Multivalent Adhesion and Friction Dynamics Depend on Attachment

Jul 12, 2017 - School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel. #. The Sackler Center for Computational Molecular and Materials Scien...
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Multivalent Adhesion and Friction Dynamics Depend on Attachment Flexibility Johanna Blass,†,‡ Marcel Albrecht,§ Gerhard Wenz,§ Roberto Guerra,∥ Michael Urbakh,⊥,# and Roland Bennewitz*,†,‡ †

INM - Leibniz Institute for New Materials, Campus D2 2, Saarbrücken 66123, Germany Physics Department, Saarland University, Campus D2 2, Saarbrücken 66123, Germany § Department of Chemistry, Saarland University, Campus C4 2, Saarbrücken 66123, Germany ∥ Dipartimento di Fisica, Universitá degli Studi di Milano, Via Celoria 16, Milano 20133, Italy ⊥ School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel # The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel ‡

ABSTRACT: Self-assembled monolayers introduce chemical functionalities to material surfaces, providing a route to tune their equilibrium and dynamical properties. We report on atomic force microscopy measurements and simulations of adhesion and friction forces caused by a macromolecular host−guest system, where the host molecules are attached to silicon oxide surfaces by means of self-assembled silane layers. Different preparation routes for the silane layers lead to different flexibility of the molecular attachment. The velocity dependencies of the work of separation and of friction vary significantly for attachments with different flexibility. Stiff attachment leads to low pull-off forces at low pulling velocity and to vanishing friction forces in the limit of low sliding velocity. Flexible attachment enhances cooperative contribution of multiple molecular bonds to adhesion and friction and causes significant friction at low sliding velocity. The latter observation can be explained by the contribution of intermittent contact aging to the friction force.

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INTRODUCTION Self-assembled monolayers (SAMs) are an effective tool in nanoscience for modifying surface functionalities. They facilitate the investigation of molecular interaction by means of atomic force microscopy (AFM). In chemical force microscopy measurements, surface and AFM tip are functionalized by SAMs to minimize nonspecific tip−sample interactions and to attach molecules of specific interest. High-quality monolayers and good reproducibility are required to perform reliable force spectroscopy experiments. Convenient flat samples for chemical force microscopy are the oxide surfaces of glass slides or silicon wafers. Silane derivatives with a specific head and tail group are used, where the headgroup forms covalent bonds with the oxide and the tail group is exposed to the solution and binds the specific molecular attachment. Here, we report AFM experiments on adhesion and friction mediated by a supramolecular host−guest system in aqueous solution. Cyclodextrin host molecules were attached to oxidized silicon wafers and to AFM tips by means of a silane SAM. Specific interactions were caused by molecules with two adamantane end groups, which formed inclusion complexes with cyclodextrin molecules at tip and surface. These molecules will be referred to as ditopic connector molecules. It was found that adhesion and friction dynamics depend critically on the preparation of the silane SAM. © 2017 American Chemical Society

The formation of silane SAM on oxide surfaces has been widely studied over the last decades,1,2 and general agreement has emerged that the degree of order in the SAM depends on deposition parameters such as temperature,3 solution age,4 and water content in solution and on the surface.3,5,6 Silane SAMs are cross-linked into a two-dimensional network, which is anchored by siloxane bonds to the underlying oxide surface. It is important to note that a formation of a fully cross-linked two-dimensional network, where all silane molecules are covalently attached to the surface, is not possible due to the limited number of ethyl groups and the steric hindrance of the alkyl chain.5 The water content and the age of the solution determine the level of cross-linking of silane molecules before deposition and thus the number of siloxane bonds formed with the surface. Explicit recipes were developed to achieve well-defined monolayers in terms of layer thickness, surface homogeneity, and roughness.7 There are two main options for the preparation of silane SAM: from liquid and from vapor phase. In liquid-phase deposition (LPD), silane molecules can oligomerize in solution forming small network patches before coupling to the oxide surface.3,5 Prior to oligomerizing, a hydrolysis of alkylsilanes is required.8 Received: June 2, 2017 Revised: July 10, 2017 Published: July 12, 2017 15888

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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Figure 1. Schematic of a β-CD monolayer attached to an AFM tip and silicon wafer via a silane SAM (a) prepared from fresh silane solution by vaporphase deposition (fresh VPD) and (b) prepared from aged silane solution by liquid-phase deposition (aged LPD).

