What we do (not) understand about carbon nanomembranes - Jahresbericht 201 - Uni Bielefeld
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What we do (not) understand about carbon
nanomembranes
Jürgen Schnack
Department of Physics – University of Bielefeld – Germany
http://obelix.physik.uni-bielefeld.de/∼schnack/
Seminar, Bielefeld University, D0, 11 December 2020
Jahresb
à á á à p ? 6 Introduction
Introduction
Jürgen Schnack, CMD for CNM 1/36
à á á à p ? 6 Introduction
There are various carbon-based
nanostructures . . .
Jürgen Schnack, CMD for CNM 2/36
à á á à p ? 6 Introduction
. . . and carbon-based cross-linked SAMs (I).
www.advmat.de
www.MaterialsViews.com
REVIEW
Figure 2. Schematic for the formation of carbon nanomembranes (CNMs) and graphene from molecular precursors. a) Schematic illustration of the
fabrication route for CNMs and graphene: self-assembled monolayers are prepared on a substrate (i), then crosslinked by electron irradiation to form
A. Turchanin, A. Gölzh
CNMs of monomolecular äuser,
thickness (ii). Advanced Materials
The CNMs are released 28, 6075-6103
from the underlying (2016).
substrate (iii), and further annealing at 900 °C transforms them
into graphene. b) Chemical structures of the different precursor molecules discussed in this review. Adapted with permission.[46] Copyright 2013, ACS
Publications.
bonds between the reactive end groups and the substrate atoms 2e (see Figure 2b) form densely packed arrangements[19] with
and the van der Waals interactions between the carbon atoms the (√3 × √3) unit cells of the adsorption positions and with
in the core of the precursor molecules. To obtain SAMs with Jürgen Schnack,
the (2√3 × √3) superstructures of the molecular backbones. In CMD for CNM 3/36
desired molecular arrangements, such parameters like immer- these monolayers, the surface area per molecule is the same
sion duration, temperature, concentration, and solvent polarity (21.6 Å2); thus, the surface density of carbon atoms can be pre-
à á á à p ? 6 Introduction
. . . and carbon-based cross-linked SAMs (II).
www.advmat.de
full papers R. Jordan, A. Gölzhäuser, et al.
tip of a scanning tunneling microscope;
COMMUNICATION
biomedical field as artificial nacre[17] and as a novel material
resistance was then determined by a two-point
used in surgery. [18]
So far, a common feature of all developedmeasurement in UHV. Figure 2A shows an
freestanding polymer nanomembranes is the crosslinking ofSEM the image of a tungsten tip touching a
polymer itself to ensure the mechanical stability of the layer. nanosheet that suspends over an 11 ! 11 mm2
However, for the fabrication of chemical- or bioresponsive square opening. Additional resistivity measure-
polymer-based nanomembranes, the high crosslinking natu- ments were carried out under ambient condi-
rally reduces the interactions between the polymer chainstions. and To this end, nanosheets heated directly
the environment and thus impairs the sensitivity and flexibilityon gold substrates in UHV where transferred
of the films. Analogously to crosslinked polymer films
onto silicon oxide, and their sheet resistance
versus polymer brushes on substrates, a brush reacts more
quickly and has a higher sensitivity towards external stimuli.
was determined under ambient conditions by a
The entire layer has a better accessibility, even for larger four-point measurement (see SI). The sheet
molecules, and the strong chain stretching results in resistivity
a values measured in UHV and in
considerably lower chain entanglement of the preorganized ambient conditions are in a very good agree-
polymers along the surface normal. Hence, on surfaces, ment. soft A measurable electrical current is
and stimuli-responsive polymer brushes have been the system detected after annealing at "800 K. Here, the
of choice for the development of adaptive layers as actuators
[19–23]
sheet resistivity corresponds to "108 kV sq#1.
and sensors. Upon annealing to temperatures between 800
In this Full Paper, we report on the first freestanding
Figure 1. Fabrication scheme and microscopy images of supported and suspended carbon and 1200 K, we find linear current/voltage
polymer brush, grafted from a crosslinked monolayer
nanosheets.
