Article pubs.acs.org/Langmuir
Nanoscale Contact Mechanics of Biocompatible Polyzwitterionic Brushes Zhenyu Zhang,†,∥ Andrew J. Morse,† Steven P. Armes,† Andrew L. Lewis,‡ Mark Geoghegan,§ and Graham J. Leggett*,† †
Department of Chemistry, University of Sheffield, Brook Hill, Sheffield S3 7HF, U.K. Biocompatibles UK Ltd., Chapman House, Farnham Business Park, Weydon Lane, Farnham, Surrey GU9 8QL, U.K. § Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, U.K. ‡
S Supporting Information *
ABSTRACT: Friction force microscopy has been used to demonstrate that biocompatible, lubricious poly(2(methacryloyloxy)ethylphosphorylcholine) (PMPC) brushes exhibit different frictional properties depending on the medium (methanol, ethanol, 2-propanol, and water; the latter also with different quantities of added salt). The chemical functionalization of the probe (amine-, carboxylic acid-, and methyl-terminated probes were used) is not as important as the medium in determining the contact mechanics. For solvents such as methanol, where the adhesion between AFM probe and PMPC brushes is negligible, a linear friction−load relationship is observed. In contrast, the friction−load plot is nonlinear in ethanol or water, media in which stronger adhesion is measured. For ethanol, the data indicate Johnson−Kendall−Roberts (JKR) mechanics, whereas the Derjaguin−Muller−Toporov (DMT) model provided a good fit for the data acquired in water. Contact mechanics on zwitterionic PMPC brushes immersed in aqueous solutions of varying ionic strength followed the same trend, with high adhesion energies being correlated with a nonlinear friction−load relationship. These results can be rationalized by treating the friction force as the sum of a loaddependent term, attributed to molecular plowing, and an area-dependent shear term. In a good solvent for PMPC such as methanol, the shear term is negligible and the sliding interaction is dominated by molecular plowing. However, the adhesion energy is significantly larger in water and ethanol and the shear term is no longer negligible.
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INTRODUCTION It is well-known that the friction force Ff between two macroscopic bodies is linearly dependent on the applied load FN. Thus, Ff = μFN, where μ is the coefficient of friction and is independent of the contact area.1,2 Over the past few decades, there has been growing interest in understanding the frictional behavior of microscopic contacts. Various models based on continuum mechanics have been developed to describe single asperity contacts, and these have been tested extensively using friction force microscopy (FFM).3,4 The common feature of all such single-asperity theories is that the total contact area is a sublinear function of FN (typically, it varies as FN2/3).5,6 Despite the remarkable success of continuum models, they suffer from some serious limitations. At atomic length scales, where the discreteness of atoms often has a direct effect on physical properties, there is no reason to believe that continuum level models should be capable of reproducing the observed tribological behavior. Deviations from continuum models have sometimes been observed at the nanoscale, which have been attributed to the breakdown of continuum mechanics.7 In fact, a number of atomic-scale phenomena have been observed during sliding that are not consistent with any continuum theories.8−11 For example, Socoliuc et al. found that a © XXXX American Chemical Society
continuum approach cannot account for the lateral contact stiffness, which was found to be almost load-independent,12 when operating at the lowest accessible loads for atomic force microscopy (AFM) tips with radii of less than 15 nm. Mesoscale contacts are such that the area of contact is significantly greater than atomic dimensions but nevertheless remains microscopic. This category includes most measurements made using FFM, which has generated a great deal of debate regarding the precise nature of the contact mechanics. For contacts between molecular materials, it has proved very difficult to identify the appropriate contact mechanics model for single asperity contacts. Indeed, many authors have eschewed single asperity models altogether and instead analyzed their data using Amontons’ law of macroscopic friction.8,9,11 Analyses of friction−load relationships in condensed media have begun to shed some light on these important problems. Until recently, the influence of the medium in which sliding occurs has been usually ignored. However, work in this Received: May 16, 2013 Revised: July 1, 2013
A