For the first protocol (fresh VPD), the silicon was silanized by using a fresh silane solution, which was deposited from vapor phase. The clean silicon sample and 75 μL of the silane solution were placed into a desiccator. Before evacuation up to a pressure of 2 mbar, the chamber was floated with dry nitrogen to remove the remaining humidity inside the chamber. The sample was removed after 45 min, and rinsed with tetrahydrofuran (THF) and water. For the second set of samples (aged VPD), the silane solution was stored in saturated water vapor at room temperature for 7 days in a sealed chamber to mimic an aging of the silane solution when stored in laboratory conditions for a longer time scale. The samples were prepared in the same way as for the first samples. The third batch of samples (aged LPD) was prepared by liquid-phase deposition of an artificially aged silane solution. The silane was diluted in THF with a concentration of 0.1%, and the same amount of water was added. The solution was stored for 7 days in a sealed beaker. After the storage period, a cleaned silicon wafer was incubated in the solution for 2 h, and rinsed with THF and water. For attaching the cyclodextrin moelcules, the silanized wafer remained in 1 mM solution of mono(6-deoxy-6-amino)CD diluted in water overnight at room temperature. The silicon cantilevers (Nanosensors PPP-Cont AFM Probes, NanoandMore, Wetzlar, German) with a normal spring constant of 0.27−0.33 N/m were functionalized in the same way as the surfaces. Both the surface and the cantilevers were stored in water and used within 3 days after preparation. AFM Measurements. AFM measurements were carried out with a Nanowizard 3 setup (JPK Instruments, Berlin, Germany) in liquid at room temperature. The unspecific interactions between AFM tip and surface were determined in force measurements performed in pure water without guest molecules prior to every experiment. The results for the three different surface preparations were averaged into one data set, which serves as control in friction and adhesion measurements, respectively. Subsequently, the connector molecules were added with 10 mmol concentration into the solution, and the effect on the adhesion and friction was investigated. To exclude tip wear and investigate the adhesive friction, the normal force was kept below 1 nN in all adhesion and friction measurements. The maximum pull-off force was analyzed for 300 force−distance curves recorded at three different surface positions for each surface preparation. For each surface position, the most probable rupture force was obtained by fitting a Gaussian function to the histogram of pull-off forces. No change in the distribution of forces was found over the 300 repetitions, confirming that the covalent attachment of the supramolecular hosts was not altered. The friction force between AFM tip and surfaces functionalized with β-CD molecules attached to differently prepared

Hence, water in the silane solution promotes the oligomerization of silane molecules resulting in a loosely bound network attached via a smaller number of siloxane bonds to the surface.6,9 On the other hand, it has been demonstrated that self-assembly of the monolayer is progressing in a thin water film adsorbed on the surface.2 The water layer is crucial for the formation of a homogeneous layer and leads to a decrease of the roughness as compared to silanization of a dry wafer.3 Vapor phase deposition (VPD) prevents the molecules from oligomerizing before binding to the oxide, resulting in a two-dimensional network that offers more covalent bonds to the surface.5 A scheme of our experiment with silane layers prepared by liquid and vapor phase deposition is shown in Figure 1. The goal of this study was to identify the role of different silane attachments in single-molecule force spectroscopy and in adhesion and friction due to cooperative rupture and formation of multiple bonds. Our supramolecular system based on surfacebound cyclodextrin hosts and ditopic adamantance connector guest molecules is an excellent model to study the effects of varying attachment flexibility for three reasons. First, the cyclodextrin hosts are directly bound to the silane SAM so that no additional molecular linker adds flexibility. Second, the inclusion complex is probed in thermodynamic equilibrium,10 and thus the single-bond rupture force is independent of the pulling velocity. Finally, the symmetric functionalization of both contacting surfaces with host molecules allows for effective control experiments without specific interactions by simply not adding connector molecules. We prepared the silane SAM in three different ways. The first SAM, referred to as fresh VPD, was prepared by vapor phase deposition directly after receiving the silane solution. For the second SAM (aged VPD), water was added to the silane solution prior to vapor-phase deposition by storing the solution in a sealed container with saturated humidity at room temperature for 1 week. The third SAM (aged LPD) was prepared by liquid-phase deposition from silane diluted in tetrahydrofuran (THF), which contained 0.1% water. The three preparation methods were chosen to mimic typical aging processes in the laboratory.

