Rodlike Macromolecules Research Articles

Naturally derived colloidal rods in microfluidic flows.

Naturally derived colloidal rods (CR) are promising building blocks for developing sustainable soft materials. Engineering new materials based on naturally derived CR requires an in-depth understanding of the structural dynamics and self-assembly of CR in dispersion under processing conditions. With the advancement of microfabrication techniques, many microfluidic platforms have been employed to study the structural dynamics of CR under flow. However, each microfluidic design has its pros and cons which need careful evaluation in order to fully meet the experimental goal and correctly interpret the data. We analyze recent results obtained from naturally derived CR and relevant rod-like macromolecules under microfluidic flows, with emphasis on the dynamical behavior in shear- and extensional-dominated flows. We highlight the key concepts required in order to assess and evaluate the results obtained from different CR and microfluidic platforms as a whole and to aid interconnections with neighboring fields. Finally, we identify and discuss areas of interest for future research directions.

Modified Poisson-Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions.

We present a soft-potential-enhanced Poisson-Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulation with the explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1M and ion sizes ranging from small ions, such as Na+ or Cl-, to softer and larger ions with a size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.

Shear Flow Behavior of Bidisperse Rodlike Colloids

A priori prediction of the flow properties of polydisperse rodlike macromolecules is a prerequisite for the understanding of many industrial and biological processes. Using mixtures of two naturall...

Pattern method for higher harmonics of first normal stress difference from molecular orientation in oscillatory shear flow

This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: rigid dumbbells suspended in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. Previously, the explicit analytical expressions of the zeroth, second, and fourth harmonics of the alternating first normal stress difference response in LAOS have been derived. In this paper, we correct and extend these expressions by seeking an understanding of the next higher harmonic. Specifically, this paper continues a series of studies that shed light on molecular theory as a useful approach in investigating the response of polymeric liquids to oscillatory shear. Following the general method of Bird and Armstrong [“Time-dependent flows of dilute solutions of rodlike macromolecules,” J. Chem. Phys. 56, 3680 (1972)], we derive the expression of the first normal stress coefficient up to and including the sixth harmonic. Our analysis relies on the extension of the orientation distribution function to the sixth power of the shear rate. Our expression is the only one to have been derived from a molecular theory for a sixth harmonic and thus provides the first glimpse of the molecular origins of a first normal stress difference higher than the fourth.

Structural Transition in Dilute Solutions of Rod-Like Macromolecules

On the basis of experimental data obtained for the viscosity in aqueous solutions of hydroxypropyl methylcellulose (metolose), it has been found that a structural transition takes place in dilute solutions of rod-like macromolecules with the increasing temperature. Namely, macromolecules form clusters in which they are arranged in parallel to one another. It is shown that this transition is a set of local phase transitions of the first kind.

Stick-slip kinetics in a bistable bar immersed in a heat bath

Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that ‘stick-slip’ kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.

Elasticity as the Basis of Allostery in DNA.

Allosteric interactions in DNA are crucial for various biological processes. These interactions are quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. Here, we show that trends in the interaction energy of ligands binding to DNA can be explained within an elastic birod model, which accounts for the deformation of each strand as well as the change in stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The strain fields produced by the ligands decay with distance from the binding site. The interaction energy of two ligands decays exponentially with the distance between them and oscillates with the periodicity of the double helix in quantitative agreement with experimental measurements. The trend in the computed interaction energy is similar to that in the perturbation of groove width produced by the binding of a single ligand, which is consistent with molecular simulations. Our analysis provides a new framework to understand allosteric interactions in DNA and can be extended to other rod-like macromolecules whose elasticity plays a role in biological functions.

Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response

We examine the simplest relevant molecular model for large-amplitude shear (LAOS) flow of a polymeric liquid: the suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the shear rate amplitude and frequency dependences of the first and third harmonics of the alternating shear stress response. We include a detailed comparison of these predictions with the corresponding results for the simplest relevant continuum model: the corotational Maxwell model. We find that the responses of both models are qualitatively similar. The rigid dumbbell model relies entirely on the dumbbell orientation to explain the viscoelastic response of the polymeric liquid, including the higher harmonics in large-amplitude oscillatory shear flow. Our analysis employs the general method of Bird and Armstrong ["Time-dependent flows of dilute solutions of rodlike macromolecules," J. Chem. Phys. 56, 3680 (1972)] for analyzing the behavior of the rigid dumbbell model in any unsteady shear flow. We derive the first three terms of the deviation of the orientational distribution function from the equilibrium state. Then, after getting the "paren functions," we use these for evaluating the shear stress for LAOS flow. We find the shapes of the shear stress versus shear rate loops predicted to be reasonable.

