Effects of temperature, size of water droplets, and surface roughness on nanowetting properties investigated using molecular dynamics simulation

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Effects of temperature, size of water droplets, and surface roughness

on nanowetting properties investigated using molecular dynamics simulation

Cheng-Da Wu

b

_{, Li-Min Kuo}

a

_{, Shiang-Jiun Lin}

a

_{, Te-Hua Fang}

b,⇑

_{, Shy-Feng Hsieh}

a

Department of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, No. 415 Chien Kung Road, Kaohsiung 80807, Taiwan, ROC b

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, No. 415 Chien Kung Road, Kaohsiung 80807, Taiwan, ROC

a r t i c l e

i n f o

Article history:

Received 22 August 2011

Received in revised form 15 September 2011 Accepted 19 September 2011

Available online 22 October 2011

Keywords: Wetting properties Water

Dynamic contact angle Temperature Molecular dynamics

a b s t r a c t

The wetting properties of water nanodroplets on a gold substrate are studied using molecular dynamics (MD) simulations. The effects of temperature, droplet size, and surface roughness are evaluated in terms of molecular trajectories, internal energy, dynamic contact angle, and the radial distribution function. The simulation results show that the wetting ability and spreading speed of water greatly increases with increasing temperature. The dynamic contact angle of water on the gold substrate decreases with increasing temperature and decreasing droplet size and surface roughness, which leads to an increase in wetting ability. The compactness of a water droplet increases with decreasing temperature and droplet size, and slightly increases with degree of roughness. The internal energy of a water droplet decreases with increasing surface roughness, indicating that droplets form more stably on a rough surface.

1. Introduction

Water plays an important role in physical, chemical, biological, and medical researches. The determination of the wetting proper-ties of water on a metal surface is extremely important in many of its technological applications. The wetting of water is well under-stood on the macroscopic scale[1–5], whereas many new nanoscale wetting phenomena occur and completely different from the behaviors on the macroscopic scale. For various nanoscale applica-tions, the motion of ﬂuids on various surfaces, such as self-assem-bled monolayers[6], polymers [7], graphite [8], and metals[9], has been studied.

Young[10]proposed that an interface between two phases has an interfacial energy that is proportional to the contact surface area. The contact angle is determined by surface tension induced by the interfacial energy if a liquid droplet is on a smooth solid surface. On the nanoscale, the wetting of a surface is essentially determined by the molecular interactions between the liquid and the surface. The prediction of wetting ability for a particular liquid/surface combi-nation inevitably requires detailed information regarding their chemical composition, surface structure, geometry, environment temperature, and the dynamics of the liquid and surface interface. Such information is inherently contained in the atomistic simula-tion of materials. Hence, the molecular dynamics (MD) simulasimula-tion of a metal surface and a liquid interface is capable of exploring

the nature of surface wetting. Atomistic simulation avoids experi-mental noise and turbulence problems and can be used to analyze molecular trajectories and thermodynamic properties. Many nano-systems have been analyzed using MD, such as surface friction

[11,12], dip-pen nanolithography[13], nanoscratching [14], and nanoimprinting[15,16]. Ju et al.[17]studied the effect of tempera-ture on water nanodroplet formation and found that the average number of hydrogen bonds per water molecule decreased and the ratio of surface water molecules increased as the temperature was increased from 270 to 320 K. Sedighi et al. [18] and Park et al.[19]varied the interaction energy of the surface with respect to the liquid and found that the wetting ability can be signiﬁcantly enhanced by increasing the interaction energy.

The objective of the present work is to investigate the effects of temperature, nanodroplet size, and surface roughness on the wet-ting properties of water on an Au substrate using MD simulation. The results are discussed in terms of molecular trajectories, inter-nal energy, dynamic contact angle, spreading area, and the radial distribution function (RDF).

2. Methodology

Fig. 1a and b shows schematic MD models of a water droplet on smooth and rough Au surfaces, respectively. The physical model in-cludes a water nanodroplet and an Au substrate. To discuss the inﬂuence of droplet size on the wetting property, the whole water droplets were composed of 1714, 4712, and 8274 thermostat mol-ecules with diameters of 4.5, 6.0, and 7.5 nm, respectively. The Au 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.commatsci.2011.09.024

⇑ Corresponding author. Tel.: +886 7 3814526 5336; fax: +886 7 3831373. E-mail address:[email protected](T.-H. Fang).

