Rod Concentration Research Articles

Phase diagrams of charged colloidal rods: Can a uniaxial charge distribution break chiral symmetry?

We construct phase diagrams for charged rodlike colloids within the second-virial approximation as a function of rod concentration, salt concentration, and colloidal charge. Besides the expected isotropic-nematic transition, we also find parameter regimes with a coexistence between a nematic and a second, more highly aligned nematic phase including an isotropic-nematic-nematic triple point and a nematic-nematic critical point, which can all be explained in terms of the twisting effect. We compute the Frank elastic constants to see if the twist elastic constant can become negative, which would indicate the possibility of a cholesteric phase spontaneously forming. Although the twisting effect reduces the twist elastic constant, we find that it always remains positive. In addition, we find that for finite aspect-ratio rods the twist elastic constant is also always positive, such that there is no evidence of chiral symmetry breaking due to a uniaxial charge distribution.

Routine Coronary Calcium Scan Can Precisely Measure Vertebral Bone Density Without a Quantitative Calibration Phantom.

We aimed to assess accuracy and precision of quantitative computed tomography (QCT) and phantomless in thoracic bone mineral density (BMD) assessment using coronary artery calcium scan (CACS). A total of 513 subjects underwent CACS with a calibration phantom. The thoracic spine BMD and concentration of calcium hydroxyapatite in phantom rods, as well CT Hounsfield unit of both, were measured. The thoracic BMD and phantom-rods calcium concentration were obtained using phantomless. The accuracy and precision error of QCT and phantomless were compared. The mean biases from true calcium concentration of phantom rods were 2.9% and 3.8% for the QCT and phantomless, respectively (P < 0.001). The biases of thoracic BMD from QCT by phantomless were 3.8% with a similar precision error in both methods. The thoracic BMD can be assessed accurately and precisely using QCT and phantomless with a routine CACS.

Soft-mode of charged chiral fibrous viruses (fd).

The frictional forces in suspensions vary depending on the size, shape, and the surface of the particles, which are either charged or neutral. For anisotropic particles with no spatial gradient in the order parameter under external parameters, they exhibit either a continuous phase transition or "freezing" of the order parameter fluctuation. They are known as the collective soft-mode, which has a finite cutoff dispersion where the relaxation time diverges. From microscopic dynamics of charged chiral fd-viruses, the soft-mode is revealed with a rotation restoring "twist", obtained from both polarized (VV) and depolarized (VH) small angle dynamic light scattering. Here, I have found the minimum spatial coherence length at a lower I-N binodal concentration, which is due to the reverse of electrostatic repulsive forces with an increase in the concentration of charged chiral rods.

The reason why a sheath exists in enamel

The stress of prism rods in enamel is reduced by the existence of sheaths. A finite element model including prism rods and sheaths was created, and we found that the sheath effectively reduces the stress concentration of the prism rods under both transverse loading (x-loading) and shear loading (zx-loading). In addition, the smaller the elastic modulus of the sheath, the larger the reduction in stress concentration. We believe this is why sheaths exist in enamel, although they are very small.

Optical Resonances of Colloidal Gold Nanorods: From Seeds to Chemically Thiolated Long Nanorods

Following an adapted three-step seed-mediated method, we synthesize colloidal Au thin and long (L > 100 nm) nanorods (NRs) and characterize the metallic nanostructures evolving from the initial Au nanoparticle (NPs) seeds to thiolate-functionalized NRs, using HRTEM and ultraviolet, visible, and near-infrared absorption spectroscopy (UV–vis–NIR). For the long NRs we analyze the role of several solvents and rod concentration on the spectral features of the assembled products, which are further studied with simulated spectra. Superimposed to a broad resonance in the range 700–900 nm, which corresponds to short (L < 100 nm) interacting nanorods, the growth of long nanorods is clearly identified with the emergence of a robust resonance at 960 nm, linked to the three half-wavelength antenna plasmon mode. This mode is enhanced when the nanorod concentration decreases and splits into two peaks when the thiolate coverage chemically modifies the rod surface by a thin layer of nanometer size. This behavior is explained with a dielectric model based on ab initio calculations of thiolate–gold cluster surfaces.

