Origins of hydration lubrication
Open accessAbstract
Why is friction in healthy hips and knees so low? Hydration lubrication, according to which hydration shells surrounding charges act as lubricating elements in boundary layers (including those coating cartilage in joints), has been invoked to account for the extremely low sliding friction between surfaces in aqueous media, but not well understood. Here we report the direct determination of energy dissipation within such sheared hydration shells. By trapping hydrated ions in a 0.4-1 nm gap between atomically smooth charged surfaces as they slide past each other, we are able to separate the dissipation modes of the friction and, in particular, identify the viscous losses in the subnanometre hydration shells. Our results shed light on the origins of hydration lubrication, with potential implications both for aqueous boundary lubricants and for biolubrication.
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Claims the paper makes
1 of 40 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured
- Premisecitation
In all relevant studies to date, the measured friction may have been dominated by other dissipation pathways, such as polymer chains disentangling past each other or distortion of sheared liposomes.
“This is because in all relevant studies to date, including refs 4-11, the measured friction may have been dominated by other dissipation pathways, such as polymer chains disentangling past each other 10,11 or distortion of sheared liposomes 9 .”
Quote in the paperSubstantial claim1 of 3 sources checked- cites [4] Sakuma, H., Otsuki, K. & Kurihara, K. Viscosity and lubricity of aqueous NaCl solution confined between mica surfaces studied by shear resonance measurement. Phys. Rev. Lett. 96, 046101–046104 (2006). source
- cites [9] Goldberg, R. et al. Boundary lubricants with exceptionally low friction coefficients based on 2D close-packed phosphatidylcholine liposomes. Adv. Mater. 23, 3517–3521 (2011). source
- cites [10] Chen, M., Briscoe, W. H., Armes, S. P. & Klein, J. Lubrication at physiological pressures by polyzwitterionic brushes. Science 323, 1698–1702 (2009). source
The Published paper section describes viscous dissipation in the interpenetration zone of sliding polymer brushes and reports that entanglement increased friction in earlier brush studies. It does not address distortion of sheared liposomes or establish that other dissipation pathways may have dominated measured friction in all relevant studies. (LLM, conf=0.85)
Experimental — accuracy not yet measured
- Findingown data
From the slope qF_s/q(ln(v_s))≈0.5×10^-6 N in Fig. 4, a value for Ω≈2×10^-23 m^3 is extracted.
“From the slope qF s /q(ln(n s ))E0.5 Â 10 À 6 N in Fig. 4, we extract a value for OE2 Â 10 À 23 m 3 .”
Quote in the paperSubstantial claim - Findingown data
In the high-load regime, the variation of shear force with sliding velocity is close to logarithmic, F_s = A + B ln(v_s), over some orders of magnitude in v_s.
“the variation is close to logarithmic, F s ¼ A þ B.ln(n s ), where A and B are constants, over some orders of magnitude in n s .”
Quote in the paperSubstantial claim - Findingown data
In the low-load regime, the variation of shear force with sliding velocity is much closer to linear, F_s - F_s,0 = C v_s.
“the variation is much closer to linear, F s -F s,0 ¼ C.n s , where F s,0 (Methods) and C are independent of n s .”
Quote in the paperSubstantial claim - Findingcitation
At D≈2 nm, there is characteristic repulsion arising from tightly bound hydration shells surrounding Na+ counterions trapped between negatively charged mica surfaces.
“At Doca 2 nm, we observe the characteristic repulsion arising from the tightly bound hydration shells [14][15][16][17][18] surrounding the Na þ counterions trapped between the negatively charged mica surfaces.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [14] Hensen, E. J. M. & Smit, B. Why clays swell. J. Phys. Chem. B 106, 12664–12667 (2002). source
- cites [15] Israelachvili, J. N. Intermolecular and Surface Forces 3rd edn Academic (2011). source
- cites [16] Lane, J. M. D., Chandross, M., Stevens, M. J. & Grest, G. S. Water in nanoconfinement between hydrophilic self-assembled monolayers. Langmuir 24, 5209–5212 (2008). source
- Findingown data
In the low-load regime, the surface separation is D_l = 0.85±0.15 nm.
