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C: Physical Properties of Materials and Interfaces

Thermal Friction Enhancement in Zwitterionic Monolayers
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The Journal of Physical Chemistry C

Cite this: J. Phys. Chem. C 2022, 126, 5, 2797–2805
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https://doi.org/10.1021/acs.jpcc.1c09542
Published February 1, 2022

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Abstract

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We introduce a model for zwitterionic monolayers and investigate its tribological response to changes in applied load, sliding velocity, and temperature by means of molecular-dynamics simulations. The proposed model exhibits different regimes of motion depending on temperature and sliding velocity. We find a remarkable increase of friction with temperature, which we attribute to the formation and rupture of transient bonds between individual molecules of opposite sliding layers, triggered by the out-of-plane thermal fluctuations of the molecules’ orientations. To highlight the effect of the molecular charges, we compare these results with analogous simulations for the charge-free system. These findings are expected to be relevant to nanoscale rheology and tribology experiments of locally-charged lubricated systems such as, e.g., experiments performed on zwitterionic monolayers, phospholipid micelles, or confined polymeric brushes in a surface force apparatus.

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Introduction

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The possibility of controlling nano- and mesoscale friction and mechanical response in a variety of diverse physical systems has been investigated extensively in recent years. (1−4) In particular, in confined geometries, friction is affected by temperature, usually exhibiting a regular “thermolubric” behavior, with friction decreasing as temperature increases at microscopic scales. (5−9) The rationale for this standard behavior is random thermal fluctuations assisting the sliding interface in the negotiation of interlocking barriers, thus promoting advancement.
The reverse, namely, friction increasing with temperature, is far less common, although it has been observed in specific situations. (3,10−14) Certainly, inverted thermolubricity in poor heat-transfer conditions may promote instabilities in the frictional dynamics: the heat dissipated by friction itself can raise temperature, thus triggering a further increase in friction, eventually possibly leading to some kind of lockup, which cuts off this runaway condition.
Inverted thermolubricity was considered primarily as an ingredient for phenomenological models, (15,16) but it was also investigated in atomic-scale friction within the most basic and fundamental model, namely, the Prandtl-Tomlinson (PT) model, (17) where it was shown that a peak in friction may arise in a range of temperatures corresponding to a transition from a multiple-slip regime (low T) to a single-slip regime (high T). However, that simple model fails to reproduce the observed features of the temperature and velocity dependence of friction and of the corresponding force traces measured via atomic-force microscopy (AFM).
Modeling via molecular dynamics (MD) simulations, as a sort of controlled computational “experiment”, has been revealed to be extremely useful in investigating frictional processes of complex systems, (18−20) possibly avoiding interpretative pitfalls arising from indirect or ex-situ characterization of contact surfaces.
In this work, we investigate the possibility of an inverted thermal dependence of friction between zwitterionic head groups in relative sliding motion. We investigate if, and how, the thermal disordering and rearrangement of such zwitterionic head groups leads to an increase of friction, at least over suitable temperature ranges, especially those experimentally relevant.
We simulate zwitterionic molecules, flexible linear macromolecules that can be tethered to a surface with the aim of modifying its distinctive properties. These molecules can have charge-free or zwitterionic terminations, depending on the specific surface features that are addressed. (21) Applications involving zwitterionic molecules include colloid stabilization, regulation in wetting and adhesion, and the formation of protective coatings, among many others. (22−24) Even though vast theoretical research on zwitterionic molecule lubrication has been carried out, (25−27) there remain unanswered questions about the microscopic mechanisms of friction, especially under the influence of temperature, on surfaces decorated or covered with these complex molecules.
Here, we develop a coarse-grained model to study friction between two preassembled zwitterionic monolayers. (28−30) Our simulations demonstrate how the modification of the geometric rearrangement of locally zwitterionic molecular portions gives rise to different interlocking configurations at the sliding interface, leading to distinct frictional regimes, as a function of temperature.

Methods

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The Model

We propose a model inspired by surface force apparatus (SFA) experiments with confined self-assembled vesicles formed by organic polymers composed of hydrophobic tails and hydrophilic heads consisting of short zwitterionic chains. (31−33) The self-arranged vesicles can sit inside the SFA confined contact, as sketched in Figure 1a: this arrangement provides a highly sensitive setup for the measurement of the frictional shear stress between well-characterized flat surfaces with molecular layers sticking out of them in mutual shearing motion and under a controlled normal load. (34) The solid surfaces and the viscoelastic deformability of the vesicles cooperate in generating an essentially atomically flat interface between the exposed surfaces of two contacting vesicles. This flat interface extends over the size of a vesicle, namely, several micrometers across. All shearing occurs in this sliding interface, which is therefore responsible for all observed frictional forces. (31−33,35,36)

Figure 1

Figure 1. (a) Sketch of the experimental SFA setup. (b) Three representations of one molecular unit in the vesicle wall. Left: a radically simplified sticks scheme, as in panel (a). Center: the simulated united-atom molecule. Right: the detailed chemical structure of a dipalmitoylphosphatidylcholine molecule. (c) The initial regularly spaced configuration of the system (side view). Magenta, purple, red, blue, green, and cyan spheres represent SUB and SUP layers, cations, anions, and NP1 and NP2 particles, respectively. Gray particles represent the R1, R2, and R3 neutral residues in between the cation and the anion. The yellow sphere represents the pulling stage advancing with constant speed. The dashed line marks the sliding interface. (d) Top view restricted to the particles above the black dashed line in (c); purple SUP particles are drawn smaller for better readability.

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A minimal model for simulating the frictional properties of this interface must include at least the exposed zwitterionic head groups of the molecules sticking out from the vesicle, as sketched in Figure 1b. We simulate these heads in a united-atom style as a string of 5 point-like particles. From the interface point of view, the rest of the molecules, namely, the glycerol group and the long alkyl tails have the role of providing a directed support to the heads and transmitting the load and shear forces acted by the SFA setup. In a coarse-grained representation of the hydrophobic inner part of the vesicle, we model this part of the system by parallel rigid layers, one for each contacting vesicle: we name them SUP and SUB layers. The lateral arrangement of molecules in these two layers is modeled using triangular lattices whose periodicity a/2 of 0.41 nm sets the equilibrium intermolecular spacing (see Figure 1d). This spacing a is the characteristic distance between neighboring molecules, matched to the typical areal number density of these vesicle-forming polymers, namely, 1.72 molecules/nm2. (37) To prevent trivial and unrealistic perfect-commensuration effects, we impose a relative angle of rotation ϕ between the layers’ crystalline directions (opposite rotations by ±ϕ/2 for each layer). The value of ϕ = 19.65° and the numbers of lattice repetitions in the rigid layers are adapted in order to fit a supercell periodic in the horizontal xy plane accommodating both lattices, as detailed in the Supporting Information. We represent the experimental mesoscopic interface within a rectangular simulation supercell with dimensions lx = 8.32 nm and ly = 14.41 nm. The supercell contains 206 molecules in each layer and 4 times as many atoms in each of the SUP and SUB rigid layers.
The link between the zwitterionic molecular part and the rigid layers is provided by the NP1 and NP2 units of each molecule that represent the nonpolar tails as a pair of point-like particles. Each of these pairs of bonded atoms remains “planted” in one (out of four) of the lattice nodes in either the SUP or the SUB layer. The intralayer–molecule interaction results in keeping these nonpolar sections close to vertical alignment and regularly spaced, while allowing for a limited degree of elastic deformability; see Figure 1b,c.
The SUB-layer particles (magenta particles in Figure 1c) are kept fully frozen. Those in the SUP layer (purple particles in Figure 1c,d) are constrained to form an identical, yet misaligned, rigid layer, allowed to translate in the three directions.
Each embedded macromolecule therefore consists of a chain of seven particles, as depicted in Figure 1b. It starts with a cation (CA, red particle) followed by three uncharged residues (R1–R3, gray), an anion (AN, blue), and two uncharged particles, NP1 (green) and NP2 (cyan). Inspired by the dipalmitoylphosphatidylcholine molecule, we set the masses (in a.m.u.) of the molecular beads to 60 for CA, 15 for R1–R3, 80 for AN, and 50 for NP1 and NP2. The CA and AN beads carry an associated charge of q = 0.25 and −q, respectively, in elementary-charge units, while all other beads are neutral. For comparison, we also consider a charge-free version of the model with q = 0 for all beads. Successive atoms in each chain are connected by elastic springs representing both the stretching and the angular degrees of freedom. All equilibrium angles θeq are 180°, except for the NP2–NP1–AN angle, which we set to 111°, representative of a sp3 skeleton oxygen, attempting to keep the zwitterionic heads tilted away from being vertical. (38)
The intramolecular harmonic interactions follow the standard expression
for linear springs, and
for angular springs. Table 1 lists the parameters adopted for both kinds of intramolecular bonding interaction.
Table 1. Intramolecular Interaction Parameters for the Bonded Interactionsa
Harmonic Bonds
particle 1particle 2kbond (N·m–1)req (nm)
CAR14800.16
R1R2
R2R3
R3AN
ANNP1
NP1NP20.67
Harmonic Angular Interactions
particle 1particle 2particle 3kangle (eV·rad–2)θeq (degree)
CAR1R220180
R1R2R3
R2R3AN
R3ANNP1
ANNP1NP22111
a

All interactions not listed here involve non-bonded atoms and are of the Morse-type, eq 1.

For the nonbonded pairwise particle–particle interactions, we adopt a Morse potential
with a standard shift and a linear term added so that both potential energy and force drop to zero at a cutoff distance Rc; see the Supporting Information. The stiffness parameter α = 15 nm–1 and the cutoff distance Rc = 1 nm are the same for all interaction pairs. The values of the potential well depth D0 and equilibrium spacing r0 are listed in Table 2. Note that, while all nonbonded beads interact pairwise through Morse terms, as an exception, cross-layer interactions are restricted to the polar heads of the molecules (CA, R1–R3, and AN spheres in Figure 1) with spurious cross-layer terms removed by the D0 = 0 values in Table 2.
Table 2. Values for the Morse Interaction Parameters between Pairs of Particles
particle 1particle 2D0 (eV)r0 (nm)
defaultdefault0.0100.41
SUPNP1/2 (SUP layer)5.00.41
SUPNP1/2 (SUB layer)0.0
SUBNP1/2 (SUB layer)5.0
SUBNP1/2 (SUP layer)0.0
SUBSUP0.0
NP1 (SUP layer)NP1 (SUP layer)5.00.82
NP1 (SUP layer)NP1 (SUB layer)0.0
NP1 (SUB layer)NP1 (SUB layer)5.0
NP2 (SUP layer)NP2 (SUP layer)5.0
NP2 (SUP layer)NP2 (SUB layer)0.0
NP2 (SUB layer)NP2 (SUB layer)5.0
Within the cutoff radius, Coulombic pairwise interactions are computed directly in real space, while outside that distance interactions are evaluated in reciprocal space. For the reciprocal space, a particle–particle particle–mesh solver (PPPM) (39,40) is used with a precision of 10–4 eV·nm–1, which proved to be sufficiently accurate; see further details in the Supporting Information.

Simulations

We adopt LAMMPS (41) as the simulation platform for integrating the equations of motion
(1)
In addition to the conservative forces Fiu explicitly provided by the force fields described in the previous section, we impose a finite temperature using a Langevin thermostat with a damping rate γiu applied to all particles forming the molecules and Gaussian random forces ξiu. (42) This thermostat is set to act only along the coordinates u = y, z in order to prevent any spurious thermostat-originated frictional damping along the most relevant sliding direction u = x. (43,44)Figure S1 illustrates the robustness of the friction simulated in our model against the precise value of γiy = γiz = γ adopted. Eventually, we select a value of γ = 1 ps–1 for all simulations.
While experiments with this kind of setup are usually carried out in (typical aqueous) solution, here, with the aim of providing a qualitative phenomenology (independent of the specific solvent nature), we adopt a suitably enlarged residue size r0 and exploit a Langevin approach effectively taking care of degrees of freedom inherent in the real, physical system, which are not explicitly included in our model. (45) Besides, a real solvent introduces electrostatic screening, which is partly accounted for in this model by the relatively small charges on the AN and CA residues. As we intend to address a general mechanism without focusing on a specific system, we leave out all distance, frequency, and temperature dependence of the screening that a real solvent would entail.
For each simulation, we prepare an initial configuration by executing a sufficiently long “running in” simulation starting from the initial state shown in Figure 1c, letting the dynamics evolve with the appropriate load, temperature, and fixed sliding velocity of the SUP layer until a steady state is reached. In the appropriate steady-state configuration, we attach a pulling stage to the SUP layer (yellow sphere in Figure 1c) through a spring of stiffness k = 1 eV·nm–2 ≃ 0.16 N·m–1, equivalent to a shear stress per unit elongation k/(supercell area) = 1.34 × 109 MPa·m–1. We carry out the simulations with the stage advancing at constant speed in the x direction: xstage = vstaget. A default vstage = 5 m·s–1, in the range of a typical MD approach, is adopted, but we explore other velocities too. In each simulation, the total advancement of the stage amounts to 100 nm. We obtain the instantaneous shear stress from the spring elongation. We start averaging this shear stress when the system enters a steady sliding state until the end of the simulation. This corresponds to one discarding an initial transient of 20–25 nm until at least the first slip event takes place.
We report the averaged shear stress with vertical bars reflecting the root mean squared fluctuations observed along the corresponding friction trace. Large bars indicate stick–slip dynamics, while small bars originate from smooth sliding.
We apply relatively moderate values of loads (L) in the 0–20 MPa range, relevant for SFA experiments on organic macromolecules.

Results

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Figure 2a displays the frictional shear stress as a function of temperature. Consider first the green symbols, reporting the simulations of the default model, the one involving zwitterionic head groups. At low temperature, a smooth-sliding regime (Figure 2c) characterized by extremely small friction is observed. In the smooth-sliding regime, the two layers remain substantially flat and well ordered due to the Coulombic interactions between cations and anions in the same layer (see Figures 3a and 4a): chains of opposite layers do not entangle, and they slide on top of each other encountering a quite small corrugation due to the discommensuration associated with the mutual angular misalignment. Starting from approximately T ≥ 200 K, stick–slip dynamics sets in (see Figure 2d), and friction increases substantially. As temperature is raised, thermal fluctuations promote out-of-plane chain movements leading to transient interlocking (see Figures 3b and 4b). The cationic chain head reaching through the opposite layer forms transient bonds with the anions belonging to two adjacent chains in the countersurface. The fraction of these bonds can be quantified through the “hooking fraction” h, i.e., the degree of interpenetration, defined quantitatively in the Supporting Information and reported in Figure 5a for the 300 K dynamics of Figure 2d. These bonds are responsible for the “stick” intervals, where the SUP remains essentially static and the driving spring elongates. The shear stress drops to nearly 0 after each slip and so does the hooking fraction (see Figure 3c and Figure 5a). The smooth-sliding and stick–slip motions of Figure 2c,d can be inspected in short movies reporting the last 6 ns of the simulations (i.e., the last 30 nm of the stage advancement in the shear traces), available as Movies S1 and S2. The transition from smooth sliding to stick–slip that we observe for increasing temperature depends on the sliding velocity and on the stiffness of the driving spring with smaller velocities and softer springs favoring stick–slip over smooth sliding. (18,46) An important parameter of a tribological contact is the critical velocity vc above which intermittent stick–slip dynamics tends to disappear. In our simulations, we can observe this disappearance as a function of vstage at T = 150 K in Figure 6. With the adopted model parameters, our simulations show clear stick–slip dynamics for vstage < 3 m·s–1 and smooth sliding for vstage > 6 m·s–1. The model therefore predicts a critical velocity of ≃5 m·s–1. However, vc can change by several orders of magnitude depending on system parameters. For example, at T = 50 K (see dot-dashed line in Figure 6a), the critical velocity is extremely small, and simulations capable of observing stick–slip would be far too long. It is therefore unfeasible to evaluate vc systematically through simulations. Experimentally, in ref (47), this critical velocity is reported for SFA experiments involving squalane films. In those experiments, an increase of vc with increasing temperature was observed: that result is compatible with the outcome of the present model.

Figure 2

Figure 2. (a) Nonmonotonic variation of the frictional shear stress and (b) the distance between the rigid layers as a function of temperature for zwitterionic and charge-free systems. vstage = 5 m·s–1, L = 10 MPa. (c–f) Shear traces for the pointed temperatures in panel (a). Symbols in (c–f) refer to the snapshots in Figure 3.

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Figure 3

Figure 3. Side views of 5 nm y-thick slices of simulation snapshots. Each snapshot corresponds to the time instant marked by the corresponding symbol in panels c–f of Figure 2. (a) Smooth sliding, zwitterionic system, T = 150 K, (b) stick point, zwitterionic system, T = 300 K, (c) slip point, zwitterionic system, T = 300 K, (d) high friction state, charge-free system, T = 300 K, (e) stick point, charge-free system, T = 150 K, and (f) slip point, system, T = 150 K.

