Influence of Molecule-Surface and Molecule-Molecule Interactions on

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Influence of Molecule-Surface and Molecule-Molecule Interactions on Two-Dimensional Patterns formed by Functionalised Aromatic Molecules Sara Fortuna, and Karen Johnston J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 09 Mar 2018 Downloaded from http://pubs.acs.org on March 9, 2018

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The Journal of Physical Chemistry

Influence of Molecule–Surface and Molecule-Molecule Interactions on Two-Dimensional Patterns formed by Functionalised Aromatic Molecules Sara Fortuna∗,†,‡ and Karen Johnston∗,¶ †Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy ‡http://www.sarafortuna.eu ¶Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose Street, Glasgow, G1 1XJ, United Kingdom E-mail: [email protected]; [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Molecules self-assemble on surfaces forming a variety of patterns that depend on the relative strength between the intermolecular and molecule–surface interactions. In this study, the effect of the physisorption/chemisorption interplay on self-assembly is investigated using Monte Carlo simulations. The molecules are modelled as hexagonal tiles capable of assuming two distinct adsorption states, with different diffusion properties, on a hexagonal lattice. The self-assembled structures that emerge by tuning the molecule–surface and molecule–molecule interactions are systematically mapped out to develop understanding of their phase behaviour. The resulting phase diagrams will guide the engineering of novel molecules to obtain desired collective structural properties for development of innovative two-dimensional devices.

1. Introduction Controlling the self-organisation of molecular adlayers is key for the development of novel two-dimensional devices, such as graphene nanostructure spintronics 1 or conjugated aromatic polymer anodes for ion batteries. 2 While the nature and strength of molecule–surface interactions control the interfacial and electronic properties of adsorbed molecules, the monolayer patterns formed are controlled by the interplay between molecule–surface and molecule– molecule interactions. 3 Therefore, in order to control the monolayer structure, one can adjust the interactions by changing the chemical properties of the molecular adlayer. Molecular functionalisation, 4 such as the introduction of groups capable of hydrogenbonding 5 or bulky groups, 6 is one way to adjust the molecular interactions and is well documented to affect the observed monolayer patterns. 7–9 Halogenation of molecules can heavily modify these patterns, especially for aromatic molecules. For instance pentacene is known to form two different ordered phases on Au(111) but its fluorination leads to the formation of only one single phase, in the form of ordered arrays. 10 Further examples include metallorganic molecules, such as phthalocyanines, which are known to exhibit non2


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standard molecule–surface coupling that is stronger than typical physisorption but weaker than chemisorption leading to a variety of self-assembled patterns and surface reconstructions. 11,12 In this case the assemblies can be further controlled by fluorination, as observed for copper phtalocyanine patterning on Cu(100) and Cu(111). 13 The effect of fluorination on monolayer structure is also observed in benzene on metal surfaces. 14,15 In all cases, molecular functionalisation controls the interaction parameters that drives the system towards a particular monolayer structure 3 and there are striking examples where functionalised molecules exist in two or more distinct adsorption states. Kohn-Sham density functional theory calculations have found that that on platinum heteroaromatic s-triazine can exist in multiple adsorption states, 16 and phenol 17 and benzene derivatives 18–20 exist in two states. It has been shown that on platinum the relative stability of the chemisorbed and physisorbed states of benzene molecules can be tuned by adjusting the ring functionalisation 17–20 and, hence, that the molecule–surface interaction can be used to control the structure of the self-assembled monolayer. 21 The collective molecular behavior is affected by the interplay among different interactions and lattice models have been shown to capture experimentally observed patterns. For instance hexagonal and square lattice models 22 successfully described self-assembled molecular systems on surfaces. 21,23–27 The effect of the strength of the molecule–surface interaction was recently taken into account in a three-dimensional model for the study of triangular molecules at the solid-liquid interface 28 and in two dimensional models for the study of molecules on platinum surfaces. 21 If the adsorbed molecules are rigid, flat molecules presenting hexagonal symmetry, e.g. due to the presence of one or more fused benzene rings, the suitable symmetry for a lattice model is a hexagonal (or equivalent triangular) one. The phase behavior of hexahalogenated molecules was previously studied analytically 29 and by Monte Carlo simulations. 21 In our previous study, we showed that hexahalogenated molecules can form either ordered, packed monolayers or disordered monolayers, depending on their preferred adsorption state. 21 Only the weakly bound (physisorbed) state allowed for

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free diffusion along the surface resulting in a ordered packed state. 21 Our model gave qualitative agreement to experiment and found that benzene monolayers were disordered and halogenation (chloro- and bromination) resulted in ordering, 21 which was qualitatively similar to experimental results that fluorination increased ordering of pentacene monolayers. 10 In this paper, we generalise our model to describe molecules with hexagonal symmetry (such as hexasubstituted benzene rings 20 and larger aromatic compounds). We systematically map out the phase behaviour of self-assembled monolayers by varying the molecule–surface and intermolecular interactions, and show that these systems express a rich phase behavior. This study will enable us to understand what phases are possible, and facilitate the design of molecules and surfaces that would give a desired structure for two-dimensional devices.

2. Methods

(a) chemisorbed

(b) physisorbed

Figure 1: Possible molecular states. Molecules in their chemisorbed state (a) are locked in their position, while physisorbed molecules are free to diffuse on the hexagonal lattice (b).

We simulate the self-assembly of non-overlapping hexagonal molecules on a hexagonal

0-0

0-30

30-30

lattice in the NVT ensemble. On the lattice each molecule i can be in one of two possible adsorption states si (as in Fig. 1): chemisorbed (si = chem) or physisorbed (si = phys) . Each lattice site can be occupied by only one molecule. Two adjacent molecules, i and j, interact with each other via the interaction parameter, Eijside . When both molecules are in different adsorption states i.e. when si = sj , it is assumed that the interaction is negligible and Eijside = 0. Molecules interact with the surface phys chem via the interaction parameter Eads when physisorbed, and Eads when chemisorbed. The

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Hamiltonian of the system is:

H=

X

si Eads +

i

where s ,sj

Eiji

=

1 X si ,sj E 2 i,j ij

with i 6= j

   E side

if si = sj

  0

otherwise

ij

(1)

(2)

si and Eads is the adsorption energy for molecule i, which can be in either the physisorbed phys si si chem (Eads = Eads ) or chemisorbed states (Eads ). The first summation is taken over all = Eads

molecules and the second summation is only over adjacent molecules. All energies are in units of kB T , where kB is the Boltzmann constant. At each simulation step a molecule is selected at random and either a chemisorbed/physisorbed transition occurs or a translation to the next lattice site is attempted. Only one move can be attempted at each simulation step. Only physisorbed molecules can translate to adjacent sites. If a molecule is chemisorbed only a transition to a physisorbed state is possible. All the attempted moves are accepted or rejected following the Metropolis acceptance probability. 30 We do not account for rotations, therefore Eijside is constant for all the molecular orientations. The system is composed of 1000 molecules interacting via the Hamiltonian in Eq. (1) on a 50 × 50 hexagonal lattice with periodic boundary conditions, corresponding to a coverage of 0.4. To verify the effect of the coverage, selected parameter combinations were also run with 972 molecules on a 54 × 54 lattice corresponding to a coverage of 0.33. A chain of 400 simulations is built, with each simulation consisting of 5,000,000 equilibration steps followed by 5,000,000 production steps. Every chain starts at 0.4kB T and every successive simulation is run by decreasing the temperature by ∆kB T = 0.002 and using the last configuration of the former simulation as starting configuration. The low temperature configurations are then heated back to 0.4kB T following the same protocol. Each simulation chain is repeated 10 times. Averages are calculated over the production steps of the 10

