Effect of Wetting and Dewetting Dynamics on Atomic ForceMicroscopy MeasurementsA. A. Hemeda,†,‡ S. Pal,§ A. Mishra,† M. Torabi,† M. Ahmadlouydarab,∥ Z. Li,⊥ J. Palko,†

and Y. Ma*,†

†School of Engineering, University of California, Merced, Merced, California 95343, United States‡Aerospace Engineering Department, Cairo University, Giza 12613, Egypt§Department of Mechanical Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada∥Faculty of Chemical and Petroleum Engineering, University of Tabriz, Tabriz, Iran⊥Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634, United States

ABSTRACT: Water bridge dynamics between an atomicforce microscopy (AFM) tip and a flat substrate is studied byusing a multibody dissipative particle dynamics (MDPD)model. First, the numerical model is validated by comparingthe present results of droplet contact angles and liquid bridgeswith those reported in the literature. Then, the ability ofMDPD to capture the meniscus shape and behavior fordifferent operating conditions and geometric parameters isexamined for both static and dynamic cases. Hence, severalparametric studies and analyses of the AFM tip configurationand its operating conditions are reported. It is found that acritical capillary number of about 0.001 is calculated based on 5% change on the force measurements between the static anddynamic results. It is also demonstrated that the hysteresis behavior in the capillary force exerted on the AFM tip can besuccessfully predicted by using the MDPD model when the tip approaches or retracts from the substrate. Moreover, there is anexcellent agreement in the results of breakup distance for different water bridge volumes between the predictions of the MDPDmodel and the theory. Also, the hysteresis of capillary force exerted on an AFM tip composed of multibody design is studied.The prediction on the transition of the capillary force vs distance between the AFM tip and the substrate is in good agreementwith the experimental results. Therefore, we demonstrate a validated MDPD model which can successfully capture liquid bridgedynamics. This model can be used as a powerful design tool for meniscus manipulation technology, such as dip-pennanolithography, as well as for studying dynamic, e.g., tapping mode AFM tip, interactions with a liquid bridge.

1. INTRODUCTION

Atomic force microscopy (AFM)1,2 is a scanning probemicroscopy technique extensively used in, for example, (1)imaging of surface topography with atomic-level resolution forsemiconductors,3,4 polymers,5−7 and biomolecules and bio-logical membranes;8−11 (2) atomic level manipulation ofbiological and semiconductor microstructures;8,12 (3) measur-ing nanomechanical properties of biological molecules,membranes and polymers;13,14 and (4) measuring atomic-level forces.15−17 At the heart of this technology lies the criticalunderstanding of the interaction between a nanoscale AFM tipand the substrate.The forces acting between the tip and the substrate are van

der Waals forces, electrostatic potentials, and capillaryforces.2,16,18,19 Capillary forces influence the tip−substrateinteraction through the formation of a small liquid bridgebetween the tip and the substrate due to condensation inhumid ambient conditions.15 Liquid bridges formed betweensolid−solid interfaces are ubiquitous in nature and are studiedin a variety of applications, such as powder technology,18,20

capillary gripping,21 and self-assembly.22 Formation of theliquid bridge can significantly reduce AFM imaging resolutionand introduce errors in nanomechanical measurements due tothe capillary force exerted on the AFM tip by the liquidbridge.23,24 Because of such adverse influence, capillary forcesbetween the AFM tip and substrate have attracted significantattention.25−29 Aside from AFM imaging and measurements,there are similar capillary effects in dip pen nanolithography(DPN), which have also been investigated widely.30 There isalso significant evidence that an AFM tip may alter the surfacetopography by depositing undesirable impurities on thescanned surface.31

The typical radii of AFM tips vary from 5 to 100 nm whilethe gap between the tip and the substrate is in the range of∼0−50 nm. At these length scales, quantitative measurementsof the liquid bridge geometry, capillary force, and contact

Received: August 16, 2019Revised: September 13, 2019Published: September 19, 2019

Article

pubs.acs.org/LangmuirCite This: Langmuir 2019, 35, 13301−13310

© 2019 American Chemical Society 13301 DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

Dow

nloa

ded

via

CL

EM

SON

UN

IV o

n Ja

nuar

y 17

, 202

0 at

20:

53:2

6 (U

TC

).Se

e ht

tps:

//pub

s.ac

s.or

g/sh

arin

ggui

delin

es f

or o

ptio

ns o

n ho

w to

legi

timat

ely

shar

e pu

blis

hed

artic

les.

angles on the surfaces of both the tip and the substrate aredifficult even with state-of-the-art technologies.25,32 Theoreti-cal investigation of capillary forces due to liquid bridgesapplying Kelvin−Laplace and Young−Laplace equations33−35

can provide insights into the energy barrier and dissipationassociated with the formation and rupture of the liquid bridge.The treatment of the liquid bridge as a continuous mediumwithout considering Brownian motions in these studies is,however, debatable.36,37 More specific and accurate insightsinto the structure of the liquid bridge and its energetics havebeen developed by using either atomistic or coarse-grainsimulations.36−40 In these models, the motion of each atom orparticle is simulated in a system by using methods includingmolecular dynamics (MD),38−40 Monte Carlo,25,41,42 densityfunctional theory (DFT),43 and lattice density functionaltheory (LDFT).29 These prior works have addressed hystereticbehavior, minimum neck radius of the meniscus, and effects onthe capillary force from relative humidity and tip−substratedistance. However, because of their extremely computationallyexpensive nature,44 the computational domains are typicallylimited to only a few nanometers, and the simulation time islimited to the order of nanoseconds. Therefore, they are notsuitable for investigating systems with length scale up tomicrometers and time scale up to microseconds, which aretypically associated with tapping or scanning mode AFMimaging.To circumvent the above scaling issue, mesoscopic

simulations are often applied, which allow for modeling largersystems and longer time scales compared with atomic-levelsimulations. For instance, dissipative particle dynamics (DPD)is a mesoscale simulation technique proposed by Hooger-brugge and Koelman45 which has been extensively used tomodel hydrodynamics behavior46−49 and especially complexliquid−vapor interfaces,50−54 thereby making it an ideal choicefor the current problem. In this study, we demonstrate thecapability of a variant of this promising tool, multibodydissipative particle dynamics (MDPD), in modeling liquidbridge interactions with the AFM tip and substrate andespecially in characterizing the associated capillary forces. Bysuitably choosing the parameters that govern the interactionsbetween the MDPD particles, we simulate a fluid havinghydrodynamic properties, such as density and surface tension,similar to water. This allows us to capture both qualitative andquantitative aspects of the interactions among the liquidbridge, AFM tip, and the substrate.We validate our model by comparing our results with well-

