Theory of Intrachain Relaxation Spectra for Polymer Networks Possessing a Short- or Long-Scale Ordering. Effects of the Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included Rods

We discuss the relaxation properties of polymer networks possessing either short-scale ordering caused by rigidity of network strands or long-scale liquid crystalline order. The main topics of the paper are the equilibrium and local dynamic properties of a polymer network ordered due to nematic-like interactions of the network segments with included rod-like particles. A simplified three chain network model is used. Lagrange multipliers in the equations of motion of hard rods are replaced by their averaged values. This approximation corresponds to modelling the rod-like particles by elastic Gaussian springs, their mean-square lengths independent of the ordering. Nematic-like interactions between network segments and rods are taken into account in terms of the Maier-Saupe mean-field approximation. Nematic ordering of rods induces ordering of the network segments. Relaxation spectrum of the ordered network splits into two main branches for the parallel and perpendicular components of the chain segments with respect to the director. We calculate the relaxation times of a polymer network as functions of the wave number. The relaxation spectrum of an isotropic network and that of the ordered network with included rods are compared.     

The Estimation of Statistical Parameters Determining the Relaxation Times of Nematic Elastomers: A Three‐Chain Network Model

A simplified “three‐chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean‐square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely‐jointed‐rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod‐like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively.     

Theory of relaxation properties of two‐dimensional polymer networks, 1. Normal modes and relaxation times

The local relaxation properties of polymer networks with a two‐dimensional connectivity are considered. We use the mesh‐like network model in which the average positions of junctions form the regular spatial structure consisting of square repeating units (network cells). The two‐dimensional polymer network consisting of “bead and spring” Rouse chains and the simplified coarse‐grained network model describing only the large‐scale collective relaxation of a network are studied. For both dynamic network models the set of relaxation times and the transformation from Cartesian coordinates of network elements to normal modes are obtained. Using the normal mode transformation obtained, in Part 2 of this series the exact analytical expressions for various local dynamic characteristics of the polymer network having a two‐dimensional connectivity will be calculated.     

Magnetic Field‐Induced Shape Transitions in Multiphase Polymer‐Liquid Crystal Blends

Summary: This paper presents a computational study of phase separation‐phase ordering‐texturing in blends of polymer coils and rod‐like nematic liquid crystals under the presence of magnetic fields, using an extended version of the Matsuyama‐Evans‐Cates model (Phys. Rev. E 2000 , 61, 2977). This work demonstrates that demixing in these blends leads to droplet morphologies with tunable droplet shapes and director textures. In contrast to filled nematics, where solids are suspended in a nematic liquid crystal matrix, demixing in coil‐mesogenic rods blends leads to nematic emulsions, in which the deformable viscoelastic polymer drops are suspended in a nematic matrix. Under strong anchoring conditions, the imposition of a magnetic field leads to a director re‐orientation that due to strong anchoring produces a droplet shape change. Magnetic field‐induced shape transitions in these blends are shown to be second order with a finite critical field threshold that diverges as anchoring strength vanishes. A morphological‐texture diagram summarizes the magnetic field‐anchoring conditions that promote anisotropic shapes. This work presents additional material processing routes to design and control bi‐phasic morphologies in polymer‐liquid crystal blend.

Computed morphology phase diagram in terms of magnetic field strength Λ_M and anchoring strength. Λ_ϕQ.     

Dynamics of entangled supramolecular polymer networks in presence of high‐order associations of strong hydrogen bonding groups

Dynamics of entangled polymer chains in the melt state are deliberately excluded in most of the studies on supramolecular polymer networks by utilizing nonentangled precursor chains. Relaxation of the system mainly depends on the dissociation of the associative groups in latter case and nonentangled chains deliver nothing to resist afterward. Conversely, in an entangled system, relaxation of polymer chains and dissociation of associative groups can occurred parallel. Supramolecular networks based on an entangled precursor polymer with different levels of strong associating ureidopyrimidinone (UPy) groups are synthesized to screen the corresponding effects on the dynamics of the system. Binary‐associated UPy groups phase separate into collective assemblies by stacking and form high‐order, needle‐like domains at higher UPy contents. Relaxation of polymer chains is significantly hindered due to the trapping of polymer segments between UPy stacks. Above a certain threshold of UPy content (~4 mol%), the plateau level and final relaxation time of networks show a significant jump, which is attributed to the onset of high‐order association of UPy groups.     