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phys chem = Eads = 0.0 Eads (b)

phys chem = −0.5, Eads = 0.0 Eads (c)

side Eij = −0.5

phys chem = 0.0, Eads = −0.5 Eads (a)

(e)

(f)

(g)

(h)

(i)

side Eij = 0.0

(d)

side Eij = 0.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 2: Patterns formed at kB T = 0.002. Insets show an enlarged detail of each snapshot. Physisorbed (chemisorbed) molecules are shown as green (orange). simulations run with the same parameter set. No hysteresis effects were observed, therefore, in the next section we will discuss only the results obtained upon cooling. phys We generalise our former study 21 by exploring a larger parameter space Eads = [−0.5, 0.0], chem Eads = [−0.5, 0.0] and Eijside = [−0.5, 0.5]. As we are interested in exploring trends, and

keeping in mind that all the energy parameters are in units of kB T and can therefore be rescaled, only their ratio is important. Each parameter is chosen among 0, ±0.001, ±0.005, phys chem ±0.01, ±0.05, ±0.1,±0.5. By combining Eads , Eads , Eijside we obtain 637 systems each

ruled by a different parameter set.

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3. Results and Discussion In the following, we first look at low temperature limiting cases. Then we look at the details of the structural transitions encountered to produce the observed patterns. The behaviour of the system is described by the heat capacity at constant volume

CV =

(∆E)2 , kB T 2

and several different order parameters: (i) the fraction of physisorbed molecules, χphys , (ii) the total number of neighbors of each molecule, N neigh , (iii) the number of chemisorbed neighbors of each chemisorbed molecule, N cc , (iv) the number of physisorbed neighbors of each physisorbed molecule, N pp , (v) and the number of unlike neighbors

N pc = N cp = N neigh − N pp − N cc The peaks in the running standard deviations of these order parameters enables us to further locate the locus of structural transitions. Finally, after characterising the observed defects on the self-assembled structures, we collect our results in a number of phase diagrams associated with the choice of parameters.

3.1 Low temperature phases By first looking at few limiting cases, a number of low-temperature (kB T = 0.002) patterns are observed (Fig. 2).

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Strong, attractive molecule–molecule interactions with Eijside = −0.5 lead to packed patterns (Fig. 2a-c). The molecules can be all physisorbed, for instance when the chemisorbed interaction is switched off, as shown in Fig. 2a, or all chemisorbed when the physisorption interaction is switched off, as shown in Fig. 2c. When both chemisorption and physisorption interactions are set to zero, a single chemisorbed cluster is observed (Fig. 2b). This chemisorbed configuration arises from the fact that molecules are not mobile in the chemisorbed state while they can freely diffuse in the physisorbed state. When a first chemisorbed cluster forms, further molecules from the physisorbed state can add to it and then be locked in their position favouring a large packed chemisorbed pattern at low temperature. When the molecule–molecule interaction is switched off, i.e. Eijside = 0.0, the system does not pack, as shown in Figs. 2d-f. The system freezes in a disordered state whose adsorption state of the frozen molecules depends on the relative strength of the adsorption energies phys chem (Fig. 3). When Eads = Eads half of the molecules are chemisorbed, and the rest are phys chem physisorbed (Fig. 2e). When Eads Eads = 0.0 they are all physisorbed (Fig. 2d) when phys phys chem chem Eads Eads = 0 they are all chemisorbed (Fig. 2f). In the case when Eads and Eads

are both negative but much weaker (closer to zero) the number of physisorbed/chemisorbed chem molecules depends on their respective interaction strength. For instance, when Eads = 0.001 phys chem and Eads = 0.01 only 40% of the molecules are chemisorbed whereas when Eads = 0.01 phys and Eads = 0.001 then 60% are chemisorbed (Fig. 3).

In the case of repulsive intermolecular interactions (for instance when Eijside = 0.5) we would expect molecules to avoid occupying adjacent lattice sites. When the coverage is greater than

1 3

(as is the case when the coverage is 0.4) we observe a number of strategies

to escape higher energy configurations. Depending on the physisorption and chemisorption strength we observe the formation of: • an ordered layer of physisorbed molecules with dislocations and defects in the form of phys chem chemisorbed molecules when Eads Eads = 0.0 (Fig. 2g),

• a frozen state composed of branched chains and ribbons of alternating physisorbed/chemisorbed 8


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1

phys −Eads

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


chem −Eads

phys chem for Eijside = 0.0 Figure 3: Fraction of chemisorbed molecules as a function of Eads and Eads at kB T = 0.002.

phys chem molecules when Eads = Eads = 0.0 (Fig. 2h), and

• an ordered layer of chemisorbed molecules with dislocations and defects in the form of phys chem physisorbed molecules when Eads Eads = 0.0 (Fig. 2i).

If the coverage is below or equal to 0.33, we might expect to observe complete order. phys chem Interestingly, when Eads Eads = 0.0 (Fig. 4a) complete order is not achieved and defects

in the form of vacancies or insertions are present. It is the non-mobile chemisorption state that causes these defects. Chemisorbed molecules would have to first become physisorbed in order to migrate to a new adsorption site, but this process is hindered due to repulsive chem intermolecular interactions between molecules in the same adsorption state. When Eads phys Eads = 0.0 (Fig. 4b), physisorbed molecules at defect sites can escape and freely diffuse to

fill all the vacancies enabling complete order to be reached. The formation of defects can be better understood by observing their occurrence at fixed values of adsorption energies along increasing values of Eijside (Fig. 5). Defects appear in chem different forms, depending on the interplay among interactions. For instance, at Eads = phys −0.05, Eads = −0.01, and going from Eijside = −0.05 to 0.00 first the packed structures chem become fragmented as the side-side interactions weaken with respect to Eads (Fig. 5, top

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phys chem Eads = 0.0, Eads = −0.5

side Eij = 0.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a)

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phys chem Eads = −0.5, Eads = 0.0

(b)

Figure 4: Patterns formed at kB T = 0.002. Physisorbed molecules (green), chemisorbed molecules (orange). At coverage 0.33. Structural defects are highlightd by black circles. phs chem Eads = −0.05, Eads = −0.01

-0.05

-0.01

-0.005

0.005

0.01

0.05

0.1

0.5

0.05

0.1

0.5

side − − − − − − − − − − − − Eij −−−−−−−−−−> phs chem Eads = −0.01, Eads = −0.05

-0.05

-0.01

-0.005

0.005

0.01

side − − − − − − − − − − − − Eij −−−−−−−−−−>

phys chem Figure 5: Defect formation in the patterns formed at fixed Eads and Eads at 0.002kB T . Physisorbed (chemisorbed) molecules are shown in green (orange).

panels). When the side interactions are close to zero the structure is completely fragmented. Fragmentation persists at 0.005 and defects of physisorbed molecules emerge at more positive Eijside (0.01). The more repulsive the intermolecular interaction, the higher the number of chem ) a new ordered state emerges with grain physisorption defects. When Eijside ∼ (−Eads chem ) the grain boundaries increase and the patterns boundary defects. When Eijside ≥ (−Eads chem again appear fragmented. A similar observation applies for the case in which Eads = −0.01 phys phys and Eads = −0.05 (Fig. 5, bottom panels). However, when Eijside ≥ (−Eads ), the pattern

remains ordered with grain boundary and chemisorption defects.