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METHODS Surface Functionalization. Silicon wafers were supplied by Si-Mat, Kaufering, Germany, and cleaned with piranha, a mixture of sulfuric acid (95−98%) and hydrogen peroxide (30 wt %) in the ratio 3:1, subsequently rinsed with water, and dried with nitrogen. The silicon wafers were first silanized with 3isothiocyanatpropyl-triethoxysilane (the synthesis is described in ref 10) following the three different protocols. 15889

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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axis, is plotted in Figure 2a as a function of the pulling velocity varied over 3 orders of magnitude. The three forms of silane

silane layers is studied in sliding experiments. The adhesive interaction causes a torsion of the cantilever beam, which is recorded in the lateral deflection signal. The hysteresis included in the friction loop reveals the dissipated energy during sliding across the surface. The average of the lateral force of forward ffwd ̅ and backward fbwd ̅ sliding equals the friction force fL̅ = (ffwd ̅ − fbwd ̅ )/2. Lateral force measurements were calibrated using the wedge method in air11 (sample TGG01 from Micromash, Sofia, Bulgaria) and applying the correction factor for experiments in liquid introduced by Tocha et al.12 Simulations. We model our system following ref 13. In brief, an hemispherical tip is homogeneously covered by Nmax host complexes, represented by ideal rubber bands with springconstant kmol and rest length l0 (see Figure 5a). The complexes can bind to (or unbind from) the substrate following thermally activated rates Ron and Roff expressed by ⎤ ⎡ 1 0 R on = R on exp⎢ −θ(l − l0) k mol(l − l0)2 /kBT ⎥ ⎦ ⎣ 2 0 R off = R off exp[θ(l − l0)k mol(l − l0)δl /kBT ]

Figure 2. Experimental results: (a) Work of separation for βcyclodextrin-functionalized AFM tip and surface in adamantane connector solution; the control experiments were experiments performed in water for each silane preparation and averaged into one data set. Three different preparations of the silane SAM are compared. The error bars represent the standard deviation of the mean work values for three different surface positions. (b−d) Representative force curves recorded with different pulling velocities on a surface functionalized with a silane layer (b) deposited from vapor phase using fresh solution (fresh VPD), (c) deposited from vapor phase of aged solution (aged VPD), and (d) deposited from liquid phase in aged solution (aged LPD).

(1)

where and are characteristic attempt rates, δl the rupture barrier length, and kBT the thermal energy. The N(t) connected complexes (up to Nmax) form angles αi with the substrate and have elongations (li − l0) modulated by the Heaviside stepfunction θ to avoid repulsive contributions that are negligible within the rubber-band assumption. The tip, with mass M, diameter D, and coordinates (X, Z), is connected to the cantilever holder at (Xholder, Zholder) through springs of lateral and normal stiffnesses Kx and Kz, respectively. The tip is subject to a viscous damping γ, accounting for liquid environment. Tip and holder are initially placed at Xholder = X = 0, Zholder = Z = Z0. The resulting equations of motion are R0on

R0off

attachment exhibit logarithmic pulling-velocity dependencies of the work of separation with different slopes. For the fresh VPD silane attachment, the work of separation is by a factor of 2 higher than for the control experiments without connector molecules at all pulling velocities. After the work of separation was subtracted for the control experiment, the work of separation for the aged VPD is double that for the fresh VPD silane attachment, and the work of separation for the aged LPD is 4 times greater than that for the fresh VPD silane attachment, again at all pulling velocities. The control experiments for the three different silane preparations resulted in the same work of separation within scatter and were averaged for the presentation in the figures. In Figure 2b−d, representative force−distance curves are shown for the different silane SAM preparations and a variation of pulling velocities. For the fresh VPD silane attachment, a force plateau at about 300 pN was observed at low pulling velocity for distances up to 5 nm. This distance corresponds roughly to the expected height of the molecular attachment consisting of silane layers at surface and tip, cyclodextrin host molecules, and connector guest molecules. At higher pulling velocities, the shape of the force−distance curve changed to a triangular shape with a pull-off force of 800 pN at a distance of about 3 nm. The change in shape of the force−distance curves from an almost flat force plateau at low pulling velocity to a triangular shape with a distinct pull-off force at high pulling velocities was also observed for the aged LPD sample (Figure 2d), where the force plateau had a value of around 700 pN and the triangular force curve at high pulling velocity had a maximum pull-off force at 1800 pN. For both samples prepared from aged solutions, the force curves extended to a final rupture at distances of 12−15 nm, which is significantly longer than the expected length of the molecular attachment. While the characteristic shape of the force

MẌ = Kx(Xholder − X ) − MγẊ N

+

∑ −kmolθ(li − l0) cos(αi) i=1

(2a)

MZ̈ = K z(Z holder − Z) − MγŻ + A subZ −7 N

+

∑ −kmolθ(li − l0) sin(αi) i=1

(2b)

in which the term AsubZ−7 takes into account for a short-range repulsion between the tip and substrate. The bonds form vertically, and follow the motion of the tip along X or Z direction; thus no force along the transverse Y direction is generated. Integration of the equations of motion has been performed by a velocity-Verlet algorithm with a time step Δt = 1 μs, while formation/rupture of the complexes is stochastically governed at each time step according to the probabilities Pon = RonΔt and Poff = RoffΔt. The employed parameters are Ron = 10 kHZ, Roff = 0.1 kHz, Nmax = 70, kmol = 0.04−0.0025 N/m, l0 = 2 nm, δl = 0.2 nm, Z0 = 0.1 nm, kBT = 25.85 meV, Kx = 50 N/m, Kz = 0.32 N/m, γ = 13.3 ms−1, M = 1.15 × 10−9 kg, and D = 20 nm.

