Modeling the Interaction between AFM Tips and Pinned Surface

Article pubs.acs.org/Langmuir

Modeling the Interaction between AFM Tips and Pinned Surface Nanobubbles Zhenjiang Guo,† Yawei Liu,† Qianxiang Xiao,† Holger Schönherr,*,‡ and Xianren Zhang*,† †

State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China Physical Chemistry I, Department of Chemistry and Biology & Research Center of Micro and Nanochemistry and Engineering (Cμ), University of Siegen, Adolf-Reichwein-Str. 2, 57076 Siegen, Germany

‡

ABSTRACT: Although the morphology of surface nanobubbles has been studied widely with different AFM modes, AFM images may not reflect the real shapes of the nanobubbles due to AFM tip−nanobubble interactions. In addition, the interplay between surface nanobubble deformation and induced capillary force has not been well understood in this context. In our work we used constraint lattice density functional theory to investigate the interaction between AFM tips and pinned surface nanobubbles systematically, especially concentrating on the effects of tip hydrophilicity and shape. For a hydrophilic tip contacting a nanobubble, its hydrophilic nature facilitates its departure from the bubble surface, displaying a weak and intermediate-range attraction. However, when the tip squeezes the nanobubble during the approach process, the nanobubble shows an elastic effect that prevents the tip from penetrating the bubble, leading to a strong nanobubble deformation and repulsive interactions. On the contrary, a hydrophobic tip can easily pierce the vapor−liquid interface of the nanobubble during the approach process, leading to the disappearance of the repulsive force. In the retraction process, however, the adhesion between the tip and the nanobubble leads to a much stronger lengthening effect on nanobubble deformation and a strong long-range attractive force. The trends of force evolution from our simulations agree qualitatively well with recent experimental AFM observations. This favorable agreement demonstrates that our model catches the main intergradient of tip−nanobubble interactions for pinned surface nanobubbles and may therefore provide important insight into how to design minimally invasive AFM experiments.

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INTRODUCTION The existence of interface nanobubbles was first proposed by Parker et al., who supposed that nanobubbles were responsible for the long-range attraction observed between neighboring hydrophobic objects in aqueous solution.1 The existence of surface nanobubbles was then confirmed experimentally by atomic force microscopy (AFM) measurements, which also indicated that nanobubbles are stable at least for hours.2−11 According to the classical Laplace equation, the internal pressure of surface nanobubbles, which possess small radii of curvature, is much larger than the atmospheric pressure. This pressure was initially thought to drive the gas into the liquid very rapidly, and thus the lifetime of nanobubbles should not exceed tens of microseconds.12 The unexpected stability of nanobubbles has been researched widely13 and has been explained with different models,14,15 including the dynamic equilibrium model.16,17 the contamination model,18 and the high gas density of model19 as well as more recently contact line pinning20−23 and the gas oversaturation model.24,25 Contact line pinning has been confirmed in many studies, and hence this must be taken into account for any model.19,20,23,24 Among the various techniques employed for investigating nanobubbles, which include AFM,2−10,26−31 X-ray reflectivity,32,33 and interference microscopy,34 among others, AFM is © XXXX American Chemical Society

by far the most often used. AFM has a force-sensitive cantilever with one end fixed on a support and a sharp nanosized tip fixed to the other end. Using a highly accurate positioning device, the AFM tip and sample are approaching toward, contacting, and finally retracting from the substrate. The interaction forces will result in the deformation or movement of the cantilever. In the experiment, the tip−sample interaction force is obtained as a function of the tip to sample separation distance.29,30,35 As demonstrated by most AFM investigations, nanobubbles behave as soft matter and exhibit complex force−distance curves.29,30 Furthermore, the shape and wettability (hydrophobicity) of the AFM tip seem to result in significant effects on the measurement of nanobubbles.29,30 For instance, using both hydrophilic and hydrophobic AFM tips, Walczyk and Schönherr investigated the tip−nanobubble interactions and suggested that the hydrophilic tip allows for a better estimation of the height of surface nanobubbles.30 Although the morphology of surface nanobubbles has been studied widely with different AFM modes, AFM images may not reflect the real shapes of the nanobubbles.30 This deviation is related to AFM tip-induced nanobubble deformation or to Received: November 11, 2015 Revised: December 23, 2015