3.2 Phase transitions In this section we investigate the structures that emerge at different temperatures. By looking at the phase behavior along kB T , the peaks in the heat capacity enable the identification of

10


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1 Echem=0.0, Ephys=-0.5 Echem=0.0, Ephys=0.0 Echem=-0.5, Ephys=0.0 q=-0.5 q=-0.5q=0.0 q=-0.5q=0.0 q=0.5 q=0.0 q=0.5 attractive side-side interactions

N(1,1) N-N0-N11 N cp

0.2 0.1 0.3 0.21.55 0.3 0 2.0 0.1 0 (f) (e) 1.5 kT1.043 (q) 1.5 (r) 1.0 1.0 2 0.5 0.5 0.5 1

Cv (a.u.)

Cv (a.u.)

X(dw) N

0.1 0 2.0 1.5

0.2 0.1 0 0.3 0.2 0.1 0.3 0.2(k) 0 (e) 0.1 0 0.5 (l) 0.3 0.8 2.0 1.5 1.5 1.5 0.4 kT kT kT1.0 0.6 1.5 1.0 1.0 0.3 0.4 1.0 0.2 (f) 0.5 0.5 0.5 0.2 0.5 0.1

(n

Cv (a.u.)

0.6 0.4 0.2 1 (h) 0.8 2.5 0.6 2.0 (i) 0.4 1.5 0.2 1.0 0.8 2.5 0.6 2.0 (i) (k) 0.4 (j) 1.5 0.2 1.0 0.8 0.6 (k) 0.4 (j) 0.2

(n (o

q=0.5

0.1

2.8 2.8 0.3 0.1 0.2 0.3 5 0 2.8 0.1 0 0.2 0.1 0.3 0.2 5 0.3 0 (c) 0.1 0 2.5 0.2 0.1 0 0.3 0.2 0.1 0.3 0.2(h) 0 2.5 0.1 0 0.2 0.1 0.3 0.2 50 (m) 0.3 2.5 0 kkT 4 4 BT BT BT 2.6 kkT 2.6 kkT kT 4 (m) kT kT2.6 kT kT 2.0 2.0 2.0 3 (c) 3 (h) 3 (h) 2.4 2.4 2.4 (c) 2 2 2 1.5 1.5 1.5 1 1 1 2.2 2.2 2.2side 0 0interactions 1.0 1.0= −0.5, corre1.0 Figure 6: Self-assembly 05for attractive intermolecular with E ij 5 5 (n) 0.8 (i) (d) (d) 0.8 0.8 2.0 2.0 2.0 4 (d) 4 (i) sponding to the low temperature phases in Fig. 2a-c.43 The top panels1.5show 0.6 0.6 the variation 0.6 1.5 1.5 (n) 3 3 0.4 0.4 0.4 1.0 1.0 1.0 (i) 2 2 2 of CV in arbitrary units 1(a.u.) with temperature. The panels show averages0.2 0.2 0.2 0.5 0.5 0.5 running 1 1 lower 0 0 0 0 0 0 0 0 (calculated over 10 points) of order parameters with5 temperature. Also in(o)blue0.80 (e) 5 5 0.5 (j) indicated (e) 0.8 2.0 2.0 2.0 0.4 4 4 4 0.6 1.5 1.5 1.5 solid lines are the respective deviations 10 points) and0.6 3 (e) running standard 3 (j) 3 (o) (calculated over 0.3 (j) 0.4 0.4 1.0 1.0 1.0 0.2 2 2 2 0.2 0.2 0.5 0.5 0.5 0.1 1 1 1 10× magnified. 0 0 0 0 0 0 0 0 0 0 0.1 0.2 0.3 0 0.1 0 0.2 0.1 0.3 0.2 0.3 0 0.1 0 0.2 0.1 0 0.3 0.2 0.1 0.3 0.2 0.3 0 0.1 0 0.2 0.1 0.3 0.2 0.3 0

0.1

1.5 (l) (k) 1.0

kT

kT

0.2

0.3(q (r

kT

0.2

kT

0.3

(m

N(0,0)

(n

(o

N(1,1)

N(0,0) N(1,1)

N(0,0)

N

1.0 0.5 0.5

kT

(p (o

(p (q

0.2 0.1 0.3 0.2(q) (r) 0.3 (l) 0.8 0 1.5 kT 0.6 1.0 (k) 0.4 0.5 0.2

kT

0.3 1.55 0 4 1.03 2 0.5 1

1

(h) 0.8

N

0.2

(m)

Cv (a.u.)

Cv (a.u.)

(m) (g)

q=0.5

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

(a)

q=0.0 q=0.5

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

Cv (a.u.) Cv (a.u.)

Cv (a.u.)

X(dw) Cv (a.u.)

Cv (a.u.) Cv (a.u.)

Cv (a.u.)

(m)

1 1 1 1 1 1 1 (h) (n) 0.8 0.8 0.8 (b) 0.8 0.8 0.8 0.8 0.6 (h) 0.6 0.6 (n) 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 (b) P 0.2 0.2 0.2 0.2 0.2 A 0.2 0.2 Echem=0.0,1Ephys=-0.5 Ephys=0.0 1 Echem=0.0,1Ephys=0.0 1 Echem=-0.5, 1 1 1 2.8 2.8 2.8 (c) (i) (o) (h) (n) 0.85 0.8 0.85 (b) 0.8 0.8 0.8 0.8 2.5 2.5 2.6 2.6 2.6 0.64 (i) 0.6 0.64 (o) 0.6 0.6 0.6 0.6 2.0 2.0 3 (h) 3 (n) 0.42 0.4 0.42 0.4 0.4 0.4 0.4 2.4 2.4 2.4 (c) (b) 1.5 1.5 0.21 0.2 0.21 0.2 0.2 0.2 0.2 2.2 2.2 2.2 1.0 1.0 2.8 2.8 2.8 5 (i) (o) (d) q=-0.5 (j) (d) (p) q=-0.5 0.8 q=0.0 q=0.5 0.8 q=0.0 q=0.5 2.0 q=-0.5q=0.05 (c) 2.0 2.0 2.5 2.5 4 4 2.6 2.6 2.6 0.6 0.6 1.5 1.5 1.5 (i) (o) 2.0 2.0 3 (j) 3 (p) (c) 0.4 (f) 1.0 1.0 2.4 (a) 2.4 (f)0.4 (a) 2.4 (k) 2 (f)1.0 2 (k) 1.5 1.5 0.2 0.2 0.5 0.5 0.5 1 1 2.2 2.2 2.2 1.0 1.0 5 5 0.5 (d) (j) (e) (p) (e) 0.8 (k) (q) 0.8 2.0 2.0 2.0 (d) 4 (j) 4 (p) 0.4 0.6 0.6 1.5 1.5 1.5 3 (k) 3 (q) 0.3 0.4 0.4 1.0 1.0 1.0 2 2 0.2 P 0.2 0.2 0.5 0.5 0.5 1 1 0.1 A

N

0.1 50 1.5 4 (e) 1.03 (f) 2 0.5 1

q=-0.5q=0.0 q=0.5

(m) (g)

q=0.5

(m) (g)

phys Eads = 0.0

Cv (a.u.)

