Spatial displacements of spins between radio frequency pulses in a Double-Quantum (DQ) nuclear magnetic resonance pulse sequence generate additional terms in the effective DQ Hamiltonian. We derive a simple expression that allows the estimation and control of these contributions to the initial rise of the DQ build up function by variation of experimental parameters in systems performing anomalous diffusion. The application of polymers is discussed.

The deuteron transverse relaxation properties of polyethylene oxide melts of four different molecular weights, covering the range from the onset of entanglements to the regime of fully entangled chains, are investigated using Hahn echo decays over an extensive time interval up to ten times the effective transverse spin relaxation time. The results are compared to predictions based on the Rouse and reptation formalisms, taking into account the dynamical heterogeneity of linear polymer chains produced by the end segments. The experimental results can be described qualitatively by a combination of both models, with the contribution of reptation dynamics increasing with growing chain length. The transition is continuous, rather than being characterized by sharp regime boundaries. Up to a molecular weight of 300.000 g/mol, the predicted limit of pure reptation dynamics is not yet reached. Quantitative deviations from the predicted decays as computed by numerical procedures become observable toward the long-time limit of the Hahn echo decays and are being discussed in terms of shortcomings of the available reptation theories.

A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times. With an increase in observation time, the contribution from end effects to the FID increases. In the regime of incoherent reptation, contributions to the FID from central segments yield an exponent of 1/4 for the stretched decay and contributions from end segments yield an exponent of 3/16. In the regime of coherent reptation, the central segments generate a stretching exponent of 1/2, whereas the end segments contribute with an exponent of 1/4. These predictions are shown to be in qualitative agreement with the experimental FIDs of perdeuterated poly(ethylene oxide) with molecular masses of 132 kg/mol and 862 kg/mol.

The dynamics of entangled polymer melts not only is of fundamental theoretical interest but also has wide-reaching consequences for developing a theoretical foundation for investigating biological macromolecules and complex systems relevant to material sciences. Despite several decades of intensive experimental and theoretical research in this field, open questions remain regarding segmental dynamics over the wide range of time scales from local to global motion. This work employs a novel approach based on nuclear magnetic relaxation to scrutinize the character of dipolar interactions in entangled polymer melts, thereby accessing unique information about segmental diffusion and rotation. The main focus is set on the separate consideration of intra- and intermolecular contributions to the proton dipolar interactions, which have been previously shown to possess a different, nontrivial time dependence. A combination of well-established field-cycling T-1 relaxometry and recently developed methods based on spin echo is utilized to investigate dipolar couplings in entangled poly(ethylene oxide) melts of various molecular weights. Isolation of the intermolecular contributions to the corresponding experimental quantities provides a means to observe segmental translations taking place during more than 6 orders of magnitude in time. Time dependences of the mean-square displacement obtained in this way revealed apparent exponents of the power laws significantly deviating from predictions of the widely used tube-reptation model of polymer dynamics in the regime of entangled motion. In addition to that, the relative ratio of intermolecular dipolar interactions over the intramolecular counterpart is probed through their corresponding contributions to the transverse relaxation rate. A strong deviation from the tube-reptation model predictions for the evolution of this quantity is observed in the whole range probed experimentally. The obtained data do not reflect the restricted character of segmental motion anticipated in the corresponding time regime. It is emphasized that similar results, both in amplitude and in qualitative behavior, have been previously demonstrated in polybutadiene and polyethylene-alt-propylene, thereby allowing to discuss the universality of the observed deviation.

Variable-temperature proton magnetic relaxation dispersion (PMRD) profiles are collected in the induced nematic phases of the binary liquid crystalline mixtures composed of smectic mesogens: 5-butyl-2-(4-isothiocyanatophenyl)-1,3-dioxane (4DBT) and 4-dodecyl-4-cyanobiphenyl (12CB) and the low viscous nematogen 4-(trans-4-n-hexylcyclohexyl)-isothiocyanatobenzene (6CHBT), with a view to assess the influence of local organisations on the power spectrum of director fluctuation modes. Two distinct compositions of the binary mixture i.e. 50mol% of 12CB (without a smectic phase) and 70mol% of 12CB (with a smectic phase) are used. Fast Field Cycling nuclear magnetic resonance relaxometry is employed to measure proton spin-lattice relaxation rates (R-1) as a function of Larmor frequency (10kHz-30MHz). PMRD data analysis with the choice of a suitable model indicated nematic clusters of moderate size (similar to 200 angstrom) found in the broad nematic region of 50mol% 12CB, whose size is almost invariant with temperature. On the other hand, cybotactic clusters, i.e. local smectic organisations of relatively larger size (similar to 2000-3000 angstrom), are observed near the nematic-smectic transition (T>T-AN) of 70mol% 12CB. Interestingly, the shape geometry of such local organisations accessed from PMRD analysis is weakly anisotropic near T-AN,T- while being isotropic near T-NI for 70mol% 12CB. [GRAPHICS] .

