. M.
Leblanc
, “Characterization and 2D self-assembly of CdSe quantum dots at the air-water interface
,” J. Am. Chem. Soc.
127
(42
), 14640
–14646
(2005
).6.
Y.-J.
Li
, W.-J.
Huang
, and S.-G.
Sun
, “A universal approach for the self-assembly of hydrophilic nanoparticles into ordered monolayer films at a toluene/water interface
,” Angew. Chem., Int. Ed.
45
(16
), 2537
–2539
(2006
).7.
J.
Wang
, D.
Wang
, N. S.
Sobal
, M.
Giersig
, M.
Jiang
, and H.
Möhwald
, “Stepwise directing of nanocrystals to self-assemble at water/oil interfaces
,” Angew. Chem., Int. Ed.
45
(47
), 7963
–7966
(2006
).8.
T. P.
Bigioni
, X.-M.
Lin
, T. T.
Nguyen
, E. I.
Corwin
, T. A.
Witten
, and H. M.
Jaeger
, “Kinetically driven self assembly of highly ordered nanoparticle monolayers
,” Nat. Mater.
5
(4
), 265
–270
(2006
).9.
A.
Böker
, J.
He
, T.
Emrick
, and T. P.
Russell
, “Self-assembly of nanoparticles at interfaces
,” Soft Matter
3
, 1231
–1248
(2007
).10.
Y.
Shi
, C.
Tu
, Q.
Zhu
, H.
Qian
, J.
Ren
, C.
Liu
, X.
Zhu
, D.
Yan
, E. S.-W.
Kong
, and P.
He
, “Self-assembly of CdTe nanocrystals at the water/oil interface by amphiphilic hyperbranched polymers
,” Nanotechnology
19
, 445609
(2008
).11.
A.
Dong
, J.
Chen
, P. M.
Vora
, J. M.
Kikkawa
, and C. B.
Murray
, “Binary nanocrystal superlattice membranes self-assembled at the liquid-air interface
,” Nature
466
, 474
(2010
).12.
M. D.
Goodman
, L.
Zhao
, K. A.
DeRocher
, J.
Wang
, S. K.
Mallapragada
, and Z.
Lin
, “Self-assembly of CdTe tetrapods into network monolayers at the air/water interface
,” ACS Nano
4
(4
), 2043
–2050
(2010
).13.
Z.
Jiang
, X.-M.
Lin
, M.
Sprung
, S.
Narayanan
, and J.
Wang
, “Capturing the crystalline phase of two-dimensional nanocrystal superlattices in action
,” Nano Lett.
10
(3
), 799
–803
(2010
).14.
L.
Cheng
, A.
Liu
, S.
Peng
, and H.
Duan
, “Responsive plasmonic assemblies of amphiphilic nanocrystals at oil-water interfaces
,” ACS Nano
4
(10
), 6098
–6104
(2010
).15.
J.
Chen
, A.
Dong
, J.
Cai
, X.
Ye
, Y.
Kang
, J. M.
Kikkawa
, and C. B.
Murray
, “Collective dipolar interactions in self-assembled magnetic binary nanocrystal superlattice membranes
,” Nano Lett.
10
(12
), 5103
–5108
(2010
).16.
Y.
Justo
, I.
Moreels
, K.
Lambert
, and Z.
Hens
, “Langmuir–Blodgett monolayers of colloidal lead chalcogenide quantum dots: Morphology and photoluminescence
,” Nanotechnology
21
, 295606
(2010
).17.
D.
Vanmaekelbergh
, “Self-assembly of colloidal nanocrystals as route to novel classes of nanostructured materials
,” Nano Today
6
(4
), 419
–437
(2011
).18.
H.
Ma
and J.
Hao
, “Ordered patterns and structures via interfacial self-assembly: Superlattices, honeycomb structures and coffee rings
,” Chem. Soc. Rev.
40
, 5457
–5471
(2011
).19.
J. J.
Choi
, K.
Bian
, W. J.
Baumgardner
, D.-M.
Smilgies
, and T.
Hanrath
, “Interface-induced nucleation, orientational alignment and symmetry transformations in nanocube superlattices
,” Nano Lett.
12
(9
), 4791
–4798
(2012
).20.
F.
Pietra
, F. T.
Rabouw
, W. H.
Evers
, D. V.
Byelov
, A. V.
Petukhov
, C.
de Mello Donegá
, and D.
Vanmaekelbergh
, “Semiconductor nanorod self-assembly at the liquid/air interface studied by in situ GISAXS and ex situ TEM
,” Nano Lett.
12
(11
), 5515
–5523
(2012
).21.
H.
Evers
, B.
Goris
, S.
Bals
, J.