“where D ¼ D l ¼ 0.85 ± 0.15 nm (Methods)”
Quote in the paperSubstantial claim - Findingown data
When lower loads are applied so that the equilibrium separation of the surfaces significantly exceeds ca 0.8 nm, the effective viscosity within the gap in the linear regime tends, within the scatter of the data, towards that of bulk water.
“We also confirmed (see Supplementary Fig. 1 and Supplementary Note 1) that when lower loads are applied so that the equilibrium separation of the surfaces significantly exceeds the value (ca 0.8 nm) at which the confined water molecules all belong to the hydration shells, the effective viscosity within the gap in the linear regime tends-within the scatter of the data-towards that of bulk water.”
Quote in the paperSubstantial claim - Findingcitation
Normal force profiles across 0.1 M salt solutions reveal longer-ranged repulsion arising from counterion osmotic pressure down to D≈2 nm.
“Figure 1 shows the normalized force profiles F n (D)/R versus D across water (always taken as a control for system cleanliness before adding salt) and across the 0.1 M salt solutions, revealing the longer-ranged repulsion arising from counterion osmotic pressure 18,20 down to DE2 nm.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [18] Pashley, R. M. Hydration forces between mica surfaces in aqueous electrolyte solutions. J. Colloid Interface Sci. 80, 153–162 (1981). source
- cites [20] Evans, D. F. & Wennerstrom, H. The Colloidal Domain 2nd edn Wiley (1999).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Findingown data
This value of the hydration shell viscosity is some 250-fold larger than the viscosity of bulk water η_H2O = 8.8×10^-4 Pa.s at 25°C.
“This value Z eff of the hydration shell viscosity is some 250-fold larger than the viscosity of bulk water Z H20 ¼ 8.8 Â 10 À 4 Pa.s at 25 °C.”
Quote in the paperSubstantial claim - Findingown data
Viscous dissipation within hydration shells, for the ions examined, is some 250-fold larger than the viscosity either of bulk water or of similarly confined non-hydration water.
“Our results reveal that viscous dissipation within hydration shells-for the ions examined-is some 250-fold larger than the viscosity either of bulk water or of similarly confined non-hydration water.”
Quote in the paperSubstantial claim - Premisecitation
The molecular-level understanding of friction in healthy human joints remains elusive.
“and its molecular-level understanding remains elusive 2 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [2] Dowson, D. Bio-tribology. Faraday Discuss. 156, 9–30 (2012). source
- Premisecitation
Friction coefficients of order 10^-3 at pressures exceeding 100 atm, typical of articulating cartilage surfaces in healthy human joints, cannot be reproduced by any synthetic surfaces.
“Thus, friction coefficients of order 10 À 3 , at pressures exceeding 100 atm, typical of articulating cartilage surfaces in healthy human joints 1 , cannot be reproduced by any synthetic surfaces”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [1] Dowson, D., Wright, V. & Longfield, M. D. Human joint lubrication. Biomed. Eng 4, 160–165 (1969).
- Premisereasoning
There is little microscopic understanding of the hydration lubrication mechanism, especially of the frictional dissipation within the subnanometre hydration shells that form its basic elements.
“However, there is little microscopic understanding of this mechanism, especially of the frictional dissipation within the subnanometre hydration shells that form its basic elements.”
Quote in the paperSubstantial claim - Interpretationreasoning
The study provides a framework for understanding lubrication processes in living systems where hydration layers are ubiquitous.
“Moreover, it provides a framework for understanding lubrication processes in living systems where hydration layers are ubiquitous.”
Quote in the paperSubstantial claim - Interpretationreasoning
In the high-load regime, the sliding of the two surfaces may be understood in terms of a process where a potential energy ΔE of sliding surface-localized ions past each other needs to be overcome.
“Thus, in this regime, the sliding of the two surfaces may be understood in terms of a process where a potential energy DE of sliding surface-localized ions past each other needs to be overcome (Methods)”
Quote in the paperSubstantial claim - Interpretationreasoning
The magnitude of Ω and ΔE and thus of the friction force F_s depends on the relative position of the localized counterions on the opposing surfaces sliding past each other.
“This mechanism also accounts for the relatively large scatter in F s in Fig. 2b: the magnitude of O and DE and thus of the friction force F s depends on the relative position of the localized counterions on the opposing surfaces sliding past each other.”