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RESULTS AND DISCUSSION Experimental Results. The adhesion between AFM tip and surface, mediated by the cyclodextrin−adamantane interaction, was determined in force spectroscopy measurements, where the tip was pulled out of contact. The work of separation, that is, the area bounded by the force−distance curve and the zero-force 15890

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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Figure 4. Experimental results: (a) Mean friction force acting on the AFM tip sliding on the three differently prepared layers, and the corresponding control experiments. The error bars are the standard deviation of the average friction force of 50 friction loops. (b−d) Representative friction loops recorded for a sliding velocity of 800 nm/s on (b) the fresh VPD, (c) the aged VPD, and (d) the aged LPD sample.

Figure 3. Details of experimental force versus distance curves for the last rupture, indicating the unbinding force for single adamantane− cyclodextrin complexes. The three different silane attachments lead to different effective force loading rates of 43 nN/s for fresh VPD, 10 nN/s for aged VPD, and 2.5 nN/s for aged LPD. The pulling velocity was 1 μm/s.

friction force for the fresh VPD sample showed a logarithmic increase for velocities higher than 50 nm/s. Below 50 nm/s the friction force was comparable to the friction measured in control experiments in the absence of connector molecules. Also, similar to the work of separation, the friction forces for the aged VPD and aged LPD samples were significantly higher than that for the fresh VPD samples. For both aged VPD and aged LPD attachment layers, the friction force only slightly depends on velocity, and thus significant friction was found even at low velocities, at which no friction was detected for fresh VPD samples. Representative friction loops, that is, lateral force curves recorded while scanning the tip one line back and forth, are shown in Figure 4b−d for the three different silane attachments. The area included by the friction loops, divided by twice their length, is the friction force reported in Figure 4a. Spikes in the friction loop revealed an irregular stick−slip motion of the AFM tip for all surfaces. The peak lateral force at the spikes of 1000− 1500 pN was similar for all three silane attachments, but the number of spikes was higher for the aged VPD and aged LPD samples. Furthermore, the leading slope of the spikes revealed the effective lateral contact stiffness keff during the sticking of tip. The lateral contact stiffness varied for the silane preparation methods, from about 1 N/m for the VPD samples to 0.2 N/m for the aged LPD sample. As was already observed in adhesion experiments, the liquid deposition from an aged solution leads to a more compliant attachment. The experimental results revealed a strong influence of the preparation method for the silane attachment layer on effective stiffness, adhesion, and friction of the supramolecular host−guest system. Not only the force values but also their pulling-velocity dependence varied between silane layers prepared by vaporphase or liquid-phase deposition using solutions of different water content. We start the discussion of the results from an analysis of the effective stiffness experienced by a single molecular bond with different attachment procedure. We then introduce the results of simulations of adhesion and friction experiments, where the bonding molecules are individually attached to the surface by spring-like linkers of varying stiffness.

maximum corresponding to the last step in the force curve, at which the cantilever returns to its relaxed position, is close to 100 pN or a multiple thereof, indicating the rupture of a single adamantane−cyclodextrin bond or simultaneous rupture of a few bonds. All three silane attachments led to the same single-bond rupture force of 100 pN. This value depends predominantly on the cantilever stiffness.14 The slope of the force curve at the moment of rupture revealed the effective stiffness of the molecular system and the effective loading rate. The stiffness as well as the rupture length varied greatly for the three different silane layers, although all force curves were recorded by cantilevers with a stiffness of kN = 0.32(2)N/m. In the case of the fresh VPD sample, the stiffness was the highest with 0.043 N/ m, while the effective stiffness was much lower for the aged VPD sample with 0.010 N/m and for the aged LPD sample with 0.0025 N/m. Correspondingly, the effective force loading rate varied by a factor of 14 between aged LPD and fresh VPD samples. The rupture length for the unbinding of the last complex is somewhat uncertain as it is unknown at which part of the tip apex the binding host molecule was attached. The zero of the distance axis is defined by the repulsive contact between tip apex and surface. However, one can estimate the rupture length as the rupture force divided by the effective stiffness. This gives a rupture length of about 2.5 nm for the fresh VPD sample, as expected for the size of the molecular complex, and longer lengths of 10 and 40 nm for the aged VPD and aged LPD samples, respectively, which are in rough agreement with the rupture distances in Figure 3. Although the three curves in Figure 3 are example curves, we can conclude that the deposition of silane from aged solutions leads to rather compliant attachment layers. Friction experiments for the AFM tip sliding on the surfaces are summarized in Figure 4a. The friction force is the average of the lateral force and is equivalent to the work dissipated per unit sliding distance. Its dependence on the sample preparation can thus be compared to the work of separation presented above. Similar to the pull-off experiments reported in Figure 2a, the 15891

