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Anisotropy diffusion of water nanodroplets on phosphorene: Effects of pre-compressive deformation and temperature
Computational Materials Science 178 (2020) 109623
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Anisotropy diffusion of water nanodroplets on phosphorene: Effects of pre-compressive deformation and temperature Lijun Denga, Ling Wana, Nian Zhoub, Shan Tangc, , Ying Lid, ⁎
T
⁎
a
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China c State Key Laboratory of Structural Analysis for Industrial Equipment, International Research Center for Computational Mechanics, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China d Department of Mechanical Engineering and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA b
ARTICLE INFO
ABSTRACT
Keywords: Diffusion Phosphorene Deformation Temperature
Diffusion of water across surfaces generally involves motion on an uneven and vibrating but otherwise stationary substrate. Based on molecular dynamics simulations, we study the diffusion behavior of water nanodroplets on the compressed phosphorene at different temperatures. The compression is applied in three different ways: equal biaxial compression, uniaxial compression along armchair and zigzag directions As the compressive strain increases, the diffusion coefficients are first reduced and then increased in all three cases at T = 300 K. When the compressive strain exceeds 1.6%, the diffusion coefficient grows the fastest for the case of equal biaxial compression. As the temperature increases, two different modes are observed at the lower strain level ( 1.4% ) and relatively higher strain level ( 1.4% ). In the regime of lower level of strain, the diffusion coefficient exhibits an oscillating trend as the temperature increases. In the regime of higher level of strain, the diffusion coefficient increases linearly as the temperature increases. The fastest diffusion occurs under the equal biaxial compressive loading at the strain level of 2.4% and temperature T = 340 K. The different diffusion behaviors of water nanodroplets are found to be related to the surface morphologies of phosphorene under compression, as well as friction coefficient and diffusion energy barrier of water molecules. Our results show that compressive deformation of phosphorene and temperature are important to control the dynamics of water molecules on the phosphorene. The phenomena reported here enrich the knowledge of molecular mechanisms for nanofluidic systems, and may inspire more applications with phosphorene and other 2D materials.
1. Introduction As a newly identified two-dimensional (2D) nanomaterial, phosphorene attracts extensive interests due to its direct band gap [1,2]. After that, many unique properties, such as electrical [3,4], optical [5] and mechanical properties [6,7] are uncovered, making phosphorene receive more attentions recently. Among them, using a few layers of phosphorene, the field-effect transistor has been fabricated successfully [8], which is a highly desirable device for bio-detection and bio-sensing [9,10]. As photo-thermal agents [11], phosphorus nanosheets (multiple layers of black phosphorene) also show the excellent potential in killing some cancer cells [12]. Moreover, phosphorene exhibits low disruption to protein’s structure [13] and can be a carrier of small drug molecules [14]. These demonstrate that phosphorene is a potential nanomaterial in biomedical applications. However, Martel et al. [15] show that the phosphorene can be oxidized easily in the water, which is a ⁎
disadvantage for biological applications because biological systems often contain a large amount of water. Subsequently, this limitation is overcome by Ruoff et al. [16]. They reveal that the phosphorene is easily oxidized because it reacts with the dissolved oxygen in water, not water itself. Actually, phosphorene in oxygen-depleted water is stable. This property, combined with its biological applications, makes phosphorene an excellent candidate for nanofluidic systems [17]. Consequently, wider applications of this novel nanomaterial require more extensive studies on its interactions with biomolecules, including the diffusive properties of water nanodroplets on its surface. In recent years, the diffusive properties of water nanodroplets on 2D materials, such as graphene [18,19], boron nitride (BN) sheet [20], tungsten disulfide (WS2 ) and molybdenum disulfide (MoS2 ) [21], attract great attentions. In the nanoscale, the surface of these 2D materials plays an essential role in fluid motion due to the high ratio of surface area to volume. Additionally, the surfaces of these 2D materials
Corresponding authors. E-mail addresses: [email protected] (S. Tang), [email protected] (Y. Li).
https://doi.org/10.1016/j.commatsci.2020.109623 Received 15 December 2019; Received in revised form 19 February 2020; Accepted 24 February 2020 0927-0256/ © 2020 Elsevier B.V. All rights reserved.
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are easily affected by additional physical fields, such as mechanical deformation, temperature and electric/magnetic field. Hence, many researchers have studied the diffusion of water molecules on the 2D materials under imposed external fields. For example, Kargar et al. [22] have studied the deformation of water nanodroplets on graphene under the electric field, and found that the nanodroplet is elongated in the direction of imposed electric field. Ma et al. [23] have investigated the diffusion of water nanodroplets on graphene under the imposed compressive strain and reported that the compressive deformation leads to exceedingly fast diffusion of water nanodroplets. Rajegowda et al. [24] have explored the motion of water nanodroplets on boron nitride surface by temperature gradient, which leads to fast movement of water molecules. These works indicate that the external physical fields have a pronounced effect on the diffusion of water nanodroplets on the surface of 2D materials. These effects can be a crucial point for potential application on water-droplets’ self-removal [25,26], water-droplets’ transport [27] and water-droplets’ control [28], three important aspects in the field of water nanodroplets. Nevertheless, the fundamental understanding on diffusion of water nanodroplets on phosphorene is still limited [29,30,17]. The diffusion behavior of water nanodroplets on phosphorene under compression at different temperatures has not been studied, to the best of our knowledge, which deserves in-depth understanding for future applications of phosphorene. In this study, we use molecular dynamics (MD) simulations, which are widely adopted in the study of the interactions of (bio) molecules with nanomaterials, to investigate the diffusion of water nanodroplets on phosphorene under compression at different temperatures. We find that the diffusion of water nanodroplets on the phosphorene surface is highly anisotropy. The strain-weaken and temperature-enhanced water diffusion are observed at different ranges of strain and temperature, respectively. In order to further understand this interesting diffusion behavior, the morphology of phosphorene and trajectory of water nanodroplet are investigated in detail. This diffusion behavior is further explained by interfacial friction coefficient and diffusion energy barrier between phosphorene and water. Finally, the effects of Lennard-Jones (L-J) parameters and size of water nanodroplets on the diffusion behavior are given.
equilibrium states. The MD simulations are performed with a 35 × 50 × 1 supercell (161.2 × 163.6 Å) for phosphorene and 294 molecules for water nanodroplet. Periodic boundary conditions are applied along the x , y and z directions. A vacuum of 2.5 nm is employed along the direction perpendicular to the plane of phosphorene, to avoid slab’s interaction with its periodic images. TIP4P/2005 potential [31] and the improved Dreiding force field [32] are used for the water molecules and phosphorene, respectively. The interaction between water and black phosphorus is described by Lennard-Jones (L-J) 6–12 potentials between the oxygen and phosphorus atoms with parameters lj = 10.7 meV and lj = 0.324 nm [29,33]. The O–H distance and the H–O–H angle are fixed by the SHAKE algorithm [34]. The electrostatic interaction is considered by the particle–particle particle-mesh (PPPM) solver [35]. A cut-off distance of 1.0 nm is used for the L-J potential and PPPM solver. The linear momentum of the phosphorene is kept to be zero. The equilibration phase is firstly carried out in the canonical (NVT) ensemble for a total of 500 ps with a 2 fs time step. The temperature of the water molecules in the starting box-like configuration is initialized at 1 K and then increases to 300 K with 50 K increments. A continuous optimization is applied to the system for 2.5 ns until the energy and pressure reach equilibrium under the NPT ensemble controlled by the Nose–Hoovers thermostat [36]. The box dimensions along the armchair and zigzag directions are allowed to fluctuate freely in response to the barostat (pressured fixed at 0 atm) in this process. Therefore, phosphorene shows a little bending after the equilibration (cf. Fig. 1c). The dimension of phosphorene changes from the original 161.2 × 163.6 Å to 160.2 × 162.6 Å. After this equilibration period (a total of 3 ns), the compressive strain is then applied by a strain rate 1 × 10 8 fs in the NVT ensemble. The temperature is set to 300 K in this process. After that, the temperature of phosphorene is increased to the target temperature (290, 310, 320, 330, 340 K) in the NVT ensemble and the thermostat on the water molecules is removed (i.e. microcanonical ensemble). In other words, the case considered here is that water nanodroplet diffuses on a heated phosphorene. Finally, the coordinates and velocities of all the atoms are recorded every 2 ps for at least 24 ns, and the trajectory of the last 12 ns is extracted for further analysis. All MD simulations were performed by Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software [37]. Note that the strain discussed here is defined as the compressive strain and T is the temperature of phosphorene. The phosphorene with the size of 160.2 × 162.6 Å is treated as the initial one, i.e., = 0 . If x = 1.0% is applied to the phosphorene, the size of phosphonene is changed from 160.2 × 162.6 Å to 158.6 × 162.6 Å. The first-principle calculations are carried out by the Vienna ab initio simulation package (VASP) [38], with core-electron interactions described by PAW pseudo-potentials [39]. The generalized gradient
2. Computational model and methods As a typical 2D material, phosphorene has its own atomistic structure. Fig. 1a shows the special configuration of phosphorene. The x and y directions are defined as armchair and zigzag directions, respectively. The z-axis is perpendicular to the plane of phosphorene. Fig. 1b is the front view of phosphorene from the y direction, wherein the brown and lavender parts represent the top and bottom phosphorus atoms respectively. Fig. 1c shows the phosphorene/water nanodroplet system, in which a water nanodroplet lies on the phosphorene at the initial and
Fig. 1. (a) Top view of the phosphorene’s atomistic structure. Zigzag and armchair boundaries are along the y and x directions, respectively. (b) Front view of phosphorene from the y direction. The top and bottom phosphorus atoms are grouped into two types by different colors. (c) Initial box-like configuration of 294 water molecules before equilibration and final well-formed droplet after equilibration.