A. Turchanin A) A "1etnmal.,
thick SAM of biphenyl
Advanced molecules is
Materials irradiated
21, 1233 by(2009);
electrons. This results etcurves
I. Amin (Fig. 6,
al., Small 2B,1623
C, and E). Increasing the
(2010).
(nanosheet) that provides mechanical stability and structural
in a mechanically stable crosslinked SAM (nanosheet) that can be removed from the substrate annealing temperature to "1200 K, drops the
integrity. Because of the morphological similarity, we refer to
and transferred onto other solid surfaces. When transferred onto TEM grids, nanosheets suspend sheet resistivity to "100 kV sq#1, demonstrat-
over holes. Upon heating to T > 1000 Kthis in as a ‘‘polymer carpet.’’
vacuum (pyrolysis), nanosheets transform into a
ing the clear metallic nature of the film. This
graphitic phase. B) Optical microscopy image of the section of a "5 cm2 nanosheet that was
transferred from a gold surface to an oxidized silicon wafer (300 nm SiO2). Some folds in the large resistivity is only one order of magnitude
2. Results
sheet are visible, and originate from wrinkling and
during the Discussion
transfer process. C) Optical microscopy higher than that of a Jdefect-free graphene
ürgen Schnack, CMD for CNM 4/36
[4]
image of a line pattern of 10 mm stripes of nanosheet. The pattern was fabricated by e-beam monolayer, and "100 times lower than the
For the
lithography and then transferred onto oxidized fabrication
silicon. of the
Note that polymer carpets,
small lines are aalmost
!1-nm-thin
à á á à p ? 6 Introduction
Problems for theory
• Systems contain very many carbon atoms.
• Structure very likely irregular. Defects?
• Quantum Methods, even DFT, cannot deal with
such systems. No way!
. . . and there are more questions to come.
Jürgen Schnack, CMD for CNM 5/36
à á á à p ? 6 Thank God, we have computers
Thank God, we have computers
“Espresso-doped multi-core”
128 cores, 384 GB RAM
. . . but that’s not enough!
Jürgen Schnack, CMD for CNM 6/36
à á á à p ? 6 Contents for you today
Contents for you today
√
1. Carbon nanomembranes
2. Classical molecular dynamics
3. Mechanical properties
4. Structure of CNMs
5. Open problems
Jürgen Schnack, CMD for CNM 7/36
à á á à p ? 6 CMD
Classical Molecular Dynamics
Jürgen Schnack, CMD for CNM 8/36
à á á à p ? 6 CMD
Classical Molecular Dynamics
• CMD can model very large systems
(∼ 10.000.000 particles).
• CMD can find ground states and model dynamics.
• CMD can model thermal equilibrium and non-equilibrium.
• But how should this be realistic for carbon-based com-
pounds, where the chemical bond is of quantum nature?
Jürgen Schnack, CMD for CNM 9/36à á á à p ? 6 CMD
sp hybridization modes
sp, sp2, and sp3 hybridization modes.