Quote in the paperSubstantial claim - Premisereasoning
Earlier findings on lubricated sliding between hydrated surface layers including hydrated ions, surfactants, polymers or liposomes could not reveal the underlying process because the measured friction was a convolution of the hydration lubrication with other dissipation pathways.
“Earlier findings on lubricated sliding between hydrated surface layers including hydrated ions [3][4][5] , surfactants [6][7][8] , polymers [10][11][12] or liposomes 9 could not reveal the underlying process.This is because the measured friction was a convolution of the hydration lubrication with other dissipation pathways, such as the activated processes described above, or deformation [6][7][8][”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [3] Raviv, U. & Klein, J. Fluidity of bound hydration layers. Science 297, 1540–1543 (2002). source
- cites [6] Briscoe, W. H. et al. Boundary lubrication under water. Nature 444, 191–194 (2006). source
- cites [9] Goldberg, R. et al. Boundary lubricants with exceptionally low friction coefficients based on 2D close-packed phosphatidylcholine liposomes. Adv. Mater. 23, 3517–3521 (2011). source
- Premisecitation
Molecular dynamics simulations of hydrated K+ ions confined to films of thickness D between mica surfaces show an approximately two orders of magnitude enhancement of low-shear-rate viscosity relative to bulk water at D=0.94 nm, consistent with our findings.
“Molecular dynamics simulations of hydrated K þ ions, confined to films of thickness D between mica surfaces 31 , show an approximately two orders of magnitude enhancement of low-shear-rate viscosity (relative to bulk water) at D ¼ 0.94 nm, and are thus also consistent with our findings.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [31] Leng, Y. & Cummings, P. T. Fluidity of hydration layers nanoconfined between mica surfaces. Phys. Rev. Lett. 94, 026101 (2005). source
- Interpretationreasoning
The ratio τ_H2O,Na+/τ_H2O ≈100 is consistent with the ~250-fold enhancement of the hydration shell viscosity relative to bulk water.
“The ratio (t H2O,Na þ /t H2O )E100 is thus consistent with the B250-fold enhancement of the hydration shell viscosity Z eff relative to Z H20 .”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [28] Tabor, D. Gases, Liquids and Solids 3rd edn Cambridge Univ. (1991). source
- cites [30] Ferry, J. D. Viscoelastic Properties of Polymers 3rd edn Wiley (1985).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- The authors state this as an assumption: The exchange time of water molecules in the hydration shell of Na+ can be taken as approximately the relaxation time of water within the hydration shells.
- The authors state this as an assumption: Liquid viscosity is proportional to molecular relaxation times (η=Gτ) as long as the shear rate is much lower than τ^-1.
- Interpretationcitation
The logarithmic variation of friction with sliding velocity at high loads is characteristic of Eyring-like rate-activated processes arising from the overcoming of energy barriers.
“The logarithmic variation of the friction with sliding velocity at high loads (Fig. 3) is characteristic of Eyring-like rate-activated processes arising from the overcoming of energy barriers, as seen in a number of solid-friction or boundary lubrication studies 21,22 .”
Quote in the paperSubstantial claim0 of 2 sources checked - Interpretationown data
This insight largely accounts for the massive friction reduction via the hydration lubrication mechanism recently described in many systems.
“This insight largely accounts for the massive friction reduction via the hydration lubrication mechanism recently described in many systems 3,[5][6][7][8][9][10][11] , and has implications for better design of boundary lubricants and their interfacial vectors in biomedical contexts.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [3] Raviv, U. & Klein, J. Fluidity of bound hydration layers. Science 297, 1540–1543 (2002). source
- cites [5] Donose, B. C., Vakarelski, I. U. & Higashitani, K. Silica surface lubrication by hydrated cations adsorption from electrolyte solutions. Langmuir 21, 1834–1839 (2005). source
- cites [6] Briscoe, W. H. et al. Boundary lubrication under water. Nature 444, 191–194 (2006). source
- Interpretationcitation
The measured value of the hydration shell dissipation is consistent with the exchange rate ω_H2O,Na+ of water molecules in the hydration shell of Na+ with bulk water.