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DOI: 10.1021/acs.langmuir.5b04162 Langmuir XXXX, XXX, XXX−XXX

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Finally, the local density ρi and the Lagrange multiplier κ can be obtained by an iteration algorithm. The simulation box that we chose has a size of 70 × 70 × 70 in lattice units, with a substrate at the bottom of the box normal to the z-direction. Periodic boundaries conditions were employed both in x- and y-directions, while a mirror boundary condition was used in the z-direction. In our simulations, the substrate was covered with a ring pattern of R = 20 (in lattice units) to pin the interface nanobubble. For the substrate, εff and εsf were set to 1.0 and 0.5, respectively, implying that the substrate was hydrophobic. We also built an AFM tip suspended above the substrate with an adjustable vertical distance. The value of εsf was set to 0.8 or 0.4, respectively, implying that the tip was hydrophilic or hydrophobic (Figure 1a).

the physics of interacting tips, deformation of the gas−water interface due to attractive forces,30 and inappropriate mapping of the surface due to systematic issues with the feedback loop parameters. The latter situation may arise if there are e.g. lateral differences in energy dissipation (tip−nanobubble vs tip− substrate), which are not corrected for by the amplitude feedback in conventional intermittent contact mode AFM.36 In fact, when contacted with an AFM tip, a surface nanobubble may behave as a vapor bridge and hence deforms to balance the applied stress from the tip, resulting in a complex interaction with the tip. Therefore, the response of surface nanobubbles to the perturbation by an AFM tip30 has not fully been understood. In particular, the molecular details for the tip−nanobubble interaction have not been studied yet. To elucidate the interaction mechanism and to study the possible interplay between nanobubble deformation and induced attraction, we used in our work constraint lattice density functional theory (constraint LDFT)37,38 to investigate the interaction between AFM tips and pinned surfaces nanobubble in a systematic manner.

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MODEL AND METHODS In LDFT, the grand potential can be expressed39,40 as Ω = kBT ∑ [ρi ln ρi + (1 − ρi ) ln(1 − ρi )] i

ε − ff 2

∑ ∑ ρi ρi+ a + ∑ ρi (φi − μ) i

a

Figure 1. (a) Simulation morphology of the substrate and the tip. The substrate was covered with a ring pattern of R = 20 (in lattice units) to represent physical roughness that provides the contact line pinning force. The AFM tip was modeled approximately with a hemispherical end on the top of a solid cylinder with a radius of 10. (b) Schematic of the location of tip and nanobubble. R and r represent the lateral radius of the nanobubble and the tip, respectively. d is the distance between tip and substrate, and h is the height of the nanobubble.

(1)

i

where kB is the Boltzmann constant, T is the absolute temperature, ρi is the local density at site i, εff and εsf are the fluid−fluid and the solid−fluid interaction strength, respectively, and φi is the fluid−solid interaction (εsf) summing over the nearest neighbor of site i. At a constant chemical potential, the density distribution at equilibrium (i.e., at a stable or metastable state) can be obtained by solving ∂Ω/∂ρi = 0. The constrained LDFT is a new method, which introduces a functional χi defined as

In our work, we used reduced units with the reduced temperature T* = kB/εff and the chemical potential μ* = μ/εff. The reduced distance is defined as r* = r/σ with σ being the lattice spacing. If the typical lattice spacing was chosen to represent the lattice gas model of water molecules, 0.37 nm,41 the nanobubbles we studied here have a base diameter of 14.8 nm in this work, smaller than the typical experimental ones. Hereafter the asterisk was omitted to simplify the description. In our simulations, T = 0.8 and μ = −3.035 describing a supersaturation environment. Since the level of supersaturation s = exp[(μc − μ)/kBT] and the chemical potential at vapor− liquid coexistence state μc = −3.0, the chemical potential of μ = −3.035 corresponds to a supersaturation of s = 104.5% and ζ = s − 1 = 4.5%.

