Evangelos
Liamas
a,
Simon D.
Connell
b,
Shivaprakash N.
Ramakrishna
c and
Anwesha
Sarkar
*a
aFood Colloids and Bioprocessing Group, School of Food Science and Nutrition, University of Leeds, UK. E-mail: A.Sarkar@leeds.ac.uk
bMolecular and Nanoscale Physics Group, School of Physics and Astronomy, University of Leeds, UK
cLaboratory for Surface Science and Technology, Department of Materials, ETH Zurich, Switzerland
First published on 23rd December 2019
The understanding of friction in soft materials is of increasing importance due to the demands of industries such as healthcare, biomedical, food and personal care, the incorporation of soft materials into technology, and in the study of interacting biological interfaces. Many of these processes occur at the nanoscale, but even at micrometer length scales there are fundamental aspects of tribology that remain poorly understood. With the advent of Friction Force Microscopy (FFM), there have been many fundamental insights into tribological phenomena at the atomic scale, such as ‘stick-slip’ and ‘super-lubricity’. This review examines the growing field of soft tribology, the experimental aspects of FFM and its underlying theory. Moving to the nanoscale changes the contact mechanics which govern adhesive forces, which in turn play a pivotal role in friction, along with the deformation of the soft interface and dissipative phenomena. We examine recent progress and future prospects in soft nanotribology.
Due to the exciting advances in FFM enabling tremendous progress in decoding complex physical, biological and technological lubrication mechanisms at the nanoscale, there have been some excellent reviews.11–15 Many, if not most, of these reviews focus on summarizing particular contact mechanics at the nanoscale in conventional ‘hard’ interfaces with a well-defined single-asperity elastic contact. However, there are no reviews that discuss nanotribology in deformable i.e. low modulus ‘soft’ surfaces, such as polymers, hydrogels, and soft biological interfaces (oral, ocular, dermal, and respiratory), which is one of the outstanding challenges in modern nanotribology. In this Review, we specifically provide a critical analysis of FFM focusing on the booming area of nanotribology in soft surfaces, describing the rapid evolution of FFM, the gradual transition from the use of sharp tips16 to well-defined colloidal probes,17 and more recently performing friction measurements incorporating flexibility into the material physics and chemistry of the contact surfaces.18 We explore the frictional laws applying to soft surfaces at the nanoscale, highlighting the effect of adhesion force on the frictional behaviour of soft surfaces, which is an outstanding challenge in modern tribology. We extensively review studies where FFM has been used on soft surfaces to measure these tiny lateral forces, and discuss the impact that (i) surface interactions, (ii) surface roughness, (iii) intrinsic material properties, and (iv) experimental conditions have on the frictional properties of hard-on-soft and soft-on-soft contact systems. We examine aspects of molecular dynamics (MD) simulations that allow the prediction of frictional behaviour at the nanoscale for hard and soft contacts. Lubrication on soft surfaces is a complex multidisciplinary area, and we touch upon the key surface interactions altered by grafting polymer brushes and hydrogels. Readers might refer to more extensive reviews on polymer brushes, hydrogels and hydration lubrication elsewhere.19–21 Finally, we outline the systems where FFM using soft surfaces can be applied, before looking into the future opportunities, including the fabrication of precisely tailored soft probes for FFM along with the growing need for new mathematical models to overcome the current limitations of FFM-based approaches for soft tribology.
Fig. 1 Evolution of friction force microscopy (FFM) with major milestones leading to its use in soft surfaces. Development of FFM dates back to Mate et al.16 who used a tungsten tip against a graphite surface. They were the first to observe a ‘stick-slip’ phenomenon, which occurs when the tip sticks to one lattice site of the sample until the lateral force becomes strong enough to jump to the next site. Friction ‘anisotropy’ and ‘superlubricity’ were firstly observed by Hirano et al.24 and Overney et al.,23 respectively, although this phenomenon was demonstrated elegantly later by Dienwiebel et al.29 by measuring lateral forces as a function of rotational angle. In the case of ‘anisotropy’, friction between two crystal surfaces depends on their molecular alignment, where friction is highest when the crystal lattices are commensurate. On the other hand, ‘superlubricity’ or ultra-low friction occurs when the lattices of two crystal surfaces in contact are out of registry by lattice mismatch or angular misalignment, because the sum of the forces that act on the atoms of each surface cancel each other. Toikka et al.17 was the first group to use a colloidal probe to measure lateral force using a hard probe/hard surface system. Subsequently, Matzelle et al.30 studied a hard probe/soft surface, while Bogdanovic et al.31 used materials other than glass to create a relatively soft cellulose-based colloidal probe. Kim et al.32 used a soft colloidal probe/soft surface system for the first time to study friction on hydrogel contact lenses, while Li et al.33 used a hydrogel probe/hydrogel surface to understand the lubrication mechanism of crosslinked hydrogel layers. |