established behaviors of liquid bridges reported in the

literature including the monotonic nature of the change incapillary force with tip−substrate distance and the dependenceof typical rupture distance on the volume of the liquid bridge.A particularly powerful and unique capability of the MDPDsimulation tool is its ability to automatically capture thehysteresis effect of the liquid bridge through particle−particleinteractions between the liquid bridge and the solid tip or thesubstrate. Recent progress in surface wettability engineeringhas enabled control and manipulation of droplets and liquidmenisci at micro/nanoscales.55−57 In this paper, we demon-strate a mesoscale design and simulation tool for characterizingdynamic capillary interactions in micro/nanosystems. Thepaper is organized as follows. In section 2, the numerical modelof MDPD is given. In section 3, we first validate our model bycomparing with prior numerical and experimental work, andthen the results of the AFM tip force and gap distancerelationship are presented and discussed for both static anddynamic studies. Also, the effects of AFM tip design, surfaceswettability, and offset on the force measurement are reported.This is followed by concluding remarks in section 4.

2. NUMERICAL MODELThe configuration of the AFM tip−liquid−substrate inter-action is presented in Figure 1. The AFM tip is assumed to bea hydrophilic spherical body with radius Rt and static contactangle θA located at distance d away from the substrate. Thecontact angle of a sessile droplet on the flat substrate is θS.Here, the same material properties are used for both surfaces,i.e., θA= θS = θ. The effects of surfaces wettabilities are studied(i.e., hydrophilic and hydrophobic materials) via variation inequilibrium contact angle.In this work, the many-body dissipative particle dynamic

model is useda mesh-free particle-based method applied tosimulate complex fluids at mesoscales.45,49,54 The meniscus,tip, and substrate are modeled with three different types ofMDPD particles. The tip and substrate particles are frozen toemulate solid-like behavior.45,49,54 The x−z cross section of themeniscus of the liquid bridge is presented schematically inFigure 1b. Newton’s second law governs the motion of MDPDparticles (beads):

rx

vdd

ii

= (1)

mvx

F F F Fdd

( )ii

j iij ij ijC D R∑ = = + +

≠ (2)

Figure 1. Schematic of the computational domain, i.e., AFM tip, water bridge, and flat substrate, with geometrical, operational, and conditionalparameters: (a) AFM tip located at a gap distance of d above a substrate with a single water droplet; (b) side view of the formed water bridge whenthe AFM approaches the substrate.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13302

where the subscript “i” corresponds to a particle with positionri, velocity vi, and experiencing the total force of Fi, and thesubscript “j” corresponds to MDPD neighbors of particle iwithin the influence region with corresponding cutoff radii Rcand Rd. The superscripts “C”, “D”, and “R” stand forconservative, dissipative, and random force components,respectively, and these forces are defined as follows:49,58

F A r R e B r R e( , ) ( ) ( , )ij ij ij ij i j ij ijC

c c d dω ρ ρ ω = + + (3)

F r R e v e( , ) ( . )ij ij ij ij ijD

D cζω = − · (4)

F r R t e( , )ij ij ij ijR

R c1/2φω θ = Δ −

(5)

where rij = ri − rj, eij = rij/|rij|, and vij = vi − rj. In theconservative force expression, Aij and B are the attractive andrepulsion force amplitudes, respectively. ωc and ωd areweighting functions with two cutoff radii of Rc and Rd = αRc,respectively, with α = 0.75. ωd is given by ωd(rij, Rd) = max(1− rij/Rd, 0), and similarly ωc(rij, Rc) = max(1 − rij/Rc, 0). ζ andϕ are the dissipative and random force amplitudes,respectively. Stability conditions require that ωR(rij, Rc) =

r R( , )ijD cω = max(1 − rij/Rc, 0), and ϕ2 = 2ζkBT where kB is

the Boltzmann constant and T is the temperature of thesystem. The parameter θij is sampled from a Gaussian whitenoise distribution with unit bandwidth, and Δt is the time step.For the local density function, ρi, in the conservative force

(repulsion term), Warren proposed an empirical formula withthe cutoff range Rd (i.e., Rd = αRc):

59

R

r

R15

21i

j i

ij

d3

d

2ikjjjjj

y{zzzzz∑ρ

π = −≠ (6)

This model was used in almost all prior MDPD work to modelboth fluid−fluid and fluid−solid interactions for interfacialflows.49,53,60,61

One characteristic of the MDPD method that must beaddressed in the simulation of solid surfaces is the ability ofparticles to interpenetrate. To retain a sharp liquid/solidinterface, the “bounce-back” approach is used in this presentwork to prevent the particle penetration into the solid walls.46

As a result, an extra numerical force due to the bounce-backcondition (∑i2mivi/Δt) is added to the net force exerted onthe solid body. Hence, the reported force in this work iscalibrated by removing this momentum term due to bounceback from the net force on the solid boundaries.Because MDPD is a coarse-grained particle simulation

method, reduced units are commonly used to link to physicalquantities. The majority of MDPD studies use dimensionlessmass, distance, and time units that are not rigorously tied tophysical scales, therefore restricting the scope to onlyqualitative insights.61−63 Only recently, attempts were madeto map MDPD scales to physical scales by choosing variousMDPD parameters, such as cutoff radius.64,65

Parameters used in eq 2 are first selected to describe a liquidwhose properties match the density, surface tension,66,67 andviscosity68 of water. These assignments are necessary forquantitative validation of MDPD results. For the static modelof the water bridge between the AFM tip and substrate, theviscosity of the working fluid may be disregarded (due to thevery low capillary number as will be discussed in section 3). Areference length of Rc = 1.0 nm is assigned for static cases. As a

result, each MDPD particle contains about six water molecules.For the MDPD model, unit values of cutoff distance Rc,particle mass m, and system energy kBT are considered in thepresent work. In addition, the attraction and repulsive forceamplitudes between liquid MDPD particles are Aij = −40 andB = 25. (Interaction parameters between liquid and solid areassigned to represent surface wettability as discussed later.)Finally, the amplitude of the dissipative force is assigned thevalue ζ = 5.61. Based on these parameter values, the fluiddensity, kinematic viscosity, and surface tension are calculatedas ρ = 6.0, v = 1.24, and σ = 7.31 in MDPD units. From thefluid density ρ and surface tension σ ratios between the real(SI) and MDPD units, the conversion of mass and time fromMDPD units to the real units is