“This measured value of the hydration shell dissipation is consistent with the exchange rate o H2O,Na þ of water molecules in the hydration shell of Na þ with bulk water molecules 23 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [23] Cotton, F. A. & Wilkinson, G. Advanced Inorganic Chemistry 5th edn Wiley (1998).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- The authors state this as an assumption: The exchange time of water molecules in the hydration shell of Na+ can be taken as approximately the relaxation time of water within the hydration shells.
- Interpretationcitation
Energy dissipation occurs predominantly when phonons are generated in the irreversible conversion of potential to kinetic energy following the overcoming of the energy maximum.
“Energy dissipation occurs predominantly when phonons (degraded into heat) are generated in the irreversible conversion of potential to kinetic energy following the overcoming of the energy maximum 25 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [25] Tabor, D. inFundamentals of Friction: Macroscopic and Microscopic Processes eds Singer I. L., Pollock H. M. 3–20Kluwer (1992). source
- Interpretationown data
It is not the subnanometre confinement that leads to the much higher viscous dissipation of the hydration water, but rather its being within the primary hydration shell surrounding the counterion charges.
“In other words, it is not the subnanometre confinement that leads to the much higher viscous dissipation of the hydration water, but rather its being within the primary hydration shell surrounding the counterion charges.”
Quote in the paperSubstantial claim - Premisecitation
The number density of counterions trapped between the surfaces is ρ_c/i = (2σ^-/D_l), where σ^- ≈ 2 nm^-2 is the areal density of ionizable lattice sites on the mica surface.
“At the surface separation D l , the number density r c/i of counterions trapped between the surfaces is r c/i ¼ (2s À /D l ), where s À E2 nm À 2 is the areal density of ionizable lattice sites on the mica surface, each of which is associated with a trapped, hydrated Na þ counterion 3,18,20,26 .”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [3] Raviv, U. & Klein, J. Fluidity of bound hydration layers. Science 297, 1540–1543 (2002). source
- cites [18] Pashley, R. M. Hydration forces between mica surfaces in aqueous electrolyte solutions. J. Colloid Interface Sci. 80, 153–162 (1981). source
- cites [20] Evans, D. F. & Wennerstrom, H. The Colloidal Domain 2nd edn Wiley (1999).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
Essentially all the water molecules in the gap D_l≈0.85 nm belong to primary hydration shells of the trapped counterions.
“This implies that essentially all the water molecules in the gap D l E0.85 nm belong to primary hydration shells of the trapped counterions.”
Quote in the paperSubstantial claim
- May combine two claims. 12
- The quote only partly states this claim. 2
- Classified as probably not a substantial claim. 6
May combine two claims.
FindingreasoningThe number of water molecules per Na+ ion trapped in the gap is n_w ≈ 6, comparable with the number 4-7 of water molecules in the first hydration shell of a Na+ ion.
“The number of water molecules n w per Na þ ion trapped in the gap is then given by n w ¼ r H2O /r c/i E6, where r H2O is the number density of water molecules ¼ (density of water)/(mass of a water molecule).Thus, n w is comparable with the number, 4-7, of water molecules in the first (most tightly held) hydration shell of a Na þ ion 23,27 .”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [23] Cotton, F. A. & Wilkinson, G. Advanced Inorganic Chemistry 5th edn Wiley (1998).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [27] Saluja, P. P. S. Environment of ions in aqueous solutions. Int. Rev. Sci. Electrochem. Part 1 Phys. Chem. 2 6, 1–51 (1976).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Findingown dataThe present study identifies the dissipation pathway and the viscous losses in the bound hydration layers alone, which are characterized by an effective viscosity orders of magnitude larger than that of non-hydration water.
“In particular, we identify the dissipation pathway and the viscous losses in the bound hydration layers alone, which are characterized by an effective viscosity orders of magnitude larger than that of non-hydration water.”
Quote in the paperSubstantial claimThe quote only partly states this claim.
Findingown dataThe effective shear viscosity of the confined film in the low-load regime is η_eff = 0.22±0.07 Pa.s.
“from the measured slope C of the blue band in Fig. 4, we may extract the effective viscosity of the confined film, Z eff ¼ 0.22±0.07Pa.s.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
PremisecitationHydration lubrication has been invoked to account for the extremely low sliding friction observed at high pressures between charged surfaces in high-salt solution, or when coated by surfactants, liposomes or hydrated polymer brushes.
