Supporting Information Available
Tuning Structural and Mechanical Properties of Two-Dimensional
Molecular Crystals: The Roles of Carbon Side Chains
Huanyao Cun,†1 Yeliang Wang,†1* Shixuan Du,†1* Lei Zhang,† Lizhi Zhang,† Bing Yang,† Xiaobo He,† Yue Wang,‡ Xueyan Zhu, § Quanzi Yuan, § Ya-Pu, Zhao, § Min Ouyang,|| Werner A. Hofer,⊥
Stephen J. Pennycook,# and Hong-jun Gao†
†
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
‡
Key Lab of Supramolecular Structure and Materials, Jilin University, Changchun 130023, China;
§
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
||
Department of Physics, University of Maryland, Maryland 20742, USA;
⊥
Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool, L69 3BX, UK;
#
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
1
These authors contribute equally to this work
Contents:
S1. Self-assembled patterns of QA16C molecules on Ag(110) with increasing coverage.
S2. Molecular packing density of eight observed structures.
S3. QA1C and QA4C molecule on Ag(110): models and STM images.
S4. Adsorption configurations of molecular backbone on Ag(110).
S5. Thermally-driven structural evolution of QA16C film.
S6. Definition of the total number of carbon atoms adsorbed on surface.
S7. Elastic property calculations and results.
Table S1. Parameters of the eight structures of QA16C on Ag(110).
Table S2. Adsorption energies of carbon chains on Ag(110).
Table S3. Adsorption energies of backbones on Ag(110).
S1. Self-assembled structures of QA16C molecules on Ag(110) surface with increasing coverage.
Figure S1. (A) STM images illustrating the coexistence and development of different structures of
QA16C molecules with increasing coverage on a Ag(110) surface. The arrows indicate increasing coverage. The scanning parameters from the top-left are: -1.78 V, 0.08 nA; -1.14 V, 0.08 nA; -1.01 V, 0.08 nA; -1.01 V, 0.09 nA; -1.01 V, 0.08 nA; -1.03 V, 0.08 nA, respectively. The scale bar is 10 nm. (B) Tentative models for different structures (Models of III, V and VIII are shown in Fig. S4). The carbon side chains are omitted for clarity. The variation of the ratio of different structures is strongly related to the molecular coverage. Before annealing, we scanned the sample at room temperature. During the period of one hour, we did not observe any shift of the ratio between I and II, and we also did not find any change of the domain size. It suggests that there is no shift of the ratio as a function of time and no dynamics of the domains at room temperature (without annealing ).
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S2. Molecular packing density of eight structures.
Figure S2. Molecular packing density of the eight different structures demonstrated in Figures 1B. The
molecular packing density is defined as the number of molecules per unit cell. The dashed line divides the eight structures into two different groups, corresponding to low and high molecular coverage. The average area occupied by one molecule is either larger (low density group) or smaller (high density group) than the area of the molecule, which is 2.99 nm2 including the extended alkyl chains. For example, in III the area is only 2.22 nm2. This feature of III is also confirmed by the short distance between two adjacent molecular rows, which is about 1.30 nm, i.e., 31.6% shorter than the length of a free alkyl chain (1.90 nm). Therefore we conclude that the alkyl chains do not lie flat on the substrate for the six high-density structures (III-VIII), but are partially uplifted from the surface and reach into the vacuum. In a short, the molecules are lying flat on the surface in the low coverage regime; the carbon side chains of the molecules are partially uplifted in the high coverage regime.
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S3. QA1C and QA4C on Ag(110): models and STM images.
Figure S3. Molecular ball-and-stick models of the QA1C and QA4C molecules and the STM images of
close packed self-assembled patterns on Ag(110) surface. In the images, each protrusion represents a single molecule. The side-chain of the QA1C and QA4C molecules is much shorter than that of QA16C molecule as described in the main text. With respect to the high-packed directions of [001] and [1-10] of Ag(110) lattice, the unit cell of the QA1C pattern can be described by the matrix:
The unit cell of the QA4C pattern can be described by the matrix:
The molecular packing densities of QA1C and QA4C patterns are 0.652 nm-2 and 0.706 nm-2, respectively, however, the value of structure VIII of QA16C is 0.565 nm-2. QA1C and QA4C molecules have shorter side chains but their self-assembled motif have higher packing densities than that of QA16C. The interval among adjacent molecular backbones in QA16C motif is clearly large than that of QA1C and QA4C patterns. This suggests that the side chain of the QA16C remain partially on the surface due to a steric effect. By calculation of molecular density of of QA16C, six carbon atoms must adsorb on the surface in structure VIII, which can prevent a closer spacing of the molecules.
