Rigid Rod-like Polymer Research Articles

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number.

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Enhancement of drag and mixing in a dilute solution of rodlike polymers at low Reynolds numbers

We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds number by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent-like chaotic flow with a wide range of active scales. This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field transported by the flow. By comparing the results of numerical simulations of the model in two- and three-dimensions, we show that the phenomena observed are qualitatively independent on the dimensionality of the space.

Effectiveness of Hydroxyurea in the Management of the Painful Crisis in Sickle Cell Anemia

Background: Sickle cell syndromes are inbred disorders distinguished by the presence of blade (Sickle) hemoglobin in red blood corpuscles. The sickling of red cells in patients with SCA is caused by the polymerization of molecules of non-oxygenated hemoglobin S (α2ß2s) into rigid rod-like polymers. In the open-label study of hydroxyurea therapy, the synthesis of embryo hemoglobin increased in most patients with SCA resulting in a humane myelotoxicity and rise in painful crises. By suppressing the sickling process, increased levels of embryo hemoglobin sinew the less frequency of painful crises.

Room Temperature to 150 °C Lithium Metal Batteries Enabled By a “Molecular Ionic Composite” Solid Electrolyte

Molecular ionic composites (MICs) are a new class of solid electrolyte materials developed recently in our group. These materials are constructed from various ionic liquids and a highly charged rigid rodlike polymer, poly(2,2′-disulfonyl-4,4′-benzideneterephthalamide) (PBDT). MICs demonstrate an unprecedented combination of thermal properties (stability up to 300 °C), mechanical properties (E′ up to ~ 1 GPa), and ion transport properties (ionic conductivity up to 8 mS/cm).[1-3] Here we present preparation and characterization of a MIC membrane based on the PBDT polymer, 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (Pyr14TFSI) and LiTFSI. This MIC membrane is robust and flexible, and exhibits ionic conductivity ~ 0.2 mS/cm at room temperature. Due to the electrochemical and mechanical stability of the MIC membrane at elevated temperature, Li/MIC/LiFePO4 coin cells demonstrate excellent cycling performance over a wide temperature range from 20 to 150 °C. This study demonstrates that MIC materials represent a promising electrolyte platform for safe and wide-temperature-range lithium batteries.

Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness of the Doi model for large data and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity.

Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor.

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

A rod-like phenolic π-conjugated polymer with pillar[5]arene units in its main chain

A new rigid rod-like phenolic π-conjugated polymer containing pillar[5]arene units in its main chain was prepared. First, a pillar[5]arene-containing π-conjugated polymer was prepared by Pd-catalyzed copolymerization of 4,4’-diphenyldiboronic acid with a pillar[5]arene bearing two triflate moieties in one hydroquinone unit and eight ethoxy groups in the other units. Then, deprotection of the ethyl moieties using BBr3 gave a rigid rod-like phenolic π-conjugated polymer. The phenolic polymer showed high thermal stability, with a 10 wt% loss temperature (T10) of 300 °C in a nitrogen atmosphere, which is higher than that of a pillar[5]arene containing 10 phenolic moieties (T10 = 164 °C). Moreover, the phenolic π-conjugated polymer showed selective gas adsorption properties: it was highly selective for the adsorption of CO2, but did not take up N2 or methane.

Role of Chain Morphology and Stiffness in Thermal Conductivity of Amorphous Polymers.

Designing thermally conductive polymer is of scientific interest and practical importance for applications like thermal interface materials, electronics packing, and plastic heat exchangers. In this work, we study the fundamental relationship between the molecular morphology and thermal conductivity in bulk amorphous polymers. We use polyethylene as a model system and performed systematic parametric study in molecular dynamics simulations. We find that the thermal conductivity is a strong function of the radius of gyration of the molecular chains, which is further correlated to persistence length, an intrinsic property of the molecule that characterizes molecular stiffness. Larger persistence length can lead to more extended chain morphology and thus higher thermal conductivity. Further thermal conductivity decomposition analysis shows that thermal transport through covalent bonds dominates the effective thermal conductivity over other contributions from nonbonded interactions (van der Waals) and translation of molecules disregarding the morphology. As a result, the more extended chains due to larger persistence length provide longer spatial paths for heat to transfer efficiently and thus lead to higher thermal conductivity. In addition, rigid rod-like polymers with very large persistence length tend to spontaneously crystallize and form orientated chains, leading to a thermal conductivity increase by more than 1 order of magnitude. Our results will provide important insights into the design of thermally conductive amorphous polymers.

Effects of the extensional rate on two-dimensional turbulence of semi-dilute polymer solution flows

An experimental study has been performed to investigate the relationship between the extensional viscosity of polymers and the turbulent drag reduction. In order to obtain the flow which is mostly dominated by extensional flow, two-dimensional (2D) grid turbulence made by flowing soap films was used. Extensional rate added to the flow was controlled by changing the conformation of the grid. Polyethylene oxide, as a flexible polymer, and hydroxypropyl cellulose, as a rigid rod-like polymer were added to the flow. Several extensional rates affect polymer behaviors, which induce different effects. Drag reduction effects of polymers under several extensional rates were visualized and analyzed by image processing. Rheological properties of the polymer solutions were also measured by a rheometer. The results indicated that the mechanisms of energy transfer are different in the streamwise and normal directions. The critical concentration to observe drag reduction effects in 2D turbulence was changed by the extensional rate. When extensional rate is higher, the effects were started to observe from lower concentration. These results were confirmed to correspond to the drag reduction effects obtained by classical pressure drop experiments in a pipe flow.