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Figure 4

Figure 4. (a, b) Top views of the snapshots of Figure 3a (150 K) and 3b (300 K), including a horizontal slice from the sliding plane in between the chains to immediately above the rigid SUP layer. This slice is the unshaded part of the side views (c) and (d). Black dashed circles highlight SUB chains intersecting the SUP chains’ cation plane. The end cation of each of those SUB chains feels a relatively strong Coulomb interaction with the two top-chain anions, generating the interlocking spots responsible for the stick.

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Figure 5

Figure 5. (a) Percentile hooking fraction h as a function of the stage displacement correlated with the frictional shear stress for the same simulation as in Figure 2d. (b) The total potential energy U for the same simulation.

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Figure 6

Figure 6. Stick–slip to smooth-sliding transition as a function of velocity. (a) The frictional shear stress as a function of the sliding velocity, zwitterionic system, L = 10 MPa. (b–e) Shear traces for the pointed velocities in panel (a) at 150 K. Dashed line: fit of T = 150 K and vstage > 6 m·s–1. Dot-dashed line: fit of the T = 50 K, including all points.

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Coming back to Figure 2a, as temperature increases to T ≃ 600 K, friction increases less and less until it peaks near 800 K. The transient bonds are numerous and relatively short-lived. The energy of each one of such bonds can be estimated (neglecting the small Morse contributions) by the difference in Coulomb attraction of a cation placed in between two adjacent anions of the opposite layer (distance ≃ 0.41 nm) and placed in its flat-layer configuration (distance ≃ 0.51 nm), which gives ≃85 meV. This transient bond energy is close to the thermal energy kBT ≃ 86 meV for T ≃ 1000 K, precisely in the temperature region of the observed friction peak. For even higher T > 1000 K, these bonds are destabilized and eventually friction decreases. In order to analyze the effect of the molecular charges on friction, we run analogous simulations for the charge-free system, reported as red curves in Figure 2. Remarkably, across the temperature range from T = 0 K to T = 550 K, friction is significantly larger than that for the zwitterionic system. The reason for this difference is that, even at 0 K, both molecular layers are significantly disordered due to the lack of long-range interactions. The chain-orientation disorder leads to a tilt-angle disorder too and to a significant corrugation of the two mutually sliding layers of the molecular heads (CA). This corrugation is also reflected in the consistently larger average SUP–SUB distance, shown in Figure 2b, compared to that in the zwitterionic case. Due to this extra corrugation, the hooked fraction of the charge-free system remains significant, even down to low temperatures.
The shear traces for the charge-free system (Figure 2e,f) exhibit stick–slip of smaller amplitude than those for the zwitterionic system. As illustrated in Figure 3d,e and in Movies S1, S2, S3, and S4, this is due to the charge-free molecules showing a larger density of protruding chains ready to interlock before the slip event has exhausted the energy stored in the pulling spring (Figure 3f). For T > 300 K, thermal fluctuations start to undermine the weaker Morse-type bonds of the protruding chains, leading to a progressive decrease in friction.
So far, the applied load L was fixed to 10 MPa. To explore how L affects the discussed phenomenology, we perform friction load cycles between 0 and 20 MPa and then back to 0 MPa as reported in Figure 7. The outcome of these simulations indicates that the shear stress does not change significantly upon loading, despite the chain-layer compression visible in Figure 7b,d. Additionally, the unloading data retrace those of the loading simulations with no visible hysteresis. For this reason, each point in Figure 7 is obtained as an average over both loading and unloading traces for that given load. The frictional shear traces for different loads are reported in Figures S2 and S3. The traces of the zwitterionic system, Figure S2, show that the critical velocity remains practically unchanged for all the investigated loads at T ≃ 150 K. Given such a weak friction dependence on load, it is essentially meaningless to define a friction coefficient for this model. From Figure 7, we expect the same conclusion at any T in the considered range. The charge-free reference system exhibits a marginally significant friction increase with load.

Figure 7

Figure 7. (a, c) Frictional shear stress and (b, d) the average distance between the rigid layers as a function of load L with vstage = 5 m·s–1.

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As for the velocity dependence, in the stick–slip regime, it is also expected to be very mild. Indeed, Figure S4 shows essentially no dependence as long as the dynamics is stick–slip. The zwitterionic system at T = 150 K reaches smooth sliding for vstage > 6 m·s–1. The resulting friction linear increase, practically invisible in Figure S4, is clear in Figure 6a. Likewise, the smooth-sliding dynamics at 50 K also produces velocity-linear friction over all simulated velocities. In contrast, the charge-free system has stick–slip dynamics at all simulated temperatures resulting in velocity-independent friction.
Figure 5 and analogous plots for different dynamical conditions exhibit clear signs of correlation between the hooking fraction h and the frictional shear stress. We expect that h should also correlate with the total potential energy U. Specifically, we expect a decrease in total potential energy as the number of hooked stick points increases. This anticorrelation is illustrated in Figure S5 for the charge-free system at T = 0 K. However, at T = 300 K, the total potential energy is extremely noisy due to thermal fluctuations (see Figure 5), and these anticorrelations are hard to detect visually.
Figure S6 illustrates these correlations with scatter plots for the zwitterionic (panel a) and charge-free (panel b) models at T = 300 K, related to the traces of Figure 2d,f. These scatter plots provide qualitative hints of these correlations. For a quantitative evaluation of these correlations, we calculate the Pearson correlation coefficient (48)
(2)
and report it as a function of load and temperature in Figure 8. ρUh is systematically negative, confirming the expected anticorrelation. At T = 300 K, the charge-free model exhibits more negative anticorrelation compared to the zwitterionic model at all the investigated loads (Figure 8a). As a function of temperature, so far, the zwitterionic and charge-free models behave quite differently. The zwitterionic model has null h at low temperatures (smooth sliding), and therefore, ρUh is undefined. As stick–slip develops, ρUh becomes more and more negative. In contrast, the charge-free system exhibits stick–slip down to a temperature of zero with the correspondingly largely negative ρUh. As temperature is raised, these correlations approach zero and correspondingly friction decreases (Figure 2a).

Figure 8

Figure 8. Correlation coefficient ρUh between the hooked fraction and total potential energy, eq 2, for the zwitterionic and charge-free systems at vstage = 5 m·s–1 as a function of (a) the applied load and (b) the temperature. As in smooth sliding h ≡ 0, ρUh is defined for stick–slip dynamics only.

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Discussion and Conclusions

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In this work, we have introduced and studied a model that offers a microscopic implementation for friction mediated by thermally activated formation and rupture of interfacial contacts, a subject which so far has been explored by means of phenomenologic theory. (12,49−56) This kind of theory has been found to have wide applications in describing friction and wear in dry and lubricated contacts over a broad range of lengths and revealed the origin of new, unexpected phenomena such as non-Amonton’s variation of friction force with normal load and nonmonotonic dependence of friction on sliding speed and temperature. The microscopic model proposed here advances understanding mechanisms underlying the phenomenological theory and offers new pathways for the rational control of frictional response.
The main outcome of this model consists of a remarkable increase in friction with temperature. Depending on the operating conditions, sliding can occur with stick–slip or smooth advancement. The high-friction stick state results from the interlocking of molecular chains promoted by thermal fluctuations. In the proposed model, Coulombic interactions between the zwitterionic macromolecules enhance the intermolecular interactions, favoring flat and ordered layers and smooth sliding at low temperatures. We can imagine different types of intermacromolecule interactions, for example, hydrogen bonding or solvent-mediated couplings, that could support a similar kind of low-temperature ordering. Thermally activated interlocking is therefore also likely to account for thermally enhanced friction in more general contexts, as for example, in the experiments of ref (47).
Zwitterionic macromolecules are promising systems for the control of friction by externally applied electric fields. The change in the orientation of the molecular zwitterionic heads due to the field may affect interlocking and, therefore, friction. (57) We hope that this model stimulates further experiments in this and related directions.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c09542.

  • Details of the chain arrangement, supercell geometry, and intermolecular interactions; the average shear stress as a function of the damping parameter γ (Figure S1); the definition of the hooking fraction h; the frictional shear traces of the zwitterionic (Figure S2) and charge-free (Figure S3) systems for the load dependence of Figure 7a,c; shear stress and SUP–SUB distance dependence on the sliding velocity for zwitterionic and charge-free systems (Figure S4); correlation of the hooking fraction, shear stress, and total potential energy for the charge-free system at T = 0 K (Figure S5); scatter plots illustrating the anticorrelation between the total potential energy and the hooking fraction that determine the T = 300 K points in Figure 8b for zwitterionic and charge-free systems (Figure S6); technical details about 4 short supporting movies illustrating the MD simulations corresponding to the last 30 nm of the stage’s displacement in the shear traces of Figure 2c–f (PDF)

  • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2c (MP4)

  • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2d (MP4)

  • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2e (MP4)

  • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2f (MP4)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Roberto Guerra - Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano 20133, Italy;  Orcidhttps://orcid.org/0000-0002-1278-8021
    • Andrea Vanossi - CNR-IOM, Consiglio Nazionale delle Ricerche, Istituto Officina dei Materiali, c/o SISSA, Via Bonomea 265, 34136 Trieste, Italy;  International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy;  Orcidhttps://orcid.org/0000-0002-6058-8403
    • Michael Urbakh - Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel;  Orcidhttps://orcid.org/0000-0002-3959-5414
    • Nicola Manini - Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, Milano 20133, Italy;  Orcidhttps://orcid.org/0000-0003-4374-6374
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors acknowledge support from the grant PRIN2017 UTFROM of the Italian Ministry of University and Research. A.V. also acknowledges support by ERC Advanced Grant ULTRADISS, contract No. 8344023, and by the European Unions Horizon 2020 research and innovation programme under grant agreement No. 899285. M.U. acknowledges the financial support of the Israel Science Foundation, Grant 1141/18. All the authors thank Carlos Drummond, Di Jin, Jacob Klein, Erio Tosatti, and Yu Zhang for the useful discussions.