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laboratory has shown that the friction−load relationship for free-standing polyester films immersed in ethanol is linear but becomes nonlinear in either perfluorodecalin or hexadecane.13 On the other hand, changing the medium from ethanol to perfluorodecalin for self-assembled monolayers led to a switch between linear and sublinear friction−load relationships.14 Ruths15 has also demonstrated that the medium has a significant influence on the frictional behavior of monolayers. More recently, Busuttil et al. and Nikogeorgos et al. examined the relationship between contact mechanics and hydrogen bond thermodynamics for carboxylic acid- and hydroxylterminated SAMs.16−18 They observed a sublinear friction− load relationship in most media, but a linear response when the surface was solvated by polar molecules (hydrogen bond acceptors) present in the medium. They rationalized these findings by treating the friction force as the sum of an areadependent term and a load-dependent term, associated with “molecular plowing”, in which energy is dissipated in conformational changes in the molecular film. This model17,18 is characterized by a coefficient of friction, μ, and an areadependent shear term, characterized by a surface shear strength, τ, giving, for the friction force18 ⎛ R ⎞2/3 FF = μ(FN + Fa) + π ⎜ ⎟ τ(FN + Fa)2/3 ⎝K⎠
There have been a number of studies of brush friction using FFM, as detailed above. Just as for SAMs there are important unanswered questions concerning the mechanics of the tip− brush contact, so for polymer brushes the relationship between the polymer structure, the medium, and the contact mechanics is not well understood. FFM is very sensitive to changes in lubricity resulting from changes in the extent of polymer solvation, and large differences in the coefficient of friction determined from FFM data have been reported in media that exhibit good and poor solvent characteristics.22,40,41 However, little work has addressed our understanding of the contact mechanics of solvated polymer brushes on the nanoscale. The primary goals of the present study were (i) to examine the nanotribological properties of PMPC brushes in a range of media, (ii) to determine the most appropriate contact mechanics model for data analysis, and (iii) to investigate the relationship between friction and adhesion in these systems. Various liquids were selected that ranged from good to poor solvent for PMPC chains, while the surface chemistry of the AFM probe was controlled by functionalization with an appropriate SAM.
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EXPERIMENTAL METHODS
Materials. Silicon wafers (⟨100⟩ orientation, boron-doped, 0−100 Ω cm) were purchased from Compart Technology (Peterborough, UK). 2-(Methacryloyloxy)ethylphosphorylcholine monomer (MPC, >99% purity) was kindly donated by Biocompatibles UK Ltd. and used as received. 2-Bromoisobutyryl bromide (BIBB, 98%), triethylamine (TEA, 99%), copper(I) bromide [Cu(I)Br, 99.999%], copper(II) bromide [Cu(II)Br2, 99.999%], and 2,2′-bipyridine (bpy, 99%) were purchased from Sigma-Aldrich UK. All were used as received apart from the TEA, which was refluxed over potassium hydroxide, distilled, and stored over fresh potassium hydroxide prior to use. This was kept for up to 30 days, after which it was distilled prior to further use. 3Aminopropyltriethoxysilane (APTES, >98%) was purchased from Fluka and used as received. Methanol, ethanol, and 2-propanol (HPLC grade) were purchased from Fisher Scientific (Loughborough, UK) and used as received. Tetrahydrofuran (THF) was supplied from a Grubbs dry solvent system. Deionized water was obtained using an Elga Elgastat Option 3 system. Preparation of Surface-Initiated Silicon Wafers. Silicon wafers were washed in turn with acetone, 2-propanol, and water to remove any grease or other contaminants. The washed substrate was then immersed in a cleaning bath containing a mixture of ammonia solution (28 mL, 35 wt %), hydrogen peroxide solution (28 mL, 30 wt %), and water (142 mL) at 70 °C. After 15 min, the bath was removed from the heat and overflowed three times with deionized water to remove any surface contaminants. The cleaned substrate was then removed, washed with deionized water, and dried under a stream of nitrogen gas. Clean silicon wafers were stored in sealed Petri dishes for up to 30 days prior to use. The clean silicon wafer substrate was then exposed to APTES vapor under reduced pressure (in a glass chamber containing liquid APTES pumped down to 0.2 mbar and then sealed) for 30 min and then annealed for a further 30 min at 110 °C. This protocol was utilized to functionalize the silicon wafer surface with primary amine groups. The substrate was then immersed in dry THF (100 mL) under a nitrogen atmosphere. TEA (1.39 mL) was added, followed by BIBB (1.24 mL), and the reaction solution was allowed to stand for 3 h without stirring at 20 °C. The substrate was removed, washed in turn with THF, water, methanol, and acetone, and then dried under a nitrogen stream. The initiator-coated wafer yielded a water contact angle of 67 ± 2°. The total surface layer thickness (i.e., the native silicon dioxide layer plus the ATRP initiator) was approximately 2.2 nm, as judged by ellipsometry. Preparation of PMPC-Coated Silicon Wafers. Methanol and water were separately deoxygenated using a nitrogen purge for 30 min.