Fig. 2 Scanning electron microscopy images of the sharp tip and colloidal probes glued onto AFM cantilevers. (a) Commercial AFM cantilevers made from silicon or silicon nitride, having a sharp tip with a radius of a few nanometers, are widely being used to measure friction (adapted with permission from J. Sondhauss, M. Lantz, B. Gotsmann and A. Schirmeisen, Langmuir, 2015, 31, 5398–5405.35 Copyright 2015 American Chemical Society). Following the introduction of colloidal probes in FFM, several materials have been used to study friction, including (b) polydimethylsiloxane (PDMS) (our laboratory, unpublished work), (c) borosilicate glass (adapted from J. M. Coles, J. J. Blum, G. D. Jay, E. M. Darling, F. Guilak and S. Zauscher, J. Biomech., 2008, 41, 541–548,36 Copyright 2008, with permission from Elsevier), and (d) polyethylene (PE) (adapted with permission from S. N. Ramakrishna, P. C. Nalam, L. Y. Clasohm and N. D. Spencer, Langmuir, 2013, 29, 175–182.28 Copyright 2013 American Chemical Society). |
Ducker et al.34 were the first to use a colloidal probe in 1991 to measure normal forces between a silica colloidal particle (3.5 μm radius) attached to a silicon nitride cantilever and a flat silica surface in sodium chloride solutions. They found general agreement with DLVO theory, with the exception of some unexpectedly high forces at close range <3 nm. Nevertheless, it was only in 1997 that Toikka et al.17 used a colloidal probe to measure lateral forces. Interestingly, this was driven by interest in the force required to remove a single particle of iron oxide from a silica surface.
Since then, colloidal probe FFM has been used to study frictional interactions on a plethora of combinations between hard and soft materials. For instance, Matzelle et al.30 studied the tribological properties of soft hydrogel surfaces (N-isopropylacrylamide) for the first time using micrometer-sized hard glass spheres over a range of loads (<110 nN) for applications in medical devices, such as catheters. The key research challenge of understanding the friction and adhesion occurring at the hydrogel soft contact lens/ocular tissue interface led to the first use of soft-on-soft contact mechanics at the nanoscale i.e. a relatively soft polystyrene colloidal probe (modulus ≈ 3 GPa) sliding against a hydroxyethyl methacrylate-based hydrogel (modulus ranging 0.5–1 MPa) by Kim et al.32 (Fig. 1). Here, they found that ionic functional groups reduced surface adhesion and friction against a hydrophobic probe. Due to the technical difficulties of attaching an ultra-soft particle (e.g. hydrogel particle) to an AFM cantilever, friction between ultra-soft systems at the nanoscale was not measured until 2016. It was only recently, when Li et al.33 were able to perform FFM experiments between a hydrogel probe and hydrogel surface. They used an elegant approach where a polystyrene colloidal probe was coated with a poly(dimethyl acrylamide-co-methacryloyl oxybenzophenone) (PDMAA-co-MABP)-based hydrogel layer to elucidate lubrication on a hydrogel substrate. They reported very low friction coefficients (μ = 0.006) between the hydrated hydrogel surfaces, which increase with the sliding speed, and revealed that pressure-induced deswelling and hydration lubrication in the contact region dominates friction. Consequently, measuring friction between the hydrogel-coated probe and hydrogel surface offers new opportunities to understand frictional dissipation in deformable soft biological samples.
Ff = μL | (1) |
Fig. 3 Macro to nanoscale contact area and contact mechanics models. (a) While at the macroscale the contact area may appear flat (top), at the microscale the surface can be a rough, multi-asperity interface (middle) that consists of nanoscale asperities (bottom). (b) Dependence of the contact area on the applied load, between a sphere and a flat plane, for the Hertz, JKR, DMT, and intermediate models. The calculations (adapted with permission from J. Y. Park and M. Salmeron, Chem. Rev., 2014, 114, 677–71141 Copyright 2014 American Chemical Society) were performed for radius R = 100 nm, reduced modulus K = 50 GPa, interfacial energy γ = 250 mJ m−2, and equilibrium separation distance z0 = 3 Å. (c) Frictional response versus applied load between a silicon nitride sharp tip (inset) and poly(ethylene terephthalate) (PET) surfaces under an ethanol (left), perfluorodecalin (middle), and hexadecane (right) environment (adapted with permission from C. R. Hurley and G. J. Leggett, Langmuir, 2006, 22, 4179–4183.42 Copyright 2006 American Chemical Society). The adhesion varies upon the type of solvent due to the different dielectric constants altering adhesive van der Waals forces. Consequently the friction versus load curves range from linear (ethanol) to sub-linear, the latter fitted to DMT (hexadecane) or a JKR model (perfluorodecalin). (d) Schematic representation of the interaction forces acting at the colloidal probe–nanoparticle contact (left), and friction versus load at high (JKR-type adhesion) and low (DMT-type adhesion) particle density (right) (adapted with permission from S. N. Ramakrishna, P. C. Nalam, L. Y. Clasohm and N. D. Spencer, Langmuir, 2013, 29, 175–182.28 Copyright 2013 American Chemical Society). |