References

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    Vanossi, A.; Dietzel, D.; Schirmeisen, A.; Meyer, E.; Pawlak, R.; Glatzel, T.; Kisiel, M.; Kawai, S.; Manini, N. Recent highlights in nanoscale and mesoscale friction. Beilstein J. Nanotechnol. 2018, 9, 1995– 2014,  DOI: 10.3762/bjnano.9.190
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    Recent highlights in nanoscale and mesoscale friction
    Vanossi, Andrea; Dietzel, Dirk; Schirmeisen, Andre; Meyer, Ernst; Pawlak, Remy; Glatzel, Thilo; Kisiel, Marcin; Kawai, Shigeki; Manini, Nicola
    Beilstein Journal of Nanotechnology (2018), 9 (), 1995-2014CODEN: BJNEAH; ISSN:2190-4286. (Beilstein-Institut zur Foerderung der Chemischen Wissenschaften)
    Friction is the oldest branch of non-equil. condensed matter physics and, at the same time, the least established at the fundamental level. A full understanding and control of friction is increasingly recognized to involve all relevant size and time scales. We review here some recent advances on the research focusing of nano- and mesoscale tribol. phenomena. These advances are currently pursued in a multifaceted approach starting from the fundamental at.-scale friction and mech. control of specific single-asperity combinations, e.g., nanoclusters on layered materials, then scaling up to the meso/microscale of extended, occasionally lubricated, interfaces and driven trapped optical systems, and eventually up to the macroscale. Currently, this "hot" research field is leading to new technol. advances in the area of engineering and materials science.
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  4. 4
    Krim, J. Controlling friction with external electric or magnetic fields: 25 examples. Front. Mech. Eng. 2019, 5, 22,  DOI: 10.3389/fmech.2019.00022
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  5. 5
    Sang, Y.; Dubé, M.; Grant, M. Thermal Effects on Atomic Friction. Phys. Rev. Lett. 2001, 87, 174301,  DOI: 10.1103/PhysRevLett.87.174301
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    Thermal Effects on Atomic Friction
    Sang, Yi; Dube, Martin; Grant, Martin
    Physical Review Letters (2001), 87 (17), 174301/1-174301/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We model friction acting on the tip of an at. force microscope as it is dragged across a surface at nonzero temps. We find that stick-slip motion occurs and that the av. frictional force follows | ln v|2/3, where v is the tip velocity. This compares well to recent exptl. work, permitting the quant. extn. of all microscopic parameters. We calc. the scaled form of the av. frictional force's dependence on both temp. and tip speed as well as the form of the friction-force distribution function.
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  6. 6
    Dudko, O. M.; Filippov, A.; Klafter, J.; Urbakh, M. Dynamic force spectroscopy: a Fokker Planck approach. Chem. Phys. Lett. 2002, 352, 499– 504,  DOI: 10.1016/S0009-2614(01)01469-5
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    Dynamic force spectroscopy: a Fokker-Planck approach
    Dudko, O. K.; Filippov, A. E.; Klafter, J.; Urbakh, M.
    Chemical Physics Letters (2002), 352 (5,6), 499-504CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
    In this Letter recent observations using dynamic force spectroscopy can be described by a generalized Tomlinson model which includes the contribution of an external noise. The measured friction forces depend on the microscopic potential and dissipation inherent to the system as well as on the mech. properties of the setup (i.e. spring const.) and the external noise. Tuning the noise and spring const. offers ways to ext. information about the microscopic properties.
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  7. 7
    Szlufarska, I.; Chandross, M.; Carpick, R. Recent advances in single-asperity nanotribology. J. Phys. D 2008, 41, 123001,  DOI: 10.1088/0022-3727/41/12/123001
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    Recent advances in single-asperity nanotribology
    Szlufarska, Izabela; Chandross, Michael; Carpick, Robert W.
    Journal of Physics D: Applied Physics (2008), 41 (12), 123001/1-123001/39CODEN: JPAPBE; ISSN:0022-3727. (Institute of Physics Publishing)
    A review. As the size of electronic and mech. devices shrinks to the nanometer regime, performance begins to be dominated by surface forces. For example, friction, wear, and adhesion are known to be central challenges in the design of reliable micro- and electromech. systems (MEMS/NEMS). Because of the complexity of the phys. and chem. mechanisms underlying at.-level tribol., it is still not possible to accurately and reliably predict the response when two surfaces come into contact at the nanoscale. Fundamental scientific studies are the means by which these insights may be gained. Recent advances in the exptl., theor., and computational studies of nanotribol. are reviewed. In particular, it is focussed on the latest developments in at. force microscopy and mol. dynamics simulations and their application to the study of single-asperity contact.
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  8. 8
    Brukman, M.; Gao, G.; Nemanich, R.; Harrison, J. Temperature dependence of single-asperity diamond-diamond friction elucidated using AFM and MD simulations. J. Phys. Chem. C 2008, 112, 9358– 9369,  DOI: 10.1021/jp711959e
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    Temperature Dependence of Single-Asperity Diamond-Diamond Friction Elucidated Using AFM and MD Simulations
    Brukman, Matthew J.; Gao, Guangtu; Nemanich, Robert J.; Harrison, Judith A.
    Journal of Physical Chemistry C (2008), 112 (25), 9358-9369CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Complementary exptl. (at. force microscopy) and theor. (mol. dynamics) techniques were used to investigate friction between diamond-diamond junctions as a function of temp. The simulation and exptl. conditions were designed to correspond as closely as possible. In the at. force microscopy (AFM) expts., two microcryst.-diamond (μCD) AFM tips of differing contact radii were used to examine the friction of diamond (111) and (001) single crystals from 24 to 225 K in an ultrahigh vacuum. At all temps., the exptl. detd. dependence of friction on load was consistent with the occurrence of single-asperity interfacial friction, where friction is proportional to contact area. In addn., the behavior of the contact was fit well by the Derjaguin-Muller-Toporov continuum model. Friction measurements within a given series were highly repeatable; however, as is typical with AFM measurements, there was some variation in measurements taken from different regions of the sample and with different tips. Interfacial shear strength, or the intrinsic resistance to sliding, decreased slightly with increasing temp. for both surfaces. To shed addnl. insight into the AFM results, MD simulations were performed with the diamond single crystals of the same orientation. The calcns. also show that the av. friction force decreased slightly as the temp. increased for both diamond surfaces and for all sliding directions. Both AFM and MD results agree with the numerical anal. of friction as a function of temp. published by Sang et al. (Sang, Y.; Dube, M.; Grant, M.Phys. Rev. Lett.2001, 87, 174301).
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  9. 9
    Steiner, P.; Roth, R.; Gnecco, E.; Baratoff, A.; Maier, S.; Glatzel, T.; Meyer, E. Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite. Phys. Rev. B 2009, 79, 045414  DOI: 10.1103/PhysRevB.79.045414
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    9
    Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite
    Steiner, Pascal; Roth, Raphael; Gnecco, Enrico; Baratoff, Alexis; Maier, Sabine; Glatzel, Thilo; Meyer, Ernst
    Physical Review B: Condensed Matter and Materials Physics (2009), 79 (4), 045414/1-045414/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    The friction between an atomically sharp tip and a solid surface (NaCl and highly oriented pyrolytic graphite) is analyzed theor. in the framework of a modified Tomlinson model in 2 dimensions. Lateral forces are studied as a function of temp., load, and magnitude of actuation. The actuation leads to a redn. in friction and allows one to enter a dynamic superlubricity regime. In addn., our model is able to describe other ultralow friction states as static superlubricity and thermolubricity. We find a good agreement between the calcns. and the exptl. results.
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  10. 10
    Schirmeisen, A.; Jansen, L.; Holscher, H.; Fuchs, H. Temperature dependence of point contact friction on silicon. Appl. Phys. Lett. 2006, 88, 123108,  DOI: 10.1063/1.2187575
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    Temperature dependence of point contact friction on silicon
    Schirmeisen, Andre; Jansen, Lars; Hoelscher, Hendrik; Fuchs, Harald
    Applied Physics Letters (2006), 88 (12), 123108/1-123108/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    Point contact friction and adhesion between a Si tip and an untreated Si(111) wafer are measured as a function of sample temp. in ultrahigh vacuum by friction force microscopy. While the friction coeff. changes drastically in the temp. range from 50 K to room temp., and shows a reproducible max. near 100 K, the simultaneously recorded adhesion shows much less temp. dependence. Interestingly, the velocity dependence of friction shows a logarithmic increase below 150 K although it is nearly const. above 150 K. This peculiar behavior has profound consequences for tribol. properties of devices manufd. from Si.
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  11. 11
    Barel, I.; Urbakh, M.; Jansen, L.; Schirmeisen, A. Multibond dynamics of nanoscale friction: the role of temperature. Phys. Rev. Lett. 2010, 104, 066104  DOI: 10.1103/PhysRevLett.104.066104
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    Multibond Dynamics of Nanoscale Friction: The Role of Temperature
    Barel, Itay; Urbakh, Michael; Jansen, Lars; Schirmeisen, Andre
    Physical Review Letters (2010), 104 (6), 066104/1-066104/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The main challenge in predicting sliding friction is related to the complexity of highly nonequil. processes, the kinetics of which are controlled by the interface temp. Our expts. reveal a nonmonotonic enhancement of dry nanoscale friction at cryogenic temps. for different material classes. Concerted simulations show that it emerges from two competing processes acting at the interface: the thermally activated formation as well as rupturing of an ensemble of at. contacts. These results provide a new conceptual framework to describe the dynamics of dry friction.
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  12. 12
    Barel, I.; Urbakh, M.; Jansen, L.; Schirmeisen, A. Temperature dependence of friction at the nanoscale: when the unexpected turns normal. Tribol. Lett. 2010, 39, 311– 319,  DOI: 10.1007/s11249-010-9675-4
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    Sheng, P.; Wen, W. Electrorheological fluids: mechanisms, dynamics, and microfluidics applications. Annu. Rev. Fluid Mech. 2012, 44, 143– 174,  DOI: 10.1146/annurev-fluid-120710-101024
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    Zhu, J.; Zeng, Q.; Wang, Y.; Yan, C.; He, W. Nano-crystallization-driven high temperature self-lubricating properties of magnetron-sputtered WS 2 coatings. Tribol. Lett. 2020, 68, 50,  DOI: 10.1007/s11249-020-01290-0
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    Nano-crystallization-Driven High Temperature Self-lubricating Properties of Magnetron-Sputtered WS2 Coatings
    Zhu, Jianing; Zeng, Qunfeng; Wang, Yongfu; Yan, Chao; He, Wanjun
    Tribology Letters (2020), 68 (1), 50CODEN: TRLEFS; ISSN:1023-8883. (Springer)
    Abstr.: In consideration of high temp. conditions, this paper focuses on the self-lubricating properties of tungsten disulfide coatings at high temp. A low coeff. of friction (CoF) about 0.07-0.2 for tungsten disulfide coatings can be attained at temps. of 100-400°C. The chem. stability, mech. and tribolgical properties were investigated by energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), XPS, SEM (SEM), nano-indentation tester and ball-on-disk tribometer, resp. According to XRD and XPS spectra, the as-sputtered tungsten disulfide coatings existed as 2h-tungsten disulfide structure. The crystal transition of tungsten disulfide coatings from amorphous to (002) basal plane-oriented lubricating film, which was obtained by the synergistic effect of load and friction, and provided anti-friction performance at 100-400°C. At 500°C, the tungsten oxide formed by oxidn. of tungsten disulfide on the sample surface with lower hardness reduces the coeff. of friction and improves wear resistance. The wear resistance and anti-friction performance are discussed in terms of morphol. of the wear scars, anti-oxidn. capability of the coating and tribochem. reaction product of the friction pair.
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  15. 15
    Singh, A. K.; Singh, T. N. Stability of the rate, state and temperature dependent friction model and its applications. Geophys. J. Int. 2016, 205, 636– 647,  DOI: 10.1093/gji/ggw012
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    Tian, K.; Goldsby, D. L.; Carpick, R. W. Rate and state friction relation for nanoscale contacts: thermally activated Prandtl-Tomlinson Model with chemical aging. Phys. Rev. Lett. 2018, 120, 186101,  DOI: 10.1103/PhysRevLett.120.186101
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    Rate and State Friction Relation for Nanoscale Contacts: Thermally Activated Prandtl-Tomlinson Model with Chemical Aging
    Tian, Kaiwen; Goldsby, David L.; Carpick, Robert W.
    Physical Review Letters (2018), 120 (18), 186101CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Rate and state friction (RSF) laws are widely used empirical relationships that describe macroscale to microscale frictional behavior. They entail a linear combination of the direct effect (the increase of friction with sliding velocity due to the reduced influence of thermal excitations) and the evolution effect (the change in friction with changes in contact "state," such as the real contact area or the degree of interfacial chem. bonds). Recent at. force microscope (AFM) expts. and simulations found that nanoscale single-asperity amorphous silica-silica contacts exhibit logarithmic aging (increasing friction with time) over several decades of contact time, due to the formation of interfacial chem. bonds. Here we establish a phys. based RSF relation for such contacts by combining the thermally activated Prandtl-Tomlinson (PTT) model with an evolution effect based on the physics of chem. aging. This thermally activated Prandtl-Tomlinson model with chem. aging (PTTCA), like the PTT model, uses the loading point velocity for describing the direct effect, not the tip velocity (as in conventional RSF laws). Also, in the PTTCA model, the combination of the evolution and direct effects may be nonlinear. We present AFM data consistent with the PTTCA model whereby in aging tests, for a given hold time, static friction increases with the logarithm of the loading point velocity. Kinetic friction also increases with the logarithm of the loading point velocity at sufficiently high velocities, but at a different increasing rate. The discrepancy between the rates of increase of static and kinetic friction with velocity arises from the fact that appreciable aging during static contact changes the energy landscape. Our approach extends the PTT model, originally used for cryst. substrates, to amorphous materials. It also establishes how conventional RSF laws can be modified for nanoscale single-asperity contacts to provide a phys. based friction relation for nanoscale contacts that exhibit chem. bond-induced aging, as well as other aging mechanisms with similar phys. characteristics.
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  17. 17
    Tshiprut, Z.; Zelner, S.; Urbakh, M. Temperature-induced enhancement of nanoscale friction. Phys. Rev. Lett. 2009, 102, 136102,  DOI: 10.1103/PhysRevLett.102.136102
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    Temperature-Induced Enhancement of Nanoscale Friction
    Tshiprut, Z.; Zelner, S.; Urbakh, M.
    Physical Review Letters (2009), 102 (13), 136102/1-136102/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We introduce a novel mechanism of temp. dependence of friction at the nanoscale which is detd. by a decrease of the slip length with temp. T. We find that the effect of temp. on the slip length may result in a rich temp. dependence of friction, including a peak and/or plateau in F as a function of T, and a sharp increase or decrease of F with T. This mechanism is of primary importance in the multiple-slip regimes of motion when the tip slips over a no. of lattice spacings. The influence of normal load and driving velocity on the temp. dependence of friction is discussed. We predict that the presence of surface defects or adsorbate may strongly influence the temp. dependence of friction.
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    Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 2013, 85, 529,  DOI: 10.1103/RevModPhys.85.529
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    Modeling friction: From nanoscale to mesoscale
    Vanossi, Andrea; Manini, Nicola; Urbakh, Michael; Zapperi, Stefano; Tosatti, Erio
    Reviews of Modern Physics (2013), 85 (2), 529-552CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
    A review. The physics of sliding friction is gaining impulse from nanoscale and mesoscale expts., simulations, and theor. modeling. This Colloquium reviews some recent developments in modeling and in atomistic simulation of friction, covering open-ended directions, unconventional nanofrictional systems, and unsolved problems.
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    Manini, N.; Braun, O. M.; Vanossi, A. In Fundamentals of Friction and Wear on the Nanoscale, 2nd ed.; Gnecco, E., Meyer, E., Eds.; Springer: Berlin, 2015; p 175.
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    Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A. Friction and nonlinear dynamics. J. Phys.: Condens. Matter 2016, 28, 293001,  DOI: 10.1088/0953-8984/28/29/293001
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    Friction and nonlinear dynamics
    Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
    Journal of Physics: Condensed Matter (2016), 28 (29), 293001/1-293001/22CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    The nonlinear dynamics assocd. with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in exptl. techniques and computational resources has stimulated the development of more refined and accurate math. and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
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    Perkin, S.; Klein, J. Soft matter under confinement. Soft Matter 2013, 9, 10438– 10441,  DOI: 10.1039/c3sm90141f
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    Soft matter under confinement
    Perkin, Susan; Klein, Jacob
    Soft Matter (2013), 9 (44), 10438-10441CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    A review. 'Soft matter' encompasses myriad systems both in synthetic and in biol. contexts-and often in combination. 'Confinement' in the context of this themed issue can include situations such as soft (or biol.) materials at solid surfaces, at liq.-liq. interfaces, adjacent to bio-membranes, the crowded and fluctuating intra-cellular space, in synthetic nano-pores and natural porous materials, and inside polymer brushes. Work in the area of soft materials in confinement is very interdisciplinary in nature, both in terms of the applications and systems under investigation and the methods (exptl. and theor.) used to approach them. Diverse approaches and highlights, emphasizing the commonalities of confined soft matter from the importance of entropy to ion-specific effects was provided.
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    Ma, S.; Zhang, X.; Yu, B.; Zhou, F. Brushing up functional materials. NPG Asia Mater. 2019, 11, 24,  DOI: 10.1038/s41427-019-0121-2
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    Myshkin, N. K.; Kovalev, A. V. Polymer tribology; World Scientific, 2009; pp 3– 37.
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    Chen, M.; Briscoe, W. H.; Armes, S. P.; Klein, J. Lubrication at physiological pressures by polyzwitterionic brushes. Science 2009, 323, 1698– 1701,  DOI: 10.1126/science.1169399
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    Lubrication at Physiological Pressures by Polyzwitterionic Brushes
    Chen, Meng; Briscoe, Wuge H.; Armes, Steven P.; Klein, Jacob
    Science (Washington, DC, United States) (2009), 323 (5922), 1698-1701CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    The very low sliding friction at natural synovial joints, which have friction coeffs. of μ < 0.002 at pressures up to 5 megapascals or more, has to date not been attained in any human-made joints or between model surfaces in aq. environments. We found that surfaces in water bearing polyzwitterionic brushes that were polymd. directly from the surface can have μ values as low as 0.0004 at pressures as high as 7.5 megapascals. This extreme lubrication is attributed primarily to the strong hydration of the phosphorylcholine-like monomers that make up the robustly attached brushes, and may have relevance to a wide range of human-made aq. lubrication situations.
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    Kreer, T. Polymer-brush lubrication: a review of recent theoretical advances. Soft Matter 2016, 12, 3479– 3501,  DOI: 10.1039/C5SM02919H
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    Polymer-brush lubrication: a review of recent theoretical advances
    Kreer, T.
    Soft Matter (2016), 12 (15), 3479-3501CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    A review. This review compiles recent theor. advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biol. problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equil. and out-of-equil. situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromol. inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative anal. approaches, expts. and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using mol. dynamics simulations.
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    De Beer, S.; Müser, M. H. Alternative dissipation mechanisms and the effect of the solvent in friction between polymer brushes on rough surfaces. Soft Matter 2013, 9, 7234– 7241,  DOI: 10.1039/c3sm50491c
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    Alternative dissipation mechanisms and the effect of the solvent in friction between polymer brushes on rough surfaces
    de Beer, Sissi; Mueser, Martin H.
    Soft Matter (2013), 9 (30), 7234-7241CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    Surfaces covered with end-anchored polymers under good solvent conditions have excellent tribol. properties. The friction between such surfaces is commonly attributed to steady-state interdigitation of the opposing polymer brushes. However, this conclusion tends to be based on idealized geometries neglecting surface roughness. Using mol. dynamics simulations, we find that there are qual. differences between the friction of rough and flat polymer-brush surfaces. For rough surfaces the dissipation due to transient interdigitation and capillary- and shape-hysteresis is just as important or can even dominate over steady-state interdigitation. Having a mix of dissipation mechanisms that are all intertwined affects the obsd. friction force in linear-response as well as in the shear-thinning exponents and effective viscosity. Moreover, we find that the effect of the solvent viscosity is sublinear.
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    De Beer, S.; Kutnyanszky, E.; Schön, P. M.; Vancso, G. J.; Müser, M. H. Solvent-induced immiscibility of polymer brushes eliminates dissipation channels. Nat. Commun. 2014, 5, 3781,  DOI: 10.1038/ncomms4781
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    27
    Solvent-induced immiscibility of polymer brushes eliminates dissipation channels
    de Beer, Sissi; Kutnyanszky, Edit; Schoen, Peter M.; Vancso, G. Julius; Mueser, Martin H.
    Nature Communications (2014), 5 (), 3781pp.CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Polymer brushes lead to small friction and wear and thus hold great potential for industrial applications. However, interdigitation of opposing brushes makes them prone to damage. Here we report mol. dynamics simulations revealing that immiscible brush systems can form slick interfaces, in which interdigitation is eliminated and dissipation strongly reduced. We test our findings with friction force microscopy expts. on hydrophilic and hydrophobic brush systems in both sym. and asym. setups. In the sym. setup both brushes are chem. alike, while the asym. system consists of two different brushes that each prefer their own solvent. The trends obsd. in the exptl. measured force traces and the friction redn. are similar to the simulations and extend to fully immersed contacts. These results reveal that two immiscible brush systems in mech. contact slide at a fluid-fluid interface while having load-bearing ability. This makes them ideal candidates for tribol. applications.
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  28. 28
    Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J.-F.; Jérôme, R.; Klein, J. Lubrication by charged polymers. Nature 2003, 425, 163– 165,  DOI: 10.1038/nature01970
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    28
    Lubrication by charged polymers
    Raviv, Uri; Giasson, Suzanne; Kampf, Nir; Gohy, Jean-Francois; Jerome, Robert; Klein, Jacob
    Nature (London, United Kingdom) (2003), 425 (6954), 163-165CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Long-ranged forces between surfaces in a liq. control effects from colloid stability to biolubrication, and can be modified either by steric factors due to flexible polymers, or by surface charge effects. In particular, neutral polymer brushes' may lead to a massive redn. in sliding friction between the surfaces to which they are attached, whereas hydrated ions can act as extremely efficient lubricants between sliding charged surfaces. Here we show that brushes of charged polymers (polyelectrolytes) attached to surfaces rubbing across an aq. medium result in superior lubrication compared to other polymeric surfactants. Effective friction coeffs. with polyelectrolyte brushes in water are lower than about 0.0006-0.001 even at low sliding velocities and at pressures of up to several atmospheres (typical of those in living systems). We attribute this to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments. Our findings may have implications for biolubrication effects, which are important in the design of lubricated surfaces in artificial implants, and in understanding frictional processes in biol. systems.
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  29. 29
    Yu, J.; Banquy, X.; Greene, G. W.; Lowrey, D. D.; Israelachvili, J. N. The boundary lubrication of chemically grafted and cross-linked hyaluronic acid in phosphate buffered saline and lipid solutions measured by the surface forces apparatus. Langmuir 2012, 28, 2244– 2250,  DOI: 10.1021/la203851w
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    29
    The Boundary Lubrication of Chemically Grafted and Cross-Linked Hyaluronic Acid in Phosphate Buffered Saline and Lipid Solutions Measured by the Surface Forces Apparatus
    Yu, Jing; Banquy, Xavier; Greene, George W.; Lowrey, Daniel D.; Israelachvili, Jacob N.
    Langmuir (2012), 28 (4), 2244-2250CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    High mol. wt. hyaluronic acid (HA) is present in articular joints and synovial fluid at high concns.; yet despite numerous studies, the role of HA in joint lubrication is still not clear. Free HA in soln. does not appear to be a good lubricant, being neg. charged and therefore repelled from most biol., including cartilage, surfaces. Recent enzymic expts. suggested that mech. or phys. (rather than chem.) trapped HA could function as an "adaptive" or "emergency" boundary lubricant to eliminate wear damage in shearing cartilage surfaces. In this work, HA was chem. grafted to a layer of self-assembled amino-propyl-triethoxy-silane (APTES) on mica and then cross-linked. The boundary lubrication behavior of APTES and of chem. grafted and cross-linked HA in both electrolyte and lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) solns. was tested with a surface forces app. (SFA). Despite the high coeff. of friction (COF) of μ ≈ 0.50, the chem. grafted HA gel significantly improved the lubrication behavior of HA, particularly the wear resistance, in comparison to free HA. Adding more DOPC lipid to the soln. did not improve the lubrication of the chem. grafted and cross-linked HA layer. Damage of the underlying mica surface became visible at higher loads (pressure >2 MPa) after prolonged sliding times. It has generally been assumed that damage caused by or during sliding, also known as "abrasive friction", which is the main biomedical/clin./morphol. manifestation of arthritis, is due to a high friction force and, therefore, a large COF, and that to prevent surface damage or wear (abrasion) one should therefore aim to reduce the COF, which has been the traditional focus of basic research in biolubrication, particularly in cartilage and joint lubrication. Here we combine our results with previous ones on grafted and cross-linked HA on lipid bilayers, and lubricin-mediated lubrication, and conclude that for cartilage surfaces, a high COF can be assocd. with good wear protection, while a low COF can have poor wear resistance. Both of these properties depend on how the lubricating mols. are attached to and organized at the surfaces, as well as the structure and mech., viscoelastic, elastic, and phys. properties of the surfaces, but the two phenomena are not directly or simply related. We also conclude that to provide both the low COF and good wear protection of joints under physiol. conditions, some or all of the four major components of joints-HA, lubricin, lipids, and the cartilage fibrils-must act synergistically in ways (physisorbed, chemisorbed, grafted and/or cross-linked) that are still to be detd.
