Rolling Moment Resistance of Particles on Surfaces

In the brief presentation attached, I am summarizing my lab's recent work in the field of adhesion and work-of-adhesion measurements, and hoping to see who else is working in the field.  Here is some intro to the topic (by no means, it is complete - maybe we can add some recent work to this list as discussions develop)

 Rolling resistance moment is a restoration moment that opposes the rotational motion of a particle adhered on a surface. Particle removal and strength/stability of particle networks depend on rolling resistance more than axial adhesion since the rolling forces are few orders of magnitude lower than the axial detachment forces.   Rolling resistance moment of an adhesion bond between a particle and flat substrate controls the motion of particles on surfaces, the strength/stability of network of adhered round objects in a diverse spectrum of applications (e.g. particles, powders, blood cells and nanotubes) on micro/nano-scale as in sintering and compaction. Also, it is essential in detachment and removal of micro/nano-particles from surfaces.  Many adhesion models and theories have been proposed and discussed to understand the axial (out-of-plane) stiffness and strengths of particle-surface bonds. In [1], a unifying framework for existing theories (namely, Hertz, JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov), M-D (Maugis- Dugdale)) is proposed and transition between these theories and their applicability zones is established for ranges of external loads and an elasticity parameter. In one-dimensional (axial) adhesion models and theories the pressure field in the contact area is assumed symmetric. Studying particle rolling, however, requires a two-dimensional adhesion model and analysis where the stress at the bond interface is asymmetric during pre-rolling and rolling.  In [2] an expression for this rolling moment was derived by considering an external force applied at the centre of the spherical particle. This external force creating a moment with respect to the bond zone causes an asymmetric pressure distribution in the contact area, resulting in the pressure variations in contact area at the leading edge and at the trailing edge of the contact with the surface. The resulting asymmetric pressure field in the contact area creates a restoring moment in small rotational angles. Under external excitation, this restoring force along with the rotational inertia of the particle could result in free oscillatory vibrations of the particle with respect to its contact [3, 4]. In spite of the fact that extensive research has been dedicated for measuring the adhesion force between a particle and a substrate by detaching particles using AFM techniques, the rolling motion and resistance of a particle on a substrate has rarely been experimentally explored. The main disadvantage of axial detachment based-AFM techniques in such experiments is that the particle has to be fixed/glued to the tip of a probe; therefore it is essentially a destructive technique for the particle. Rolling resistance moment is particularly critical for various applications from biology to semiconductor manufacturing since it controls the stability of network of adhered round objects (e.g. particle, cells and nanotubes) on micro/nano-scale. While the rolling resistant moment can be estimated based on the adhesion model [2] and experimental method based on ultrasonic base excitation is reported in [3, 4].  Adhesion and frictional forces between spherical micron sized particles on the basis of rolling resistance moment and atomic force microscopy was studied in the past [5]. The rolling resistance moment and hence the adhesion force between a micro-particle on a substrate was determined in the past based on acoustic excitation and interferometric sensing [3, 4].  Many argue that this (detachment distance/the shift in contact area ξ) should be related to the lattice size and/or the molecular length of the particle and surface materials. However, there is no theoretical prediction for this critical value. 

Particle adhesion and force studies were performed with the aid of micromanipulators in the past [6, 7, 8]. For example, Saito et al analyzed the interaction forces between the microsphere, the substrate and the manipulation probe, and proposed a method to pickup and manipulate a microsphere [6]. They also suggested the existence of a maximum rolling resistance, i.e., an external moment has to be grater than a certain threshold to roll a particle.  Sitti performed pushing study on 500 nm Au-coated latex particles on a silicon substrate with atomic force microscope (AFM) probe [8]. The sliding, rolling and rotation motion of the particles were observed, and the particle-substrate frictional properties were estimated. No rolling resistance data was provided while its effect in the control loop was reported. However, the pushing process cannot be visually observed in situ in real-time because the pushing and imaging processes uses the same AFM cantilever probe.

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