Abstract
Stick-slip, characterized by intermittent bursts of irregular signals of di erent amplitudes, durations and separations, is a common phenomenon observed in a variety of out-ofequilibrium disordered systems. Examples include the Barkhausen noise in soft magnetic materials, plastic deformation of crystals, the motion of rupture fronts, contact line pinning-depinning processes, and earthquakes. A common feature of the stick-slip phenomena is that the slip size exhibits a power-law distribution in a variety of macroscopic systems with di erent microscopic details of these systems. This nding has prompted many theoretical and experimental investigations aimed at nding some common mechanism or universal law underpinning these phenomena, which are also referred to as avalanche dynamics.
In this thesis, I report our atomic-force-microscopy (AFM) studies of the stick-slip dynamics in two model systems; one is a three-phase contact line (CL) moving over a solid ber surface and the other is frictional stick-slip at the area between two solids. For the rst system, we used a hanging- ber AFM to push a thin glass ber moving downward through a liquid-air interface and measured uctuations of the capillary force acting on the CL at the intersection between the liquid-air interface and the ber surface, which is coated by a layer of alkylsilane aggregates to generate a random pinning force eld for the CL. For the second system, we used a lateral AFM to drive a hanging-beam probe sliding over an ultra ne sandpaper surface under a normal load and measured uctuations of the frictional force between the probe and the sandpaper. The measured force curves as a function of traveling distance for both systems show clear sawtooth-like uctuations, which is a hallmark of the stick-slip motion in the systems. By analyzing the statistical properties of the force trajectories, we found three statistical laws applying to both systems. The maximum force Fc needed to trigger each slip event follows the generalized extreme value distribution, and the local force gradient k0 of the pinning force eld follows an exponential distribution. The slip length xs follows a power-law distribution but the power-law exponents for the two systems are di erent. For the moving CL, the measured exponent agrees with the prediction of the Alessandro{Beatrice{ Bertotti{Montorsi (ABBM) model, which is a mean- led theory for the avalanche dynamics in over-damped systems. For the solid friction, the measured exponent is smaller than that for the moving CL and can be explained by a new theoretical model for the motion of an under-damped spring-block under a Brownian-correlated pinning force eld. For the rst time, our study veri ed the prediction of the ABBM model for a moving CL system and revealed the novel statistical laws of stick-slip dynamics. These statistical laws may also be applied to other stick-slip systems. The under-damped spring-block model developed in the present study provides a long-sought physical mechanism for the avalanche dynamics in frictional stick-slip.
Furthermore, I report an experimental study of the rheology of the smectic liquid crystal (LC), which exhibits nonlinear rheological properties that are caused by the generation of focal conic defects (FCDs) in the system. Because of the complicated structures and interactions of the FCDs, the rheology of the smectic LC is usually described by an empirical power-law relation between the shear stress and shear rate. The origin of this nonlinear behavior has remained elusive.
In this work, we used the hanging- ber AFM to measure the shear stress acting on the moving ber surface and its relaxation when the ber suddenly stops its motion. It was found that the shear stress has two components: one is a viscous component, which decays exponentially with time and the other is an elastic component, which decays as a power-law with time. The viscous stress is proportional to the shear speed similar to a Newtonian uid, whereas the elastic stress has a constant term and a weak power-law term (with an exponent of 0:3). The superimposition of the two stresses gives rise to the commonly observed power-law with a larger power-law exponent of 0:6. With the simultaneous measurement of the steady-state stress and stress relaxation, we provided a quantitative description of the viscous e ect and elastic e ect of the smectic LC and explained the physical origin of its nonlinear rheology. Our work shed new light on the physical mechanism of the nonlinear rheology for a common type of viscoelastic material.
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