“Over the past decade, the concept of hydration lubrication has been invoked to account for the extremely low sliding friction observed at high pressures between charged surfaces in high-salt solution [3][4][5] , or when coated by surfactants [6][7][8] , liposomes 9 or hydrated polymer brushes [10][11][12] boundary layers resembling those at articular cartilage surfaces 12,13 .”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [3] Raviv, U. & Klein, J. Fluidity of bound hydration layers. Science 297, 1540–1543 (2002). source
- cites [4] Sakuma, H., Otsuki, K. & Kurihara, K. Viscosity and lubricity of aqueous NaCl solution confined between mica surfaces studied by shear resonance measurement. Phys. Rev. Lett. 96, 046101–046104 (2006). source
- cites [5] Donose, B. C., Vakarelski, I. U. & Higashitani, K. Silica surface lubrication by hydrated cations adsorption from electrolyte solutions. Langmuir 21, 1834–1839 (2005). source
May combine two claims.
Study design and conductown dataτΩ≈3×10^-20 J >> 4kBT, which is the assumption underlying equation 3.
“We can check that indeed tOE3 Â 10 À 20 J4 4k B T (E4 Â 10 À 21 J), which is the assumption underlying in equation 3.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims. The quote only partly states this claim.
Study design and conductown dataContact areas between the surfaces were evaluated using the Hertzian contact mechanics relation and compared with contact areas obtained by directly measuring the flattening of the optical fringe tips, generally within 30% of each other over all experiments.
“Comparison of these values with contact areas obtained by directly measuring the flattening of the optical fringe tips (as in Fig. 2b in the main paper) in the high-load regime were generally within 30% of each other over all experiments.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
PremisecitationHydration shells formed by water molecules are tenaciously attached to the charges they surround and cannot be easily squeezed out on compression.
“According to this, hydration shells formed by water molecules are tenaciously attached to the charges they surround, and so cannot be easily squeezed out on compression [14][15][16][17][18]”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [14] Hensen, E. J. M. & Smit, B. Why clays swell. J. Phys. Chem. B 106, 12664–12667 (2002). source
- cites [15] Israelachvili, J. N. Intermolecular and Surface Forces 3rd edn Academic (2011). source
- cites [16] Lane, J. M. D., Chandross, M., Stevens, M. J. & Grest, G. S. Water in nanoconfinement between hydrophilic self-assembled monolayers. Langmuir 24, 5209–5212 (2008). source
May combine two claims.
PremisecitationHydration shells are labile and respond to shear in a fluid manner.
“yet are labile and so respond to shear in a fluid manner.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites [14] Hensen, E. J. M. & Smit, B. Why clays swell. J. Phys. Chem. B 106, 12664–12667 (2002). source
- cites [15] Israelachvili, J. N. Intermolecular and Surface Forces 3rd edn Academic (2011). source
- cites [16] Lane, J. M. D., Chandross, M., Stevens, M. J. & Grest, G. S. Water in nanoconfinement between hydrophilic self-assembled monolayers. Langmuir 24, 5209–5212 (2008). source
May combine two claims.
Study design and conductown dataShear forces vary reversibly with shear velocity and normal load, indicating that no surface damage occurs during shear.
“We note that, within the scatter for a given contact point, the shear forces vary reversibly with the shear velocity and with normal load, indicating that no surface damage occurs during the shear (Methods).”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Study design and conductreasoningOnly experiments where both F_n(D) and F_s profiles were reversible and reproducible with respect to load and sliding velocities, and thus clearly undamaged, are reported.
“Only experiments where both F n (D) and F s profiles were reversible and reproducible (within the scatter) with respect to load and sliding velocities, and thus clearly undamaged, are reported”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataResults are reported from all nine independent experiments in which no damage occurred.
“(results are reported from all nine independent experiments in which no damage occurred, that is, different pairs of mica sheets, with different contact points in each”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Study design and conductcitationThe D_h and D_l values are the mean of 23 and 25 measurements in the high-load and low-load regimes respectively, where the quoted uncertainty is twice the standard error in the mean.
