Liquid-crystalline behaviour of benzobisthiazole derivatives as a rigid rod polymer model

Novel materials with a new type of rigid core, namely benzobisthiazole, have been synthesized. The exhibition of liquid-crystallinity is found to be dependent upon the linkage between the rigid core and the alkyloxy phenyl terminal moieties. An interesting feature is the occurrence of tilted smectic phases (smectic C and smectic F) even though there is no significant central dipole moment transverse to the molecule.     

Brownian dynamics of grafted polymer chains: time dependent properties

Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean square displacements are discussed in terms of stretched exponentials, and the behavior of the resulting “Kohlrausch exponents” γ is presented in detail.     

Solid-state NMR and rigid body molecular dynamics to determine domain orientations of monomeric phospholamban

Solid-state NMR spectroscopy, in conjunction with rigid body molecular dynamics calculations, shows that monomeric phospholamban in lipid bilayers has two distinct helical domains, with an interhelical angle within 60-100 degrees, ruling out the possibility of a continuous alpha-helical structure for this protein.     

General description of optical dichroic orientation factors for relating optical anisotropy of bulk polymer to orientation of structural units

The relationship between the optical anisotropy of high polymeric materials in bulk and the orientation of structural units within the materials was described in general by using several types of mean values of the orientation distribution function of three Eulerian angles, i.e., the orientation factors, under some assumptions about the symmetry of the function being applicable for the most of the industrial products. A newly defined biaxial orientation factor, F_θηⁱ = 〈sin² θ_j cos 2η_j〉, where θ_j and η_j are the polar and azimuthal angles of the jth axis within the structural unit with respect to the bulk axes, may relate the biaxial orientation of the structural units to the dichroic orientation factors, which are measurable optical anisotropic indices of the bulk materials. Some applications of the results to the birefringence and infrared and dye dichroism are also discussed.     

A single particle model to simulate the dynamics of entangled polymer melts

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter n(ij) for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C(800)H(1602) chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties.     

Describing the component dynamics in miscible polymer blends: towards a fully predictive model

We have recently proposed [D. Cangialosi et al., J. Chem. Phys. 123, 144908 (2005)] an extension of the Adam-Gibbs [J. Chem. Phys. 43, 139 (1965)] theory, combined with the concept of self-concentration, to describe the temperature dependence of the relaxation time for the component segmental dynamics in miscible polymer blends. Thus, we were able to obtain the dynamics of each component in the blend starting from the knowledge of the dynamic and thermodynamic data of the pure polymers, with a single fitting parameter (alpha) which had to be obtained from the fitting of the experimental data. In the present work we demonstrate that this model is also suitable to describe the polymer segmental dynamics in concentrated polymer solutions. From this result we have developed a new route for determining the value of the alpha parameter associated with any given polymer. Once this value is known for the two components of a possible polymer blend, our model for polymer blends dynamics becomes fully predictive.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Computer simulation of macromolecular systems with amphiphilic monomer units: Biomimetic models

The review presents the basic models used to analyze the self-assembly of protein macromolecules and the main results of studying the self-organization of macromolecules in terms of the concepts of amphiphilicity of an individual monomer unit. The features of the coil-globule transition of these macro-molecules in solutions with different concentrations are described in terms of the statistics of the distribution of monomer units and chain rigidity. It is shown that this model is efficient for interpreting and analyzing experimental data for the study of synthetic and biological macromolecules.     

Long time behaviour of a stochastic model for continuous flow bioreactor

The global dynamics of a deterministic model in wastewater treatment has been investigated in Zhang (J Math Chem 50:2239–2247, 2012). The stochastic version, which can be used for continuous flow bioreactor and membrane reactor is presented in this study. Precisely, we assume there is some uncertainty in the part describing the recycle, which results in a set of stochastic differential equations with white noise. We first show that the stochastic model has always a unique positive solution. Then long time behavior of the model is studied. Our study shows that both the washout equilibrium and non-washout equilibrium are stochastically stable. At the end, we carry out some numerical simulations, which support our theoretical conclusions well.     

