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Chin. Phys. B, 2020, Vol. 29(11): 114703    DOI: 10.1088/1674-1056/abb664
Special Issue: SPECIAL TOPIC — Water at molecular level
SPECIAL TOPIC—Water at molecular level Prev   Next  

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

Bin-Ze Tang(唐宾泽)1, †, Xue-Jia Yu(余雪佳)1, †, Sergey V. Buldyrev2,, ‡, Nicolas Giovambattista3,4,§, and Li-Mei Xu(徐莉梅)1,5,
1 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
2 Department of Physics, Yeshiva University, 500 West 185th Street, New York, NY 10033, United States
3 Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210, United States
4 Ph.D. Programs in Chemistry and Physics, The Graduate Center of the City University of New York, New York, NY 10016, United States
5 Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

The formation of nanoscale water capillary bridges (WCBs) between chemically heterogeneous (patchy) surfaces plays an important role in different scientific and engineering applications, including nanolithography, colloidal aggregation, and bioinspired adhesion. However, the properties of WCB of nanoscale dimensions remain unclear. Using molecular dynamics simulations, we investigate the geometrical and thermodynamic properties of WCB confined between chemically heterogeneous surfaces composed of circular hydrophilic patches on a hydrophobic background. We find that macroscopic capillary theory provides a good description of the WCB geometry and forces induced by the WCB on the confining surfaces even in the case of surface patches with diameters of only 4 nm. Upon stretching, the WCB contact angle changes from hydrophobic-like values (θ > 90°) to hydrophilic-like values (θ < 90°) until it finally breaks down into two droplets at wall separations of ∼ 9–10 nm. We also show that the studied nanoscale WCB can be used to store relevant amounts of energy EP and explore how the walls patch geometry can be improved in order to maximize EP. Our findings show that nanoscale WCB can, in principle, be exploited for the design of clean energy storage devices as well as actuators that respond to changes in relative humidity. The present results can also be of crucial importance for the understanding of water transport in nanoporous media and nanoscale engineering systems.

Keywords:  water capillary bridge      energy density      morphology transition      hydrophilicity  
Received:  27 July 2020      Revised:  01 September 2020      Published:  03 November 2020
Fund: Project support by the National Natural Science Foundation of China (Grant Nos. 11525520 and 11935002) and the National Key Research and Development Program of China (Grant No. 2016YFA0300901).
Corresponding Authors:  These authors contributed equally. Corresponding author. E-mail:   

Cite this article: 

Bin-Ze Tang(唐宾泽), Xue-Jia Yu(余雪佳), Sergey V. Buldyrev, Nicolas Giovambattista§, and Li-Mei Xu(徐莉梅)¶ Energy stored in nanoscale water capillary bridges formed between chemically heterogeneous surfaces with circular patches 2020 Chin. Phys. B 29 114703

Fig. 1.  

(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, rb is the corresponding base radius, and θ is the water contact angle.

Fig. 2.  

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.

Fig. 3.  

(a) Contact angle θ and (b) radius of the capillary bridge base radius rb (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 $\eta =\displaystyle \frac{h}{2{V}^{1/3}}$, $\delta =\displaystyle \frac{{r}_{{\rm{b}}}}{{V}^{1/3}}$, and V and rb 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 rb = 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.

Fig. 4.  

(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, Fγ(h), and another component due to the pressure of water within the capillary bridge, FP(h).

Fig. 5.  

Potential energy EP 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.

patch diameter d = 4 nm d = 5 nm d = 6 nm d = 7 nm
potential energy/nN⋅nm 2.36 2.74 2.95 3.43
energy density/kJ⋅m−3 2722.36 3200.76 4220.97 5715.18
Table 1.  

Potential energy EP and potential energy density ρE 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 EP and ρE correspond to increasing the wall separations from h = 2.5 nm to hbr.

Stripe 40° 90° 108°
Energy density/kJ⋅m−3 7563.93 10519.13 6332.27 4054.71
Table 2.  

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

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