M LDPD DPD3ρ

ρ=

*(7)

T MDPD DPDσσ

= * (8)

where the superscript “∗” stands for the real (SI) unitquantities. For instance, a surface tension of 70.6 mN m−1 at298 K and a density of 998 kg/m3 are considered for water;therefore, MDPD = 1.64 × 10−25 kg and TDPD = 1.28 × 10−11 s,where the length scale is Rc = 1.0 nm. Note that other scalesmay be obtained due to the free-length scale of the MDPD atvery low capillary number or static cases.26,61

For dynamic simulations, the length scale will be a functionof the viscosity value and related to system capillary number.65

The length scale for dynamic cases can be written as

LDPD

2ikjjjj

y{zzzz

ρρ

νν

σσ

=* *

* (9)

where v is the kinematic viscosity of the working fluid. Forwater, with the data given above, the length scale will be aboutRc = 11 nm. Now, the conversions of mass and time from eqs 7and 8 are MDPD = 2.2 × 10−22 kg and TDPD = 1.49 × 10−10 s.This case will only be considered in dynamic scenarios whenthe AFM tip moves (approaching and retracting from the flatsubstrate) with significant velocity. These cases are discussedthoroughly at the end of the following section.

3. RESULTS AND DISCUSSIONIn this section, both static and dynamic modeling of the fluid−structure interactions of AFM tip with water droplets on a flatsubstrate are presented.Here, we first apply the MDPD model to a 3-D droplet on a

flat substrate and compare the results with prior work tovalidate the present approach. The effect of the attraction forceamplitude Asl (Aij between liquid and solid) on the surfacecontact angle on a flat plate is shown in Figure 2. Note thatvariation of the parameter Asl is commonly used to obtaindifferent contact angle with flat substrates.60,69,70 Two sideviews of the droplet with two different Asl are shown in Figure2 as insets. Comparisons with Asl−θ results by Chen et al.,Chang et al., and Zhang et al. are depicted in Figure 2.62,65,69

The figure shows that the present results match very well withthe available data in the literature. One possible reason for thesmall differences in data sets is the random force in the MDPDmodel. Further comparisons with other work are given in thefollowing subsections.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13303

3.1. Static Results. Here, the AFM is held stationary atdifferent distances from the flat substrate (see Figure 1b).Statistical analysis is conducted based on the MDPDsimulations with the consideration of Brownian motion toobtain desired averaged quantities.71 The droplet is initiallyassigned a cylindrical shape at t = 0. This droplet eventuallyreaches the steady-state shape at t = 200 when there is nolonger change in the local contact angle along the three-phasecontact line. Then, averages of system quantities are calculatedduring a time interval between 200 and 800 DPD time. In thissection, a case with an AFM tip of radius Rt = 40 nm (40MDPD units) and tip and substrate contact angles of θA = θS =55° (or Asl = −35) are considered. The liquid (water) volumeis set to be 4600 nm3. These conditions approximately matchthe experimental work of Sirghi et al.72 In the MDPD model,the meniscus exhibits a very sharp change in density from ρ to0 across the interface with the air. The contour ρ/2 is taken asthe representative boundary of the meniscus profile, and this isused to calculate the local contact angle, i.e., θ1 on the AFM tipand θ2 on the substrate. The force exerted on the AFM tip iscalculated from the sum of the vertical component of the forceson the AFM particles via eq 2 and shown in Figure 3a. Notethat the force is nondimensionalized with the force value at d ≈0, i.e., F/F0. Acceptable agreement is obtained compared to the

work of Sirghi et al.72 as shown in this figure. One possiblereason for the difference observed in force is a difference incontact angle for the experimental and computational data. Acontact angle of zero is reported for the experiments, whereasthe contact angle for simulations is 55°; a zero-contact anglecannot be readily achieved in MDPD modeling.Theoretically, the capillary force consists of two compo-

nents: (1) a Laplace component FL = πr12Δp originating from

the pressure difference Δp between inside and outside ofmeniscus and (2) a tension force FT = 2πr1σ sin(θ1 + φ1)originating from the surface tension of the liquid, σ, at thecontact line, where r1, θ1, and φ1 are shown in Figure 1. As thetip retracts, r1 decreases monotonically, as shown in Figure 3a,while θ1 + φ1 remains almost constant (see Figure 3b), leadingto a monotonically decreasing FT. For FL, a second-orderdependence on r1 ensures a steady decrease as well,overshadowing any changes in Δp. The investigation isperformed by considering a gap distance d between thesubstrate and the AFM tip. The gap d is kept constant in eachsimulation, and it is gradually changed between differentsimulations to provide the values of θ1 and θ2 in a staticsituation. Note that r1 will asymptotically decrease with d untilthe breakup distance db. After a breakup, the r1 value remainsconstant as well as the rest of the parameters, e.g., θ1 + φ1.The breakup distance db is a critical parameter for the stable

liquid bridge during retraction. Eventually, the liquid bridgewill become unstable and breakup if d is greater than thethreshold value db. Extensive work showed that there is arelationship between db and the volume of the liquid bridge V:db is approximately proportional to the cube root of V, i.e., db∝ V1/3.72 Such behavior is also seen in the present work, asshown in Figure 4a. Moreover, the maximum capillary forceexerted on the AFM tip linearly increases with V1/3 over therange studied as depicted in Figure 4b. In other words, theforce F mainly results from the interplay of water dropletvolume (and consequently the relative humidity via the Kelvinequation) and AFM tip position (gap distance). In Figure 4c,the effect of Rtip on the force at two different gap distances, d =5 and d = 10, is shown. The results show generally increasingthe force with increasing tip radius converging to valuescorresponding to a flat plate. This observed behavior isexpected due to the increasing capillary pressure and linetension forces, which reach their maximum values for a flatplate when Rtip → ∞.