“The D h and D l values are the mean of 23 and 25 measurements in the high-load (ca 5-8 mN) and low-load (ca 0.1-0.2mN) regimes respectively, where the quoted uncertainty is twice the standard error in the mean given by Peter's formula 33 .”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [33] Squires, G. L. Practical Physics McGraw-Hill (1968). source
May combine two claims.
Study design and conductcitationThe present study traps hydrated ions in the gap between molecularly smooth surfaces and measures friction at pressures and shear rates one to two orders of magnitude higher than previously achieved.
“The present study overcomes these limitations by trapping hydrated ions in the gap between molecularly smooth surfaces, and measuring the friction between them as they slide at pressures and shear rates one to two orders of magnitude higher than previously achieved 3 .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [3] Raviv, U. & Klein, J. Fluidity of bound hydration layers. Science 297, 1540–1543 (2002). source
May combine two claims.
PremisecitationThe viscosity of water that is not in hydration layers but is likewise confined to subnanometre films by mica surfaces has an effective value comparable to η_H2O and so is also some two orders of magnitude smaller than η_eff.
“We emphasize that the viscosity of water that is not in hydration layers surrounding a charge, but is likewise confined to subnanometre films by mica surfaces, has an effective value that is comparable to Z H20 (ref.29) and so is also some two orders of magnitude smaller than Z eff .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [29] Raviv, U., Laurat, P. & Klein, J. Fluidity of water confined to sub-nanometre films. Nature 413, 51–54 (2001). source
May combine two claims.
Study design and conductreasoningThe relative offset of the opposing lattices was not controlled in the study, and the scatter in the F_s versus F_n plot is attributed to such differences between different experiments and contact points.
“This relative offset of the opposing lattices was not controlled in our study, and we attribute the scatter in the F s versus F n plot in Fig. 2b to such differences between different experiments and contact points.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningIn the low-load regime, D_l = 0.85±0.15 nm, the dissipation is in the sheared hydration shells themselves.
“the behaviour in the lower-load regime, D l ¼ 0.85±0.15nm, reveals the dissipation in the sheared hydration shells themselves.”
Quote in the paperSubstantial claim
The authors state this as an assumption.
The exchange time of water molecules in the hydration shell of Na+ can be taken as approximately the relaxation time of water within the hydration shells.
“The value of o H2O,Na þ E10 9 s À 1 corresponds to an exchange time t H2O,Na þ ¼ (1/o H2O,Na þ )E10 À 9 s, which may be taken as approximately the relaxation time of water within the hydration shells.”
The authors state this as an assumption.
Liquid viscosity is proportional to molecular relaxation times (η=Gτ) as long as the shear rate is much lower than τ^-1.
“On general grounds 30 , one expects liquid viscosity Z to be proportional to molecular relaxation times t, Z ¼ Gt (where G is a limiting high-frequency modulus), as long as the shear rate is much lower than t À 1 , as is the case in the present study.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
High-load separation has two stated uncertainties
MinorThe high-load separation is reported as 0.48 ± 0.16 nm in the Results but as 0.48 ± 0.15 nm in the Discussion. Both refer to D_h, so the stated uncertainty is inconsistent.
“D ¼ D h ¼ 0.48±0.16 nm (Methods)”
“The surface separation D h ¼ 0.48±0.15nm”
High-load logarithmic slope is attributed to the low-load figure
MinorThe Methods attribute the logarithmic slope used to estimate the activated volume to Fig. 4. The text identifies Fig. 4 as the low-load, approximately linear regime and places the high-load logarithmic data in Fig. 3.
“From the slope qF s /q(ln(n s ))E0.5 Â 10 À 6 N in Fig. 4, we extract a value for OE2 Â 10 À 23 m 3 .”
“In the lower loads regime, lower data set in Fig. 3 and on an expanded scale in Fig. 4, where D ¼ D l ¼ 0.85 ± 0.15 nm (Methods), the variation is much closer to linear, F s -F s,0 ¼ C.n s”
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An overview of functional biolubricants
Yang, L., Zhao, X., Ma, Z., Ma, S., & Zhou, F. (2022) · Friction · doi:10.1007/s40544-022-0607-8 · Cited by 50 · see citing works
“Friction 1(1): 1–23 (2013) [50] Ma L R, Gaisinskaya-Kipnis A, Kampf N, Klein J.”