2
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Fig. 2. (a) Snapshots of a water nanodroplet on phosphorene at different simulation time. (a-1) Mean squared displacement (MSD) vs. time for the water nanodroplet. Scale bars: 2 nm. Effects of (b) compressive strain and (c–e) temperature T on the diffusion coefficients D of water nanodroplet.
approximation (GGA) with the general exchange and correlation functions of Perdewe-Burkee-Ernzerhof (PBE) [40] is employed to investigate the exchanging and correlation effects of electrons interactions. A correction to density functional theory (DFT-D) is adopted for considering the interaction of Van der Waals force (VDW) for more accurate calculation [41]. The SCF tolerance quality is set to 1.0 × 10 6 eV/atom. The cut-off energy is 400 eV for the plane-wave basis functions and 4 × 3 × 1 Monkhorste-Pack-point mesh is employed in all the first-principle calculations.
3. Results 3.1. Diffusion coefficients of water nanodroplets Fig. 2a shows snapshots of a water nanodroplet diffusing on phosphorene surface ( = 0 ). For the ease of illustration, CASE XY, CASE X and CASE Y are defined as the case of equal-biaxial compression, uniaxial compression along x direction and y direction, respectively. The corresponding strains are represented by xy, x and y . The phosphorus 3
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atoms are colour-coded according to their heights (H) along the z axis, thus indicating that the water droplets reside within valleys of the ripples (blue regions). Fig. 2a-1 shows the mean squared displacement (MSD) vs. time at = 0 , which is used to estimate the diffusion coefficients of the water nanodroplet within the x y plane according to the Einstein relation [42]:
D = lim t
MSD 4t
MSD = < |(r (t )
of morphology in CASE Y ( y = 1.0%, 1.6%, 2.4%). The surface morphologies change a little and all show regular wavy shape. The surface morphology of phosphorene with regular waves, regular folded lines and irregular uneven surface are defined as MC, MB and MA, respectively. Combining the results of diffusion coefficients D vs. temperature (cf. Fig. 2c, d), it indicates that the increase of temperature can facilitate the diffusion of water nanodroplet on phosphorene with MB (regular folded lines) and MA (irregular uneven surface). However, the increase of temperature leads to two different modes with MC (regular waves) at different strain level: at the lower strain level ( 1.4%), the D is oscillating with temperature; at the higher strain level ( 1.4%), the D increases with temperature. It demonstrates that the surface morphology of phosphorene caused by compressive strain governs the diffusion of water nanodroplet at different temperatures. The similar importance of surface morphology in the adhesion of the villin headpiece on phosphorene [13] and water on graphene oxide [47] have been revealed by other researchers. Moreover, in order to better understand the relationship between this oscillation effect and phosphorene’s surface morphology, a further discussion is carried out. q is defined as the impact factor of temperature at different strain levels of y , given by
(1)
r (t 0 )|2 >
(2)
where D is the two-dimensional diffusion coefficient, t is the time, <….> represents the average of all water molecules. Because the MSD vs. time curve is not straight, the Minimum Covariance Determinant (MCD) [43] method is used to detect outliers and then fit for the diffusion coefficient D. Fig. 2b–e plot diffusion coefficients vs. compressive strain or temperature. Six different imposed strains ( = 0, 0.6%, 1.0%, 1.6%, 2.0%, 2.4%) and temperatures (T = 290, 300, 310, 320, 330, 340 K) are investigated. 1.4% and 1.4% are defined as i and ii respectively (cf. The regions Fig. 2b). In the region i , the diffusion coefficient D gradually decreases as the strain increases in the three deformation cases (CASE XY, CASE X and CASE Y). In the region ii , the diffusion coefficient D increases faster with the increasing strain in CASE XY (black triangle) or CASE X (red star), but it increases in an oscillating way with the increasing strain in CASE Y (blue circle). At the small compressive strain level (region i ), the diffusion coefficient D is smaller than that without any compressive deformation. It means that the small compressive strain is not conducive to diffusion of water nanodroplets. One of the possible reasons is that the thermal vibration of phosphoenene under small compressive strain (strain below 1.0%) can not effectively promote the moving of water nanodroplets. It is very different from the graphene. Ma et al. [23] have showed that the diffusion coefficient of water nanodroplets on the graphene increases linearly with the compressive strain. Fig. 2c shows diffusion coefficient D vs. the temperature T at the strain level = 2.4% . It shows the diffusion coefficient D linearly increases with temperature T in the three deformation cases, although it has a little oscillation for CASE Y. The magnitude of diffusion coefficient D is about twice (T = 340 K) of that at T = 290 K in the CASE XY. The same is observed for = 1.6% in Fig. 2d. However, for = 1.0% (Fig. 2e), the diffusion coefficients D in these three loading cases are oscillating as T increases. The thermal vibration of phosphorene and the friction force between water nanodroplets and phosphorene are two important driving forces for the diffusion of water droplets. The most possible reason resulting in the oscillating trend shown in Fig. 2e is the competitive contributions to water nanodroplets motion from thermal vibration of phosphorene and friction force. Further work should be carried out to elaborate the detailed underlying mechanisms. In a word, similar to electrical conductance [44], thermal conductivity [45] and optical properties [46] of phosphorene, the diffusion of water nanodroplet on phosphorene under compression at different temperatures also shows strong anisotropy.
q=
Dmax Dmin Dmin
(3)
where Dmax and Dmin are the maximum and minimum diffusion coefficients from T = 290 K to T = 340 K at strain level less than 1.4%, such as Dmax = 0.73 × 10 4 cm2 /s and Dmin = 0.52 × 10 4 cm2 /s at strain level y = 1.0% (cf. Fig. 2e). Hence, a lower q means a lower oscillation amplitude of diffusion coefficients D. Fig. 4a shows the simplified diagram of phosphorene with regular waves (MC). h and d are the distances between peaks and valleys along z and y directions, respectively. The value of h, d and h/ d varying with y are summarized in the Table 1. The h and d are obtained by the average of ten configurations at different time in T = 300 K. The effects of temperature on h and d are ignored, because no evident changes in the h and d are observed for the various temperature considered in our study. It can be seen that the value of h/ d is higher as y increases. From Fig. 4b, q decreases with the y increasing. Therefore, a higher value of h / d means a lower q, indicating the oscillation of D caused by temperature has a lower amplitude at a higher value of h/ d . In other words, the influence of temperature on the diffusion of water nanodroplet on phosphorene with regular waves (MC) is smaller with a higher h/ d . 3.3. Trajectory of water nanodroplets Fig. 5 shows the trajectory of a water nanodroplet moving on the phosphorene under different levels of stain and temperatures in a total simulation time of 12 ns. The distance from the point on the trajectory to the origin of coordinates represents the distance from the current position of water nanodroplet to its reference position. The x and y axes in Fig. 5 represent the moving distance of water nanodroplet along x and y directions, respectively. Fig. 5a plots the trajectory in three different situations ( xy = 0.6%, x = 0.6%, y = 0.6%) at a constant temperature T = 300 K. It is clearly identified that the displacement along y direction traveled by water nanodroplet is larger than that along x direction at the end of 12 ns. For example, the displacement along y direction traveled by water nanodroplet at the strain level y = 0.6% is about 100 Å but 75 Å along x direction. Fig. 5b plots the trajectory in other three different situations ( xy = 2.4%, x = 2.4%, y = 2.4%) at a constant temperature T = 300 K. We can see that the displacement along y direction traveled by water nanodroplet is larger than that along x direction shown by the blue line ( y = 2.4%). However, no such feature exists, as observed from the black line ( xy = 2.4%) and red line ( x = 2.4%). This feature that water molecules are more favorable to move along the y direction is defined as ‘travel preference of water
3.2. Morphology of phosphorene under compression Fig. 3 shows the snapshots of phosphorene’s morphology under different levels of compressive strain. The color of plots represents the height (H) of phosphorous atoms along z (out-of-plane) direction. The blue represents the valley and red represents the bulge, which qualitatively judges the flatness of phosphorene. The black cube indicates the simulation box. The top row shows the variation of surface morphology in CASE X ( x = 1.0%, 1.6%, 2.4%). It shows that the morphology of phosphorene changes a lot with increasing strain, from regular waves ( x = 1.0%) to irregular uneven surface ( x = 2.4%). The middle row shows the variation of surface morphology in CASE XY. It shows that the surface morphology changes from regular waves ( = 0 ) to regular folded lines ( = 2.4% ). The bottom row shows the variation 4
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Fig. 3. Snapshots for morphology of phosphorene under different levels of compressive strain. The morphologies of phosphorene with regular waves, regular folded lines and irregular uneven surface are defined as MC, MB and MA, respectively. The H labeled with color represents the height of phosphorous atoms along z (out-ofplane). The top, middle and bottom rows show the variation of phosphorene’s morphology with compressive strain for CASE X, CASE XY and CASE Y, respectively.