wikipedia: orbital hybridization
Jürgen Schnack, CMD for CNM 10/36à á á à p ? 6 CMD
Very sophisticated carbon potential
N
X ~p2 i
H(~r1,~p1;~r2,~p2; . . . ) = + V (~r1,~r2, . . . )
i=1
2m
N
X N
X
V (~r1,~r2, . . . ) = U2(|~ri −~rj |, Zi) + U3(|~ri −~rj |, |~ri −~rk |, Θijk , Zi)
i6=j i6=(jU2 (rij , 1.0)
U2 (rij , 2.0)
U2 (rij , 3.0)
-2.5 U2 (rij , 4.0)
à á á à p ? 6 U2 (rij , 5.0) CMD
U2 (rij , 6.0)
-3
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Coordination dependence rij [Å]
Abbildung 0.1: Die Funktionenschar U2 (r, Z) für unterschiedliche Koordinationen Z
1
0 20
18
-0.5 16
14
-1
U2 (rij , Z) [eV]
12
h(◊, Z) [eV]
-1.5 10
8
-2 U2 (rij , 1.0) 6
U2 (rij , 2.0)
U2 (rij , 3.0) 4 h(◊, 2.0)
-2.5 U2 (rij , 4.0) h(◊, 3.0)
U2 (rij , 5.0) 2 h(◊, 4.0)
U2 (rij , 6.0) h(◊, 6.0)
-3 0
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 0 90 120 180 250.5
rij [Å] ◊ [¶ ]
Abbildung 0.1: Die Funktionenschar U2 (r, Z) für unterschiedliche Koordinationen Z Abbildung 0.2: Die Funktionenschar h(◊, Z)
Coordination influences strength and direction of bonding.
20
18
N. A. Marks, Phys. Rev. B 63, 035401 (2000).
16
A. Mrugalla, Master thesis (2013)
14
12
h(◊, Z) [eV]
10
8
6
4 h(◊, 2.0) Jürgen Schnack, CMD for CNM 12/36
h(◊, 3.0)
2 h(◊, 4.0)
h(◊, 6.0)à á á à p ? 6 CMD
What can be achieved realistically?
• Structure calculations.
• Dynamical self-organization (1).
• Mechanical properties, such as vibrational
spectra and response to mechanical stress.
• Sorry, no electronic properties,
such as conductance or heat conductance.
(1) R. C. Powles, N. A. Marks, and D. W. M. Lau, Phys. Rev. B 79, 075430 (2009).
Jürgen Schnack, CMD for CNM 13/36à á á à p ? 6 Modulus
Mechanical properties
(Young’s modulus)
F. Gayk, J. Ehrens, T. Heitmann, P. Vorndamme, A. Mrugalla, and J. Schnack, Physica E 99, 215 (2018).
Jürgen Schnack, CMD for CNM 14/36à á á à p ? 6 Modulus
Question
What is the predictive power
of classical carbon potentials
for structure and moduli
for known carbon materials?
. . . before we start to investigate unknown materials!
Jürgen Schnack, CMD for CNM 15/36à á á à p ? 6 Modulus
Ground state distances for graphene, CNT, and diamond
Table 1: Ground-state dimensions in Å of graphene, CNT, and diamond for the
investigated potentials (LAMMPS).
(* No proper ground state structure found; † anisotropic.)
potential graphene CNT diamond
C-C distance C-C distance lattice const.
EDIP 1.42 1.42 3.56
REBO-II 1.42 1.42 3.58
ABOP 1.42 1.424, 1.417 † 3.46
Tersoff 89 1.46 1.46 3.57
Tersoff 90 * * 3.56
Tersoff 94 1.55 * 3.56
Tersoff BNC 1.44 1.44 -
Tersoff EA 1.48 1.48 3.57
AIREBO+LJ+t 1.40 1.41 3.58
AIREBO+LJ 1.40 1.40 3.58
AIREBO+t 1.40 1.40 3.58
AIREBO 1.40 1.40 3.58
experimental 1.42 1.42 3.567
Jürgen Schnack, CMD for CNM 16/36à á á à p ? 6 Modulus
Young’s modulus for graphene
1500
1400 1400
1300
Tersoff 1989 1200 Tersoff 1989
1200 REBO-II Tersoff 1990
E / GPa
E / GPa
EDIP 1000 Tersoff 1994
1100 ABOP Tersoff EA 2005
1000 AIREBO+LJ+t 800 Tersoff BNC 2012
AIREBO+LJ
900 AIREBO+t
AIREBO 600
800
700 400
0 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04
1/N 1/N
Young’s modulus of graphene for various sizes and potentials. N denotes the num-
ber of atoms in the approximately square graphene sheets. Open boundary condi-
tions are applied.
Experimental value: 1000 GPa.
