A Simple Method to Measure the Contact Angle of Metal Droplets on Graphite

The determination of solid–liquid interfacial tension plays an important role in science and technology. Here, we propose a simple method to directly measure the contact angle between metal droplets and a graphite substrate for the determination of metal–graphite interfacial tension. The proposed method involves the synthesis of micro- and nanosized metal droplets on graphite by arc melting. Owing to its small volume, the rapid cooling of the prepared metal droplets on the graphite substrate leads to the freezing of equilibrium contact configuration after solidification. We observe that the measured contact angle between micro- and nanosized Au (or Ag) particles and the graphite substrate is almost size independent, even though the size of the particles synthesized herein is 1–3 orders of magnitude smaller than that studied in previous works. In addition, the interfacial tensions of Au and Ag on the step edges (edge plane) of graphite are found to be larger than that on the (0001) plane (basal plane). The proposed method provides a simple approach to determine the solid–liquid interfacial tension and may be effective in the study of interface related science and technology. A simple method to directly measure the contact angle between metal droplets and graphite by the fast cooling of metal droplets on graphite. The contact angle between micro- and nanosized Au (Ag) particles and graphite is almost size independent. The contact angle and interfacial tension of Au (Ag) on the step edges of graphite are much larger than that on the basal plane of graphite. A simple method to directly measure the contact angle between metal droplets and graphite by the fast cooling of metal droplets on graphite. The contact angle between micro- and nanosized Au (Ag) particles and graphite is almost size independent. The contact angle and interfacial tension of Au (Ag) on the step edges of graphite are much larger than that on the basal plane of graphite.


Introduction
Matter interaction at homogenous or heterogeneous interfaces is a fundamental and interesting topic in interfacial science [1][2][3][4][5][6] and is important in determining the characteristics of numerous applications, such as metal matrix composites [7][8][9], carbon-supported metal catalysts [10][11][12], thermal conduction [13,14], and friction/wear behaviors [15][16][17].Recently, Fan et al. [6] elucidated the underlying mechanism of capillary force balance at the contact line and validated Young's equation based on the mechanical interpretation.The interfacial energy (tension) between metal and nonmetal determines the physical and chemical behavior of the metal on the nonmetal substrate.Characterization of the wetting behavior of a metal on a substrate is the primary approach to detect their interactions based on the Young's equation: where γ M and γ S are the surface tensions of metal and substrate, respectively; γ MS is the interfacial tension between the metal and the substrate; θ is the contact angle at equilibrium.The contact angle is uniquely determined by γ M , γ S , and γ MS , and Eq. ( 1) describes the balance of the three interfacial tensions parallel to the metal-substrate interface illustrated in Fig. 1.
Graphite, a member of the carbon material family, has important applications including electrodes [18,19], solid lubricants and superlubricity [20][21][22], metal brazing [23,24] reinforced composites [25,26], etc.Most of them are closely related to the interfacial interaction.However, only a few experimental studies have been conducted on the interfacial interaction between metal and graphite.By using the sessile drop technique, Kaiser et al. [27] measured the wetting angle of molten Ge on graphite and other substrates and determined the surface tension of Ge as 591 mN/m at the melting point.The method involves the direct measurement of the wetting angle by melting metals on the graphite substrate [28][29][30].Lee et al. [28] conducted wetting experiments under a purified Ar atmosphere at 1300 K and measured the contact angles of liquid Au and Ag on the (0001) plane of graphite as 129° and 124°, respectively [28].Naidich and Kolesnichenko [31] determined the contact angle of Ag on graphite to be 136° at 1253 K under vacuum conditions.In addition, the effects of alloying on interfacial interaction in AgSn-, AgCu-, and CuCr-graphite systems were investigated by the sessile drop method [30,[32][33][34].Some investigations demonstrated that the temperature (above and near the melting point) has minimal influence on the contact angle of Ag and AgSn droplets on the graphite substrate [30,35] but considerable influence on that of Cu and CuSnTi on the graphite substrate [34,36].
Based on the above brief review, it is noted that the sessile drop method has a limitation: The measurement of contact angle relies on a special instrument that should combine metal heating in a protected environment (with inert gas or (1) M cos = S − MS , vacuum conditions) with an imaging system [37].To the best of our knowledge, only a few studies have focused on the wetting of graphite by solid metals [38][39][40].For example, Gangopadhyay [38] investigated the effect of solute segregation on the interfacial tension of Pb and Au alloyed with Ni on graphite and reported that the contact angle of solid Au on graphite is 131°, which is slightly higher than that of liquid Au on graphite (129°) [28].Wang et al. [39] investigated the wettability of Pb-Ni alloy on graphite using a scanning Auger microprobe.The alloy was prepared using liquid droplets, which were cooled rapidly for solidification.The contact angle of pure Pb particles on graphite was determined to be ~ 119°.
Herein, inspired by the existing methods for the fabrication and characterization of nanosized molten metals [41], we developed a simple technique to determine the wettability of metal droplets on highly oriented pyrolytic graphite (HOPG).Metal droplets with micro-and nanoscale diameters were prepared by arc melting.The small size of metal droplets allows them to cool rapidly such that their equilibrium contact configurations can be frozen after shutting off the arc.The contact angles of pure Au, Ag, Cu, Pb, and Ge micro-and nanosized metal droplets on the basal plane of HOPG were measured.The results showed that the contact angles of Au and Ag droplets on the edge plane (step edges) of HOPG were larger than those on the basal plane.Finally, the interfacial tension between the considered metals and HOPG, and the corresponding adhesion work were calculated based on the Young's equation.