QA1C
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S4. Adsorption configurations of the molecular backbone on Ag(110).
Figure S4. (A-D) The four most stable configurations calculated by DFT, labeled as L(h), L(v), R(h)
and R(v), respectively. For all the eight different structures as revealed in Figure 1B in the main text, their backbones can be assigned to one of these four configurations by taking into account the chirality of QA16C molecules on the surface. In these four configurations each oxygen atom of a QA16C molecule adsorbs on top of a silver atom. The adsorption energy of each configuration is calculated by DFT and given in Table S3. (E-G) Models for structures III, V and VIII, respectively. The unit cells are outlined by dotted lines.
A B C D G [11 [00 E F
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S5. Thermally-driven structural evolution of QA16C film.
Figure S5. Thermally-driven structural evolution. Annealing experiments are used to separate
energetically stable configurations from metastable configurations. (A) STM image of low-density structures, showing that structures I and II coexist before annealing. (B) Annealing the sample in A at 380 K for 15 minutes leaves only structure II. (C) Enlarged image of II. (D) STM image of high-density structures, showing that structures III, IV, V, VI coexist before annealing. (E) Annealing D leaves only structures III and VIII. The color dashed lines are used to highlight domain boundaries between different structures. For clarity, enlarged images of the structures III and VIII are shown in (F) and (G). The scale bar is 10 nm for (A), (D) and (E), 20 nm for (B), and 4 nm for (C), (F) and (G).
In order to gain deep insight into the underlying mechanism, we evaluated all interactions separately and structure-by-structure, as summarized in Table S4. The annealing data indicate that II, III and VIII are the three most stable and energetically favorable molecular configurations, which agrees very well with the prediction from the energy per unit area calculation as shown in Figure 2 in the main text. The results also show that kinetic effects play a significant role in molecular ordering process. In particular, when diffusion barriers cannot be overcome, metastable arrangements arise, leading to the coexistence of multiple locally-ordered phases. However, at elevated temperature the thermal energy drives the system to evolve into its global energy minimum.
Our above observations with a combination of the calculations of absorption energy provide a clear basis with which to understand the evolution of the molecular film. For structures I and II at low coverage, the main gain in adsorption energy is due to an increase of number of molecules on the surface. More molecules on the surface result in a decrease of surface energy of II compared to I. This explains the annealing results at low coverage (B). With increasing coverage, however, the space on the surface for the carbon chains becomes limited, leading to more carbon atoms of the chains tilting up
8 from the surface. The treatment of the molecular layer as a surface energy modification can correctly predict the thermal stability of structure VIII (E).
S6. Definition of the total number of carbon atoms per side chain adsorbed on surface.
Based on the STM images of eight different structures, we can obtain the number of molecules per unit cell (n) and the area per unit cell (Sunit) for each structure, as well as the area of one molecule Smol.
in every structure, Smol. = Sunit /n. The area of backbone SBB is assigned to the area of the backbone
lying flat on the substrate with the configuration assigned by simulations. We further define the area occupied by carbon chains (Sc-c) lying on the Ag(110) surface as Sc-c= Smol. - SBB. Obviously, Sc-c
changes with Smol. in the eight different structures. Based on measurements of the flat-lying chains with
sixteen carbon atoms in a parallel-line structure (II), we obtain the average area for each carbon atom
SC-average per side chain. We define the number of carbon atoms per side chain adsorbed on the Ag(110)
surface (NC) as NC = Sc-c / SC-average = (Smol. - SBB)/ SC-average for each structure. Finally, we acquire the
number of carbon atoms NC adsorbed on the surface for each individual structure (see the values in
Table 1 and Table S1). The carbon chain of the QA16C molecule remain partially on the surface, for example, six carbon atoms per side chain must adsorb on the surface in structure VIII.
The alkyl chains play a key role during the whole structural change process, especially in stabilizing the energetically metastable structures. They not only act as spacers between two neighboring molecules, but also stabilize a particular adlayer structure due to their interaction with the surface and their mutual vdW interactions.