(1)
where Fa is the pull-off force, R is the tip radius, and K is the elastic modulus of the film. These findings are in agreement with earlier work by other workers, who proposed the separation of the friction force into area- and pressuredependent terms.3,19 In the limit of very low adhesion, when the surface is highly solvated, the second term tends to zero and the friction−load relationship becomes linear. Under other circumstances, the friction−load relationship is nonlinear. For self-assembled monolayers, Derjaguin−Muller−Toporov (DMT) mechanics generally provides a good fit to the friction−load relationship5 with the exception of perfluorodecalin, for which the Johnson−Kendall−Roberts (JKR) model provides a better fit.6 There has been growing interest in the design of novel polymeric lubricants, and FFM has been widely used to study such systems.20−26 In a good solvent for the polymer and at relatively low applied loads, all polymer-bearing surfaces exhibit relatively low friction coefficients. In particular, polymer brushes are known to behave as effective lubricants, and the mechanisms underlying this behavior have been the focus of much attention over the past few decades.18,27−32 Poly(2(methacryloyloxy)ethylphosphorylcholine) (PMPC) is a polyzwitterion bearing both positive and negative charge. Like many polybetaines, PMPC exhibits so-called “antipolyelectrolyte” behavior; i.e., its dimensions are relatively insensitive to added salt, in contrast to conventional polyelectrolytes, which usually shrink due to electrostatic screening. In aqueous solution, PMPC causes very little disruption to hydrogen-bonded water molecules; this is considered to be important for its strong resistance to biofouling since protein adsorption is suppressed.33,34 Besides its excellent lubricious properties, PMPC is also notable for its high biocompatibility.35,36 This combination of characteristics makes PMPC highly attractive for coating various biomedical devices and implants,37 and so for applications involving moving contacts (e.g., prosthetic joints) it is important to understand the contact mechanics of PMPC brushes in various environments.38,39 B
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MPC (4.00 g, 0.0135 mol, 60 equiv) was added to a flask and placed under nitrogen using three pump−refill cycles. Methanol (2.0 mL) and water (2.0 mL) were added, and the mixture was stirred to aid dissolution. Meanwhile, the ATRP initiator-functionalized substrate was cut into suitable sizes (ca. 1 cm2) and placed under nitrogen using three pump−refill cycling of up to six tubes in a Radley’s Carousel 12 Reaction Station. Cu(I)Br (32.3 mg, 0.2251 mmol, 1 equiv), Cu(II)Br (15.1 mg, 0.0676 mmol, 0.3 equiv), and bpy (98.7 mg, 0.6319 mmol, 2.8 equiv) were added to the MPC monomer solution, with ultrasonication and stirring being employed to aid dissolution (relative molar ratios were MPC:Cu(I)Br:Cu(II)Br2:bpy = 60:1:0.3:2.8). The reaction solution was injected equally into the carousel tubes over the ATRP initiator-functionalized wafers until the substrates were immersed in the polymerization solution. These were maintained at ambient temperature and pressure without stirring. Once polymerization was terminated, the substrates were removed and rinsed with excess methanol, water, and methanol again to remove unreacted MPC monomer and any ATRP catalyst. These substrates were then soaked in methanol overnight to remove any nongrafted PMPC chains and then dried under a dry nitrogen stream. The final PMPC-coated wafer was hydrophilic. The mean thickness of the PMPC brush layer was 103 nm, as determined at five random points along a polymercoated silicon wafer using a Jobin Yvon UVISEL spectroscopic ellipsometer. Representative samples were checked routinely by XPS and contact angle goniometry to ensure the formation of well-defined initiator and brush layers during each synthesis steps. Preparation of Self-Assembled Monolayers. Silicon nitride triangular AFM probes (NP-10, Veeco, Cambridge, U.K.) were