(d) (e)

chem E = −0.5 (g) ads (a)

Cv (a.u.)

5 4 3 2 1

(a)

N(1,1) N(0,0) N(0,0) N Cv (a.u.)

N(1,1) N(0,0) N(0,0) Ncc N pp N Cv (a.u.)

5 4 (d) 3 (c) 2 (a) 1

(g)

q=-0.5q=0.0

(m)

N(1,1) N-N0-N1

(b) (c)

A

phys = 0.0 Eads

Cv (a.u.)

(b)

P

(g)

chem Eads = 0.0 (a)

X(dw) N

(a)

X(dw) Cv (a.u.)

q=-0.5

N(1,1) N(0,0) N(0,0) N Cv (a.u.)

neigh X(dw) N N

1 0.8 0.6 0.4 0.2 1 0.85 0.64 3 0.42 0.21

phys Eads = −0.5

N(1,1) N-N0-N1

χphys X(dw) Cv (a.u.)

Cv (a.u.)

(a)

chem Eads = 0.0

N(1,1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Echem=0.0, Ephys=-0.5 Echem=0.0, Ephys=0.0 Echem=-0.5, Ephys=0.0

kT

kT

kT

kT

kT

kT

kT

the sequence of structural transitions that lead to the observed low temperature patterns. The structures encountered can be further characterised by a number of order parameters defined earlier: χphys , N neigh , N cc , N pp , and N cp (Fig. 6-8). 3.2.1 Attractive intermolecular interactions For attractive intermolecular interphys chem actions with Eads = 0.0 and Eads = Eijside = −0.5, leading to the zero temperature ph-

ysisorbed packed pattern of Fig. 2a, two major transitions can be observed (Fig. 6a-f). The first is a high temperature physisorption/chemisorption transition characterised by a peak in CV (Fig. 6a), and associated with a rapid variation in χphys (Fig. 6b), no large variations in N neigh (Fig. 6c) and N cc (Fig. 6d), and a smooth variation in N pp (Fig. 6e) and N cp (Fig. 6f) at 0.23kB T . This CV peak appears as shoulder on the main CV peak at 0.12kB T (Fig. 6a), 11


0.1

0.2

kT

0.3


which is associated with a rapid change in N neigh and N pp (Fig. 6c,e). The low temperature value of N pp , which is close to its maximum value of 6, indicates the packing of the system in a physisorbed state. The case leading to the chemisorbed pattern of Fig. 2b follows a different route (Fig. 6gphys chem = 0.0) but l). In this case, the molecules do not interact with the surface (Eads = Eads

have attractive intermolecular interactions between molecules in the same adsorption state (Eijside = −0.5). Only one sharp CV peak is present and physisorption/chemisorption and packing transitions both take place at the same temperature, as shown in Fig. 6 g-l. Interestingly, even though there is no energetic preference with respect to the adsorption state, the molecules pack in a chemisorbed state, which is an effect of their arrested translational mobility in that phase. phys chem When Eads = 0.0 and Eads = Eijside = −0.5 (Fig. 6m-r), then CV exhibits a main peak

and a weak shoulder as shown in Fig. 6m. The shoulder is the low temperature packing peak, now at 0.27kB T . The higher temperature main peak at 0.30kB T is the physisorption/chemisorption transition. Here all the order parameters sharply decreases (Fig. 6n-r) with only N pp going to zero (Fig. 6q), while χphys (Fig. 6n) and N cp (Fig. 6r) continues to decrease and N neigh (Fig. 6o) and N cc (Fig. 6p) continues to increase at both temperatures. The low temperature structure is once again a chemisorbed packed pattern (Fig. 2c).

3.2.2 Zero intermolecular interactions When the intermolecular interactions are set to zero (Eijside = 0) leading to the disordered patterns of Fig. 2d-f, there appears to be a single structural transition only when the molecule–surface interaction is active (Fig. 7a-r). phys chem When Eads = 0.0 and Eads = −0.5 there is a large peak in CV (Fig. 7a). This is a

physisorption/chemisorption transition leading to all molecules in their favoured physisorbed state (Fig. 7b). Packing, of course, does not take place and N neigh is constant with temperature (Fig. 7c). As the temperature decreases, the number of like neighbors in the unfavoured adsorption state decreases (Fig. 7d) while the number of like neighbours increases in the

12


Page 12 of 24

Page 13 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


favoured state (Fig. 7e). Also the number of unlike neighbors drops to zero (Fig. 7f). As expected, when all the interactions are set to zero, no transition is observed, all the order parameters are constant along the temperature (Fig. 7g-l) and the system stays disordered. phys chem = 0.0 the observed On the other hand, in the scenario in which Eads = −0.5 and Eads

large peak in the CV (Fig. 7m) is once again associated with a physisorption/chemisorption transition leading to all molecules in their favoured adsorption state, which in this case is chemisorbed (Fig. 7n). As the molecules do not interact with each other, packing still does not take place as highlighted by the constant values of N neigh (Fig. 7o). As the temperature decreases the number of like neighbors in the favoured adsorption state increases (Fig. 7p) while the number of like neighbours decreases in the unfavoured state (Fig. 7q), and the number of unlike neighbors drops to zero (Fig. 7r).

3.2.3 Repulsive intermolecular interactions Finally, we present the self-assembly when the intermolecular interactions are repulsive (Eijside = 0.5, Fig. 2g-i) and molecules occupying adjacent lattice sites will attempt to minimise repulsive interactions by minimising the number of neighbors in the same adsorption state (Fig. 8a-r). When the physisorption phys chem state is energetically favorable, for instance with Eads = 0.0 and Eads = −0.5, decreasing

the temperature first shows a shoulder on the main CV peak at ≈ 0.12kB T (Fig. 8a) with a minimal variation in χphys (Fig. 8b), the onset of N neigh drop (Fig. 8c), and a slow decrease in N cc (Fig. 8d). The main peak in CV at lower temperature of ≈ 0.06kB T (Fig. 8a) corresponds to a more significant physisorption/chemisorption transition (Fig. 8b). There is a decrease in the total number of neighbors, N pp (Fig. 8e). Below this temperature N cc (Fig. 8d) and N pp (Fig. 8e) fall to zero leaving only unlike neighbours (Fig. 8f). When both physisorbed and chemisorbed adsorption energies are zero, there is only one peak in CV (Fig. 8g), not associated with any variation in χphys (Fig. 8h) which corresponds

13



Page 14 of 24

Echem=0.0, Ephys=-0.5 Echem=0.0, Echem=0.0, Ephys=0.0 Ephys=-0.5 Echem=-0.5, Ephys=0.0

1 Echem=0.0, Ephys=-0.5 Echem=0.0, Echem=0.0, Ephys=0.0 Ephys=-0.5 Echem=-0.5, Ephys=0.0 q=0.5 q=-0.5 q=-0.5q=-0.5 q=-0.5q=0.0q=0.0 q=0.0 no side-side q=0.0 q=0.5q=0.5 interactions

N(1,1) N-N0-N11

0.1 50 1.5 4 (e) 1.03 (f) 2 0.5 1

q=0.5 (m)

Cv (a.u.)