Experimental Details
Figure 2a shows the experimental setup for the fabrication of metal nanoparticles on HOPG by electric arc (EA) melting of bulk metal in a vacuum chamber.The bulk HOPG was purchased from Nanjing XFNANO Materials Technology, Co., Ltd., China.In the experiments, a bulk HOPG substrate with a clean surface was first obtained by mechanical exfoliation [42,43].As shown in Fig. 2b, the layered structure of the exfoliated HOPG has two planes: basal and edge planes.The basal plane of HOPG consists of layers of Fig. 1 Schematic illustration of an equilibrated metal droplet on a highly oriented pyrolytic graphite substrate with the metallophobic and metallophilic states corresponding to a contact angle of a > 90° and b < 90°, respectively graphite stacked along the [0001] direction, and the surface steps in the HOPG substrate form the edge plane that contains dangling bonds [44].Pure metal ingots were stacked on the HOPG substrate and placed on the copper plate electrode of an EA furnace (WK-series vacuum electric arc furnace).After the chamber was pumped to reach a pressure of 10 -3 Pa, Ar gas with a purity of 99.99% was injected with a pressure of ~ 400 Pa as the protective gas.Subsequently, the tungsten tip was controlled to move toward the metal ingot/ HOPG substrate and ignited the EA, which was turned off immediately after ignition.Figure 2c and d show the scanning electron microscopy (SEM, Zeiss, Sigma 500) images of the fabricated Au micro-and nanoparticles distributed on the basal and edge planes of HOPG.The spherical shape of the fabricated particles was ascribed to the rapid cooling of the prepared metal droplets on the HOPG substrate.Owing to their small volumes and the good thermal conductance of the metal and HOPG, the particles rapidly solidified such that their equilibrium contact configurations were frozen under the constrain of surface tension.

Contact Angle of Liquid Particles on the Basal Plane of HOPG
Au and Ag particles on the HOPG substrate prepared with the method in Fig. 2a are almost uniformly distributed on the HOPG surface (typically shown in Fig. 2c).However, the contact region is difficult to directly characterize from the side view in SEM, especially when the contact angle is more than 90°.To address this issue, we used a microprobe to manipulate metal particles for easy measurement of contact angle.As illustrated in Fig. 3a and b, the manipulation can be simply realized by controlling a microprobe to approach and push metal particles (see Supplementary Movie S1 for details).Through this manipulation, the contact angle of some particles can be readily measured by matching its circular shape with a circle (red line) (diameter of D) and drawing a straight line (blue line) to measure the diameter (L) of the contact region, as shown in Fig. 3c.On the basis of simple geometric relation, the contact angle can be calculated as follows: where plus and minus were applied for metallophobic and metallophilic cases (Fig. 1), respectively.When the contact angle is π/2, L/D = 1.For particle 1 in Fig. 3c, its D and L were measured as 5.737 and 4.721 μm, respectively.According to Eq. ( 2), the contact angle was 124.6°.Similarly, the contact angle measured from particle 2 was 126.5°.
Interfacial wettability between metal particles and HOPG was determined by following the procedures in Fig. 3 (Movie S1).Typical results for the measured contact angles at Au-HOPG and Ag-HOPG heterointerfaces are shown in Fig. 4. We found that the contact angles of Au (Ag) particles on the basal plane of the HOPG are size independent, and this result is similar to a previous finding [28].However, the size of the prepared metal droplets in our experiments was 1-2 orders of magnitude smaller than that in the literatures.Therefore, we conclude that the contact angle of Au and Ag with HOPG substrate is almost size independent down to tens of nanometers.Meanwhile, the contact angle of Au particles on the basal plane of the HOPG was measured as 132.2° ± 4.4°, similar to the reported values of 129° ± 3° (as black boxes shown in Fig. 4a) [28] and 131° [38] by directly measuring the contact angle of Au melts on a graphite substrate.Herein, 4.4° and 3° represent the standard deviations.We also fabricated Au particles by the same method with a large diameter (up to a hundred microns; see Fig. S1 in Sec. 1 of the Supplementary Materials (SM)).Their measured contact angle was also ~ 132°, demonstrating the robustness of our method and findings.From the combination of all data, the average contact angle of Au particles was determined to be 132.1°± 4.1°.Similarly, the contact angle of Ag particles on the basal plane of HOPG was measured as 125.9° ± 2.5°, which also agrees with the reported values of 124° [28,29] and 125° [30] (Fig. 4b) obtained by directly measuring the contact angle of Ag melts on graphite substrates.These agreements indicate that the contact angle measured by our method corresponds to the contact angle of metal melts on graphite, which we attributed to the small size of metal melts that allow them to cool rapidly to preserve their contact configuration in the liquid state.