chemically functionalized by deposition of a self-assembled monolayer of either dodecanethiol (HS(CH2)11CH3), or mercaptoundecanoic acid (HS(CH 2) 10COOH), or 11-amino-1-undecanethiol (HS(CH2)11NH2) (Sigma-Aldrich UK). Gold wire (>99%, Testbourne, Hampshire, UK), chromium chips (99.99%, 0.7−3.5 mm, Agar Scientific, Essex, UK), and absolute ethanol (HPLC grade, Fisher) were all used as received. All probes were cleaned by immersion in piranha solution, which is a mixture of hydrogen peroxide and concentrated (95%) sulfuric acid in a 3:7 volume ratio for a minimum of 30 min. (Caution! Piranha solution is an extremely strong oxidizing agent that has been known to detonate spontaneously upon contact with organic material.) Following treatment with piranha solution, the probes were rinsed thoroughly with deionized water and dried in an oven at approximately 80 °C. SAMs were prepared on probes covered by a thin film of evaporated gold. To coat the cantilevers with gold, an Edwards Auto 306 bell jar vacuum coater system was used to deposit an initial layer of chromium of 1 nm thickness at a deposition rate of approximately 0.02 nm s−1. Following deposition of this adhesion layer, the cantilevers were allowed to cool for approximately 20 min prior to deposition of a gold coating of 10 nm thickness at a typical deposition rate of 0.03 nm s−1. Freshly prepared gold-coated probes were immediately sealed in clean Petri dishes which contained 1 mM solutions of the thiols in degassed ethanol for a minimum of 18 h to ensure complete formation of the monolayer. Prior to use, the functionalized tips were rinsed with clean degassed ethanol and gently dried in a stream of nitrogen. Friction Force Microscopy. Friction force measurements were performed using a Digital Instruments Multimode atomic force microscope with Nanoscope IV controller (Veeco, Cambridge, U.K.) operating in contact mode. Friction response was taken from friction loops acquired by obtaining forward−reverse scan cycles along a single line with the microscope employed in scope mode. The size of the scan was maintained at 1.0 μm and the scan rate at 3.05 Hz. The friction signal was obtained by subtracting the mean signals in both directions, giving a resultant force that is twice the frictional force. Force curves were obtained at a minimum of 500 locations on the sample surface for each tip and solvent system. Measurements recorded under ethanol (HPLC grade, Fisher Scientific) or deionized water or mixtures were acquired using a liquid cell fitted with a silicone O-ring. The nominal spring constant for the tip used in present study is 0.06 N m−1. The actual spring constants of the cantilevers were
calibrated by measuring their thermal spectra, following the method of Hutter and Bechhoeffer.42 The lateral signal was converted from volts to nanonewtons by using the wedge method, in which the cantilever is scanned across a calibration grating (TGF11, MikroMasch, Tallinn, Estonia) and the friction signal is measured as a function of applied load.43,44 The tip radius was characterized by translating the probe across a calibration grating (TGG01, Mikromash, Tallinn, Estonia) at 0° and 90° scanning angles.
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RESULTS Force Measurement. Force measurements were made normal to the sample surface in four solvents (methanol, water, ethanol, and 2-propanol) using CH3-, COOH-, and NH2terminated AFM probes. Previous studies suggested that methanol, water, and ethanol are all good solvents for PMPC, while 2-propanol is only a marginal solvent.45−48 The approaching parts of the force curves measured using NH2functionalized probes are shown in Figure 1a. The force curve
Figure 1. Normal load detected as a function of the z-displacement of the piezoelectric scanner, which represents the interaction between PMPC brushes and the NH2-terminated AFM probe when immersed in various solvents. The approach curve (a) represents increasing load, and the retraction curve (b) represents decreasing load.