Figure 2. Comparison of water droplet contact angle on a flat wallusing present MDPD method and data from Zhang et al.,65 Chang etal.,69 and Chen et al.62

Figure 3. Comparison of F/F0 using the present numerical work and experimental work of Sirghi et al.62 Effect of gap distance d on the angle θ1 +φ1 and radius r1 in (b) for the theoretical analysis of the tension force.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13304

3.2. Dynamic Results. In this section, the dynamic effectof the AFM tip is studied. First, a reference case is considered.Then, the effects of surface wettability, operating conditions,and AFM tip design on AFM tip force are studied.3.2.1. Breakup of the Liquid Bridge. The system

configuration is similar to the test case in section 3.1. TheAFM is initially placed at a distance of d = 15 MDPD units andnot in contact with the water film (see the inset in Figure 5).

Then, the AFM tip approaches the substrate with a constantvelocity of v = 0.01. After reaching d = dmin = 2.0 at t = 1300(red line in Figure 5), the AFM tip is then retracted from thesubstrate (blue line in Figure 5). The initial water dropletshape can be arbitrary, as surface tension rapidly reshapes thedroplet to be a spherical cap, as shown in the inset in Figure 5at t = 0. Note that a settling time of 5 DPD time units isconsidered between the approach and retraction stages to

decrease the system oscillations. The tip is held at theminimum distance dmin with zero velocity during this interval.The change in AFM force measurement, F, versus the gapdistance, d, is depicted in Figure 5. Based on the slope of theF−d curve, the whole process can be divided into four stagesnumbered I−IV as shown in Figure 5. Note that the verticaldashed lines in Figure 5 separate these stages. In the first andlast stages I and IV, the AFM is not in contact with waterdroplet on the substrate. Therefore, the F−d slope is zero inthese two stages. For the two other stages, II and III, the F−dslope depends on the AFM tip shape, wettability, and tipspeed. For example, for the given spherical design with v = 0.1,the F−d slope changes in both approaching and retractingprocesses. The maximum force is obtained at closest approach(d = dmin = 2.0 for these simulations), which is in agreementwith prior work.72 Note that when the AFM tip travels at highspeed and touches the substrate, a breakup occurs and a smallbubble forms that remains for a while. For this reason, aminimum separation distance of 2.0 is chosen here to avoidthis bubble. Also, at such high AFM tip speed, the waterdroplet may not re-form back to its equilibrium positioncompared to the static measurements as previously given insection 3.1. Because of this inertia, the AFM tip experienceslarger resistance (opposite force) which cancels a portion ofthe adhesion force between the AFM tip and droplet as givenlater in stage II. At the end of the retraction process, a zero netforce exerted on the AFM tip was calculated after the breakupof the water bridge (t > 3335 or d > db, where db is the breakupdistance). Two characteristic lengths are defined: dt and dh. dtis the travel distance of the AFM tip on approach from the startof touching the water droplet until the minimum separationdistance dmin = 2. dh is the difference between db and dt + dmin,i.e., the difference in separation between the separationdistance at droplet contact on approach and the breakup ofthe bridge on retraction. In most experimental work, the AFM

Figure 4. Effect of V1/3 on breakup gap db in (a) and force exerted on the AFM tip F in (b).72 The effect of Rtip on the force at two distance of 5 and10 nm in (c). The red star denotes the reference case in Figure 3.

Figure 5. Dynamic force−distance, F−d, relationship and definitionof four stages during tip approach and retraction. Stages I−IV aredefined by different slopes in the F−d curve. Tip velocity v = 0.01.Gap distances, dt and dh, corresponding to the process are indicated.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13305

tip touches the substrate, i.e., dmin = 0. Hence in experiments,dt is approximately the droplet height, and dh is the differencebetween db and dt.3.2.2. Effect of Tip Velocity. Here, the effects of tip velocity

on the dynamic breakup of the liquid bridge are studied, andthe results are compared with those for the static case insection 3.1. In all discussions, the superscript “static” stands forthe reference static simulations in section 3.1. The ratios Fmax/Fmaxstatic and db/db

static are considered for the maximum force (atdmin = 2.0) and breakup distance to the static results,respectively, as shown in Figure 6. It is found that these ratios

approach a value of 1.0 when the velocity is <0.001. This canbe related to capillary number, Ca

Ca vρνσ

=(10)

Hence, a Ca of 0.001 can be considered to be a critical valuewhere the dynamic simulations are the same as the static oneswithin an error of <5%. Note that there is no change in dt withvelocity while the changes in db and dh are essentially identicalduring this dynamic process.3.2.3. Effects of Offset Distance. In the previous results, the

AFM tip center is assumed to be aligned with the center of thewater bridge in the horizontal direction. In this subsection, anoffset distance l separates the centers in the x-direction, asshown in the inset of Figure 7a. The AFM tip movesdownward with v = 0.05 until d = dmin = 2.0 and then retractsback with the same speed. The effect of the offset distance l onthe characteristic lengths dt and dh are shown in Figure 7.Moreover, two different radii of the AFM tip are considered

here, Rt = 40 and Rt = 10. Also, two different static contactangles of the AFM tip of 55° and 120° are shown in Figures 7aand 7b, respectively. The blue shaded areas in Figure 7represent the water droplet at t = 0 to compare the lengthswith the droplet height (note the change in axes scales). Asshown in both figures, the droplet height is equal to 9 DPDunit at t = 0 for all cases. As shown in this figure, dt decreaseswith l, which is consistent with previous experimental work ofWang et al.73 On the other hand, the trend of dh is stronglydependent on the contact angle of AFM tip. dh decreases with lwhen the tip material is hydrophilic, while dh increases with lwhen the tip material is hydrophobic. This trend is alsoconsistent with the experimental results of Wang et al.73