Validating the Method for Contact Angle Measurement
To reveal the intrinsic mechanism, we first estimate how rapidly the heat distributes evenly within the particles through the characteristic solidification time (τ) as τ ≈ ρCL 2 /(4κ), where L, ρ, C, and κ denote the particle size, density, heat capacity, and thermal conductance, respectively.Substituting typical values of L = 1 μm, ρ = 19.32 g/cm 3 , C = 129 J/ (kg•K), and κ = 317 W/(mK) for Au, the obtained timescale was as low as τ ~ 10 −9 s.Considering that the HOPG is a good thermal conductor at temperatures below the melting temperature of the particles [45], this estimated value could provide a lower bound of cooling rate.To precisely calculate the particle cooling rates through heat transfer to the HOPG substrate, we applied finite element analysis (FEA) to For comparison, the reported contact angles measured by directly melting metals are also plotted [28] simulate the cooling of an Au particle (see details in Sect. 2 of the SM) on the HOPG.The initial temperature of the melted Au particle was set to T m = 1334 K.At a conservative estimate, if we consider the time taken by the temperature at the maximum point (point A in Fig. 5a) to decrease to 90% of the melting temperature, we obtain τ = 1.4 ns (Fig. 5b) by monitoring the temperature at point A. Considering the effect of the heat of crystallization (Q 0 ) on the cooling of the Au particle, the initial temperature of the melted Au particle increases from T m to T m + ΔT due to Q 0 (see details in Sect. 2 of the SM).Similarly, we consider the time taken by the temperature at the maximum point (point A in Fig. 5c) to decrease to 90% of the melting temperature.Certainly, the heat of crystallization reduced the cooling rate of the Au particles: The cooling time required time to reach 1200 K increased from 1.4 (Fig. 5b) to 3.4 ns (Fig. 5d).However, this result showed that the cooling was still extremely fast.
To further reveal the mechanism underlying the observed spherical shape of metal particles after cooling, molecular dynamics (MD) simulation was performed to investigate the mechanism underlying rapid cooling-based crystallization (see details in Sect. 2 of the SM).First, FEA results showed that the timescale for the temperature decreases from the melting point of Au (T m = 1334 K) down to 0.9T m was 1.4-3.4ns, which is much smaller than the characteristic timescale for a liquid droplet adjusting its equilibrium contact configuration, τ ≈ δ 2 /D = 10 −6 s, where we take the value of δ = 1 nm as the critical size of nucleation and the value of D = 10 −12 m 2 /s as the self-diffusivity of Au atoms in liquid state [46].Such estimations revealed that the microsized metal liquid cools so rapidly that a crystal nucleus can only be formed at a temperature far below the melting point, which was further verified by the MD simulation (Fig. 6).Our simulation results showed that when the cooling of an Au liquid drop occurs rapidly, the nucleation occurs at temperature as low as 637 K (0.48T m ).We also observed that the perfect spherical shape of the Au liquid drop does not change before and after nucleation.Another MD simulation with a cooling rate of ~ 111 K/ns was carried out to make the cooling rate consistent with that in our experiments (96-214 K/ns as estimated by using FEA).As shown in Fig. 7, no crystal nucleus was formed even after the temperature cooled down to 1000 K (0.75T m ).The above simulation results demonstrated that the rapid cooling drastically delays crystallization.Given that the atom diffusivity in supercooled liquids increases exponentially as the temperature decreases, the growth of crystal nuclei is limited by diffusion, and the crystallization of microsized particles is dominated by nucleation (Fig. 6b).Diffusion fails to change the contact configuration.Therefore, the contact configuration actually corresponds to the metal melts on HOPG.