nanodroplet’. Meanwhile, the morphology of phosphorene at y = 2.4%, xy = 0.6%, x = 0.6% and y = 0.6% all belongs to MC, implying that water molecules are more favorable to move along the y direction with MC. Fig. 5c plots the trajectory at different temperatures with a constant strain y = 2.4%. It shows a strong ‘travel preference of water nanodroplet’ and the temperature has no obvious effect. To further understand the ‘travel preference of water nanodroplet’ caused by MC, a series of calculations are carried out and the results are plotted in Fig. 6. is a ratio defined by = y / x , where y and x are the displacements of water nanodroplet traveled along y and x directions in a total of 12 ns, respectively. A higher means an obvious ‘travel preference of water nanodroplet’. Fig. 6 shows vs. the compressive strain with three deformation cases. Each data point is the average of the results obtained from three individual MD simulations by adjusting the initial position of water nanodroplet. The black circle, red star and blue square represent results of CASE XY, CASE X and CASE Y, respectively. The temperature is fixed at 300 K. The dotted purple area indicates that the morphology of phosphorene under these strains exhibits the characteristics of MC. The black dotted line represents the contour of = 1. The ‘travel preference of water nanodroplet’ is pronounced when the morphology of phosphorene is more like MC, especially when y 1.6%. The rest do not show this. They are evenly distributed above and below the black dotted line of = 1.
=
1 AkB T
t 0
dt < F (t ) F (0) >
(4)
where F (t ) is the total tangential force exerted by the water droplet on the phosphorene surface and calculated from the data shown in Fig. 7a and b (F = (Fx 2 + Fy2) ); kB is the Boltzmann constant, and T is the water temperature. The droplet-surface contact area A in all situations are taken as 7.06 nm2 , although it is slightly affected by the imposed strain and temperature. A similar methodology has been adopted by Zheng et al. [51]. The force auto-correlation function < F (t ) F (0) > can be computed in our equilibrium MD simulations. The same method can be found from Xiong [52] and Zhou’s work [53]. From the equilibrium MD simulations, the instantaneous lateral forces F (t ) between water and phosphorene were output every 100 fs. Fig. 8a shows the frictional coefficient vs. the time under the compressive strain xy = 2.4% at temperature T = 320 K. It can be seen from Fig. 8 that the correlation function < F (t ) F (0) > decays exponentially with time t . Within 1.5 ps, saturates. From the plateau regime, we obtain = 0.42 × 106 Ns/m3 . Fig. 8b shows the friction coefficient as a function of xy at three different temperatures. A higher is less favorable to the diffusion of water [24,52,48]. We find that the decreases with the temperature at xy = 1.6, 2.0, 2.4%. Hence, it may be the reason that diffusion coefficients D increase with the temperature (the black dotted line in Fig. 2c). When xy = 0, 0.6%, 1.0%, the does not exhibit a simple relationship with temperature. On the other hand, the first increases and then decreases with the strain. It explains the opposite trend for the diffusion coefficients D under xy (see the black triangle of Fig. 2b). Fig. 8c shows the as a function of T at the strain level x = 2.4% and y = 2.4%. decreases with temperature both at x = 2.4% and y = 2.4%. It is consistent with the observed trend of the corresponding diffusion coefficients. Note that the friction coefficient in our work is about 4 × 105 Ns/m3 , whereas it is about 1 × 10 4 Ns/m3 at water-graphene interface [48], 2 × 105 Ns/m3 at water-molybdenum disulfide (MoS2 ) interface [53] and 3 × 105 Ns/m3 at water-hexagonal boron nitride (BN) interface [54]. This indicates that the diffusion of water on phosphorene surface is more difficult, meaning that phosphorene is
4. Discussion 4.1. Friction coefficient of water nanodroplet on phosphorene The interfacial friction coefficient ( ) at the droplet/phosphorene interface is investigated to further address the characteristics of water diffusion on phosphorene. The friction coefficient is the intrinsic property to characterize the interfacial dynamics [48]. It can be expressed via the Green–Kubo (GK) relationship, which relates to the auto-correlation function of fluctuating pairwise forces at equilibrium [49,50], given by 5
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Fig. 4. (a) A simplified diagram of phosphorene with regular waves (MC). h and d are defined as the distances between peak and valley along z and y directions, respectively. (b) The temperature impact factor q as a function of the y .
more hydrophilic than graphene, which has been observed in previous studies [55,56].
Table 1 The values of h, d and h/ d with different y . The units of h and d are Å. The h and d are obtained by the average of ten configurations at different time at T = 300 K. y
0 0.3% 0.6% 0.8% 1.0% 1.2%
h (Å)
d (Å)
h/d
13 14.2 16.2 17.4 18.5 19.4
76 77.5 78 81 80.2 79.8
0.171 0.183 0.207 0.214 0.23 0.243
4.2. Diffusion energy barrier of water on phosphorene To better understand the anisotropy diffusion of water nanodroplet, the diffusion energy barrier of a single water molecule on the phosphorene is estimated by the first-principle calculations. The diffusion energy barrier is an important indicator for the diffusion [57,58]. Fig. 9a shows the simulation setup including a water molecule adsorbed on a phosphorene (2 × 2 × 1 unit cells), and the shape of the water molecule is based on Ma’s research [19]. The top and bottom of 9a show the views of the system from z and y directions, respectively. Two colors of phosphorene represent two different layers of phosphorus 6
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Fig. 5. Trajectory of water nanodroplet on phosphorene under (a, b) different levels of compressive stain and (c) temperatures over 12 ns.
Fig. 6. Ratio
vs. strain
for CASE XY, CASE X and CASE Y.
atoms. The vertical distance from oxygen atom in water molecule to the first layer of phosphorus atom is defined as d 0 . Fig. 9b shows four different adsorption sites, represented by , , and . All adsorption sites are the positions where the oxygen atom is projected on the x y plane. The adsorption site is in the middle of atoms I and J. The is the intersection of the line passing the first adadsorption site sorption site along the y axis and the line with atoms I and M. The positions of adsorption site and are similar to and , respectively. In our MD simulations, the phosphorene has a little residual deformation after equilibrium under the NPT ensemble with normal pressure and temperature, which is also observed in previous works [59]. To be comparable with MD simulations, a pre-compressive strain xy = 0.6% is then applied to the initial configuration of phosphorene. This phosphorene with a tiny deformation is used as our new initial configuration for the first-principle calculations, i.e., = 0 . The compressive strain is applied by setting the lattice constant with a smaller value than that of the equilibrium structure. The present approach for applying compressive strains is also adopted in previous study [60]. Fig. 9c and d show the adsorption energy Eads vs. d 0 at different adsorption sites at strain level = 0 . The lowest point on the adsorption energy vs. d 0 curve is defined as the optimal Eads . The optimal Eads of and are about −43.9 meV and −44.5 meV, respectively. The optimal Eads of and are about −84.2 meV and −81.5 meV, respectively. A higher absolute value of the Eads implies a stronger adsorption and more stable system. In other words, the water molecule is preferred to be attached on the bottom phosphorus atoms, which is consistent with Zhang et al. [29] and Ruoff et al. [16]. In addition, the energy difference between with is 39.7 meV, which can be approximated as the required energy for the water molecule to move along the x direction; the energy difference between and or and is less than 3 meV, which can be approximated as the required energy for the water molecule to move along the y direction. Hence, the required energy for the water molecule to move along the x direction is much higher than that
Fig. 7. Change of the tangential force along (a) x direction and (b) y direction acting on the water nanodroplet over 12 ns.
along the y direction, implying that water molecules are easier to move along the y direction. This phenomenon is also observed from the adsorption of various organic molecules on phosphorene by Otyepka et al. [61]. This may be an possible reason for the ‘travel preference’ of water nanodroplet along y direction (Figs. 5 and 6). The diffusion energy barrier is defined as E = (Eads )max (Eads )min , where (Eads )max and (Eads )min are the maximum and minimum of optimal Eads for , , and , respectively. E vs. is plotted in Fig. 10. The black triangle, red star and blue circle represent the CASE XY, CASE X and CASE Y, respectively. A higher diffusion energy barrier means that diffusion is more difficult. The E increases first and then decreases as the strain increases, implying that the diffusion coefficient D first decreases and then increases. It is consistent with our previous results (cf. Fig. 2b). The E for the CASE XY is smaller than the others. It means that equal biaxial compression is the most beneficial one to the diffusion of water molecule on phosphorene under different compressive deformations. 7
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Fig. 9. Water adsorption structures and adsorption energy Eads vs. distance d0 . (a) The adsorption structure shown from z direction (top) and y direction (bottom). (b) Four different adsorption sites: , , and . Eads as a function of d0 for (c) , and (d) , .
