The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

https://www.bc.edu/content/dam/files/schools/cas_sites/physics/pdf/Ren/p85.pdf

Advances in the science and technology of carbon nanotubes and their composites: a review

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Department of Materials Science, University of Patras, 26504 Rio Patras, Greece, Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vass. Constantinou Avenue, 116 35 Athens, Greece, Institut de Biologie Moleculaire et Cellulaire, UPR9021 CNRS, Immunologie et Chimie Therapeutiques, 67084 Strasbourg, France, and Dipartimento di Scienze Farmaceutiche, Universita di Trieste, Piazzale Europa 1, 34127 Trieste, Italy

Chemistry of Carbon Nanotubes

Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites

The curling of a graphitic sheet to form carbon nanotubes produces a class of materials that seem to have extraordinary electrical and mechanical properties. In particular, the high elastic modulus of the graphite sheets means that the nanotubes might be stiffer and stronger than any other known material, with beneficial consequences for their application in composite bulk materials and as individual elements of nanometre-scale devices and sensors. The mechanical properties are predicted to be sensitive to details of their structure and to the presence of defects, which means that measurements on individual nanotubes are essential to establish these properties. Here we show that multiwalled carbon nanotubes can be bent repeatedly through large angles using the tip of an atomic force microscope, without undergoing catastrophic failure. We observe a range of responses to this high-strain deformation, which together suggest that nanotubes are remarkably flexible and resilient.

Bending and buckling of carbon nanotubes under large strain

Magnetoresistance oscillations periodic with respect to the flux $\frac{h}{e}$ have been observed in submicron-diameter Au rings, along with weaker $\frac{h}{2e}$ oscillations. The $\frac{h}{e}$ oscillations persist to very large magnetic fields. The background structure in the magnetoresistance was not symmetric about zero field. The temperature dependence of both the amplitude of the oscillations and the background are consistent with the recent theory by Stone.

/pdf/observation-of-h-e-aharonov-bohm-oscillations-in-normal-2omj8vva47.pdf

Observation of h/e Aharonov-Bohm oscillations in normal-metal rings.

We review some of the recent surprising theoretical and experimental results obtained on the transport properties of small disordered metal samples. Even in the presence of disorder, the quantum mechanical interference of electron wavefunctions can still be observed. The Aharonov-Bohm effect is a particularly clear demonstration of this. In doubly connected structures (such as loops of wire) threaded by a magnetic flux, the electrical conductance oscillates because of the Aharonov-Bohm effect. In fact, because the electron trajectories are diffusive (i.e. random walks), even a lone wire (a singly connected structure) will exhibit a random pattern of conductance fluctuations as a function of the magnetic field because of the same interference effects. All that is required for the observation of these interferences is that the electrons retain ‘phase memory’ duing the period of transit through the sample. The length over which memory is maintained (the phase coherence length) can be much larger tha...

Aharonov-Bohm effect in normal metal quantum coherence and transport

is preferred over sliding, and it is expected to have an equally important role in the microscopic domain. Although progress has been made in our understanding of the dynamics of sliding at the atomic level 4 ,w e have no comparable insight into rolling owing to a lack of experimental data on microscopic length scales. Here we produce controlled rolling of carbon nanotubes on graphite surfaces using an atomic force microscope. We measure the accompanying energy loss and compare this with sliding. Moreover, by repro- ducibly rolling a nanotube to expose different faces to the substrate and to an external probe, we are able to study the object over its complete surface. The microscopic aspects of tribology have been explored by means of the surface force apparatus (SFA) 5 and atomic force microscopy (AFM) 6 , which have identified the intrinsic dependence of sliding friction on contact area 7,8 and crystallographic orientation 9,10 . Further, AFM has been used to perform friction mapping of surfaces with atomic resolution 4 and has identified stick-slip motion in the sliding of nanometre-scale objects 11 . Using AFM manipulation 12,13 of multiwall carbon nanotubes (CNTs), we have observed sliding and rolling. CNTs, with a range of available sizes down to the molecular scale, serve as interesting model systems for tribological studies. In addition, nanotubes are expected to play a part in future nanometre-scale electrical-mechanical devices, and rolling fullerenes have been proposed as ideal lubricants 14-16 . Our evidence for sliding and rolling comprises sequences of topogra- phical images of manipulated nanotubes and lateral force data acquired during the manipulation to measure energy loss. Samples were prepared by solvent evaporation on mica and graphite substrates from an ethanol solution of raw carbon soot produced by the carbon arc technique 17 . The multiwall CNTs were imaged and manipulated under ambient conditions. The nanomanipulator AFM system 18,19 , designed for manipulation, comprises an advanced visual interface, teleoperation capabilities for manual control of the AFM tip and haptic (touch) presentation of the AFM data (Topometrix Discoverer). Normal force, lateral force and AFM tip trajectory are recorded simultaneously for strict correlation. The AFM tip is used to apply lateral forces at locations along the tube to produce translations and rotations. These tubes are free of pinning material and move without deformation. The lateral force values have been calibrated from measured cantilever and tip geometry, literature values for the cantilever (Si) elastic moduli and the detector response from the z-translation of the cantilever. We estimate the absolute error in this calibration to be about 30%, with the largest contribution in the uncertainty coming

Nanometre-scale rolling and sliding of carbon nanotubes

We present a procedure for producing high-aspect-ratio cantilevered micro- and nanorod arrays of a PDMS-ferrofluid composite material. The rods have been produced with diameters ranging from 200 nm to 1 mum and aspect ratios as high as 125. We demonstrate actuation of these superparamagnetic rod arrays with an externally applied magnetic field from a permanent magnet and compare this actuation with a theoretical energy-minimization model. The structures produced by these methods may be useful in microfluidics, photonic, and sensing applications.

Sean Washburn

Papers

Bending and buckling of carbon nanotubes under large strain

Observation of h/e Aharonov-Bohm oscillations in normal-metal rings.

Aharonov-Bohm effect in normal metal quantum coherence and transport

Nanometre-scale rolling and sliding of carbon nanotubes

Magnetically actuated nanorod arrays as biomimetic cilia.