Casavola
, M.
de Graaf
, R.
van Roij
, M.
Dijkstra
, and D.
Vanmaekelbergh
, “Low-dimensional semiconductor superlattices formed by geometric control over nanocrystal attachment
,” Nano Lett.
13
, 2317
(2013
).22.
W.
van der Stam
, A.
Gantapara
, Q. A.
Akkerman
, G.
Soligno
, J. M.
Meeldijk
, R.
van Roij
, M.
Dijkstra
, and C.
de Mello Donega
, “Self-assembly of colloidal hexagonal bipyramid and bifrustum-shaped ZnS nanocrystals into two dimensional superstructures
,” Nano Lett.
14
, 1032
(2014
).23.
C. S. S.
Sandeep
, J. M.
Azpiroz
, W. H.
Evers
, S. C.
Boehme
, I.
Moreels
, S.
Kinge
, L. D. A.
Siebbeles
, I.
Infante
, and A. J.
Houtepen
, “Epitaxially connected PbSe quantum-dot films: Controlled neck formation and optoelectronic properties
,” ACS Nano
8
(11
), 11499
–11511
(2014
).24.
W.
Walravens
, J.
De Roo
, E.
Drijvers
, S.
ten Brinck
, E.
Solano
, J.
Dendooven
, C.
Detavernier
, I.
Infante
, and Z.
Hens
, “Chemically triggered formation of two-dimensional epitaxial quantum dot superlattices
,” ACS Nano
10
(7
), 6861
–6870
(2016
).25.
B. H.
Savitzky
, R.
Hovden
, K.
Whitham
, J.
Yang
, F.
Wise
, T.
Hanrath
, and L. F.
Kourkoutis
, “Propagation of structural disorder in epitaxially connected quantum dot solids from atomic to micron scale
,” Nano Lett.
16
(9
), 5714
–5718
(2016
).26.
J. J.
Geuchies
, C.
van Overbeek
, E. H.
, B.
Goris
, A.
de Backer
, A. P.
Gantapara
, F. T.
Rabouw
, J.
Hilhorst
, J. L.
Peters
, O.
Konovalov
, A. V.
Petukhov
, M.
Dijkstra
, L. D. A.
Siebbeles
, S.
van Aert
, S.
Bals
, and D.
Vanmaekelbergh
, “In situ study of the formation mechanism of two-dimensional superlattices from PbSe nanocrystals
,” Nat. Mater.
15
, 1248
(2016
).27.
S.
Maiti
, A.
André
, R.
Banerjee
, J.
Hagenlocher
, O.
Konovalov
, F.
Schreiber
, and M.
Scheele
, “Monitoring self-assembly and ligand exchange of PbS nanocrystal superlattices at the liquid/air interface in real time
,” J. Phys. Chem. Lett.
9
(4
), 739
–744
(2018
).28.
H.
Itasaka
, K.-I.
Mimura
, and K.
Kato
, “Extra surfactant-assisted self-assembly of highly ordered monolayers of BaTiO3 nanocubes at the air-water interface
,” Nanomaterials
8
, 739
(2018
).29.
A.
Castelli
, J.
de Graaf
, S.
Marras
, R.
Brescia
, L.
Goldoni
, L.
Manna
, and M. P.
Arciniegas
, “Understanding and tailoring ligand interactions in the self-assembly of branched colloidal nanocrystals into planar superlattices
,” Nat. Commun.
9
(1
), 1141
(2018
).30.
C.
van Overbeek
, J. L.
Peters
, S. A. P.
van Rossum
, M.
Smits
, M. A.
van Huis
, and D.
Vanmaekelbergh
, “Interfacial self-assembly and oriented attachment in the family of PbX (X = S, Se, Te) nanocrystals
,” J. Phys. Chem. C
122
(23
), 12464
–12473
(2018
).31.
M. P.
Boneschanscher
, W. H.
Evers
, J. J.
Geuchies
, T.
Altantzis
, B.
Goris
, F. T.
Rabouw
, S. A. P.
van Rossum
, H. S. J.
van der Zant
, L. D. A.
Siebbeles
, G.
Van Tendeloo
, I.
Swart
, J.
Hilhorst
, A. V.
Petukhov
, S.
Bals
, and D.
Vanmaekelbergh
, “Long-range orientation and atomic attachment of nanocrystals in 2D honeycomb superlattices
,” Science
344
, 1377
(2014
).32.
J. L.
Peters
, K. H. W.
van den Bos
, S.
Van Aert
, B.
Goris
, S.
Bals
, and D.
Vanmaekelbergh
, “Ligand-induced shape transformation of PbSe nanocrystals
,” Chem. Mater.
29
(9
), 4122
–4128
(2017
).33.