⎧ 0 ρi < 0.5 i ∈ vapor ⎪ χi = ⎨ ⎪ ⎩ 1 ρi > 0.5 i ∈ liquid

to distinguish the liquid phase from vapor phase.38 The constraint on the volume of droplets/bubbles reads Ω′ = κ[N L0 − NL]

(2)

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in which κ is the Lagrange multiplier, N0L is the given volume, and NL = ∑iχi. The constrained grand potential is defined as

RESULTS AND DISCUSSION 1. Different Interactions between AFM Tip and Interface Nanobubble. In our simulations, we first built the simulation model containing a rough substrate and an AFM tip, as is shown in Figure 1. The ring-shaped pattern (R = 20) on the substrate was chosen to represent physical roughness providing the pinning force for stabilizing nanobubbles, and the AFM tip was modeled approximately with a hemispherical end on top of a solid cylinder with a radius of 10. We first simulated the surface nanobubble in the absence of any AFM tip under the same environment. The simulation results indicate that in the absence of the tip the roughness on the substrate can stabilize a nanobubble with a height of 7 and a contact angle of 43.9° measured from the vapor side. h and d

ΩC = Ω + Ω′ = kBT ∑ [ρi ln ρi + (1 − ρi ) ln(1 − ρi )] i

ε − ff 2

∑ ∑ ρi ρi+ a + ∑ ρi (φi − μ) + κ[NL0 − ∑ χi ] i

a

i

i

(3)

By solving the equations ∂ΩC /∂ρi = 0 and ∂ΩC /∂κ = 0, the local density ρi is obtained as ρi =

1

(

∂χ

1 + exp εff ∑a ρi + a − φi + μ + κ ∂ρi i

)

∀i (4) B


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metastable state for a given tip−sample separation distance. In other words, independent from the movement direction of the hydrophilic tip (approaching to or retracting from the substrate), the state of nanobubble is exactly the same, showing a pathway independence for the force−distance dependence for surface nanobubbles probed with a hydrophilic AFM tip. With the grand potential obtained from our simulations (e.g., Figure 2a), we can determine the capillary force between the tip and the nanobubble with the equation F(d) = −(∂Ω/∂d)μ , T − p(∂V /∂d)μ , T through thermodynamic integration,42,43 with V and p the volume and pressure of system, respectively. Since we used grand canonical ensemble and the volume of system was fixed in our simulations, the equation can be simplified to F(h) = −(∂Ω/∂d)μ , T . With the equation above we determined the force as a function of the tip−substrate distance (Figure 3a). First of all, this figure shows that the same interaction force is observed in both the approach and retraction processes at a given tip− substrate distance. This observation agrees well with experimental results that no significant hysteresis was found in the force curves for hydrophilic AFM tips.30 The force curves displayed in Figure 3a show that when the tip approaches the nanobubble the attractive force first appears at d = 10, a distance slightly larger than the height of the unperturbed nanobubble of d = 7, and then gradually decreases with distance and finally reaches zero at d = 7. Then the interaction force changes to repulsive, and the interaction strength monotonously increases with decreasing d. Clearly, both the trend of force evolution as a function of the tip− substrate distance and the absence of force hysteresis agree very well with the experimental observations of Walczyk and Schönherr.30 This agreement demonstrates that our model catches the main intergradient of tip−nanobubble interaction. In order to investigate the shape deformation of the surface nanobubbles caused by the presence of the hydrophilic AFM tip, we performed statistics on the density profile of the metastable state and determined the height and contact angle of the nanobubbles at different tip−substrate distances (see Figure 3b,c). It is found that when the tip−substrate distance exceeds a threshold value of d = 10, the tip detaches from the nanobubble and leaves it intact (Figure 3). When the distance is less than the threshold value, both the height and contact angle of the nanobubble monotonously decrease as the hydrophilic tip approaches (7 < d < 10) and then squeezes the nanobubble (d < 7). For a distance larger than the height of intact nanobubble, while the threshold value, namely, 7 < d < 10, is not exceeded, both the height and contact angle of nanobubbles weakly increase with the increase of the distance (see density profile in Figure 3a) as a result of the weak attraction between the tip and the nanobubble (Figure 2a). However, when the tip−substrate distance is smaller than the height of intact nanobubble, namely, d < 7, the nanobubble is squeezed by the tip with a flattened shape (see density profile in Figure 3a) and is characterized with decreasing nanobubble height and contact angle (Figure 3b,c). The shape deformation of the nanobubble resulting from the force exerted by the AFM tip induces the repulsive force seen in the corresponding force curve (Figure 2b). In other words, the nanobubble seems to be strongly flattened at short distances (upon approach) and weakly lengthened (upon retraction) at large distances by the hydrophilic tip (Figure 3). This is because of the strong attraction between fluid molecules and the hydrophilic tip,

