Supplementary materials for substituent effects on packing entropy and film
morphologies in the nucleation of functionalized pentacenes on SiO2 substrate:
molecular dynamics simulations
Shuang Chen and Jing Maa)
Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic
Chemistry of MOE, School of Chemistry and Chemical Engineering, Nanjing
University, Nanjing 210093, P. R. China
a)
Email: majing@nju.edu.cn
LIST OF CONTENTS
Discussion about the free energy.
Fig. S1. CVFF interaction energy curves of (a) T-shaped, (b) sandwich, (c)
parallel-displaced benzene dimers, respectively.
Fig. S2. Variation of binding energy with the intermolecular distance, slip distance
along the molecular long and short axes, and tilt angle of pentacene dimers, calculated
by using different methods and basis sets, respectively.
Fig. S3. Variation of binding energy with the adsorption height of benzene molecule
on the SiO2 surface, calculated by using MP2/6-31G(d) and CVFF, respectively.
Fig. S4. Variations of order parameters with the coverage.
Fig. S5. Variation of free energy change with the coverage.
Fig. S6. Comparison of distributions of intermolecular distance, r, rotation angle, ω,
and tilt angle, φ, of functionalized pentacenes between (a) amorphous phases, (b)
1
monolayers on the SiO2 surface, and (c) crystals.
2
Discussion about the free energy
During the nucleation, the free energy of the studied system, including the
deposited molecules and substrate, can be approximately traced as
after adding the 1st molecule: F1  U M  VMS  US  VS
(1)
involving the average kinetic energy of one molecule, UM, the average potential
energy from the interaction between one molecule and substrate, VMS, the average
kinetic energy of substrate, US, and the average potential energy of substrate, VS;
2
after adding the 2nd molecule: F2  2U M  2VMS  C22VMM  US  VS  TSpack
(2)
where VMM is the average potential energy from the interaction between two
molecules, and Spack is the packing entropy;
3
after adding the 3rd molecule: F3  3U M  3VMS  C32VMM  US  VS  TSpack
(3);
······
after adding the (N-1)th molecule:
N 1
FN 1   N 1U M   N  1VMS  CN2 1VMM  US  VS  TSpack
N
after adding the Nth molecule: FN  NU M  NVMS  CN2 VMM  US  VS  TSpack
(4);
(5).
According to these equations, the change in free energy is expressed as follows
F
N
N 1
 FN  FN 1  U M  VMS   N  1VMM  T  S pack
 S pack

N
(6).
As the equations presented here, the free energy would increase with the molecule
deposited, but it is not proportional to the number of the deposited molecules, N, on
the substrate. There are some “jumps” in the free energy landscape, because the VMM
and VMS terms are quite sensitive to the molecular orientations.
3
(a) T-shaped
20
10
r
0
-10
4.0
CVFF
4.5
5.0
5.5
6.0
r (Å)
6.5
7.0
7.5
8.0
(b) Sandwich
10
r
5
0
-5
3.0
CVFF
3.5
4.0
4.5
5.0
r (Å)
5.5
6.0
6.5
Interaction Energy (kcal/mol)
30
7
15
Interaction Energy (kcal/mol)
Interaction Energy (kcal/mol)
40
6
(c) Parallel-displaced
5
4
3
r = 3.2 Å
2
d
1
CVFF
0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
d (Å)
FIG. S1. CVFF interaction energy curves of (a) T-shaped, (b) sandwich, (c) parallel-displaced benzene dimers, respectively.
4
Binding Energy (kcal/mol)
20
(a)
(b)
r
dx
dy
(c)
(d)
φ
0
-20
CVFF
MP2/6-31G(d)
MP2/6-31G(d, p)
MP2/6-31+G(d)
-40
3.0
3.5
4.0
4.5
5.0 0.0
Intermolecular Distance, r (Å)
0.4
0.8
1.2
1.6
Slip Distance along x direction, dx (Å)
2.0 0.0
0.4
0.8
1.2
1.6
Slip Distance along y direction (Å)
2.0 0
20
40
60
80
100
Tilt Angle,  (°)
FIG. S2. Variation of binding energy with (a) the intermolecular distance, r, (b) slip distance along the molecule long axis, dx, (r = 3.5 Å), (c)
slip distance along the molecular short axis, dy, (r = 3.5 Å), and (d) tilt angle, φ, (r = 5.0 Å) of pentacene dimers, calculated by using MP2 with
different basis sets and CVFF, respectively. The influence of basis sets (6-31G(d), 6-31G(d, p), and 6-31+G(d)) on interlayer translation of
pentacene dimer is highlighted in (a).
5
Binding Energy (kcal/mol)
20
MP2/6-31G(d)
CVFF
0
Pn
-20
Benzene
Simplified
H
H
SiO2
Cluster model
Si14O22H24
-40
2.5
3.0
3.5
4.0
4.5
5.0
Adsorption Height, H (Å)
FIG. S3. Variation of binding energy with the adsorption height, H, of benzene
molecule on the SiO2 surface, calculated by using MP2/6-31G(d) and CVFF,
respectively. The simplified model is also illustrated in insets.
6
rM
Radial: Qr  0
Order Parameters, Q
Order Parameters, Q
1.0
Orientational
t-Bu Pn
TIPS Pn
Trajectory 1
0.5
0.0
2D
-0.5
Order Parameters, Q
Order Parameters, Q
Pn
1
 3cos2   1 g ( )d
2
1
Q    3cos 2   1 g ( )d
2
Q  
2