Computational Materials Science 53 (2012) 25–30

Contents lists available atSciVerse ScienceDirect

Computational Materials Science

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m m a t s c i

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substrate comprised a perfect face-centered cubic (FCC) single crystal with a length, width, and height of 12.0, 12.0, and 1.8 nm, respectively. The Au substrate consists of three ﬁxed layers of atoms at the bottom to support the entire system, three thermostat layers above them, and free layers on the surface. The initial sys-tem is controlled to be at a sys-temperature of 300 K. A periodic boundary condition (PBC) is imposed on surface plane X- and Y-axes. In mathematical models and computer simulations, a PBC

[20]is often used to simulate a large system by modeling a small part that is far from its edge. To investigate the inﬂuence of tem-perature, the temperature was varied in a range of 250–400 K. Morse potential is used here to describe the interaction among Au atoms. The potential form is expressed as:

UM¼ D exp 2f f

a

ðrij r0Þ 2 exp f

a

ðrij r0Þ ð1Þ where rijis the distance between atoms i and j, r0is the equilibrium

distance between two atoms, D is the bonding energy between two atoms, and

a

is the material parameter. For the intra-molecular interaction of water, the potential energy of bond stretching is de-ﬁned as: Es¼ 1 2ksðl l0Þ 2 ð2Þ

where ksis the spring constant which controls the width of the

po-tential near the minimum, l is the bond length, and l0is the bond

length at equilibrium. The potential energy of bond bending is de-scribed by a simple harmonic angle potential energy expression:

Eh¼

1

2khðh h0Þ2 ð3Þ

where h is the bending angle and h0is the bending angle at

equilib-rium. The inter-molecular interaction between water–water is de-scribed by pairwise additive Lennard-Jones potential. It is expressed as: ELJ¼ 4

e

r

rij 12

r

rij 6 " # ð4Þ

where

e

is the cohesive energy and

r

is the equilibrium distance be-tween water molecules.Table 1shows the potential parameters for the interactions between Au atoms and water molecules[21–24].

The canonical ensemble in the system is NTV, and the temper-ature is controlled by the Nose–Hoover method. The time integra-tion of mointegra-tion is performed using Gear’s ﬁfth-order predictor– corrector method[20]with a time step of 0.5 fs. To increase calcu-lation efﬁciency, the Verlet neighbor-list method[20]is used. The lists of neighbor atoms are calculated every 10 time steps with a cut-off radius of 1 nm.

3. Results and discussion 3.1. Effect of temperature

Fig. 2shows a series of snapshots of the wetting behavior of a water droplet with a diameter of 6 nm on an Au substrate for tem-peratures of 250–400 K. The color of the water molecules repre-sents their internal energy, which is the sum of the molecular kinetic energy and potential energy. With time, the water droplet gradually spreads outwards on the surface. The wetting ability and spreading speed of water greatly increases with increasing temperature because at higher temperatures, the kinetic energy is sufﬁcient for the molecule to overcome the hydrogen bonding. In the spreading simulations, the water droplet easily forms a spherical shape at a low temperature of 250 K, whereas the surface is almost covered by the water molecules at a high temperature of 400 K (complete wetting condition), as shown in Fig. 2. Fig. 3

shows the variation of the average internal energy of each water molecule with time for temperatures of 250–400 K. When the spreading begins, the average internal energy of each molecule in the droplet is quite high due to the unstable spreading interactions between water–water and water–Au substrate. A large decay for all energy curves occurs in the ﬁrst 100 ps; a larger decay appears at higher temperature. After the decay, the energy variation is low, indicating that the system had gradually approached its thermal equilibrium state. The internal energy signiﬁcantly increases with temperature due to molecules having high kinetic energy at high temperature.Fig. 4shows the evolution of the dynamic contact an-gle of the water droplet on the substrate with time for tempera-tures of 250–400 K. The value of the dynamic contact angle decreases with increasing temperature, which results in an in-crease in wetting ability. The dynamic contact angles after 200 ps are 113°, 87°, 76°, and 58° for temperatures of 250, 300, 360, and 400 K, respectively. This indicates that the interface between the water droplet and the Au substrate is hydrophilic (contact angle <90°) for temperatures above 360 K and hydrophobic (contact an-gle >90°) for temperatures below room temperature.Fig. 5shows the RDF (g(r)) of the water droplet on the Au substrate at equilib-rium for various temperatures. The g(r) function describes how the atomic density varies as a function of the distance away from one particular atom. InFig. 5, the RDF peaks are initially high and then decrease with temperature, which indicates that the number of neighbor atoms for O and H atoms decreases with temperature. The continuous increase in the height of the peaks in g(r) also indi-cates that the internal structure in the water droplet is a well-or-dered and compact structure; i.e., a solid crystal. The relatively low peaks in g(r) at high temperature are characteristic of a liquid. Fig. 1. Schematic illustration of MD models. A water droplet with a diameter of

6 nm is placed on (a) ﬂat and (b) rough Au substrates, respectively.

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(3) The compactness of a water droplet increases with decreas-ing temperature and droplet size; it slightly increases with the degree of roughness.

(4) The internal energy of a water droplet decreases with increasing surface roughness, indicating that droplets form more stably on a rough surface.

Acknowledgment

This work was supported by the National Science Council of Tai-wan under Grants 2628-E-151-003-MY3 and NSC-100-2221-E-151-018-MY3.

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