are defined as the height of a nanobubble and the distance between tip and substrate, respectively (see Figure 1b). We also built a flat substrate without ring pattern and found that a nonpinned surface nanobubble was not stable, which is in accordance with previous studies.21−23,25 Then, we considered the effect of the AFM tip on the nanobubble shape and the corresponding tip−nanobubble interaction. We changed the strength of fluid−solid interaction εsf between tip and fluid to control the hydrophobicity of AFM tips. At a fixed tip−substrate distance, we investigated the variety of grand energy profile as a function of bubble volume via applying the constrained LDFT method (see, for example, Figure 2). Thus, at the given tip−substrate distance we can

Figure 2. Grand energy vs surface nanobubble volume calculated for a pinned nanobubble for (a) a hydrophilic tip (εsf = 0.8) and (b) a hydrophobic tip (εsf = 0.4) and the rough substrate at T = 0.8 and μ = −3.035. The insets give several typical configurations corresponding to different tip−nanobubble distance. The arrows in (b) indicate the approach and retraction processes. “★” marks the point of the metastable state with intact nanobubble that is not affected by the tip.

identify the metastable states of nanobubbles that corresponds to local minimum of free energy. Then we changed the distance sequentially, and obtained the varying morphology of nanobubbles with moving tip (see, e.g., Figure 3). 1.1. Hydrophilic AFM Tip. For a hydrophilic AFM tip (εsf = 0.8), surface nanobubbles at different tip−substrate distances were simulated with the constraint LDFT. The grand energies obtained as a function of the tip−substrate distance d are shown in Figure 2a. From the grand energy profiles, we can determine the metastable states of the nanobubbles bridging between the substrate and the tip. Figure 2a indicates that there exists only one local minimum value of the grand energy for a hydrophilic tip at a given tip− substrate distance, which means that there is only one C


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Figure 3. (a) Capillary force between hydrophilic tip and nanobubble and the morphology of the nanobubbles for different tip−substrate distances in the approach (red arrow) and retraction process (black arrow). The morphology of the nanobubbles can be identified from the density profiles. (b) Corresponding values of height and (c) the contact angle of the nanobubble as a function of the tip−substrate distance. The value of height and contact angle of intact nanobubble without tip is shown by red horizontals.

which induces a thin wetting film covering the tip. In this case, the penetration of the AFM tip into the nanobubble, which is featured with the creation of extra vapor−liquid area, is inhibited, and the bubble shows an elastic effect when it is squeezed by AFM tip. Thus, for d < 7 the nanobubble deformation and the interaction were found to be dominated by the force arising from the surface tension acting the tip. It is the large surface tension of the AFM tip that prevents the tip from penetrating the bubble, and as a result the tip tends to stay at the vapor−liquid interface of the nanobubbles and experiences a larger repulsive force (Figure 2a). On the other hand, the hydrophilic nature of the tip also facilitates its detachment from contact with the nanobubbles during a retraction process (d > 7). As a result, the attraction between AFM tip and nanobubble is rather weak and persists only

within a short distance, above which the AFM tip detaches and the nanobubble becomes intact. 1.2. Hydrophobic Tip. For a hydrophobic tip with εsf = 0.4, the grand energy at different tip−substrate distances is shown in Figure 2b. The figure shows that within the range of tip− substrate distances the grand energy possesses two local minima, meaning that there are two possible metastable states. Hence, the pathway dependence of the interaction between AFM tip and a nanobubble needs to be considered here; i.e., we need to differentiate the approach or retraction processes and determine the corresponding metastable states. Next, we determined the interaction force as a function of the tip− nanobubble distance (Figure 4a). When the tip approaches the nanobubble, the system evolution begins from a metastable state with an intact nanobubble at large tip−substrate distances. However, when D