Considering that friction is determined by factors such as plastic deformation,43 wear,44 surface roughness,28 and lubrication,45 creating a universal law that describes friction across all length scales from macro down to nano is a major challenge. With the development of FFM, it became possible to control all the aforementioned factors and study friction at the nanoscale, where single asperity interactions dominate and friction is proportional to the normal load, the real contact area, and in many cases to the sliding speed.41
The contact area (A) between an AFM tip and a flat surface, when the load is limited to cause only elastic deformation, can be given by the Hertzian model46 (eqn (2)):
(2) |
(3) |
However, the Hertz model does not take into consideration the adhesion between the contact surfaces, which plays a major role in friction since it affects the contact area between the tip and the surface. Generally, when adhesion between the tip and surface is small or zero, a linear Amontons’ type relationship between friction and load is observed at the nanoscale.42,46 In contrast, when the adhesion is significant at the contact, the friction–load follows a sublinear relation that is described well by single asperity contact mechanics models such as the Johnson–Kendall–Roberts (JKR)48 and the Derjaguin–Muller–Toporov (DMT)49. Such behaviour is often explained by the dependence of the friction force (Ff) on two terms, a load-dependent term and an interfacial shear term46,47 (eqn (4)):
Ff = μL + σAasp | (4) |
(5) |
(6) |
• the materials are elastically isotropic;
• the deformation in the contact is purely elastic and is described by classical continuum elasticity theory;
• the diameter of the tip is significantly larger than the diameter of the contact area;
• the Young's modulus and the Poisson's ratio remain constant during deformation;
• no chemical bonds are formed during adhesion;
• the curvature of the particle in the contact area is described by a paraboloid; and
• the contact area is significantly larger than the atomic/molecular dimensions.
A nice illustration on the relation between contact area and load, using the different models, was given by Park and Salmeron41 (Fig. 3b). They showed that under the DMT and JKR models, a finite contact area exists even at zero applied load between the tip and the surface, which arises from the adhesion. Many studies have successfully used friction models that take into account the adhesive contribution according to DMT/JKR. For instance, it has been shown that friction between an AFM tip and poly(ethylene terephthalate) (PET) surfaces is reduced in the presence of ethanol as a result of a reduction in adhesion, leading to a linear friction–load dependence42 (Fig. 3c). However, in perfluorodecalin and hexadecane that have significantly smaller dielectric constants and refractive indices, the adhesion was remarkably larger as a result of stronger dispersion forces according to the Lifshitz theory of van der Waals forces.52 Consequently, in perfluorodecalin, where the adhesion was the largest, the friction-load was best described by JKR, while for hexadecane that had a smaller adhesion compared to perfluorodecalin the DMT model was the best fit. The JKR-DMT transition was shown elegantly in a study by Ramakrishna et al.,28 where the roughness of a surface was controlled with nanoparticles, and then correlated to the adhesion forces and to their frictional properties (Fig. 3d). Friction reduced as particle density decreased (although it sharply increased once the colloidal probe made contact with the underlying flat substrate), confirming that the friction–load relationship is governed by the real contact area, such as asperities on real surfaces. It was shown that JKR contact adhesion dominated the frictional response at high particle density, where many particles came into contact with the colloidal probe. However, when the particle density is reduced, a transition to DMT contact mechanics is observed and adhesion is dominated by long range non-contact forces from the underlying substrate, nanometres distant.
The most appropriate contact model to use in a given system can be determined using the dimensionless Tabor parameter53 (τ) which takes account of the ratio of elastic deformation to the range of adhesive forces, i.e. the balance between JKR and DMT respectively, given by eqn (7):
(7) |
(8) |
However, the Maugis–Dugdale model requires a complicated fitting in the absence of a single parameter relating contact area and normal load. In 1999 Carpick et al.55 proposed a general transition equation (GTE) that provides a very close approximation of the Maugis–Dugdale model and is more convenient to use for fitting data from FFM experiments given by eqn (9):
(9) |
Fig. 4 summarizes the literature where FFM has been used to study the frictional properties of soft materials, using either a sharp tip or a colloidal probe. The y-axis separates the samples studied according to their Young's moduli, while the x-axis indicates the material of the tip, divided into sharp tips to the left of the diagram, or the Young's modulus of the colloidal probe used to the right of the divide. Sharp tips have the benefit that they can be used to study single asperity contacts, and it can be seen that sharp tips have been used against samples with a wide range of moduli, spanning from MPa to GPa. Although they are commercially available and, thus, convenient to use, they are limited to silicon (Si) and silicon nitride (Si3N4). On the other hand, colloidal probes offer an unlimited palette of materials that can be used, some of which are now commercially available, ranging from borosilicate glass and gold to polystyrene (PS) and poly(methyl methacrylate) (PMMA).
