Continuum theory for the piezoelectric response of chiral nanotubes under uniaxial and torsional stresses

We develop and solve a continuum theory for the piezoelectric response of nanotubes under applied uniaxial and torsional stresses. We find that the piezoelectric response is controlled by the chiral angle, the aspect ratio, and two dimensionless parameters specifying the ratio of the strengths of the electrostatic and elastic energies. The model is solved in two limiting cases and the solutions are discussed. These systems are found to have several unexpected physical effects not seen in conventional bulk systems, including a strong stretch-twist coupling and the development of a significant bound charge density in addition to a surface charge density. The model is applied to estimate the piezoelectric response of a boron-nitride nanotube under uniform tensile stress.Comment: 8 pages, 4 figures. Submitted to Physical Review

Carbon Nanotubes in Helically Modulated Potentials

We calculate effects of an applied helically symmetric potential on the low energy electronic spectrum of a carbon nanotube in the continuum approximation. The spectrum depends on the strength of this potential and on a dimensionless geometrical parameter, P, which is the ratio of the circumference of the nanotube to the pitch of the helix. We find that the minimum band gap of a semiconducting nanotube is reduced by an arbitrarily weak helical potential, and for a given field strength there is an optimal P which produces the biggest change in the band gap. For metallic nanotubes the Fermi velocity is reduced by this potential and for strong fields two small gaps appear at the Fermi surface in addition to the gapless Dirac point. A simple model is developed to estimate the magnitude of the field strength and its effect on DNA-CNT complexes in an aqueous solution. We find that under typical experimental conditions the predicted effects of a helical potential are likely to be small and we discuss several methods for increasing the size of these effects.Comment: 12 pages, 10 figures. Accepted for publication in Physical Review B. Image quality reduced to comply with arxiv size limitation

Continuum Theory for Piezoelectricity in Nanotubes and Nanowires

We develop and solve a continuum theory for the piezoelectric response of one dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in BN nanotubes. We find that the polarization of a nanotube depends on its aspect ratio, and a dimensionless constant specifying the ratio of the strengths of the elastic and electrostatic interactions. The solutions of the model as these two parameters are varied are discussed. The theory is applied to estimate the electric potential induced along the length of a BN nanotube in response to a uniaxial stress.Comment: 4 pages in RevTex4, 2 epsf figure

Rostral Middle Frontal Gyrus Thickness is Associated with Perceived Stress and Depressive Symptomatology

Elevated stress perception and depression commonly co-occur and have shared genetic and environmental influences, suggesting they may rest upon a common underlying neurobiology. The rostral middle frontal gyrus (RMFG), part of the dorsolateral prefrontal cortex, is critical for executive function, including emotion regulation and working memory. Variability in RMFG cortical thickness has been associated with both depression and stress-related phenotypes, although the directionality of these associations has been inconsistent thus far. The current study examined healthy participants (n=879) who completed the ongoing family-based Human Connectome Project were included in analyses. RMFG cortical thickness was computed from structural magnetic resonance imaging (MRI) scans using FreeSurfer. Depression symptoms, positive affect, personality traits, and perceived stress were assessed using self-report questionnaires: the PROMIS depression scale, the PANAS-X, and the PSS, respectively. After accounting for effects of sex, age, ethnicity, average whole-brain cortical thickness, twin status, and familial structure, as well as correcting for multiple tests, bilateral RMFG thickness was associated with increased perceived stress (left RMFG: p=.0017; right RMFG: p=.0013). Moreover, left RMFG cortical thickness was significantly positively associated with depressive symptoms (p=.0053) and negatively associated with positive affect at levels approaching significance after correcting for multiple testing (p=.0196). Follow-up simultaneous linear models revealed unique associations between bilateral RMFG cortical thickness and perceived stress when accounting for associations with positive affect and depressive symptoms. Heritability analyses showed that bilateral RMFG thickness, depressive symptoms, and perceived stress were all significantly heritable. After decomposing variability between the constructs, shared genetic and environmental contributions to variability were observed among self-reported sadness, positive affect, and perceived stress, as well as between right and left RMFG cortical thickness. Collectively, these findings suggest that increased RMFG cortical thickness is associated with depressive symptoms and linked to the subjective perception of stress. More broadly, these results suggest that stress perception and depressive symptoms share a common underlying biology. What remains unclear from this cross-sectional study is the origin of individual differences in RMFG cortical thickness: it is possible that stress exposure and/or the presence of depressive symptoms may give rise to differences in brain structure, or it may be the case that increased RMFG thickness contributes to stress-related cognitive biases that promote vulnerability to depression