Theory of relaxation properties of two‐dimensional polymer networks, 2. Local dynamic characteristics

Using normal mode transformation obtained in Part 1 of this series^[1], the exact analytical expressions for the mean‐square displacements of junctions and non‐junction beads, the autocorrelation functions of the end‐to‐end chain vectors between neighboring junctions, and those of subchain vectors of a two‐dimensional regular network consisting of "bead and spring" Rouse chains are obtained. Contributions of intra‐ and interchain relaxation processes to the local dynamic characteristics considered are compared. The time behavior of dynamic quantities obtained is estimated for different scales of motions. The possibility of describing long‐time relaxation of a two‐dimensional network by a simplified coarse‐grained network model is demonstrated. It is shown that the local relaxation properties of a two‐dimensional polymer network (as well as a three‐dimensional network) on scales smaller than the average distance between cross‐links are very close to those of a single Rouse chain. The large‐scale collective relaxation of the polymer networks having a two‐dimensional connectivity differs considerably from that of the three‐dimensional networks.     

Motion of star‐branched chains in polymer networks: a Monte Carlo study

A simple model of branched polymers in confined space is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions (good solvent conditions). A single star molecule is trapped in a network of linear polymer chains of restricted mobility. The simulations are carried out using the classical Metropolis algorithm. Static and dynamic properties of the star‐branched polymer are determined using various networks. The dependence of the longest relaxation time and the self‐diffusion coefficient on chain length and network properties are discussed and the proper scaling laws formulated. The possible mechanism of motion is discussed. The differences between the motion of star‐branched polymers in such a network are compared with the cases of a dense matrix of linear chains and regular rod‐like obstacles.     

Solid Polymer Electrolyte Based on Pluronic P123 Triblock Copolymer‐Siloxane Organic‐Inorganic Hybrid

A novel organic‐inorganic hybrid electrolyte based on poly(ethylene oxide)‐poly(propylene oxide)‐poly(ethylene oxide) triblock copolymer (Pluronic P123) complexed with LiClO₄ via the co‐condensation of an epoxy trialkoxysilane and tetraethylorthosilicate was prepared. Characterization was made by a variety of techniques including powder X‐ray diffraction, AC impedance, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and multinuclear solid state NMR measurements. The hybrid with [O]/[Li] = 16 exhibited a mesophase with a certain degree of ordering, which arose by the self‐assembly of P123 with the silica network. The P123 triblock copolymer acts as a structure‐directing surfactant to organize with silica networks and as a polymer matrix to dissolve alkali lithium salts as well. The DSC results indicated the formation of transient crosslinking between Li⁺ ions and the ether oxygens of the EO and PO segments, resulting in an increase the T_g with increasing salt concentrations. Variable temperature ⁷Li‐{¹H} MAS NMR spectra revealed the presence of two different local environments for lithium cations, probably due to the lithium cations in the polymer‐rich domain and in the silica‐rich domain, respectively. A combination of XRD and conductivity results suggests that the drastically enhanced conductivity for the ordered hybrid electrolyte is closely related to the formation of mesophase, which may provide unique Li⁺ conducting pathways.     

Size‐selective purification of hepatitis B virus‐like particle in flow‐through chromatography: Types of ion exchange adsorbent and grafted polymer architecture

Hepatitis B virus‐like particles expressed in Escherichia coli were purified using anion exchange adsorbents grafted with polymer poly(oligo(ethylene glycol) methacrylate) in flow‐through chromatography mode. The virus‐like particles were selectively excluded, while the relatively smaller sized host cell proteins were absorbed. The exclusion of virus‐like particles was governed by the accessibility of binding sites (the size of adsorbents and the charge of grafted dextran chains) as well as the architecture (branch‐chain length) of the grafted polymer. The branch‐chain length of grafted polymer was altered by changing the type of monomers used. The larger adsorbent (90 μm) had an approximately twofold increase in the flow‐through recovery, as compared to the smaller adsorbent (30 μm). Generally, polymer‐grafted adsorbents improved the exclusion of the virus‐like particles. Overall, the middle branch‐chain length polymer grafted on larger adsorbent showed optimal performance at 92% flow‐through recovery with a purification factor of 1.53. A comparative study between the adsorbent with dextran grafts and the polymer‐grafted adsorbent showed that a better exclusion of virus‐like particles was achieved with the absorbent grafted with inert polymer. The grafted polymer was also shown to reduce strong interaction between binding sites and virus‐like particles, which preserved the particles’ structure.     