Depletion-interaction effects on the tunneling conductivity of nanorod suspensions

We study by simulation and theory how the addition of insulating spherical particles affects the conductivity of fluids of conducting rods, modeled by spherocylinders. The electrical connections are implemented as tunneling processes, leading to a more detailed and realistic description than a discontinuous percolation approach. We find that the spheres enhance the tunneling conductivity for a given concentration of rods and that the enhancement increases with rod concentration into the regime where the conducting network is well established. By reformulating the network of rods using a critical path analysis, we quantify the effect of depletion-induced attraction between the rods due to the spheres. Furthermore, we show that our conductivity data are quantitatively reproduced by an effective-medium approximation, which explicitly relates the system tunneling conductance to the structure of the rod-sphere fluid.

Anisotropic absorption of CdSe/ZnS quantum rods embedded in polymer film

An approach to achieving of spatially homogeneous, ordered ensemble of semiconductor quantum rods in polymer film of polyvinyl butyral is reported. The CdSe/ZnS quantum rods are embedded to the polymer film. Obtained film is stretched up to four times to its initial length. A concentration of quantum rods in the samples is around 2×10 -5 M. The absorption spectra, obtained in the light with orthogonal polarization, confirm the occurrence of spatial ordering in a quantum rod ensemble. Anisotropy of the optical properties in the ordered quantum rod ensemble is examined. The presented method can be used as a low-cost solution for preparing the nanostructured materials with anisotropic properties and high concentration of nanocrystals.

Effect of Rod Length on the Morphology of Block Copolymer/Magnetic Nanorod Composites

The organization of magnetic nanorods in microphase-separated diblock copolymers composed of poly(styrene-b-2-vinylpyridine) (PS-PVP) as a function of rod length and rod concentration was investigated using both transmission electron microscopy and small-angle X-ray scattering. Our results reveal that the nanorods were sequestered into the PVP domains, which is attributed to the preferential interaction between pyridine-tethered nanorods and PVP. Meanwhile, the addition of nanorods in PS-PVP caused chain stretching. To minimize the energy penalty, nanorods tended to align parallel to the interface between PS and PVP to increase the conformational entropy. As the length of nanorods increased, the increasing van der Waals interaction and magnetic interaction caused extensive rod aggregation, which suppressed the domain size of PVP and amplified the local compositional fluctuations. This creates conditions to induce disorder in the polymer morphology and nanorods undergo macrophase separation.

Glass Transition in Suspensions of Charged Rods: Structural Arrest and Texture Dynamics

We report on the observation of a glass transition in suspensions of very long and thin, highly charged colloidal rods (fd-virus particles). Structural particle arrest is found to occur at a low ionic strength due to caging of the charged rods in the potential setup by their neighbors through long-ranged electrostatic interactions. The relaxation time of density fluctuations as probed by dynamic light scattering is found to diverge within a small concentration range. The rod concentration where structural particle arrest occurs is well within the full chiral-nematic state, far beyond the two-phase isotropic-nematic coexistence region. The morphology of the suspensions thus consists of nematic domains with various orientations. We quantify the dynamics of the resulting texture with image-time correlation spectroscopy. Interestingly, the decay times of image correlation functions are found to diverge in a discontinuous fashion at the same concentration of charged rods where structural particle arrest is observed. At the glass-transition concentration, we thus find both structural arrest and freezing of the texture dynamics.

Structural arrest and texture dynamics in suspensions of charged colloidal rods

There is an abundance of experiments and theories on the glass transition of colloidal systems consisting of spherical particles. Much less is known about possible glass transitions in suspensions of rod-like colloids. In this study we present observations of a glass transition in suspensions of very long and thin rod-like, highly charged colloids. We use as a model system fd-virus particles (a DNA strand covered with coat proteins) at low ionic strength, where thick electric double layers are present. Structural arrest as a result of particle-caging is observed by means of dynamic light scattering. The glass-transition concentration is found to be far above the isotropic–nematic coexistence region. The morphology of the system thus consists of nematic domains with different orientations. Below the glass-transition concentration the initial morphology with large shear-aligned domains breaks up into smaller domains, and equilibrates after typically 50–100 hours. We quantify the dynamics of the transitional and the equilibrated texture by means of image time-correlation. A sharp increase of relaxation times of image time-correlation functions is found at the glass-transition concentration. The texture dynamics thus freezes at the same concentration where structural arrest occurs. We also observe a flow instability, which sets in after very long waiting times (typically 200–300 hours), depending on the rod concentration, which affects the texture morphology.