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    Røn, T.; Javakhishvili, I.; Patil, N. J.; Jankova, K.; Zappone, B.; Hvilsted, S.; Lee, S. Aqueous lubricating properties of charged (ABC) and neutral (ABA) triblock copolymer chains. Polymer 2014, 55, 4873– 4883,  DOI: 10.1016/j.polymer.2014.07.049
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    Gaisinskaya-Kipnis, A.; Klein, J. Normal and frictional interactions between liposome-bearing biomacromolecular bilayers. Biomacromolecules 2016, 17, 2591– 2602,  DOI: 10.1021/acs.biomac.6b00614
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    Normal and Frictional Interactions between Liposome-Bearing Biomacromolecular Bilayers
    Gaisinskaya-Kipnis, Anastasia; Klein, Jacob
    Biomacromolecules (2016), 17 (8), 2591-2602CODEN: BOMAF6; ISSN:1525-7797. (American Chemical Society)
    Highly efficient lubricating boundary layers at biosurfaces such as cartilage have been proposed to comprise phospholipids complexed with biomacromols. exposed at the surfaces. To gain insight into this, a systematic study on the normal and frictional forces between surfaces bearing a sequentially deposited model alginate-on-chitosan bilayer, bearing different adsorbed phosphatidylcholine (PC) liposomes, was carried out using a surface force balance. Structures of the resulting surface complexes were detd. using at. force microscopy (AFM) and cryo-SEM (cryo-SEM). The liposome/lipid-polymer complexes could maintain their integrity up to high pressures in terms of both normal and shear interactions between the surfaces, which were repeatable, reproducible, and revealed very low friction (coeff. of friction μ down to 10-3-10-4, depending on the PC used) up to pressures of hundreds of atm. We attribute this remarkable lubrication capability ultimately to hydration lubrication acting at the hydrated phosphocholine headgroups of the PC lipids, either exposed at the liposome surfaces or through complexation with the polyelectrolyte bilayer. Values of μ, while low, were roughly an order of magnitude higher than for the same PC vesicles adsorbed on bare mica, a difference attributed to their lower d. on the bilayer; the bilayer, however, stabilized the PC-vesicles far better than bare mica against rupture and shear at high compressions and sliding.
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  32. 32
    Angayarkanni, S. A.; Kampf, N.; Klein, J. Surface interactions between boundary layers of poly (ethylene oxide)–liposome complexes: Lubrication, bridging, and selective ligation. Langmuir 2019, 35, 15469– 15480,  DOI: 10.1021/acs.langmuir.9b01708
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    32
    Surface Interactions between Boundary Layers of Poly(ethylene oxide)-Liposome Complexes: Lubrication, Bridging, and Selective Ligation
    Angayarkanni, S. A.; Kampf, Nir; Klein, Jacob
    Langmuir (2019), 35 (48), 15469-15480CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Poly(ethylene oxide), PEO, is widely exploited in biomedical applications, while phosphatidylcholine (PC) lipids (in the form of bilayers or liposomes) have been identified as very efficient boundary lubricants in aq. media. Here we examine, using a surface force balance (SFB), the interactions between surface-adsorbed layers of PEO complexed with small unilamellar vesicles (SUVs, i.e. liposomes) or with bilayers of PC lipids, both well below and a little above their main gel-to-liq. phase-transition temps. TM. The morphol. of PEO layers (adsorbed onto mica), to which liposomes were added, was examd. using at. force microscopy (AFM) and cryo-SEM (cryo-SEM). Our results reveal that the PC lipids could attach to the PEO either as vesicles or as bilayers, depending on whether they were above or below TM. Under water (no added salt), excellent lubrication, with friction coeffs. down to 10-3-10-4, up to contact stresses of 6.5 MPa (comparable to those in the major joints) was obsd. between two surfaces bearing such PEO-PC complexes. At 0.1 M KNO3 salt concn. (comparable to physiol. salt levels), the friction between such surfaces was considerably higher, attributed to bridging by the polymer chains. Remarkably, such bridging could be suppressed and the friction could be restored to its previous low value if the KNO3 was replaced with NaNO3, as a result of the different PEO-mica ligation properties of Na+ compared to those of K+. Our results provide insight into the properties of PEO-PC complexes in potential applications, and large interfacial effects that can result from the seemingly innocuous replacement of K+ by Na+ ions.
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    Lin, W.; Liu, Z.; Kampf, N.; Klein, J. The role of hyaluronic acid in cartilage boundary lubrication. Cells 2020, 9, 1606,  DOI: 10.3390/cells9071606
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    Lin, W.; Klein, J. Recent progress in cartilage lubrication. Adv. Mater. 2021, 33, 2005513,  DOI: 10.1002/adma.202005513
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    Recent Progress in Cartilage Lubrication
    Lin, Weifeng; Klein, Jacob
    Advanced Materials (Weinheim, Germany) (2021), 33 (18), 2005513CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. Healthy articular cartilage, covering the ends of bones in major joints such as hips and knees, presents the most efficiently-lubricated surface known in nature, with friction coeffs. as low as 0.001 up to physiol. high pressures. Such low friction is indeed essential for its well-being. It minimizes wear-and-tear and hence the cartilage degrdn. assocd. with osteoarthritis, the most common joint disease, and, by reducing shear stress on the mechanotransductive, cartilage-embedded chondrocytes (the only cell type in the cartilage), it regulates their function to maintain homeostasis. Understanding the origins of such low friction of the articular cartilage, therefore, is of major importance in order to alleviate disease symptoms, and slow or even reverse its breakdown. This progress report considers the relation between frictional behavior and the cellular mech. environment in the cartilage, then reviews the mechanism of lubrication in the joints, in particular focusing on boundary lubrication. Following recent advances based on hydration lubrication, a proposed synergy between different mol. components of the synovial joints, acting together in enabling the low friction, has been proposed. Addnl., recent development of natural and bio-inspired lubricants is reviewed.
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    Goldberg, R.; Schroeder, A.; Barenholz, Y.; Klein, J. Interactions between adsorbed hydrogenated soy phosphatidylcholine (HSPC) vesicles at physiologically high pressures and salt concentrations. Biophys. J. 2011, 100, 2403– 2411,  DOI: 10.1016/j.bpj.2011.03.061
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    Interactions between Adsorbed Hydrogenated Soy Phosphatidylcholine (HSPC) Vesicles at Physiologically High Pressures and Salt Concentrations
    Goldberg, Ronit; Schroeder, Avi; Barenholz, Yechezkel; Klein, Jacob
    Biophysical Journal (2011), 100 (10), 2403-2411CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Using a surface force balance, normal and shear interactions were measured as a function of surface sepn. between layers of hydrogenated soy phosphatidylcholine (HSPC) small unilamellar vesicles (SUVs) adsorbed from dispersion at physiol. high salt concns. (0.15 M NaNO3). Cryo-SEM shows that each surface is coated by a close-packed HSPC-SUV layer with an overlayer of liposomes on top. A clear attractive interaction between the liposome layers is seen upon approach and sepn., followed by a steric repulsion upon further compression. The shear forces reveal low friction coeffs. (μ = 0.008-0.0006) up to contact pressures of at least 6 MPa, comparable to those obsd. in the major joints. The spread in μ-values may be qual. accounted for by different local liposome structure at different contact points, suggesting that the intrinsic friction of the HSPC-SUV layers at this salt concn. is closer to the lower limit (μ = ∼0.0006). This low friction is attributed to the hydration lubrication mechanism arising from rubbing of the hydrated phosphocholine-headgroup layers exposed at the outer surface of each liposome, and provides support for the conjecture that phospholipids may play a significant role in biol. lubrication.
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    Klein, J. Polymers in living systems: from biological lubrication to tissue engineering and biomedical devices. Polym. Adv. Technol. 2012, 23, 729– 735,  DOI: 10.1002/pat.3038
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    Polymers in living systems: from biological lubrication to tissue engineering and biomedical devices
    Klein, Jacob
    Polymers for Advanced Technologies (2012), 23 (4), 729-735CODEN: PADTE5; ISSN:1042-7147. (John Wiley & Sons Ltd.)
    A review. The roles of macromols. in living systems as information storage systems (as DNA) and in biochem. synthesis have been much studied and are relatively well understood. Far less is known about their phys. behavior at biol. surfaces and interfaces. This review considers in particular the roles of polymers in biol. lubrication and its relation both to diseases such as osteoarthritis and to remedies such as tissue engineering. The lubricating behavior of common bio-interfacial macromols. including mucins, hyaluronan, lubricin, and aggrecan are described, and insights into the mechanism of biolubrication are examd. in the light of the recently revealed role of hydration lubrication in water-based (including living) systems. Copyright © 2012 John Wiley & Sons, Ltd.
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    Tieleman, D. P.; Sansom, M. S.; Berendsen, H. J. Alamethicin Helices in a Bilayer and in Solution: Molecular Dynamics Simulations. Biophys. J. 1999, 76, 40– 49,  DOI: 10.1016/S0006-3495(99)77176-6
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    Alamethicin helices in a bilayer and in solution: Molecular dynamics simulations
    Tieleman, D. Peter; Sansom, Mark S. P.; Berendsen, Herman J. C.
    Biophysical Journal (1999), 76 (1, Pt. 1), 40-49CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Alamethicin is an a-helical channel-forming peptide, which inserts into lipid bilayers in a voltage-dependent, asym. fashion. Nanosecond mol. dynamics simulations have been used to compare alamethicin conformation and dynamics in three different environments: (1) in water; (2) in methanol; and (3) inserted into a lipid (palmitoyl-oleoyl-phosphatidylcholine) bilayer to form a transmembrane helix. In the bilayer and in methanol, there was little change (Cα RMSD ≈ 0.2 nm over 2 ns and 1 ns) from the initial helical conformation of the peptide. In water there were substantial changes (Cα RMSD ≈ 0.4 nm over 1 ns), esp. in the C-terminal segment of the peptide, which lost its α-helical conformation. In the bilayer and in methanol, the alamethicin mol. underwent hinge-bending motion about its central Gly-X-X-Pro sequence motif. Anal. of H-bonding interactions revealed that the polar C-terminal side chains of alamethicin provided an "anchor" to the bilayer/water interface via formation of multiple H-bonds that persisted throughout the simulation. This explains why the preferred mode of helix insertion into the bilayer is N-terminal, which is believed to underlie the asymmetry of voltage activation of alamethicin channels.
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    Böckmann, R. A.; De Groot, B. L.; Kakorin, S.; Neumann, E.; Grubmüller, H. Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. Biophys. J. 2008, 95, 1837– 1850,  DOI: 10.1529/biophysj.108.129437
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    Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations
    Bockmann Rainer A; de Groot Bert L; Kakorin Sergej; Neumann Eberhard; Grubmuller Helmut
    Biophysical journal (2008), 95 (4), 1837-50 ISSN:.
    Membrane electroporation is the method to directly transfer bioactive substances such as drugs and genes into living cells, as well as preceding electrofusion. Although much information on the microscopic mechanism has been obtained both from experiment and simulation, the existence and nature of possible intermediates is still unclear. To elucidate intermediates of electropore formation by direct comparison with measured prepore formation kinetics, we have carried out 49 atomistic electroporation simulations on a palmitoyl-oleoyl-phosphatidylcholine bilayer for electric field strengths between 0.04 and 0.7 V/nm. A statistical theory is developed to facilitate direct comparison of experimental (macroscopic) prepore formation kinetics with the (single event) preporation times derived from the simulations, which also allows us to extract an effective number of lipids involved in each pore formation event. A linear dependency of the activation energy for prepore formation on the applied field is seen, with quantitative agreement between experiment and simulation. The distribution of preporation times suggests a four-state pore formation model. The model involves a first intermediate characterized by a differential tilt of the polar lipid headgroups on both leaflets, and a second intermediate (prepore), where a polar chain across the bilayer is formed by 3-4 lipid headgroups and several water molecules, thereby providing a microscopic explanation for the polarizable volume derived previously from the measured kinetics. An average pore radius of 0.47 +/- 0.15 nm is seen, in favorable agreement with conductance measurements and electrooptical experiments of lipid vesicles.
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    Comments on P3M, FMM, and the Ewald method for large periodic Coulombic systems
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    Computer Physics Communications (1996), 95 (2&3), 93-110CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
    Prompted by the need to simulate large mol. or gravitational systems and the availability of multiprocessor computers, alternatives to the std. Ewald calcn. of Coulombic interactions have been developed. The two most popular alternatives, the fast multipole method (FMM) and the particle-particle particle-mesh (P3M) method are compared here to the Ewald method for a single processor machine. Parallel processor implementations of the P3M and Ewald methods are compared. The P3M method is found to be both faster than the FMM and easier to implement efficiently as it relies on commonly available software (FFT subroutines). Both the Ewald and P3M method are easily implemented on parallel architectures with the P3M method the clear choice for large systems.
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    Journal of Computational Physics (1995), 117 (1), 1-19CODEN: JCTPAH; ISSN:0021-9991.
    Three parallel algorithms for classical mol. dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-at. forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for mol. dynamics models which can be difficult to parallelize efficiently - those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a std. Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers - the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C90 processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex mol. dynamics simulations are also discussed.
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    Rottler, J.; Robbins, M. O. Growth, microstructure, and failure of crazes in glassy polymers. Phys. Rev. E 2003, 68, 011801,  DOI: 10.1103/PhysRevE.68.011801
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    Growth, microstructure, and failure of crazes in glassy polymers
    Rottler, Jorg; Robbins, Mark O.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2003), 68 (1-1), 011801/1-011801/18CODEN: PRESCM ISSN:. (American Physical Society)
    We report on an extensive study of craze formation in glassy polymers. Mol. dynamics simulations of a coarse-grained bead-spring model were employed to study the mol. level processes during craze nucleation, widening, and breakdown for a wide range of temp., polymer chain length N, entanglement length Ne, and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at const. drawing stress. The extension ratio is detd. by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is Ne/3. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for N/Ne∼10, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theor. models of craze widening, which were based on continuum level hydrodynamics.
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    Galuschko, A.; Spirin, L.; Kreer, T.; Johner, A.; Pastorino, C.; Wittmer, J.; Baschnagel, J. Frictional forces between strongly compressed, nonentangled polymer brushes: molecular dynamics simulations and scaling theory. Langmuir 2010, 26, 6418– 6429,  DOI: 10.1021/la904119c
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    Frictional Forces between Strongly Compressed, Nonentangled Polymer Brushes: Molecular Dynamics Simulations and Scaling Theory
    Galuschko, A.; Spirin, L.; Kreer, T.; Johner, A.; Pastorino, C.; Wittmer, J.; Baschnagel, J.
    Langmuir (2010), 26 (9), 6418-6429CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    By means of mol. dynamics simulations and scaling theory we study the response of opposing polymer brushes to const. shear motion under good solvent conditions. Model systems that contain explicit solvent mols. (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their mol. parameters, chain length and grafting d. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg no., W, beyond linear response. For instance, we find that the kinetic friction const. scales as μ ∼ W0.57 for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent expts.
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    We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the exptl. conditions and time scales. The overall behavior can be described in terms of two Deborah nos.
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    Friction and adhesion mediated by supramolecular host-guest complexes
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    The adhesive and frictional response of an AFM tip connected to a substrate through supramol. host-guest complexes is investigated by dynamic Monte Carlo simulations. Here, the variation of the pull-off force with the unloading rate recently obsd. in expts. is unraveled by evidencing simultaneous (progressive) breaking of the bonds at fast (slow) rates. The model reveals the origin of the obsd. plateaus in the retraction force as a function of the tip-surface distance, showing that they result from the tip geometrical features. In lateral sliding, the model exhibits a wide range of dynamic behaviors ranging from smooth sliding to stick-slip at different velocities, with the av. friction force detd. by the characteristic formation/rupture rates of the complexes. In particular, it is shown that for some mol. complexes friction can become almost const. over a wide range of velocities. Also, we show the possibility of exploiting the ageing effect through slide-hold-slide expts., in order to infer the characteristic formation rate. Finally, our model predicts a novel "anti-ageing" effect which is characterized by a decrease of the static friction force with the hold time. Such an effect is explained in terms of enhancement of adhesion during sliding, esp. obsd. at high driving velocities.
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    Self-assembled monolayers introduce chem. functionalities to material surfaces, providing a route to tune their equil. and dynamical properties. The authors report on at. force microscopy measurements and simulations of adhesion and friction forces caused by a macromol. host-guest system, where the host mols. are attached to silicon oxide surfaces by means of self-assembled silane layers. Different prepn. routes for the silane layers lead to different flexibility of the mol. attachment. The velocity dependencies of the work of sepn. 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 mol. 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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    Although the basic laws of friction are simple enough to be taught in elementary physics classes and although friction has been widely studied for centuries, in the current state of knowledge it is still not possible to predict a friction force from fundamental principles. One of the highly debated topics in this field is the origin of static friction. For most macroscopic contacts between two solids, static friction will increase logarithmically with time, a phenomenon that is referred to as aging of the interface. One known reason for the logarithmic growth of static friction is the deformation creep in plastic contacts. However, this mechanism cannot explain frictional aging obsd. in the absence of roughness and plasticity. Here, we discover mol. mechanisms that can lead to a logarithmic increase of friction based purely on interfacial chem. Predictions of our model are consistent with published exptl. data on the friction of silica.
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    Earthquakes have long been recognized as being the result of stick-slip frictional instabilities. Over the past few decades, lab. studies of rock friction have elucidated many aspects of tectonic fault zone processes and earthquake phenomena. Typically, the static friction of rocks grows logarithmically with time when they are held in stationary contact, but the mechanism responsible for this strengthening is not understood. This time-dependent increase of frictional strength, or frictional ageing, is one manifestation of the evolution effect' in rate and state friction theory. A prevailing view is that the time dependence of rock friction results from increases in contact area caused by creep of contacting asperities. Here we present the results of at. force microscopy expts. that instead show that frictional ageing arises from the formation of interfacial chem. bonds, and the large magnitude of ageing at the nanometer scale is quant. consistent with what is required to explain observations in macroscopic rock friction expts. The relative magnitude of the evolution effect compared with that of the direct effect'-the dependence of friction on instantaneous changes in slip velocity-det. whether unstable slip, leading to earthquakes, is possible. Understanding the mechanism underlying the evolution effect would enable us to formulate phys. based frictional constitutive laws, rather than the current empirically based laws', allowing more confident extrapolation to natural faults.
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    Physical Review Letters (2017), 118 (7), 076103/1-076103/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Rate and state friction (RSF) laws are widely used empirical relationships that describe the macroscale frictional behavior of a broad range of materials, including rocks found in the seismogenic zone of Earth's crust. A fundamental aspect of the RSF laws is frictional "aging," where friction increases with the time of stationary contact due to asperity creep and/or interfacial strengthening. Recent at. force microscope (AFM) expts. and simulations found that nanoscale silica contacts exhibit aging due to the progressive formation of interfacial chem. bonds. The role of normal load (and, thus, normal stress) on this interfacial chem. bond-induced (ICBI) friction is predicted to be significant but has not been examd. exptl. Here, we show using AFM that, for nanoscale ICBI friction of silica-silica interfaces, aging (the difference between the max. static friction and the kinetic friction) increases approx. linearly with the product of the normal load and the log of the hold time. This behavior is attributed to the approx. linear dependence of the contact area on the load in the pos. load regime before significant wear occurs, as inferred from sliding friction measurements. This implies that the av. pressure, and thus the av. bond formation rate, is load independent within the accessible load range. We also consider a more accurate nonlinear model for the contact area, from which we ext. the activation vol. and the av. stress-free energy barrier to the aging process. Our work provides an approach for studying the load and time dependence of contact aging at the nanoscale and further establishes RSF laws for nanoscale asperity contacts.
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    Physical Review Letters (2019), 123 (11), 116102CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Studying the frictional properties of interfaces with dynamic chem. bonds advances understanding of the mechanism underlying rate and state laws, and offers new pathways for the rational control of frictional response. In this work, we revisit the load dependence of interfacial chem.-bond-induced (ICBI) friction exptl. and find that the velocity dependence of friction can be reversed by changing the normal load. We propose a theor. model, whose anal. soln. allows us to interpret the exptl. data on timescales and length scales that are relevant to exptl. conditions. Our work provides a promising avenue for exploring the dynamics of ICBI friction.
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    ACS Applied Materials & Interfaces (2017), 9 (40), 35333-35340CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
    Single-asperity wear expts. and simulations have identified different regimes of wear including Eyring- and Archard-like behaviors. A multibond dynamics model has been developed based on the friction model of Filippov et al. This new model captures both qual. distinct regimes of single-asperity wear under a unified theor. framework. In this model, the interfacial bond formation, wearless rupture, and transfer of atoms are governed by three competing thermally activated processes. The Eyring regime holds under the conditions of low load and low adhesive forces; few bonds form between the asperity and the surface, and wear is a rare and rate-dependent event. As the normal stress increases, the Eyring behavior of wear rate breaks down. A nearly rate-independent regime arises under high load or high adhesive forces, in which wear becomes very nearly, but not precisely, proportional to sliding distance. In this restricted regime, the dependence of wear rate per unit contact area is nearly independent of the normal stress at the point of contact. In true contact between rough elastic surfaces, where contact area is expected to grow linearly with normal load, this would lead to behavior very similar to that described by the Archard equation. Detailed comparisons to exptl. and mol. dynamics simulation investigations illustrate both Eyring and Archard regimes, and an intermediate crossover regime between the two.
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    Karuppiah, K. K.; Zhou, Y.; Woo, L. K.; Sundararajan, S. Nanoscale friction switches: friction modulation of monomolecular assemblies using external electric fields. Langmuir 2009, 25, 12114– 12119,  DOI: 10.1021/la901221g
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    Nanoscale friction switches: friction modulation of monomolecular assemblies using external electric fields
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    Langmuir : the ACS journal of surfaces and colloids (2009), 25 (20), 12114-9 ISSN:.
    This paper presents experimental investigations to actively modulate the nanoscale friction properties of a self-assembled monolayer (SAM) assembly using an external electric field that drives conformational changes in the SAM. Such "friction switches" have widespread implications in interfacial energy control in micro/nanoscale devices. Friction response of a low-density mercaptocarboxylic acid SAM is evaluated using an atomic force microscope (AFM) in the presence of a DC bias applied between the sample and the AFM probe under a nitrogen (dry) environment. The low density allows reorientation of individual SAM molecules to accommodate the attractive force between the -COOH terminal group and a positively biased surface. This enables the surface to present a hydrophilic group or a hydrophobic backbone to the contacting AFM probe depending upon the direction of the field (bias). Synthesis and deposition of the low-density SAM (LD-SAM) is reported. Results from AFM experiments show an increased friction response (up to 300%) of the LD-SAM system in the presence of a positive bias compared to the friction response in the presence of a negative bias. The difference in the friction response is attributed to the change in the structural and crystalline order of the film in addition to the interfacial surface chemistry and composition presented upon application of the bias.
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  1. Melisa M. Gianetti, Roberto Guerra, Andrea Vanossi, Michael Urbakh, Nicola Manini. Electric-field frictional effects in confined zwitterionic molecules. Physical Chemistry Chemical Physics 2023, 25 (28) , 19037-19045. https://doi.org/10.1039/D3CP00914A
  2. Roberto Guerra-Gonzalez, Vidal Moises Bastida-Silva, Jose Luis Rivera, Fernando Iguazu Ramirez-Zavaleta, Enrique Lima. n-Pentanol Lubrication of Silica Layers Passivated with Hydroxyl Groups Under Constant Shear Stress and Load and Isothermal Conditions. Tribology Letters 2023, 71 (2) https://doi.org/10.1007/s11249-023-01731-6
  3. Jose Luis Rivera, Vidal Moises Bastida-Silva, Roberto Guerra-Gonzalez, Fernando Iguazu Ramirez-Zavaleta, Enrique Lima. n-Pentanol lubrication of silica layers passivated with hydroxyl groups under constant shear stress and load, and isothermal conditions. 2022https://doi.org/10.21203/rs.3.rs-2270937/v1
  4. Yi Liu, Rui Xu, Jianli Wang, Shanhong Wan, Liuyang Bai. Atomistic insight into flash temperature during friction. International Communications in Heat and Mass Transfer 2022, 138 , 106317. https://doi.org/10.1016/j.icheatmasstransfer.2022.106317
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  • Abstract

