Supporting Information for Letter: “Alkyl-Based
Surfactants at a Liquid Mercury Surface:
Computer Simulation of Structure, Self-Assembly
and Phase Behavior”
Anton Iakovlev,† Dmitry Bedrov,∗,‡ and Marcus Müller†
Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz
1, 37077 Göttingen, Germany, and Department of Materials Science & Engineering,
University of Utah, 122 South Central Campus Dr., Salt Lake City, 84112, Utah, USA
E-mail: [email protected]
∗
To whom correspondence should be addressed
Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077
Göttingen, Germany
‡
Department of Materials Science & Engineering, University of Utah, 122 South Central Campus Dr.,
Salt Lake City, 84112, Utah, USA
†
S1
The alkane films were simulated at T = 298 K. The RESPA multiple time step algorithm
was used to integrate the equation of motion. 1 We used the time step of 0.5 fs for all
bonded interactions. For the non-bonded interactions between atoms with separations within
7 Å we used the time step of 1.5 fs, and for the separations between 7 Å and 15 Å we
used 3 fs, respectively. The maximal cut-off for the Hg-Hg interactions was 9 Å. A preequilibrated mercury film of thickness about 8 nm and cross-section of 10 × 10 nm2 was
brought in contact with alkane films on both sides as shown in Figure 1. The number of
molecules in the alkane film was chosen such that it yielded the surface coverage σ of 2.0
and 1.5 nm−2 for C12 and C22 systems, respectively. Then equilibration simulations were
conducted until the density profiles become stationary. Systems with lower values of alkane
surface coverage were created by removing certain amount of alkane molecules from each
side of the film and re-equilibrating the system. Depending on the alkane surface coverage
the sampling time was varied between 15 and 30 ns. Wider systems with the cross-section of
30 × 30 nm2 were created by replicating in the x- and y-direction the smaller (10 × 10 nm2 )
systems and then subsequently equilibrating for at least 10 ns. Afterwards for the C22
alkanes (σ = 1.5 nm−2 ), the system was additionally equilibrated at T = 330 K for 5 ns.
Subsequently, the temperature was reduced back to 298 K and the simulations were carried
out for another 30 ns. This system was the larges among simulated alkane systems on liquid
mercury and contained 288000 Hg atoms and 1350 C22 molecules on each side of the Hg film
such that the overall number or particles simulated was 347400.
We have used the LAMMPS package 2 in order to carry out highly parallelized Molecular
Dynamics (MD) simulations of alkylthiol self-assembled monolayers (SAMs) on the surface
of liquid mercury. The temperature was fixed at T = 293 K with the help of Nose–Hoover
chains of ten coupled thermostats. 3 All thiol systems had the cross-section of 29.808 ×
30.312 nm2 . Such large systems are required in order to avoid a self-interaction of the
surfactants, since R-S-Hg-S-R complexes may reach upto 5 nm when unfolded. The number
of H(CH2 )18 -S-Hg-S-(CH2 )18 H molecules per interface was 240, 378, 728 which corresponds
S2
to octadecanethiol surface coverages of 0.5312, 0.8367 and 1.6114 nm−2 , respectively. Thus
say for σ = 1.6114 nm−2 we had in total 56784 surfactant “beads” from both sides of the
Hg film. The Hg film consisted of 285670 atoms. Hence the maximal overall number of
atoms in the simulation was 342454. Initially the Hg film was equilibrated for 8 ns without
surfactants. Then for the values of σ equal to 0.5312 and 0.8367 ns−2 the surfactants were
uniformly placed from both sides of the Hg film with alkyl tails in all-trans configurations
standing perpendicular to the Hg surface. After such initialization all surfactants are well
mixed and lay down flat with their molecular axes on the surface of Hg film after equilibration
times of 1-2 ns. For σ = 1.6114 nm−2 we have first pre-estimated the percentage of standing
molecules in a simulation with a smaller system. Then we have pre-set the larger system
with the island of standing molecules with approximately the same percentage of standing
thiols as in the smaller system on both sides of the Hg film. We used an experimentally
reported 4 rectangular centered unit cell containing two sulfurs as the initial arrangement
of the headgroups in the islands of standing molecules. The alkyl tails in the islands were
left untilted as above. Such initial set-up of surfactant systems with “standing” islands
allows to substantially reduce the time required for the equilibration. All octadecanethiol
systems were equilibrated for 20 ns. The measurements were carried out in steps of 10 ps in
the course of the following 87 ns of simulations. The dodecanethiols system at the surface
coverage of σ = 1.6114 nm−2 was obtained by trimming the longer molecules in the respective
octadecanethiol system. Such system set-up required 54 ns to be fully equilibrated, because
the island of standing molecules has to be partially melted away. The shape of the resulting
island of standing dodecanethiols was substantially fluctuating compared to the island of
longer octadecanethiols. Thus the sampling time for this system was taken to be extra long
and comprised 168 ns in order to be sure that we have sampled all possible configurations.
The time step for all bonded and non-bonded interactions was taken to be 0.5 and 2 fs,
respectively. The cut-off radius for non-bonded interactions of bulk as well as bound mercury
was 9 Å. The cut-off radius for the surfactant-bulk Hg interactions was 9 Å as well. And the
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cut-off radius for the non-bonded interactions of surfactants with themselves was 15 Å.
Details on the force fields used in our simulations are given below in Tables S1 and S2.