Rodlike Macromolecules through Spatial Overlapping of Thiophene Dendrons

Two novel dendritic macromonomers 7 and 8 functionalized with electroactive conjugated thiophene oligomers were synthesized by stepwise cross-coupling reactions and the introduction of a vinyl group at the focal point. Both macromonomers were polymerized into dendronized polymers 9 and 10 by using a radical polymerization method. The photophysical and redox behaviors of dendronized polymers 9 and 10 are significantly different from those of the corresponding macromonomers. This difference may result from the spatial overlapping of thiophene dendrons through π-π interactions when the dendrons are connected to a polymer backbone. The dendronized polymers can organize into large-area two-dimensional sheets with a thickness of 4.8 nm. Polymer 9, which has all-dendritic thiophene side chains, exhibited enhanced conductivity by partial doping with iodine or nitrosonium tetrafluoroborate (NOBF(4)). The novel amphiphilic dendronized polymer 15 was synthesized by the atom-transfer radical polymerization of macromonomer 7 from a poly(ethylene glycol) (PEG) macroinitiator and was found to have a self-organized structure in water.

Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: Molecular dynamics simulation

Brownian diffusion of rod-like polymers in the presence of randomly distributed spherical obstacles is studied using molecular dynamics simulations. It is observed that dependence of the reduced diffusion coefficient of these macromolecules on the available volume fraction can be described reasonably by a power law function. Despite the case of obstructed diffusion of flexible polymers in which reduced diffusion coefficient has a weak dependence on the polymer length, this dependence is noticeably strong in the case of rod-like polymers. Diffusion of these macromolecules in the presence of obstacles is observed that is anomalous at short time scales and normal at long times. Duration time of the anomalous diffusion regime is found that increases very rapidly with increasing both the polymer length and the obstructed volume fraction. Dynamics of diffusion of these polymers is observed that crosses over from Rouse to reptation type with increasing the density of obstacles.

The mechanics of short rod-like molecules in tension

The rapid development of single molecule experimental techniques in the last two decades has made it possible to accurately measure the force–extension response as well as the transverse fluctuations of individual rod-like macromolecules. This information is used in conjunction with a statistical mechanical model based on the treatment of the molecule as a fluctuating elastic rod to extract its bending and extension moduli. The models most commonly used to interpret the experimental data assume that the magnitude of the Brownian fluctuations are independent of the length of the macromolecule, an assumption that holds only in the asymptotic limit of infinitely long rods, and is violated in most experiments. As an alternative, we present a theoretical treatment of a finite length, fluctuating rod and determine its mechanical behavior by measuring the transverse Brownian fluctuations under the action of large stretching forces. To validate our theory, we have applied our methods to an experiment on short actin filaments whose force–extension relation is difficult to measure, but whose transverse deflections can be captured by current microscopy techniques. An important consequence of the short contour lengths is that the boundary conditions applied in the experiment affect the fluctuations and can no longer be neglected as is commonly done when interpreting data from force–extension measurements. Our theoretical methods account for boundary conditons and can therefore be deployed in conjunction with force–extension measurements to obtain detailed information about the mechanical response of rod-like macromolecules.

Micrometer-Sized Fibrillar Protein Aggregates from Soy Glycinin and Soy Protein Isolate

Long, fibrillar semiflexible aggregates were formed from soy glycinin and soy protein isolate (SPI) when heated at 85 degrees C and pH 2. Transmission electron microscopy analysis showed that the contour length of the fibrils was approximately 1 microm, the persistence length 2.3 microm, and the thickness a few nanometers. Fibrils formed from SPI were more branched than the fibrils of soy glycinin. Binding of the fluorescent dye Thioflavin T to the fibrils showed that beta-sheets were present in the fibrils. The presence of the fibrils resulted in an increase in viscosity and shear thinning behavior. Flow-induced birefringence measurements showed that the behavior of the fibrils under flow can be described by scaling relations derived for rodlike macromolecules. The fibril formation could be influenced by the protein concentration and heating time. Most properties of soy glycinin fibrils are comparable to beta-lactoglobulin fibrils.

