Rod Number Density Research Articles

Diffusion of Rodlike Polymers: Pulsed Gradient Spin Echo NMR of Poly(γ-stearyl-α,l-glutamate) Solutions and the Importance of Helix Stability.

Many natural and synthetic polymers and particles have a rodlike shape, leading to important and intriguing solution behavior, such as high intrinsic viscosities and liquid crystalline phases. Much of what is known about suspensions of rods has been learned by studying helical polypeptides, even though such molecules are not perfectly rigid, smooth cylinders. Previous optical tracer self-diffusion studies of poly(γ-benzyl-α,l-glutamate) (PBLG) revealed that the molecule initially resists topological constraints imposed by neighboring molecules, but diffusion strongly decreases as concentration rises beyond a certain number density. In contrast, the tracer self-diffusion coefficient of truly rigid tobacco mosaic virus begins decreasing immediately with concentration. We used pulsed gradient spin echo NMR to measure another polypeptide, poly(γ-stearyl-α,l-glutamate) (PSLG), to gain physical insight into the question of polypeptide diffusion in crowded isotropic solutions. The PSLG molecule, with long alkyl sidechains, is semiflexible like PBLG but does not exhibit the same ability to evade topological constraints. Instead, PSLG follows a simple exponential decay, D/ DKR = A e(-κν/ν*) + B, where DKR is the Kirkwood-Riseman expectation for rod diffusion, ν is the number density of rods, ν* is the Onsager expectation for the number density at the onset of liquid crystal formation, A = 1 ± 0.1, B = 0.1 ± 0.01, and κ = 4.5 ± 0.5. The results emphasize the importance of helix stability when choosing rodlike polypeptides as model systems, particularly with regard to the chain ends.

Systematic analysis for electrical conductivity of network of conducting rods by Kirchhoff's laws and block matrices

In recent years, high-aspect-ratio materials, such as metallic nanowires and carbon nanotubes, have become attractive alternatives for the next generation of transparent conductive films. The functionality of the films is represented by their opto-electric performance, which is primarily affected by the nano- or micro-structures inside the films. In this study, we focus on the analysis of the electrical conductivity of two-dimensional networks of conducting rods by treating parts of the networks as a linear circuit system. For the analysis, multi-nodal representation is used to assign the nodes and edges of the circuit. Based on Kirchhoff's laws, the relation between the current and electrical potential is formulated using a block matrix equation. After a series of block-matrix manipulations, the equation can be reduced to yield several simple equations expressed in terms of the incidence matrices and the weighted graph Laplacians. Among these, the equation representing the Ohm's-law-like relation between the total current and the bias voltage can be used to derive the explicit expression for the normalized conductivity, which can quantify the effect of the network. During the analysis, we also deduce the normalized number of edges, that is, the combination of variables used in the system. The normalized number of edges can be related to the reduced number density of rods by using a proper statistical model. Moreover, we found the direct relation between the normalized number of edges and the backbone fraction, which is a representative quantity related with the electrical conductivity.

Mechanistic constitutive model for wormlike micelle solutions with flow-induced structure formation

We present a tensor constitutive model for predicting stress and flow-induced structure formation in dilute wormlike micellar solutions. The micellar solution is treated as a dilute suspension of rigid Brownian rods whose length varies dynamically. Consistent with the mechanism presented by Turner and Cates [J. Phys.: Condens. Matter 4, 3719 (1992)], flow-induced alignment of the rods is assumed to promote increase of rod length that corresponds to the formation of flow-induced structures observed in experiments. At very high deformation rate, hydrodynamic stresses causes the rod length to decrease. These mechanisms are implemented in a phenomenological equation governing the evolution of rod length, with the number density of rods appropriately modified to ensure conservation of surfactant mass. The model leads first to an increase in both shear and extensional viscosity as deformation rate increases and then to a decrease at higher rates. If the rate constant for flow-induced rod growth is sufficiently large, the model predicts a multivalued relation between stress and deformation rate in both shear and uniaxial extension. Predictions for shear and extensional flow at steady state are in reasonable agreement with experimental results. By design, the model is simple enough to serve as a tractable constitutive relation for computational fluid dynamics studies.

Second virial coefficient of rod-shaped molecules and molecular dynamics simulations of the isotropic phase.