3.2.4. Effect of Wettability. In this subsection, we study theeffect of the surface wettabilities, characterized by contactangles of the AFM tip, θA, and substrate, θS, on the AFM tipforce generated by the liquid bridge. The wettability is againcontrolled by tuning the parameter Asl as discussed before. Thecase in section 3.2.1 is used as a reference in this study.Contour plots of the effect of these contact angles on thenondimensional maximum force, Fmax/Fmax

ref , the fraction ofmass deposited on the AFM tip after bridge rupture, XA, andthe values of dt and dh are shown in Figures 8a to 8d,respectively. The red asterisk in these figures refers to theresults of the reference case in section 3.2.1. The maximumforce (Figure 8a) shows a trend which roughly depends on thesum of θA + θS. The maximum force occurs when the twosurfaces are highly hydrophilic as expected and decreases asthey become less hydrophilic, i.e., more repulsive force. For thefraction of the droplet retained on the tip after bridge rupture,XA in Figure 8b, there are four scenarios. First, if θA < 90° andθS < 90°, the deposited mass on the AFM tip linearly increaseswith θS and linearly decreases with θA. In the second case,when θA < 90° and θA < θS + 5°, there is almost no massdeposited on the tip, XA = 0, as shown in the inset for thisdomain. For the third case, when θA < 90° and θS + 5° > 90°,the droplet is totally attached to the AFM tip during retractionas shown in the inset for this domain. Finally, XA is about 0.5along the line θA = θS, and it changes dramatically within about5° difference in contact angles when θA < 90°. This alsosupports the trend of the maximum force in Figure 8a. InFigure 8c, dt is independent of θA and increases with θSbecause of the increase in the droplet height with θS, i.e., dt ≈ h− dmin where h is the droplet height. Finally, dh is depicted in

Figure 6. Effect of AFM tip velocity on F/Fstatic and db/dbstatic.

Figure 7. Effect of offset distance between the AFM tip and droplet center, l, on the characteristic lengths dt and dh when v = 0.05. The contactangle of AFM tip θA is 55° in (a) and 120° in (b).

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13306

Figure 8d. It has a peak value when 90A Sθ θ≅ ≅ °. dbdecreases when θA < 90° or θS < 90° because both surfacesthen show poor adhesion to the water droplet.3.2.5. Transition in the Slope of Capillary Force vs Gap

Distance. In this subsection, the AFM tip is composed of two

different regions (bodies): a spherical tip and a truncatedconical region.74 The configuration is shown in Figure 9a. Thesemiconical angle, β, ranges from −25° to 60°. The sphericaltip and cone base radii are chosen to be 5.0 DPD units. Usingthis composite tip, we model the transition of liquid between

Figure 8. Contour plots of the effect of contact angles for AFM tip, θA, and substrate, θS, on (a) the nondimensional force Fmax/Fmaxref on the AFM

tip at d = dmin = 2, (b) mass fraction deposited on the AFM tip after retraction XA, and characteristic lengths (c) dt and (d) dh. The asteriskindicates the reference case in section 3.2.1 with v = 0.05.

Figure 9. Analysis of the F−d relationship for AFM tip made of different bodies. (a) Schematic plot of the computational domain. (b) F−d curvewhen β = 30° and definition of six stages based on average slope. (c) Effect of β on the slope for each stage of the F−d curve. (d) Effect of β on themaximum force exerted on the AFM tip with this design.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13307

the two surfaces. The droplet volume is assigned to be 4600DPD volume units, and the contact angle is 60° for bothsurfaces. The AFM tip is initially located at a distance of 12DPD from the surface, i.e., larger than the droplet height(about 11 DPD length units). Note that the volume is largerthan the one used in previous sections to be able to have alarger wetted area on the conical part of the tip. The AFM tipspeed is chosen to be v = 0.01. The F−d curve is depicted inFigure 9b. There are six stages, numbered I−VI, shown in thefigure. These stages are defined based on the change in theslope of the F−d curve or the transition between the differentsurfaces of the AFM tip. Dashed lines indicate the separationbetween the stages. The slopes of the F−d curve in the regionsI and VI are approximately equal to zero because the AFM isnot in contact with the droplet. The average slopes in the otherregions (green lines in Figure 9b) are highly dependent on theconfiguration of the wetted surface. The results are in goodagreement with prior experimental work of Wang et al.73

However, the experimental work includes seven stages. Theextra stage accounts for AFM tip and the substrate interactionwhen they are in direct contact which is not included in thepresent model.To study the effect of the geometry of the AFM tip on the

measured force, different semiconical angles β are considered.The effect of this angle on the F−d slopes in the various stagesis shown in Figure 9c. Because the slopes in the regions I andVI are zeros, they are omitted from this figure. The slopes inthe stages II and V are almost constant with β. During thesestages, the droplet is in contact with the semi spherical cap, andthere is no effect of β. The magnitude of these slopes is smallbecause the tip radius is quite small. Finally, the slopes instages III and IV are monotonically decreasing with β. This isdue to the increase of the wetted area and the perimeter of thethree-phase contact line with increasing β. Hence, the exertedforce on the AFM tip is expected to increase in these stageswhen β increases, giving higher absolute value of the slope.The maximum force at dmin = 2 is reported in Figure 9d. Again,the maximum force increases with β because of the increase inthe wetted area and the perimeter of the three-phase contactline. The force is largely independent of β when β ≤ 15°, asshown in this figure. Such study would help in the customdesign of the AFM tip composed of multibody design.

4. CONCLUSIONIn summary, we have demonstrated that the behavior ofmicro/nanoscale liquid menisci dynamics relevant to AFM canbe predicted by an MDPD model. To validate this model, anumerical prediction of capillary forces acting on the AFM tipapproaching and retracting from a flat substrate is comparedwith experiment. Qualitative agreement is demonstrated.Further validation is given by the excellent agreement in thecomparison of the breakup threshold distance for differentwater bridge volumes between the predictions of the MDPDmodel and theory.The model captures meniscus behavior as a function of

surface wettability. Several parametric studies and analyses ofthe AFM tip configuration and its operating conditions arereported. For instance, the effect of capillary number on thedynamic responses of the AFM tip is studied, and there was athreshold of 0.001 at which the results will be identical to thestatic results with 5% error margin. Besides, the effect of theoffset distance between the AFM tip center and water dropleton the force measurement is reported, and there was a good

agreement with the experimental work. Moreover, the fourscenarios of the fraction of the droplet retained on the tip afterbridge rupture are reported with different wettability. Also, theeffect of water film transition of AFM tip composed ofmultibody design is simulated, and the corresponding effect onthe force−distance relationship is studied. Our model can beused as a powerful design tool for meniscus manipulationtechnology, such as dip-pen nanolithography, as well as forestimating capillary force contributions in AFM force measure-ments and studying dynamic, for example, tapping mode andAFM tip, interactions with a liquid bridge.