Diffusion of rigid rodlike polymer in isotropic solutions studied by dissipative particle dynamics simulation

Dissipative particle dynamics (DPD) was employed to simulate the diffusion of rigid rodlike polymers in isotropic solutions. In a dilute solution range, the simulated diffusion behavior is in good agreement with that as described by the Kirkwood theory. In a semi-dilute range, the simulation shows that the DPD model adopting soft repulsive interactions can effectively reproduce the entanglement effect on both rotational and translational diffusions. The rotational diffusion coefficient Dr obeys the asymptotic scaling law Dr ∼ (νL3)−2 (ν is the number of polymers per volume and L is the polymer length) for the large νL3, which corresponds to formation of a completely enclosed tube in the Doi-Edwards theory. The parallel translational diffusion coefficient D‖ decreases with ν increase, which can be attributed to the friction effect of surrounding medium. The perpendicular translational diffusion coefficient D⊥ decays more drastically with ν increase, which is caused by the topological constraint.

Three dimensional simulation dynamics for the dilute colloidal suspensions of rod-like polymer particles flowing in the bulk and near solid boundaries

Numerical simulations and algorithms are developed to analyze the dynamics of rigid rod-like polymer particles. We developed a theoretical model based on the equations of Jeffrey for the dynamics of rigid polymer particles in fluids and the molecular dynamics by mechanical restitution for the diffusive collisions of the particles at the solid boundaries. The simulations are developed to calculate the dynamic equilibrium probability distribution functions (PDF) distributions for rod-like polymer particles in colloidal suspensions in a fluid under hydrodynamic flow inside pores with solid boundaries. They are carried out for idealized atomically flat and the realistic rough surface boundaries. To accomplish this, we investigate the influence of the surface roughness on the choice of the hydrodynamic boundary conditions. The simulation results for the PDF distributions for the spatial positions and orientations of rod-like polymer particles are calculated, over several orders of magnitude of the rotational Peclet number. They demonstrate the importance and significance of modeling in a three-dimensional spatial frame as compared to the simulation results over a two-dimensional spatial frame. In particular we are able to produce a complete topography for the PDF distributions segmented as a hierarchy in the depletion layer by covering a complete range of orientations in 3D spatial frames. These simulations permit to calculate the nematic order parameter over its tensorial representation for the colloidal suspensions of rod-like polymer particles locally, and throughout the pore space including the depletion layer. Our results for the nematic order parameter are hence innovating and represent a new input for these systems. Open image in new window

Phase diagrams of binary mixtures of liquid crystals and rodlike polymers in the presence of an external field

We theoretically study phase separations in mixtures of a low molecular-weight-liquid crystalline molecule (LC) and a rigid-rodlike polymer (rod) under an external field, such as magnetic or electric fields. By taking into account two orientational order parameters of the rod and the LC, we define four nematic phases (N(0), N(1), N(2), N(3)) on the temperature-concentration plane. Depending on the sign of the dielectric anisotropy Δε(i) of the rod (i = 1) and LC(i = 2), we examine the phase behavior of rod/LC mixtures in the case of Δε(1) > 0, Δε(2) > 0 (a), Δε(1) < 0, Δε(2) > 0 (b), Δε(1) > 0, Δε(2) < 0 (c), and Δε(1) < 0, Δε(2) < 0 (d). We predict a variety of phase separations induced by an external field.

Structure and Dynamics of Supramolecular Polymers Formed by Tris-3,7-dimethyloctyl-cis-1,3,5-cyclohexanetricarboxamide in n-decane via Hydrogen Bonding

Dynamic viscoelastic, dielectric and dynamic flow birefringence measurements were carried out in a highly viscoelastic system (DO3CH/C10), solutions of tris-3,7-dimethyloctyl-cis-1,3,5-cyclohexanetricarboxamide (DO3CH) in n-decane (C10), for a wide concentration (c) range to investigate structure and dynamics of supramolecular polymers formed in the system due to intermolecular hydrogen bonding. The DO3CH/C10 system showed pronounced viscoelastic behavior possessing two relaxation modes: a fast mode with a relaxation time (τ1) independent of c and strength G1 ∝ c2, and a slow mode with the other relaxation time (τ2) highly dependent of c and strength G2 ∝ c1∼1.3. In dielectric and dynamic flow birefringence behavior, singe relaxation modes were clearly observed, which corresponded to the slow relaxation mode with τ2 in viscoelastic behavior. These reveal that two kinds of supramolecular polymers are formed in the system, i.e. a rigid rodlike supramolecular polymer of ca. 45 nm length, which is formed by ∼100 DO3CH molecules via 3-fold hydrogen bonding of amide groups and bear a macro-electric dipole moment of ca. 1100 D, and a flexible supramolecuar polymer with little optical anisotropy and electric dipole moment, which is formed by almost randomly connected DO3CH molecules via hydrogen bonding bearing many defects responsible for a “phantom-crossing” mechanism at entanglement points.