Using solution thermodynamics to describe the dispersion of rod-like solutes: application to dispersions of carbon nanotubes in organic solvents

We report a simple model describing the solubility of rods in solvents, expressing the final result explicitly in terms of the surface entropy and the enthalpy of mixing. This model can be combined with any expression for the mixing enthalpy depending on the requirements. For example, in one instance it predicts the dispersed concentration of rods to decrease exponentially with the Flory–Huggins parameter of the dispersion. Using a different enthalpy function, it predicts a Gaussian peak when concentration is plotted versus solvent surface energy. The model also suggests specific solvent–rod interactions to be important and shows the dispersed concentration to be very sensitive to ordering at the solvent–rod interface. We have used this model to describe experimental results for the concentration of dispersed nanotubes in various solvents. Qualitative agreement with these predictions is observed experimentally. However, we suggest that the fact that quantitative agreement is not found may be explained by solvent ordering at the nanotube surface.

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.

A lattice model of the translational dynamics of nonrotating rigid rods

We present a lattice model of oriented, nonrotating, rigid rods in three dimensions with random walk dynamics, computer simulation results for the model, and a theory for the translational diffusion constant of the rods in the perpendicular direction, D(⊥), in the semidilute regime. The theory is based on the "tube model" of Doi-Edwards (DE) theory for the rotational diffusion constant of rods that can both translate and rotate in continuous space. The theory predicts that D(⊥) is proportional to (νL(3))(-2), where ν is the concentration of rods and L is the length of the rods, which is analogous to the Doi-Edwards scaling law for rotational diffusion. The simulations find that, as νL(3) is increased, the approach to the limit of DE scaling is slow, and the -2 power in the DE scaling law is never quite achieved even at the highest concentration (νL(3) = 200) simulated. We formulate a quantitative theory for the prefactor in the scaling relationship using only DE ideas, but it predicts a proportionality constant that is much too small. To explain this discrepancy, we modify the DE approach to obtain a more accurate estimate of the average tube radius and take into account effects of perpendicular motion of rods that are not included in the original DE theory. With these changes, the theory predicts values of D(⊥) that are in much better agreement with the simulations. We propose a new scaling relationship that fits the data very well. This relationship suggests that the DE scaling law is the correct description of the scaling for infinitely thin rods only in the limit of infinite concentration, and that corrections to the DE scaling law because of finite concentration are significant even at concentrations that are well inside the semidilute regime. The implications of these results for the DE theory of rotating rods are discussed.

Phase behavior of lyotropic rigid-chain polymer liquid crystal studied by dissipative particle dynamics

The phase behavior of lyotropic rigid-chain liquid crystal polymer was studied by dissipative particle dynamics (DPD) with variations of the solution concentration and temperature. A chain of fused DPD particles was used to represent each mesogenic polymer backbone surrounded with the strongly interacted solvent molecules. The free solvent molecules were modeled as independent DPD particles, where each particle includes a lump of solvent molecules with the volume roughly equal to the solvated polymer segment. The simulation shows that smectic-B (S(B)), smectic-A (S(A)), nematic (N), and isotropic (I) phases exist within certain regions in the temperature and concentration parameter space. The temperature-dependent S(B)∕S(A), S(A)∕N, and N∕I phase transitions occur in the high concentration range. In the intermediate concentration range, the simulation shows coexistence of the anisotropic phases and isotropic phase, where the anisotropic phases can be the S(B), S(A), or N phases. Mole fraction and compositions of the coexisted phases are determined from the simulation, which indicates that concentration of rigid rods in isotropic phase increases as the temperature increases. By fitting the orientational distribution function of the systems, the biphasic coexistence is further confirmed. From the parameter α obtained for the simulation, the distribution of the rigid rods in the two coexistence phases is quantitatively evaluated. By using model and simulation methods developed in this work, the phase diagrams of the lyotropic rigid-chain polymer liquid crystal are obtained. Incorporating the solvent particles in the DPD simulation is critical to predict the phase coexistence and obtain the phase diagrams.

Twist distortion in rod/liquid crystal mixtures

A simple model is introduced to describe the twist distortion in mixtures of a rigid rod-like molecule (rod) and a liquid crystal (LC) molecule. We take into account the coupling between rods and LCs and calculate the equilibrium reorientation angles of rods and LCs when an external field applies. We find that the dependence of the critical threshold on the rod concentration is changed due to the ratio of the twist elastic constant K 22,2 to the dielectric or magnetic anisotropy χ2 of the rod. The theory can qualitatively describe the observed properties of carbon nanotube/LC mixtures. We also discuss the reorientation dynamics.