Segmental dynamics of a highly entangled melt of linear polyethylene-alt-propylene with a molecular weight of 200 kDa was studied with a novel proton nuclear magnetic resonance (NMR) approach based upon 1H → 2H isotope dilution as applied to a solid-echo build-up function ISE(t), which is constructed from the NMR spin echo signals arising from the Hahn echo (HE) and two variations of the solid-echo pulse sequence. The isotope dilution enables the separation of inter- and intramolecular contributions to this function and allows one to extract the segmental mean-squared displacements in the millisecond time range, which is hardly accessible by other experimental methods. The proposed technique in combination with time-temperature superposition yields information about segmental translation in polyethylene-alt-propylene over 6 decades in time from 10-6 s up to 1 s. The time dependence of the mean-squared displacement obtained in this time range clearly shows three regimes of power law with exponents, which are in good agreement with the tube-reptation model predictions for the Rouse model, incoherent reptation and coherent reptation regimes. The results at short times coincide with the fast-field cycling relaxometry and neutron spin echo data, yet, significantly extending the probed time range. Furthermore, the obtained data are verified as well by the use of the dipolar-correlation effect on the Hahn echo, which was developed before by the co-authors. At the same time, the amplitude ratio of the intermolecular part of the proton dynamic dipole-dipole correlation function over the intramolecular part obtained from the experimental data is not in agreement with the predictions of the tube-reptation model for the regimes of incoherent and coherent reptation.

A thorough theoretical description of the recently suggested method [A. Lozovoi et al. J. Chem. Phys. 144, 241101 (2016)] based on the proton NMR dipolar-correlation effect allowing for the investigation of segmental diffusion in polymer melts is presented. It is shown that the initial rise of the proton dipolar-correlation build-up function, constructed from Hahn Echo signals measured at times t and t/2, contains additive contributions from both inter- and intramolecular magnetic dipole-dipole interactions. The intermolecular contribution depends on the relative mean-squared displacement of polymer segments from different macromolecules, which provides an opportunity for an experimental study of segmental translational motions at the millisecond range that falls outside the typical range accessible by other methods, i.e., neutron scattering or NMR spin echo with the magnetic field gradients. A comparison with the other two proton NMR methods based on transverse spin relaxation phenomena, i.e., solid echo and double quantum resonance, shows that the initial rise of the build-up functions in all the discussed methods is essentially identical and differs only in numerical coefficients. In addition, it is argued that correlation functions constructed in the same manner as the dipolar-correlation build-up function can be applied for an experimental determination of a mean relaxation rate in the case of systems possessing multi-exponential magnetization decay.

Superparamagnetic iron oxide particles find their main application as contrast agents for cellular and molecular magnetic resonance imaging. The contrast they bring is due to the shortening of the transverse relaxation time T 2 of water protons. In order to understand their influence on proton relaxation, different theoretical relaxation models have been developed, each of them presenting a certain validity domain, which depends on the particle characteristics and proton dynamics. The validation of these models is crucial since they allow for predicting the ideal particle characteristics for obtaining the best contrast but also because the fitting of T 1 experimental data by the theory constitutes an interesting tool for the characterization of the nanoparticles. In this work, T 2 of suspensions of iron oxide particles in different solvents and at different temperatures, corresponding to different proton diffusion properties, were measured and were compared to the three main theoretical models (the motional averaging regime, the static dephasing regime, and the partial refocusing model) with good qualitative agreement. However, a real quantitative agreement was not observed, probably because of the complexity of these nanoparticulate systems. The Roch theory, developed in the motional averaging regime (MAR), was also successfully used to fit T 1 nuclear magnetic relaxation dispersion (NMRD) profiles, even outside the MAR validity range, and provided a good estimate of the particle size. On the other hand, the simultaneous fitting of T 1 and T 2 NMRD profiles by the theory was impossible, and this occurrence constitutes a clear limitation of the Roch model. Finally, the theory was shown to satisfactorily fit the deuterium T 1 NMRD profile of superparamagnetic particle suspensions in heavy water.

The proton spin dynamics in polymer melts is determined by intramolecular and intermolecular magnetic dipole-dipole interactions among the proton spins. During many decades it was postulated that the main contribution is a result of intramolecular magnetic dipole-dipole interactions of protons belonging to the same polymer segment. This postulate is far from reality. The relative weights of intra- and intermolecular contributions are time (or frequency) dependent and sensitive to details of polymer chain dynamics. It is shown that for isotropic models of polymer dynamics, in which already at short times the segmental displacements are not correlated with the polymer chain's initial conformation, the influence of the intermolecular dipole-dipole interactions becomes stronger with increasing evolution time (i.e. decreasing frequency) than the corresponding influence of the intramolecular counterpart. On the other hand, an inverted situation is predicted by the tube-reptation model: here the influence of the intramolecular dipole-dipole interactions increases faster with time than the contribution from intermolecular interactions. This opens a new perspective for experimental investigations of polymer dynamics by proton NMR, and first results are reported.

