Concentration of Hydrogen in the Upper Atmosphere of the Earth in the 300-600 Km Altitude Range According to Ionospheric Data

Concentration of hydrogen in upper atmosphere according to ionospheric dat

Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: Application to polymer melts

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades. © 2007 American Institute of Physics

Deuteron and proton spin-lattice relaxation dispersion of polymer melts: Intrasegment, intrachain, and interchain contributions

Proton and deuteron field-cycling NMR relaxometry was applied to deuterated and undeuterated bulk polyethyleneoxide and polybutadiene melts and mixtures thereof with molecular weights above the critical value. Spin-lattice relaxation data due to intrasegment (quadrupolar) couplings and intra- and interchain (dipolar) interactions were evaluated. Diverse dynamic limits are identified both with the proton and deuteron frequency dispersion data. The comparison between the intrachain and the interchain contributions leads to the conclusion that only model theories based on largely isotropic chain dynamics can account for the experimental findings. The extremely anisotropic character of the well-known tube/reptation model is too restrictive in this respect. © 2007 American Institute of Physics

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by a stretched exponential function Cp(t) ∝ exp([-(t/ τ*p)βp , where βp is the stretching parameter dependent on the number p of the Rouse mode and τ*p is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉nRR In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〉b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied

The twice-renormalized Rouse formalism of polymer dynamics: Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice-renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended to include the terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts (such as the reptation (tube) model or the polymer mode-mode coupling formalism), the predictions perfectly coincide with all the results of recent spin-lattice relaxation dispersion and diffusion experiments as well as with computer simulations. On the other hand, the twice-renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity is largely a manifestation of collective multichain modes. In the rigorous sense, no such multichain treatment has yet been established to our knowledge. The necessity to consider interchain cooperativity in any real comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions. © 2000 MAIK "Nauka/Interperiodica"

Numerical study of dynamical properties of entangled polymer melts in terms of renormalized rouse models

The dynamic properties of n-renormalized Rouse models (n = 1, 2) were numerically investigated. Within two decay orders of magnitude, the damping of normal Rouse modes of a polymer chain was shown to be approximated by the stretched exponential function Cp(t) ∝ exp{- (t/τp*)βp}, where βp is the stretching parameter dependent on the number p of the Rouse mode and τp* is the characteristic decay time. The dependence of the stretching parameter on the mode number has a minimum. It was found that the nonexponential form of autocorrelation functions of the normal modes affects the dynamic characteristics of a polymer chain: the mean-square segment displacement 〈r2(t)〉nRR and the autocorrelation function of the tangential vector 〈b(t)b(0)〉NRR. In comparison with the Markov approximation, the 〈r2(t) 〉TRR and 〈b(t)b(0)〉TRR values in the twice-normalized Rouse model change over time at a lesser rate: ∝t 0.31 and ∝t-0.31 at times t ≪ τ p TRR, respectively. The effect of the finite dimensions of the polymer chain on the relaxation times of the normal modes was studied. Copyright © 2005 by Pleiades Publishing, Inc

Polymer chain dynamics predicted by n-renormalized rouse models: Numerical studies

Features of the renormalized and twice renormalized Rouse models were examined numerically. Based on numerical evaluations of the generalized Langevin equation in renormalization approaches, nonexponential normal mode autocorrelation functions were derived, that can be described over two orders of magnitude by stretched exponential functions. The mode number dependence of the stretching parameter was evaluated. The consequences of the nonexponential correlation functions on dynamical properties are discussed. As a basis for predictions for the behavior of diffusion and spin-lattice relaxation dispersion, the time dependence of the mean-squared segment displacement and of the autocorrelation function of the segment tangential vector, respectively, were obtained taking into account finite chain lengths

The twice renormalized rouse formalism of polymer dynamics. Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation

The twice renormalized Rouse formalism, a refined version of Schweizer's renormalized Rouse treatment of chain dynamics in entangled polymers, is presented. The time scale of validity is extended including terminal chain relaxation and center-of-mass diffusion. In clear contrast to the laws concluded from other polymer dynamics concepts such as the reptation (tube) model or the polymer mode-mode coupling formalism, the predictions perfectly compare with all results of recent spin-lattice relaxation dispersion and diffusion experiments as well as computer simulations. On the other hand, the twice renormalized Rouse formalism fails to explain the rubber-elastic plateau of stress relaxation. It is inferred that this is a consequence of the single-chain nature of the present approach not accounting for the fact that viscoelasticity largely is a manifestation of collective many-chain modes. In the rigorous sense, no such multi-chain treatment has been established so far to our knowledge. The necessity to consider inter-chain cooperativity in any really comprehensive polymer dynamics theory is concluded from low-frequency spin-lattice relaxation data, which are shown to reflect fluctuations of long-distance intermolecular dipole-dipole interactions

Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur