Energy stored in nanoscale water capillary bridges formed between chemically heterogeneous surfaces with circular patches

(a) Top view of one of the chemically heterogeneous surfaces considered in this work. The surface is hydrophobic with a silica-based structure and is hydroxylated over a region of diameter d = 5 nm. The Si, O, and H atoms are denoted by gray, red, and white spheres, respectively. The surfaces expand across the simulation box; periodic boundary conditions apply along the x- and y-axes. (b) and (c) Snapshots of a water capillary bridge formed between two surfaces separated by a distance h = 3 and 7 nm, respectively. Water molecules within the capillary bridge that are confined between the hydrophilic patches of the surfaces are colored in blue; water molecules located beyond the hydrophilic patches are shown in red. (d) Illustration of a capillary bridge with the main parameters employed in this work. h is the wall separations, r₀ and R₂ are the curvature radii of the capillary bridge, r_b is the corresponding base radius, and θ is the water contact angle.

Profiles of the water capillary bridges as function of separation h for surface patch diameter (a) d = 4 nm, (b) d = 5 nm, (c) d = 6 nm, and (d) d = 7 nm. The water capillary bridge profiles obtained from the MD simulations are denoted by open circles. Solid and dashed lines represent the capillary bridge profiles predicted by capillarity theory and obtained by fitting the MD data (circles) using Eq. (1), respectively. The dashed line is obtained by considering all the MD data points (circles) in the fitting procedure. The solid line is the best fit obtained when the points closest to the upper and lower surfaces are omitted in the fitting procedure.

(a) Contact angle θ and (b) radius of the capillary bridge base radius r_b (see Fig. 1(d)) as function of the wall separations h and for different surface patch diameters d. The profiles of the water capillary bridges are shown in Fig. 2. (c) θ(η) for different δ, where $\eta ={\displaystyle \frac{h}{2V^{1/3}}}$, $\delta ={\displaystyle \frac{r_{\mathrm{b}}}{V^{1/3}}}$, and V and r_b are the volume and base radius of the bridge, respectively. Data are obtained from recalculation of (a) (circle) and from macroscopic CT prediction (dashed lines). δ are calculated at V = 101 nm³ and r_b = d/2 + 0.1 nm where d corresponds to the patch size. The horizontal dashed line corresponds to θ = 90° and separates the hydrophobic-like (θ > 90°) and hydrophilic-like (θ < 90°) contact angles.

(a) Force exerted by the water capillary bridges on the confining surfaces as function of separation h obtained from the MD simulation (solid circles with error bars). Lines are the corresponding predictions for the forces on the walls from capillary theory. Positive (negative) values correspond to repulsive (attractive) forces between the surfaces. (b) and (c) Capillarity theory states that the force acting on the walls has two contributions, a force component due to the water–vapor surface tension, F_γ(h), and another component due to the pressure of water within the capillary bridge, F_P(h).

Potential energy E_P stored in the water capillary bridge as function of the wall separation h. Results are included for all surface patch diameters d studied and for all values of h at which the water capillary bridge remains stable.

Potential energy E_P and potential energy density ρ_E stored in AS WCB formed between (a) homogeneous surfaces and (b) chemically heterogeneous surfaces. The homogeneous surfaces are characterized by a water contact angle θ = 20°, 30°, 60°, 80°, and 108°. The heterogeneous surfaces are hydrophobic (θ = 108°) and are decorated by circular patches of diameter d = 4 nm, 5 nm, 6 nm, 7 nm (see Fig. 1). In all cases, the calculations of E_P and ρ_E correspond to increasing the wall separations from h = 2.5 nm to h_br.

Potential energy density ρ_E stored in translationally symmetric WCB expanding between heterogeneous surfaces with stripe-like hydrophilic patches (from Ref. [13]). For comparison, we also include the ρ_E for TS WCB (of the same volume) formed between homogeneous surfaces characterized by water contact angles θ = 40°, 90°, and 108°.