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The inter-shell spacing of multi-walled carbon nanotubes was determined by analyzing the high resolution transmission electron microscopy images of these nanotubes. For the nanotubes that were studied, the inter-shell spacing ${\hat{d}_{002}}$ is found to range from 0.34 to 0.39 nm, increasing with decreasing tube diameter. A model based on the results from real space image analysis is used to explain the variation in inter-shell spacings obtained from reciprocal space periodicity analysis. The increase in inter-shell spacing with decreased nanotube diameter is attributed to the high curvature, resulting in an increased repulsive force, associated with the decreased diameter of the nanotube shells.Comment: 4 pages. RevTeX. 4 figure

We used the atomic force microscope to manipulate and unfold individual molecules of the titin I27 domain and reconstructed its free energy surface using Jarzynski's equality. The free energy surface for both stretching and unfolding was reconstructed using an exact formula that relates the nonequilibrium work fluctuations to the molecular free energy. In addition, the unfolding free energy barrier, i.e., the activation energy, was directly obtained from experimental data for the first time. This Letter demonstrates that Jarzynski's equality can be used to analyze nonequilibrium single-molecule experiments, and to obtain the free energy surfaces for molecular systems, including interactions for which only nonequilibrium work can be measured.

We stretched a DNA molecule using atomic force microscope and quantified the mechanical properties associated with B and S forms of double-stranded DNA (dsDNA), molten DNA, and single-stranded DNA (ssDNA). We also fit overdamped diffusion models to the AFM time series and used these models to extract additional kinetic information about the system. Our analysis provides additional evidence supporting the view that S-DNA is a stable intermediate encountered during dsDNA melting by mechanical force. In addition, we demonstrated that the estimated diffusion models can detect dynamical signatures of conformational degrees of freedom not directly observed in experiments.

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When analyzing single-molecule data, a low-dimensional set of system observables typically serve as the observational data. We calibrate stochastic dynamical models from time series that record such observables (our focus throughout is on a molecule's end-to-end distance). Numerical techniques for quantifying noise from multiple time scales in a single trajectory, including experimental instrument and inherent thermal noise, are demonstrated. The techniques are applied to study time series coming from both simulations and experiments associated with the nonequilibrium mechanical unfolding of titin's I27 domain. The estimated models can be used for several purposes: (1) detect dynamical signatures of "rare events" by analyzing the effective diffusion and force as a function of the monitored observable; (2) quantify the influence that experimentally unobservable conformational degrees of freedom have on the dynamics of the monitored observable; (3) quantitatively compare the inherent thermal noise to other noise sources, e.g. instrument noise, variation induced by conformational heterogeneity, etc.; (4) simulate random quantities associated with repeated experiments; (5) apply pathwise (i.e. trajectory-wise) hypothesis tests to assess the goodness-of-fit of models and even detect conformational transitions in noisy signals. These items are all illustrated with several examples.

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Molecular nanowires inside single-walled carbon nanotubes are produced by capillary filling. Bismuth was drawn into single-walled carbon nanotubes, where it formed single-crystal nanowires of nanometer dimensions. Metal was introduced in its gas, solution, and solid phases, with the solution phase process the most efficient and versatile method of filling. The majority of fillings are one-dimensional nanowires with high length to diameter ratios. The strong capillary effect in single-walled carbon nanotubes should allow these materials to host a wide variety of nanoscale materials.