Cv (a.u.)

q=0.0 q=0.5q=0.5

(m) (g)

(a)

q=0.5 (m)

Cv (a.u.)

Cv (a.u.)

phys Eads = 0.0

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

(a) (a)

(m)

chem E = −0.5 (g) ads (a)

Cv (a.u.)

phys = 0.0 Eads

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

chem (a) (a)Eads = 0.0

q=0.5 q=-0.5q=0.0q=0.0

(m) (g) Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

X(dw) Cv (a.u.)

A

1 11 1 1 11 1 1 1 1 (h) (n) (h) 0.8 0.8 0.8 0.8 (b) 0.8 0.8 0.8 0.8 (b) 0.8 0.8 0.8 0.6 (h) 0.6 0.6 (b) 0.6 (n) 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 (b) (b) P P 0.2 0.2 0.2 0.2 0.2 0.2 0.2 A 0.2 0.2 A 0.2 0.2 Echem=0.0,1Ephys=-0.5 Echem=0.0, Echem=-0.5, Ephys=0.0 11 Echem=0.0, 1Ephys=0.0 1Ephys=-0.5 11 1 1 1 1 2.8 2.8 2.8 2.8 5 (c) (i) (c) (o) (h) (n) (h) 0.85 0.8 0.8 0.85 (b) 0.8 0.8 0.8 0.8 (b) 0.8 0.8 0.8 2.5 2.5 2.5 2.5 4 2.6 2.6 0.6 2.6 2.6 0.64 (i) 0.6 0.6 0.64 (o) 0.6 0.6 0.6 0.6 0.6 0.6 (b) 2.0 2.0 2.0 2.0 3 (h) 3 (c) 3 (n) (i) (c) 0.42 0.4 0.4 0.42 0.4 0.4 0.4 0.4 0.4 0.4 2.4 2.4 0.4 2.4 2.4 (c) 2 (b) 1.5 1.5 0.2 1.5 1.5 (b) 0.21 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1 1 2.2 2.2 2.2 2.2 1.0 1.0 1.0 1.0 2.8 2.8 2.8 2.8 5 5 q=-0.5 (i) (o)q=0.5 q=0.5 (d) q=-0.5 (j) (c) (p) q=-0.5 q=-0.5 0.8 q=0.0q=0.0 0.8 q=0.0 0.8 q=0.5 0.8 (d) q=0.05 (c) 2.0 2.0 2.0 2.0 (d) 2.5 2.5 2.5 2.5 4 4 4 2.6 2.6 2.6 0.6 0.6 0.6 0.6 1.5 (d) 1.5 2.6 1.5 1.5 (i) (o) 2.0 2.0 2.0 2.0 3 (j) 3 (c) 3 (p) (c) (c) (i) (k) 0.4 (a) 0.4 (f)0.4 (a) 0.4 1.0 1.0 (a) 2.4 2.4 (f)1.0 2.4 2.4 (k) (j) 2 (f)1.0 2 (a) 2 (k) 1.5 1.5 0.2 1.5 1.5 0.2 0.2 0.2 0.5 0.5 2.2 0.5 0.5 1 1 1 2.2 2.2 2.2 1.0 1.0 1.0 1.0 5 5 5 0.5 (d) (j) (e) (p) (e) 2.0 (k) (q) 0.8 0.8 0.8 0.8 (e) 2.0 2.0 2.0 (d) (d) 4 (j) 4 4 0.4 0.6 0.6 0.6 0.6 1.5 1.5 1.5 1.5 (d) (p) 3 (k) 3 (e) 3 (q) (k) 0.3 0.4 0.4 0.4 0.4 1.0 1.0 1.0 1.0 (j) 2 2 2 0.2 P P 0.2 0.2 0.2 0.5 0.5 0.5 0.5 1 1 1 0.1 0.2 A A 0.2

kT

0.3 1.55 0 4 1.03 2 0.5 1

00 50.1 2.0 1.5 1.5

4 1.5 (l) (k) 1.0 1.0 3 1.0 2 0.5 0.5 0.5 1

(n)

(n) (o)

0.2 0.1 0.1 0.3 0.2 0.21.550.3 0.3 0 2.0 0.1 0 (f) (e) 1.5 kT kT1.043 (q) 1.5 (r) 1.0 1.0 2 0.5 0.5 0.5 1

(f)kT (e)

0.2 0.1 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2(k) 0.3 0 (e) 0.1 0 0.5 (f) (l)0.3 0.8 2.0 2.0 1.5 1.5 1.5 1.5 0.4 kT kT kT kT1.0 0.6 1.5 1.5 1.0 1.0 1.0 0.3 0.4 1.0 1.0 0.2 (f) 0.5 0.5 0.5 0.5 0.2 0.5 0.5 0.1

q=0.5

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

Cv (a.u.)

X(dw) N

Cv (a.u.)

(d) (e)

P

N(1,1) N(0,0) N(0,0) N Cv (a.u.)

5 4 3 2 1

(a)

N(1,1) N-N0-N1

N(1,1) N(0,0) N(0,0) N Cv (a.u.)

5 4 (d) 3 (c) 2 (a) 1

(g)

q=-0.5q=-0.5 q=0.0

neigh X(dw) N N

(b) (c)

A

N cp N(1,1) N-N0-N11

(b)

P

X(dw) N

(a)

(g)

phys Eads = −0.5

X(dw) Cv (a.u.) χphys X(dw) Cv (a.u.)

q=-0.5

(a)

N(1,1) N(0,0) N(0,0) N Cv (a.u.) N(1,1) N(0,0) N(0,0) N pp N Ncc Cv (a.u.)

X(dw) N

1 0.8 0.6 0.4 0.2 1 0.85 0.64 3 0.42 0.21

(g)

N(1,1) N-N0-N1

X(dw) Cv (a.u.)

Cv (a.u.)