Effect of a Low-Dielectric Interior on DNA Electrostatic Response to Twisting and Bending

We study the effects of a low-dielectric core of rod-like macromolecules on their electrostatic persistence lengths. We use the exact solution of the linear Poisson-Boltzmann equation for the potential of a charge on the surface of a low-dielectric cylinder. We apply the results to the B-DNA molecule, modeled as a double helical array of discrete charges wound on the surface of a low-dielectric rod. For this charge geometry, we calculate the change in the electrostatic twist persistence as compared to DNA with a water-permeable core. We also discuss possible effects of the low-dielectric molecular core on DNA bending persistence.

Synthesis of Water-soluble Silicon Oxide Material by Sol-gel Reaction in Tetraalkoxysilane-aminoalkyltrialkoxysilane Binary System

A series of water-soluble silicon oxide materials was synthesized by the sol-gel reaction of tetramethoxysilane (TMOS)/3-aminopropyltrimethoxysilane (APTMOS) mixtures catalyzed by hydrochloric acid with varying TMOS/APTMOS ratios. Increase in TMOS composition made the products less water-soluble, and the richest TMOS composition for the water-soluble silicon oxide materials was found to be TMOS/APTMOS = 7/3 (mol/mol). Ultraviolet-visible spectroscopy of a 10 wt% aqueous solution of the product with TMOS/APTMOS = 7/3 showed a high transmittance in the visible region. Its infrared spectrum showed an absorptionband attributable to the Si–O bond, and the 29Si dipole decoupled/magic angle spinning–nuclear magnetic resonance spectrum exhibited signals in the regions of T3, Q3, and Q4, indicating a dense siloxane network structure. A peak due to an ordered structure with a 1.76 nm periodicity was observed in the x-ray diffraction profile, and a stripe pattern was observed in the transmission electron microscopy image. These results indicate that the rodlike silicon oxide macromolecules with a 1–2-nm diameter stack parallel. Thus a silicon oxide material with nano-ordered structure was successfully formed and such a structure produced the water solubility.

Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson–Boltzmann theory

In this paper, we show that the far field electrostatic potential created by a highly charged finite size cylinder within the nonlinear Poisson–Boltzmann (PB) theory, is remarkably close to the potential created within the linearized PB approximation by the same object at a well-chosen fixed potential. Comparing the nonlinear electrostatic potential with its linear counterpart associated to a fixed potential boundary condition (called the effective surface potential), we deduce the effective charge of the highly charged cylinder. Values of the effective surface potential are provided as a function of the bare surface charge and Debye length of the ionic solution. This allows to compute the anisotropic electrostatic interaction energy of two distant finite rods.

Degradation of chitosan and starch by 360-kHz ultrasound

Effects of 360-kHz ultrasound on aqueous solutions of chitosan and starch were studied. This treatment is an efficient procedure for reduction of molecular weight of both polysaccharides. It has been demonstrated that at the applied ultrasound frequency degradation is caused both by OH radicals and mechanochemical effects. In Ar-saturated 2×10 −2 mol dm −3 chitosan solutions, pH 3, at an ultrasound dose rate of 170 W kg −1, the average sonochemical chain scission yield in the sonication time range of 0–90 min is ca. 8×10 −11 mol J −1. This yield has been shown to depend on polymer concentration, ultrasound power and gas used to saturate the solution. Scission is accompanied by side reactions leading to the formation of carbonyl groups. Ultrasound-induced chain scission of starch proceeds with lower yield, one of the reasons being probably the different chain conformation when compared with rod-like chitosan macromolecules.