acquired in 2-propanol exhibits a comparatively abrupt change of gradient at the point where contact is made between the probe and the surface. However, for the three other liquids, the transition is much more gradual; the force increases only slowly over a distance of some 100 nm. This behavior is typical for a polymer brush layer under compression in a good solvent49,50 and is caused by the reduced configurational entropy of the polymer chains, which increases the osmotic pressure as the probe approaches the surface. The separation distance of the probe and sample surface is convolved with the elastic deformation of the PMPC brush, but the qualitative behavior is clear. In a good solvent, the osmotic pressure within a PMPC brush leads to highly extended chains; indeed, it has been reported that there are up to 25 water molecules associated C
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with each MPC residue.33 Thus, a repulsive force is expected when these highly hydrated PMPC brushes are compressed by an AFM probe. However, the low modulus of the brush layers (and their extended nature) means that the repulsive force increases relatively slowly as the probe penetrates through the layer. The sharper transition observed in the force−displacement plots acquired in 2-propanol indicates that the polymer chains are harder to deform in this solvent. This finding is consistent with the relatively collapsed conformation adopted by PMPC chains in 2-propanol.51 Figure 1b shows the retraction parts of the force curves. The adhesion force between the probe and the PMPC brushes is very weak in 2-propanol, and a linear reduction in this force with separation distance was observed during retraction, culminating in a single, discrete pull-off event. In the other solvents, the retraction curves extended over much longer distances (up to 500 nm for ethanol, but somewhat shorter length scales for water and methanol). Moreover, a sawtooth appearance was observed which suggested multiple separation events. Because of the complexity of the shape of these pull-off curves, the data could not be treated quantitatively to extract the adhesion energy. Qualitatively, the magnitude of the adhesive interaction between the probe and the PMPC brush followed the order ethanol > water > methanol >2-propanol, as shown in Table 1.
⎛ α + 1 + L /L a c = ⎜⎜ a0 1+α ⎝
tip chemistry −NH2 −COOH −CH3
solvent
critical load, Lc (nN)
ethanol water ethanol water ethanol water
1 0.683 1 7.89 × 10−16 1 0.147
−0.622 −0.728 −1.343 −1.170 −1.127 −0.632
force minimum (nN) 6.80 2.79 8.08 2.95 2.27 2.66
± ± ± ± ± ±
(2)
where a is contact radius, a0 is the contact radius at zero load, L is the applied load, Lc is the critical load, and α is the “transition parameter” that helps to identify which type of contact mechanics offers the best fit to the experimental data. For all types of probes immersed in water, values of α close to zero were obtained, suggesting that DMT mechanics is the most appropriate model to describe the friction−load relationship in the low load regime. Fitted values of transition parameters and critical loads for friction−load plots acquired in water and ethanol are shown in Table 1. In ethanol, a sublinear friction−load relationship was observed for all of the SAM-functionalized probes across the entire range of loads studied, as shown in Figure 2c. Application of the GTE equation indicated a transition parameter of 1.0 for all types of probes, suggesting that the data are well fitted by JKR mechanics. This is in contrast to the friction−load plots acquired in water in the low load regime, which are best described using the DMT model. Larger friction forces were measured for the amine-functionalized probe than for the others. Ethanol is expected to solvate amine groups less extensively than carboxylic acids, which are good hydrogen bond donors and acceptors. A consequence of this may be that the tip−sample interaction is stronger for an amine-functionalized probe than for a carboxylic acid-functionalized probe. Such effects may be important when the frictional interaction is strongly influenced by adhesion, as is indicated by the observation of JKR mechanics in this case. Methyl-functionalized probes yield similar friction forces to those experienced by the carboxylic acid-functionalized probes, which is consistent with the formation of a strongly bound solvation layer at the tip surface in the latter case. This explanation is consistent with recent work in this laboratory, in which solvation of the probe caused a substantial reduction in the magnitude of both adhesion and friction forces.18 In 2-propanol (Figure 2d), the friction−load plot was linear in all cases. Straight lines could be fitted to the data by linear regression. The slope of the friction−load plot was very much smaller for the CH3-terminated probe than for the others. The corresponding coefficients of friction are 0.75, 0.67, and 0.11 for NH2-, COOH-, and CH3-terminated probes, respectively. Effect of Ionic Strength. Friction−load plots were obtained in aqueous solutions of salts at varying concentrations (Figure 3). In both deionized water and 1 mM NaCl, the friction−load relationship consisted of two components: at low loads, the relationship was sublinear, but at loads above ca. 15 nN it became linear. However, at higher ionic strengths (e.g., in 10 or 100 mM NaCl) the relationship remained linear across the full range of loads studied. Although Figure 3 only shows data for NH2-functionalized probes, similar behavior was observed for probes functionalized with CH3 or COOH groups (see Supporting Information). Figure 4 shows the force−displacement plots on the normal direction acquired in aqueous solutions in the presence of added salt using the NH2-terminated AFM probe. As the ionic strength increases from 0 to 100 mM NaCl, there is a reduction in the work done. By increasing the salt concentration, the strength of adhesion between the probe and the PMPC brush is reduced (Figure 4a).
