Session H39: Student Prize Session followed by Focus Session: Friction

Restricted Defect Dynamics in Colloidal Peanut Crystals

We report that monolayers of hard peanut-shaped colloidal particles consisting of two connected spherical lobes order into a crystalline phase at high area fractions. In this ``lobe- close-packed'' (LCP) crystal, the peanut particle lobes occupy triangular lattice sites, much like close-packed spheres, while the connections between lobe pairs are randomly oriented, uniformly populating the three crystalline directions of the underlying lattice. Using optical microscopy, we directly observe defect nucleation and dynamics in sheared LCP crystals. We find that many particle configurations form obstacles blocking dislocation glide. Consequently, in stark contrast to colloidal monolayers of close-packed spheres, single dislocation pair nucleation is not the only significant energetic barrier to relieving an imposed shear strain. Dislocation propagation beyond such obstructions can proceed only through additional mechanisms such as dislocation reactions. We discuss the implications of such restricted defect mobility for the plasticity of LCP crystals.   

Elastic Theory of Defects in Toroidal Crystals

Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers and carbon nanomaterials. We investigate the structural properties of toroidal crystals and we provide a unified description based on the elastic theory of defects in curved geometries.   

Hopping Conduction and Bacteria: Transport Properties of Disordered Reaction-Diffusion Systems

Reaction-diffusion (RD) systems are used to model everything from the formation of animal coat patterns to the spread of genes in a population to the seasonal variation of plankton density in the ocean. In all of these problems, disorder plays a large role, but determining its effects on transport properties in RD systems has been a challenge. We present here both analytical and numerical studies of a particular disordered RD system consisting of particles which are allowed to diffuse and compete for resources ($2A\to A$) with spatially homogeneous rates, reproduce ($A\to2A$) in certain areas (``oases''), and die ($A\to0$) everywhere else (the ``desert''). In the low oasis density regime, transport is mediated through rare ``hopping events'' in which a small number of particles diffuse through the desert from one oasis to another; the situation is mathematically analogous to hopping conduction in doped semiconductors, and this analogy, along with some ideas from first passage percolation theory, allows us to make some quantitative predictions about the transport properties of the system on a large scale.   

Hard Discs on the Hyperbolic Plane

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.   

Experimental Observation of Quantized Vortex Reconnection and Turbulence in Superfluid Helium

We present experimental studies of the first direct visualization of reconnecting quantum vortices and the decay of superfluid turbulence in $^{4}$He. Micron-sized solid hydrogen particles are used for particle tracking. The cores of the superfluid vortices trap the hydrogen particles, thereby allowing direct visualization of the dynamics of the line-like defects. We generate superfluid turbulence by driving a thermal counterflow. After pulsing the counterflow, the system relaxes through a cascade of reconnection events. We examine the dynamics of pairs of particles trapped on reconnecting vortices and observe that these particles separate as power laws in time with a scaling exponent distributed about the predicted value of $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern- .15em\lower.25ex\hbox{$\scriptstyle 2$} $. We show that reconnection leads to power-law tails in the velocity probability distribution function, which is in stark contrast to the Gaussian tails that are ubiquitous in classical turbulence and thermal motion.   

Slippery or sticky boundary conditions: control of wrinkling in metal-capped thin polymer films by selective adhesion to substrates

As demonstrated by countless studies, sheets are more easily bent than stretched. Under planar forces, a thin sheet will thus deform out of plane by forming wrinkles. Surface buckling or wrinkling can be generated in various systems such as rigid thin films supported on elastomers, or gels that could be swollen or dried. Here, we describe an original and simple method to control the spatial layout of wrinkles in polymer/metal bilayer systems. To generate surfaces with a tailor-made buckling pattern, we have tuned the boundary conditions at the polymer-substrate interface by using chemically patterned substrates with highly contrasted surface free energies ($\gamma )$, easily produced by microcontact printing of alkanethiols on gold substrates. In addition, to explain our original variant of the experiments, we will also expand the existing mechanisms and models described in the literature to take into account the adhesion at the polymer-substrate interface.   