Synthesis and characterization of L‐leucine containing chiral vinyl monomer and its polymer,poly(2‐(methacryloyloxyamino)‐4‐methyl pentanoic acid)

A chiral monomer containing L ‐leucine as a pendant group was synthesized from methacryloyl chloride and L ‐leucine in presence of sodium hydroxide at 4 °C. The monomer was polymerized by free radical polymerization in propan‐2‐ol at 60 °C using 2,2′‐azobis isobutyronitrile (AIBN) as an initiator under nitrogen atmosphere. The polymer, poly(2‐(Methacryloyloxyamino)‐4‐methyl pentanoic acid) is thus obtained. The molecular weight of the polymer was determined to be: M_w is 6.9 × 10³ and M_n is 5.6 × 10³. The optical rotation of both chiral monomer and its polymer varies with the solvent polarity. The amplification of optical rotation due to transformation of monomer to polymer is associated with the ordered conformation of chiral monomer unit in the polymeric chain due to some secondary interactions like H‐bonding. The synthesized monomer and polymer exhibit intense Cotton effect at 220 nm. The conformation of the chain segments is sensitive to external stimuli, particularly the pH of the medium. In alkaline medium, the ordered chain conformation is destroyed resulting disordered random coils. The ordered coiling conformation is more firmly present on addition of HCl. The polymer exhibits swelling‐deswelling characteristics with the change of pH of the medium, which is reversible. The Cotton effect decreases linearly with the increase of temperature which is reversible on cooling. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2228–2242, 2009     

Chain Architecture Dependent 3‐Dimensional Supramolecular Assembly of Rod‐Coil Molecules with a Conjugated Hexa‐p‐phenylene Rod

Summary: We have prepared hexa‐p‐phenylene based rod‐coil molecules with identical coil volume fractions, but different poly(propylene oxide) (PPO) coil architectures (linear versus dibranched), and investigated their self‐assembling behavior in the solid state by small angle X‐ray scattering (SAXS) and transmission electron microscopy (TEM) techniques. Rod‐coil molecules with a linear PPO coil showed a honeycomb‐like lamellar assembly of rod segments with hexagonally arrayed PPO coil perforations. In contrast, the rod‐coil molecules with dibranched PPO coils self‐organized into rod bundles with a body centered tetragonal symmetry surrounded by a PPO coil matrix. These results demonstrate that the steric hindrance at the rod/coil interface arising from coil architectural variation is a dominant parameter governing supramolecular rod assembly in the rod‐coil system.

TEM images and schematic illustrations of the self‐assembled structures of rod‐coil molecules with linear (left) and dibranched (right) PPO coils, respectively.     

Colloid‐Assisted Self‐Assembly of Robust,Three‐Dimensional Networks of Carbon Nanotubes over Large Areas

Natural materials, such as bone and spider silk, possess remarkable properties as a result of sophisticated nanoscale structuring. They have inspired the design of synthetic materials whose structure at the nanoscale is carefully engineered or where nanoparticles, such as rods or wires, are self‐assembled. Although much work has been done in recent years to create ordered structures using diblock copolymers and template‐assisted assembly, no reports describe highly ordered, three‐dimensional nanotube arrays within a polymeric material. There are only reports of two‐dimensional network structures and structures on micrometer‐size scales. Here, we describe an approach that uses plasticized colloidal particles as a template for the self‐assembly of carbon nanotubes (CNTs) into ordered, three‐dimensional networks. The nanocomposites can be strained by over 200% and still retain high conductivity when relaxed. The method is potentially general and so may find applications in areas such as sensing, photonics, and functional composites.

     

Self‐assembly of N‐carboxyethylchitosan near the isoelectric point

For the first time the possibility to obtain nanostructures by self‐assembly of chitosan polyampholytic derivative was demonstrated. The self‐assembly of N‐carboxyethylchitosan (CECh) took place only near its isoelectric point (pH 5.0–5.6). Out of the pH range 5.0–5.6, CECh aqueous solutions behaved as real solutions. Dynamic light scattering and atomic force microscopy analyses revealed that spherically shaped or rod/worm‐like nanosized assemblies were formed depending on the polymer molar mass, pH value, and polymer concentration. CECh of two different molar masses was studied in concentrations ranging from 0.01 to 0.1 mg/mL. The structures from CECh of weight‐average molar mass (M_w ) 4.5 × 10³ g/mol were spherical regardless the pH and polymer concentration. In contrast, CECh of high molar mass (HMMCECh, M_w = 6.7 × 10⁵ g/mol) formed self‐assemblies with spherical shape only at pH 5.0 and 5.6. At pH 5.2 spherical nanoparticles were obtained only at polymer concentration 0.01 mg/mL. The mean hydrodynamic diameter (D_h) of the obtained nanoparticles was in the range from 30 to 980 nm. On increasing the concentration, aggregation of the nanoparticles appeared, and at HMMCECh concentration 0.1 mg/mL, rod/worm‐like structures were obtained. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6712–6721, 2008     