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Figure 4. (a) Capillary force between hydrophobic tip and nanobubble and the morphology of the nanobubbles for different tip−substrate distances in the approach (red arrow) and retraction process (black arrow). The morphology of the nanobubbles can be identified from the density profiles. (b) Corresponding values of height and (c) the contact angle of the nanobubble as a function of the tip−substrate distance. The value of height and contact angle of intact nanobubble without tip is shown by red horizontals.

rupture is noticed. Only when the tip is sufficiently far from the nanobubble, the grand energy of the metastable state becomes larger than that with an intact nanobubble, and thus the tip detaches from the nanobubble. Another feature in the force curve measured with the hydrophobic tip is that a repulsive force is not found, which is totally different from the observations made with the hydrophilic tip (see above). This is difference can be attributed to different tip−nanobubble interactions. When the hydrophobic AFM tip approaches and squeezes the nanobubble, it can easily puncture the nanobubble surface, without causing significant nanobubble deformation (compare the density profiles in Figure 4a). As a result, no repulsive force is found. This observation again qualitatively agrees with the experimental reports in ref 30: a hydrophobic tip was found to induce a much weaker repulsive force that the force observed

the distance decreases below a threshold value, the metastable state with intact nanobubble vanishes, as indicated by the curve of grand energy (Figure 2b), and the tip suddenly touches and deforms the nanobubble. As expected, the approach and retraction processes show different trends for the observed forces. For the retraction process, the grand energy of the metastable state increases with increasing distance (Figure 2b). Upon retraction of the hydrophobic tip there is a long-range attractive force (Figure 4a). The nanobubble can be significantly lengthened by the adhering tip and remains in contact for separation distances much larger than that observed during approach (Figure 4b), in agreement with experimental data.30 For example, for an approach process the nanobubble transforms to a vapor bridge connecting the tip and substrate at d = 13, but for the retraction process, the vapor bridge can be lengthened to d = 20 before its E


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Figure 5. (a) Simulation morphology of substrate and the cone-shaped tip. (b) The capillary force between hydrophobic and hydrophilic coneshaped tips and the nanobubble. (i) The height and (j) the contact angle of nanobubble for different distances between hydrophobic and hydrophilic cone-shaped tip and substrate and the morphology of the nanobubble in (c) and (f) d = 2 (d) and (g) d = 7 (e) and (h) d = 12. In (c−e) the tip is hydrophobic, and in (f−h) the tip is hydrophilic. In the snapshots shown above, only the fluid particles at the interfaces (include both liquid−solid surface and vapor−liquid interfaces) are shown for clarity.

for a hydrophilic tip. The disappearance of the repulsive force in our simulation may be caused by the absence of long-range forces in our model, in which we used a lattice model, in which only the interaction between the nearest neighbors was considered. In addition, in the approach process, it is surprising to find from Figure 4a that at a tip−substrate distance of 14, the force will reach a much stronger attraction and then return to a moderate value when the tip−substrate distance is slightly changed. This may be due to the fact that there is a dynamic process, in which the nanobubble becomes suddenly higher and touches the tip. On the basis of experimental data, this possibility can is expected if the surface tension is close to or smaller than the cantilever stiffness. A detailed comparison of Figures 3 and 4 shows that the hydrophilic and hydrophobic tips affect the nanobubble shape

and thus force curves in different ways. For a hydrophilic tip, the elastic effect of the nanobubble plays an essential role in the interaction. In this case, the hydrophilic nature of the tip facilitates its departure from the nanobubble surface to the bulk solution, causing a weak and intermediate-range attraction. On the other hand, a thin wetting film covering the tip results in a high film tension that prevents the tip from penetrating the bubble. Thus, during an approach process, when the tip can squeeze the nanobubble, the elastic effect of the nanobubble leads to a strong bubble deformation and repulsive interactions. For a hydrophobic tip, the situation is different. Here it is the adhering effect that dominates the interaction. In the approach process, the hydrophobic tip can easily pierce the vapor−liquid interface of the nanobubble to reach the hydrophobic interior of the nanobubble, leading to the disappearance of the elastic effect and hence the repulsive force without causing significant F


