Abstract
Computer simulations of friction between polymer brushes are usually simplified compared to real systems in terms of solvents and geometry. In most simulations, the solvent is only implicit with infinite compressibility and zero inertia. In addition, the model geometries are parallel walls rather than curved or rough as in reality. In this work, we study the effects of these approximations and more generally the relevance of solvation on dissipation in polymer-brush systems by comparing simulations based on different solvation schemes. We find that the rate dependence of the energy loss during the collision of brush-bearing asperities can be different for explicit and implicit solvent. Moreover, the non-Newtonian rate dependences differ noticeably between normal and transverse motion, i.e., between head-on and off-center asperity collisions. Lastly, when the two opposing brushes are made immiscible, the friction is dramatically reduced compared to an undersaturated miscible polymer-brush system, irrespective of the sliding direction.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Milner S T. Polymer brushes. Science 251: 905–914 (1991)
Azzaroni, O. Polymer brushes here, there, and everywhere: Recent advances in their practical applications and emerging opportunities in multiple research fields. J Polym Sci Part A: Polym Chem 50: 3225–3258 (2012)
van der Waarden M. Stabilisation of carbon-black dispersions in hydrocarbons. J Colloid Sci 5: 317–325 (1950)
Stanislav J F. Use of polymers in oil recovery processes. In Proceedings of the First Conference of European Rheologists, Graz, Austria, 1982: 210–211.
Jain P, Baker G L, Bruening M L. Applications of polymer brushes in protein analysis and purification. Annu Rev Anal Chem 2: 387–408 (2009)
Chang Y, Liao S-C, Higuchi A, Ruaan R-C, Chu C-W, Chen W-Y. A highly stable nonbiofouling surface with well-packed grafted zwitterionic polysurfobetaine for plasma protein repulsion. Langmuir 24: 5453–5458 (2008)
Wattendorf U, Merkle H P. PEGylation as a tool for biomedical engineering of surface modified particles. J Pharm Sci 97: 4655–4669 (2008)
Cohen Stuart M A, Huck W T S, Genzer J, Müller M, Ober C, Stamm M, Sukhorukov G B, Szleifer I, Tsukruk V V, Urban M, Winnik F, Zauscher S, Luzinov I, Minko S. Emerging applications of stimuli-responsive polymer materials. Nature Mater 9: 101–113 (2010)
Bajpai A K, Shukla S K, Bhanu S, Kankane S. Responsive polymers in controlled drug delivery. Prog Polym Sci 33: 1088–1118 (2008)
Merlitz H, He G-L, Wu C-X, Sommer J-U. Nanoscale brushes: How to build a smart surface coating. Phys Rev Lett 102: 115702 (2009)
Tokareva I, Minko S, Fendler J H, Hutter E. Nanosensors based on responsive polymer brushes and gold nanoparticle enhanced transmission surface plasmon resonance spectroscopy. J Am Chem Soc 126: 15950–15951 (2004)
Yu Y, Kieviet B D, Kutnyanszky E, Vancso G J, de Beer S. Cosolvency-induced switching of the adhesion between poly(methyl methacrylate) brushes. ACS Macro Lett 4: 75–79 (2015)
Bureau L, Léger L. Sliding friction at a rubber/brush interface. Langmuir 20: 4523–4529 (2004)
Chen M, Briscoe W H, Armes S P, Klein J. Lubrication at physiological pressures by polyzwitterionic brushes. Science 323: 1698–1701 (2009)
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 5: 3781 (2014)
Klein J, Kumacheva E, Mahalu D, Perahia D, Fetters L J. Reduction of frictional forces between solid surfaces bearing polymer brushes. Nature 370: 634–636 (1994)
Lee S, Spencer N D. Aqueous lubrication of polymers: Influence of surface modification. Tribol Int 38: 922–930 (2005)
Li A, Benetti E M, Tranchida D, Clasohm J N, Schönherr H, Spencer N D. Surface-grafted, covalently cross-linked hydrogel brushes with tunable interfacial and bulk properties. Macromolecules 44: 5344–5351 (2011)
O’Shea S J, Welland M E, Rayment T. An atomic force microscope study of grafted polymers on mica. Langmuir 9: 1826–1835 (1993)
Sui X, Zapotoczny S, Benetti E M, Schön P, Vancso G J. Characterization and molecular engineering of surface-grafted polymer brushes across the length scales by atomic force microscopy. J Mater Chem 20: 4981–4993 (2010)
Moro T, Takatori Y, Ishihara K, Konno T, Takigawa Y, Matsushita T, Chung U-I, Nakamura K, Kawaguchi H. Surface grafting of artificial joints with a biocompatible polymer for preventing periprosthetic osteolysis. Nature Mater 3: 829–836 (2004)
Lee S, Spencer N D. Sweet, hairy, soft, and slippery. Science 319: 575–576 (2008)