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    Figure 1

    Figure 1. (a) Sketch of the experimental SFA setup. (b) Three representations of one molecular unit in the vesicle wall. Left: a radically simplified sticks scheme, as in panel (a). Center: the simulated united-atom molecule. Right: the detailed chemical structure of a dipalmitoylphosphatidylcholine molecule. (c) The initial regularly spaced configuration of the system (side view). Magenta, purple, red, blue, green, and cyan spheres represent SUB and SUP layers, cations, anions, and NP1 and NP2 particles, respectively. Gray particles represent the R1, R2, and R3 neutral residues in between the cation and the anion. The yellow sphere represents the pulling stage advancing with constant speed. The dashed line marks the sliding interface. (d) Top view restricted to the particles above the black dashed line in (c); purple SUP particles are drawn smaller for better readability.

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    Figure 2

    Figure 2. (a) Nonmonotonic variation of the frictional shear stress and (b) the distance between the rigid layers as a function of temperature for zwitterionic and charge-free systems. vstage = 5 m·s–1, L = 10 MPa. (c–f) Shear traces for the pointed temperatures in panel (a). Symbols in (c–f) refer to the snapshots in Figure 3.

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    Figure 3

    Figure 3. Side views of 5 nm y-thick slices of simulation snapshots. Each snapshot corresponds to the time instant marked by the corresponding symbol in panels c–f of Figure 2. (a) Smooth sliding, zwitterionic system, T = 150 K, (b) stick point, zwitterionic system, T = 300 K, (c) slip point, zwitterionic system, T = 300 K, (d) high friction state, charge-free system, T = 300 K, (e) stick point, charge-free system, T = 150 K, and (f) slip point, system, T = 150 K.

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    Figure 4

    Figure 4. (a, b) Top views of the snapshots of Figure 3a (150 K) and 3b (300 K), including a horizontal slice from the sliding plane in between the chains to immediately above the rigid SUP layer. This slice is the unshaded part of the side views (c) and (d). Black dashed circles highlight SUB chains intersecting the SUP chains’ cation plane. The end cation of each of those SUB chains feels a relatively strong Coulomb interaction with the two top-chain anions, generating the interlocking spots responsible for the stick.

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    Figure 5

    Figure 5. (a) Percentile hooking fraction h as a function of the stage displacement correlated with the frictional shear stress for the same simulation as in Figure 2d. (b) The total potential energy U for the same simulation.

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    Figure 6

    Figure 6. Stick–slip to smooth-sliding transition as a function of velocity. (a) The frictional shear stress as a function of the sliding velocity, zwitterionic system, L = 10 MPa. (b–e) Shear traces for the pointed velocities in panel (a) at 150 K. Dashed line: fit of T = 150 K and vstage > 6 m·s–1. Dot-dashed line: fit of the T = 50 K, including all points.

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    Figure 7

    Figure 7. (a, c) Frictional shear stress and (b, d) the average distance between the rigid layers as a function of load L with vstage = 5 m·s–1.

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    Figure 8

    Figure 8. Correlation coefficient ρUh between the hooked fraction and total potential energy, eq 2, for the zwitterionic and charge-free systems at vstage = 5 m·s–1 as a function of (a) the applied load and (b) the temperature. As in smooth sliding h ≡ 0, ρUh is defined for stick–slip dynamics only.