R. K.
Mallavajula
and L. A.
Archer
, “Nanocrystal self-assembly assisted by oriented attachment
,” Angew. Chem., Int. Ed.
50
(3
), 578
–580
(2011
).34.
J. J.
De Yoreo
, P. U. P. A.
Gilbert
, N. A. J. M.
Sommerdijk
, R. L.
Penn
, S.
Whitelam
, D.
Joester
, H.
Zhang
, J. D.
Rimer
, A.
Navrotsky
, J. F.
Banfield
, A. F.
Wallace
, F. M.
Michel
, F. C.
Meldrum
, H.
Cölfen
, and P. M.
Dove
, “Crystallization by particle attachment in synthetic, biogenic, and geologic environments
,” Science
349
(6247
), aaa6760
(2015
).35.
E.
Kalesaki
, C.
Delerue
, C.
Morais Smith
, W.
Beugeling
, G.
Allan
, and D.
Vanmaekelbergh
, “Dirac cones, topological edge states, and nontrivial flat bands in two-dimensional semiconductors with a honeycomb nanogeometry
,” Phys. Rev. X
4
, 011010
(2014
).36.
C.
Delerue
and D.
Vanmaekelbergh
, “Electronic band structure of zinc blende CdSe and rock salt PbSe semiconductors with silicene-type honeycomb geometry
,” 2D Mater.
2
(3
), 034008
(2015
).37.
W.
Beugeling
, E.
Kalesaki
, C.
Delerue
, Y. M.
Niquet
, D.
Vanmaekelbergh
, and C.
Morais Smith
, “Topological states in multi-orbital HgTe honeycomb lattices
,” Nat. Commun.
6
, 1
(2015
).38.
J. L.
Peters
, T.
Altantzis
, I.
Lobato
, M. A.
Jazi
, C.
van Overbeek
, S.
Bals
, D.
Vanmaekelbergh
, and S. B.
Sinai
, “Mono- and multilayer silicene-type honeycomb lattices by oriented attachment of PbSe nanocrystals: Synthesis, structural characterization, and analysis of the disorder
,” Chem. Mater.
30
(14
), 4831
–4837
(2018
).39.
K.
Whitham
, D.-M.
Smilgies
, and T.
Hanrath
, “Entropic, enthalpic, and kinetic aspects of interfacial nanocrystal superlattice assembly and attachment
,” Chem. Mater.
30
(1
), 54
–63
(2018
).40.
G.
Soligno
and D.
Vanmaekelbergh
, “Understanding the formation of PbSe honeycomb superstructures by dynamics simulations
,” Phys. Rev. X
9
, 021015
(2019
).41.
J. J.
Geuchies
, G.
Soligno
, E.
Geraffy
, C. P.
Hendrikx
, C.
van Overbeek
, F.
Montanarella
, M. R.
Slot
, O. V.
Konovalov
, A. V.
Petukhov
, and D.
Vanmaekelbergh
, “Unravelling three-dimensional adsorption geometry of PbSe nanocrystal monolayers at a liquid-air interface using synchrotron x-ray scattering techniques
” (submitted).42.
M. R.
Khadilkar
and F. A.
Escobedo
, “Phase behavior of polyhedral nanoparticles in parallel plate confinement
,” Soft Matter
12
, 1506
–1516
(2016
).43.
Z.
Fan
and M.
Grünwald
, “Orientational order in self-assembled nanocrystal superlattices
,” J. Am. Chem. Soc.
141
(5
), 1980
–1988
(2019
).44.
H.
Zhang
and J. F.
Banfield
, “Energy calculations predict nanoparticle attachment orientations and asymmetric crystal formation
,” J. Phys. Chem. Lett.
3
(19
), 2882
–2886
(2012
).45.
P.
Pieranski
, “Two-dimensional interfacial colloidal crystals
,” Phys. Rev. Lett.
45
, 569
–572
(1980
).46.
J.
de Graaf
, M.
Dijkstra
, and R.
van Roij
, “A triangular tessellation scheme for the adsorption free energy at the liquid-liquid interface: Towards non-convex patterned colloids
,” Phys. Rev. E
80
, 051405
(2009
).47.
J.
de Graaf
, M.
Dijkstra
, and R.
van Roij
, “Adsorption trajectories and free-energy separatrices for colloidal particles in contact with a liquid-liquid interface
,” J. Chem. Phys.
132
, 164902
(2010
).48.
A. R.
Morgan
, N.
Ballard
, L. A.
Rochford
, G.
Nurumbetov
, T. S.
Skelhon
, and S. A. F.
Bon
, “Understanding the multiple orientations of isolated superellipsoidal hematite particles at the oil-water interface
,” Soft Matter
9
, 487
(2013
).49.
