Structuring of Fluid Adlayers upon Ongoing Unimolecular Adsorption

Fluids with spatial density variations of single or mixed molecules play a key role in biophysics, soft matter, and materials science. The fluid structures usually form via spinodal decomposition or nucleation following an instantaneous destabilization of the initially disordered fluid. However, in practice, an instantaneous quench is often not viable, and the rate of destabilization may be gradual rather than instantaneous. In this work we show that the commonly used phenomenological descriptions of fluid structuring are inadequate under these conditions. We come to that conclusion in the context of surface catalysis, where we employ kinetic Monte Carlo simulations to describe the unimolecular adsorption of gaseous molecules onto a metal surface. The adsorbates diffuse at the surface and, as a consequence of lateral interactions and due to an ongoing increase of the surface coverage, phase separate into coexisting low- and high-density regions. The typical size of these regions turns out to depend much more strongly on the rate of adsorption than predicted from recently reported phenomenological models. We discuss how this finding contributes to the fundamental understanding of the crossover from liquid-liquid to liquid-solid demixing of solution-cast polymer blends.

Figure 1

Surface coverage $\theta$ as a function of the dimensionless time ${\nu }_{\text{ads}}t$, with ${\nu }_{\text{ads}}$ the rate of adsorption and $t$ the time. The symbols represent all kMC results obtained in this work and the solid line is given by Eq. (6). The inset shows how the increase in coverage implies that the unstable region of the phase diagram is entered, provided that $J$ is larger than the critical value of 0.44. See main text.

Figure 2

Configurations of adsorbates at a $256\times 256$ periodic lattice with a coupling parameter $J=0.5$ and a dimensionless adsorption rate of ${\nu }_{\text{ads}}=0.0001{\nu }_{\text{hop}}$ for times ${\nu }_{\text{ads}}t=0$, 0.061, 0.122, 0.305, 0.610, with ${\nu }_{\text{hop}}$ the attempt frequency of a hop. The dark areas represent vacant sites, whereas the light areas are occupied by the adsorbate.

Figure 3

Structural length scale $R_{*}$ as a function of time $t$, with the time in units of the adsorption rate ${\nu }_{\text{ads}}$. For long times, the structural length develops as $R_{*}=R_0(t/t_0{)}^{1/3}$, with $t_0$ the time at which the coverage crosses the binodal value.

Figure 4

Characteristic length scale $R_0$ of the adlayer structure as a function of the adsorption rate ${\nu }_{\text{ads}}$ for a varying coupling parameter $J$. The length scale and adsorption rate are given in units of the lattice spacing and hopping attempt frequency ${\nu }_{\text{hop}}$, respectively.