phosphorene structure but is described by graphene’s potential parameters, which are set as lj = 3 meV and lj = 0.4 nm [19]. In order to reduce computational complexity, only equal biaxial compression is discussed here. Fig. 11 shows the diffusion coefficients D of water nanodroplet on pseudo-phosphorene as a function of xy . The D is first reduced and then increased as the imposed strain increases, which is similar to that for water on phosphorene but different from that for water on graphene [23]. The magnitude of diffusion coefficients D changes a lot, which is caused by the different L-J parameters. Hence, it concludes that the L-J parameters may play a crucial role on the magnitude of diffusion coefficients but has no evident influence on the trend of diffusion coefficients under compression. The size of water nanodroplets also can affect the diffusion [65,66]. In order to verify the validity of our main conclusion for different size of water nanodroplets, two other water-phosphorene systems are also built: 525 and 812 water molecules on phosphorene. Fig. 12a and b show the snapshots of 525 water molecules and 812 water molecules moving on phosphorene surfaces ( = 0 ). According to the above
Fig. 8. (a) Theoretical calculation of the friction coefficient for water nanodroplet on phosphorene. Inset: Time-dependency of the force auto-correlation function. The dotted line is the fitting result. (b) The friction coefficient vs. xy at different temperatures. (c) The friction coefficient vs. T at strain levels x = 2.4% and y = 2.4% .
4.3. Influences of L-J parameters and size of water nanodroplets The L-J parameters for the interaction between water nanodroplet and 2D materials play important roles on the adsorption and diffusion of water [62]. It can affect the diffusion speed or the diffusion tendency of water on 2D materials [63,64]. To investigate the influence of L-J parameters on the diffusion of water on phosphorene under compression, we construct a model material: a pseudo-phosphorene with 8
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Fig. 10. Diffusion energy barrier E vs. the imposed strain for CASE XY, CASE X and CASE Y.
Fig. 11. Effect of xy on the diffusion of water nanodroplet on pseudo-phosphorene at T = 300 K . The dotted line is a guide to the eye.
Fig. 12. Snapshots of (a) 525 and (b) 812 water molecules on phosphorene. Scale bars: 2 nm. Effects of xy (c) and T (d) on the diffusion coefficients D for 525 and 812 water molecules on phosphorene.
method, the compressive strain is applied to phosphorene at different temperatures. In order to reduce computational cost, only equal biaxial compression is discussed here. The results are shown in Fig. 12c and d. The trend of D vs. the imposed strain or temperature is the same as the previous ones (cf. Fig. 2) but the magnitude of D decreases. Therefore, the size of water nanodroplets will not affect our main conclusion. The reason of the decrease of D is that the water nanodroplet is larger with more water molecules. A larger water nanodroplet corresponds to the lower diffusion speed, which is also reported in other 2D materials [23,30].
increases, the diffusion coefficients increase linearly in three deformation cases. The surface morphology of phosphorene and the trajectory of water nanodroplet are also analyzed. An obvious ‘travel preference’ of water nanodroplet is observed when water nanodroplet diffuses on phosphorene with regular waves. Subsequently, we calculate the friction coefficient and diffusion energy barrier E , which are two critical factors for diffusion of water nanodroplets. The interfacial friction coefficient increases first and then decreases as xy increases at a constant temperature. It reduces as the temperature increases when xy 1.6%, which is consistent with our results for the diffusion coefficients. Similarly, the E is first increased and then decreased as the strain increases, meaning the diffusion of water nanodroplets first slows down and then speeds up. Finally, extension is made to analyze the effects of L-J parameters and size of water nanodroplets on the diffusion coefficients. In summary, nanodroplet transport on compressed phosphorene surface at different temperatures has been studied systematically, which can give molecular insights on developing novel phosphorenebased nanofluidic devices. The proposed method is not limited to phosphorene, which may be found to be useful in biotechnology for other applications involving water droplets and 2D materials.
5. Concluding remarks In this work, MD simulations have been performed to investigate the diffusion of water nanodroplets on phosphorene under compression at different temperatures. Three compressive loadings xy, x , y are imposed to phosphorene. Our results show that the diffusion coefficients D of water nanodroplet are first reduced and then increased with the strain increasing in three deformation cases at T = 300 K. As T increases, the diffusion coefficients D present two different modes: in the regime of lower strain (e.g. = 1.0% ), the diffusion coefficients oscillate with the increase of T; in the regime of higher strain (e.g. = 2.4% ), as T
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CRediT authorship contribution statement
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Lijun Deng: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. Ling Wan: Conceptualization, Investigation, Methodology, Resources, Validation, Visualization, Writing - review & editing. Nian Zhou: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing original draft, Writing - review & editing. Shan Tang: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Validation, Writing - review & editing. Ying Li: Conceptualization, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement S.T. appreciates the support from NSF of China (Project No. 11872139, 11472065). References [1] W. Lu, H. Nan, J. Hong, Y. Chen, Z. Chen, L. Zheng, X. Ma, Z. Ni, C. Jin, Z. Zhang, Plasma-assisted fabrication of monolayer phosphorene and its raman characterization, Nano Res. 7 (6) (2014) 853–859. [2] H. Liu, Y. Du, Y. Deng, P.D. Ye, Cheminform abstract: semiconducting black phosphorus: Synthesis, transport properties and electronic applications, Chem. Soc. Rev. 44 (9) (2015) 2732–2743. [3] Z.X. Hu, X. Kong, J. Qiao, B. Normand, W. Ji, Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus, Nanoscale 8 (5) (2016) 2740–2750. [4] H. Liu, K. Hu, D. Yan, R. Chen, S. Wang, Recent advances on black phosphorus for energy storage, catalysis, and sensor applications, Adv. Mater. 30 (32) (2018) 1800295. [5] A. Carvalho, W. Min, Z. Xi, A.S. Rodin, H. Su, A.H.C. Neto, Phosphorene: from theory to applications, Nat. Rev. Mater. 1 (11) (2016) 16061. [6] L. Wang, K. Cai, Absorption and temperature effects on the tensile strength of a black phosphorus ribbon in argon environment, Comput. Mater. Sci. 150 (2018) 15–23. [7] V. Sorkin, Y.W. Zhang, Effect of edge passivation on the mechanical properties of phosphorene nanoribbons, Extre. Mech. Lett. 14 (2017) 2–9. [8] L. Li, Y. Yu, G.J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X.H. Chen, Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol. 9 (5) (2014) 372–377. [9] H. Im, X.-J. Huang, B. Gu, Y.-K. Choi, A dielectric-modulated field-effect transistor for biosensing, Nat. Nanotechnol. 2 (7) (2007) 430–434. [10] M.T. Martinez, Y.C. Tseng, N. Ormategui, I. Loinaz, R. Eritja, J. Bokor, Label-free dna biosensors based on functionalized carbon nanotube field effect transistors, Nano Lett. 9 (2) (2009) 530–536. [11] Z. Sun, H. Xie, S. Tang, X.-F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, P.K. Chu, Ultrasmall black phosphorus quantum dots: synthesis and use as photothermal agents, Angew. Chem. Int. Ed. 54 (39) (2015) 11526–11530. [12] H. Wang, X. Yang, W. Shao, S. Chen, J. Xie, X. Zhang, J. Wang, Y. Xie, Ultrathin black phosphorus nanosheets for efficient singlet oxygen generation, J. Am. Chem. Soc. 137 (35) (2015) 11376–11382. [13] Z. Wei, T. Huynh, X. Peng, Z. Bo, Y. Chao, B. Luan, R. Zhou, Revealing the importance of surface morphology of nanomaterials to biological responses: adsorption of the villin headpiece onto graphene and phosphorene, Carbon 94 (11) (2015) 895–902. [14] W. Tao, X. Zhu, X. Yu, X. Zeng, Q. Xiao, X. Zhang, X. Ji, X. Wang, H. Zhang, L. Mei, Black phosphorus nanosheets as a robust delivery platform for cancer theranostics, Adv. Mater. 29 (32) (2017) 1603276. [15] A. Favron, R. Martel, Photooxidation and quantum confinement effects in exfoliated black phosphorus, Nat. Mater. 14 (8) (2015) 826–832. [16] H. Yuan, J.S. Qiao, H. Kai, S. Bliznakov, E. Sutter, X.J. Chen, L. Da, F. Meng, S. Dong, J. Decker, Interaction of black phosphorus with oxygen and water, Chem. Mater. 28 (22) (2016) 8330–8339. [17] Z.-Q. Zhang, H.-L. Liu, Z. Liu, Z. Zhang, G.-G. Cheng, X.-D. Wang, J.-N. Ding, Anisotropic interfacial properties between monolayered black phosphorus and water, Appl. Surf. Sci. 475 (2019) 857–862. [18] J.E. Andrews, S. Sinha, P.W. Chung, S. Das, Wetting dynamics of a water nanodrop on graphene, Phys. Chem. Chem. Phys. 18 (34) (2016) 23482–23493.