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      We model friction acting on the tip of an at. force microscope as it is dragged across a surface at nonzero temps. We find that stick-slip motion occurs and that the av. frictional force follows | ln v|2/3, where v is the tip velocity. This compares well to recent exptl. work, permitting the quant. extn. of all microscopic parameters. We calc. the scaled form of the av. frictional force's dependence on both temp. and tip speed as well as the form of the friction-force distribution function.
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      Dudko, O. K.; Filippov, A. E.; Klafter, J.; Urbakh, M.
      Chemical Physics Letters (2002), 352 (5,6), 499-504CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
      In this Letter recent observations using dynamic force spectroscopy can be described by a generalized Tomlinson model which includes the contribution of an external noise. The measured friction forces depend on the microscopic potential and dissipation inherent to the system as well as on the mech. properties of the setup (i.e. spring const.) and the external noise. Tuning the noise and spring const. offers ways to ext. information about the microscopic properties.
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    7. 7
      Szlufarska, I.; Chandross, M.; Carpick, R. Recent advances in single-asperity nanotribology. J. Phys. D 2008, 41, 123001,  DOI: 10.1088/0022-3727/41/12/123001
      7
      Recent advances in single-asperity nanotribology
      Szlufarska, Izabela; Chandross, Michael; Carpick, Robert W.
      Journal of Physics D: Applied Physics (2008), 41 (12), 123001/1-123001/39CODEN: JPAPBE; ISSN:0022-3727. (Institute of Physics Publishing)
      A review. As the size of electronic and mech. devices shrinks to the nanometer regime, performance begins to be dominated by surface forces. For example, friction, wear, and adhesion are known to be central challenges in the design of reliable micro- and electromech. systems (MEMS/NEMS). Because of the complexity of the phys. and chem. mechanisms underlying at.-level tribol., it is still not possible to accurately and reliably predict the response when two surfaces come into contact at the nanoscale. Fundamental scientific studies are the means by which these insights may be gained. Recent advances in the exptl., theor., and computational studies of nanotribol. are reviewed. In particular, it is focussed on the latest developments in at. force microscopy and mol. dynamics simulations and their application to the study of single-asperity contact.
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    8. 8
      Brukman, M.; Gao, G.; Nemanich, R.; Harrison, J. Temperature dependence of single-asperity diamond-diamond friction elucidated using AFM and MD simulations. J. Phys. Chem. C 2008, 112, 9358– 9369,  DOI: 10.1021/jp711959e
      8
      Temperature Dependence of Single-Asperity Diamond-Diamond Friction Elucidated Using AFM and MD Simulations
      Brukman, Matthew J.; Gao, Guangtu; Nemanich, Robert J.; Harrison, Judith A.
      Journal of Physical Chemistry C (2008), 112 (25), 9358-9369CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Complementary exptl. (at. force microscopy) and theor. (mol. dynamics) techniques were used to investigate friction between diamond-diamond junctions as a function of temp. The simulation and exptl. conditions were designed to correspond as closely as possible. In the at. force microscopy (AFM) expts., two microcryst.-diamond (μCD) AFM tips of differing contact radii were used to examine the friction of diamond (111) and (001) single crystals from 24 to 225 K in an ultrahigh vacuum. At all temps., the exptl. detd. dependence of friction on load was consistent with the occurrence of single-asperity interfacial friction, where friction is proportional to contact area. In addn., the behavior of the contact was fit well by the Derjaguin-Muller-Toporov continuum model. Friction measurements within a given series were highly repeatable; however, as is typical with AFM measurements, there was some variation in measurements taken from different regions of the sample and with different tips. Interfacial shear strength, or the intrinsic resistance to sliding, decreased slightly with increasing temp. for both surfaces. To shed addnl. insight into the AFM results, MD simulations were performed with the diamond single crystals of the same orientation. The calcns. also show that the av. friction force decreased slightly as the temp. increased for both diamond surfaces and for all sliding directions. Both AFM and MD results agree with the numerical anal. of friction as a function of temp. published by Sang et al. (Sang, Y.; Dube, M.; Grant, M.Phys. Rev. Lett.2001, 87, 174301).
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    9. 9
      Steiner, P.; Roth, R.; Gnecco, E.; Baratoff, A.; Maier, S.; Glatzel, T.; Meyer, E. Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite. Phys. Rev. B 2009, 79, 045414  DOI: 10.1103/PhysRevB.79.045414
      9
      Two-dimensional simulation of superlubricity on NaCl and highly oriented pyrolytic graphite
      Steiner, Pascal; Roth, Raphael; Gnecco, Enrico; Baratoff, Alexis; Maier, Sabine; Glatzel, Thilo; Meyer, Ernst
      Physical Review B: Condensed Matter and Materials Physics (2009), 79 (4), 045414/1-045414/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      The friction between an atomically sharp tip and a solid surface (NaCl and highly oriented pyrolytic graphite) is analyzed theor. in the framework of a modified Tomlinson model in 2 dimensions. Lateral forces are studied as a function of temp., load, and magnitude of actuation. The actuation leads to a redn. in friction and allows one to enter a dynamic superlubricity regime. In addn., our model is able to describe other ultralow friction states as static superlubricity and thermolubricity. We find a good agreement between the calcns. and the exptl. results.
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    10. 10
      Schirmeisen, A.; Jansen, L.; Holscher, H.; Fuchs, H. Temperature dependence of point contact friction on silicon. Appl. Phys. Lett. 2006, 88, 123108,  DOI: 10.1063/1.2187575
      10
      Temperature dependence of point contact friction on silicon
      Schirmeisen, Andre; Jansen, Lars; Hoelscher, Hendrik; Fuchs, Harald
      Applied Physics Letters (2006), 88 (12), 123108/1-123108/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      Point contact friction and adhesion between a Si tip and an untreated Si(111) wafer are measured as a function of sample temp. in ultrahigh vacuum by friction force microscopy. While the friction coeff. changes drastically in the temp. range from 50 K to room temp., and shows a reproducible max. near 100 K, the simultaneously recorded adhesion shows much less temp. dependence. Interestingly, the velocity dependence of friction shows a logarithmic increase below 150 K although it is nearly const. above 150 K. This peculiar behavior has profound consequences for tribol. properties of devices manufd. from Si.
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    11. 11
      Barel, I.; Urbakh, M.; Jansen, L.; Schirmeisen, A. Multibond dynamics of nanoscale friction: the role of temperature. Phys. Rev. Lett. 2010, 104, 066104  DOI: 10.1103/PhysRevLett.104.066104
      11
      Multibond Dynamics of Nanoscale Friction: The Role of Temperature
      Barel, Itay; Urbakh, Michael; Jansen, Lars; Schirmeisen, Andre
      Physical Review Letters (2010), 104 (6), 066104/1-066104/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The main challenge in predicting sliding friction is related to the complexity of highly nonequil. processes, the kinetics of which are controlled by the interface temp. Our expts. reveal a nonmonotonic enhancement of dry nanoscale friction at cryogenic temps. for different material classes. Concerted simulations show that it emerges from two competing processes acting at the interface: the thermally activated formation as well as rupturing of an ensemble of at. contacts. These results provide a new conceptual framework to describe the dynamics of dry friction.
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    12. 12
      Barel, I.; Urbakh, M.; Jansen, L.; Schirmeisen, A. Temperature dependence of friction at the nanoscale: when the unexpected turns normal. Tribol. Lett. 2010, 39, 311– 319,  DOI: 10.1007/s11249-010-9675-4
      There is no corresponding record for this reference.
    13. 13
      Sheng, P.; Wen, W. Electrorheological fluids: mechanisms, dynamics, and microfluidics applications. Annu. Rev. Fluid Mech. 2012, 44, 143– 174,  DOI: 10.1146/annurev-fluid-120710-101024
      There is no corresponding record for this reference.
    14. 14
      Zhu, J.; Zeng, Q.; Wang, Y.; Yan, C.; He, W. Nano-crystallization-driven high temperature self-lubricating properties of magnetron-sputtered WS 2 coatings. Tribol. Lett. 2020, 68, 50,  DOI: 10.1007/s11249-020-01290-0
      14
      Nano-crystallization-Driven High Temperature Self-lubricating Properties of Magnetron-Sputtered WS2 Coatings
      Zhu, Jianing; Zeng, Qunfeng; Wang, Yongfu; Yan, Chao; He, Wanjun
      Tribology Letters (2020), 68 (1), 50CODEN: TRLEFS; ISSN:1023-8883. (Springer)
      Abstr.: In consideration of high temp. conditions, this paper focuses on the self-lubricating properties of tungsten disulfide coatings at high temp. A low coeff. of friction (CoF) about 0.07-0.2 for tungsten disulfide coatings can be attained at temps. of 100-400°C. The chem. stability, mech. and tribolgical properties were investigated by energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), XPS, SEM (SEM), nano-indentation tester and ball-on-disk tribometer, resp. According to XRD and XPS spectra, the as-sputtered tungsten disulfide coatings existed as 2h-tungsten disulfide structure. The crystal transition of tungsten disulfide coatings from amorphous to (002) basal plane-oriented lubricating film, which was obtained by the synergistic effect of load and friction, and provided anti-friction performance at 100-400°C. At 500°C, the tungsten oxide formed by oxidn. of tungsten disulfide on the sample surface with lower hardness reduces the coeff. of friction and improves wear resistance. The wear resistance and anti-friction performance are discussed in terms of morphol. of the wear scars, anti-oxidn. capability of the coating and tribochem. reaction product of the friction pair.
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    15. 15
      Singh, A. K.; Singh, T. N. Stability of the rate, state and temperature dependent friction model and its applications. Geophys. J. Int. 2016, 205, 636– 647,  DOI: 10.1093/gji/ggw012
      There is no corresponding record for this reference.
    16. 16
      Tian, K.; Goldsby, D. L.; Carpick, R. W. Rate and state friction relation for nanoscale contacts: thermally activated Prandtl-Tomlinson Model with chemical aging. Phys. Rev. Lett. 2018, 120, 186101,  DOI: 10.1103/PhysRevLett.120.186101
      16
      Rate and State Friction Relation for Nanoscale Contacts: Thermally Activated Prandtl-Tomlinson Model with Chemical Aging
      Tian, Kaiwen; Goldsby, David L.; Carpick, Robert W.
      Physical Review Letters (2018), 120 (18), 186101CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Rate and state friction (RSF) laws are widely used empirical relationships that describe macroscale to microscale frictional behavior. They entail a linear combination of the direct effect (the increase of friction with sliding velocity due to the reduced influence of thermal excitations) and the evolution effect (the change in friction with changes in contact "state," such as the real contact area or the degree of interfacial chem. bonds). Recent at. force microscope (AFM) expts. and simulations found that nanoscale single-asperity amorphous silica-silica contacts exhibit logarithmic aging (increasing friction with time) over several decades of contact time, due to the formation of interfacial chem. bonds. Here we establish a phys. based RSF relation for such contacts by combining the thermally activated Prandtl-Tomlinson (PTT) model with an evolution effect based on the physics of chem. aging. This thermally activated Prandtl-Tomlinson model with chem. aging (PTTCA), like the PTT model, uses the loading point velocity for describing the direct effect, not the tip velocity (as in conventional RSF laws). Also, in the PTTCA model, the combination of the evolution and direct effects may be nonlinear. We present AFM data consistent with the PTTCA model whereby in aging tests, for a given hold time, static friction increases with the logarithm of the loading point velocity. Kinetic friction also increases with the logarithm of the loading point velocity at sufficiently high velocities, but at a different increasing rate. The discrepancy between the rates of increase of static and kinetic friction with velocity arises from the fact that appreciable aging during static contact changes the energy landscape. Our approach extends the PTT model, originally used for cryst. substrates, to amorphous materials. It also establishes how conventional RSF laws can be modified for nanoscale single-asperity contacts to provide a phys. based friction relation for nanoscale contacts that exhibit chem. bond-induced aging, as well as other aging mechanisms with similar phys. characteristics.
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    17. 17
      Tshiprut, Z.; Zelner, S.; Urbakh, M. Temperature-induced enhancement of nanoscale friction. Phys. Rev. Lett. 2009, 102, 136102,  DOI: 10.1103/PhysRevLett.102.136102
      17
      Temperature-Induced Enhancement of Nanoscale Friction
      Tshiprut, Z.; Zelner, S.; Urbakh, M.
      Physical Review Letters (2009), 102 (13), 136102/1-136102/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We introduce a novel mechanism of temp. dependence of friction at the nanoscale which is detd. by a decrease of the slip length with temp. T. We find that the effect of temp. on the slip length may result in a rich temp. dependence of friction, including a peak and/or plateau in F as a function of T, and a sharp increase or decrease of F with T. This mechanism is of primary importance in the multiple-slip regimes of motion when the tip slips over a no. of lattice spacings. The influence of normal load and driving velocity on the temp. dependence of friction is discussed. We predict that the presence of surface defects or adsorbate may strongly influence the temp. dependence of friction.
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    18. 18
      Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 2013, 85, 529,  DOI: 10.1103/RevModPhys.85.529
      18
      Modeling friction: From nanoscale to mesoscale
      Vanossi, Andrea; Manini, Nicola; Urbakh, Michael; Zapperi, Stefano; Tosatti, Erio
      Reviews of Modern Physics (2013), 85 (2), 529-552CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
      A review. The physics of sliding friction is gaining impulse from nanoscale and mesoscale expts., simulations, and theor. modeling. This Colloquium reviews some recent developments in modeling and in atomistic simulation of friction, covering open-ended directions, unconventional nanofrictional systems, and unsolved problems.
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    19. 19
      Manini, N.; Braun, O. M.; Vanossi, A. In Fundamentals of Friction and Wear on the Nanoscale, 2nd ed.; Gnecco, E., Meyer, E., Eds.; Springer: Berlin, 2015; p 175.
      There is no corresponding record for this reference.
    20. 20
      Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A. Friction and nonlinear dynamics. J. Phys.: Condens. Matter 2016, 28, 293001,  DOI: 10.1088/0953-8984/28/29/293001
      20
      Friction and nonlinear dynamics
      Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
      Journal of Physics: Condensed Matter (2016), 28 (29), 293001/1-293001/22CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      The nonlinear dynamics assocd. with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in exptl. techniques and computational resources has stimulated the development of more refined and accurate math. and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
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    21. 21
      Perkin, S.; Klein, J. Soft matter under confinement. Soft Matter 2013, 9, 10438– 10441,  DOI: 10.1039/c3sm90141f
      21
      Soft matter under confinement
      Perkin, Susan; Klein, Jacob
      Soft Matter (2013), 9 (44), 10438-10441CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      A review. 'Soft matter' encompasses myriad systems both in synthetic and in biol. contexts-and often in combination. 'Confinement' in the context of this themed issue can include situations such as soft (or biol.) materials at solid surfaces, at liq.-liq. interfaces, adjacent to bio-membranes, the crowded and fluctuating intra-cellular space, in synthetic nano-pores and natural porous materials, and inside polymer brushes. Work in the area of soft materials in confinement is very interdisciplinary in nature, both in terms of the applications and systems under investigation and the methods (exptl. and theor.) used to approach them. Diverse approaches and highlights, emphasizing the commonalities of confined soft matter from the importance of entropy to ion-specific effects was provided.
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    22. 22
      Ma, S.; Zhang, X.; Yu, B.; Zhou, F. Brushing up functional materials. NPG Asia Mater. 2019, 11, 24,  DOI: 10.1038/s41427-019-0121-2
      There is no corresponding record for this reference.
    23. 23
      Myshkin, N. K.; Kovalev, A. V. Polymer tribology; World Scientific, 2009; pp 3– 37.
      There is no corresponding record for this reference.
    24. 24
      Chen, M.; Briscoe, W. H.; Armes, S. P.; Klein, J. Lubrication at physiological pressures by polyzwitterionic brushes. Science 2009, 323, 1698– 1701,  DOI: 10.1126/science.1169399
      24
      Lubrication at Physiological Pressures by Polyzwitterionic Brushes
      Chen, Meng; Briscoe, Wuge H.; Armes, Steven P.; Klein, Jacob
      Science (Washington, DC, United States) (2009), 323 (5922), 1698-1701CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The very low sliding friction at natural synovial joints, which have friction coeffs. of μ < 0.002 at pressures up to 5 megapascals or more, has to date not been attained in any human-made joints or between model surfaces in aq. environments. We found that surfaces in water bearing polyzwitterionic brushes that were polymd. directly from the surface can have μ values as low as 0.0004 at pressures as high as 7.5 megapascals. This extreme lubrication is attributed primarily to the strong hydration of the phosphorylcholine-like monomers that make up the robustly attached brushes, and may have relevance to a wide range of human-made aq. lubrication situations.
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    25. 25
      Kreer, T. Polymer-brush lubrication: a review of recent theoretical advances. Soft Matter 2016, 12, 3479– 3501,  DOI: 10.1039/C5SM02919H
      25
      Polymer-brush lubrication: a review of recent theoretical advances
      Kreer, T.
      Soft Matter (2016), 12 (15), 3479-3501CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      A review. This review compiles recent theor. advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biol. problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equil. and out-of-equil. situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromol. inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative anal. approaches, expts. and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using mol. dynamics simulations.
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    26. 26
      De Beer, S.; Müser, M. H. Alternative dissipation mechanisms and the effect of the solvent in friction between polymer brushes on rough surfaces. Soft Matter 2013, 9, 7234– 7241,  DOI: 10.1039/c3sm50491c
      26
      Alternative dissipation mechanisms and the effect of the solvent in friction between polymer brushes on rough surfaces
      de Beer, Sissi; Mueser, Martin H.
      Soft Matter (2013), 9 (30), 7234-7241CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      Surfaces covered with end-anchored polymers under good solvent conditions have excellent tribol. properties. The friction between such surfaces is commonly attributed to steady-state interdigitation of the opposing polymer brushes. However, this conclusion tends to be based on idealized geometries neglecting surface roughness. Using mol. dynamics simulations, we find that there are qual. differences between the friction of rough and flat polymer-brush surfaces. For rough surfaces the dissipation due to transient interdigitation and capillary- and shape-hysteresis is just as important or can even dominate over steady-state interdigitation. Having a mix of dissipation mechanisms that are all intertwined affects the obsd. friction force in linear-response as well as in the shear-thinning exponents and effective viscosity. Moreover, we find that the effect of the solvent viscosity is sublinear.
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    27. 27
      De Beer, S.; Kutnyanszky, E.; Schön, P. M.; Vancso, G. J.; Müser, M. H. Solvent-induced immiscibility of polymer brushes eliminates dissipation channels. Nat. Commun. 2014, 5, 3781,  DOI: 10.1038/ncomms4781