The second virial coefficient, B(2) is computed of linear rigid rods composed of m equally spaced sites interacting with sites on other rods via the hard-sphere or Weeks-Chandler-Andersen (WCA) pair potentials. The dependence of B(2) on a wide range of separation distance between the sites L and m for both types of potential is computed. Molecular dynamics simulations were carried out of the thermodynamic, static, and percolation properties of the WCA rigid rods in the isotropic phase as a function of rod number density ρ. Simple scaling relationships are discovered between thermodynamic and other static properties as a function of ρ and m, which extend well into the semidilute density range. The percolation threshold distance (PTD) between the centers of mass of the rods complies well with a mean-field random orientation approximation from low density well into the semidilute regime. The corresponding site-site PTD proved more problematic to represent by simple functions, but at high rod density, scales better with the number of sites density rather than the rod number density.

Kinetic theory and simulations of active polar liquid crystalline polymers

A kinetic model is derived for active polar liquid crystalline polymers, that is, ensembles of polar, large molecular weight, rigid rod, “swimmers” in a viscous solvent. The model couples polarity and particle-activation physics to the Doi–Hess theory for passive liquid crystalline polymers (LCP). Our model extends the polar hydrodynamic liquid crystal model of the Marchetti group to active large molecular weight rods at arbitrary equilibrium volume fractions. The Doi–Hess–Smoluchowski equation inherits contributions due to spatial inhomogeneity and translational diffusion of the rod number density, rod polarity and self-propulsion, and the hydrodynamic equations inherit additional extra stress contributions. By suppression of LCP physics, our model recovers kinetic and mesoscopic active suspension theories of athermal, polar and apolar, micron-scale swimmers. The authors' full orientation space, 2D physical space, Smoluchowski–Navier–Stokes solver is generalized to the new model and implemented on the full system of 125 nonlinear PDEs from which we explore the coupling of rotational and translational diffusion, nano-rod density gradients, polarity and self-propulsion, and flow feedback through polar and nematic stresses. For this paper, results are presented for the dilute regime where the stable passive isotropic phase is driven far from equilibrium by activation physics, the analog of non-Brownian active “pusher” suspensions. We present a rich family of excitable and stationary patterns, previously seen in Landau–de Gennes-type coarse-grained models of apolar and polar active nematics and boundary-driven passive nematics at semi-dilute concentrations where the passive isotropic state is unstable. We find fluctuating, periodic and stationary patterns, including 1D banded and diverse 2D patterns, tunable by the relative strengths of rotational and translational diffusivity with all other physical parameters held constant.

LCP droplet dispersions: a two-phase, diffuse-interface kinetic theory and global droplet defect predictions

Advanced, predictive numerical tools for liquid crystalline polymers (LCPs) are well established. These tools yield descriptive features (steady and unsteady behavior, gradient morphology) of LCPs in the bulk and in confined geometries; some are applicable to LCP hydrodynamics. Our goal here is to expand the hydrodynamic toolkit (a predictive theory, algorithms, and simulations) to two-phase fluids consisting of an immiscible LCP phase (initialized as droplets) dispersed in a viscous or polymeric phase. To do so, we bridge the modeling and simulation gap between molecular dynamics and Monte Carlo discrete lattice models for polymer-dispersed liquid crystal (LC) droplets and continuum scale, diffuse interface methods for LC droplets in viscous fluids. We give a brief overview of molecular-to-continuum scales of modeling and simulations for single LCP phases, and of their relative benefits and limitations. We likewise recall the sharp versus diffuse interface methods for coupling of two immiscible fluid phases in a hydrodynamic theory. From this assessment, we present a kinetic scale, diffuse interface strategy for hydrodynamic simulations of LCP droplet dispersions. The Fokker–Planck or Smoluchowski equation due to Doi and Hess for the orientational distribution function of the LCP phase is generalized to a two-phase, energy-based theory. Although feasible for simulations by adaptation of existing kinetic solvers, we first put the two-phase kinetic model through analogous preliminary benchmarks that were applied to the Doi–Hess theory for LCPs. We project onto the scalar zeroth moment and tensorial second-moment of the rod number density function to achieve a generalized Landau-deGennes two-phase model for equilibria and imposed shear of LCP droplets in a viscous fluid. A numerical algorithm in two space dimensions is developed and implemented to study global droplet defect structure versus interfacial anchoring energy. Simulations reveal topological defects (surface boojums for tangential anchoring and interior degree 1/2 or radial defects for normal anchoring) and details of their respective cores. These predictions support the hypothesis in [I. Lin et al., Science, 2011, 332, 1297–1300] that anchoring boundary conditions between the LCP and surrounding fluid phase can be satisfied by the formation of extremely localized defect cores which self-organize the orientational order external to the cores, without the need for bend-splay-twist mediated, continuous elastic strain.

