Theory of friction: Coulomb drag between two closely spaced solids

Persson, B. N. J.; Zhang, Zhenyu

doi:10.1103/physrevb.57.7327

Cited by 55 publications

(59 citation statements)

References 15 publications

(12 reference statements)

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“…al measured dissipation using a conducting probe over metal and quartz substrates at tip-sample separations down to 2 nm and temperatures from 4 -300K [3]. Friction over Au (111) was found to be 7 orders of magnitude larger than predicted by Coulomb drag theories [6]; several alternative mechanisms have been suggested [7][8][9]. In this Letter we explore noncontact friction over polymer films.…”

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confidence: 85%

Dielectric Fluctuations and the Origins of Noncontact Friction

2006

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Dielectric fluctuations underlie a wide variety of physical phenomena, from ion mobility in electrolyte solutions and decoherence in quantum systems to dynamics in glass-forming materials and conformational changes in proteins. Here we show that dielectric fluctuations also lead to noncontact friction. Using high sensitivity, custom fabricated, single crystal silicon cantilevers we measure energy losses over poly(methyl methacrylate), poly(vinyl acetate), and polystyrene thin films. A new theoretical analysis, relating non-contact friction to the dielectric response of the film, is consistent with our experimental observations. This work constitutes the first direct, mechanical detection of friction due to dielectric fluctuations.The fundamental relationship between random forces and friction plays a pivotal role in physics, chemistry, and biology. Surprisingly, the origin of force fluctuations and friction between objects in close proximity, but not in physical contact, remains poorly understood. Such non-contact friction is important in a variety of seemingly disparate fields, including micro-and nanomechanics, trapped ions for quantum computation, and measurements of quantum gravitation at small length scales. The non-contact friction measurements reported here are motivated by recent advances in the mechanical detection of magnetic resonance [1,2]; the sensitivity in these measurements has so far been limited by non-contact friction between a cantilever tip and the sample surface [3].The advent of high sensitivity single crystal silicon cantilevers [4,5] provides a new opportunity to elucidate the mechanisms of non-contact friction. These cantilevers' combination of low spring constant and low intrinsic losses enable the detection of non-contact friction with unprecedented sensitivity. Initial work on non-contact friction using high sensitivity cantilevers by Stipe et. al measured dissipation using a conducting probe over metal and quartz substrates at tip-sample separations down to 2 nm and temperatures from 4 -300K [3]. Friction over Au (111) was found to be 7 orders of magnitude larger than predicted by Coulomb drag theories [6]; several alternative mechanisms have been suggested [7][8][9]. In this Letter we explore noncontact friction over polymer films.A single high-sensitivity silicon cantilever was used as shown in Fig. 1(a). The cantilever approached the surface in a perpendicular orientation to avoid snap-in to contact [4] and the motion of the cantilever was parallel to the surface. The cantilever was 250m long, 5m wide, and 340 nm thick, with a spring constant k = 7 × 10 −4 N/m, a fundamental resonance frequency ω c /2π = 7.385 kHz, and a quality factor Q = 31000 ( Fig. 1(b)) [5]. The tip region of the cantilever has been thinned from 340 nm to < 100 nm using a reactive ion etch. The cantilever tip has a radius of ~ 30nm and has been coated with a thin layer of platinum using a shadow mask technique [4].We measure the total friction Γ t by recording the cantilever ringdown time τ, Fig. 1(c...

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confidence: 85%

Dielectric Fluctuations and the Origins of Noncontact Friction

2006

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“…A number of authors approached this question [10][11][12][13][14][15][16][17][18][19][20] with different and often contradictory conclusions, even questioning the possibility of quantum friction 20,21 as formulated by Pendry 14 in spite of several extensive studies, e.g., by Persson and Volokitin. [15][16][17][18]22,23 In order to ellucidate this question, we here provide a new derivation of energy dissipation rate and quantum friction using a completely nonlocal description of the dynamical response of a metallic slab.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal microscopic theory of quantum friction between parallel metallic slabs

2011

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We present a new derivation of the friction force between two metallic slabs moving with constant relative parallel velocity, based on T = 0 quantum-field theory formalism. By including a fully nonlocal description of dynamically screened electron fluctuations in the slab, and avoiding the usual matching-condition procedure, we generalize previous expressions for the friction force, to which our results reduce in the local limit. Analyzing the friction force calculated in the two local models and in the nonlocal theory, we show that for physically relevant velocities local theories using the plasmon and Drude models of dielectric response are inappropriate to describe friction, which is due to excitation of low-energy electron-hole pairs, which are properly included in nonlocal theory. We also show that inclusion of dissipation in the nonlocal electronic response has negligible influence on friction.

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“…Early theories modelled friction by considering interaction of surface features such as asperities [4,8,13,37,38], but static friction and stick-slip are observed even in asperity free and atomically smooth interfaces [35,29], and dissipation of energy via phonons seems to play a crucial role [35,48,11]. Other models attribute friction to a drag effect due to energy loss through phonon generation [3,9,41], or electronic drag not due to van der Waals forces but to currents in the electron cloud [39]. In seeking greater insight, attention turns to microscopic effects such as atom-scale deformations [49], macro-microscale stress interactions during relaxation [42], or third body effects of adsorbed molecules acting as pins [26], and building from these to reproduce macro-scale behaviour is where discontinuous models may help.…”

Section: Closing Remarks and Friction-inspired Modelsmentioning

confidence: 99%

“…[35,39,46,48]), and this is typical of interactions not only in mechanics, but in other physical, chemical and biological systems (e.g. [5,30,28,15,19]).…”

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confidence: 99%

On the mathematical basis of solid friction

Jeffrey

2015

Nonlinear Dyn

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Noname manuscript No.(will be inserted by the editor)The mathematical description of friction between solid bodies Mike R. Jeffrey May 8, 2014 Abstract A piecewise-smooth ordinary differential equation model of a dry-friction oscillator is studied, as a paradigm for the role of nonlinear and hysteretic terms in discontinuities of dynamical systems. The friction discontinuity is a switch in direction of the contact force in the transition between left and rightward slipping motion. Nonlinear terms introduce dynamics that is novel in the context of piecewise-smooth dynamical systems theory (in particular they are outside the standard Filippov convention), but are shown to account naturally for static friction, and moreover provide a simple route to including hysteresis. The nonlinear terms are understood in terms of dummy dynamics at the discontinuity, given a formal derivation here. The result is a three-parameter model built on the minimal mathematical features necessary to account for the key characteristics of dry friction. The effect of compliance can be distinguished from the contact model, and numerical simulations reveal that all behaviours persist under smoothing and under small random perturbations, but nonlinear effects can be made to disappear abruptly amid sufficient noise.

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Theory of friction: Coulomb drag between two closely spaced solids

Cited by 55 publications

References 15 publications

Dielectric Fluctuations and the Origins of Noncontact Friction

Dielectric Fluctuations and the Origins of Noncontact Friction

Nonlocal microscopic theory of quantum friction between parallel metallic slabs

On the mathematical basis of solid friction

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