Stability of equilibria of nematic liquid crystalline polymers

We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b* (6.7314863965), the only equilibrium state is isotropic and it is stable; when b* <b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.

Biaxial Nematic Phase in Mixtures of a Liquid Crystal and a Rodlike Polymer

A simple mean field theory is introduced to describe a biaxial nematic phase in mixtures of a low-molecular-weight liquid crystalline molecule (LC) and a rigid-rodlike polymer (ROD), such as carbon nanotubes (CNTs) and liquid crystalline polymers. When the two components favor perpendicular orientations, we predict a biaxial nematic phase on the temperature-concentration plane, depending on the anisotropic interaction between ROD and LC.

Biaxial nematic phases in rod/liquid crystal mixtures

A novel biaxial nematic phase is theoretically predicted in mixtures of a low-molecular-weight liquid crystalline molecule and a rigid rod-like polymer, such as carbon nanotubes and liquid crystalline polymers, where the two components favour a mutually perpendicular orientation. We demonstrate that rods dispersed in nematic liquid crystals induce the second orientational ordering and yield a biaxial nematic phase on the temperature–concentration plane, depending on an anisotropic interaction between a rod and a liquid crystal.

Exact multiplicity of nematic states for an Onsager model

Isotropic–nematic phase transition due to excluded volume effects is considered for the 2D Onsager model of rigid rod-like polymers with a general interaction kernel involving a finite number of Fourier modes. Nematic phases appear above a concentration threshold. We prove the existence of continuous branches of nematic states bifurcating from the isotropic phase at concentrations proportional to the Fourier coefficients of the interaction kernel. The bifurcation structure is shown to depend on the size of the spectral gaps of the interaction operator. Exact multiplicity of nematic phases is proved for a class of two-mode trigonometric kernels. Our arguments use simple bifurcation and variational tools applied to an equivalent finite dimensional problem that involves multi-variable Bessel functions.

Theory of binary mixtures of a rodlike polymer and a liquid crystal

We present a mean field theory to describe phase separations in mixtures of a low molecular-weight-liquid crystalline (LC) molecule and a rigid-rodlike polymer (rod) such as carbon nanotubes (CNTs) and LC polymers. By taking into account two orientational order parameters of the rod and the LC, we find three nematic phases (N(0),N(1),N(2)) on the temperature-concentration plane, depending on the attractive or repulsive interactions between the rod and the LC. We discuss the phase behavior of the systems where the rod and the LC are oriented to be parallel or perpendicular with each other and find that the phase diagrams of the parallel alignment are different from that of the perpendicular one. We predict the appearances of a lower critical solution temperature (LCST) and an upper one, a tricritical point, a critical point, and the first- and the second-order nematic-isotropic phase transitions. The theory can qualitatively describe the phase diagram with a LCST observed in a rod/LC mixture. We also predict a variety of phase separations in CNT/LC mixtures.

Application of Polymer Solubility Theory to Solution Phase Dispersion of Single-Walled Carbon Nanotubes

Single-walled carbon nanotubes below 1.5 μm in length are effectively rigid rod-like polymers, but polymer solubility theory has not yet been applied to their solution phase dispersion despite its success in modeling other polymer systems. In this work, we experimentally determine the solubility of arc discharge single-walled carbon nanotubes (SWNT) covalently functionalized with aryl carboxylic acid or aryl hydroxyl groups in aqueous solution using UV−vis−nIR photoabsorption spectroscopy. Empirically, stable suspension is observed when the optical density at 632 nm is above 0.05. The critical level of functionalization required for surfactant-free aqueous suspension is found to be >1.5 and >5.1 functional groups per 100 carbons for the carboxylic acid and hydroxyl aryl groups, respectively. Solubility parameters are estimated by using established polymer solubility theory (Fedors and Refined Solubility Parameter group additivity models), molecular simulations (Maiti Dissipative Particle Dynamics), or a combination of both (Maiti-RSP and Maiti-Fedors). Flory−Huggins interaction parameters are calculated for suspensions of both chemistries in water and dimethyl formamide (DMF). Comparison of experiment and model indicates that the combined Maiti-RSP model best describes increasing solubility with increasing functionalization.

Electric activity in rigid rod-like polymer, poly(β-hydroxybutyrate)

Poly(β-hydroxybutrate) (PHB), one of the most promising environmental friendly polymers, was found to be rich in electric activities. Our experimental results demonstrated that the PHB exhibited ferroelectric behavior, as well as pyroelectric behavior. A remanent polarization of the PHB system was as large as 67mC/m2 at 100°C from a displacement–field hysteresis loop, while it possessed pyroelectric coefficient as large as 20μC/m2K after a poling procedure. The remanent polarization exhibited unique temperature dependence and it increased rapidly at the temperatures higher than 80°C. The polarization due to the ester dipole ordering is likely formed in the direction perpendicular to the helical axis.