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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Figure 5. (a) Setup of the simulation of the experiment. (b) Force−distance curves simulated for a attachment stiffness of kmol = 0.04 N/m motivated by the value determined for the fresh VPD sample. Force curves are presented for three different pulling velocities. The lower panel (c) indicates the number of connected bonds as a function of the position of the pulling spring.

Figure 6. Results of the simulation: (a) Force curves for varying attachment stiffness and a pulling velocity of 750 nm/s. The lower panel indicates the number of connected bonds as a function of the cantilever position. (b) Work of separation as a function of the pulling velocity for varying attachment stiffness.

the remaining free bonds, a loosely bound network is formed whose compliance leads to a low effective stiffness in the force− distance curves. The attachment of preoligomerized patches is more relevant in liquid-phase than in vapor-phase deposition, as preoligomerized molecules are less likely to evaporate than individual molecules. In line with this picture, we observed the lowest stiffness for the aged LPD samples and an intermediate stiffness for the aged VPD samples. The force−distance curves exhibit linear behavior before the final single-bond rupture. While we do not have direct insight into the molecular structure of each silane layer, the linear characteristic indicates that up to 100 pN force the layers act as linear spring, and not as the nonlinear entropic spring often observed for a molecular linker such as poly(ethylene glycol). The dependence of the effective stiffness on the silane preparation method is confirmed by the variation of the lateral contact stiffness in the friction loops. Simulation Results. The simulation setup is depicted in Figure 5a, and the details are given in the Methods. Seventy molecular bonds are individually attached to the surfaces of flat sample and curved AFM tip by linkers of varying stiffness. Note that the notion of cross-linked silane patches that are loosely attached to the surfaces is not reflected in this simulation. Rather, all binding partners are directly attached to the surface by a molecular linker with stiffness kmol. Parameters of the simulation such as tip radius, cantilever mass and stiffness, molecular kinetics, or rupture forces are chosen to represent the

We point out that only the preparation method introduced above as fresh VPD leads to experimental results, which match the simulation results well. Finally, we discuss characteristic differences between simulation and experimental results with respect to the structure of the silane layers and cooperative effects in adhesion and friction. Stiffness Variation for Different Silane Attachment Layers. In a significant fraction of our force spectroscopy experiment, the final detachment of the tip from the surface corresponded to the unbinding of a single cyclodextrin− adamantane complex. The well-defined binding configuration just before rupture allows for a direct comparison of the effective stiffness of the molecular system consisting of silane attachment layer and supramolecular host−guest couples. We interpret the variation of the stiffness as an effect of the structure of the silane layer. A well-ordered monolayer with many siloxane bonds attached to the oxide surface exhibits the highest stiffness, while a highly cross-linked layer with fewer bonds connected to the surface includes long elastic paths connecting points of attachment to the tip and surface, which results in higher flexibility. In our results, silane layers prepared from an aged solution containing water exhibit higher flexibility than the stiffest layers, which were produced from a fresh solution with low water content (fresh VPD). Water leads to a hydrolysis of silane molecules, which promotes their oligomerization already in solution.8 When oligomerized patches attach to the surface with 15892

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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Figure 7. Results of the simulation: (a) Lateral force curve for varying attachment stiffness of and a sliding velocity of 800 nm/s. The lower panel indicates the number of connected bonds. (b) Friction as a function of the sliding velocity for varying attachment stiffness. The inset is a detail showing that friction forces approach zero at at low velocities, linearly for the case of compliant linker molecules.