Xu, J., & Li, J. (2015) · Friction · doi:10.1007/s40544-015-0100-8 · Cited by 49 · see citing works
“[24], Copyright 2015, Nature Publishing Group).”
Articular Cartilage‐Inspired Surface Functionalization for Enhanced Lubrication
Wang, Y., Sun, Y., Gu, Y., et al. (2019) · Advanced Materials Interfaces · doi:10.1002/admi.201900180 · Cited by 51 · see citing works
Supramolecular repair of hydration lubrication surfaces
Wang, Y., Sun, Y., Avestro, A., McGonigal, P. R., & Zhang, H. (2021) · Chem · doi:10.1016/j.chempr.2021.11.001 · Cited by 51 · see citing works
Contrasting Changes in Strongly and Weakly Bound Hydration Water of a Protein upon Denaturation
Hishida, M., Kaneko, A., Yamamura, Y., et al. (2023) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.3c02970 · Cited by 48 · see citing works
Yang, Y., & Zhang, H. (2024) · Advanced Functional Materials · doi:10.1002/adfm.202401547 · Cited by 51 · see citing works
Interfacial friction at action: Interactions, regulation, and applications
Yi, Z., Wang, X., Li, W., Qin, X., Li, Y., Wang, K., Guo, Y., Li, X., Zhang, W., & Wang, Z. (2023) · Friction · doi:10.1007/s40544-022-0702-x · Cited by 47 · see citing works
Zhang, T., Lu, Q., Zhang, X., Liu, S., Ye, Q., & Zhou, F. (2022) · Tribology International · doi:10.1016/j.triboint.2022.107737 · Cited by 45 · see citing works
Biomimetic chitosan nanoparticles with simultaneous water lubricant and anti-inflammatory
Yang, L., Huang, H., Zeng, H., Zhao, X., Wang, R., Ma, Z., Fan, Z., Liang, Y., Ma, S., & Zhou, F. (2022) · Carbohydrate Polymers · doi:10.1016/j.carbpol.2022.120503 · Cited by 46 · see citing works
Probing the frictional properties of soft materials at the nanoscale
Liamas, E., Connell, S. D., Ramakrishna, S. N., et al. (2019) · Nanoscale · doi:10.1039/c9nr07084b · Cited by 45 · see citing works
Recent understanding of solid-liquid friction in ionic liquids
He, Y., Li, H., Qu, C., Cao, W., & Ma, M. D. (2020) · Green Chemical Engineering · doi:10.1016/j.gce.2020.10.006 · Cited by 45 · see citing works
Research progress of cartilage lubrication and biomimetic cartilage lubrication materials
An, H., Liu, Y., Yi, J., Xie, H., Li, C., Wang, X., & Chai, W. (2022) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2022.1012653 · Cited by 43 · see citing works
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- Authors
- Ma, L., Gaisinskaya-Kipnis, A., Kampf, N., & Klein, J.
- Affiliations
- State Key Laboratory of Tribology (CN)
- Weizmann Institute of Science (IL)
- Corresponding author
- Klein, Jacob
- Venue
- Nature Communications
- Published
- 2015-01-14
- Volume
- 6
- Issue
- 1
- Pages
- 6060-6060
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W1991834170
- Cited by
- 390
- References
- 30
- Citations by year
- 2026: 30 · 2025: 47 · 2024: 66 · 2023: 36 · 2022: 50 · 2021: 33 · 2020: 37 · 2019: 32 · 2018: 17 · 2017: 18 · 2016: 14 · 2015: 9 · 2014: 1
- FWCI
- 13.20
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Nature Communications (publishedVersion)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- McCutchen Foundation
- Minerva Foundation
- Israel Science Foundation
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Electrostatics and Colloid Interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Force Microscopy Techniques and Applications
- Physical Sciences › Engineering › Mechanical Engineering › Lubricants and Their Additives
- Keywords
- hydration lubrication, friction, energy dissipation, hydration shell, biolubrication, hydrated ions, zwitterion, sliding friction, cartilage, joint lubrication, viscous losses, charged surfaces
- MeSH terms
- Joints, Lubrication, Models, Theoretical, Friction
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