Fig. 4 Material properties of tip/colloidal probes and surfaces used in friction force microscopy (FFM). The y-axis separates the samples studied according to Young's modulus, while the x-axis indicates the modulus and material of the tip. The left side of the figure illustrates FFM studies using a sharp tip, either silica,58–70 or silicon nitride.32,42,68,71–95 On the right side of the figure are shown the FFM studies using a colloidal probe made from: collagen;96 latex;97 polyethylene (PE);25,28,45,98 polyethylene glycol (PEG);99 poly(methyl methacrylate) PMMA;26,27,95,100 polystyrene (PS);33,71,101 cellulose;31,102–109 and silica.35,36,98,110–117 The volume of the symbol corresponds to the number of studies using the specific system of materials. Colloidal probes of the same material are in groups, while the green-shaded area represents the knowledge gap on friction between soft surfaces that requires future research attention. |
Silica-based colloidal probes are the most widely popular choice to measure friction on materials with Young's modulus in the GPa range, mainly due to their availability and ease of altering the surface interactions using chemical derivatisation. Cellulose has been studied extensively in the work of Rutland et al.31,102,103,105–107,109 Polymers, such as PMMA, PS, and polyethylene (PE), are also widely used due to their easily tuneable properties. Although both sharp tips and colloidal probes with elastic modulus (E) > 1 GPa have been used to study friction on surfaces with E down to a few kPa, there is a clear knowledge gap in using colloidal probes and samples that have a Young's modulus of less than 100 MPa (green-shaded area) where most biological interfaces range and soft-on-soft contacts predominate. At the present time, the question is open as to whether a hard-on-soft contact can capture the features of a soft-on-soft contact. We now focus on FFM studies carried out on soft materials (Fig. 5), and more specifically we discuss how surface interactions and topography affect friction in soft contact mechanics, before we examine the impact of intrinsic properties of the material (e.g. polymer entanglement, molecular weight) on friction and other experimental factors, such as loads, scanning distance and sliding speeds.
Fig. 5 Nanoscale friction in soft surfaces. (a) Friction as a function of applied load between a bare cellulose probe (left) and nanofibrillated surfaces with grafted CMC-g-PEG polymer brushes (right), highlighting the efficacy of polymer brushes in reducing friction due to electrosteric repulsion, with a 30 times reduction at zero load (republished with the permission of Royal Society of Chemistry, from “Direct measurements of non-ionic attraction and nanoscaled lubrication in biomimetic composites from nanofibrillated cellulose and modified carboxymethylated cellulose”, A. Olszewska, J. J. Valle-Delgado, M. Nikinmaa, J. Laine and M. Osterberg, Nanoscale, 2013, 5, 11837–11844, Copyright 2013;104 permission conveyed through the Copyright Clearance Center). (b) Friction between a hydrogel-coated (PDMAA-co-MABP) probe and hydrogel surfaces in air (left) and in water (right) at various sliding speeds with the inset showing a schematic representation of the soft contact mechanics (adapted with permission from K. Li, C. K. Pandiyarajan, O. Prucker and J. Ruhe, Macromol. Chem. Phys., 2016, 217, 526–536.33 Copyright 2016 John Wiley & Sons, Inc.). Hydrogel friction is reduced by an order of magnitude once hydrated (hydration lubrication). (c) Friction force versus load for PDMS polymer brushes of different chain lengths with the inset presenting a schematic of the polyethylene bead sliding over polymer brushes (adapted with permission from L. J. Landherr, C. Cohen, P. Agarwal and L. A. Archer, Langmuir, 2011, 27, 9387–9395.118 Copyright 2011 American Chemistry Society). The friction is reduced by an order of magnitude for polymer brush coated surfaces as compared to bare silicon or SAM surfaces. However, lower molecular mass chains have reduced friction compared to longer chains, and increasing grafting density reduces friction by creating a more uniform surface. (d) Three-dimensional AFM images of surfaces patterned with pillars of increasing density (bottom) and the corresponding frictional forces against a borosilicate colloidal probe (top) (adapted with permission of Taylor & Francis Ltd from “Adhesion and friction behavior of positively or negatively patterned polymer surfaces measured by AFM”, X. L. Zhang, F. Liu, W. Z. Wang, G. W. Yi and J. H. Jia, J. Adhes. Sci. Technol., 2013, 27, 2603–2614.113). It shows that increased spacing between the pillars leads to increased friction due to the collision effect between the colloidal probe and the pillars. The s-0 refers to a smooth surface, while p-1, p-2, and p-3 indicate surface with pillars of increasing density. (e) Friction force for a silicon nitride probe sliding on soft polystyrene surfaces of different molecular weights (reprinted from “Evaluation of nanotribological behavior of amorphous polystyrene: the macromolecular weight effect”, A. Ghorbal and A. Ben Brahim, Polym. Test., 2013, 32, 1174–1180.91 Copyright 2013, with permission from Elsevier). The friction is increased with increasing molecular weight due to increased interaction and dissipation in the longer polymer chains, similar to panel c. (f) Speed-dependence of friction on polyacrylamide (PAAm) hydrogels (reprinted with permission from T. Shoaib, J. Heintz, J. A. Lopez-Berganza, R. Muro-Barrios, S. A. Egner and R. M. Espinosa-Marzal, Langmuir, 2018, 34, 756–765.112 Copyright 2018 American Chemical Society). While initially friction is decreased with increasing velocity due to reducing slip-stick (polymer chain adsorption and release is a kinetic process), when it reaches a transition velocity the friction increases with speed, possibly due to increased deformation of the hydrogel. |