Simulation of transient banded textures of sheared nematic polymers

Abstract

Nematic polymers, under certain conditions, develop a transient banded texture after cessation of simple shear flow when observing the sheared sample between crossed polars. Here we present a viscoelastic model that describes the formation mechanism of this well-characterized but yet unexplained phenomenon for a typical uniaxial rigid rod nematic polymer. It predicts that the relaxation of shear-flow enhanced scalar order parameter spatial fluctuations produces spatially periodic torques on the director, thereby producing a transient banded texture when viewing the sample between crossed polars. Our numerical results and digitized optical pattern are in good agreement with reported experimental observations.     

The Local and Collective Mobility in Polymer Chains and Networks with Included Rigid Particles Elastically Connected with the Network

Summary: The theory of molecular mobility of a polymer network with included rod-like particles is developed. The case is considered when the length of rods is comparable or greater than the average distance between neighboring cross-links of the primary network. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The junctions of this model describe the great network fragments (domains) the sizes of which are near to the average distance between neighboring rods.The quasi-elastic interactions between rods and network fragments lead to a broad relaxation spectrum for included rods as compared with free rods which are characterized by a single relaxation time of rotational diffusion. The frequency dependence of the dielectric loss factor of included rods is calculated for rods with permanent dipole moments directed parallel to the long axes of the rods chaotically distributed in the network. The frequency dependence of dynamic modulus of a polymer network with included rods is obtained. The increment in the dynamic modulus of the relatively short network motions (smaller than the distance between rods) also is taken into account. The broad relaxation spectrum of included rods leads to appearance of several maximums on the frequency dependences of both the dielectric loss factor and dynamical modulus.     

Theoretical analysis of the local orientation effect and the lift‐hyperlayer mode of rodlike particles in field‐flow fractionation

We investigated theoretically the effects of the cross‐stream migration and the local average orientation of rodlike particles on the shape‐based separation using field‐flow fractionation. The separation behavior was analyzed by comparing the retention ratios of spheres and rods. The retention ratio of a rod was evaluated through the derivation of its cross‐sectional concentration profile by considering the rod migration and the local average orientation. Our study in various flow conditions showed that the rod migration, caused by the hydrodynamic interaction with a wall, can affect the separation behavior as a lift‐hyperlayer mode. We also demonstrated that the local average orientation, which is a function of a local shear rate and a rotational diffusivity, results in the transverse diffusivity that is different from its perpendicular diffusivity. These results suggest that the experimental separation behaviors of rods in field‐flow fractionation may not be fully explained by the current theory based on the normal mode and the steric mode. We also characterized each condition where one of the normal mode, the steric mode of spheres, and the lift‐hyperlayer mode of rods is dominant.     

Ordered Arrangements of Semiflexible Polymers at the Interface with Solids

The molecular arrangements and conformations of dense systems of semiflexible polymer chains near solid surfaces have been investigated by Monte Carlo simulations. At variance with the results obtained for more flexible chains, the mean square end‐to‐end distance and the mean square radius of gyration of chains in contact with the surfaces are found to be much higher than in the bulk. This is related to the increased length of the surface trains and to the increased tendency of such trains to form rod‐like strands. As a result, the first layer of polymer units in contact with the surfaces consists of two‐dimensional domains of locally parallel chain segments. The width of these domains is several times the transverse diameter of the chains.     

Simulation of transient banded textures of sheared nematic polymers

Nematic polymers, under certain conditions, develop a transient banded texture after cessation of simple shear flow when observing the sheared sample between crossed polars. Here we present a viscoelastic model that describes the formation mechanism of this well-characterized but yet unexplained phenomenon for a typical uniaxial rigid rod nematic polymer. It predicts that the relaxation of shear-flow enhanced scalar order parameter spatial fluctuations produces spatially periodic torques on the director, thereby producing a transient banded texture when viewing the sample between crossed polars. Our numerical results and digitized optical pattern are in good agreement with reported experimental observations.     

Chirality Induction through Nano‐Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self‐Assembly of X‐Shaped Bolapolyphiles

The single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self‐assembly of X‐shaped polyphiles, where glycerol‐capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side‐chains fill their respective separate channel networks. This new self‐assembly mode can be considered as a two‐color symmetry‐broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub‐10 nm periodicities using achiral compounds.