Figure 1

Simulation snapshots of crystallization. The snapshots show cross sections through our simulation box. The surfaces are made of fixed particles that are equal in size to the model protein particles. Fixed particles that attract the model protein particles are light gray (${ϵ}_w=ϵ$); fixed particles that are repulsive are dark gray. The model protein particles themselves are shown in blue and yellow. Blue particles are in a locally liquidlike environment, while yellow particles are in a locally crystalline environment. Panel (A) is a snapshot of nucleation in a droplet of liquid in a pit with rough walls. Note the layer of liquid particles (blue) between the yellow growing crystal and the wall. Panel (B) is a snapshot of nucleation occurring at a flat rough surface with a thin adsorbed liquid layer.Reuse & Permissions

Figure 2

(A) The free-energy barrier to nucleation, $\Delta G^{*}$, as a function of the radius of the pit, $R$, in units of the protein diameter $\sigma$. The pit sides are made of fixed particles with the same diameter as the model protein and so are rough on the length scale of the protein. (B) The nucleus free energy, $\Delta G$, as a function of the number of particles, $n$, in the nucleus. Shown are curves for homogeneous nucleation, heterogeneous nucleation on a wall with a rough surface, and heterogeneous nucleation in a pit with optimal size (radius $R=8$, depth $D=9$).Reuse & Permissions

Figure 3

Snapshots of a fluid in contact with a pit which is formed from a cylinder cut from an fcc crystal with its $\{111\}$ plane facing the fluid. The cylinders both have radius $R=7$ and depth $D=3$. The two panels show pores cut from fcc crystals of different densities, ${\rho }_{\mathrm{wall}}$. The snapshots are cross sections through the centers of the pits. In (A) the density of the substrate crystal matches that of the nucleating crystal at coexistence, ${\rho }_{\mathrm{wall}}={\rho }_{\mathrm{eq}}=0.88$. We see a defect-free crystal nucleating and growing out of the pit. In (B) the lattice constant of the substrate is $\approx 4\%$ smaller than that of the nucleating crystal (${\rho }_{\mathrm{wall}}=1.0$). Note the defect in the nucleating crystal caused by this mismatch in lattice constant. The dark gray, light gray, blue, and yellow particles are purely repulsive wall particles, wall particles that attract the fluid particles (${ϵ}_w=ϵ$), liquid particles, and crystalline particles, respectively.Reuse & Permissions

Figure 4

Schematic that summarizes the nucleation behavior as a function of pit radius $R$ and roughness of the wall, $\Gamma$. Both are in units of the protein diameter $\sigma$. Small pits will fill with a protein liquid due to capillary condensation, and if the walls are rough, then nucleation of a crystal is rapid in this liquid. If the walls are smooth, then ordering occurs at the wall with noncrystallographic symmetry, and this inhibits crystallization.Reuse & Permissions