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approach process, and it is the elastic effect that leads to strong nanobubble deformation and repulsive interactions. By contrast, for hydrophobic tips, it is the adhering effect that dominates the interaction. In the approach process, the hydrophobic tip can easily pierce the vapor−liquid interface of the nanobubble, leading to the absence of significant nanobubble deformation and the disappearance of the repulsive force. In retraction process, however, the hydrophobic adhesion between the tip and the nanobubble leads to a much strong lengthening effect on the nanobubble deformation. That is why a strong and much long-ranged attractive force was observed for the hydrophobic tip. The model discussed in this article catches the main intergradient of tip−nanobubble interactions for pinned surface nanobubbles and may therefore provide important insight into how to design minimally invasive AFM experiments.

nanobubble deformation. In the retraction process, however, the adhesion between the tip and the nanobubble leads to a much stronger lengthening effect than that observed for a hydrophilic tip. Thus, for the hydrophobic tip stronger and much more long-ranged attractive forces were observed (Figure 4). 2. Influence of the Shape of the AFM Tip. The shape of AFM tips is known to determine how a nanoscale contact is formed, e.g., in AFM-based nanoindentation.44 To investigate how the shape of AFM tip affects the deformation of a given pinned surface nanobubble, we also built a cone-shaped tip for comparison (Figure 5a). We changed the interaction strength between tip and liquid εsf to realize the different hydrophilicity of AFM tips. Again εsf = 0.4 corresponds to a hydrophobic tip and εsf = 0.8 to a hydrophilic tip. The tip has the same lateral radius as the hemispherical tip. The interaction force between the cone-shaped tip and a nanobubble was obtained in a similar way as discussed above. The results obtained are shown in Figure 5b. The Figure indicates that for both hydrophobic and hydrophilic tips the force curve does not show any hysteresis, and in particular the strength of induced force is lower than that for hemispherical tips (Figures 3 and 4). Another difference between cone-shaped and hemispherical tips is observed at εsf = 0.4. For the coneshaped tip the strength of attractive force increases with a decrease of the tip−substrate distance, which is opposite to what is found for the hemispherical tip. We ascribe this observation to the different evolution of contact angles on the hydrophobic tip surface for different tip morphologies. The height and contact angle of the nanobubble at different distances between tip and substrate are shown in Figures 5i and 5j. The height and contact angle are almost not affected by the hydrophilic cone-shaped tip. Moreover, for the hydrophobic tip both the height and contact angle of the nanobubble increase with a decrease of tip−sample distance, again opposite to the observation with the hemispherical tip, and in a weaker manner. Therefore, the shape of AFM tip does affect the obtained force strongly, especially for hydrophobic tips. For hydrophobic tips, the height and contact angle values increase with increasing tip−substrate distance, and in general, the coneshaped tip results in a weaker attraction than the hemisphereshaped tip. But for the hydrophilic tip, the effect of tip shape becomes rather weak. From our view, a sharp-ended hydrophilic tip maybe a good choice to measure of the nanobubble, which is in good agreement with Walczyk and Schönherr’s suggestion.30

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (H.S.). *E-mail: [email protected] (X.Z.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by National Natural Science Foundation of China (Nos. 21276007 and 91434204).

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REFERENCES

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CONCLUSIONS Using constraint lattice density functional theory, the interactions between AFM tips and pinned surface nanobubbles were studied in a systematic manner. In particular, the effect of different tip shape and wettability was unraveled. In general, the force−distance curves obtained match qualitatively well with experimental data reported recently in the literature. Our simulation results show that the hydrophilic tip and hydrophobic tip affect the nanobubble shape and thus force curves in different ways. For a hydrophilic tip, it is the elastic effect of nanobubble that plays an essential role. In this case, the hydrophilic nature of the tip facilitates its departure from the nanobubble surface to the bulk solution, resulting in a weak and intermediate-range attraction. On the other hand, a thin wetting film covering the tip prevents the tip from penetrating the bubble during an G


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Modeling the Interaction between AFM Tips and Pinned Surface

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