■ AUTHOR INFORMATIONCorresponding Author*Tel +1 (209) 228-4046. E-mail yma5@ucmerced.edu.

ORCIDZ. Li: 0000-0002-0936-6928Y. Ma: 0000-0001-9721-3333Author ContributionsA.A.H. and S.P. contributed equally to this work.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe support for our research by the National ScienceFoundation (Award 1718194) is greatly appreciated.

■ REFERENCES(1) Binnig, G.; Quate, C. F.; Gerber, C. Atomic Force Microscope.Phys. Rev. Lett. 1986, 56 (9), 930.(2) Butt, H. J.; Cappella, B.; Kappl, M. Force Measurements with theAtomic Force Microscope: Technique, Interpretation and Applica-tions. Surf. Sci. Rep. 2005, 59 (1−6), 1−152.(3) Albrecht, T. R.; Quate, C. F. Atomic Resolution Imaging of aNonconductor by Atomic Force Microscopy. J. Appl. Phys. 1987, 62(7), 2599.(4) Fukui, K. I.; Onishi, H.; Iwasawa, Y. Atom-Resolved Image of theTiO2(110) Surface by Noncontact Atomic Force Microscopy. Phys.Rev. Lett. 1997, 79 (21), 4202.(5) Drake, B.; Prater, C. B.; Weisenhorn, A. L.; Gould, S. A. C.;Albrecht, T. R.; Quate, C. F.; Cannell, D. S.; Hansma, H. G.; Hansma,P. K. Imaging Crystals, Polymers, and Processes in Water with theAtomic Force Microscope. Science (Washington, DC, U. S.) 1989, 243(4898), 1586.(6) Jones, D. M.; Smith, J. R.; Huck, W. T. S.; Alexander, C. VariableAdhesion of Micropatterned Thermoresponsive Polymer Brushes:AFM Investigations of Poly(N-Isopropylacrylamide) Brushes Pre-pared by Surface-Initiated Polymerizations. Adv. Mater. 2002, 14(16), 1130.(7) Ochoa, N. A.; Pradanos, P.; Palacio, L.; Pagliero, C.; Marchese,J.; Hernandez, A. Pore Size Distributions Based on AFM Imaging andRetention of Multidisperse Polymer Solutes: Characterisation ofPolyethersulfone UF Membranes with Dopes Containing DifferentPVP. J. Membr. Sci. 2001, 187 (1−2), 227.(8) Fotiadis, D.; Scheuring, S.; Muller, S. A.; Engel, A.; Muller, D. J.Imaging and Manipulation of Biological Structures with the AFM.Micron 2002, 33 (4), 385.(9) Muller, D. J.; Fotiadis, D.; Scheuring, S.; Muller, S. A.; Engel, A.Electrostatically Balanced Subnanometer Imaging of BiologicalSpecimens by Atomic Force Microscope. Biophys. J. 1999, 76 (2),1101.(10) Rotsch, C.; Braet, F.; Wisse, E.; Radmacher, M. AFM Imagingand Elasticity Measurements on Living Rat Liver Macrophages. CellBiol. Int. 1997, 21 (11), 685.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13308

(11) Muller, D. J.; Schabert, F. A.; Buldt, G.; Engel, A. ImagingPurple Membranes in Aqueous Solutions at Sub-NanometerResolution by Atomic Force Microscopy. Biophys. J. 1995, 68 (5),1681.(12) Oyabu, N.; Sugimoto, Y.; Abe, M.; Custance, O.; Morita, S.Lateral Manipulation of Single Atoms at Semiconductor SurfacesUsing Atomic Force Microscopy. Nanotechnology 2005, 16 (3), S112.(13) Burnham, N. A.; Colton, R. J. Measuring the NanomechanicalProperties and Surface Forces of Materials Using an Atomic ForceMicroscope. J. Vac. Sci. Technol., A 1989, 7 (4), 2906.(14) Gaboriaud, F.; Dufrene, Y. F. Atomic Force Microscopy ofMicrobial Cells: Application to Nanomechanical Properties, SurfaceForces and Molecular Recognition Forces. Colloids Surf., B 2007, 54(1), 10.(15) Jones, R.; Pollock, H. M.; Cleaver, J. A. S.; Hodges, C. S.Adhesion Forces between Glass and Silicon Surfaces in Air Studied byAFM: Effects of Relative Humidity, Particle Size, Roughness, andSurface Treatment. Langmuir 2002, 18 (21), 8045.(16) Fang, H. H.; Chan, K.-Y.; Xu, L.-C. Quantification of BacterialAdhesion Forces Using Atomic Force Microscopy (AFM). J.Microbiol. Methods 2000, 40 (1), 89.(17) Ojaghlou, N.; Tafreshi, H. V.; Bratko, D.; Luzar, A. DynamicalInsights into the Mechanism of a Droplet Detachment from a Fiber.Soft Matter 2018, 14 (8924), 8924.(18) Rabinovich, Y. I.; Esayanur, M. S.; Moudgil, B. M. CapillaryForces between Two Spheres with a Fixed Volume Liquid Bridge:Theory and Experiment. Langmuir 2005, 21 (24), 10992.(19) Butt, H. Biophys. J. 1991, 60 (4), 777−785.(20) Muguruma, Y.; Tanaka, T.; Tsuji, Y. Numerical Simulation ofParticulate Flow with Liquid Bridge between Particles (Simulation ofCentrifugal Tumbling Granulator). Powder Technol. 2000, 109 (1−3),49.(21) Lambert, P.; Delchambre, A. Design Rules for a CapillaryGripper in Microassembly (ISATP 2005). The 6th IEEE InternationalSymposium on Assembly and Task Planning: From Nano to MacroAssembly and Manufacturing, 2005. 2005, DOI: 10.1109/ISATP.2005.1511452.(22) Masuda, Y.; Tomimoto, K.; Koumoto, K. Two-DimensionalSelf-Assembly of Spherical Particles Using a Liquid Mold and ItsDrying Process. Langmuir 2003, 19 (13), 5179.(23) Van Noort, S. J. T.; Van Der Werf, K. O.; De Grooth, B. G.;Van Hulst, N. F.; Greve, J. Height Anomalies in Tapping ModeAtomic Force Microscopy in Air Caused by Adhesion. Ultra-microscopy 1997, 69 (2), 117.(24) Thundat, T.; Warmack, R. J.; Allison, D. P.; Bottomley, L. A.;Lourenco, A. J.; Ferrell, T. L. Atomic Force Microscopy ofDeoxyribonucleic Acid Strands Adsorbed on Mica: The Effect ofHumidity on Apparent Width and Image Contrast. J. Vac. Sci.Technol., A 1992, 10 (4), 630.(25) Jang, J.; Schatz, G. C.; Ratner, M. A. Capillary Force in AtomicForce Microscopy. J. Chem. Phys. 2004, 120 (3), 1157.(26) Zitzler, L.; Herminghaus, S.; Mugele, F. Capillary Forces inTapping Mode Atomic Force Microscopy. Phys. Rev. B: Condens.Matter Mater. Phys. 2002, DOI: 10.1103/PhysRevB.66.155436.(27) Binggeli, M.; Mate, C. M. Influence of Capillary Condensationof Water on Nanotribology Studied by Force Microscopy. Appl. Phys.Lett. 1994, 65 (4), 415.(28) Xiao, X.; Qian, L. Investigation of Humidity-DependentCapillary Force. Langmuir 2000, 16 (21), 8153.(29) Men, Y.; Zhang, X.; Wang, W. Capillary Liquid Bridges inAtomic Force Microscopy: Formation, Rupture, and Hysteresis. J.Chem. Phys. 2009, 131 (18), 184702.(30) Piner, R. D.; Zhu, J.; Xu, F.; Hong, S.; Mirkin, C. A. Dip-Pen”Nanolithography. Science (Washington, DC, U. S.) 1999, 283 (5402),661.(31) Jaschke, M.; Butt, H. J. Deposition of Organic Material by theTip of a Scanning Force Microscope. Langmuir 1995, 11 (4), 1061−1064.