A key surface interaction that is particularly relevant for soft and biological interfaces in hydration lubrication concerns the effect of water structure up to a few nanometres away from the surface. The behaviour of this layer includes the influence of hydration shells from the surface or surrounding ions, the availability of bulk water and steric disruption by polymer chains. It was shown that friction of a polystyrene colloidal probe coated with a PDMAA-co-MABP hydrogel sliding on dry PDMAA-co-MABP hydrogels is high and is reduced with increasing sliding velocity (Fig. 5b).33 However, on hydrated hydrogels, friction is significantly lower than that in the dry hydrogels and progressively increases with the sliding velocity due to increasing polymer concentration in the contact area during shearing. This suggests that in hydrated hydrogels the viscous drag of water within the hydrogel at the interface is the main cause of hydration lubrication. Furthermore, at high loads (>60 nN), friction is increased due to the accumulation of the polymer in the contact area arising from hydrogel compression. It has also been shown that ionic functional groups or biopolymeric molecules, such as mucins tethered at the surface can entrap water that cannot be squeezed out but remain labile resulting in better lubrication and reduced adhesion.32,119 For a comprehensive understanding of hydration lubrication, readers may refer to thorough reviews by Klein's group.120,121
Under ambient non-hydrated conditions, capillary forces arising from a meniscus of water between the probe and surface are another factor that tends to dominate friction. It can significantly increase adhesion and, consequently, friction is strongly dependent on humidity.99 It was shown that on hydrophilic silica surfaces, and at low sliding speed, capillary forces provide a major contribution to friction.84 However, as the speed increases, μ is reduced because there is less time for a stable meniscus to build up at the interface. A similar study on mica and silica surfaces against a cellulose probe also showed that capillary adhesion dominates friction but further revealed a hysteresis between loading and unloading friction–load curves, suggesting a larger condensate due to slow evaporation of the formed meniscus.109
Individual components in lubricants, such as polymers or proteins, can significantly alter the frictional properties, depending on their ability to adsorb on the surface. For instance, poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) (PEO-PPO-PEO) is an effective lubricant on polypropylene (PP) and polyethylene (PE) surfaces but not on cellulose surfaces, which is attributed to the ability of the lubricant to attach to PP and PE but not to cellulose.61 Similar results were reported for mucin, which reduces the friction between a PMMA colloidal probe sliding on a PMMA surface.100 In contrast, when the lubricating properties of mucin were measured with a sharp Si3N4 tip against a PDMS surface, friction was increased as a result of the tip ploughing through the mucin layers adsorbed on the surface.86 However, when the tip was rendered hydrophobic with octadecyltrichlorosilane (OTS) the presence of mucin reduced the friction as compared to the bare hydrophobic PDMS because it blocked the strong hydrophobic attractive force. This suggests that surface chemistry at the interface due to adsorption of mucin to the surface can be an important factor that cannot be ignored.
Further evidence that surface chemistry dictates the ability of lubricants to reduce friction was shown upon adsorption of proteoglycans on polycarbonate urethanes (PCU) used in medical devices, and hydrophobic or hydrophilic self-assembled monolayers (SAMs) as a model system.115 It was shown that on hydrophilic SAM surfaces, proteoglycan adsorption has a negligible impact on friction, while proteoglycan adsorption on hydrophobic PCU surfaces significantly decreases friction when compared to the bare hydrophobic surfaces. The decrease in friction is even larger on surface-modified PCU surfaces that are locally softer than PCU surfaces. In contrast, when proteoglycan is adsorbed on hydrophobic SAMs the impact on friction is negligible. Although both SAMs, PCU, and modified PCU are hydrophobic, the difference arises from the higher contact pressure on the non-deformable SAM on gold, compared to lower contact pressure on softer PCU due to the increase in the probe–surface contact area highlighting the impact of surface deformability on the lubricating ability of molecules.