Jürgen Schnack, CMD for CNM 17/36à á á à p ? 6 Modulus
Young’s modulus for CNT
1300 1300
1200 1200
1100
1100
1000
1000 Tersoff 1989
900
E / GPa
E / GPa
Tersoff 1989 Tersoff 1990
900 REBO-II 800 Tersoff 1994
EDIP Tersoff EA 2005
800 ABOP 700
Tersoff BNC 2012
AIREBO+LJ+t 600
700 AIREBO+LJ
500
AIREBO+t
600 AIREBO 400
500 300
0 0.002 0.004 0.006 0.008 0 0.002 0.004 0.006 0.008
1/N 1/N
Young’s modulus of a (20,20) CNT with armchair geometry along the tube, taken as
x-direction, for various sizes and potentials. N denotes the number of atoms of the
tube. Open boundary conditions are applied.
Experimental value: 1000 GPa.
Jürgen Schnack, CMD for CNM 18/36à á á à p ? 6 Modulus
Young’s modulus for diamond
GPa
1130
1110
1090
1070
1050
z
y
x
Structure and directions as well as Young’s modulus of diamond taken in various
directions on the northern hemisphere around the positive x-direction for N = 8631
and the EDIP potential. Open boundary conditions are applied.
Experimental values: 1.05 TPa . . . 1.21 TPa
Jürgen Schnack, CMD for CNM 19/36à á á à p ? 6 Modulus
Conclusion
For the investigated observables
(bond length & Young’s modulus)
and the chosen carbon materials
EDIP and REBO-II
perform overall well.
F. Gayk, J. Ehrens, T. Heitmann, P. Vorndamme, A. Mrugalla, and J. Schnack, Physica E 99, 215 (2018).
Jürgen Schnack, CMD for CNM 20/36à á á à p ? 6 Structure
How to find the
Structure of CNMs?
Jürgen Schnack, CMD for CNM 21/36à á á à p ? 6 Structure
Questions
• The structure or a structure?
• Structure very likely a metastable state, a local
energy minimum. Glas-like?
• How to model? Initial conditions, cooling, . . . ?
• Which structures are correct? Observables?
• X-ray structure determination impossible!
Jürgen Schnack, CMD for CNM 22/36à á á à p ? 6 Structure
That’s how we do it
z −Fz
z
random
Vwall
Model: includes only carbon atoms (+ surface);
Initial state: randomized carbon positions in SAM, vertical force field;
Cooling: Nose-Hoover or alike;
LAMMPS: EDIP and analytical forces included in our version.
Jürgen Schnack, CMD for CNM 23/36Tabelle 7.2 und sind, verglichen mit den experimentellen Werten (≥10 GPa, siehe Ab-
à á á à p ? schnitt
6 6.7), deutlich zu groß. Offensichtlich machen die Sechsecke die linke Struktur Structure
in Abbildung 17 stabiler als die rechte. Außerdem wird durch den geringeren Impuls
Examples of CMNs
die Struktur weniger durchmischt und erhält einen weniger isotropen E-Modul.
eV eV
Abbildung 17: TPT, T = 700 K; k = 30 Å
(links) und k = 200 Å
(rechts)
F. Gayk, Master Thesis, Bielefeld University (2018)
J. Ehrens et al., arXiv:2011.00880
Tabelle 7.2: E-Module (bezüglich: Boxvolumen|Oberflächennetzvolumen)
Ex / GPa Ey / GPa
TPT (T=700 K, k = 30 eV
Å
) 436| 847 334| 649
eV
TPT (T=700 K, k = 200 Å ) 215| 448 220| 457
TPT (T=300 K, k = 60 eV
Å
) 325| 987 316| 960
Jürgen Schnack, CMD for CNM 24/36
TPT (T=1100 K, k = 60 eV
Å
) 351| 866 339| 838Die zugehörigen E-Module betragen links Ex = 231|730 GPa bzw. Ey = 230|725 GPa
à á á à p ? und6 rechts Ex = 487|916 GPa bzw. Ey = 455|856 GPa. Obwohl die rechte Struk- Structure
tur größere Löcher hat, ist sie wegen ihrer geringeren Dicke stabiler. Offensichtlich
führen auch große LöcherExamples of CMNs
zu keinem E-Modul, welches in die Größenordnung der
experimentellen Werte von ≥10 GPa kommt.