(32) Sprakel, J.; Besseling, N. a M.; Leermakers, F. A. M.; CohenStuart, M. A. Equilibrium Capillary Forces with Atomic ForceMicroscopy. Phys. Rev. Lett. 2007, DOI: 10.1103/PhysRev-Lett.99.104504.(33) van Honschoten, J. W.; Tas, N. R.; Elwenspoek, M. The Profileof a Capillary Liquid Bridge between Solid Surfaces. Am. J. Phys. 2010,78 (3), 277.(34) Restagno, F.; Bocquet, L.; Biben, T. Metastability andNucleation in Capillary Condensation. Phys. Rev. Lett. 2000, 84(11), 2433.(35) Sahagun, E.; García-Mochales, P.; Sacha, G. M.; Saenz, J. J.Energy Dissipation Due to Capillary Interactions: HydrophobicityMaps in Force Microscopy. Phys. Rev. Lett. 2007, DOI: 10.1103/PhysRevLett.98.176106.(36) Stifter, T.; Marti, O.; Bhushan, B. Theoretical Investigation ofthe Distance Dependence of Capillary and van Der Waals Forces inScanning Force Microscopy. Phys. Rev. B: Condens. Matter Mater.Phys. 2000, 62 (20), 13667.(37) Pakarinen, O. H.; Foster, A. S.; Paajanen, M.; Kalinainen, T.;Katainen, J.; Makkonen, I.; Lahtinen, J.; Nieminen, R. M. Towards anAccurate Description of the Capillary Force in Nanoparticle-SurfaceInteractions. Modell. Simul. Mater. Sci. Eng. 2005, 13, 1175.(38) Argyris, D.; Ashby, P. D.; Striolo, A. Structure and Orientationof Interfacial Water Determine Atomic Force Microscopy Results:Insights from Molecular Dynamics Simulations. ACS Nano 2011, 5(3), 2215.(39) Choi, H. J.; Kim, J. Y.; Hong, S. D.; Ha, M. Y.; Jang, J.Molecular Simulation of the Nanoscale Water Confined between anAtomic Force Microscope Tip and a Surface. Mol. Simul. 2009, 35(6), 466.(40) Ko, J. A.; Choi, H. J.; Ha, M. Y.; Hong, S. Do; Yoon, H. S. AStudy on the Behavior of Water Droplet Confined between an AtomicForce Microscope Tip and Rough Surfaces. Langmuir 2010, 26 (12),9728.(41) Kim, H.; Smit, B.; Jang, J. Monte Carlo Study on the WaterMeniscus Condensation and Capillary Force in Atomic ForceMicroscopy. J. Phys. Chem. C 2012, 116 (41), 21923.(42) Jang, J.; Schatz, G. C.; Ratner, M. A. Capillary Force on aNanoscale Tip in Dip-Pen Nanolithography. Phys. Rev. Lett. 2003,DOI: 10.1103/PhysRevLett.90.156104.(43) Paramonov, P. B.; Lyuksyutov, S. F. Density-FunctionalDescription of Water Condensation in Proximity of NanoscaleAsperity. J. Chem. Phys. 2005, 123 (8), 084705.(44) Pivkin, I. V.; Caswell, B.; Karniadakisa, G. E. DissipativeParticle Dynamics. Rev. Comput. Chem. 2010, 85.(45) Hoogerbrugge, P. J.; Koelman, J. M. V. A. SimulatingMicroscopic Phenomena with Dissipative Particle Dynamics. Euro-phys. Lett. 1992, 19 (3), 155−160.(46) Ranjith, S. K.; Patnaik, B. S. V; Vedantam, S. No-Slip BoundaryCondition in Finite-Size Dissipative Particle Dynamics. J. Comput.Phys. 2013, 232 (1), 174−188.(47) Fan, X.; Phan-Thien, N. N.; Yong, N. T.; Wu, X.; Xu, D.Microchannel Flow of a Macromolecular Suspension. Phys. Fluids2003, 15 (1), 11.(48) Symeonidis, V.; Karniadakis, G. E.; Caswell, B. A SeamlessApproach to Multiscale Complex Fluid Simulation. Comput. Sci. Eng.2005, 7 (3), 39.(49) Moeendarbary, E.; Ng, T. Y.; Zangeneh, M. Dissipative ParticleDynamics: Introduction, Methodology and Complex Fluid Applica-tions a Review. Int. J. Appl. Mech. 2009, 01 (04), 737−763.(50) Warren, P. B. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat.Interdiscip. Top. 2003, 68 (6), 1−8.(51) Arienti, M.; Pan, W.; Li, X.; Karniadakis, G. Many-BodyDissipative Particle Dynamics Simulation of Liquid/Vapor andLiquid/Solid Interactions. J. Chem. Phys. 2011, 134 (20), 204114.(52) Novik, K. E.; Coveney, P. V. Using Dissipative ParticleDynamics to Model Binary Immiscible Fluids. Int. J. Mod. Phys. C1997, 08 (04), 909.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13309