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Anisotropy diffusion of water nanodroplets on phosphorene: Effects of pre-compressive deformation and temperature Lijun Denga, Ling Wana, Nian Zhoub, Shan Tangc, , Ying Lid, ⁎
T
⁎
a
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China c State Key Laboratory of Structural Analysis for Industrial Equipment, International Research Center for Computational Mechanics, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China d Department of Mechanical Engineering and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA b
ARTICLE INFO
ABSTRACT
Keywords: Diffusion Phosphorene Deformation Temperature
Diffusion of water across surfaces generally involves motion on an uneven and vibrating but otherwise stationary substrate. Based on molecular dynamics simulations, we study the diffusion behavior of water nanodroplets on the compressed phosphorene at different temperatures. The compression is applied in three different ways: equal biaxial compression, uniaxial compression along armchair and zigzag directions As the compressive strain increases, the diffusion coefficients are first reduced and then increased in all three cases at T = 300 K. When the compressive strain exceeds 1.6%, the diffusion coefficient grows the fastest for the case of equal biaxial compression. As the temperature increases, two different modes are observed at the lower strain level ( 1.4% ) and relatively higher strain level ( 1.4% ). In the regime of lower level of strain, the diffusion coefficient exhibits an oscillating trend as the temperature increases. In the regime of higher level of strain, the diffusion coefficient increases linearly as the temperature increases. The fastest diffusion occurs under the equal biaxial compressive loading at the strain level of 2.4% and temperature T = 340 K. The different diffusion behaviors of water nanodroplets are found to be related to the surface morphologies of phosphorene under compression, as well as friction coefficient and diffusion energy barrier of water molecules. Our results show that compressive deformation of phosphorene and temperature are important to control the dynamics of water molecules on the phosphorene. The phenomena reported here enrich the knowledge of molecular mechanisms for nanofluidic systems, and may inspire more applications with phosphorene and other 2D materials.
1. Introduction As a newly identified two-dimensional (2D) nanomaterial, phosphorene attracts extensive interests due to its direct band gap [1,2]. After that, many unique properties, such as electrical [3,4], optical [5] and mechanical properties [6,7] are uncovered, making phosphorene receive more attentions recently. Among them, using a few layers of phosphorene, the field-effect transistor has been fabricated successfully [8], which is a highly desirable device for bio-detection and bio-sensing [9,10]. As photo-thermal agents [11], phosphorus nanosheets (multiple layers of black phosphorene) also show the excellent potential in killing some cancer cells [12]. Moreover, phosphorene exhibits low disruption to protein’s structure [13] and can be a carrier of small drug molecules [14]. These demonstrate that phosphorene is a potential nanomaterial in biomedical applications. However, Martel et al. [15] show that the phosphorene can be oxidized easily in the water, which is a ⁎
disadvantage for biological applications because biological systems often contain a large amount of water. Subsequently, this limitation is overcome by Ruoff et al. [16]. They reveal that the phosphorene is easily oxidized because it reacts with the dissolved oxygen in water, not water itself. Actually, phosphorene in oxygen-depleted water is stable. This property, combined with its biological applications, makes phosphorene an excellent candidate for nanofluidic systems [17]. Consequently, wider applications of this novel nanomaterial require more extensive studies on its interactions with biomolecules, including the diffusive properties of water nanodroplets on its surface. In recent years, the diffusive properties of water nanodroplets on 2D materials, such as graphene [18,19], boron nitride (BN) sheet [20], tungsten disulfide (WS2 ) and molybdenum disulfide (MoS2 ) [21], attract great attentions. In the nanoscale, the surface of these 2D materials plays an essential role in fluid motion due to the high ratio of surface area to volume. Additionally, the surfaces of these 2D materials
Corresponding authors. E-mail addresses: [email protected] (S. Tang), [email protected] (Y. Li).
https://doi.org/10.1016/j.commatsci.2020.109623 Received 15 December 2019; Received in revised form 19 February 2020; Accepted 24 February 2020 0927-0256/ © 2020 Elsevier B.V. All rights reserved.
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are easily affected by additional physical fields, such as mechanical deformation, temperature and electric/magnetic field. Hence, many researchers have studied the diffusion of water molecules on the 2D materials under imposed external fields. For example, Kargar et al. [22] have studied the deformation of water nanodroplets on graphene under the electric field, and found that the nanodroplet is elongated in the direction of imposed electric field. Ma et al. [23] have investigated the diffusion of water nanodroplets on graphene under the imposed compressive strain and reported that the compressive deformation leads to exceedingly fast diffusion of water nanodroplets. Rajegowda et al. [24] have explored the motion of water nanodroplets on boron nitride surface by temperature gradient, which leads to fast movement of water molecules. These works indicate that the external physical fields have a pronounced effect on the diffusion of water nanodroplets on the surface of 2D materials. These effects can be a crucial point for potential application on water-droplets’ self-removal [25,26], water-droplets’ transport [27] and water-droplets’ control [28], three important aspects in the field of water nanodroplets. Nevertheless, the fundamental understanding on diffusion of water nanodroplets on phosphorene is still limited [29,30,17]. The diffusion behavior of water nanodroplets on phosphorene under compression at different temperatures has not been studied, to the best of our knowledge, which deserves in-depth understanding for future applications of phosphorene. In this study, we use molecular dynamics (MD) simulations, which are widely adopted in the study of the interactions of (bio) molecules with nanomaterials, to investigate the diffusion of water nanodroplets on phosphorene under compression at different temperatures. We find that the diffusion of water nanodroplets on the phosphorene surface is highly anisotropy. The strain-weaken and temperature-enhanced water diffusion are observed at different ranges of strain and temperature, respectively. In order to further understand this interesting diffusion behavior, the morphology of phosphorene and trajectory of water nanodroplet are investigated in detail. This diffusion behavior is further explained by interfacial friction coefficient and diffusion energy barrier between phosphorene and water. Finally, the effects of Lennard-Jones (L-J) parameters and size of water nanodroplets on the diffusion behavior are given.
equilibrium states. The MD simulations are performed with a 35 × 50 × 1 supercell (161.2 × 163.6 Å) for phosphorene and 294 molecules for water nanodroplet. Periodic boundary conditions are applied along the x , y and z directions. A vacuum of 2.5 nm is employed along the direction perpendicular to the plane of phosphorene, to avoid slab’s interaction with its periodic images. TIP4P/2005 potential [31] and the improved Dreiding force field [32] are used for the water molecules and phosphorene, respectively. The interaction between water and black phosphorus is described by Lennard-Jones (L-J) 6–12 potentials between the oxygen and phosphorus atoms with parameters lj = 10.7 meV and lj = 0.324 nm [29,33]. The O–H distance and the H–O–H angle are fixed by the SHAKE algorithm [34]. The electrostatic interaction is considered by the particle–particle particle-mesh (PPPM) solver [35]. A cut-off distance of 1.0 nm is used for the L-J potential and PPPM solver. The linear momentum of the phosphorene is kept to be zero. The equilibration phase is firstly carried out in the canonical (NVT) ensemble for a total of 500 ps with a 2 fs time step. The temperature of the water molecules in the starting box-like configuration is initialized at 1 K and then increases to 300 K with 50 K increments. A continuous optimization is applied to the system for 2.5 ns until the energy and pressure reach equilibrium under the NPT ensemble controlled by the Nose–Hoovers thermostat [36]. The box dimensions along the armchair and zigzag directions are allowed to fluctuate freely in response to the barostat (pressured fixed at 0 atm) in this process. Therefore, phosphorene shows a little bending after the equilibration (cf. Fig. 1c). The dimension of phosphorene changes from the original 161.2 × 163.6 Å to 160.2 × 162.6 Å. After this equilibration period (a total of 3 ns), the compressive strain is then applied by a strain rate 1 × 10 8 fs in the NVT ensemble. The temperature is set to 300 K in this process. After that, the temperature of phosphorene is increased to the target temperature (290, 310, 320, 330, 340 K) in the NVT ensemble and the thermostat on the water molecules is removed (i.e. microcanonical ensemble). In other words, the case considered here is that water nanodroplet diffuses on a heated phosphorene. Finally, the coordinates and velocities of all the atoms are recorded every 2 ps for at least 24 ns, and the trajectory of the last 12 ns is extracted for further analysis. All MD simulations were performed by Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software [37]. Note that the strain discussed here is defined as the compressive strain and T is the temperature of phosphorene. The phosphorene with the size of 160.2 × 162.6 Å is treated as the initial one, i.e., = 0 . If x = 1.0% is applied to the phosphorene, the size of phosphonene is changed from 160.2 × 162.6 Å to 158.6 × 162.6 Å. The first-principle calculations are carried out by the Vienna ab initio simulation package (VASP) [38], with core-electron interactions described by PAW pseudo-potentials [39]. The generalized gradient
2. Computational model and methods As a typical 2D material, phosphorene has its own atomistic structure. Fig. 1a shows the special configuration of phosphorene. The x and y directions are defined as armchair and zigzag directions, respectively. The z-axis is perpendicular to the plane of phosphorene. Fig. 1b is the front view of phosphorene from the y direction, wherein the brown and lavender parts represent the top and bottom phosphorus atoms respectively. Fig. 1c shows the phosphorene/water nanodroplet system, in which a water nanodroplet lies on the phosphorene at the initial and
Fig. 1. (a) Top view of the phosphorene’s atomistic structure. Zigzag and armchair boundaries are along the y and x directions, respectively. (b) Front view of phosphorene from the y direction. The top and bottom phosphorus atoms are grouped into two types by different colors. (c) Initial box-like configuration of 294 water molecules before equilibration and final well-formed droplet after equilibration.
