Features of polymer chain dynamics as revealed by intermolecular nuclear magnetic dipole-dipole interaction: Model calculations and field-cycling NMR relaxometry

Proton NMR phenomena such as spin-lattice relaxation, free-induction decays, and solid echoes are analyzed with respect to contributions by intermolecular dipole-dipole interactions in polymer melts. The intermolecular dipole-dipole correlation function is calculated by taking into account the correlation hole effect characteristic for polymer melts. It is shown that the ratio between the intra- and intermolecular contributions to NMR measurands depends on the degree of isotropy of chain dynamics anticipated in different models. This, in particular, refers to the tube/reptation model that is intrinsically anisotropic in clear contrast to n -renormalized Rouse models, where no such restriction is implied. Due to anisotropy, the tube/reptation model predicts that the intramolecular contribution to the dipole-dipole correlation function increases with time relative to the intermolecular contribution. Therefore, the intramolecular contribution is expected to dominate NMR measurands by tendency at long times (or low frequencies). On the other hand, the isotropic nature of the n -renormalized Rouse model suggests that the intermolecular contribution tends to prevail on long-time scales (or low frequencies). Actually, theoretical estimations and the analysis of experimental spin-lattice relaxation data indicate that the intermolecular contribution to proton NMR measurands is no longer negligible for times longer than 10 -7s- 10-6s corresponding to frequencies below the megahertz regime. Interpretations not taking this fact into account need to be reconsidered. The systematic investigation of intermolecular interactions in long-time/low frequency proton NMR promises the revelation of the dynamic features of segment displacements relative to each other in polymer melts. © 2010 American Institute of Physics

Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems

We discuss a scheme for the numerical solution of one-dimensional initial value problems exhibiting strongly localized solutions or finite-time singularities. To accurately and efficiently model such phenomena we present a full space-time adaptive scheme, based on a variable order spatial finite-difference scheme and a 4th order temporal integration with adaptively chosen time step. A wavelet analysis is utilized at regular intervals to adaptively select the order and the grid in accordance with the local behavior of the solution. Through several examples, taken from gasdynamics and nonlinear optics, we illustrate the performance of the scheme, the use of which results in several orders of magnitude reduction in the required degrees of freedom to solve a problem to a particular fidelity

Recent NMR investigations on molecular dynamics of polymer melts in bulk and in confinement

Polymer dynamics in the melt state cover a wide range in time and frequency, for both molecular weights below and above the entanglement length. Nuclear Magnetic Resonance (NMR) offers a number of techniques that cover a broad section of this frequency range, with frequency dependent (i.e., magnetic field dependent) relaxometry providing the widest window. Combining fast field cycling techniques with frequency-temperature superposition has recently improved the understanding of polymer melt dynamics from the local to global range. At the same time, a detailed theoretical approach that separates intra- and intermolecular contributions to relaxation times has been developed. These methods are shown to improve the description of segmental dynamics in polymers, being related to time-dependent diffusion coefficients, and to distinguish between these two different relaxation contributions for a number of model compounds. The findings represent the foundation for a more thorough understanding of polymers under external restrictions and bear potential to provide a conceptually new access to biopolymer dynamics and interactions. © 2013 Elsevier Ltd

On the theory of double quantum NMR in polymer systems: The second cumulant approximation for many spin i = 1/2 systems

General analytical expressions for Double Quantum Nuclear Magnetic Resonance (DQ NMR) kinetic curves of many-spin I = 1/2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the initial part of the kinetic curves and provide a reasonable approximation up to times of about the effective spin-relaxation time. For the case when the system contains two isolated spins, this result exactly reproduces known expressions. In the case of polymer melts, the intermolecular magnetic dipole-dipole interactions significantly influence the time dependence of the DQ NMR kinetic curves. © 2013 AIP Publishing LLC

Induction heating system for die tooling of press for isothermal stamping of large-sized parts

The paper describes the installation for stamping large-sized parts. The use of induction heating for heating the working tool of the stamp in the operating mode is considered. A system with 4 flat inductors is described. This solution allows for the most efficient hot stamping operation compared to other known solutions. An example of the result of numerical simulation of the temperature field distribution is demonstrated. © Published under licence by IOP Publishing Ltd.This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 075-11-2019-028

On the theory of the proton free induction decay and Hahn echo in polymer systems: The role of intermolecular magnetic dipole-dipole interactions and the modified Anderson-Weiss approximation

The influence of the intermolecular magnetic dipole-dipole interaction on the free induction decay (FID) as well as on the Hahn-echo of proton spins in polymer melts is investigated. It is shown that for isotropic models of polymer dynamics, when polymer segment displacements do not correlate with an initial chain conformation, the influence of the intermolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing more rapidly with evolution time than the corresponding influence of the intramolecular magnetic dipole-dipole interactions. On the other hand, the situation is inverted for the tube-reptation model: here the influence of the intramolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing faster with time than the contribution from intermolecular interactions. A simple expression for the relative mean squared displacements of polymer segments from different chains is obtained from the intermolecular contribution to the FID. A modified Anderson-Weiss approximation, taking into account flip-flop transitions between different spins, is proposed and on that basis, the conditions for extracting the relative intermolecular mean squared displacements of polymer segments from the intermolecular contribution to the proton FID is established. Systematic investigations of intermolecular contributions, which were considered as an unimportant factor for FID and Hahn echo in polymer systems by most previous works, actually cannot be considered as negligible and opens a new dimension for obtaining information about polymer dynamics in the millisecond regime. © 2012 American Institute of Physics

The electron spin-lattice relaxation in pyrolyzed poly-2-methyl-5-ethinylpyridine

The temperature and field dependences of the rate of electron spin-lattice relaxation (ESLR) have been studied on poly-2-methyl-5-ethinyl pyridine (PMEP), which had been pyrolyzed at various temperatures. The experimental results are interpreted from the aspect of the theoretical calculations predicting the diversity of these dependences in the case of linear-and laminar-structure polymers. The results of the evaluations are compared with those of elemental analysis and IR-spectroscopy. © 1982