(53) Cupelli, C.; Henrich, B.; Glatzel, T.; Zengerle, R.; Moseler, M.;Santer, M. Dynamic Capillary Wetting Studied with DissipativeParticle Dynamics. New J. Phys. 2008, 10 (4), 043009.(54) Mishra, A.; Hemeda, A. A.; Torabi, M.; Palko, J.; Goyal, S.; Li,D.; Ma, Y. A Simple Analytical Model of Complex Wall in MultibodyDissipative Particle Dynamics. J. Comput. Phys. 2019, 396, 416.(55) Tsai, Y. T.; Choi, C. H.; Gao, N.; Yang, E. H. Tunable WettingMechanism of Polypyrrole Surfaces and Low-Voltage DropletManipulation via Redox. Langmuir 2011, 27 (7), 4249.(56) Hemeda, A. A.; Tafreshi, H. V. General Formulations forPredicting Longevity of Submerged Superhydrophobic SurfacesComposed of Pores or Posts. Langmuir 2014, 30, 10317.(57) Hemeda, A. A.; Tafreshi, H. V. Liquid-Infused Surfaces withTrapped Air (LISTA) for Drag Force Reduction. Langmuir 2016, 32(12), 2955−2962.(58) Boromand, A.; Jamali, S.; Maia, J. M. Viscosity MeasurementTechniques in Dissipative Particle Dynamics. Comput. Phys. Commun.2015, 196, 149−160.(59) Warren, P. B. Hydrodynamic Bubble Coarsening in Off-CriticalVapor-Liquid Phase Separation. Phys. Rev. Lett. 2001, 87 (22),225702−225704.(60) Chen, C.; Zhuang, L.; Li, X.; Dong, J.; Lu, J. A Many-BodyDissipative Particle Dynamics Study of Forced Water-Oil Displace-ment in Capillary. Langmuir 2012, 28 (2), 1330.(61) Ahmadlouydarab, M.; Hemeda, A. A.; Ma, Y. Six Stages ofMicrodroplet Detachment from Microscale Fibers. Langmuir 2018, 34(1), 198−204.(62) Chen, C.; Gao, C.; Zhuang, L.; Li, X.; Wu, P.; Dong, J.; Lu, J.Langmuir 2010, 26 (16), 9533−9538.(63) Ahmadlouydarab, M.; Lan, C.; Das, A. K.; Ma, Y. Coalescenceof Sessile Microdroplets Subject to a Wettability Gradient on a SolidSurface. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top.2016, 94 (3), 1−12.(64) Kumar, A.; Asako, Y.; Abu-Nada, E.; Krafczyk, M.; Faghri, M.From Dissipative Particle Dynamics Scales to Physical Scales: ACoarse-Graining Study for Water Flow in Microchannel. Microfluid.Nanofluid. 2009, 7, 467.(65) Zhang, K.; Li, Z.; Maxey, M.; Chen, S.; Karniadakis, G. E.Langmuir 2019, 35 (6), 2431.(66) Ghoufi, A.; Malfreyt, P. Mesoscale Modeling of the WaterLiquid-Vapor Interface: A Surface Tension Calculation. Phys. Rev. E -Stat. Nonlinear, Soft Matter Phys. 2011, 83 (5), 1−5.(67) Ghoufi, A.; Malfreyt, P. Calculation of the Surface Tension andPressure Components from a Non-Exponential Perturbation Methodof the Thermodynamic Route. J. Chem. Phys. 2012, 136 (2), 024104.(68) Joly, L. Capillary Filling with Giant Liquid/Solid Slip:Dynamics of Water Uptake by Carbon Nanotubes. J. Chem. Phys.2011, 135 (21), 214705.(69) Chang, C. C.; Sheng, Y. J.; Tsao, H. K. Wetting Hysteresis ofNanodrops on Nanorough Surfaces. Phys. Rev. E: Stat. Phys., Plasmas,Fluids, Relat. Interdiscip. Top. 2016, 94 (4), 1−8.(70) Li, Z.; Hu, G. H.; Wang, Z. L.; Ma, Y. B.; Zhou, Z. W. ThreeDimensional Flow Structures in a Moving Droplet on Substrate: ADissipative Particle Dynamics Study. Phys. Fluids 2013, 25, 072103.(71) Espanol, P.; Warren, P. Statistical Mechanics of DissipativeParticle Dynamics. Europhys. Lett. 1995, 30 (4), 191−196.(72) Sirghi, L.; Szoszkiewicz, R.; Riedo, E. Volume of a NanoscaleWater Bridge. Langmuir 2006, 22 (3), 1093−1098.(73) Wang, Y.; Wang, H.; Bi, S.; Guo, B. Nano-WilhelmyInvestigation of Dynamic Wetting Properties of AFM Tips throughTip-Nanobubble Interaction. Sci. Rep. 2016, DOI: 10.1038/srep30021.(74) Pal, S.; Lan, C.; Li, Z.; Hirleman, E. D.; Ma, Y. SymmetryBoundary Condition in Dissipative Particle Dynamics. J. Comput.Phys. 2015, 292, 287−299.

■ NOTE ADDED AFTER ASAP PUBLICATIONThis paper was published ASAP on October 1, 2019, with anerror in the title of the paper. The corrected version wasreposted on October 3, 2019.

Langmuir Article

DOI: 10.1021/acs.langmuir.9b02575Langmuir 2019, 35, 13301−13310

13310