Low-frequency electrostatic wave in a metallic electron-hole-ion plasma with nanoparticles

AbstractWe investigate the dispersion property of a low-frequency electrostatic wave in a dense metallic electron-hole-ion plasma with nanoparticles. The latter are charged due to the field emission, and hence the metallic nanoparticles/nanotubes can be regarded as charged dust rods surrounded by degenerate electrons and holes, and non-degenerate ions. By using a quantum hydrodynamic model for the electrons and holes, we obtain the electron and hole number density perturbations, while the ion and dust rod number density perturbations follow the classical expressions. A dispersion relation for the low-frequency electrostatic wave in our multi-species dense metallic plasma is derived and analyzed. The possibility of exciting non-thermal electrostatic waves is also discussed.

Catalyst-free growth and characterization of gallium nitride nanorods

Self-assembled high-density gallium nitride (GaN) nanorod arrays have been grown on (0 0 0 1) Al 2O 3 substrates by metal-organic molecular beam epitaxy (MOMBE) using radio-frequency radical nitrogen. The corresponding microstructure and optical properties of nanorods were investigated by scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), energy-dispersive spectroscopy (EDS), X-ray diffraction (XRD), micro-Raman (μ-Raman) spectroscopy and temperature-dependent photoluminescence (PL). It was found that the length and diameter of nanorods varies with the growth temperatures, and the rod number density can reach around 10 10 cm −2. HRTEM and corresponding diffraction patterns have revealed that the GaN nanorods have a dislocation-free, single-crystal hexagonal wurtzite structure. μ-Raman scattering reveals that the self-assembled nanorods are strain free in consistent with XRD and HRTEM results. In particular, the PL spectra show an abnormal behavior with increasing temperature. The so-called “S-shape” behavior, a red–blue–red shift of emission peak with increasing temperature, might result from the fluctuation in compositional contents or crystallographic defects. In contrast to previous works, the process requires neither catalyst nor the effect of nanometer-sized confinement such as carbon nanotubes. These strain-free GaN nanorods may find many important applications on the future development of optical nanodevices.

Dynamic simulation of three dimensional architectural and mechanical alterations in human trabecular bone during menopause

A three dimensional (3D) computational simulation of dynamic process of trabecular bone remodeling was developed with all the parameters derived from physiological and clinical data. Contributions of the microstructural bone formation deficits: trabecular plate perforations, trabecular rod breakages, and isolated bone fragments, to the rapid bone loss and disruption of trabecular microarchitecture during menopause were studied. Eighteen human trabecular bone samples from femoral neck (FN) and spine were scanned using a micro computed tomography (μCT) system. Bone resorption and formation were simulated as a computational cycle corresponding to 40-day resorption/160-day formation. Resorption cavities were randomly created over the bone surface according to the activation frequency, which was strictly based on clinical data. Every resorption cavity was refilled during formation unless it caused trabecular plate perforation, trabecular rod breakage or isolated fragments. A 20-year-period starting 5 years before and ending 15 years after menopause was simulated for each specimen. Elastic moduli, standard and individual trabeculae segmentation (ITS)-based morphological parameters were evaluated for each simulated 3D image. For both spine and FN groups, the time courses of predicted bone loss pattern by microstructural bone formation deficits were fairly consistent with the clinical measurements. The percentage of bone loss due to trabecular plate perforation, trabecular rod breakage, and isolated bone fragments were 73.2%, 18.9% and 7.9% at the simulated 15 years after menopause. The ITS-based plate fraction (pBV/BV), mean plate surface area (pTb.S), plate number density (pTb.N), and mean rod thickness (rTb.Th) decreased while rod fraction (rBV/BV) and rod number density (rTb.N) increased after the simulated menopause. The dynamic bone remodeling simulation based on microstructural bone formation deficits predicted the time course of menopausal bone loss pattern of spine and FN. Microstructural plate perforation could be the primary cause of menopausal trabecular bone loss. The combined effect of trabeculae perforation, breakage, and isolated fragments resulted in fewer and smaller trabecular plates and more but thinner trabecular rods.