eV Å
Abbildung 21: k = 60 Å
, T = 300 K, v = 35 ps
; BPT, N = 4900 (links) und NPTH,
N = 2500 (rechts)
F. Gayk, Master Thesis, Bielefeld University (2018) Å
In Abbildung 21 sind die zu BPT und NPTH gehörenden Resultate für v = 35 ps
J. Ehrens et al., arXiv:2011.00880
38
Jürgen Schnack, CMD for CNM 25/36à á á à p ? 6 Structure
Examples of CMNs
7.4. DFT Struktur als Ausgangszustand
eV
Abbildung 26: DFT Struktur (links); k = 60 Å
, T = 300 K auf DFT Struktur (rechts)
Randomized and cooled DFT structure (1).
7.4.2. Atome
(1) P. Cabrera-Sanfelix, entfernen
A. Arnau, and D. Sanchez-Portal, Phys. Chem. Chem. Phys. 12, 1578 (2010).
(2) F. Gayk, Master Thesis, Bielefeld University (2018)
Da allerdings auch dieser E-Modul zu groß ist, wird versucht durch zufälliges Löschen
einiger Atome die Dichte zu verringern. Es werden Anteile von p = 5 %, p = 10 %
und p = 20 % gewählt. Die Resultate für p = 5 % und p = 20 % befinden sich in
Abbildung 27. Qualitativ sind keine großen Unterschiede zu erkennen.
Jürgen Schnack, CMD for CNM 26/36à á á à p ? 6 Structure
Examples of CMNs
CNM have got holes (pores)! In simulations this depends on initial conditions: more
violence ⇒ more holes.
Jürgen Schnack, CMD for CNM 27/36in Abbildung 17 stabiler als die rechte. Außerdem wird durch den geringeren Impuls
6.7. Beulentest mit dem Rasterkraftmikroskop
die Struktur weniger durchmischt und erhält einen weniger isotropen E-Modul.
Beim Beulentest wird die CNM über dem Loch eines Trägers fixiert und ein Druck-
à á á à p ? 6 unterschied zwischen beiden Seiten erzeugt (siehe Abbildung 13). Die Größe der ent-
Structure
stehenden Beule wird mit einem Rasterkraftmikroskop vermessen und erlaubt eine
Berechnung des E-Moduls. Weitere Informationen zum Verfahren befinden sich in
Young’s modulus of CMNs Referenz [44]. In Abbildung 14 sind die E-Module und weitere Eigenschaften für die
drei verwendeten SAMs aufgelistet.
eV eV
Abbildung 17: TPT, T = 700 K; k = 30 Å
(links) und k = 200 Å
(rechts)
Abbildung 13: Aufbau des Beulentests [44]
Tabelle 7.2: E-Module (bezüglich: Boxvolumen|Oberflächennetzvolumen)
Ex / GPa Ey / GPa
TPT (T=700 K, k = 30 eV
Å
) 436| 847 334| 649
TPT (T=700 K, k = 200 eV
Å
) 215| 448 220| 457
TPT (T=300 K, k = 60 eV
Å
) 325| 987 316| 960
TPT (T=1100 K, k = 60 eV
Å
) 351| 866 339| 838
BPT (T=700 K, k = 60 eV
Å
) 202| 736 191| 695
NPTH (T=700 K, k = 60 eVÅ
) 536|1367 500|1277
Abbildung 14: E-Module aus Beulentest [44]
In Abbildung 18 sind die Resultate für die gleiche SAM für zwei unterschiedli-
che Fluktuationsstärken dargestellt. Hier gibt es auf den ersten Blick keine großen
Unterschiede in der Art der Vernetzung. Durch die größere kinetische Energie bei
identischer Simulationsdauer ist die rechte Struktur etwas höher gewandert. Das grö-
Theoretical Young’s moduli closer to graphene;
ßere Volumen ist vermutlich auch der Grund dafür, dass die mit Oberflächennetz
factor 10 . . . 50 bigger than experiment.
berechneten E-Module in der rechten Struktur etwas kleiner sind (siehe Tabelle 7.2).