(a)

chem Eads = 0.0 (m)

0.2 0.1 0 0.3 0.2 0.1 0.2(l) 0 (e)0.1 (r) 0.3 (q) 0.8 0.80.3 1.5 1.5 kT kT kT(k) 0.6 0.6 1.0 1.0 0.4 0.4 (f) 0.5 0.5 0.2 0.2

(p) (o) (p) (q)

0.2

0.3(q) (r)

kT

N(0,0) N(1,1)

N

N(0,0) N(1,1)

N

N(0,0) N(1,1)

N

N(0,0)

N

2.8 2.80.3 0.1 0.2 0.3 5 0 2.8 00 0.2 0.1 0.1 0.3 0.2 0.2 50.3 0.3 0 (c) 0.1 0 2.8 0.2 0.1 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2(h) 0.3 0 (c) 0.1 0 2.5 0.2 0.1 0 0.3 0.2 0.1 0.2 0.3 0 0.1 0.2 0.3 50 50.1 (m) 0.3 2.5 2.5 T 4 2.6 2.6 T kT kBkT T kT kT 2.5 4 4 4 2.6 kT kT kB kT kT kT kBkT kT2.6 kT 2.0 2.0 2.0 3 (c) 3 (h) 3 (c) 3 (m) 2.0 (m) (h) (c) 2.4 2.4 2.4 2.4 (c) 2 2 2 2 1.5 1.5 1.5 1.5 1 1 1 1 2.2 2.2 2.2 2.2 side 0 0 0 1.0 1.0 with 1.0 Figure05 7: Self-assembly for zero intermolecular interactions Eij(n) =1.00.0, corresponding 5 5 5 (i) (d) (n) (d) 2.0 0.8 0.8 0.8 0.8 (d) 2.0 2.0 2.0 4 4 4 4 to the3 low The top 0.6 0.6 0.6 show the0.6variation of CV in 1.5phases in Fig. 1.52 d-f. 1.5 1.5 panels (d) temperature 3 (i)3 (d) 3 (n) 0.4 0.4 0.4 0.4 1.0 1.0 1.0 1.0 (i) 2 2 temperature. 2 arbitrary units (a.u.)21 with show (calculated 0.2 lower panels 0.2 0.2 running averages 0.2 0.5 0.5 The 0.5 0.5 1 1 1 0 0 00 0 0 00 0 0 0 0 over 10 points) of order parameters with temperature. Also indicated in blue solid lines (o) are (e) (e) 5 5 5 5 (j) 0.5 0.8 (o) 0.8 (e) 2.0 0.8 2.0 2.0 2.0 0.4 0.6 4 4 4 4 0.6 0.6 1.5 1.5 1.5 1.5 (j)3 (e) the respective running deviations (calculated over 3 (e) 3 standard 3 (o) (j) 10× magnified. 0.3 10 points) and 0.4 0.4 1.0 1.0 1.0 1.0 0.2 0.4 2 2 2 2 0.2 0.2 0.5 0.5 0.5 0.5 0.1 0.2 1 1 1 1 0 0 00 0 0 00 0 0 0 0 0 0.1 0.2 0.3 0 0.1 00 0.2 0.1 0.1 0.3 0.2 0.2 0.3 0.3 0 0.1 0 0.2 0.1 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2 0.3 0.3 0 0.1 0 0.2 0.1 0 0.3 0.2 0.1 0.3 0.2 0.3 0 0.1 0.2 0.3

N(1,1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

kT goes kT kT to 0.16 kT kTand in N cc kT (Fig. kT 8j) kT and N pp kT (Fig. 8k) to a decrease kT in N neigh which (Fig.kT8i)kT

both going to zero. A slight increase in unlike neighbours N cp is also observed (Fig. 8l). The order parameter standard deviations are observed to be double peaks (Fig. 8i-l). In this case, the low temperature structure has chains of alternating physisorbed and chemisorbed molecules (Fig. 2h). Two unresolved peaks on the CV are also observed when the most favourable adsorption phys chem state is chemisorbed, for instance with Eads = −0.5 and Eads = 0.0 (Fig. 8m). A drop in

χphys (Fig. 8n) is associated only with the low temperature main transition at 0.11kB T , while N neigh (Fig. 8o) and N cc (Fig. 8p) tend to drop at both the temperatures identified by the CV peaks. N pp is minimised at 0.11kB T (Fig. 8q) while the onset of N cp drop is observed at the same temperature (Fig. 8r). 14


Page 15 of 24


Echem=0.0, Ephys=-0.5 Echem=0.0, Ephys=0.0 Echem=-0.5, Echem=0.0, Ephys=0.0Ephys=-0.5

Cv (a.u.) Cv (a.u.) Cv (a.u.)





Cv Cv (a.u.) (a.u.)

Cv (a.u.)

Cv (a.u.) χphys X(dw) Cv Cv (a.u.) (a.u.) neigh X(dw) N N

Cv (a.u.) N(1,1) N(0,0) N(0,0) Ncc N pp N Cv (a.u.) Cv (a.u.) N(1,1) N-N0-N11 N cp N(0,0) N(1,1)

N

Cv (a.u.)

N(1,1) N(0,0) N(0,0) N Cv (a.u.) N(1,1) N-N0-N1 N

N(0,0) N(1,1)

Cv (a.u.)

X(dw) N

X(dw) Cv (a.u.)

Cv (a.u.) Cv (a.u.)

Cv (a.u.)

X(dw) Cv (a.u.) N(1,1) N(0,0) N(0,0) N Cv (a.u.) N(1,1) N-N0-N1 N

N(0,0) N(1,1)

Cv (a.u.)

X(dw) N

Cv (a.u.)

Cv (a.u.)