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Fig. 2. (a) Snapshots of a water nanodroplet on phosphorene at different simulation time. (a-1) Mean squared displacement (MSD) vs. time for the water nanodroplet. Scale bars: 2 nm. Effects of (b) compressive strain and (c–e) temperature T on the diffusion coefficients D of water nanodroplet.
approximation (GGA) with the general exchange and correlation functions of Perdewe-Burkee-Ernzerhof (PBE) [40] is employed to investigate the exchanging and correlation effects of electrons interactions. A correction to density functional theory (DFT-D) is adopted for considering the interaction of Van der Waals force (VDW) for more accurate calculation [41]. The SCF tolerance quality is set to 1.0 × 10 6 eV/atom. The cut-off energy is 400 eV for the plane-wave basis functions and 4 × 3 × 1 Monkhorste-Pack-point mesh is employed in all the first-principle calculations.
3. Results 3.1. Diffusion coefficients of water nanodroplets Fig. 2a shows snapshots of a water nanodroplet diffusing on phosphorene surface ( = 0 ). For the ease of illustration, CASE XY, CASE X and CASE Y are defined as the case of equal-biaxial compression, uniaxial compression along x direction and y direction, respectively. The corresponding strains are represented by xy, x and y . The phosphorus 3
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atoms are colour-coded according to their heights (H) along the z axis, thus indicating that the water droplets reside within valleys of the ripples (blue regions). Fig. 2a-1 shows the mean squared displacement (MSD) vs. time at = 0 , which is used to estimate the diffusion coefficients of the water nanodroplet within the x y plane according to the Einstein relation [42]:
D = lim t
MSD 4t
MSD = < |(r (t )
of morphology in CASE Y ( y = 1.0%, 1.6%, 2.4%). The surface morphologies change a little and all show regular wavy shape. The surface morphology of phosphorene with regular waves, regular folded lines and irregular uneven surface are defined as MC, MB and MA, respectively. Combining the results of diffusion coefficients D vs. temperature (cf. Fig. 2c, d), it indicates that the increase of temperature can facilitate the diffusion of water nanodroplet on phosphorene with MB (regular folded lines) and MA (irregular uneven surface). However, the increase of temperature leads to two different modes with MC (regular waves) at different strain level: at the lower strain level ( 1.4%), the D is oscillating with temperature; at the higher strain level ( 1.4%), the D increases with temperature. It demonstrates that the surface morphology of phosphorene caused by compressive strain governs the diffusion of water nanodroplet at different temperatures. The similar importance of surface morphology in the adhesion of the villin headpiece on phosphorene [13] and water on graphene oxide [47] have been revealed by other researchers. Moreover, in order to better understand the relationship between this oscillation effect and phosphorene’s surface morphology, a further discussion is carried out. q is defined as the impact factor of temperature at different strain levels of y , given by
(1)
r (t 0 )|2 >
(2)
where D is the two-dimensional diffusion coefficient, t is the time, <….> represents the average of all water molecules. Because the MSD vs. time curve is not straight, the Minimum Covariance Determinant (MCD) [43] method is used to detect outliers and then fit for the diffusion coefficient D. Fig. 2b–e plot diffusion coefficients vs. compressive strain or temperature. Six different imposed strains ( = 0, 0.6%, 1.0%, 1.6%, 2.0%, 2.4%) and temperatures (T = 290, 300, 310, 320, 330, 340 K) are investigated. 1.4% and 1.4% are defined as i and ii respectively (cf. The regions Fig. 2b). In the region i , the diffusion coefficient D gradually decreases as the strain increases in the three deformation cases (CASE XY, CASE X and CASE Y). In the region ii , the diffusion coefficient D increases faster with the increasing strain in CASE XY (black triangle) or CASE X (red star), but it increases in an oscillating way with the increasing strain in CASE Y (blue circle). At the small compressive strain level (region i ), the diffusion coefficient D is smaller than that without any compressive deformation. It means that the small compressive strain is not conducive to diffusion of water nanodroplets. One of the possible reasons is that the thermal vibration of phosphoenene under small compressive strain (strain below 1.0%) can not effectively promote the moving of water nanodroplets. It is very different from the graphene. Ma et al. [23] have showed that the diffusion coefficient of water nanodroplets on the graphene increases linearly with the compressive strain. Fig. 2c shows diffusion coefficient D vs. the temperature T at the strain level = 2.4% . It shows the diffusion coefficient D linearly increases with temperature T in the three deformation cases, although it has a little oscillation for CASE Y. The magnitude of diffusion coefficient D is about twice (T = 340 K) of that at T = 290 K in the CASE XY. The same is observed for = 1.6% in Fig. 2d. However, for = 1.0% (Fig. 2e), the diffusion coefficients D in these three loading cases are oscillating as T increases. The thermal vibration of phosphorene and the friction force between water nanodroplets and phosphorene are two important driving forces for the diffusion of water droplets. The most possible reason resulting in the oscillating trend shown in Fig. 2e is the competitive contributions to water nanodroplets motion from thermal vibration of phosphorene and friction force. Further work should be carried out to elaborate the detailed underlying mechanisms. In a word, similar to electrical conductance [44], thermal conductivity [45] and optical properties [46] of phosphorene, the diffusion of water nanodroplet on phosphorene under compression at different temperatures also shows strong anisotropy.
q=
Dmax Dmin Dmin
(3)
where Dmax and Dmin are the maximum and minimum diffusion coefficients from T = 290 K to T = 340 K at strain level less than 1.4%, such as Dmax = 0.73 × 10 4 cm2 /s and Dmin = 0.52 × 10 4 cm2 /s at strain level y = 1.0% (cf. Fig. 2e). Hence, a lower q means a lower oscillation amplitude of diffusion coefficients D. Fig. 4a shows the simplified diagram of phosphorene with regular waves (MC). h and d are the distances between peaks and valleys along z and y directions, respectively. The value of h, d and h/ d varying with y are summarized in the Table 1. The h and d are obtained by the average of ten configurations at different time in T = 300 K. The effects of temperature on h and d are ignored, because no evident changes in the h and d are observed for the various temperature considered in our study. It can be seen that the value of h/ d is higher as y increases. From Fig. 4b, q decreases with the y increasing. Therefore, a higher value of h / d means a lower q, indicating the oscillation of D caused by temperature has a lower amplitude at a higher value of h/ d . In other words, the influence of temperature on the diffusion of water nanodroplet on phosphorene with regular waves (MC) is smaller with a higher h/ d . 3.3. Trajectory of water nanodroplets Fig. 5 shows the trajectory of a water nanodroplet moving on the phosphorene under different levels of stain and temperatures in a total simulation time of 12 ns. The distance from the point on the trajectory to the origin of coordinates represents the distance from the current position of water nanodroplet to its reference position. The x and y axes in Fig. 5 represent the moving distance of water nanodroplet along x and y directions, respectively. Fig. 5a plots the trajectory in three different situations ( xy = 0.6%, x = 0.6%, y = 0.6%) at a constant temperature T = 300 K. It is clearly identified that the displacement along y direction traveled by water nanodroplet is larger than that along x direction at the end of 12 ns. For example, the displacement along y direction traveled by water nanodroplet at the strain level y = 0.6% is about 100 Å but 75 Å along x direction. Fig. 5b plots the trajectory in other three different situations ( xy = 2.4%, x = 2.4%, y = 2.4%) at a constant temperature T = 300 K. We can see that the displacement along y direction traveled by water nanodroplet is larger than that along x direction shown by the blue line ( y = 2.4%). However, no such feature exists, as observed from the black line ( xy = 2.4%) and red line ( x = 2.4%). This feature that water molecules are more favorable to move along the y direction is defined as ‘travel preference of water
3.2. Morphology of phosphorene under compression Fig. 3 shows the snapshots of phosphorene’s morphology under different levels of compressive strain. The color of plots represents the height (H) of phosphorous atoms along z (out-of-plane) direction. The blue represents the valley and red represents the bulge, which qualitatively judges the flatness of phosphorene. The black cube indicates the simulation box. The top row shows the variation of surface morphology in CASE X ( x = 1.0%, 1.6%, 2.4%). It shows that the morphology of phosphorene changes a lot with increasing strain, from regular waves ( x = 1.0%) to irregular uneven surface ( x = 2.4%). The middle row shows the variation of surface morphology in CASE XY. It shows that the surface morphology changes from regular waves ( = 0 ) to regular folded lines ( = 2.4% ). The bottom row shows the variation 4
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Fig. 3. Snapshots for morphology of phosphorene under different levels of compressive strain. The morphologies of phosphorene with regular waves, regular folded lines and irregular uneven surface are defined as MC, MB and MA, respectively. The H labeled with color represents the height of phosphorous atoms along z (out-ofplane). The top, middle and bottom rows show the variation of phosphorene’s morphology with compressive strain for CASE X, CASE XY and CASE Y, respectively.