Entropic forces and directed alignment of hard squares in suspensions of rods and disks

We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.

ZnO Nanorod−Thermoplastic Polyurethane Nanocomposites: Morphology and Shape Memory Performance

The impact of dispersed alkylthiol-modified ZnO nanorods, as a function of rod aspect ratio and concentration, on the shape memory character of a thermoplastic polyurethane with low hard-segment density (LHS-TPU) is examined relative to the enhanced performance occurring for carbon nanofiber (CNF) dispersion. Solution blending resulted in uniform dispersion within the LHS-TPU of the ZnO nanorods at low volume (weight) fractions (<2.9% v/v (17.75% w/w)). Tensile modulus enhancements were modest though, comparable to values observed for spherical nanofillers. Shape memory characteristics, which in this LHS-TPU result when strain-induced crystallites retard the entropic recovery of the deformed chains, were unchanged for these low volume fraction ZnO nanocomposites. Higher ZnO loadings (12% v/v (50% w/w)) exhibited clustering of ZnO nanorods into a mesh-like structure. Here, tensile modulus and shape recovery characteristics were improved, although not as great as seen for comparable CNF addition. Wide angle X-ray diffraction and NMR revealed that the addition of ZnO nanorods did not impact the inherent strain induced crystallization of the LHS-TPU, which is in contrast to the impact of CNFs and emphasizes the impact of interactions at the polymer−nanoparticle interface. Overall, these findings reinforce the hypothesis that the shape memory properties of polymer nanocomposites are governed by the extent to which nanoparticle addition, via nanoparticle aspect ratio, hierarchical morphology, and interfacial interactions, impacts the molecular mechanism responsible for trapping elastic strain.

Modeling the phase behavior of polydisperse rigid rods with attractive interactions with applications to single-walled carbon nanotubes in superacids

The phase behavior of rodlike molecules with polydisperse length and solvent-mediated attraction and repulsion is described by an extension of the Onsager theory for rigid rods. A phenomenological square-well potential is used to model these long-range interactions, and the model is used to compute phase separation and length fractionation as a function of well depth and rod concentration. The model closely captures experimental data points for isotropic/liquid crystalline phase coexistence of single-walled carbon nanotubes (SWCNTs) in superacids. The model also predicts that the isotropic-biphasic boundary approaches zero as the acid strength diminishes, with the possibility of coexistence of isotropic and liquid crystalline phases at very low concentrations; this counterintuitive prediction is confirmed experimentally. Experimental deviations from classical theories for rodlike liquid crystals are explained in terms of polydispersity and the balance between short-range repulsion and long-range attractions. The predictions of the model also hold practical importance for applications of SWCNT/superacid solutions, particularly in the processing of fibers and films from liquid crystalline SWCNT/superacid mixtures.

Enhanced Diffusion and Ordering of Self-Propelled Rods

Starting from a minimal physical model of self-propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self-propulsion enhances longitudinal diffusion and modifies the mean-field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New results at large scales are a lowering of the density of the isotropic-nematic transition and a strong enhancement of boundary effects in confined self-propelled systems.

The effect of NaCl addition on the rheological behavior of cetyltrimethylammonium p-toluenesulfonate (CTAT) aqueous solutions and their mixtures with hydrophobically modified polyacrylamide aqueous solutions

In this paper, the influence of NaCl addition, up to very large concentrations, on the rheological properties of cetyltrimethylammonium p-toluenesulfonate (CTAT) solutions and their mixtures with two hydrophobically modified polyacrylamides (HMPAM) has been studied under simple shear. The CTAT concentrations employed were above the critical rod concentration. As salt is added to CTAT aqueous solutions, the zero-shear viscosity first increases, goes through a maximum, and at very high ionic strengths increases once more. The overlap concentration of worm-like micelles decreases as the concentration of NaCl increases. The results are explained by the salt addition-induced growth of worm-like micelles and salting out effects at the highest contents of NaCl. The influence of ionic environment on the rheological properties of CTAT with two HMPAM solutions with different contents of hydrophobic moieties was also studied under simple shear. When NaCl is added to HMPAM/CTAT solutions, the same trends observed in CTAT/NaCl solutions were repeated but the viscosity increases were largely magnified. The large viscosity enhancements with salt increments in HMPAM/CTAT solutions were explained by the formation of an interpenetrated network of hydrophobically modified polymer chains and worm-like micelles with hydrophobic sequences embedded within its structure.