Jones E. Joint lubrication. Lancet 223: 1426 (1934)
McCutchen C W. The frictional properties of animal joints. Wear 5: 1–17 (1962)
Wilkins J. Proteolytic destruction of synovial boundary lubrication. Nature 219: 1050–1051 (1968)
Alexander S. Adsorption of chain molecules with a polar head a scaling description. J Phys-Paris 38(8): 983–987 (1977)
de Gennes P G. Conformations of polymers attached to an interface. Macromolecules 13: 1069–1075 (1980)
Milner S T, Witten T A, Cates M E. Theory of the grafted polymer brush. Macromolecules 21: 2610–2619 (1988)
Binder K, Kreer T, Milchev A. Polymer brushes under flow and in other out-of-equilibrium conditions. Soft Matter 7: 7159–7172 (2011)
Murat M, Grest G S. Interaction between grafted polymeric brushes: A molecular-dynamics study. Phys Rev Lett 63: 1074–1077 (1989)
Grest G S. Interfacial sliding of polymer brushes: A molecular dynamics simulation. Phys Rev Lett 76: 4979–4982 (1996)
Kreer T, Müser M H, Binder K, Klein J. Frictional drag mechanisms between polymer-bearing surfaces. Langmuir 17: 7804–7813 (2001)
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 26: 6418–6429 (2010)
Spirin L, Galuschko A, Kreer T, Johner A, Baschnagel J, Binder K. Polymer brush lubrication in the limit of strong compression. Eur Phys J E 33: 307–311 (2010)
de Beer S. Switchable friction using contacts of stimulus-responsive and nonresponding swollen polymer brushes. Langmuir 30: 8085–8090 (2014)
Klein J. Shear, friction and lubrication forces between polymer-bearing surfaces. Annu Rev Mater Sci 26: 581–612 (1996)
Léger L, Raphaël E, Hervet H. Surface-anchored polymer chains: Their role in adhesion and friction. Adv Polym Sci 138: 185–225 (1999)
Maeda N, Chen N, Tirrell M, Israelachvili, J N. Adhesion and friction mechanisms of polymer-on-polymer surfaces. Science 297: 379–382 (2002)
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 9: 7234–7241 (2013)
Wang N, Trunfio-Sfarghiu A-M, Portinha D, Descartes S, Fleury E, Berthier Y, Rieu J-P. Nanomechanical and tribological characterization of the MPC phospholipid polymer photografted onto rough polyethylene implants. Colloids Surf B 108: 285–294 (2013)
Briels W J. Transient forces in owing soft matter. Soft Matter 5: 4401–4411 (2009)
Persson B N J. Theory of rubber friction and contact mechanics. J Phys Chem 115: 3840 (2001)
Tabor, D. Hysteresis losses in the friction of lubricated rubber. Rubber Chem Technol 33: 142–150 (1958)
Nommensen P A, Duits M H G, van den Ende D, Mellema J. Steady shear behavior of polymerically stabilized suspensions: Experiments and lubrication based modeling. Phys Rev E 59: 3147–3154 (1999)
Balko S M, Kreer T, Costanzo P J, Patten T E, Johner A, Kuhle T L, Marques C M. Polymer brushes under high load. PLoS ONE 8: e58392 (2013)
Klein J, Kamiyama Y, Yoshizawa H, Israelachvili J N, Fredrickson G H, Pincus P, Fetters L J. Lubrication forces between surfaces bearing polymer brushes. Macromolecules 26: 5552–5560 (1993)
Drummond C. Electric-field-induced friction reduction and control. Phys Rev Lett 109: 154302 (2012)
Koplik J, Banavar J R. Slip, immiscibility and boundary conditions at the liquid-liquid interface. Phys Rev Lett 96: 044505 (2006)
de Beer S, Müser M H. Friction in (im-) miscible polymer brush systems and the role of transverse polymer tilting. Macromolecules 47: 7666–7673 (2014)
Lo Verso F, Yelash L, Egorov S A, Binder K. Interactions between polymer brush-coated spherical nanoparticles: The good solvent case. J Chem Phys 135: 214902 (2011)
Persson B N J, Albohr O, Tartaglino U, Volokitin A I, Tosatti E. On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J Phys: Condens Matt 17: R1–R62 (2005)
Kong L-T, Denniston C, Müser M H. The crucial role of chemical detail for slip-boundary conditions: Molecular dynamics simulations of linear oligomers between sliding aluminum surfaces. Modelling Simul Mater Sci Eng 18: 034004 (2010)
Grest G S, Kremer K. Molecular dynamics simulation for polymers in the presence of a heat bath. Phys Rev A 33: 3628 (1986)
He G, Müser M H, Robbins M O. Adsorbed layers and the origin of static friction. Science 284: 1650–1652 (1999)
Priezjev N V, Troian S M. Molecular origin and dynamic behavior of slip in sheared polymer films. Phys Rev Lett 92: 018302 (2004)
Mukherji D, Marques C M, Kremer K. Polymer collapse in miscible good solvents is a generic phenomenon driven by preferential adsorption. Nat Commun 5: 4882 (2014)