nanodroplet’. Meanwhile, the morphology of phosphorene at y = 2.4%, xy = 0.6%, x = 0.6% and y = 0.6% all belongs to MC, implying that water molecules are more favorable to move along the y direction with MC. Fig. 5c plots the trajectory at different temperatures with a constant strain y = 2.4%. It shows a strong ‘travel preference of water nanodroplet’ and the temperature has no obvious effect. To further understand the ‘travel preference of water nanodroplet’ caused by MC, a series of calculations are carried out and the results are plotted in Fig. 6. is a ratio defined by = y / x , where y and x are the displacements of water nanodroplet traveled along y and x directions in a total of 12 ns, respectively. A higher means an obvious ‘travel preference of water nanodroplet’. Fig. 6 shows vs. the compressive strain with three deformation cases. Each data point is the average of the results obtained from three individual MD simulations by adjusting the initial position of water nanodroplet. The black circle, red star and blue square represent results of CASE XY, CASE X and CASE Y, respectively. The temperature is fixed at 300 K. The dotted purple area indicates that the morphology of phosphorene under these strains exhibits the characteristics of MC. The black dotted line represents the contour of = 1. The ‘travel preference of water nanodroplet’ is pronounced when the morphology of phosphorene is more like MC, especially when y 1.6%. The rest do not show this. They are evenly distributed above and below the black dotted line of = 1.
=
1 AkB T
t 0
dt < F (t ) F (0) >
(4)
where F (t ) is the total tangential force exerted by the water droplet on the phosphorene surface and calculated from the data shown in Fig. 7a and b (F = (Fx 2 + Fy2) ); kB is the Boltzmann constant, and T is the water temperature. The droplet-surface contact area A in all situations are taken as 7.06 nm2 , although it is slightly affected by the imposed strain and temperature. A similar methodology has been adopted by Zheng et al. [51]. The force auto-correlation function < F (t ) F (0) > can be computed in our equilibrium MD simulations. The same method can be found from Xiong [52] and Zhou’s work [53]. From the equilibrium MD simulations, the instantaneous lateral forces F (t ) between water and phosphorene were output every 100 fs. Fig. 8a shows the frictional coefficient vs. the time under the compressive strain xy = 2.4% at temperature T = 320 K. It can be seen from Fig. 8 that the correlation function < F (t ) F (0) > decays exponentially with time t . Within 1.5 ps, saturates. From the plateau regime, we obtain = 0.42 × 106 Ns/m3 . Fig. 8b shows the friction coefficient as a function of xy at three different temperatures. A higher is less favorable to the diffusion of water [24,52,48]. We find that the decreases with the temperature at xy = 1.6, 2.0, 2.4%. Hence, it may be the reason that diffusion coefficients D increase with the temperature (the black dotted line in Fig. 2c). When xy = 0, 0.6%, 1.0%, the does not exhibit a simple relationship with temperature. On the other hand, the first increases and then decreases with the strain. It explains the opposite trend for the diffusion coefficients D under xy (see the black triangle of Fig. 2b). Fig. 8c shows the as a function of T at the strain level x = 2.4% and y = 2.4%. decreases with temperature both at x = 2.4% and y = 2.4%. It is consistent with the observed trend of the corresponding diffusion coefficients. Note that the friction coefficient in our work is about 4 × 105 Ns/m3 , whereas it is about 1 × 10 4 Ns/m3 at water-graphene interface [48], 2 × 105 Ns/m3 at water-molybdenum disulfide (MoS2 ) interface [53] and 3 × 105 Ns/m3 at water-hexagonal boron nitride (BN) interface [54]. This indicates that the diffusion of water on phosphorene surface is more difficult, meaning that phosphorene is
4. Discussion 4.1. Friction coefficient of water nanodroplet on phosphorene The interfacial friction coefficient ( ) at the droplet/phosphorene interface is investigated to further address the characteristics of water diffusion on phosphorene. The friction coefficient is the intrinsic property to characterize the interfacial dynamics [48]. It can be expressed via the Green–Kubo (GK) relationship, which relates to the auto-correlation function of fluctuating pairwise forces at equilibrium [49,50], given by 5
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Fig. 4. (a) A simplified diagram of phosphorene with regular waves (MC). h and d are defined as the distances between peak and valley along z and y directions, respectively. (b) The temperature impact factor q as a function of the y .
more hydrophilic than graphene, which has been observed in previous studies [55,56].
Table 1 The values of h, d and h/ d with different y . The units of h and d are Å. The h and d are obtained by the average of ten configurations at different time at T = 300 K. y
0 0.3% 0.6% 0.8% 1.0% 1.2%
h (Å)
d (Å)
h/d
13 14.2 16.2 17.4 18.5 19.4
76 77.5 78 81 80.2 79.8
0.171 0.183 0.207 0.214 0.23 0.243
4.2. Diffusion energy barrier of water on phosphorene To better understand the anisotropy diffusion of water nanodroplet, the diffusion energy barrier of a single water molecule on the phosphorene is estimated by the first-principle calculations. The diffusion energy barrier is an important indicator for the diffusion [57,58]. Fig. 9a shows the simulation setup including a water molecule adsorbed on a phosphorene (2 × 2 × 1 unit cells), and the shape of the water molecule is based on Ma’s research [19]. The top and bottom of 9a show the views of the system from z and y directions, respectively. Two colors of phosphorene represent two different layers of phosphorus 6
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Fig. 5. Trajectory of water nanodroplet on phosphorene under (a, b) different levels of compressive stain and (c) temperatures over 12 ns.
Fig. 6. Ratio
vs. strain
for CASE XY, CASE X and CASE Y.
atoms. The vertical distance from oxygen atom in water molecule to the first layer of phosphorus atom is defined as d 0 . Fig. 9b shows four different adsorption sites, represented by , , and . All adsorption sites are the positions where the oxygen atom is projected on the x y plane. The adsorption site is in the middle of atoms I and J. The is the intersection of the line passing the first adadsorption site sorption site along the y axis and the line with atoms I and M. The positions of adsorption site and are similar to and , respectively. In our MD simulations, the phosphorene has a little residual deformation after equilibrium under the NPT ensemble with normal pressure and temperature, which is also observed in previous works [59]. To be comparable with MD simulations, a pre-compressive strain xy = 0.6% is then applied to the initial configuration of phosphorene. This phosphorene with a tiny deformation is used as our new initial configuration for the first-principle calculations, i.e., = 0 . The compressive strain is applied by setting the lattice constant with a smaller value than that of the equilibrium structure. The present approach for applying compressive strains is also adopted in previous study [60]. Fig. 9c and d show the adsorption energy Eads vs. d 0 at different adsorption sites at strain level = 0 . The lowest point on the adsorption energy vs. d 0 curve is defined as the optimal Eads . The optimal Eads of and are about −43.9 meV and −44.5 meV, respectively. The optimal Eads of and are about −84.2 meV and −81.5 meV, respectively. A higher absolute value of the Eads implies a stronger adsorption and more stable system. In other words, the water molecule is preferred to be attached on the bottom phosphorus atoms, which is consistent with Zhang et al. [29] and Ruoff et al. [16]. In addition, the energy difference between with is 39.7 meV, which can be approximated as the required energy for the water molecule to move along the x direction; the energy difference between and or and is less than 3 meV, which can be approximated as the required energy for the water molecule to move along the y direction. Hence, the required energy for the water molecule to move along the x direction is much higher than that
Fig. 7. Change of the tangential force along (a) x direction and (b) y direction acting on the water nanodroplet over 12 ns.
along the y direction, implying that water molecules are easier to move along the y direction. This phenomenon is also observed from the adsorption of various organic molecules on phosphorene by Otyepka et al. [61]. This may be an possible reason for the ‘travel preference’ of water nanodroplet along y direction (Figs. 5 and 6). The diffusion energy barrier is defined as E = (Eads )max (Eads )min , where (Eads )max and (Eads )min are the maximum and minimum of optimal Eads for , , and , respectively. E vs. is plotted in Fig. 10. The black triangle, red star and blue circle represent the CASE XY, CASE X and CASE Y, respectively. A higher diffusion energy barrier means that diffusion is more difficult. The E increases first and then decreases as the strain increases, implying that the diffusion coefficient D first decreases and then increases. It is consistent with our previous results (cf. Fig. 2b). The E for the CASE XY is smaller than the others. It means that equal biaxial compression is the most beneficial one to the diffusion of water molecule on phosphorene under different compressive deformations. 7
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Fig. 9. Water adsorption structures and adsorption energy Eads vs. distance d0 . (a) The adsorption structure shown from z direction (top) and y direction (bottom). (b) Four different adsorption sites: , , and . Eads as a function of d0 for (c) , and (d) , .
phosphorene structure but is described by graphene’s potential parameters, which are set as lj = 3 meV and lj = 0.4 nm [19]. In order to reduce computational complexity, only equal biaxial compression is discussed here. Fig. 11 shows the diffusion coefficients D of water nanodroplet on pseudo-phosphorene as a function of xy . The D is first reduced and then increased as the imposed strain increases, which is similar to that for water on phosphorene but different from that for water on graphene [23]. The magnitude of diffusion coefficients D changes a lot, which is caused by the different L-J parameters. Hence, it concludes that the L-J parameters may play a crucial role on the magnitude of diffusion coefficients but has no evident influence on the trend of diffusion coefficients under compression. The size of water nanodroplets also can affect the diffusion [65,66]. In order to verify the validity of our main conclusion for different size of water nanodroplets, two other water-phosphorene systems are also built: 525 and 812 water molecules on phosphorene. Fig. 12a and b show the snapshots of 525 water molecules and 812 water molecules moving on phosphorene surfaces ( = 0 ). According to the above
Fig. 8. (a) Theoretical calculation of the friction coefficient for water nanodroplet on phosphorene. Inset: Time-dependency of the force auto-correlation function. The dotted line is the fitting result. (b) The friction coefficient vs. xy at different temperatures. (c) The friction coefficient vs. T at strain levels x = 2.4% and y = 2.4% .