Another interesting strategy adopted by nanotribologists is to graft polymer brushes onto surfaces and use FFM to study the frictional properties. The excellent lubricating properties of polymer brushes arise from the osmotic pressure within the polymer brushes that resist compression, and from the opposition to the entropy loss that would result between two opposing brush-covered surfaces if they were compressed and, therefore, ordered to some degree.21 A study on poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG)-modified SiO2 surfaces showed that the solvent environment plays a key role in the frictional properties of polymer brushes; the higher the solvation of the polymer brushes the lower the friction.122 This was also shown during the adsorption of chitosan brushes on cellulose surfaces that reduces friction due to electrosteric repulsion arising from the extended chitosan chains.103 Friction is reduced as the grafting density of the polymer brushes is increased, which is attributed to the reduced contact with the underlying surface and to interaction with a denser layer with less entanglement in long chains (Fig. 5c).123 Furthermore, the longer the length of the grafted polymers chains at a given grafting density the higher the friction, as a result of reduced chain mobility and higher viscosity of the brushes.118
The degree that surface topography will affect the frictional properties is related to the selected scan size during a FFM measurement. For instance, if the scan size is much smaller than surface asperities, then surface topography will have a small impact on frictional properties. Consequently, scan size plays a significant role in studying frictional properties. More specifically, it has been found on cellulose surfaces that for scan sizes smaller than surface asperities, μ initially decreases with increasing load and eventually becomes load independent. In contrast, for scan sizes larger than surface asperities, μ is increased with increasing load due to the asperity dominated friction.108 Similar studies attributed the scale dependence (microscale to nanoscale) of μ to surface roughness, and emphasized that friction is scale-dependent and no assumption can hold from one scale to another.85
Similar to Tg, the activation energies for α- and β-relaxations, which are related to the translation of the molecule through the medium and the change in molecular conformation respectively, can be different at a polymer surface as compared to its bulk value. More specifically, it has been found that the apparent activation energies for α- and β-relaxations are smaller at the surface of PS than its bulk value, which indicates a significant increase in the molecular motion at the surface.62,64,92 Similar results were found on PMMA films, where the activation energies for α- and β-relaxation were found to be three times lower on its surface compared to the bulk values.68 These results reveal a greater free volume and a higher molecular mobility at the polymer/air interface. The observed reduction in surface relaxation can be enhanced by the high stress from the sharp tips that activate α- and β-transition at temperatures below the glass transition temperature.35 Since decreased molecular mobility results in reduced friction, it is expected that ultrathin polymer films may have different frictional properties from thicker films. This was shown with ultrathin PVME films, where the friction is reduced with decreasing film thickness as a consequence of the reduced polymer chain mobility and the increasing polymer stiffness arising from the confinement of the polymer chains.73
The molecular weight (MW) of a polymer can have a significant impact on the interactions between the sliding body and, thus, its frictional properties. More specifically, it has been found that the friction on PS surfaces increases with the length of PS polymer chains, which is attributed to larger adhesion forces as a result of increasing interactions with polymer chains, mainly through van der Waals and acid–base interactions (Fig. 5e).91 Apart from the MW, the degree of crosslinking can also affect friction. Sliding of colloidal silica particles on polyacrylamide (PAAm) hydrogels, with Young's moduli of 2 kPa, 9 kPa, and 40 kPa, reveals two different boundary lubrication mechanisms (Fig. 5f).112 Initially, the friction decreases with increasing speed until it reaches a transition velocity where the friction starts to increase with increasing speed. Below the transition speed, the decrease in friction with increasing sliding speed is related to the continuous adsorption and desorption of the polymer chains onto the sliding body; the polymer chains that were adsorbed on the counter surface require more time to re-adsorb once the contact breaks due to the sliding motion. It was found that less cross-linked PAAm hydrogels exhibit reduced friction due to the larger relaxation time of the polymer chains, requiring more time for re-adsorption. At the same time, although the mechanism for the regime above the transition speed where friction increases with speed is not elucidated, it was found that less cross-linked PAAm hydrogels favour the transition into that regime. It can be seen that as the degree of crosslinking is reduced, friction is also reduced, at least for low sliding speeds. This was also shown in ultrathin PDMS films where μ was lower than in thicker films, which is a consequence of poor cross-linking in ultrathin films.25
Chain entanglement was found to have a similar effect on crosslinking in reducing friction but due to a different mechanism. More specifically, it was found that on PS and PMMA surfaces, friction is increased with increasing MW up to a value close to the critical MW for entanglement in bulk PS and PMMA, after which the effect of MW on μ is small.83 It was suggested that at low and up to a critical MW, the AFM tip is ploughing between polymer chains during FFM. On the onset of entanglement, the energy dissipation mechanism changes and the tip is sticking in the loops between chains and is pulling them until they break. Reduction of friction was also observed when PMMA was modified upon exposure to UV light, which was correlated to a gradual reduction in MW and, thus, chain entanglement.83
