Effects of surface affinity on the ordering dynamics of self-assembled monolayers of chain molecules: Transition from a parallel to a perpendicular structure

The effects of surface interactions on the ordering dynamics of self-assembled monolayers (SAM) of chain molecules were studied using molecular dynamics simulations. When the strength of surface–chain interactions was equal to or less than that of chain–chain interactions, domains of chain molecules adsorbed perpendicular to the surface (“upright” chains) formed on the surface. Although chain molecules adsorbed parallel to the surface (“lying” chains) were initially observed on the surface, they did not develop into two-dimensionally aligned structures. In contrast, when the strength of surface–chain interactions was at least twice that of chain–chain interactions, the proportion of upright chain molecules was initially small, and the reorientation of lying chains was observed shortly afterwards. In this case, the reorientation from lying to upright configuration developed slowly from the domain boundaries of two-dimensionally aligned structures late in the calculation period. Although the orientation processes of chain molecules on surfaces were strongly influenced by the strength of surface–chain interactions, the total adsorption rate on the surface was not. We also analyzed the maximum area of domains formed by lying chains. The development of two-dimensionally aligned domains required strong surface–chain interactions to prevent the spontaneous formation of nuclei of upright domains.

Figure 1

Schematic diagrams of the simulation model. (a) Molecules in the simulation box. (b) Top view of substrate and chain heads in which the chain molecules are fully packed. Dark and light gray circles indicate substrate atoms and chain heads, respectively. (c) Model of worm-like chain molecules, bond vectors, and bending angle.

Figure 2

Schematic diagrams of adsorbed chains on the surface. (a) Example of lying chains. Chains are classified into either upright or lying chains. (b) Example of an oriented domain of upright chains. Oriented domain is the region where the adsorbed chains form an aligned structure. (c) Example of oriented domains of lying chains. For simplicity, only the segments in the vicinity of the surface are shown. In the case of lying structures, the direction of lying chains could vary between domains, especially when the surface is sparsely covered by chains.

Figure 3

Snapshots of the structure formation processes of chain molecules for strong surface–chain interactions (${\varepsilon }_S=5.0$). Time is shown in dimensionless reduced units. The size of box in the horizontal direction is 19.98 in reduced units. The blue (dark gray) molecules indicate lying chains.

Figure 4

Snapshots of chain configuration on the surface for moderate surface–chain interactions $({\varepsilon }_S=1.0)$. The red (black) squares indicate the head segments of chain molecules. The blue (black) circles indicate the segments of lying chain molecules. The green (light gray) circles indicate the surface segments of upright chain molecules. The size of box in the horizontal direction is 19.98 in reduced units. Time is shown in dimensionless reduced units.

Figure 5

Snapshots of chain configuration on the surface for moderately strong surface–chain interactions $({\varepsilon }_S=2.0)$. The symbols and box sizes are the same as described in the caption of Fig. 4.

Figure 6

Snapshots of chain configuration on the surface for strong surface–chain interactions (${\varepsilon }_S=5.0$). The symbols and box sizes are the same as described in the caption of Fig. 4. During the intermediate period between $t=1000$ and 2000, a striped pattern was observed. The domains of upright chains appear in the boundary region of striped patterns in the late period.

Figure 7

Time evolution of surface coverage for (a) and (b) moderate surface–chain interactions $({\varepsilon }_S=1.0)$, (c) and (d) moderately strong surface–chain interactions $({\varepsilon }_S=2.0)$, and (e) and (f) strong surface chain–interactions (${\varepsilon }_S=5.0$). In (a), (c), and (d), coverage ratio was calculated from the number of adsorbed chains. The blue (black) and red (light gray) lines indicate the surface coverage of lying and upright chains, respectively. In (b), (d), and (f), coverage ratio was calculated using the number of chain segments in the vicinity of the surface. Dashed vertical lines in (c) and (d) indicate the start of growth of upright chains $(t\sim 300)$ and the time at which the growth curve of (d) becomes saturated $(t\sim 500)$. Dashed vertical lines in (e) and (f) indicate the start of growth of upright chains $(t\sim 400)$.

Figure 8

Effect of threshold for moderate surface–chain interactions $({\varepsilon }_S=1.0)$. The lines are the same as in Fig. 7.

Figure 9

Effect of threshold for strong surface–chain interactions (${\varepsilon }_S=5.0$). The lines are the same as in Fig. 7.

Figure 10

Time evolution of oriented domain ratio for (a) moderately strong surface–chain interactions $({\varepsilon }_S=2.0)$, and (b) strong surface–chain interactions (${\varepsilon }_S=5.0$). The blue (black) and red (light gray) lines indicate domains of lying and upright chains, respectively. The dashed thick line indicates the overall domain ratio. For comparison of time evolution, the dashed vertical lines in Fig. 7 are also shown in this figure.

Figure 11

Time evolution of the global orientation order parameter of lying chains for strong surface–chain interactions (${\varepsilon }_S=5.0$). For comparison of time evolution, the dashed vertical line in Fig. 7 is also shown in this figure. The rapid growth of the order parameter between $t=400$ and 1000 reflects the development of a striped pattern on the surface.

Figure 12

Dependence of surface-chain interaction on the formation of oriented domains of lying chains. (a) Maximum surface coverage of lying chains in the structure formation processes. (b) Maximum oriented domain ratio of lying chains in the structure formation processes.

Figure 13

Adsorption curves for different surface-chain interactions $({\varepsilon }_S=0.1,1.0,2.0,5.0)$. Time evolution curves of surface coverage can be expressed by power laws.

Figure 14

Surface coverage as a function of dimensionless time defined by $(t/D)k_a^2{\mathrm{\Gamma }}_m^2$. Simulation parameters were $D{k}_2/\left(k_a^2{\mathrm{\Gamma }}_m^2\right)=0.1, D{c}_0/\left(k_a{\mathrm{\Gamma }}_m^2\right)=0.01$, and ${\gamma }_{12}=0.01$. The thin solid lines represent the surface coverage by lying $\left({\theta }_1\right)$ and upright $\left({\theta }_2\right)$ chains, respectively. The thick solid line denotes the total number of adsorbed chain molecules divided by ${\mathrm{\Gamma }}_m$. The long dashed line represents $2c_0\sqrt{Dt/\pi }$, which corresponds to the diffusion-controlled limit.