S7. Elastic property calculations and results. S7.1. Theoretical considerations of QA16C film
Because of the flexibility of QA16C molecule it can form different self-assembled monolayer structures (eight). The elastic properties of the QA16C monolayer can be determined by combining STM experiments and theoretical calculations with full consideration of different molecular interactions. The stress-strain relationship of organic thin film can be approximated as a 2D isotropic system, with the strain energy density (U) as (Landau, L. D. & Lifshitz, E. M. Theory of elasticity, Course of theoretical physics, Vol. 7, Pergamon Press, Oxford, 1986):
2 2 1 (1 ) 2 1 2 E U υ υ ε υ − − = − (1)
where E is the Young’s modulus, υ is the Poisson’s ratio, and ε is the strain. The Poisson’s ratio we used for our calculation is υ=0.3 (average value for organic films; Ref. 36 in the main text; Roberts, R.J. & Rowe, R.C. Powder Tech. 1991, 65, 139), thus the equation (1) can be further simplified to:
9
2
1.6375
U = Eε (2)
Our experimental observation of the existence of different structures in molecular layers provides a unique way to determine the mechanical properties of the molecular films because the different structures can be regarded as different effective elastic states of the film. The deformation is not strictly elastic as the molecules ride up over one another, but the calculation gives an effective elastic modulus of the film. Specifically the strain ε can be directly determined by:
i j
i
S S
S
ε = − (3)
where i or j denotes one configuration among eight observed structures of QA16C on Ag(110), Si and Sj
describe the areas of one molecule in Structures i and j that can be obtained from high resolution STM images (Table S1). Correspondingly, the strain energy density U (or the deformation energy per unit volume) can also be evaluated as:
ai aj i i E E U h S − = (4)
where hi is the film thickness of Structures i, Eai and Eaj are calculated adsorption energy per area in
Structures i and j and are summarized in Table S4.
Our theoretical calculations demonstrated that Eai strongly depends on the energies of the weak
interactions, which further highlights the importance of considering all different molecular interactions in order to accurately evaluate its mechanical behavior.
S7.2. Theoretical considerations of QA1C and QA4C films
The multiple configurations are the basis of our investigations of the mechanical properties of the QA16C film. For QA1C and QA4C only one structure is formed for each kind of molecule (S3). Thus, the two dimensional mechanic property of self-assembled structure of these molecules cannot be obtained experimentally by the same method as we used on QA16C film. Most molecules only form one or two self-assembled monolayer structures. The traditional theoretical method to obtain their mechanic properties is to stretch the monolayer structure artificially and calculate Young’s modulus based on the total energy changes. For QA1C and QA4C with only one self-assembly monolayer structure, we used this method to calculate their 2D Young’s modulus.
S7.3. Film thickness estimation and Young’s modulus calculations
Estimation of the film thickness, h, is complicated due to the fact that at higher coverage the molecules ride up over one another, lifting the side chains off the substrate. The eight molecular configurations are shown in Figure 3A in the main text. In our calculations, we take h as the distance between the average position of all atoms in the molecule (except H atoms) and the first layer of the
10 substrate. In order to give a reasonable h, we use MM+ to optimize these structures, because DFT calculations for these eight structures are impossible due to the size of the unit cells. First, we build unit cells for the eight structures according to experimental results with a four-layered Ag(110) substrate. Then we construct 5×5 superstructures (3×3 for VII) for each of the eight structures. In these superstructures, the backbone orientations are the same as those shown in Table S1, and the oxygen atoms are all bonded to the nearest silver atoms according to the DFT calculations of the bare backbone on the silver substrate. This treatment assures the backbone’s orientation remains unchanged during the relaxation. The carbon chains are initially set without contact with each other and are relaxed to energetically favorable positions. Using these superstructures as clusters, we optimized these structures with MM+. After relaxation, we choose the central unit cell as the basic unit cell to consider the h. By this consideration of film thickness h (Table S1), we obtain a Young’s modulus of 0.92 ± 0.08 GPa by using the above formula.
Second, we also calculated the film thickness by considering the backbone and the carbon chains separately. In our case, the interactions between carbon chains (upC-upC) and between carbon chains and substrate (fC-Ag) are van der Waals (vdW) interactions. The MM+ calculation is good at vdW interactions. So, we can obtain reasonable information about where the carbon chains are from MM+ calculations. But the backbones of QA16C molecule have Ag-O bonds with the substrate. The interaction between backbone and the substrate can be both vdW (BB-Ag) and chemical (BB-Ag-chem), so there is possibility that the MM+ calculation may not give reasonable information about the backbone’s configuration. We therefore calculated the film thickness by considering the backbone and the carbon chains separately. In this case, we average the positions of all atoms in the QA16C molecule except H atoms by using the coordinates of the backbone optimized by DFT and those of carbon chains optimized by MM+. Using this combined consideration of film thickness, the Young’s modulus is 0.91 ± 0.07 GPa, which is only slightly different from that calculated by using the MM+ film thickness.