      27
      Solvent-induced immiscibility of polymer brushes eliminates dissipation channels
      de Beer, Sissi; Kutnyanszky, Edit; Schoen, Peter M.; Vancso, G. Julius; Mueser, Martin H.
      Nature Communications (2014), 5 (), 3781pp.CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Polymer brushes lead to small friction and wear and thus hold great potential for industrial applications. However, interdigitation of opposing brushes makes them prone to damage. Here we report mol. dynamics simulations revealing that immiscible brush systems can form slick interfaces, in which interdigitation is eliminated and dissipation strongly reduced. We test our findings with friction force microscopy expts. on hydrophilic and hydrophobic brush systems in both sym. and asym. setups. In the sym. setup both brushes are chem. alike, while the asym. system consists of two different brushes that each prefer their own solvent. The trends obsd. in the exptl. measured force traces and the friction redn. are similar to the simulations and extend to fully immersed contacts. These results reveal that two immiscible brush systems in mech. contact slide at a fluid-fluid interface while having load-bearing ability. This makes them ideal candidates for tribol. applications.
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    28. 28
      Raviv, U.; Giasson, S.; Kampf, N.; Gohy, J.-F.; Jérôme, R.; Klein, J. Lubrication by charged polymers. Nature 2003, 425, 163– 165,  DOI: 10.1038/nature01970
      28
      Lubrication by charged polymers
      Raviv, Uri; Giasson, Suzanne; Kampf, Nir; Gohy, Jean-Francois; Jerome, Robert; Klein, Jacob
      Nature (London, United Kingdom) (2003), 425 (6954), 163-165CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Long-ranged forces between surfaces in a liq. control effects from colloid stability to biolubrication, and can be modified either by steric factors due to flexible polymers, or by surface charge effects. In particular, neutral polymer brushes' may lead to a massive redn. in sliding friction between the surfaces to which they are attached, whereas hydrated ions can act as extremely efficient lubricants between sliding charged surfaces. Here we show that brushes of charged polymers (polyelectrolytes) attached to surfaces rubbing across an aq. medium result in superior lubrication compared to other polymeric surfactants. Effective friction coeffs. with polyelectrolyte brushes in water are lower than about 0.0006-0.001 even at low sliding velocities and at pressures of up to several atmospheres (typical of those in living systems). We attribute this to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments. Our findings may have implications for biolubrication effects, which are important in the design of lubricated surfaces in artificial implants, and in understanding frictional processes in biol. systems.
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    29. 29
      Yu, J.; Banquy, X.; Greene, G. W.; Lowrey, D. D.; Israelachvili, J. N. The boundary lubrication of chemically grafted and cross-linked hyaluronic acid in phosphate buffered saline and lipid solutions measured by the surface forces apparatus. Langmuir 2012, 28, 2244– 2250,  DOI: 10.1021/la203851w
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      The Boundary Lubrication of Chemically Grafted and Cross-Linked Hyaluronic Acid in Phosphate Buffered Saline and Lipid Solutions Measured by the Surface Forces Apparatus
      Yu, Jing; Banquy, Xavier; Greene, George W.; Lowrey, Daniel D.; Israelachvili, Jacob N.
      Langmuir (2012), 28 (4), 2244-2250CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      High mol. wt. hyaluronic acid (HA) is present in articular joints and synovial fluid at high concns.; yet despite numerous studies, the role of HA in joint lubrication is still not clear. Free HA in soln. does not appear to be a good lubricant, being neg. charged and therefore repelled from most biol., including cartilage, surfaces. Recent enzymic expts. suggested that mech. or phys. (rather than chem.) trapped HA could function as an "adaptive" or "emergency" boundary lubricant to eliminate wear damage in shearing cartilage surfaces. In this work, HA was chem. grafted to a layer of self-assembled amino-propyl-triethoxy-silane (APTES) on mica and then cross-linked. The boundary lubrication behavior of APTES and of chem. grafted and cross-linked HA in both electrolyte and lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) solns. was tested with a surface forces app. (SFA). Despite the high coeff. of friction (COF) of μ ≈ 0.50, the chem. grafted HA gel significantly improved the lubrication behavior of HA, particularly the wear resistance, in comparison to free HA. Adding more DOPC lipid to the soln. did not improve the lubrication of the chem. grafted and cross-linked HA layer. Damage of the underlying mica surface became visible at higher loads (pressure >2 MPa) after prolonged sliding times. It has generally been assumed that damage caused by or during sliding, also known as "abrasive friction", which is the main biomedical/clin./morphol. manifestation of arthritis, is due to a high friction force and, therefore, a large COF, and that to prevent surface damage or wear (abrasion) one should therefore aim to reduce the COF, which has been the traditional focus of basic research in biolubrication, particularly in cartilage and joint lubrication. Here we combine our results with previous ones on grafted and cross-linked HA on lipid bilayers, and lubricin-mediated lubrication, and conclude that for cartilage surfaces, a high COF can be assocd. with good wear protection, while a low COF can have poor wear resistance. Both of these properties depend on how the lubricating mols. are attached to and organized at the surfaces, as well as the structure and mech., viscoelastic, elastic, and phys. properties of the surfaces, but the two phenomena are not directly or simply related. We also conclude that to provide both the low COF and good wear protection of joints under physiol. conditions, some or all of the four major components of joints-HA, lubricin, lipids, and the cartilage fibrils-must act synergistically in ways (physisorbed, chemisorbed, grafted and/or cross-linked) that are still to be detd.
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    30. 30
      Røn, T.; Javakhishvili, I.; Patil, N. J.; Jankova, K.; Zappone, B.; Hvilsted, S.; Lee, S. Aqueous lubricating properties of charged (ABC) and neutral (ABA) triblock copolymer chains. Polymer 2014, 55, 4873– 4883,  DOI: 10.1016/j.polymer.2014.07.049
      There is no corresponding record for this reference.
    31. 31
      Gaisinskaya-Kipnis, A.; Klein, J. Normal and frictional interactions between liposome-bearing biomacromolecular bilayers. Biomacromolecules 2016, 17, 2591– 2602,  DOI: 10.1021/acs.biomac.6b00614
      31
      Normal and Frictional Interactions between Liposome-Bearing Biomacromolecular Bilayers
      Gaisinskaya-Kipnis, Anastasia; Klein, Jacob
      Biomacromolecules (2016), 17 (8), 2591-2602CODEN: BOMAF6; ISSN:1525-7797. (American Chemical Society)
      Highly efficient lubricating boundary layers at biosurfaces such as cartilage have been proposed to comprise phospholipids complexed with biomacromols. exposed at the surfaces. To gain insight into this, a systematic study on the normal and frictional forces between surfaces bearing a sequentially deposited model alginate-on-chitosan bilayer, bearing different adsorbed phosphatidylcholine (PC) liposomes, was carried out using a surface force balance. Structures of the resulting surface complexes were detd. using at. force microscopy (AFM) and cryo-SEM (cryo-SEM). The liposome/lipid-polymer complexes could maintain their integrity up to high pressures in terms of both normal and shear interactions between the surfaces, which were repeatable, reproducible, and revealed very low friction (coeff. of friction μ down to 10-3-10-4, depending on the PC used) up to pressures of hundreds of atm. We attribute this remarkable lubrication capability ultimately to hydration lubrication acting at the hydrated phosphocholine headgroups of the PC lipids, either exposed at the liposome surfaces or through complexation with the polyelectrolyte bilayer. Values of μ, while low, were roughly an order of magnitude higher than for the same PC vesicles adsorbed on bare mica, a difference attributed to their lower d. on the bilayer; the bilayer, however, stabilized the PC-vesicles far better than bare mica against rupture and shear at high compressions and sliding.
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    32. 32
      Angayarkanni, S. A.; Kampf, N.; Klein, J. Surface interactions between boundary layers of poly (ethylene oxide)–liposome complexes: Lubrication, bridging, and selective ligation. Langmuir 2019, 35, 15469– 15480,  DOI: 10.1021/acs.langmuir.9b01708
      32
      Surface Interactions between Boundary Layers of Poly(ethylene oxide)-Liposome Complexes: Lubrication, Bridging, and Selective Ligation
      Angayarkanni, S. A.; Kampf, Nir; Klein, Jacob
      Langmuir (2019), 35 (48), 15469-15480CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Poly(ethylene oxide), PEO, is widely exploited in biomedical applications, while phosphatidylcholine (PC) lipids (in the form of bilayers or liposomes) have been identified as very efficient boundary lubricants in aq. media. Here we examine, using a surface force balance (SFB), the interactions between surface-adsorbed layers of PEO complexed with small unilamellar vesicles (SUVs, i.e. liposomes) or with bilayers of PC lipids, both well below and a little above their main gel-to-liq. phase-transition temps. TM. The morphol. of PEO layers (adsorbed onto mica), to which liposomes were added, was examd. using at. force microscopy (AFM) and cryo-SEM (cryo-SEM). Our results reveal that the PC lipids could attach to the PEO either as vesicles or as bilayers, depending on whether they were above or below TM. Under water (no added salt), excellent lubrication, with friction coeffs. down to 10-3-10-4, up to contact stresses of 6.5 MPa (comparable to those in the major joints) was obsd. between two surfaces bearing such PEO-PC complexes. At 0.1 M KNO3 salt concn. (comparable to physiol. salt levels), the friction between such surfaces was considerably higher, attributed to bridging by the polymer chains. Remarkably, such bridging could be suppressed and the friction could be restored to its previous low value if the KNO3 was replaced with NaNO3, as a result of the different PEO-mica ligation properties of Na+ compared to those of K+. Our results provide insight into the properties of PEO-PC complexes in potential applications, and large interfacial effects that can result from the seemingly innocuous replacement of K+ by Na+ ions.
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    33. 33
      Lin, W.; Liu, Z.; Kampf, N.; Klein, J. The role of hyaluronic acid in cartilage boundary lubrication. Cells 2020, 9, 1606,  DOI: 10.3390/cells9071606
      There is no corresponding record for this reference.
    34. 34
      Lin, W.; Klein, J. Recent progress in cartilage lubrication. Adv. Mater. 2021, 33, 2005513,  DOI: 10.1002/adma.202005513
      34
      Recent Progress in Cartilage Lubrication
      Lin, Weifeng; Klein, Jacob
      Advanced Materials (Weinheim, Germany) (2021), 33 (18), 2005513CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. Healthy articular cartilage, covering the ends of bones in major joints such as hips and knees, presents the most efficiently-lubricated surface known in nature, with friction coeffs. as low as 0.001 up to physiol. high pressures. Such low friction is indeed essential for its well-being. It minimizes wear-and-tear and hence the cartilage degrdn. assocd. with osteoarthritis, the most common joint disease, and, by reducing shear stress on the mechanotransductive, cartilage-embedded chondrocytes (the only cell type in the cartilage), it regulates their function to maintain homeostasis. Understanding the origins of such low friction of the articular cartilage, therefore, is of major importance in order to alleviate disease symptoms, and slow or even reverse its breakdown. This progress report considers the relation between frictional behavior and the cellular mech. environment in the cartilage, then reviews the mechanism of lubrication in the joints, in particular focusing on boundary lubrication. Following recent advances based on hydration lubrication, a proposed synergy between different mol. components of the synovial joints, acting together in enabling the low friction, has been proposed. Addnl., recent development of natural and bio-inspired lubricants is reviewed.
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    35. 35
      Goldberg, R.; Schroeder, A.; Barenholz, Y.; Klein, J. Interactions between adsorbed hydrogenated soy phosphatidylcholine (HSPC) vesicles at physiologically high pressures and salt concentrations. Biophys. J. 2011, 100, 2403– 2411,  DOI: 10.1016/j.bpj.2011.03.061
      35
      Interactions between Adsorbed Hydrogenated Soy Phosphatidylcholine (HSPC) Vesicles at Physiologically High Pressures and Salt Concentrations
      Goldberg, Ronit; Schroeder, Avi; Barenholz, Yechezkel; Klein, Jacob
      Biophysical Journal (2011), 100 (10), 2403-2411CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Using a surface force balance, normal and shear interactions were measured as a function of surface sepn. between layers of hydrogenated soy phosphatidylcholine (HSPC) small unilamellar vesicles (SUVs) adsorbed from dispersion at physiol. high salt concns. (0.15 M NaNO3). Cryo-SEM shows that each surface is coated by a close-packed HSPC-SUV layer with an overlayer of liposomes on top. A clear attractive interaction between the liposome layers is seen upon approach and sepn., followed by a steric repulsion upon further compression. The shear forces reveal low friction coeffs. (μ = 0.008-0.0006) up to contact pressures of at least 6 MPa, comparable to those obsd. in the major joints. The spread in μ-values may be qual. accounted for by different local liposome structure at different contact points, suggesting that the intrinsic friction of the HSPC-SUV layers at this salt concn. is closer to the lower limit (μ = ∼0.0006). This low friction is attributed to the hydration lubrication mechanism arising from rubbing of the hydrated phosphocholine-headgroup layers exposed at the outer surface of each liposome, and provides support for the conjecture that phospholipids may play a significant role in biol. lubrication.
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    36. 36
      Klein, J. Polymers in living systems: from biological lubrication to tissue engineering and biomedical devices. Polym. Adv. Technol. 2012, 23, 729– 735,  DOI: 10.1002/pat.3038
      36
      Polymers in living systems: from biological lubrication to tissue engineering and biomedical devices
      Klein, Jacob
      Polymers for Advanced Technologies (2012), 23 (4), 729-735CODEN: PADTE5; ISSN:1042-7147. (John Wiley & Sons Ltd.)
      A review. The roles of macromols. in living systems as information storage systems (as DNA) and in biochem. synthesis have been much studied and are relatively well understood. Far less is known about their phys. behavior at biol. surfaces and interfaces. This review considers in particular the roles of polymers in biol. lubrication and its relation both to diseases such as osteoarthritis and to remedies such as tissue engineering. The lubricating behavior of common bio-interfacial macromols. including mucins, hyaluronan, lubricin, and aggrecan are described, and insights into the mechanism of biolubrication are examd. in the light of the recently revealed role of hydration lubrication in water-based (including living) systems. Copyright © 2012 John Wiley & Sons, Ltd.
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    37. 37
      Tieleman, D. P.; Sansom, M. S.; Berendsen, H. J. Alamethicin Helices in a Bilayer and in Solution: Molecular Dynamics Simulations. Biophys. J. 1999, 76, 40– 49,  DOI: 10.1016/S0006-3495(99)77176-6
      37
      Alamethicin helices in a bilayer and in solution: Molecular dynamics simulations
      Tieleman, D. Peter; Sansom, Mark S. P.; Berendsen, Herman J. C.
      Biophysical Journal (1999), 76 (1, Pt. 1), 40-49CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      Alamethicin is an a-helical channel-forming peptide, which inserts into lipid bilayers in a voltage-dependent, asym. fashion. Nanosecond mol. dynamics simulations have been used to compare alamethicin conformation and dynamics in three different environments: (1) in water; (2) in methanol; and (3) inserted into a lipid (palmitoyl-oleoyl-phosphatidylcholine) bilayer to form a transmembrane helix. In the bilayer and in methanol, there was little change (Cα RMSD ≈ 0.2 nm over 2 ns and 1 ns) from the initial helical conformation of the peptide. In water there were substantial changes (Cα RMSD ≈ 0.4 nm over 1 ns), esp. in the C-terminal segment of the peptide, which lost its α-helical conformation. In the bilayer and in methanol, the alamethicin mol. underwent hinge-bending motion about its central Gly-X-X-Pro sequence motif. Anal. of H-bonding interactions revealed that the polar C-terminal side chains of alamethicin provided an "anchor" to the bilayer/water interface via formation of multiple H-bonds that persisted throughout the simulation. This explains why the preferred mode of helix insertion into the bilayer is N-terminal, which is believed to underlie the asymmetry of voltage activation of alamethicin channels.
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    38. 38
      Böckmann, R. A.; De Groot, B. L.; Kakorin, S.; Neumann, E.; Grubmüller, H. Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations. Biophys. J. 2008, 95, 1837– 1850,  DOI: 10.1529/biophysj.108.129437
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      Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations
      Bockmann Rainer A; de Groot Bert L; Kakorin Sergej; Neumann Eberhard; Grubmuller Helmut
      Biophysical journal (2008), 95 (4), 1837-50 ISSN:.
      Membrane electroporation is the method to directly transfer bioactive substances such as drugs and genes into living cells, as well as preceding electrofusion. Although much information on the microscopic mechanism has been obtained both from experiment and simulation, the existence and nature of possible intermediates is still unclear. To elucidate intermediates of electropore formation by direct comparison with measured prepore formation kinetics, we have carried out 49 atomistic electroporation simulations on a palmitoyl-oleoyl-phosphatidylcholine bilayer for electric field strengths between 0.04 and 0.7 V/nm. A statistical theory is developed to facilitate direct comparison of experimental (macroscopic) prepore formation kinetics with the (single event) preporation times derived from the simulations, which also allows us to extract an effective number of lipids involved in each pore formation event. A linear dependency of the activation energy for prepore formation on the applied field is seen, with quantitative agreement between experiment and simulation. The distribution of preporation times suggests a four-state pore formation model. The model involves a first intermediate characterized by a differential tilt of the polar lipid headgroups on both leaflets, and a second intermediate (prepore), where a polar chain across the bilayer is formed by 3-4 lipid headgroups and several water molecules, thereby providing a microscopic explanation for the polarizable volume derived previously from the measured kinetics. An average pore radius of 0.47 +/- 0.15 nm is seen, in favorable agreement with conductance measurements and electrooptical experiments of lipid vesicles.
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    39. 39
      Hockney, R.; Eastwood, J. Computer Simulation Using Particles; Adam Hilger: New York, 1989.
      There is no corresponding record for this reference.
    40. 40
      Pollock, E.; Glosli, J. Comments on P3M, FMM, and the Ewald method for large periodic Coulombic systems. Comput. Phys. Commun. 1996, 95, 93– 110,  DOI: 10.1016/0010-4655(96)00043-4
      40
      Comments on P3M, FMM, and the Ewald method for large periodic Coulombic systems
      Pollock, E. L.; Glosli, Jim
      Computer Physics Communications (1996), 95 (2&3), 93-110CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
      Prompted by the need to simulate large mol. or gravitational systems and the availability of multiprocessor computers, alternatives to the std. Ewald calcn. of Coulombic interactions have been developed. The two most popular alternatives, the fast multipole method (FMM) and the particle-particle particle-mesh (P3M) method are compared here to the Ewald method for a single processor machine. Parallel processor implementations of the P3M and Ewald methods are compared. The P3M method is found to be both faster than the FMM and easier to implement efficiently as it relies on commonly available software (FFT subroutines). Both the Ewald and P3M method are easily implemented on parallel architectures with the P3M method the clear choice for large systems.
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    41. 41
      Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1– 19,  DOI: 10.1006/jcph.1995.1039