Development of two-level porosity during glancing angle deposition

Porous Ta and Al layers that exhibit 280-nm-wide micropores, which are interconnected by 5–50-nm-wide nanopores, were grown by glancing angle deposition (GLAD). The micropore nucleation is facilitated by patterning Si(001) substrates with inverted-pyramidal pit arrays using anisotropic etching through lithographic masks obtained by colloidal self-assembly. The microstructure consists of vertical nanorods with an average width w that increases with layer thickness t, following a power law w∝tβ. This indicates a self-similar growth mode which is controlled by purely geometric long-range atomic shadowing interactions. However, statistical analyses show a larger growth exponent βAl=0.58±0.07 for Al than for Ta with βTa=0.46±0.08, suggesting a secondary effect where the surface curvature of the high adatom mobility Al rods is lowered by diffusion-mediated lateral growth which exacerbates inter-rod competition and, in turn, leads to an enhanced rod broadening. The broadening in Al causes a close-up of the microscopic pores, a decrease in the porosity to 54% at t=750nm, and a reduction in the rod number density n, where n∝tγ and the extinction exponent γAl=−1.02±0.01. In contrast, the Ta porosity remains constant at 70%, the pore width is independent of t, and the extinction rate decreases from γ=−2.5 to −0.5. This is attributed to a transition from two- to one-dimensional shadowing, associated with the microscopic pores that initially enhance but later suppress growth competition in comparison to conventional GLAD on flat substrates where γ is expected to be ∼−1. These results provide insight into columnar competition under anisotropic shadowing conditions and also demonstrate a path to create layers with a controlled bimodal pore structure.

Catalyst-free GaN nanorods grown by metalorganic molecular beam epitaxy

High-density GaN nanorods with outstanding crystal quality were grown on c-sapphire substrates by radio-frequency plasma-assisted metalorganic molecular beam epitaxy under catalyst- and template-free growth condition. Morphological and structural characterization of the GaN nanorods was employed by X-ray diffraction, energy dispersive X-ray spectroscopy, scanning electron microscopy, and high-resolution transmission electron microscopy (HRTEM). These results indicate that the rod number density can reach 1/spl times/10/sup 10/ cm/sup -2/ and the nanorods are well-aligned with preferentially oriented in the c-axis direction. Meanwhile, no metallic (Ga) droplet was observed at the end of the rods, which is the intrinsic feature of vapor-liquid-solid method. Nanorods with no traces of any extended defects, as confirmed by TEM, were obtained as well. In addition, optical investigation was carried out by temperature- and power-dependent micro-photoluminescence (/spl mu/-PL). The PL peak energies are red-shifted with increasing excitation power, which is attributed to many-body effects of free carriers under high excitation intensity. The growth mechanism is discussed on the basis of the experimental results. Catalyst-free GaN nanorods presented here might have a high potential for applications in nanoscale photonic devices.

Area-selective growth of ruthenium dioxide nanorods on LiNbO3(100) and Zn/Si substrates

Selective and blanket growth of ruthenium dioxide (RuO2) nanorods have been achieved in chemical vapor deposition (CVD) using bis(ethylcyclopentadienyl)ruthenium. Area-selective growth is demonstrated on a substrate which consists of patterned SiO2 as the non-growth surface and LiNbO3(100) or Zn/Si as the growth surface. Regardless of blanket or selective CVD, the RuO2 nanorods are grown in the [001] direction, of square cross section and 20–60 nm in diameter. The conditions for growing nanorods selectively are to deposit at 500 ± 10 °C, 2 mbar, with a deposition flux around 7.0 × 10−7 mol cm−2 h−1. Deposition outside the narrow growth temperature window results in either a patterned RuO2 thin film without nanorods or growth without clean pattern definition. The RuO2 nanorods are vertically aligned on LiNbO3(100) in blanket CVD. When RuO2 nanorods are grown selectively on a patterned LiNbO3 substrate, their vertical growth habit is altered at the boundary between the masked and the unmasked area. The orientation of nanorods shifts from vertical to random directions, meanwhile the number density of rods diminishes towards the masked area in a narrow stripe along the border. These variations are shaped by the lateral movement of depositing species which collide on the masked area.

Ordering stripe structures of nanoscale rods in diblock copolymer scaffolds

We report a simulation on the formation of ordered stripe structures of nanoscale rods driven by symmetric diblock copolymer melts. Due to the preferential adsorption of one species of the diblock onto the mobile rods, the phase ordering process will couple with the movement of rods. We find that the self-assembly of rods on the copolymer scaffold produces the highly ordered nanowires of rods, and copolymer blends in turn form the well-oriented lamellar structure. This is due to the interplay among the micro-phase separating dynamics in the diblock copolymer, the wetting interaction between rods and diblock copolymer, and the nematic ordering dynamics of rods. We examine the influence of the domain size, the wetting strength, and the rod number density on the formation of such a nanoscale structure. Additionally, we indicate that the orientation of the pattern can be well controlled by external fields acting on the rods. The results suggest that our model system may provide a novel and simple way to control and design the ordering nanowire structure.