B.
Peng
, G.
Soligno
, M.
Kamp
, B.
de Nijs
, J.
de Graaf
, M.
Dijkstra
, R.
van Roij
, A.
van Blaaderen
, and A.
Imhof
, “Site-specific growth of polymer on silica rods
,” Soft Matter
10
, 9644
(2014
).50.
N.
Ballard
and S. A. F.
Bon
, “Equilibrium orientations of non-spherical and chemically anisotropic particles at liquid–liquid interfaces and the effect on emulsion stability
,” J. Colloid Interface Sci.
448
, 533
(2015
).51.
B. J.
Park
and D.
Lee
, “Configuration of nonspherical amphiphilic particles at a fluid–fluid interface
,” Soft Matter
8
, 7690
(2012
).52.
B. J.
Park
and D.
Lee
, “Equilibrium orientation of nonspherical Janus particles at fluid-fluid interfaces
,” ACS Nano
6
, 782
(2012
).53.
G.
Soligno
, M.
Dijkstra
, and R.
van Roij
, “Self-assembly of cubes into 2D hexagonal and honeycomb lattices by hexapolar capillary interactions
,” Phys. Rev. Lett.
116
, 258001
(2016
).54.
G.
Soligno
, M.
Dijkstra
, and R.
van Roij
, “The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations
,” J. Chem. Phys.
141
, 244702
(2014
).55.
G.
Soligno
, “Droplets, capillary interactions, and self-assembly from the equilibrium shape of fluid-fluid interfaces
,” Ph.D. thesis, Utrecht University
, 2017
, ISBN: 978-94-6332-124-2.56.
M.
Vis
, J.
Opdam
, I. S. J.
van ’t Oor
, G.
Soligno
, R.
van Roij
, R. H.
Tromp
, and B. H.
Erné
, “Water-in-water emulsions stabilized by nanoplates
,” ACS Macro Lett.
4
, 965
(2015
).57.
I.
Dević
, G.
Soligno
, M.
Dijkstra
, R.
van Roij
, X.
Zhang
, and D.
Lohse
, “Sessile nanodroplets on elliptical patches of enhanced lyophilicity
,” Langmuir
33
(11
), 2744
–2749
(2017
).58.
M.
Kamp
, G.
Soligno
, F.
Hagemans
, B.
Peng
, A.
Imhof
, R.
van Roij
, and A.
van Blaaderen
, “Regiospecific nucleation and growth of silane coupling agent droplets onto colloidal particles
,” J. Phys. Chem. C
121
(36
), 19989
–19998
(2017
).59.
G.
Soligno
, M.
Dijkstra
, and R.
van Roij
, “Self-assembly of cubic colloidal particles at fluid-fluid interfaces by hexapolar capillary interactions
,” Soft Matter
14
, 42
–60
(2018
).60.
C.
Anzivino
, F.
Chang
, G.
Soligno
, R.
van Roij
, W. K.
Kegel
, and M.
Dijkstra
, “Equilibrium configurations and capillary interactions of Janus dumbbells and spherocylinders at fluid-fluid interfaces
,” Soft Matter
15
, 2638
–2647
(2019
).61.
M.
Zanini
, A.
Cingolani
, C.-P.
Hsu
, M. A.
Fernandez Rodriguez
, G.
Soligno
, A.
Beltzung
, S.
Caimi
, D. M.
Mitrano
, G.
Storti
, and L.
Isa
, “Mechanical phase inversion of pickering emulsions via metastable wetting of rough colloids
,” Soft Matter
15
, 7888
(2019
).62.
U.
Gupta
, T.
Hanrath
, and F. A.
Escobedo
, “Modeling the orientational and positional behavior of polyhedral nanoparticles at fluid-fluid interfaces
,” Phys. Rev. Mater.
1
, 055602
(2017
).63.
R. J. K.
Udayana Ranatunga
, R. J. B.
Kalescky
, C.-c.
Chiu
, and S. O.
Nielsen
, “Molecular dynamics simulations of surfactant functionalized nanoparticles in the vicinity of an oil/water interface
,” J. Phys. Chem. C
114
(28
), 12151
–12157
(2010
).64.
K.
Schwenke
, L.
Isa
, D. L.
Cheung
, and E.
Del Gado
, “Conformations and effective interactions of polymer-coated nanoparticles at liquid interfaces
,” Langmuir
30
(42
), 12578
–12586
(2014
).65.
A. P.
Kaushik
and P.
Clancy
, “Explicit all-atom modeling of realistically sized ligand-capped nanocrystals
,” J. Chem. Phys.
136
(11
), 114702
(2012
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.