F. Gayk, Master Thesis, Bielefeld University (2018)
35
X. Zhang, C. Neumann, P. Angelova, A. Beyer, and A. Gölzhäuser, Langmuir 30, 8221 (2014).
Jürgen Schnack, CMD for CNM 28/36
29à á á à p ? 6 Structure
Alternative structure
Possible configuration of a Biphenyl layer, ARGUS Lab (1).
Not realistic, since construction principle works only for BPT.
NEXAFS shows about 60 % aromaticity, i.e. 40 % of phenyl rings are broken.
(1) D. Rhinow, N.-E. Weber, A. Turchanin, J. Phys. Chem. C 116, 12295 (2012).
Jürgen Schnack, CMD for CNM 29/36à á á à p ? 6 ODT
CNMs from spaghetti?
Jürgen Schnack, CMD for CNM 30/36previously mentioned appplications comprise SAMs on solid supports.. However, aromatic
à á á à p ? 6 ODT
SAMs can even be laterally
ly cross-linked and transferred as monomolecular
ar thin membranes on
micrometer-sized holes (see
Octadecanethiol
(s below), which provides an innovative techn
[1],[2]],[9]
nology in the field of
membrane separation .
Figure 2.1: (a) Schematic diaggram depicting a self-assembled monolayer (SAM) of alk lkanethiolates on a metal
substrate. (b) Scheme of a decan
anethiol molecule adsorbed on a solid surface. The orientat ation of the molecule with
respect to the substrate surface is defined by the tilt angle α, the twist angle β, and the pre
recession angle χ. Part a is
reprinted with permission from m ref 16. Copyright (2005) American Chemical Society.. Part b is reprinted with
permission from ref [20]. Copyri
right (2010) Royal Society of Chemistry (Great Britain).
Patrick Stohmann, Dissertation, Bielefeld, 2020.
9
Jürgen Schnack, CMD for CNM 31/36à á á à p ? 6 ODT
Octadecanethiol (ODT, C18) – initial SAM
J. C. Love, L. A. Estroff, J. K. Kriebel, R. G. Nuzzo, and G. M. Whitesides, Chem. Rev. 105, 1103 (2005).
Jürgen Schnack, CMD for CNM 32/36à á á à p ? 6 ODT
Octa-decane-thiol (ODT, C18) – first simulations
Structure is mechanically stable
Phenyls do not form
Theoretical Young’s modulus much smaller than for BPT, TPT or NPT
J. Ehrens, private communication
Jürgen Schnack, CMD for CNM 33/36à á á à p ? 6 Open questions
Open questions
• Structure correct? Discrepancy w.r.t. Young’s modulus!
• Compare to ion deflection studies (Richard Arthur Wilhelm (Wien))!
• How thick is a CNM?
• Precursor-CNM correlations? Which, if any?
• No thiols in decane-based CNMs?
• Systematic investigation of holes needed.
• Future: water permeation.
Jürgen Schnack, CMD for CNM 34/36à á á à p ? 6 Summary
Summary
• Classical Molecular Dynamics can be set up for
carbon systems using effective many-body car-
bon potentials.
• Ground-state geometries can be determined with
great accuracy (exception graphite).
• Dynamical self-assembly can be simulated.
• Prospect to simulate nano sheets with realistic,
i.e. probably irregular structure.
• Electronic properties CANNOT be modeled.
Jürgen Schnack, CMD for CNM 35/36à á á à p ? 6 The end
Thank you very much for your
attention.
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