In another study, focusing on poly(N-isopropylacrylamide) brushes, Ramakrishna et al.124 studied the effect of scanning distance on the measured friction forces. They showed that when the polymer chains are highly swollen and the sliding distance is smaller compared to the swollen brush thickness, the measured friction is mainly due to the back-and-forth lateral bending and stretching of the chains and the kinetic friction is only measured when the sliding distance overcomes the bending and stretching of the chains. However, in the case of collapsed polymer chains, no effect of sliding distance was observed on the measured friction. Other external stimuli, such as temperature and pH, can also have a significant impact on the frictional properties of a system and readers can refer elsewhere for further insight.125–127
MD studies have been used to establish friction laws in dry nanoscale contacts.50 It has been found that nanoscale friction is highly sensitive to contact mechanics, but single-asperity theories break down at the nanoscale, and friction ultimately depends linearly on the number of atoms that are interacting at the interface. While the frictional force versus load relation is non-linear for adhesive surfaces, a transition to a linear relation takes place as adhesion is decreased, which is consistent with the experimental results at the nanoscale as discussed above in section 3. The transition takes place when the contact roughness becomes large as compared to the interactions at the interface, such as when the sliding interface is damaged and becomes rougher. MD studies have been mainly used to shed light on atomic friction phenomena at hard–hard contacts. For instance, MD was used in parallel with FFM to observe friction between a platinum AFM tip sliding on Au(111).129 Both FFM and MD revealed stick-slip behaviour, proving MD as a reliable approach to interpret AFM data, while it further revealed that atomic stick-slip is thermally activated at low speeds. Similar MD studies128,130 on how the substrate crystal lattice affects friction revealed that stick-slip and superlubricity could be a result of lattice mismatch, as was elegantly presented experimentally by Dienwiebel et al.29 (Fig. 1). This role of lattice incommensurability then leads to further insights, impossible to achieve with current FFM, on the role of surface shear stress distributions at the interface131 in these matched or mismatched lattices, and its influence on the stick-slip mechanism.
Another aspect of friction that MD simulations have complemented FFM is hydration friction, as shown in an investigation into friction on graphite, both under vacuum and in water.132 While both FFM and MD showed that water has a negligible impact on friction for loads larger than 5 nN, MD simulations revealed the role of the hydration layer at the graphene/water interface, which could not be achieved by FFM alone. Similar experiments showed that although the presence of water does not affect friction at flat surfaces, at atomic step edges (such as stepped graphite surfaces) the friction is significantly increased.133 Another MD study, using two bilayers of decanol molecules separated by water, investigated the role of water and hydration friction in nanoconfinement.134 It was found that three friction regimes are present with decreasing water thickness; (1) for thick water films, friction is governed by bulk water viscosity, (2) for water films of about 1 nm, the interfacial layer is highly viscous and increases friction, and (3) at the dry friction limit, the interfacial slip sets in.
As discussed above the roughness of a surface can significantly affect friction, since it affects the contact area between the tip and substrate, and MD simulations have been used to study this area. A series of MD simulations was used to study the frictional behaviour of nanopatterned silicon surfaces and how nanopatterning can be used to tune friction at the nanoscale.135 It was found that for nanopatterned surfaces, there is always a linear dependence of load on the frictional forces, both for adhesive and non-adhesive surfaces, which is independent of the nanopattern geometry. This can represent Amontons’ law (eqn (1)) and it's relation to the real contact area. In contrast, flat surfaces exhibit a non-linear relationship between frictional force and load when adhesion is introduced in the system. It was also found that friction can be tuned by adjusting the nanopattern period and, thus, nanopatterning can be used to control adhesion and friction at the nanoscale. Another MD study examined the friction characteristics at the nanoscale between multi-asperity tips and textured surfaces.136 It was found that the number of asperities on the tip and the contact area with the substrate can significantly affect friction and cause various degrees of damage to the surface, while the ratio between the size of asperities and surface texture width is an important parameter that influences friction.
FFM can probe the friction force between a tip and a substrate, but it is difficult to recognise whether the deformation at the interface is plastic or elastic, or even whether ploughing is occurring, and this is an area in which MD can provide significant wealth of information. For instance, MD simulations allowed the study of a nanometric scratching process, where a rigid diamond sphere is sliding on face-centred cubic (fcc) single crystal copper. This enabled the first determination of the ploughing friction coefficient and the adhesion friction coefficient at the nanoscale.137 It was found that macroscale theory slightly overestimated the ploughing friction coefficient at the nanoscale, while the adhesion friction coefficient was independent of the indentation depth and was almost stable.
