Please wait a minute...
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      Accepted manuscript online:  09 September 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°.

Harrison A J, Beaudoin S P, Corti D S 2016 J. Adhes. Sci. Technol. 30 1165 DOI: 10.1080/01694243.2016.1143581
Wei Z, Sun Y, Ding W X, Wang Z R 2016 Sci. China-Phys. Mech. Astron. 59 694611 DOI: 10.1007/s11433-016-0241-7
Lai T, Li P 2019 Langmuir 35 6585 DOI: 10.1021/acs.langmuir.9b00827
Anzivino C, Chang F Q, Soligno G, Roij R V, Kegelb W K, Dijkstra M 2019 Soft Matter 15 2638 DOI: 10.1039/C8SM02361A
Shi S, Russell T P 2018 Adv. Mater. 30 1800714 DOI: 10.1002/adma.201800714
Mayer R P, Stowe R A 2005 J. Colloid Interface Sci. 285 781 DOI: 10.1016/j.jcis.2004.11.067
de Boer P C T, de Boer M P 2008 Langmuir 24 160 DOI: 10.1021/la701253u
Dodds S, Carvalho M S, Kumar S 2011 Langmuir 27 1556 DOI: 10.1021/la104369z
Goegelein C, Brinkmann M, Schroeter M, Herminghaus S 2010 Langmuir 26 17184 DOI: 10.1021/la103062s
Valenzuela G E 2019 J. Phys. Chem. C 123 1252 DOI: 10.1021/acs.jpcc.8b09907
Saavedra J H, Rozas R E, Toledo P G 2014 J. Colloid Interface Sci. 426 145 DOI: 10.1016/j.jcis.2014.03.050
Yaneva J, Milchev A, Binder K 2004 J. Chem. Phys. 121 12632 DOI: 10.1063/1.1826037
Tang B Z, Buldyrev S V, Xu L M, Giovambattista N 2020 Langmuir 36 7246 DOI: 10.1021/acs.langmuir.0c00549
de Gennes P, Brochard-Wyart F, Queéré D 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
Alencar A M, Wolfe E, Buldyrev S V 2006 Phys. Rev. E 74 026311 DOI: 10.1103/PhysRevE.74.026311
Almeida A B, Giovambattista N, Buldyrev S V, Alencar A M 2018 J. Phys. Chem. C 122 1556 DOI: 10.1021/acs.jpcc.7b08577
Swain P S, Lipowsky R 2000 Europhys. Lett. 49 203 DOI: 10.1209/epl/i2000-00126-5
Schoen M, Diestler D J 1997 Chem. Phys. Lett. 270 339 DOI: 10.1016/S0009-2614(97)00375-8
Iwamatsu M 2007 Langmuir 23 11051 DOI: 10.1021/la7013754
Hwang S H, Lee J, Khang D Y 2019 ACS Appl. Mater. Interfaces 11 8645 DOI: 10.1021/acsami.8b19580
Wu C C, Reinhoudt D N, Otto C, Subramaniam V, Velders A H 2011 Small 7 989 DOI: 10.1002/smll.201001749
Mariappan D D, Kim S, Boutilier M S H, Zhao J J, Zhao H B, Beroz J, Muecke U, Sojoudi H, Gleason K, Brun P T, Hart A J 2019 Langmuir 35 7659 DOI: 10.1021/acs.langmuir.9b00460
Chen X, Goodnight D, Gao Z, Cavusoglu A H, Sabharwal N, DeLay M, Driks A, Sahin O 2015 Nat. Commun. 6 7346 DOI: 10.1038/ncomms8346
Liu B, Qi C, Zhao X, Teng G, Zhao L, Zheng H, Zhan K, Shi J 2018 J. Phys. Chem. C 122 26671 DOI: 10.1021/acs.jpcc.8b06780
Xiong H, Devegowda D, Huang L L 2020 Langmuir 36 723 DOI: 10.1021/acs.langmuir.9b03244
Giovambattista N, Rossky P J, Debenedetti P G 2006 Phys. Rev. E 73 041604 DOI: 10.1103/PhysRevE.73.041604
Berendsen H J C, Grigera J C, Stroatsma T P 1987 J. Phys. Chem. 91 6269 DOI: 10.1021/j100308a038
Giovambattista N, Almeida A B, Alencar A M, Buldyrev S V 2016 J. Phys. Chem. C 120 1597 DOI: 10.1021/acs.jpcc.5b10377
Giovambattista N, Debenedetti P G, Rossky P J 2007 J. Phys. Chem. B 111 9581 DOI: 10.1021/jp071957s
Plimpton S 1995 J. Comput. Phys. 117 1 DOI: 10.1006/jcph.1995.1039
Werder T, Walther J H, Jaffe R L, Halicioglu T, Koumoutsakos P 2003 J. Phys. Chem. B 107 1345 DOI: 10.1021/jp0268112