      41
      Fast parallel algorithms for short-range molecular dynamics
      Plimpton, Steve
      Journal of Computational Physics (1995), 117 (1), 1-19CODEN: JCTPAH; ISSN:0021-9991.
      Three parallel algorithms for classical mol. dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-at. forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for mol. dynamics models which can be difficult to parallelize efficiently - those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a std. Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers - the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C90 processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex mol. dynamics simulations are also discussed.
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    42. 42
      Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Oxford University Press: Oxford, 1991.
      There is no corresponding record for this reference.
    43. 43
      Robbins, M. O.; Müser, M. In Modern Tribology Handbook; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 2001; pp 717– 825.
      There is no corresponding record for this reference.
    44. 44
      Rottler, J.; Robbins, M. O. Growth, microstructure, and failure of crazes in glassy polymers. Phys. Rev. E 2003, 68, 011801,  DOI: 10.1103/PhysRevE.68.011801
      44
      Growth, microstructure, and failure of crazes in glassy polymers
      Rottler, Jorg; Robbins, Mark O.
      Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2003), 68 (1-1), 011801/1-011801/18CODEN: PRESCM ISSN:. (American Physical Society)
      We report on an extensive study of craze formation in glassy polymers. Mol. dynamics simulations of a coarse-grained bead-spring model were employed to study the mol. level processes during craze nucleation, widening, and breakdown for a wide range of temp., polymer chain length N, entanglement length Ne, and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at const. drawing stress. The extension ratio is detd. by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is Ne/3. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for N/Ne∼10, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theor. models of craze widening, which were based on continuum level hydrodynamics.
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    45. 45
      Galuschko, A.; Spirin, L.; Kreer, T.; Johner, A.; Pastorino, C.; Wittmer, J.; Baschnagel, J. Frictional forces between strongly compressed, nonentangled polymer brushes: molecular dynamics simulations and scaling theory. Langmuir 2010, 26, 6418– 6429,  DOI: 10.1021/la904119c
      45
      Frictional Forces between Strongly Compressed, Nonentangled Polymer Brushes: Molecular Dynamics Simulations and Scaling Theory
      Galuschko, A.; Spirin, L.; Kreer, T.; Johner, A.; Pastorino, C.; Wittmer, J.; Baschnagel, J.
      Langmuir (2010), 26 (9), 6418-6429CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      By means of mol. dynamics simulations and scaling theory we study the response of opposing polymer brushes to const. shear motion under good solvent conditions. Model systems that contain explicit solvent mols. (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their mol. parameters, chain length and grafting d. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg no., W, beyond linear response. For instance, we find that the kinetic friction const. scales as μ ∼ W0.57 for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent expts.
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    46. 46
      Dong, Y.; Perez, D.; Voter, A.; Martini, A. The roles of statics and dynamics in determining transitions between atomic friction regimes. Tribol. Lett. 2011, 42, 99– 107,  DOI: 10.1007/s11249-011-9750-5
      There is no corresponding record for this reference.
    47. 47
      Drummond, C.; Israelachvili, J. Dynamic phase transitions in confined lubricant fluids under shear. Phys. Rev. E 2001, 63, 041506,  DOI: 10.1103/PhysRevE.63.041506
      47
      Dynamic phase transitions in confined lubricant fluids under shear
      Drummond, Carlos; Israelachvili, Jacob
      Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2001), 63 (4-1), 041506/1-041506/11CODEN: PRESCM ISSN:. (American Physical Society)
      A surface force app. was used to measure the transient and steady-state friction forces between molecularly smooth mica surfaces confining thin films of squalane, C30H62, a satd., branched hydrocarbon liq. The dynamic friction "phase diagram" was detd. under different shearing conditions, esp. the transitions between stick-slip and smooth sliding "states" that exhibited a chaotic stick-slip regime. The apparently very different friction traces exhibited by simple spherical, linear, and branched hydrocarbon films under shear are shown to be due to the much longer relaxation times and characteristic length scales assocd. with transitions from rest to steady-state sliding, and vice versa, in the case of branched liqs. The phys. reasons and tribol. implications for the different types of transitions obsd. with spherical, linear, and branched fluids are discussed.
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    48. 48
      Taylor, J. Introduction to error analysis, the study of uncertainties in physical measurements; University Science Books: New York, 1997.
      There is no corresponding record for this reference.
    49. 49
      Filippov, A.; Klafter, J.; Urbakh, M. Friction through dynamical formation and rupture of molecular bonds. Phys. Rev. Lett. 2004, 92, 135503,  DOI: 10.1103/PhysRevLett.92.135503
      49
      Friction through Dynamical Formation and Rupture of Molecular Bonds
      Filippov, A. E.; Klafter, J.; Urbakh, M.
      Physical Review Letters (2004), 92 (13), 135503/1-135503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the exptl. conditions and time scales. The overall behavior can be described in terms of two Deborah nos.
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    50. 50
      Guerra, R.; Benassi, A.; Vanossi, A.; Ma, M.; Urbakh, M. Friction and adhesion mediated by supramolecular host–guest complexes. Phys. Chem. Chem. Phys. 2016, 18, 9248– 9254,  DOI: 10.1039/C6CP00661B
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      Friction and adhesion mediated by supramolecular host-guest complexes
      Guerra, Roberto; Benassi, Andrea; Vanossi, Andrea; Ma, Ming; Urbakh, Michael
      Physical Chemistry Chemical Physics (2016), 18 (13), 9248-9254CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The adhesive and frictional response of an AFM tip connected to a substrate through supramol. host-guest complexes is investigated by dynamic Monte Carlo simulations. Here, the variation of the pull-off force with the unloading rate recently obsd. in expts. is unraveled by evidencing simultaneous (progressive) breaking of the bonds at fast (slow) rates. The model reveals the origin of the obsd. plateaus in the retraction force as a function of the tip-surface distance, showing that they result from the tip geometrical features. In lateral sliding, the model exhibits a wide range of dynamic behaviors ranging from smooth sliding to stick-slip at different velocities, with the av. friction force detd. by the characteristic formation/rupture rates of the complexes. In particular, it is shown that for some mol. complexes friction can become almost const. over a wide range of velocities. Also, we show the possibility of exploiting the ageing effect through slide-hold-slide expts., in order to infer the characteristic formation rate. Finally, our model predicts a novel "anti-ageing" effect which is characterized by a decrease of the static friction force with the hold time. Such an effect is explained in terms of enhancement of adhesion during sliding, esp. obsd. at high driving velocities.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XjsFKhsb4%253D&md5=6c0f17a334eec517fbdae476d1ebfe5b
    51. 51
      Blass, J.; Albrecht, M.; Wenz, G.; Guerra, R.; Urbakh, M.; Bennewitz, R. Multivalent adhesion and friction dynamics depend on attachment flexibility. J. Phys. Chem. C 2017, 121, 15888– 15896,  DOI: 10.1021/acs.jpcc.7b05412
      51
      Multivalent Adhesion and Friction Dynamics Depend on Attachment Flexibility
      Blass, Johanna; Albrecht, Marcel; Wenz, Gerhard; Guerra, Roberto; Urbakh, Michael; Bennewitz, Roland
      Journal of Physical Chemistry C (2017), 121 (29), 15888-15896CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Self-assembled monolayers introduce chem. functionalities to material surfaces, providing a route to tune their equil. and dynamical properties. The authors report on at. force microscopy measurements and simulations of adhesion and friction forces caused by a macromol. host-guest system, where the host mols. are attached to silicon oxide surfaces by means of self-assembled silane layers. Different prepn. routes for the silane layers lead to different flexibility of the mol. attachment. The velocity dependencies of the work of sepn. 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 mol. 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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    52. 52
      Liu, Y.; Szlufarska, I. Chemical origins of frictional aging. Phys. Rev. Lett. 2012, 109, 186102,  DOI: 10.1103/PhysRevLett.109.186102
      52
      Chemical origins of frictional aging
      Liu, Yun; Szlufarska, Izabela
      Physical Review Letters (2012), 109 (18), 186102/1-186102/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Although the basic laws of friction are simple enough to be taught in elementary physics classes and although friction has been widely studied for centuries, in the current state of knowledge it is still not possible to predict a friction force from fundamental principles. One of the highly debated topics in this field is the origin of static friction. For most macroscopic contacts between two solids, static friction will increase logarithmically with time, a phenomenon that is referred to as aging of the interface. One known reason for the logarithmic growth of static friction is the deformation creep in plastic contacts. However, this mechanism cannot explain frictional aging obsd. in the absence of roughness and plasticity. Here, we discover mol. mechanisms that can lead to a logarithmic increase of friction based purely on interfacial chem. Predictions of our model are consistent with published exptl. data on the friction of silica.
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    53. 53
      Li, Q.; Tullis, T.; Goldsby, D.; Carpick, R. Frictional ageing from interfacial bonding and the origins of rate and state friction. Nature 2011, 480, 233– 236,  DOI: 10.1038/nature10589
      53
      Frictional ageing from interfacial bonding and the origins of rate and state friction
      Li, Qunyang; Tullis, Terry E.; Goldsby, David; Carpick, Robert W.
      Nature (London, United Kingdom) (2011), 480 (7376), 233-236CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Earthquakes have long been recognized as being the result of stick-slip frictional instabilities. Over the past few decades, lab. studies of rock friction have elucidated many aspects of tectonic fault zone processes and earthquake phenomena. Typically, the static friction of rocks grows logarithmically with time when they are held in stationary contact, but the mechanism responsible for this strengthening is not understood. This time-dependent increase of frictional strength, or frictional ageing, is one manifestation of the evolution effect' in rate and state friction theory. A prevailing view is that the time dependence of rock friction results from increases in contact area caused by creep of contacting asperities. Here we present the results of at. force microscopy expts. that instead show that frictional ageing arises from the formation of interfacial chem. bonds, and the large magnitude of ageing at the nanometer scale is quant. consistent with what is required to explain observations in macroscopic rock friction expts. The relative magnitude of the evolution effect compared with that of the direct effect'-the dependence of friction on instantaneous changes in slip velocity-det. whether unstable slip, leading to earthquakes, is possible. Understanding the mechanism underlying the evolution effect would enable us to formulate phys. based frictional constitutive laws, rather than the current empirically based laws', allowing more confident extrapolation to natural faults.
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    54. 54
      Tian, K.; Gosvami, N. N.; Goldsby, D. L.; Liu, Y.; Szlufarska, I.; Carpick, R. W. Load and time dependence of interfacial chemical bond-induced friction at the nanoscale. Phys. Rev. Lett. 2017, 118, 076103  DOI: 10.1103/PhysRevLett.118.076103
      54
      Load and time dependence of interfacial chemical bond-induced friction at the nanoscale
      Tian, Kaiwen; Gosvami, Nitya N.; Goldsby, David L.; Liu, Yun; Szlufarska, Izabela; Carpick, Robert W.
      Physical Review Letters (2017), 118 (7), 076103/1-076103/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Rate and state friction (RSF) laws are widely used empirical relationships that describe the macroscale frictional behavior of a broad range of materials, including rocks found in the seismogenic zone of Earth's crust. A fundamental aspect of the RSF laws is frictional "aging," where friction increases with the time of stationary contact due to asperity creep and/or interfacial strengthening. Recent at. force microscope (AFM) expts. and simulations found that nanoscale silica contacts exhibit aging due to the progressive formation of interfacial chem. bonds. The role of normal load (and, thus, normal stress) on this interfacial chem. bond-induced (ICBI) friction is predicted to be significant but has not been examd. exptl. Here, we show using AFM that, for nanoscale ICBI friction of silica-silica interfaces, aging (the difference between the max. static friction and the kinetic friction) increases approx. linearly with the product of the normal load and the log of the hold time. This behavior is attributed to the approx. linear dependence of the contact area on the load in the pos. load regime before significant wear occurs, as inferred from sliding friction measurements. This implies that the av. pressure, and thus the av. bond formation rate, is load independent within the accessible load range. We also consider a more accurate nonlinear model for the contact area, from which we ext. the activation vol. and the av. stress-free energy barrier to the aging process. Our work provides an approach for studying the load and time dependence of contact aging at the nanoscale and further establishes RSF laws for nanoscale asperity contacts.
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    55. 55
      Ouyang, W.; Ramakrishna, S. N.; Rossi, A.; Urbakh, M.; Spencer, N. D.; Arcifa, A. Load and velocity dependence of friction mediated by dynamics of interfacial contacts. Phys. Rev. Lett. 2019, 123, 116102,  DOI: 10.1103/PhysRevLett.123.116102
      55
      Load and Velocity Dependence of Friction Mediated by Dynamics of Interfacial Contacts
      Ouyang, Wengen; Ramakrishna, Shivaprakash N.; Rossi, Antonella; Urbakh, Michael; Spencer, Nicholas D.; Arcifa, Andrea
      Physical Review Letters (2019), 123 (11), 116102CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Studying the frictional properties of interfaces with dynamic chem. bonds advances understanding of the mechanism underlying rate and state laws, and offers new pathways for the rational control of frictional response. In this work, we revisit the load dependence of interfacial chem.-bond-induced (ICBI) friction exptl. and find that the velocity dependence of friction can be reversed by changing the normal load. We propose a theor. model, whose anal. soln. allows us to interpret the exptl. data on timescales and length scales that are relevant to exptl. conditions. Our work provides a promising avenue for exploring the dynamics of ICBI friction.
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    56. 56
      Shao, Y.; Jacobs, T. D.; Jiang, Y.; Turner, K. T.; Carpick, R. W.; Falk, M. L. Multibond model of single-asperity tribochemical wear at the nanoscale. ACS Appl. Mater. Interfaces 2017, 9, 35333– 35340,  DOI: 10.1021/acsami.7b08023
      56
      Multibond Model of Single-Asperity Tribochemical Wear at the Nanoscale
      Shao, Yuchong; Jacobs, Tevis D. B.; Jiang, Yijie; Turner, Kevin T.; Carpick, Robert W.; Falk, Michael L.
      ACS Applied Materials & Interfaces (2017), 9 (40), 35333-35340CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      Single-asperity wear expts. and simulations have identified different regimes of wear including Eyring- and Archard-like behaviors. A multibond dynamics model has been developed based on the friction model of Filippov et al. This new model captures both qual. distinct regimes of single-asperity wear under a unified theor. framework. In this model, the interfacial bond formation, wearless rupture, and transfer of atoms are governed by three competing thermally activated processes. The Eyring regime holds under the conditions of low load and low adhesive forces; few bonds form between the asperity and the surface, and wear is a rare and rate-dependent event. As the normal stress increases, the Eyring behavior of wear rate breaks down. A nearly rate-independent regime arises under high load or high adhesive forces, in which wear becomes very nearly, but not precisely, proportional to sliding distance. In this restricted regime, the dependence of wear rate per unit contact area is nearly independent of the normal stress at the point of contact. In true contact between rough elastic surfaces, where contact area is expected to grow linearly with normal load, this would lead to behavior very similar to that described by the Archard equation. Detailed comparisons to exptl. and mol. dynamics simulation investigations illustrate both Eyring and Archard regimes, and an intermediate crossover regime between the two.
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    57. 57
      Karuppiah, K. K.; Zhou, Y.; Woo, L. K.; Sundararajan, S. Nanoscale friction switches: friction modulation of monomolecular assemblies using external electric fields. Langmuir 2009, 25, 12114– 12119,  DOI: 10.1021/la901221g
      57
      Nanoscale friction switches: friction modulation of monomolecular assemblies using external electric fields
      Karuppiah K S Kanaga; Zhou Yibo; Woo L Keith; Sundararajan Sriram
      Langmuir : the ACS journal of surfaces and colloids (2009), 25 (20), 12114-9 ISSN:.
      This paper presents experimental investigations to actively modulate the nanoscale friction properties of a self-assembled monolayer (SAM) assembly using an external electric field that drives conformational changes in the SAM. Such "friction switches" have widespread implications in interfacial energy control in micro/nanoscale devices. Friction response of a low-density mercaptocarboxylic acid SAM is evaluated using an atomic force microscope (AFM) in the presence of a DC bias applied between the sample and the AFM probe under a nitrogen (dry) environment. The low density allows reorientation of individual SAM molecules to accommodate the attractive force between the -COOH terminal group and a positively biased surface. This enables the surface to present a hydrophilic group or a hydrophobic backbone to the contacting AFM probe depending upon the direction of the field (bias). Synthesis and deposition of the low-density SAM (LD-SAM) is reported. Results from AFM experiments show an increased friction response (up to 300%) of the LD-SAM system in the presence of a positive bias compared to the friction response in the presence of a negative bias. The difference in the friction response is attributed to the change in the structural and crystalline order of the film in addition to the interfacial surface chemistry and composition presented upon application of the bias.
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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.1c09542.

    • Details of the chain arrangement, supercell geometry, and intermolecular interactions; the average shear stress as a function of the damping parameter γ (Figure S1); the definition of the hooking fraction h; the frictional shear traces of the zwitterionic (Figure S2) and charge-free (Figure S3) systems for the load dependence of Figure 7a,c; shear stress and SUP–SUB distance dependence on the sliding velocity for zwitterionic and charge-free systems (Figure S4); correlation of the hooking fraction, shear stress, and total potential energy for the charge-free system at T = 0 K (Figure S5); scatter plots illustrating the anticorrelation between the total potential energy and the hooking fraction that determine the T = 300 K points in Figure 8b for zwitterionic and charge-free systems (Figure S6); technical details about 4 short supporting movies illustrating the MD simulations corresponding to the last 30 nm of the stage’s displacement in the shear traces of Figure 2c–f (PDF)

    • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2c (MP4)

    • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2d (MP4)

    • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2e (MP4)

    • Last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2f (MP4)


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