1 1 Echem=0.0, Ephys=-0.5 Echem=0.0, Ephys=0.0 Echem=-0.5, Echem=0.0, Ephys=0.0Ephys=-0.5 2 q=0.5 q=0.5 q=0.5 q=-0.5 q=-0.5q=0.0 q=-0.5q=0.0q=-0.5 q=0.0 q=0.5 q=0.0 repulsive side-side interactions 3 chem chem chem Eads = 0.0 (g) (a)Eads = 0.0 (m) Eads (a) = −0.5 (m) 4 (a) (a) (g) (a) (m) (g) (a) phys phys phys = 0.0 = −0.5 Eads = 0.0 Eads Eads 5 q=0.5 q=0.5 q=0.5 q=-0.5 q=-0.5q=0.0 q=-0.5q=0.0q=-0.5 q=0.0 q=0.5q=0.0 6 7 (a) (m) (m) (g) (a) (a) P (a) (g) (a) (m) (g) (a) P 8 A A 1 1 1 1 1 11 1 1 1 1 1 (h) (n) (h) (n) 0.89 0.8 0.8 0.8 (b) 0.8 0.8 0.8 0.8 0.8 0.8 0.8 (b) 0.8 0.610 (b) 0.6 (h) 0.6 0.6 (n) 0.6 0.6 0.6 (b) 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 (b) (b) P P 0.211 0.2 0.2 0.2 0.2 0.2 0.2 0.2 A 0.2 0.2 A 0.2 0.2 Echem=0.0, Ephys=-0.5 Echem=0.0, Ephys=0.0 Echem=-0.5, Echem=0.0, Ephys=0.0 Ephys=-0.5 112 1 1 1 1 11 1 1 1 1 1 2.8 2.8 2.8 2.8 5 (c) (i) (o) (c) 0.8 (h) (n) (h) (n) 0.85 0.85 0.8 0.85 (b) 0.8 0.8 0.8 0.8 0.8 0.8 2.5 2.5 0.8 2.5 (b) 2.5 4 2.6 2.6 2.6 0.6413 (c) 0.64 (i) 0.6 0.64 (o) 0.6 0.6 0.6 0.6 0.6 2.6 0.6 0.6 0.6 (b) (h) (n) (b) (c) 2.0 2.0 2.0 2.0 3 3 3 3 (o) (c) (i) 0.4214 0.42 0.4 0.42 0.4 0.4 0.4 0.4 0.4 0.4 0.4 2.4 2.4 0.4 2.4 (c) 2.4 2 (b) (b) 1.5 1.5 0.2 1.5 1.5 0.21 0.21 0.2 0.21 0.2 0.2 0.2 0.2 0.2 0.2 1 2.2 2.2 0.2 2.2 2.2 15 1.0 1.0 1.0 1.0 2.8 q=-0.5q=0.05 (c) 2.8 2.8 2.8 5 5 5 (i) (o)q=0.0 q=0.5 q=0.5 q=0.5 (p)q=0.5 (d) (d) q=-0.5 (j) (d) (p) (d) 0.8 q=-0.5 0.8 0.8 0.8 q=0.0q=-0.5 2.0 2.0 2.0 2.0 2.5 2.5 q=0.0 2.5 (c) 2.5 416 4 4 4 2.6 2.6 2.6 0.6 0.6 2.6 0.6 0.6 1.5 1.5 1.5 1.5 (d) (j) (p) (d) (c) 2.0 2.0 2.0 2.0 317 (c) 3 (i) 3 (o) 3 (c) (c) (i) (k) 0.4 (f) 0.4 0.4 (a) (o) 1.0 1.0 1.0 (a) 2.4 (a) 2.4 (f)0.4 2.4 (k) 2.4 (a) (j) 2 (a) 2 (f)1.0 2 (k) 2 (a) 1.5 1.5 1.5 1.5 0.2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 118 1 1 1 2.2 2.2 2.2 2.2 1.0 1.0 1.0 1.0 (e) (e) 519 5 5 5 0.5 (p) (d) (j) (d) (p) (q) (e) 0.8 (k) (e) 0.8 (q) 0.8 2.0 0.8 (d) 2.0 2.0 2.0 (d) 4 (d) 4 (j) 4 4 0.4 0.6 (d) 0.6 1.5 0.6 0.6 1.5 1.5 1.5 (q) 320 (e) 3 (k) 3 (p) 3 (e) (k) 0.3 0.4 0.4 1.0 0.4 0.4 1.0 1.0 1.0 (j) 2 2 2 2 0.2 P P 0.2 0.2 0.2 0.5 0.5 0.5 121 1 1 1 0.1 0.5 A A 0.2 22 (e) 0.1 0.2 0.3 1.55 0 2.0 0.1 0 0.2 0.1 0.3 0.21.55 0.3 0 2.0 0.1 0 1.5 0.2 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2(k) 0.3 0 1.5 0.1 0 2.0 0.2 0.1 0 0.3 0.2 0.1(q) 0.2 (l) 0 (e) 0.20 0.3 0.1(q) 50 50.1 0.5 (f) (f)0.1 1.5 (e) (l)0.3 (r) 0.3 (r) 0.2 0.3 (e) 0.8 0.80.3 0.8 2.0 1.5 1.5 1.5 1.5 1.5 1.5 0.4 1.5 4 4 4 4 kT kT kT kT kT kT kT kT kT kT kT kT 0.6 0.6 0.6 1.5 1.5 1.5 1.5 23 (f) (l) (r) (f) 1.03 (e) 1.03 (k) 1.0 1.03 (q) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 3 (e) (k) 0.3 1.0 0.4 0.4 0.4 1.0 1.0 1.0 1.0 0.2 224 2 2 2 (f) (f) 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.2 0.2 0.2 0.5 0.5 0.5 0.1 0.5 1 1 1 1 25 2.8 2.80.3 0.1 0.2 0.3 5 0 2.8 0.1 0 0.2 0.1 0.3 0.2 5 0.3 0 (c) 0.1 0 2.5 0.2 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2(h) 0.3 0 2.5 0.1 0 2.8 0.2 0.1 0 0.3 0.2 0.1 0.2 0.3 0 (c)0.1 2.5 0.20 0.3 0.1 0.2 0.3 50 50.1 (m) 0.3 T 2.6 T kT 2.5 kBkT T 426 4 4 2.6 2.6 2.6 kT kT kT 4 (m) kT kT kB kT kT kT kBkT kT (c) (h) (c) 2.0 2.0 2.0 2.0 3 3 3 3 (m) (h) (c) 2.4 2.4 2.4 (c) 2.4 227 2 2 2 1.5 1.5 1.5 1.5 1 1 1 1 side 2.2 2.2 2.2 2.2 Figure 8: Self-assembly intermolecular 1.0interactions with Eij = 0.5, corre028 0 0 1.0 0 for repulsive 1.0 1.0 5 5 5 5 (n) 0.8 (d) 0.8 (i) (d) (n) (d) 0.8 0.8 2.0 2.0 2.0 2.0 (d) 29 4 (d) 4 (i) 4 (d) sponding to the 43low phases panels show the variation 0.6 0.6 in 0.6 The top 0.6 1.5 1.5 temperature 1.5 1.5 Fig. 2g-i. (n) 330 3 3 0.4 0.4 0.4 0.4 1.0 1.0 1.0 1.0 (i) 2 2 2 2 of1 CV0.5in arbitrary units (a.u.) with The panels show running averages 0.2 0.2 0.5 0.2 lower 0.2 0.5 0.5 temperature. 131 1 1 0 0 0 010 points) 0 00 0 parameters 0 0 0temperature. 0 (calculated over of order with in blue (o)Also indicated (e) 532 5 5 5 0.5 2.0 (j) (e) (o) 0.8 (e) 0.8 (e) 0.8 2.0 2.0 2.0 0.4 1.5 4 4 4 4 0.6 0.6 0.6 1.5 1.5 1.5 solid standard deviations (calculated over 10 points) and (o) 333 (e) 3 (j)lines are the 3 respective 3 (e) running 0.3 (j) 0.4 0.4 0.4 1.0 1.0 1.0 0.2 1.0 2 2 2 2 0.2 0.2 0.2 0.5 0.5 0.5 0.5 34 10× magnified. 0.1 1 1 1 1 0 0 0 0 0 00 0 0 0 0 0 35 0 0.1 0.2 0.3 0 0.1 0 0.2 0.1 0.3 0.2 0.3 0 0.1 0 0.2 0.1 00 0.3 0.2 0.1 0.1 0.3 0.2 0.2 0.3 0.3 0 0.1 0 0.2 0.1 0 0.3 0.2 0.1 0.3 0.2 0.3 0 0.1 0.20 0.3 0.1 0.2 0.3 kT kT kT kT kT kT kT kT kT kT kT kT 36 37 3.3 Phase diagrams 38 39 The observed phases and defect patterns enable the entire configurational space to be char40 41 acterised, and in Fig. 9 the observed low temperature patterns are schematised into a series 42 43 phys chem of two-dimensional Eads vs Eads phase diagrams. Each phase diagram is characterised by a 44 45 different intermolecular interaction strength Eijside (for molecules are in the same adsorption 46 47 state, see Eq. 2). In these plots an inverse logarithmic scale has been employed for clarity. 48 49 Attractive intermolecular interactions that are stronger or equal to the physisorption or 50 51 chemisorption interactions always lead to packing in the form of a large ordered cluster. In 52 53 the majority of cases all molecules are chemisorbed, which is due to no translation in the 54 55 phys phys chem chemisorbed state. Only when −Eads ≥ −Eijside and −Eads > −Eads we observe that all 56 57 58 15 59 ACS Paragon Plus Environment 60