0.0025 N/m and 200 nm/s for kmol = 0.04 N/m, the work of separation increases with pulling velocity. This velocity dependence, which can be attributed to the cooperativity of multiple reversible bonds,10,13 is strongly enhanced for a flexible attachment due to the corresponding increase in the number of connected bonds. Results of simulations of friction are presented in Figure 7. The lateral force experienced by the tip sliding across the layer of molecular bonds was not constant but exhibited a series of irregular lateral force peaks, indicating a stick−slip movement of the tip, which is caused by cooperative action of groups of connected bonds, that detach in avalanche-like events. With decreasing stiffness of the attachment molecules, the force peaks become broader and the interval between them increases. The slope of the leading edge of the peaks indicates the lateral stiffness of the contact during the sticking phase of the stick−slip motion. This lateral contact stiffness decreases with decreasing stiffness of the attachment molecules. A 4-fold decrease in the attachment stiffness kmol leads to an only 2-fold increase in the number of connected bonds. This relation explains why the overall lateral stiffness decreases for decreasing attachment stiffness. The average friction force is plotted as a function of the sliding velocity for varying attachment flexibility in Figure 7b. In the low velocity limit, friction force linearly approached zero, and the curves corresponding to the different attachment stiffnesses merge. For velocities above 200 nm/s, a logarithmic dependence of friction on sliding velocity has been found. At these sliding velocities, the softest attachment again resulted in the highest dissipative force values. However, the friction force enhancement with reduction of stiffness is less pronounced than in the case of the work of separation. At a sliding velocity of 1000 nm/s, friction for the lowest value of kmol = 0.0025 N/m is only 20% higher than that for kmol = 0.01 N/m and 65% higher than that for kmol = 0.04 N/m, in contrast to factors of 3 and 5 in the case of the work separation in the adhesion simulations at a pulling velocity of 1600 nm/s. To sum the results of simulations, flexibility of the molecular attachment leads to an increase in the number of connected bonds between tip and sample, generally resulting in higher adhesion and friction forces. A larger number of connected bonds also enhances effects of cooperativity and thus leads to stronger dependence of the work of separation and of friction on pulling velocity, while rupture forces calculated for a single

experiments. The essential results of adhesion and friction experiments are captured by the simulation.13 As an example, the variation in the shape of force curves with increasing velocity (Figure 2b) from a force plateau to a sawtooth shape is reproduced by the simulation results presented in Figure 5b. To get insight into the mechanism underlying this experimentally observed transition, we presented in Figure 5c the variation of the number of connected bonds with the cantilever position, Zholder, which have been calculated for different pulling velocities. For slow pulling, the number of connected bonds decreases linearly with Zholder and is accompanied by occasional rebinding events, reflecting a peeling-type detachment bond by bond. This regime of detachment leads to a plateau in the force curve. For fast pulling, we found a cooperative mechanism of rupture of adhesion bonds. In that case, the number of bonds is initially constant, indicating a cooperative adhesive attachment. The sequential bond rupture occurs at a higher force, exhibiting avalanche-like detachment events. The rupture terminates at a larger distance, resulting in an overall increase of the work of separation with increasing pulling velocity. In this Article, we focus on the dependence of adhesion and friction of multiple molecular bonds on the stiffness of the linker between molecule and surfaces. Simulated force−distance curves for attachments of varying flexibility are presented in Figure 6a. Lower attachment stiffness led to a higher maximum adhesion force and to a larger distance for the final detachment, which result in a larger work of separation. As shown in Figure 6b, this behavior is mainly originated from the increase in the number of connected bonds at zero normal load, which occurs with increasing flexibility of the attachment. Because of the curvature of the AFM tip, more molecular bonds may form contacts with the tip if the linker molecules are easier to stretch. To summarize the simulations of adhesion, the work of separation increases with increasing pulling velocity and with decreasing attachment stiffness; see Figures 5b and 6b. In the low velocity limit, the work of separation is velocity independent as expected for reversible bonds, which are probed in thermal equilibrium. Fast rebinding of broken bonds leads to a finite pulloff force even for slow pulling.10,13 This limiting value of the pulloff force and the value of the work of separation scale with the number of connected bonds and thus with the compliance of the attachment. Starting from pulling velocities of 50 nm/s for kmol = 15893

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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other cases described above and thus also exhibit significant differences from the simulation results. We conclude that the molecular model underlying the simulations represents the samples prepared by vapor-phase deposition from a fresh solution (fresh VPD) well, while the samples prepared from aged solutions (aged VPD and LPD) have characteristic features in adhesion and in particular in friction, which are not captured by the simulated model. We will discuss possible additional mechanisms of adhesion and friction for these compliant attachments in the following section. Adhesion and Friction for Compliant Polymeric Attachment. We have discussed in the Introduction that preparation of the silane attachment from solution containing water can lead to the formation of small patches of a silane network, which are then anchored on the oxidized silicon surface by few covalent bonds. The result is a rather flexible polymeric network carrying the molecular hosts. The strongly enhanced adhesion and in particular friction for the flexible attachment network can be explained by a wrapping of the attachment layer around the tip apex with an increased number of connected bonds. Experiments with shape-persistent polymers carrying the cyclodextrin hosts have already revealed an increase of work of separation and friction as compared to the situation where the cyclodextrin hosts are directly attached to tip and surface.15 Unexpectedly, the wrapping of compliant surface layers around the AFM tip has been reported to lead to an increased friction upon reducing the applied load.16 The observations are also in line with recent reports for very soft adhesion probes such as carbohydrate hydrogel particles17 or bacteria.18 However, to explain the surprising absence of a reduction of friction toward low sliding velocities, we will now discuss the role of contact aging. Contact aging describes the increase in the number of bonds within the contact while the AFM tip rests in contact with the surface. For our system, we believe that contact aging is a diffusive process bringing cyclodextrin hosts and connector molecules in a geometric constellation suitable for complexation, a process much slower than the unbinding and rebinding kinetics of a complex that was already established. Contact aging can be quantified by adhesion experiments measuring the pull-off force as a function of the time in contact before retracting the tip. Thanks to the fast kinetics, the supramolecular bonds approach thermodynamic equilibrium at times shorter than 10 ms, which is the lower limit of the contact time in our experiments. A logarithmic increase of the pull-off force was observed for contact times between 10 and 10 ms (see Figure 8). The most probable pull-off force was fitted with the following equation:

reversible bond do not exhibit a velocity dependence. The simulations highlight a key difference between work of separation and friction. In the low velocity limit, the work of separation is finite and velocity-independent, while dissipative friction approaches zero. The difference originates from the fact that in pull-off experiments the bonds reattach in a stretched state, and thus the interfacial adhesion energy has to be invested. In contrast, in friction measurements the bonds rebind in the unstretched state, and the energy dissipation diminishes in the limit of zero driving velocity. Comparison between Experimental and Simulation Results. The simulation results closely match the experimental results with respect to overall appearance and details in force− distance curves (Figures 2 and 6) and lateral force curves (Figures 4 and 7). Simulations help to understand the mechanisms of adhesion and friction of multiple reversible bonds by revealing the actual number of connected bonds and by offering the opportunity to vary independently microscopic parameters. We will now compare the experimental results for differently prepared silane layers with simulation results obtained for different stiffness of molecular attachment springs. We start by reminding that in simulations each molecular guest is attached by a single spring. The stiffness values for these springs have been chosen to match the effective stiffness found in adhesion experiments for the final rupture of tip−sample contact when only a single molecular bond was probed (Figure 3). Generally, the simulations reveal a larger work of separation and dissipative friction, for softer attachment springs at all velocities. The same results were observed in experiments, where the softest attachment can be attributed to the aged LPD preparation and stiffer attachment for aged VPD and fresh VPD preparation. The larger number of connected bonds for softer attachment does not only explain the increase in work required to separate the tip from sample or to slide the tip over the surface, but it also explains the stronger pulling-velocity dependence of the work of separation and of friction for softer attachment found in experiments and simulations. The simulations of speed dependencies for the work of separation and for friction performed for kmol = 0.04 N/m agree well with the corresponding experimental results for the fresh VPD samples. The measured work of separation is clearly higher than that in the control experiments without connector molecules even at very low velocities. Its magnitude increases for pulling velocities higher than 200 nm/s in quantitative agreement with the simulation results. For the friction experiments, the average friction force decreases with decreasing velocity, and, for sliding velocities below 50 nm/s, it does not exceed the values for control experiments. These observations match simulation results, where friction approaches zero in the low velocity limit. In contrast, significant differences between the simulation and experimental results are found for the softer attachment by the aged VPD or aged LPD preparations. For the aged LPD samples, the measured work of separation was in quantitative agreement with the simulations at high pulling velocities, but the velocity dependence observed in experiments was weaker and extended to the lowest pulling velocity of 50 nm/s, where simulations predict a regime of constant work of separation. In the case of friction, the differences are even more pronounced. Friction forces are larger in experiments and exhibit no sliding velocity dependence at all, resulting in strong friction at the lowest sliding velocity where simulations suggest vanishing friction. For the aged VPD samples, the experimental results lie between the two

Figure 8. Experimental result for the aged LPD attachment layer: Maximum adhesive force upon tip retraction as a function of the contact time for different pulling velocities. 15894

DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896

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revealing how the number of connected bonds with nonequal load sharing depends on the stiffness of the molecular linker. In the case of friction experiments, a good agreement between experimental and simulation results has been found only for the stiffest silane layers, which were prepared by vapor-phase deposition from a silane solution of low water content. Experiments with softer silane layers prepared from watercontaining solutions result in a weak velocity dependence of friction forces and significant friction forces at low velocities. In contrast, simulations predict vanishing friction in the limit of low velocity. This discrepancy is explained by the additional contributions to the friction forces measured at low velocities, which originate from intermittent contact aging, that is, the strengthening of the contact while remaining at rest. Contact aging manifests itself as increase of the pull-off force for increasing waiting times between approach and retraction of the AFM tip. In friction experiments, the sliding of the AFM tip proceeds in a stick−slip motion, where contact aging that occurs during the stick phases leads to an increase of the total friction force. Water molecules easily enter silane solutions by exposure to humidity. They cause an increase of cross-linking in the resulting silane monolayer and a decrease in number of covalent bonds connected to the silicon oxide substrate. The silane layer is then a rather two-dimensional attachment, which provides the flexibility to establish additional molecular bonds between AFM tip and sample. Our results demonstrate the importance of attachment flexibility for adhesion and friction experiments on selfassembled monolayers. They highlight the role of contact aging in stick−slip friction and indicate a method to tune the velocity dependence of friction by varying the relative contributions of contact aging and multivalent cooperativity.

Fpull ‐ off = F0·ln(t /t 0)

where t is the contact time scaled to the time constant t0, which depends on the pulling velocity, and F0 is a proportionality factor. The best fit to the data revealed a logarithmic increase of the pulloff force as a function of the contact time with a slope of F0 = 0.19 nN in solution including connector molecules. In the adhesion experiments reported in the Results and Discussion, a hold time of 5 s is applied for all pulling velocities. The variation of the pulling velocity leads to a variation of the actual contact time between 5.003 and 5.5 s. Because of the logarithmic increase of pull-off forces with contact time, the variation of the pull-off force caused by the contact aging for varying pulling velocities is negligible. In contrast to adhesion, the contact time in friction changes significantly with the sliding velocity, so that contact aging effects become important in friction. For the most flexible attachment (aged LPD), the stick−slip pattern exhibited a typical stretching length of 5 nm leading to a contact time in the sticking phase of 0.5 s for a sliding velocity of 10 nm/s and of 5 ms for 1000 nm/s. We thus expect an increase in friction force for decreasing sliding velocity due to contact aging. Reading from Figure 8, the increase of friction due to the contribution of aging would be about 0.5 nN for 10 nm/s and 0.05 nN for 1000 nm/s. The contact aging effect presumably balances the reduction of friction with decreasing velocity, which originates from the reduction of rupture force, resulting in an almost constant total friction force. We believe that the contact aging effect for the stiffer attachments is weaker because the host molecules have less configurational opportunities to rearrange. In addition, the higher lateral contact stiffness for the stiffer attachments leads to shorter contact times in the stick phases by a factor of 5, reducing contributions of aging compared to on the most flexible attachment. Given the lack of knowledge about the exact structure of the flexible attachment layer, we have refrained from attempts to include its effects into our simulation. In summary, the flexibility of the attachment provides the opportunity to tune the strength and dynamics of adhesion and friction. In adhesion experiments, a more flexible attachment enhances the pulling-velocity dependence of pull-off forces, whereas in friction experiments a contact aging effect balances the rate effect. Control of the quality of silane attachment layers is crucial for investigating adhesion and adhesive friction. A flexible silane network deposited from liquid phase provides high adhesion and friction forces and offers the opportunity to study the combined dynamics of cooperative interactions and contact aging. Experiments with stiffer layers deposited from vapor phase focus on cooperative dynamics of ensembles of molecular bonds and allow one to avoid contact aging effects.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Gerhard Wenz: 0000-0002-2548-7682 Michael Urbakh: 0000-0002-3959-5414 Roland Bennewitz: 0000-0002-5464-8190 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the financial support from the Volkswagen Foundation. J.B. and R.B. thank Prof. Eduard Arzt for continuing support of this study. M.U. acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG) under grant no. BA1008/21.

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CONCLUSION Adhesion and friction caused by the interaction of multiple molecular bonds are determined by a cooperative behavior of these bonds, which depends critically on the stiffness of the molecular linker to the respective surfaces. Cooperative effects lead to an increase of adhesion and friction forces with increasing pulling and sliding velocity. These trends are enhanced for softer molecular linkers. For the molecular binding partners attached to the substrates through self-assembled silane layers of varying stiffness, the results of atomic force microscope measurements of adhesion force agree well with simulation results. Simulations provide important insights into the mechanism of adhesion

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DOI: 10.1021/acs.jpcc.7b05412 J. Phys. Chem. C 2017, 121, 15888−15896