Self-Organized Criticality in Nanotribology
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SELF-ORGANIZED CRITICALITY IN NANOTRIBOLOGY Micha Adler1, John Ferrante2, Alan Schilowitz3, Dalia Yablon3, Fredy Zypman1 1Yeshiva
University, Department of Physics, 2495 Amsterdam Avenue, New York, NY 10033-3200, USA 3ExxonMobil Research and Engineering Co, Corporate Strategic Research, 1545 Route 22 East Annandale, NJ 08801, USA 2NASA-Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135, USA ABSTRACT We present experimental results on dry friction, which are consistent with the hypothesis that the stick-slip mechanism for energy release is described by self-organized criticality. The data, obtained with an Atomic Force Microscope set to measure lateral forces– examines the variation of the friction force as a function of time – or sliding distance. The materials studied were nominally flat surfaces of mica, quartz, silica and steel. An analysis of the data shows that the probability distribution of slip sizes follows a power law. Our data strongly supports the existence of self-organized criticality for nano-stick-slip in dry sliding friction. 1. INTRODUCTION The subject of the relationship between stick-slip in dry sliding friction and self-organized criticality (SOC) has raised some controversy in the last few years [1]. Today, the central question remains unanswered: to what extent is dry friction stick-slip a manifestation of SOC? The clarification of this issue has practical as well as fundamental implications. From the practical point of view, if stick-slip is indeed a mechanism for energy release in SOC, then the power law exponents can be used as parameters to characterize the tribological properties of surfaces. From a fundamental point of view, there is a growing interest to understand systems driven far away from equilibrium from a single unifying principle. There are experimental and theoretical studies, other than friction, that suggest that a many-degree of freedom system far from
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equilibrium organizes naturally in a critical state, releasing energy through fast relaxation events (avalanches) of different sizes, these sizes being distributed according to a power law probability density. The paradigm is the sand pile [2] in which grains of sand are slowly introduced at its apex. When the sand pile side slopes reach a threshold maximum angle, a critical state, energy is released in the pile through avalanches that keep the angle constant while moving additional material from the peak to the bottom of the pile. Similar studies have been performed on earthquakes [3,4], biological systems [5], the stock market [6], rainfall [7], and friction [8,9,10,11]. In the present study, we examine stick slip in dry friction using a Si tip of an Atomic Force Microscope (AFM), set to measure lateral forces. The probability distributions of slip sizes for quartz, silica, steel, and mica are examined for evidence of SOC. 2. EXPERIMENT A Digital Instruments Multimode AFM with a Si tip was right-left scanned in ambient conditions in a direction perpendicular to the cantilever, in contact mode
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