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

Manifestation of reptation motions of macromolecules on diffusional attenuation of the stimulated spin echo signal

The effect of fluctuations in the characteristic time of motion of defects and the length of the force pipe on the diffusional attenuation profile of the spin echo signal in the long wave region is discussed. When the correlation times of these fluctuations are more than the average time of pipe regeneration the diffusional attenuation has an essentially non-exponential character and can be described in terms of a random fluctuating coefficient of self-diffusion. The true coefficient of self-diffusion can be determined from the initial inclination of the diffusional attenuation profile. © 1988

Viscoelastic properties of linear polymer melts as effect of broken axial symmetry and mutual uncrossability of macromolecules

On the basis of the exact Green-Kubo formula for viscosity it is rigorously shown that the zero-shear viscosity of polymer melts is totally determined by the Fixman stress-tensor which represents interchain interactions. The Curtiss-Bird approximation for the Fixman tensor permits one to consider it as a sum of effectively single chain tensors. Considering an arbitrary conformation of a macromolecule as a state with broken axial symmetry, the mean-field part of the Curtiss-Bird stress tensor can be expressed as a sum of two terms. The first term reflects the local geometry of the chain conformation and is proportional to the local curvature of the polymer chain. It is proportional to the effective intramolecular entropic stress-tensor. The second term, which has been never considered before, reflects global properties of the spatial distribution of the probe chain segments and mutual uncrossability of polymer chains. It is proportional to the concentration gradient of the probe chain segments. This term leads to a molecular-mass independent plateau of the relaxation modulus and gives the same molecular mass dependence for the viscosity and the terminal relaxation time in polymer melts with molecular masses large enough. The plateau modulus is derived as GN 0 ∝ kBT / (ρmŜ2(0)b6), where kBT is the temperature factor, ρm is the Kuhn segment number density, Ŝ(0) is the collective structure factor of polymer melts in the long wavelength limit, and b is the Kuhn segment length. For the Gaussian thread chain model introduced by Schweizer and Curro, the plateau modulus becomes GN 0 ∝ kBT / (ρmb2)3. This expression is in qualitative agreement with well-known experimental data. © 2002 Elsevier Science B.V. All rights reserved

Length and time scales of entanglement and confinement effects constraining polymer chain dynamics

With characteristic time constants for polymer dynamics, namely τs (the segment fluctuation time), τe (the entanglement time), and τR (the longest Rouse relaxation time), the time scales of particular interest (i) τ < τss (ii) τS < t < τe, and (iii) τe < t < τR will be discussed and compared with experimental data. These ranges correspond to the chain-mode length scales (i) ℓ < b, (ii) b < ℓ < d2 /b, and (iii) d2/b < ℓ < L, where b is the statistical segment length, d is the dimension of constraints by entanglements and/or confinement, and L is the chain contour length. Based on Langevin-type equations-of-motion coarse-grained predictions for the mean-squared segment displacement and the spin-lattice relaxation dispersion will be outlined for the scenarios "freely-draining", "entangled", and "confined". In the discussion we will juxtapose "local" versus "global" dynamics on the one hand, and "bulk" versus "confined" systems on the other. © 2010 Materials Research Society

Nuclear spin-lattice relaxation dispersion and segment diffusion in entangled polymers. Renormalized Rouse formalism

A formalism for polymer melts was derived linking the spin-lattice relaxation time T1, the correlation function of chain tangent vectors and the mean-square segment displacement with memory functions. Potential normal-mode number dependences are included. In the limit of infinitely fast decaying memory functions the theory reproduces known expressions characteristic for Rouse dynamics. Interchain excluded-volume forces were taken into account in the frame of the renormalized Rouse approach [K. S. Schweizer, J. Chem. Phys. 91, 5802 (1989)]. The power law limits predicted on this basis are T 1, ∝ω1/2, T1∝ω1/4, and T1∝ω1/5 for the T1 dispersion in a sequence of regimes from high to low frequencies. The mean-square segment displacement obeys 〈r2〉∝t1/4, 〈r2〉∝ t3/8, and 〈r2〉∝2/5 in a sequence of limits for increasing times. The spin-lattice relaxation dispersion of different polymers was studied mainly by the aid of the field-cycling NMR technique. The covered proton frequency range is less than 103 Hz to more than 108 Hz. The frequency dependence can be described by a series of power laws arising from chain dynamics. Two of these, namely T 1∝ω0.5 and T1∝ω0.25 tending to appear at high and low frequencies, respectively, can be perfectly explained on the basis of the derived renormalized Rouse limits. The third power law, T1∝ω0.44, which was observed only at rather low frequencies, has no theoretical counterpart in the frame of the renormalized Rouse theory. Some hints that farther reaching polymer theories such as the mode-mode coupling approach [K. S. Schweizer, J. Chem. Phys. 91, 5822 (1989)] can help to understand this finding are discussed. © 1994 American Institute of Physics

Length and time scales of entanglement and confinement effects constraining polymer chain dynamics

With characteristic time constants for polymer dynamics, namely τs (the segment fluctuation time), τe (the entanglement time), and τR (the longest Rouse relaxation time), the time scales of particular interest (i) τ < τss (ii) τS < t < τe, and (iii) τe < t < τR will be discussed and compared with experimental data. These ranges correspond to the chain-mode length scales (i) ℓ < b, (ii) b < ℓ < d2 /b, and (iii) d2/b < ℓ < L, where b is the statistical segment length, d is the dimension of constraints by entanglements and/or confinement, and L is the chain contour length. Based on Langevin-type equations-of-motion coarse-grained predictions for the mean-squared segment displacement and the spin-lattice relaxation dispersion will be outlined for the scenarios "freely-draining", "entangled", and "confined". In the discussion we will juxtapose "local" versus "global" dynamics on the one hand, and "bulk" versus "confined" systems on the other. © 2010 Materials Research Society

Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments

© 2017 Elsevier B.V.Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under entanglement and chain connectivity constraints. Under such conditions, reorientations will be correlated with translational displacements leading to the so-called RMTD relaxation process (reorientation mediated by translational displacements). Applications to porous glasses, protein solutions, lipid bilayers, and clays will be discussed. Finally, we will address the intriguing fact that the various time limits of the segment mean-square displacement of polymers in some cases perfectly reproduce predictions of the tube/reptation model whereas the reorientation dynamics suggests strongly deviating power laws

Theory of field-gradient NMR diffusometry of polymer segment displacements in the tube-reptation model

The spin-echo attenuation in NMR field-gradient diffusometry experiments is treated for the tube model in a time scale longer than the entanglement time e. The theory comprises the Doi-Edwards [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] limits of the (anomalous) segment displacement as well as the (ordinary) center-of-mass diffusion. This formalism is to be distinguished from formalisms for anomalous diffusion on fractal networks: The reptation mechanism implies an intrinsically different character of the displacement probability density. It is shown that the expressions usually applied in NMR diffusometry are inadequate for the reptation problem and can cause misinterpretations. Applications of the formalism to polymer chains in bulk and confined in porous media are discussed. © 1995 The American Physical Society