1  r 
3    1 g (r )dr
2   rM 


1.0
0.5
0.0
1D
-0.5
0.0
0.2
0.4
0.6
0.8
1.0
Coverage,  (ML)
1.0
Trajectory 2
0.5
0.0
-0.5
1.0
Trajectory 3
0.5
0.0
Qr
Q
-0.5
rM = 5.5 Å
0.0
0.2
0.4
rM = 6.5 Å
0.6
0.8
Coverage,  (ML)
1.0 0.0
0.2
0.4
Q
rM = 8.5 Å
0.6
0.8
Coverage,  (ML)
1.0 0.0
0.2
0.4
0.6
0.8
1.0
Coverage,  (ML)
FIG. S4. Variations of radial (Qr) and orientational (Qω and Qφ) order parameters with
the coverage during the nucleation processes of functionalized pentacene molecules
for three independent MD simulations.
7
Pn
Trajectory 2
Trajectory 1
240
Trajectory 3
(kcal/mol)
1D
200
160
t-Bu Pn
1D growth
2D gorwth
2D
120
(kcal/mol)
240
200
160
F
 FN  FN 1
N
120
TIPS Pn
A
A
(kcal/mol)
3000
1500
0
0.0
0.2
0.4
0.6
0.8
Coverage,  (ML)
1.0 0.0
0.4
0.2
0.6
0.8
Coverage,  (ML)
FIG. S5. Variation of free energy changes,
1.0 0.0
0.2
0.4
0.6
0.8
1.0
Coverage,  (ML)
F
 FN  FN 1 , between two successive
N
adding steps, involving with the Nth and (N-1)th incoming functionalized pentacene
molecules, with the coverage for three independent MD simulations. The 400
ps-snapshot of standing TIPS pentacene on the SiO2 surface is also highlighted in the
inset ○
A.
8
(a) Amorphous solids
0.09
g
0.06
0.03
0.00
0.09
(b) Monolayers
g
0.06
0.03
0.00
i
0.9
(c) Crystals
i
j
r
j
0.0
φ
ω
0.3
0
6
12
18
Intermolecular Distance, r (Å)
0
20
Pn
t-Bu Pn
TIPS Pn
j
g
0.6
i
40
60
Rotation Angle,  (°)
80
0
20
40
60
80
Tilt Angle,  (°)
FIG. S6. Comparison of distributions of intermolecular distance, r, rotation angle, ω,
and tilt angle, φ, of pentacene, t-Bu pentacene, and TIPS pentacene between (a)
amorphous solids, (b) monolayers on the SiO2 surface, and (c) crystals.
9