Although MD simulations have mostly been used for hard–hard contact surfaces, the gradual shift to hard-on-soft is demonstrated in one of the most recent MD studies, where a rigid indenter of 5 nm radius was simulated sliding over an amorphous polyethylene.43 It was found that friction is mainly composed of a plough force (cohesive zone) and an adhesion force (interface zone). Elastic deformation was attributed to van der Waals interactions in the cohesive zone, while bond angle energy and dihedral energy of the molecular chain dominated plastic deformation. Also, the presence of attractive interactions significantly increased the friction, as compared to repulsive interactions between the indenter and soft polyethylene, while the higher the indentation the larger the contribution of the plough force and hence the larger the friction.
Besides soft surfaces, MD simulations have been effectively used to interpret the FFM results on soft polymer-coated surfaces. A MD study on polymer–polymer interface friction revealed three different mechanisms governing frictional behaviour and deformation;138 interfacial “brushing”, which has the major contribution, followed by “combing” and “chain scission”. These mechanisms refer to how the polymer chains are interacting with each other, either with a small section (“brushing”), sliding between chains (“brushing”) or even breakage of the chains when their path is distracted (“chain scission”). The same study also revealed three regimes, ranging from periodic stick-slip at low sliding speeds to irregular stick-slip and dynamic frictional sliding as the sliding speed increases. Immiscible polymer brush systems can greatly reduce dissipation, as was shown on PMMA (immersed in acetophenone) and PNIPAM (immersed in water) brushed surfaces in a combination FFM and MD study.139 It was reported that friction between PMMA–PNIPAM surfaces (immiscible system) was significantly lower than that between PMMA–PMMA (miscible system), while they have similar load-bearing capacity. FFM and MD were also used to study the effect of crosslinking on the tribological behaviour of polymer brushes.140 It was found that not only does μ increase with the degree of crosslinking, but also that the length of the crosslinker can affect μ with higher length leading to a decreased friction. In summary, complementing FFM with MD simulations has already started to advance our understanding of friction in soft surfaces and we expect that combining FFM experiments and MD simulations will become a standardized approach to address biophysical questions and improve interpretation of nanofrictional mechanisms in the future.
Although articular cartilage on its own has a low boundary friction coefficient, FFM has clearly uncovered that synovial fluid and its components are the major lubricants. For instance, articular cartilage coated with protein components exhibited low friction, whereas when the surface was treated with proteolytic enzymes such as trypsin hydrolysing the protein film, the friction increased.141 It is noteworthy that load-bearing regions of articular cartilage exhibit lower friction than non-load-bearing regions, indicating the presence of boundary lubricants that protect from wear and tissue degeneration when joints are starved from fluid lubrication.56 The distinct role of synovial fluid components in lubrication has been elegantly studied using hydrophobic and hydrophilic surfaces.142 It was reported that lubricin lubricates the hydrophobic surfaces effectively, while it slightly increases friction when inserted between hydrophilic surfaces. The impact of hyaluronic acid (HA) on lubrication was found to be considerably smaller, while no synergistic effect was found between lubricin and HA in terms of lubrication. FFM has also been used to study the increase in friction with the progression of osteoarthritis. It was found that μ of human femoral head cartilage increased substantially from 0.119 at Stage 0 to 0.409 at Stage 3, and this was also correlated with an increase in roughness,44 suggesting a decrease in the presence of friction-reducing protein.
Designing colloidal probes that exploit the parallel developments in material chemistry can help to address many fundamental research challenges. The investigation of this knowledge gap, regarding the capability of performing nanotribology experiments with elastic moduli ranging from tens of kPa to few MPa at the nanoscale, will be of great importance, and will find use in a wide range of future biological and technological applications, where soft materials with desired frictional properties are in demand. However, as has been demonstrated, there are many unresolved challenges in this field, with many complex interactions. For instance, the elastic modulus of a material surface can be different from its bulk value which could cause inconsistencies in the measurements, while the direct comparison between macro and nanoscales is complicated by the length scale of surface roughness and asperity contact, and the measurement itself has been shown to change the relaxation state of the soft polymeric surface. Furthermore, due to the low elastic modulus, the conditions of the well-established contact mechanics models may not be met and, consequently, there may be inconsistencies in the interpretation of the measured data across the literature. The utilisation of advanced fabrication methods, such as electron-beam lithography, will be a fascinating avenue to deliver concrete breakthroughs in measuring the interfacial friction of soft sliding nanostructured surfaces with well-defined roughness. Also combining experimental frictional measurements with continuing advances in molecular dynamics studies will be increasingly informative, allowing the rapid determination of the molecular scale mechanisms governing soft tribology. Nanoscale friction in hydrogel-based and biomaterial-based colloidal probes that emulate biological surfaces with relevant modulus and roughness offers excellent opportunities for future interdisciplinary research involving material scientists, biomaterial engineers, mechanobiologists, nanotribologists, and physicists. Such fundamental knowledge is key to eventually design a new generation of soft materials with the desired frictional properties that will tackle a variety of global challenges, from reduction in energy consumption to biological tissue repair.
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