Contact Angle Measurements for Other Materials
The wettability of Cu, Pb, and Ge particles on the basal plane of the HOPG was also investigated by following the procedures in Figs. 2 and 3.The contact angles were determined to be 124.5°± 2.9° for Cu-HOPG, 115.1° ± 4.5° for Pb-HOPG, and 126.7° ± 6.9° for Ge-HOPG (Fig. 8).The contact angle of Cu particles on the basal plane of HOPG (124.5° ± 2.9°) was smaller than that on graphite at 1373 K (140°) [31] and 1418 K (133°) with the graphite (HX30) polished on a 200 grit SiC paper; this phenomenon was ascribed to the mixed edge and basal planes in the graphite surface originating from polishing [35].The obtained contact angle of Pb particles on the basal plane of the HOPG (115.1° ± 4.5°) agrees with the reported values of 117° obtained using the solid-state wetting method [38] and 119° obtained by directly measuring the contact angle of Pb droplets on graphite substrate at 558 K [39].The contact angles of Ge particles on the basal plane in this work were determined as 126.7° ± 6.9°, which is smaller than the previously reported values (157°-166°) obtained using the sessile drops on carbon-based substrates with vacuum conditions [27].Such deviation could be from the substrate differences and vacuum conditions.

Contact Angle of Liquid Particles on the Edge Plane of HOPG
In addition to the wettability of metallic particles on the basal plane of HOPG, we investigated the wetting behavior of metal particles on the step edges (edge plane) by subjecting HOPG to mechanical exfoliation [42,43].Owing to the highly mechanical anisotropy of HOPG, the peeled graphite flakes left a lot of surface steps in the HOPG substrate (Fig. 2b).SEM images of the prepared Au particles on the edge plane of HOPG are shown in Fig. 2d.The contact angles of these Au and Ag particles can be easily determined because the values of D (particle diameter) and L (the diameter of contact region) are easily obtained through SEM (Fig. 2d, inset).As shown in Fig. 9a-b, the contact angles of Au and Ag particles on the edge plane of the HOPG determined from Eq. (2) were 141.1 ± 3.6° and 131.5 ± 5°, respectively, which are larger than those of Au and Ag particles on the basal plane.These differences in the wettabilities of the metal particles on the basal and edge planes of the HOPG were attributed to the differences in the physical/chemical properties of the two planes.The basal plane is highly inert because of the sp 2 -bonded carbon atoms, and step edges have highly active dangling bonds instead of fully coordinated sp 2 bonds [44].The active step edge of HOPG is more easily oxidized than the basal plane [48] and provides more favorable sites for liquid nucleation than the basal plane [49].We observe that the prepared Au particles on the edge plane of HOPG exhibit a denser arrangement than those on the basal plane (Fig. 2d), revealing easier nucleation in the edge plane.Although we carefully selected metal particles located in smooth regions to measure contact angles at the edge planes of the HOPG, this atomic-scale irregular surface topography may lead to differences in contact angles measured at the basal and edge planes of HOPG because the atomic-scale steps may exist in the exfoliated edge planes of the HOPG that is beyond the resolution of SEM.

Determination of Interfacial Tension Between Metals and HOPG
According to the measured contact angles above, the metal-graphite interfacial tension (γ MS ) can be estimated using Young's equation (Eq.( 1)).The surface energy of the basal plane of HOPG was adopted as 150 mN/m from the literatures [50][51][52].For the edge plane of the HOPG, the surface energy can be calculated by γ E = 1346−0.17TmN/m [36], where T is in K.The surface energy of the edge plane is expected to be an order of magnitude higher than that (150 mN/m) of the basal plane because the formation of the edge plane requires the rupture of chemical carbon-carbon bonds [52], which are stronger than the weak van der Waals force for basal planes [53].This high surface energy in the specific surface where the carbon-carbon bonds break was estimated.For example, the formation of the low-energy (111) surface of a diamond requires the breaking of carbon-carbon bonds, and the surface energy was roughly estimated as 4000 mN/m [52].Therefore, we adopted γ E = 1346−0.17TmN/m [36] as the surface energy of the edge plane of the HOPG.A previous study using Here, the surface tensions of melting Au and Ag were obtained by substituting the corresponding melting temperature (Table 1).On the basis of the measured contact angles and Eq. ( 1), the interfacial tension between the tested metals and HOPG was calculated (Table 1).The measured interfacial tension of Au and Ag on the basal planes of the HOPG (1072 mN/m for Au and 792 mN/m for Ag) was consistent with the previous results [28,36].Owing to the higher chemical activity of the edge plane than that of the basal plane in HOPG, the determined interfacial tensions (of Au and Ag) on the edge plane of the HOPG were higher than those on the basal plane (Table 1).From the calculated interfacial tension, the work of adhesion, W MS (van der Waal's interaction), can be easily deduced using the following formula:

Conclusion
Herein, a simple method to investigate the wettability of metal droplets on graphite is proposed.The contact angles of Au, Ag, Cu, Pb, and Ge on the basal plane of HOPG were determined by the direct measurement of the contact angle of the solidified metal micro-and nanoparticles on the HOPG substrate through SEM.Even though the size of the metal particles used here is 1-3 orders of magnitude smaller than that studied in the previous works, the contact angle was found to be size independent.The contact angles of Au and Ag on the basal plane of HOPG measured using our method are consistent with those reported in the previous works obtained by directly measuring contact angle at the melting state.This indicates that the prepared metal droplets in our experiments led to the freezing of the equilibrium contact configuration at a liquid state after cooling, which was further verified by the estimation and comparison of the timescales (3) W MS = S + M − MS of heat transfer and atom diffusion.Based on the obtained contact angles and the Young's equation, the metal-graphite interfacial tension and the corresponding adhesion work were determined.In addition, the wettability of metal droplets on the edge plane of HOPG was investigated.The findings revealed that the contact angles of Au and Ag on the edge plane of HOPG were larger than that on the basal plane due to the differences in physical/chemical properties of the basal and edge planes.The developed method could be extended to measure the wettability of other metals on HOPG or other substrates and probe fundamental interfacial properties in the study of interface-related science and technology.

Fig. 2
Fig. 2 Fabrication of metal nanoparticles on a highly oriented pyrolytic graphite substrate by arc melting.a Sketch of the experimental set-up for preparing metal micro-and nanoparticles on the HOPG substrate using an electric arc furnace.b Sketch of surface steps formed on the HOPG substrate resulting from mechanical exfoliation.c, d Typical SEM images of prepared Au micro-and nanoparticles on the c basal and d edge planes of the HOPG substrate

Fig. 3 Fig. 4
Fig.3Manipulation of the prepared metal nanoparticles on the highly oriented pyrolytic graphite substrate using a micromanipulator (MM3A-EM, Kleindiek Nanotechnik) as observed using a scanning electron microscope (Zeiss Sigma 500).a, b SEM images of Ag particles on the HOPG substrate a before and b after manipulation.

Fig. 5 Fig. 6 Fig. 7 Fig. 8
Fig. 5 Finite element simulation of an Au liquid cooling on a highly oriented pyrolytic graphite substrate.a Temperature distribution at τ = 1.4 ns.b Cooling of the Au particle by monitoring the temperature at point A shown in a.By considering the temperature rise due to the heat of crystallization in Au particles, the obtained c temperature distribution at τ = 3.4 ns, and d cooling of the Au particle by monitoring the temperature at point A, where the initial temperature of the Au liquid is set to T m + 393.5 K

Fig. 9
Fig. 9 Measured contact angles of a Au and b Ag particles on the edge plane of the highly oriented pyrolytic graphite substrate.The dashed lines represent the average values of the measured contact angles.The standard deviation (e.g., 3.6° for Au particles) was calculated based on the measured contact angles of at least 10 particles (with different sizes)

Table 1
Measured contact angles, surface tensions, calculated interfacial tensions, and adhesion work (W MS ) of Au-HOPG, Ag-HOPG, Cu-HOPG, Pb-HOPG, and Ge-HOPG systems based on Eqs.(1) and (3); the melting point (T m ) of the corresponding metals is also shown Bozhao Wu received his Ph.D. from Wuhan University (2022).He currently performs researches as a postdoc fellow at Wuhan University.His current research interest is surface/interface mechanics of low-dimensional materials.
Yongping Kang He is currently a postgraduate at Wuhan University.His current research interest is processing mechanics of metallic glasses and applications.Cai Lu He is currently a Ph.D. student at Wuhan University.His current research interest is nanoforming and nanomechanics of crystalline metals.