Kinetic Structure Simulations of Nematic Polymers in Plane Couette Cells. II: In-Plane Structure Transitions

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in viscous solvents have a theoretical and computational foundation from which one can model parallel plate Couette cell experiments and explore anisotropic structure generation arising from nonequilibrium interactions between hydrodynamics, molecular short- and long-range elasticity, and confinement effects. Recent progress on the longwave limit of homogeneous nematic polymers in imposed simple shear and linear planar flows [R. G. Larson and H. Ottinger, Macromolecules, 24 (1991), pp. 6270--6282], [V. Faraoni, M. Grosso, S. Crescitelli, and P. L. Maffettone, J. Rheol., 43 (1999), pp. 829--843], [M. Grosso, R. Keunings, S. Crescitelli, and P. L. Maffettone, Phys. Rev. Lett., 86 (2001), pp. 3184--3187], [M. G. Forest, Q. Wang, and R. Zhou, Rheol. Acta, 43 (2004), pp. 17--37], [M. G. Forest, Q. Wang, and R. Zhou, Rheol. Acta, 44 (2004), pp. 80--93], [M. G. Forest, Q. Wang, R. Zhou, and E. Choate, J. Non-Newtonian Fluid Mech., 118 (2004), pp. 17--31], [M. G. Forest, R. Zhou, and Q. Wang, Phys. Rev. Lett., 93 (2004), 088301] provides resolved kinetic simulations of the molecular orientational distribution. These results characterize anisotropy and dynamic attractors of sheared bulk domains and underscore limitations of mesoscopic models for orientation of the rigid rod or platelet ensembles. In this paper, we apply our resolved kinetic structure code [R. Zhou, M. G. Forest, and Q. Wang, Multiscale Model. Simul., 3 (2005), pp. 853--870] to model onset and saturation of heterogeneity in the orientational distribution by coupling a distortional elasticity potential (with distinct elasticity constants) and anchoring conditions in a plane Couette cell. For this initial study, the flow field is imposed and the orientational distribution is confined to the shear deformation plane, which affords comparison with seminal [T. Tsuji and A. D. Rey, Phys. Rev. E (3), 62 (2000), pp. 8141--8151] as well as our own mesoscopic model simulations [H. Zhou, M. G. Forest, and Q. Wang, J. Non-Newtonian Fluid Mech., submitted], [H. Zhou and M. G. Forest, Discrete Contin. Dyn. Syst. Ser. B}, to appear].

Depletion interactions induced by flexible polymers in solutions of rod-like macromolecules

An analytic integral equation treatment is developed for the entropic depletion attractions induced by flexible polymers in dilute solutions of rigid rod-like macromolecules. The polymer-induced changes in the pair correlation functions between rod-like molecules and the rod–rod second virial coefficient are compared with results derived from a scaling approach. Results from both approaches predict that, for flexible coil-like depletants with radii of gyration sufficiently large compared to the rod lengths, the rod–rod second virial coefficient shows a nonmonotonic dependence on the coil concentration with a minimum located near the semidilute threshold. Our results are analogous to prior findings for athermal mixtures of flexible coils and hard spheres, and the predicted nonmonotonicities in the second virial coefficients between dispersed particles have the same physical origins.

Time-resolved small-angle X-ray scattering and wide-angle X-ray diffraction studies on the nanostructure of melt-processable molecular composites

Novel melt-processable molecular composites were obtained from isotactic polypropylene (iPP) and liquid-crystalline oligoester (LCO). The nanostructure and thermal behaviour of molecular composites were examined by real-time synchrotron small-angle X-ray scattering and wide-angle X-ray diffraction methods, and differential scanning calorimetry. The synthesized oligoester, with low melting temperature (391 K), exhibits the ability to form a thermotropic mesophase. It was shown that strong rigid rod-like macromolecules of LCO are dispersed at the molecular scale in iPP matrix and act as reinforcing fibres.

Continuous isotropic-nematic liquid crystalline transition of F-actin solutions.

The phase transition from the isotropic (I) to nematic (N) liquid crystalline suspension of F-actin of average length ł> or =3 microm was studied by local measurements of optical birefringence and protein concentration. Both parameters were detected to be continuous in the transition region, suggesting that the I-N transition is higher than first order. Thus we report experimental evidence for a continuous I-N transition for a suspension of rodlike macromolecules. Our findings are consistent with a recent theory by Lammert, Rokhsar, and Toner [Phys. Rev. Lett. 70, 1650 (1993)], predicting that the I-N transition may become continuous due to suppression of disclinations.