Broesch D J, Frechette J 2012 Langmuir 28 15548 DOI: 10.1021/la302942k
Giovambattista N, Debenedetti P G, Rossky P J 2007 J. Phys. Chem. C 111 1323 DOI: 10.1021/jp065419b
Vogel T I 1987 SIAM J. Appl. Math 47 516 DOI: 10.1137/0147034
Vogel T I 1989 SIAM J. Appl. Math 49 1009 DOI: 10.1137/0149061
Kim S H, Kwon C H, Park K, Mun T J, Lepro’o X, Baughman R H, Spinks G M, Kim S J 2016 Sci. Rep. 6 23016 DOI: 10.1038/srep23016
Cavusoglu A, Chen X, Gentine P, Sahin O 2017 Nat. Commun. 8 617 DOI: 10.1038/s41467-017-00581-w
Xu W, Zheng H, Liu Y, Zhou X F, Zhang C, Song Y X, Deng X, Leung M, Yang Z B, Xu R X, Wang Z L, Zeng X C, Wang Z K 2020 Nature 578 392 DOI: 10.1038/s41586-020-1985-6
[1] Areal density and spatial resolution of high energy electron radiography
Jiahao Xiao(肖家浩), Zimin Zhang(张子民), Shuchun Cao(曹树春), Ping Yuan(袁平), Xiaokang Shen(申晓康), Rui Cheng(程锐), Quantang Zhao(赵全堂), Yang Zong(宗阳), Ming Liu(刘铭), Xianming Zhou(周贤明), Zhongping Li(李中平), Yongtao Zhao(赵永涛), Chuanxiang Tang(唐传祥), Wenhui Huang(黄文会), Yingchao Du(杜应超), Wei Gai(盖炜). Chin. Phys. B, 2018, 27(3): 035202.
[2] New developments in the multiscale hybrid energy density computational method
Min Sun(孙敏), Shanying Wang(王山鹰), Dianwu Wang(王殿武), Chongyu Wang(王崇愚). Chin. Phys. B, 2016, 25(1): 013105.
[3] Residual stress induced wetting variation on electric brush-plated Cu film
Meng Ke-Ke, Jiang Yue, Jiang Zhong-Hao, Lian Jian-She, Jiang Qing. Chin. Phys. B, 2014, 23(3): 038201.
[4] Three different low-temperature plasma-based methods for hydrophilicity improvement of polyethylene films at atmospheric pressure
Chen Guang-Liang, Zheng Xu, Huang Jun, Si Xiao-Lei, Chen Zhi-Li, Xue Fei, Sylvain Massey. Chin. Phys. B, 2013, 22(11): 115206.
[5] Spontaneous symmetry breaking vacuum energy in cosmology
Zhou Kang, Yue Rui-Hong, Yang Zhan-Ying, Zou De-Cheng. Chin. Phys. B, 2012, 21(7): 079801.
[6] Mitigation of laser damage growth in fused silica by using a non-evaporative technique
Jiang Yong,Liu Chun-Ming,Luo Cheng-Si,Yuan Xiao-Dong,Xiang Xia,Wang Hai-Jun,He Shao-Bo,Lü Hai-Bing,Ren Wei,Zheng Wan-Guo,Zu Xiao-Tao. Chin. Phys. B, 2012, 21(5): 054216.
[7] Irradiation effects of CO2 laser parameters on surface morphology of fused silica
Xiang Xia, Zheng Wan-Guo, Yuan Xiao-Dong, Dai Wei, Jiang Yong, Li Xi-Bin, Wang Hai-Jun, Lü Hai-Bing, Zu Xiao-Tao. Chin. Phys. B, 2011, 20(4): 044208.
[8] The generalized Stefan--Boltzmann law of a rectilinear non-uniformly accelerating Kinnersley black hole
Jiang Ji-Jian, Meng Qing-Miao, Wang Shuai. Chin. Phys. B, 2009, 18(2): 457-461.
[9] Thermal radiation and nonthermal radiation of the slowly changing dynamic Kerr--Newman black hole
Meng Qing-Miao, Wang Shuai, Jiang Ji-Jian, Deng De-Li. Chin. Phys. B, 2008, 17(8): 2811-2816.
[10] Restrictions on negative energy density for the Dirac field in flat spacetime
Yu Hong-Wei, Wu Pu-Xun, Li Fei, Shu Wei-Xing, Ren Zhong-Zhou. Chin. Phys. B, 2006, 15(5): 934-939.
[11] The negative energy density for a three-single-electron state in the Dirac field
Shu Wei-Xing, Yu Hong-Wei, Wu Pu-Xun. Chin. Phys. B, 2004, 13(12): 2025-2029.
[12] Universality principle and the development of classical density functional theory
Zhou Shi-Qi, Zhang Xiao-Qi. Chin. Phys. B, 2002, 11(10): 1051-1059.
No Suggested Reading articles found!