Kremer K, Grest G S. Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. J Chem Phys 92: 5057 (1990)
Humphrey W, Dalke A, Schulten K. VMD: Visual molecular dynamics. J Molec Graphics 14: 33–38 (1996)
Descas R, Sommer J-U, Blumen A. Grafted polymer chains interacting with substrates: Computer simulations and scaling. Macromol Theory Simul 17: 429–453 (2008)
Binder K, Milchev A. Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and interpret experiments. J Polym Sci Part B: Polym Phys 50: 1515–1555 (2012)
Murat M, Grest G S. Polymers end-grafted onto a cylindrical surface. Macromolecules 24: 704–708 (1991)
Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comp Phys 117: 1–19 (1995)
Groot R D, Warren P B. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107: 4423–4435 (1997)
Pastorino C, Kreer T, Müller M, Binder K. Comparison of dissipative particle dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems. Phys Rev E 76: 026706 (2007)
Flory P J. Thermodynamics of high polymer solutions. J Chem Phys 10: 51 (1942)
Huggins, M. L. Ann. N.Y. Thermodynamic properties of solutions of long-chain compounds. Acad Sci 43: 1–32 (1942)
Thompson P A, Robbins M O. Shear flow near solids: Epitaxial order and flow boundary conditions. Phys Rev A 41: 6830 (1990)
Auroy P, Mir Y, Auvray L. Local structure and density profile of polymer brushes. Phys Rev Lett 69: 93–95 (1992)
Lai P-Y, Binder K. Structure and dynamics of grafted polymer layers: A Monte Carlo simulation. J Chem Phys 95: 9288 (1991)
Murat M, Grest G S. Structure of grafted polymeric brushes in solvents of varying quality: A molecular dynamics study. Macromolecules 26: 3108–3117 (1993)
Cohen Stuart M A, de Vos W M, Leermakers F A M. Why surfaces modified by exible polymers often have a finite contact angle for good solvents. Langmuir 22: 1722–1728 (2006)
Dhinojwala A, Cai L, Granick S. Critique of the friction coefficient concept for wet (lubricated) sliding. Langmuir 12: 4537–4542 (1996)
Ringlein, J., and Robbins, M. O. Understanding and illustrating the atomic origins of friction. Am J Phys 72: 884–891 (2004)
Yoshizawa H, Chen Y-L, Israelachvili J N. Fundamental mechanisms of interfacial friction. 1. Relation between adhesion and friction. J Phys Chem 97: 4128–4140 (1993)
Brenner H. The slow motion of a sphere through viscous fluid towards a plane surface. Chem Eng Sci 16: 242–251 (1961)
Schindler M. A numerical test of stress correlations in fluctuating hydrodynamics. Chem Phys 375: 327–336 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is published with open access at Springerlink.com
Sissi de BEER. She obtained her PhD degree in the Physics of Complex Fluids Group of the University of Twente, the Netherlands, in 2011. Her PhD thesis describes atomic force microscopy experiments and molecular dynamics (MD) simulations of confined simple liquids. From 2011 till 2013, she worked as a postdoctoral fellow at the Jülich Supercomputing Centre (Forschungszentrum Jülich) focusing on MD simulations to study polymer brush friction. Since November 2013, Sissi is a research associate in the Materials Science and Technology of Polymers Group of the University of Twente, where she now combines simulations with experimental techniques to understand the (tribo-)mechanical response and absorptive properties of polymer brushes in (bio-)technical applications.
Martin H. MÜSER. He received his diploma in physics from Saarland University, Germany, in 1992 and his Ph.D degree in theoretical physics from Johannes Gutenberg University Mainz in 1995. He spent his postdoctoral time in the Department of Chemistry at Columbia University and in the Physics & Astronomy Department at the Johns Hopkins University. In 2002, he became a professor of applied mathematics at Western University in London, Ontario. After a sabbatical year at IBM, T. J. Watson, New York, he moved to Saarland University in 2009, where he holds the chair of material simulations in the Department of Material Science and Technology. Since 2011, he also heads the Computational Materials Research Group at the Supercomputing Centre of Forschungszentrum Jülich.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
de Beer, S., Kenmoé, G.D. & Müser, M.H. On the friction and adhesion hysteresis between polymer brushes attached to curved surfaces: Rate and solvation effects. Friction 3, 148–160 (2015). https://doi.org/10.1007/s40544-015-0078-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40544-015-0078-2