Table 1. Transition Parameter Values, Critical Loads, and Measured Force Minima Calculated by Fitting Friction− Load Data Determined via FFM for PMPC Brushes Immersed in Water or Ethanol Using Functionalized Probes According to the General Transition Equation (GTE)a transition parameter, α
⎞2/3 ⎟⎟ ⎠
0.22 0.08 0.14 0.11 0.08 0.09
a
The measured force minima correspond to the depth of the adhesive “well” in the retraction part of the force curve.
Friction−Load Relationships. Friction forces were determined for PMPC brushes using CH3-, COOH-, and NH2-terminated AFM probes immersed in methanol, ethanol, water, or 2-propanol. Figure 2 shows typical friction−load relationships. A large number of data sets were collected in these studies, with generally good reproducibility. However, for the sake of clarity only one representative data set is shown for each tip−solvent combination. In methanol, a linear friction−load relationship was observed for all types of cantilevers (Figure 2a). Rather different behavior was observed in water (see Figure 2b). For all surfacefunctionalized AFM probes, a sublinear friction−load relationship was observed at low loads. At loads ranging from 12 to 15 nN, a transition to a linear friction−load relationship was observed. The friction−load data at low loads were fitted using the general transition equation (GTE) shown below, as reported by Carpick and colleagues:52 D
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Figure 2. Variation in the friction force as a function of load obtained for PMPC brushes immersed in (a) methanol, (b) water, (c) ethanol, and (d) 2-propanol using gold-coated probes functionalized with CH3-, COOH-, and NH2-terminated SAMs. The friction−load plots were fitted using either the general transition equation (GTE) or linear regression function, where applicable.
Figure 3. Variation in the friction force as a function of load obtained for PMPC brushes immersed in aqueous solution in the presence of zero added salt or 1−100 mM NaCl using a NH2-functionalized AFM tip. The friction−load plots were fitted using the general transition equation or linear regression function where applicable.
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DISCUSSION Effect of Solvent on the Conformation of PMPC. Displacement of bound solvent molecules from the brush chains is required for adhesion to occur between the probe and the brush. Methanol is the strongest solvent for the PMPC brushes studied herein; thus the work done separating the probe from the surface is minimized in this medium. The adhesion increases slightly for water, and again for ethanol, suggesting that greater work of adhesion accompanies the reduction in the solvent binding strength. While the methanol molecules are tightly bound to the brush chains, the latter are highly compressible: during the approach part of the force curve, the tip penetrates a large distance into the brush. Because of this, there is a relatively large area of contact and the net interaction is thus measurable, despite the relatively weak interaction between the tip and brush. In contrast, the PMPC chains are only weakly solvated in 2propanol. Thus, for these collapsed brushes, the effective
Figure 4. Normal load detected as a function of the z-displacement of the piezoelectric scanner, which represents the interaction between the PMPC brush and the NH2-terminated AFM probe when immersed in aqueous media containing various levels of added salt. The retraction curve (a) represents decreasing load and the approach curve (b) represents increasing load.
contact area is significantly reduced, and the net adhesive interaction is very small. These differences are represented schematically in Figure 5. Effect of Solvent on the Contact Mechanics of PMPC Brushes. Previous studies8,13−15,53,54 on solid surfaces and monolayers have shown that the friction force Ff due to E
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large pull-off forces and friction-load behavior that was fitted by JKR mechanics. In the case of the polymer brushes, the switch from DMT to JKR mechanics may reflect not only stronger adhesion but also the relatively small elastic modulus of the brush layer compared to that of a SAM. The shear term in eq 1 depends on τ, which we have suggested is proportional to the work of adhesion, and the elastic modulus K. DMT theory is associated with weakly adhering hard contacts, whereas JKR theory involves strongly adhesive soft contacts. The observation that the friction−load plots for a PMPC brush immersed in ethanol are fitted by JKR mechanics may be attributable not only to the greater work of adhesion compared to measurements conducted in methanol but also to the comparatively small elastic moduli of the brushes. The elastic properties of a polymer brush can be understood in terms of an effective shear modulus57,58
Figure 5. Schematic representation of the relative dimensions of the AFM probe and PMPC brushes in (a) methanol (or water), (b) ethanol, and (c) 2-propanol. PMPC brushes adopt relatively extended brushlike conformations in both (a) and (b), but adopt a collapsed conformation in (c).