A diffusion model of the development of concentration heterogeneities in a photopolymerizable environment with allowance for the limited compatibility of a monomer and a polymer

A diffusion model of the development of concentration heterogeneities of a photopolymerizable composite that takes into account the transition of the monomer-polymer system from the homophase state to the heterophase state with an increase in conversion is proposed. Numerical simulation shows that a significant increase in the amplitude of these heterogeneities is determined not only by the microsyneresis of the composite but also by the efficiency of their development in the homophase state at the initial stage of polymerization. The possibility of controlling the optical properties of the final polymeric material via initiation of the polymerization by radiation of different intensities in the regions of the homophase and heterophase states of the composite is discussed. The numerical-simulation results are experimentally verified.     

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: a one-dimensional generalized Langevin equation treatment

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t) identical with x(0)x(t). We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)].     

Controlled monomer insertion into polymer main chain: synthesis of sequence ordered polystyrene containing thiourethane and trithiocarbonate units by the RAFT process

A polymer having a trithiocarbonate moiety in the main chain was applied as a polymeric precursor to the synthesis of a sequence ordered polymer by insertion polymerization of styrene into the main chain by a RAFT mechanism.     

Hydrogen-bonding dynamics in aqueous solutions of amides and acids: monomer, dimer, trimer, and polymer

Hydrogen-bonding dynamics in aqueous solutions of series of amides and acids have been investigated by means of femtosecond Raman-induced Kerr effect spectroscopy and ab initio quantum chemistry calculation. The amides and acids studied here are acetamide, 1,3-propanedicarboxamide, 1,3,5-pentanetricaroxamide, polyacrylamide with Mw=1500, acetic acid, 1,3-propanedicarboxylic acid, 1,3,5-pentanetricarboxylic acid, and poly(acrylic acid) with Mw=2000. The femtosecond damped transient feature for aqueous amide solutions, which arises from the intermolecular hydrogen bonds of amide and water, becomes clearer with the larger molecular weight of amide. A characteristic vibrational band at about 100 cm(-1) is assigned as the hydrogen-bonding vibrational mode and the ab initio quantum chemistry calculation result indicates that at least two waters, which make up the hydrogen-bonding network with amide, are necessary for this mode. The hydrogen-bonding vibrational mode at about 100 cm(-1) in aqueous amide solutions shifts to the higher frequency with the larger molecular weight amide in consequence of the stronger intermolecular interaction between amide and water. The evidence likely comes from the stronger hydrophobic interaction for polymer than oligomers and monomer. In the picosecond time region, an extra slow relaxation process with a time constant of about 60 ps has been found in the aqueous polymer solutions. The relaxation is assigned as a local motion of the constitutional repeat unit of polymers from comparison with monomer and oligomers.     

Low-temperature dispersion related to methylene units of a polymer main chain

Polymers containing dynamically isolated polymethylene segments of various lengths were obtained from the reaction of bisphenol-A-diglycidyl ether with α,ω-diamines. On the basis of the mechanical damping data of these polymers, it was established that the shortest polymethylene segment to show the ?125°C. γ dispersion, characteristic of polyethylene, must consist of at least five carbon atoms.     

Force-reactivity property of a single monomer is sufficient to predict the micromechanical behavior of its polymer

We demonstrate an accurate prediction of the micromechanical behavior of a single chain of cyclopropanated polybutadiene, which is governed by rapid isomerization of the cyclopropane moieties at ~1.2 nN, from the force-rate correlation of this reaction measured in a small series of increasingly strained macrocycles. The data demonstrate that a single physical quantity, force, uniquely defines the dynamics across length scales from >100 to <1 nm and that strain imposed through molecular design and that imposed by micromanipulation techniques have equivalent effects on the kinetics of a chemical reaction. This represents a new method of screening potential monomers for applications in stress-responsive materials that could also facilitate atomistic interpretations of single-molecule force experiments.