Furthermore, in order to test whether slight fluctuations of the backbone thickness would influence the estimate of Young’s modulus, we also calculated the Young’s modulus using different backbone thicknesses. It is found that a 0.1 angstrom fluctuation of the backbone thickness only changes the Young’s modulus about 0.01GPa. The data show that the accurate configuration of the backbones lying on the substrate is not critical to the Young’s modulus calculations. In addition, naphthalene (two benzene rings) and anthracene (three benzene rings) consist only of benzene rings. The Young’s modulus of their crystals is 8.1 GPa and 8.4 GPa, respectively. The small difference of these values suggests that benzene rings do not significantly affect the Young’s modulus because of the rigidity of benzene ring.
Based on all above results, we conclude that using the film thickness from the MM+ calculation is reasonable for calculating the Young’s modulus.
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Table S1. Parameters of the eight molecular structures of QA16C on Ag(110)
Structure I II III IV V VI VII VIII
Matrix notation
Number of molecules
per unit cell 2 1 4 2 4 3 8 2
a (nm) 2.502 2.846 4.677 3.574 4.532 2.365 2.68 2.043
b(nm) 2.726 0.958 1.895 1.191 1.781 2.502 5.75 1.734
Г (a, b) 72.2° 84.7° 92.2° 86.6° 95.9° 86.0° 95.0° 90.0°
Area of one unit cell
(nm2) 6.49 2.72 8.86 4.25 8.03 5.9 15.35 3.54 Area of one molecule
(nm2) (Si) 3.25 2.72 2.22 2.13 2.01 1.97 1.92 1.77 Molecular packing density (nm-2) 0.308 0.368 0.452 0.471 0.498 0.508 0.521 0.565 Relative increase of packing density (%) - 8.6 22.8 4.2 2 3.5 2.6 8.4 Thickness (Å) (hi) 2.89 2.89 6.09 6.73 7.97 7.97 7.97 9.29 Schematic of molecules in one unit
cell
Table S2. Adsorption energies of carbon chains on Ag(110)
Number of C-atoms on Ag(110) 3 4 5 6 7 8 9 Ead (meV) -20.0 -40.4 -62.1 -114.9 -146.1 -133.9 -148.8 Number of C-atoms on Ag(110) 10 11 12 13 14 15 16 Ead (meV) -200.3 -259.9 -266.7 -293.8 -381.9 -498.6 -575.7
The calculated energy of adsorption of the carbon chain as a function of the number of CH2 groups
interacting with the surface would be very useful for the analysis of self-assembly of molecules with long hydrocarbon chain.
− 5 5 2 9 − 6 5 1 3 − 9 10 3 5 − 6 9 2 3 − 11 2 1 6 − 3 7 5 5 − 5 6 10 14 5 0 0 6
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Table S3. Adsorption energies of the molecular backbones on Ag(110).
Backbone Ead of backbone (meV) L-QA16C (L(h)) -608
L-QA16C (L(v)) -427 R-QA16C (R(h)) -246 R-QA16C (R(v)) -537
Adsorption energy (Ead) of the four configurations of QA16C backbones on the Ag(110) surface
calculated by using DFT. The adsorption energy of the backbone per unit cell for one specific structure can be obtained by multiplying Ead (E(BB-Ag-chem)) by the total number of backbones in the unit cell,
see Table S4.
Table S4. Energies of eight observed structures of QA16C on Ag(110)
Structure I II III IV V VI VII VIII
Number of molecule per unit
cell 2 1 4 2 4 3 8 2
Number of C adsorbed on Ag(110) per chain
16 16 11 10 8 8 8 6 Composition of
backbone type in the unit cell
1 L(h) l R(v) 1 R(v) 2 L(h) 2 R(v) 1 L(v) 1 R(v) 2 R(h) 2 L(v) 1 L(v) 2 R(h) 4 L(v) 4 R(v) 1 L(v) 1 R(v) E(BB-Ag-chem) (meV) -1145 -537 -2290 -964 -1346 -919 -3856 -964 E(BB-Ag) (meV) -900 -450 -1800 -900 -1800 -1350 -3600 -900 E(fC-Ag) (meV) -2302.8 -1151.4 -2079.2 -801.09 -1071 -803.23 -2142 -459.6 E(upC-upC) (meV) 0 0 -574.9 -358.1 -998.9 -749.2 -1997.8 -640.8 Etotal per
unit cell (meV)* -4347.8 -2138.4 -6744.1 -3023.2 -5215.9 -3821.4 -11596.0 -2964.4 E per molecule
(meV/mol.) (Eai) -2173.9 -2138.4 -1686 -1511.6 -1304 -1273.8 -1449.5 -1482.2
E per unit area
(meV/nm2) -669.9 -786.1 -761.2 -711.4 -649.6 -647.7 -755.4 -837.4
