Field-gradient NMR diffusometry in poly(ethylene oxide) melts confined to nanoscopic pores of solid methacrylate matrices

Depending on the choice of matrix constituents, the diameters of strands of linear, monodisperse poly(ethylene oxide) confined to nanoscopic pores of cross-linked methacrylate matrices can be varied considerably. The samples were characterized by DSC, TEM, SEM and fringe field-gradient NMR diffusometry with respect to the strand diameter. A formalism evaluating diffusive spin echo attenuation curves based on the tube/reptation model allows the determination of the strand diameter. Values in the range 8-58 nm were found in accordance with TEM and SEM micrographs of shadow-cast freeze-fractured surfaces of the samples.     

Investigations of polymer dynamics in nanoporous media by field cycling NMR relaxometry and the dipolar correlation effect

The chain dynamics of short-chain perfluoropolyether melts confined in Vycor nanoporous media has been characterized by field cycling nuclear magnetic resonance relaxometry and the dipolar correlation effect. The slowdown of motions under confinement, leading to larger residual dipolar couplings, has been probed by looking at the quotient of stimulated and primary echoes. Using field cycling relaxometry, it has been shown that there is strong evidence of reptation-like motion, even for such short-chain polymers as shown by the frequency and molecular weight dependences of the spin-lattice relaxation time.     

Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation.     

Thermodynamic Limitations of the Reptation Model

Summary: The paper deals with the question whether the tube/reptation model of polymer chain dynamics is compatible with general laws of statistical physics. Based on a relation between the mean squared fluctuation of the number of segments in a given volume element and the isothermal compressibility of the polymer system, it follows straightforwardly that the tube/reptation model predicts fluctuations larger than permitted by thermodynamics on the time scale t ≳ τ_R, where τ_R is the Rouse relaxation time.     

Self‐diffusion and interactions in mixtures of imidazolium bis(mandelato)borate ionic liquids with polyethylene glycol: 1H NMR study

We used ¹H nuclear magnetic resonance pulsed‐field gradient to study the self‐diffusion of polyethylene glycol (PEG) and ions in a mixture of PEG and imidazolium bis(mandelato)borate ionic liquids (ILs) at IL concentrations from 0 to 10 wt% and temperatures from 295 to 370 K. PEG behaves as a solvent for these ILs, allowing observation of separate lines in ¹H NMR spectra assigned to the cation and anion as well as to PEG. The diffusion coefficients of PEG, as well as the imidazolium cation and bis(mandelato)borate (BMB) anion, differ under all experimental conditions tested. This demonstrates that the IL in the mixture is present in at least a partially dissociated state, while the lifetimes of the associated states of the ions and ions with PEG are less than ~30 ms. Generally, increasing the concentration of the IL leads to a decrease in the diffusion coefficients of PEG and both ions. The diffusion coefficient of the anion is less than that of the cation; the molecular mass dependence of diffusion of ions can be described by the Stokes–Einstein model. NMR chemical shift alteration analysis showed that the presence of PEG changes mainly the chemical shifts of protons belonging to imidazole ring of the cation, while chemical shifts of protons of anions and PEG remain unchanged. This demonstrated that the imidazolium cation interacts mainly with PEG, which most probably occurs through the oxygen of PEG and the imidazole ring. The BMB anion does not strongly interact with PEG, but it may be indirectly affected by PEG through interaction with the cation, which directly interacts with PEG. Copyright © 2015 John Wiley & Sons, Ltd.     

An efficient method for simulation of the dynamics of a large number of deformable droplets in the stokes regime

Direct simulations of the interaction of a large number of deformable droplets are necessary for more accurate predictions of rheological properties and the microstructure of liquid-liquid systems. In the present study, a mathematical model of a three-dimensional flow of a mixture of two Newtonian liquids of a droplet structure in an unbounded domain at low Reynolds numbers is considered. An efficient computational method for simulation of the dynamics of a large number of deformable drops is developed and tested. This approach is based on the boundary element method for three-dimensional problems accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). This enables direct simulations of systems of tens of thousands of deformable droplets on PCs, which is confirmed by test and demo computations. The developed method can be used for solution of a wide range of problems related to the emulsion flow in micro- and nanoscales. Also it can be used to establish the closing relations for simulation of two-phase liquid-liquid flow based on the continuum approach in macroscales.     

Conservation laws and exact solutions for nonlinear diffusion in anisotropic media

Conservation laws and exact solutions of nonlinear differential equations describing diffusion phenomena in anisotropic media with external sources are constructed. The construction is based on the method of nonlinear self-adjointness. Numerous exact solutions are obtained by using the recent method of conservation laws. These solutions are different from group invariant solutions and can be useful for investigating diffusion phenomena in complex media, e.g. in oil industry.     

Quantized separations of phase-locked soliton pairs in fiber lasers

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.