Shrinky Dinks : Dynamic Shape Transformations

Biaxially oriented polystyrene thermoplastic sheets (shrinky dinks) have been recently used by one of us (Khine, Lab on a Chip, 2008) as a template for rapid and non-photolithographic microfluidic pattern generation. This method utilizes the shrinkage properties of the shrinky dinks upon heating to generate microscale structures. During the heating process the sheets show a variety of non-trivial three dimensional intermediate structures before returning to a shrunken flat state upon completion of the process. We show that these structures arise due to the imposition of a non-uniform spatial metric on the sheet which in turn is governed by the dynamic temperature gradients generated in the sheet. Our results allow us to quantitatively describe the dynamic sequence of structures generated and suggest routes to the design and fabrication of different structures in a controllable fashion.   

The Roll of Friction in the Mechanical Failure Properties of a Polymer Particulate Composite

The mechanical failure properties of a composite containing an organic crystalline particulate and a polymer-plastizer binder have been investigated as a function of hydraulic pressure between 0.1 and 138 MPa. The results indicate that in a low pressure range between about 0.1 and 7.0 MPa crack processes are important in failure. The pressure dependence of the compressive strength is attributed to coulomb friction between surfaces of closed cracks$^{+}$, and from the observed linear increase of the strength with pressure a friction coefficient is obtained. Fiction coefficients can also be obtained from the ratio of compressive to tensile strength and in addition from the angle which the failure plane makes with the direction of the applied stress. both at 0.1 MPa$^{+}$. The friction coefficients obtained from these three separate observations are in agreement and this is taken as strong evidence for the importance of this friction in determining strength and mechanical failure for this composite. $^{+}$Dienes, J. K., 1983. J. Geophysical Research 88: 1173 -- 1179. Zuo, Q. H. and Dienes, J. K., 2002. LA-13962-MS.   

Force-driven transport in entropy barriers

We consider theoretically the transport of a point-sized Brownian particle in a two-dimensional channel with a slowly varying, periodic cross-section. Such channels are associated with the concept of an ``entropy barrier," where the change in the number of available ``states" for the Brownian particle governs the transport process. Using generalized Taylor-Aris dispersion theory and long-wavelength asymptotics, we exactly compute the mean particle velocity and effective diffusivity (dispersivity) for two cases: electrophoretic transport in an insulating channel and motion under the influence of a constant force. At the same time, we arrive at rational definitions for the concept of an entropy barrier as a function of the driving force. The agreement between simulations and the exact calculation for a constant force is excellent and represents a significant advance over existing models of the transport process.   

Friction and wear of nanocrystalline diamond coatings.

Nanocrystalline diamond films were tested for friction and wear response using a pin on disc tribometer. COF, starting with 0.7 successively drops to 0.1 as the wear progresses. Understanding this friction and wear response is important to minimize wear of these materials as tool coatings. SEM images at the periphery of wear tracks indicate the presence of ring cracks which are due to stress at the circle of contact exceeding the tensile strength. Effects of engineering the stress on the wear have been verified experimentally. Estimation of wear rate in these coatings is of high importance. AFM was used to obtain topography information on wear tracks of the film successively after 2K-200K pin revolutions in the tribometer. It is noted that peak heights of the asperities were decreasing with wear. Image analysis of the topographical evolution of the successive wear tracks could provide an estimation of the wear rate. This analysis also indicates that the distribution of asperity contact size shifts towards larger size with successive wear of the film. Previous studies of Krim, Hurtado and Kim revealed that the frictional stresses of individual asperities are dependent on the asperity contact sizes -- the larger the asperity contact size, the lower the frictional stresses. The micromechanics model of asperity friction explains well the decreasing of coefficient of friction with progression of wear.   

Ultra-high vacuum cryotribology of diamond and diamond-like films

We have used a sliding block tribometer (described in J.C. Burton, P. Taborek, and J.E. Rutledge, TRIBOLOGY LETTERS 23, 131, 2006) to measure the temperature dependence of the kinetic friction coefficient of single crystal diamond on various types of CVD diamond films including microcrystalline diamond, nanocrystalline diamond, and diamond-like carbon. We have also studied various other solid and fluid lubricants. These measurements have been performed in ultra-high vacuum and at temperatures ranging from 6 to 300 Kelvin. Although microcrystalline diamond has a low friction coefficient in air; in vacuum, the friction coefficient rises to approximately 0.7 and is independent of temperature. Nanocrystalline diamond is a much better tribological material in vacuum, particularly for T$>$240K. Near 240K there is a reversible transition to a higher friction state. We will discuss the correlation between the tribological properties and the material properties such as sp2/sp3 ratio, hydrogen content, and grain size. This work is supported by Extreme Friction: MURI AFOSR {\#} FA9550-04-1-0381   

Quartz Crystal Microbalance Studies of Temperature Rise in a Sliding Contact

The exact relation between temperature rise in a sliding contact and frictional energy dissipation is of great technological importance, but poorly understood at a fundamental level. Temperature rise is presumably due to frictional heating that results from phononic and electronic excitations, but efforts to relate temperature rise to friction and sliding velocity have proven very difficult. We have performed QCM studies of adsorbed Krypton monolayers, and also joint QCM-STM studies, to examine temperature rise associated with friction in two well characterized geometries. In the first, we utilized the static phase diagram of two-dimensional Kr adsorbed on graphite as compared to the dynamic phase diagram (with the Kr layer sliding) to determine temperature rise. In the second study, we have recorded frequency shift data for a QCM with indium electrodes in contact with an STM tip while increasing the sliding speed to a point where melting is indicated. A temperature rise on the order of 10 (40-100) degrees is observed in the first (second) geometry. Comparisons to theory yield plausible fit parameters.   

Combined ab initio and classical molecular dynamics simulations of the tribological properties of rare gas monolayers sliding on metal surfaces

Progress in the ability of understanding tribological properties in adsorbed film systems is of paramount importance to unravel fundamental issues in the emerging field of nanoscale science and technology. Many extensive studies have used a quartz-crystal microbalance (QCM) to measure the friction between adsorbed rare gas monolayers and metal substrates. In this work, we report a theoretical investigation of the tribological behavior of different rare gas-metal adsorbate systems, namely, Ar, Kr, Xe on Cu(111), and Xe on Ag(111), based on combined \textit{ab~initio} and classical molecular dynamics simulations. The frictional properties are analyzed in details as a function of system temperature, presence of interlayer defects, and load. The numerical simulations suggest that the simultaneous presence of thermal effects and of interlayer defects, lowering significantly the activation energy barrier, causes a considerable reduction of the static friction threshold. An unexpected dependence on load is also predicted. In particular, we show that friction of anticorrugating systems can be dramatically decreased by applying an external load [1]. The counterintuitive behavior that deviates from the macroscopic Amonton law is dictated by quantum mechanical effects that induce a transformation from anticorrugation to corrugation in the near-surface region. [1] M. C. Righi and M. Ferrario, Phys. Rev. Lett. \textbf{99}, 176101 (2007).   

Solid-fluid transitions at high sliding rates at Al/Al interfaces

Large scale NonEquilibrium Molecular Dynamics (NEMD) simulations (1.4 $10^{6}$ atoms) for single crystal Al have shown a transition as a function of sliding velocity from a defective solid phase to a fluid phase beyond a critical velocity, $v_{c}$, which depends very nearly linearly with the homologous temperature $T/T_{m}$ where $T_{m}$ is the melting temperature and $T$ is the sample temperature far from the interface. Above $v_{c}$, a Couette flow pattern develops with a slope which is independent of velocity. We discuss the properties of this transition and the power law dependence of the frictional force with velocity observed in this regime.