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ads ads -E(phys) -E(phys) -E(phys) -E(phys) \\\\ \\ \\\\ \\ \\\\ \\ \\ \\ \\ side side \\ \\ \\ \\ \\ \\ (d) (d) (e) (e) E(ij)=0.05 E(ij)=0.05 E(ij)=0.5 E(ij)=0.5 E(ij)=0.05 E(ij)=0.5 (e) E(ij)=0.05 E(ij)=0.5 0.1 0.01 0.01 0.001 0.001 0 0 0.1 0.1 0.01 0.01 0.001 0.001 0 0 0.1 0.1 0.01 0.01 0.001 0.001 0 (d)(d) 0.10.1 (e) E(ij)=0.5 EE(ij)=0.05 E = 0.05 = 005 ij ij 0.1 0.01 0.01 0.0010.001 0 0.1 0 0.01 0.01 0.1 0.01 0.01 0.0010.001 0 0.1 0 0.01 0.01 0.001 0.1 0.1 0.01 0.01 0.0010.0010 0 0 (d) 0.001 (d) 0.001 (e) 0.001 (e)0.10.001 E(ij)=0.05 E(ij)=0.05 E(ij)=0.5 E(ij)=0.5 0.1 0.1 0.01 0.01 0 -E(phys) 0 -E(phys) 0.1 0 -E(phys) 0 -E(phys) 0.1 0.001 0 -E(phys) 0 -E(phys)

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Page 16 of 24

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molecules are physisorbed. In the particular cases explored in Fig. 9a this is observed only phys chem when Eads = −0.5 and Eads ≤ −0.1.

When the intermolecular interactions are decreased by a factor of ten (i.e. Eijside = −0.05, phys Fig. 9b) we again observe that the patterns are physisorbed when −Eads ≥ −Eijside and phys chem −Eads > −Eads , and chemisorbed otherwise. While in most cases large islands with phys chem irregular boundaries are observed, when −Eads = 0.5 and −Eads ≤ 0.1 the chemisorbed

molecules tend to form single molecule chains and small clusters. Dimers, trimers, and isolated molecules are also observed. 16


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When the intermolecular interactions are zero (Fig. 9c), the patterns are driven only by the interplay between the adsorption energies. The phase diagram is clearly symmetrical and dominated by the presence of chains and small clusters. These are all physisorbed phys phys phys chem chem ≥ 0.01, and chemisorbed when −Eads ≥ −Eads > −Eads and −Eads when −Eads chem and −Eads ≥ 0.01. In the residual portion of the phase diagram molecules are randomly

distributed among the two states. The ratio of molecules in each adsorption state depends phys chem on the strength of Eads and Eads as already discussed in the former section and shown in

Fig. 3. In the presence of repulsive interactions between molecules, no packed patterns are obphys phys chem chem served (Fig. 9d-e). When Eads or −Eads are ≤ 0.01, the pattern = Eads and −Eads

exhibits physisorbed and chemisorbed molecules, with molecules arranged in small clusters or chains. When the chemisorption (physisorption) interaction is stronger, the molecules transition to the preferred adsorption state, forcing the molecules to move apart to minimise the repulsive intermolecular interactions. This forms an orderly state with molecules in the preferred adsorption state in alternating sites and molecules in the other state in randomly distributed sites. This effect arises since only molecules in the same adsorption state are repelled. The only difference in the phase diagrams of strong and weak repulsive intermolecular interactions occurs when there is strong physisorption and weak chemisorption, or vice versa. For example, weak intermolecular interactions Eijside = 0.05, coupled with strong phphys chem ysisorption Eads = −0.5 and weak chemisorption Eads ≤ −0.1 give rise to the presence of phys physisorbed chains and small clusters. These are instead all chemisorbed when Eads ≤ −0.1 chem and Eads = −0.5 (Fig. 9d).

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4. Conclusions In this paper we employed a hexagonal lattice model 21 to simulate the phase behaviour of gas phase deposition of generic molecules with C6 symmetry, such as benzene derivatives, on metallic surfaces. The molecules could express two distinct adsorption states: chemisorbed and physisorbed, and had variable intermolecular interactions. Molecules were allowed to freely to diffuse only in the physisorbed state, but were locked in their position when chemisorbed to mimic a strong site preference. Monte Carlo simulations were used to explore the parameter space and the emerging structures were characterised and used to map out resulting phase diagrams. Phase behavior as a function of temperature was explored and two main types of transitions were observed, namely, change of adsorption state, and packing/ordering. For attractive intermolecular interactions, the high temperature transition is a change of adsorption state and the low temperature transition is packing. When molecule–surface interactions are weak, the two transitions overlap. When there are no intermolecular interactions, the system undergoes only a single transition, which is a change of adsorption state, and the system remains disordered. For repulsive intermolecular interactions there are two transitions, which are change of adsorption state and ordering to minimise the number of neighbours. However, these transitions are not well resolved with respect to temperature. The overall phase behavior at low temperature reflects these observations. For attractive intermolecular interactions, regardless of the favoured adsorption state, molecules tend to lock into a chemisorbed packed state. All-physisorbed systems are only favoured when the mobile physisorbed state interacts with the surface much more strongly than the chemisorbed state. When molecules do not interact with each other, no packing is observed and the low temperature patterns are ruled by the ratio between the two adsorption strengths. For strongly repulsive intermolecular interactions a long range order for the preferred adsorption state is observed. When the physisorbed state is stronger than the chemisorbed state defects occur, even at low coverage, due to the lack of mobility of chemisorbed molecules. 18


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The employed model has two main approximations. The first is that the lattice approximates the surface by limiting the adsorption sites to the hollow site and neglects bridge and top sites. However, when molecules adsorb on an fcc (111) surface, it can be that the preferred adsorption site is different for the chemisorption and physisorption states of different molecules. A future direction for model development would be to use two (or more) interpenetrating lattices and allow for multiple adsorption sites. The second approximation is the representation of the intermolecular interactions. The number of parameters for the side-side interactions increases significantly for lower symmetry molecules and by different side-side interactions between different adsorption states. While steps in this direction are being made, the current model is applicable to molecules with six-fold symmetry and assumes that molecules in different adsorption states do not interact. This model demonstrating that a variety of self-assembled structure can be obtained will aid the design of self-assembly of molecular monolayers on metallic surfaces. To obtain a specific monolayer pattern molecules can be functionalised to obtain the desired intermolecular and surface interactions leading to directed assembly of the monolayer. In future work, the model can be modified to account for additional interactions and more complex molecular systems and be used to design a monolayer structure for two-dimensional device applications.

Acknowledgements We gratefully acknowledge the Academia Nazionale dei Lincei and the Royal Society of Edinburgh for financial support.

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Influence of Molecule-Surface and Molecule-Molecule Interactions on

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