adhesive, single-asperity contacts increases in proportion to the contact area at low loads (adhesion-controlled friction) and that there is a finite friction force even at zero applied external load. In contrast, experiments performed on weakly adhesive systems indicate a linear increase in friction force with load (load-controlled friction) in the low load regime. We suggest that eq 1 provides an opportunity to rationalize these data. It treats the friction force as the sum of two components: a loaddependent term that is attributed to “molecular plowing”55,56 (i.e., processes in which energy is dissipated irrecoverably via molecular deformations) and an area-dependent term that is due to shearing. The shear term is characterized by a surface shear stress τ, which is proportional to the work of adhesion at the tip−sample contact. In the case of hydrogen bond-forming monolayers, the shear term becomes vanishingly small in the limit of complete solvation of the monolayer by a polar solvent in the medium.16 Under such circumstances, the friction−load relationship approaches linearity. The data set obtained for PMPC brushes immersed in methanol is consistent with this model. Methanol is tightly bound to the polymer chains, meaning that the interaction between the AFM probe and the brush is relatively weak. The net adhesion force can be substantial only when the grafting density of the brushes allows significant compression, leading to a relatively large effective contact area. Even a rather low work of adhesion may produce a significant interaction energy if the area of contact is sufficiently large; hence, the pull-off force is not negligible. However, the interaction energy per unit area (the work of adhesion) is small. Consequently, the interaction between the tip and the PMPC brush immersed in methanol is dominated by energy dissipation through molecular plowing, and the shear term in eq 1 is negligible; the friction−load relationship is thus approximately linear. In earlier studies of SAMs in liquid mixtures, variations in the contact mechanics were rationalized in terms of the pull-off force.13,14,16,18,54 This is reasonable for a series of materials with similar mechanical properties, but the observations made for PMPC brushes here suggest that the work of adhesion is a more important parameter. In ethanol, the interaction between the solvent and the PMPC chains is weaker and the brushes are less extensively solvated. Consequently, the work of adhesion is larger than that in methanol. The shear term in eq 1 is no longer negligible, and consequently the friction−load relationship is sublinear. However, it is perhaps noteworthy that the contact mechanics is fitted by the JKR model. In previous studies of monolayer systems, DMT mechanics generally provided good fits to the friction−load relationships.13,14,16 There was, however, one exception to this rule: perfluorodecalin yielded exceptionally
μP =
3kT 2 vσ b2
(3)
where μ is the shear modulus, b is the monomer length, v is the monomer volume, and σ is the grafting density of the brush. When the polymer brush is exposed to ethanol, rather than methanol, the monomer volume is reduced, and so is the shear modulus. The behavior in water is unexpected but may also be rationalized by considering eq 1. At small loads, the loaddependent term makes a modest contribution to the friction force, and a sublinear friction−load relationship is observed. Because the work of adhesion in water is intermediate between the values obtained in ethanol and methanol, the magnitude of the shear term is not negligible, but it is smaller than that found for ethanol. The magnitude of the τ/K2/3 term lies between the values obtained for water and ethanol, and hence DMT mechanics apply. As the load is increased, molecular plowing makes a greater contribution to the dissipative process. Because the dependence of the load-dependent term on the applied load is linear, rather than sublinear, its relative significance increases more rapidly as a function of the load. Since the work of adhesion is still comparatively weak, molecular plowing starts to dominate the sliding interaction at loads greater than ca. 15 nN. Finally, the PMPC brushes are collapsed in 2-propanol. The modulus is greatly increased, and although the brush is no longer strongly solvated, the contact area is very much smaller. Consequently, the magnitude of the shear term is most likely somewhat reduced compared to that observed in ethanol. The density of the collapsed brush is probably larger than that of the extended brush, so the tip penetrates less deeply. Nevertheless, the collapsed structures possess significant conformational freedom, and many pathways are available for energy dissipation via molecular plowing. This latter effect thus dominates the tip−sample interaction, with the consequence that a linear friction−load relationship is observed. Although eq 1 has been successfully applied to self-assembled monolayers, our attempt to extract quantitative data for the PMPC brushes described herein was unsuccessful. The principal problem is the nature of the tip−sample separation process: where a sharp pull-off event is observed, the mechanics are comparatively well modeled by either JKR or DMT theory, and the force minimum is proportional to the thermodynamic work of adhesion. However, for these brush systems, the separation of the tip from the surface involved not a single discrete event but multiple separations, rendering the application of eq 1 problematic. F