4.3. Influences of L-J parameters and size of water nanodroplets The L-J parameters for the interaction between water nanodroplet and 2D materials play important roles on the adsorption and diffusion of water [62]. It can affect the diffusion speed or the diffusion tendency of water on 2D materials [63,64]. To investigate the influence of L-J parameters on the diffusion of water on phosphorene under compression, we construct a model material: a pseudo-phosphorene with 8
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Fig. 10. Diffusion energy barrier E vs. the imposed strain for CASE XY, CASE X and CASE Y.
Fig. 11. Effect of xy on the diffusion of water nanodroplet on pseudo-phosphorene at T = 300 K . The dotted line is a guide to the eye.
Fig. 12. Snapshots of (a) 525 and (b) 812 water molecules on phosphorene. Scale bars: 2 nm. Effects of xy (c) and T (d) on the diffusion coefficients D for 525 and 812 water molecules on phosphorene.
method, the compressive strain is applied to phosphorene at different temperatures. In order to reduce computational cost, only equal biaxial compression is discussed here. The results are shown in Fig. 12c and d. The trend of D vs. the imposed strain or temperature is the same as the previous ones (cf. Fig. 2) but the magnitude of D decreases. Therefore, the size of water nanodroplets will not affect our main conclusion. The reason of the decrease of D is that the water nanodroplet is larger with more water molecules. A larger water nanodroplet corresponds to the lower diffusion speed, which is also reported in other 2D materials [23,30].
increases, the diffusion coefficients increase linearly in three deformation cases. The surface morphology of phosphorene and the trajectory of water nanodroplet are also analyzed. An obvious ‘travel preference’ of water nanodroplet is observed when water nanodroplet diffuses on phosphorene with regular waves. Subsequently, we calculate the friction coefficient and diffusion energy barrier E , which are two critical factors for diffusion of water nanodroplets. The interfacial friction coefficient increases first and then decreases as xy increases at a constant temperature. It reduces as the temperature increases when xy 1.6%, which is consistent with our results for the diffusion coefficients. Similarly, the E is first increased and then decreased as the strain increases, meaning the diffusion of water nanodroplets first slows down and then speeds up. Finally, extension is made to analyze the effects of L-J parameters and size of water nanodroplets on the diffusion coefficients. In summary, nanodroplet transport on compressed phosphorene surface at different temperatures has been studied systematically, which can give molecular insights on developing novel phosphorenebased nanofluidic devices. The proposed method is not limited to phosphorene, which may be found to be useful in biotechnology for other applications involving water droplets and 2D materials.
5. Concluding remarks In this work, MD simulations have been performed to investigate the diffusion of water nanodroplets on phosphorene under compression at different temperatures. Three compressive loadings xy, x , y are imposed to phosphorene. Our results show that the diffusion coefficients D of water nanodroplet are first reduced and then increased with the strain increasing in three deformation cases at T = 300 K. As T increases, the diffusion coefficients D present two different modes: in the regime of lower strain (e.g. = 1.0% ), the diffusion coefficients oscillate with the increase of T; in the regime of higher strain (e.g. = 2.4% ), as T
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CRediT authorship contribution statement
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Lijun Deng: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. Ling Wan: Conceptualization, Investigation, Methodology, Resources, Validation, Visualization, Writing - review & editing. Nian Zhou: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing original draft, Writing - review & editing. Shan Tang: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Validation, Writing - review & editing. Ying Li: Conceptualization, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement S.T. appreciates the support from NSF of China (Project No. 11872139, 11472065). References [1] W. Lu, H. Nan, J. Hong, Y. Chen, Z. Chen, L. Zheng, X. Ma, Z. Ni, C. Jin, Z. Zhang, Plasma-assisted fabrication of monolayer phosphorene and its raman characterization, Nano Res. 7 (6) (2014) 853–859. [2] H. Liu, Y. Du, Y. Deng, P.D. Ye, Cheminform abstract: semiconducting black phosphorus: Synthesis, transport properties and electronic applications, Chem. Soc. Rev. 44 (9) (2015) 2732–2743. [3] Z.X. Hu, X. Kong, J. Qiao, B. Normand, W. Ji, Interlayer electronic hybridization leads to exceptional thickness-dependent vibrational properties in few-layer black phosphorus, Nanoscale 8 (5) (2016) 2740–2750. [4] H. Liu, K. Hu, D. Yan, R. Chen, S. Wang, Recent advances on black phosphorus for energy storage, catalysis, and sensor applications, Adv. Mater. 30 (32) (2018) 1800295. [5] A. Carvalho, W. Min, Z. Xi, A.S. Rodin, H. Su, A.H.C. Neto, Phosphorene: from theory to applications, Nat. Rev. Mater. 1 (11) (2016) 16061. [6] L. Wang, K. Cai, Absorption and temperature effects on the tensile strength of a black phosphorus ribbon in argon environment, Comput. Mater. Sci. 150 (2018) 15–23. [7] V. Sorkin, Y.W. Zhang, Effect of edge passivation on the mechanical properties of phosphorene nanoribbons, Extre. Mech. Lett. 14 (2017) 2–9. [8] L. Li, Y. Yu, G.J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X.H. Chen, Y. Zhang, Black phosphorus field-effect transistors, Nat. Nanotechnol. 9 (5) (2014) 372–377. [9] H. Im, X.-J. Huang, B. Gu, Y.-K. Choi, A dielectric-modulated field-effect transistor for biosensing, Nat. Nanotechnol. 2 (7) (2007) 430–434. [10] M.T. Martinez, Y.C. Tseng, N. Ormategui, I. Loinaz, R. Eritja, J. Bokor, Label-free dna biosensors based on functionalized carbon nanotube field effect transistors, Nano Lett. 9 (2) (2009) 530–536. [11] Z. Sun, H. Xie, S. Tang, X.-F. Yu, Z. Guo, J. Shao, H. Zhang, H. Huang, H. Wang, P.K. Chu, Ultrasmall black phosphorus quantum dots: synthesis and use as photothermal agents, Angew. Chem. Int. Ed. 54 (39) (2015) 11526–11530. [12] H. Wang, X. Yang, W. Shao, S. Chen, J. Xie, X. Zhang, J. Wang, Y. Xie, Ultrathin black phosphorus nanosheets for efficient singlet oxygen generation, J. Am. Chem. Soc. 137 (35) (2015) 11376–11382. [13] Z. Wei, T. Huynh, X. Peng, Z. Bo, Y. Chao, B. Luan, R. Zhou, Revealing the importance of surface morphology of nanomaterials to biological responses: adsorption of the villin headpiece onto graphene and phosphorene, Carbon 94 (11) (2015) 895–902. [14] W. Tao, X. Zhu, X. Yu, X. Zeng, Q. Xiao, X. Zhang, X. Ji, X. Wang, H. Zhang, L. Mei, Black phosphorus nanosheets as a robust delivery platform for cancer theranostics, Adv. Mater. 29 (32) (2017) 1603276. [15] A. Favron, R. Martel, Photooxidation and quantum confinement effects in exfoliated black phosphorus, Nat. Mater. 14 (8) (2015) 826–832. [16] H. Yuan, J.S. Qiao, H. Kai, S. Bliznakov, E. Sutter, X.J. Chen, L. Da, F. Meng, S. Dong, J. Decker, Interaction of black phosphorus with oxygen and water, Chem. Mater. 28 (22) (2016) 8330–8339. [17] Z.-Q. Zhang, H.-L. Liu, Z. Liu, Z. Zhang, G.-G. Cheng, X.-D. Wang, J.-N. Ding, Anisotropic interfacial properties between monolayered black phosphorus and water, Appl. Surf. Sci. 475 (2019) 857–862. [18] J.E. Andrews, S. Sinha, P.W. Chung, S. Das, Wetting dynamics of a water nanodrop on graphene, Phys. Chem. Chem. Phys. 18 (34) (2016) 23482–23493.
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