Table S1: Non-bonded interactions
Interaction type
Mercury bulk
2
UODI (r) = A0 e−ar − A1 e−b(r−R0 )
Hg – Hg
Parameters
A0 = 190.1990928E13 kcal/mol
A1 = 223.3335535E-02 kcal/mol
a = 12.48 1/Å
b = 0.891 1/Å2
R0 = 3.56 A
Mercury bulk – Surfactants
2
U (r) = A0 e−ar − A1 e−b(r−R0 )
Hg – CH2,3
(parametrized by us to reproduce
experimental surface energy of 5.4 kJ/mol
of alkyl groups on liquid Hg 12 )
Hg – S, Hg
Surfactants
ULJ (r) = 4[(σ/r)12 − (σ/r)6 ]
CH2 – CH2
S–S
Cross-interactions
2
U (r) = A0 e−ar − A1 e−b(r−R0 )
Hg – Hg
(this interaction should not be as strong
as of metallic mercury in the bulk)
same as for Hg – CH2,3
S4
11
11
11
11
11
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
9
9
9
9
10
10
A0 = 190.1990928E13 kcal/mol
A1 = 0.5 kcal/mol
a = 12.48 1/Å
b = 2.0 1/Å2
R0 = 3.56 A
same as for Hg – CH2,3
= 0.091014 kcal/mol
σ = 3.93 Å
= 0.212631 kcal/mol
σ = 3.91 Å
= 0.39743 kcal/mol
σ = 4.25 Å
√
ij = ii jj
σij = (σii + σjj )/2
CH3 – CH3
Ref.
Ref.
Ref.
Ref.
Ref.
Table S2: Bonded interactions
Interaction type
Bonds
Ur (r) = Kr (r − r0 )2
CH2,3 – CH2
CH2 – S
S – Hg
Bends
Uθ (θ) = Kθ (θ − θ0 )2
CH2,3 – CH2 – CH2
S – CH2 – CH2
CH2 – S – Hg
S – Hg – S
Torsions
P
Uφ (φ) = 5i=1 Ai cosi−1 φ
CH2,3 – CH2 – CH2 – CH2
(equivalent to OPLS 7
force field for alkanes)
S – CH2 – CH2 – CH2
CH2 – CH2 – S – Hg
CH2 – S – S – CH2
(symmetrized version of
potential from Ref. 8)
Parameters
2
Kr = 95.899 kcal/(mol Å )
r0 = 1.53 Å
2
Kr = 222.0 kcal/(mol Å )
r0 = 1.82 Å
2
Kr = 222.0 kcal/(mol Å )
r0 = 2.305 Å
Kθ = 62.1 kcal/(mol
θ0 = 114.4◦
Kθ = 62.5 kcal/(mol
θ0 = 114.4◦
Kθ = 47.1 kcal/(mol
θ0 = 101.1◦
Kθ = 26.0 kcal/(mol
θ0 = 178.6◦
A1
A2
A3
A4
A5
A1
A2
A3
A4
A5
A1
A2
A3
A4
A5
A1
A2
A3
A4
A5
rad2 )
5
5
6
7
Ref. 8
Ref. 9
Ref. 9
rad2 )
2
rad )
rad2 )
= 2.0071158850 kcal/mol
= −4.0122147580 kcal/mol
= 0.2710148952 kcal/mol
= 6.2894890533 kcal/mol
= 0.0000000000 kcal/mol
= 2.0071158850 kcal/mol
= −4.0122147580 kcal/mol
= 0.2710148952 kcal/mol
= 6.2894890533 kcal/mol
= 0.0000000000 kcal/mol
= 0.5099999990 kcal/mol
= −0.5700000000 kcal/mol
= 0.3000000110 kcal/mol
= 1.0800000000 kcal/mol
= −0.0000000108 kcal/mol
= −0.0889828674 kcal/mol
= −0.0405435305 kcal/mol
= 0.8999657630 kcal/mol
= 0.00000000489717245 kcal/mol
= −0.0000000807474767 kcal/mol
S5
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
10
8
8
8
8
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
Ref.
9
9
9
9
9
7
7
7
7
7
8
8
8
8
8
Figure S1: Side view of C22 system for σ = 1.49 nm−2 and system cross-section of 30×30 nm2 .
0.07
angle between S−Hg−S bonds
angle betwee xy−projections of tails
0.06
Probability
0.05
0.04
0.03
0.02
0.01
0
0
5
10
15
20
25
30
35
40
θ (Deg)
Figure S2: Orientation of octadecanethiols for the overall molecular surface coverage of 1.61
thiols per nm2 : distribution of relative angles between neighboring S-Hg-S bonds within the
sphere of radius 10 Å, which corresponds to the first three coordination spheres of bound
Hg (blue squares); distribution of relative angles between two projections of the alkyl tails
of the same molecule on the xy-plane (red circles).
S6
0.035
angle between S−Hg−S bonds
angle betwee xy−projections of tails
0.03
Probability
0.025
0.02
0.015
0.01
0.005
0
0
5
10
15
20
25
30
35
40
θ (Deg)
Figure S3: Orientation of dodecanethiols for the overall molecular surface coverage of 1.61
thiols per nm2 : distribution of relative angles between neighboring S-Hg-S bonds within the
sphere of radius 10 Å (blue squares); distribution of relative angles between two projections
of the alkyl tails of the same molecule on the xy-plane (red circles).
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