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Effect of Salt. While the approach part of the force curves in Figure 1a indicates significant variation in behavior as the medium is varied, there is comparatively little change when different amounts of salt are added to an aqueous medium (Figure 4b). This suggests that the probe penetrates to a similar depth in all cases; hence, there is comparatively little change in the elastic modulus of the brush layer as a function of the salt concentration. Given the reduced work of adhesion that is evident in Figure 4a, it is likely that the addition of salt causes a reduction in the contribution of the shear term to the friction force. At 100 mM NaCl, this reduction is sufficiently large that the dissipative process is dominated by molecular plowing. The intramolecular forces between PMPC chains are known to be affected by the addition of salt.59,60 However, the approach part of the force curve varies very little with salt concentration, which suggests that the contact area between AFM probes and PMPC brush layer is relatively unchanged by the addition of salt (Figure 4b). In contrast, the adhesion force is reduced by increasing the salt concentration (Figure 4a). These data suggest that the adhesive interactions between the probe and the surface are mainly polarization forces. The cationic and anionic charges on the PMPC chains polarize the adsorbates on the probe, creating induced dipoles that adhere to the surface. The addition of salt screens the charges on the zwitterionic PMPC chains, causing a reduction in the adhesion energy. A similar mechanism applies in alcoholic media. In this case, screening of the zwitterionic chains is not modulated by salt, but by bound solvent molecules. In the presence of either 10 or 100 mM NaCl, the friction− load relationship is linear. This suggests that there is very effective screening of the charges on the zwitterionic brushes under these conditions. Thus, the contribution made by the shear term to the friction force is negligible, and the dissipative process is dominated by molecular plowing. However, in either 1 mM NaCl or deionized water, the charge screening is less effective, and the shear term is large enough to yield a nonlinear friction−load relationship at low loads. As the applied load becomes larger, molecular plowing starts to dominate the dissipative process and the friction−load relationship becomes linear.
interaction. Addition of 10 mM NaCl yielded a linear friction− load relationship across the full range of applied loads due to screening of the charges on the zwitterionic PMPC brush chains by the added salt. One limitation of the present work is that the correlations described herein remain qualitative. This is because of the complex force curves observed for these PMPC brushes, which exhibit multiple pull-off events. However, in future studies, comparison between brushes with differing elastic moduli may enable a more quantitative investigation of the relative contributions of the shear and plowing components to the friction force for such nanoscale contacts.
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ASSOCIATED CONTENT
* Supporting Information S
Variation in friction force as a function of load for CH3- and COOH-terminated SAMs in aqueous solution. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: Graham.Leggett@sheffield.ac.uk. Present Address ∥
Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the EPSRC (grant EP/039999/1) for financial support. Dr Jeppe Madsen is acknowledged for helpful technical discussions.
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REFERENCES
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CONCLUSIONS The contact mechanics of zwitterionic poly(2(methacryloyloxy)ethylphosphorylcholine) (PMPC) brushes immersed in both lower alcohols and aqueous salt solutions may be rationalized by treating the friction force as the sum of a load-dependent term, which is attributed to molecular plowing, and an area-dependent shear term. The shear term depends on the surface shear strength, τ, which is proportional to the work of adhesion between the probe and the brush and the elastic modulus of the brush layer. In methanol, which is a strong solvent for PMPC, the shear term is negligible and the sliding interaction is dominated by molecular plowing, yielding a linear friction−load relationship. However, the work of adhesion is larger in ethanol, and the shear term is no longer negligible in this solvent. The friction−load relationship is consistent with JKR mechanics. This is in contrast to organic self-assembled monolayers, which predominantly yield data that are best fitted by DMT mechanics, because of the relatively small elastic modulus of the brush layer. In water, intermediate behavior was observed: the friction−load relationship was initially nonlinear at low loads but became linear at loads greater than 15 nN, since the molecular plowing term starts to dominate the sliding G
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