Based on a modified Anderson-Weiss approximation (N. Fatkullin, A. Gubaidullin, C. Mattea, S.Stapf, J. Chem. Phys. 137 (2012), 224907) an improved theory of proton spin solid echo in polymer melts is formulated, taking into account contribution from intermolecular magnetic dipole-dipole interactions. The solid echo build-up function defined by the relation , where , and are the respective signals arising from ( ),( ) and ( ) spin echo experiments, where is an operator rotating the spin system on the angle relatively axis , is investigated. It is shown that the intermolecular part of this function at short times , where is a characteristic time for flip-flop transitions between proton spins, contains information about the relative mean squared displacements of polymer segments at different macromolecules, opening up a new opportunity for obtaining information about polymer dynamics in the millisecond regime.

Ionic hydrogels are polymer networks that have the ability to store large amounts of water. Due to this behavior hydrogels based on sodium acrylate (SA) are mostly used in diapers and soil conditioners. In this work diffusion and exchange processes in polyelectrolyte hydrogels were followed by 23Na and 27Al magnetic resonance imaging (MRI) techniques. We present 23Na and 27Al MRI experiments of the replacement reaction in hydrogels (classical superabsorbers, hydrogels with an inherent charge gradient and with a higher charge) as a feasibility study of monitoring the combined diffusion/exchange process as well as the shrinking and local defect growth in macroscopic model hydrogels. It is shown that the contraction of the gel induced by increasing the number of physical crosslinks through aluminum ions is of non-linear nature and takes place in several steps in contrast to high charge-density hydrogels based on acrylic acid and maleic acid.

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.

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.

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.

The results of the computer-aided simulation of the dynamics of a polymer melt consisting of Fraenkel chains in straight cylindrical tubes and in bulk are discussed. Two different models are studied. In the first model, the dynamics of the polymer melt is simulated via the molecular dynamics simulation. The interaction of unbound polymer segments is described by the Lennard-Jones potential, which excludes any chain crossing of macromolecules and generates collective acoustic waves. In the second model, which serves as a reference, the system is studied via the Brownian dynamics method, in which intermolecular interactions are allowed for phenomenologically via friction and stochastic Langevin forces. In this case, cooperative effects are absent and the effect of spatial confinements makes itself evident only in a narrow near-wall layer. For the two models under consideration, there is a significant difference in the decay of dynamic correlation functions C αβ(t) = 〈b α(t)b β(t)b α(0)b β(0)〉〈b α 2 b β 2 〉−1, where averaging is performed over all macromolecular segments and b α (t) is the component of the end-to-end-segment vector (α ≠ β = x,y, and the cylindrical axis of the tube is directed along the z axis). For the first model allowing for collective effects, the dynamics of decay of C αβ (t)functions is much slower than that for the melt in bulk, and for the second model, in which the presence of the tube leads only to spatial confinements for the polymer segments in the direct vicinity of walls. This difference indicates the fundamental significance of the collective effects in the dynamics of polymer melts confined in porous media. This phenomenon is the first computer-simulated evidence of the onset stage of the so-called corset effect, which was first observed experimentally with the use of NMR relaxometry.

An important aspect in assessing the performance of a catalytically active reactor is the accessibility of the reactive sites inside the individual pellets, and the mass transfer of reactants and products to and from these sites. Optimal design often requires a suitable combination of micro- and macropores in order to facilitate mass transport inside the pellet. In an exothermic reaction, fluid exchange between the pellet and the surrounding medium is enhanced by convection, and often by the occurrence of gas bubbles. Determining mass flow in the vicinity of a pellet thus represents a parameter for quantifying the reaction efficiency and its dependence on time or external reaction conditions. Field gradient Nuclear Magnetic Resonance (NMR) methods are suggested as a tool for providing parameters sensitive to this mass flow in a contact-free and non-invasive way. For the example of bubble-forming hydrogen peroxide decomposition in an alumina pellet, the dependence of the mean-squared displacement of fluid molecules on spatial direction, observation time and reaction time is presented, and multi-pulse techniques are employed in order to separate molecular displacements from coherent and incoherent motion on the timescale of the experiment. The reaction progress is followed until the complete decomposition of H2O2.

By suggesting that the polymer dynamics in entangled polymer melts possesses the property of dynamical self-similarity, we argue that the power-law exponent of the Carreau-Yasuda law, which empirically describes the shear thinning effect of the polymer melt viscosity, is inversely proportional to the exponent of the molecular mass dependence of the terminal relaxation time. This finding is obtained in cases where the shear rate dependence of the segmental relaxation time is negligible. If such dependence is essential, the Carreau-Yasuda law is slightly modified at high shear rates: instead of a power-law dependence with a small shear rate independent exponent, a weaker logarithmic dependence is found both for shear rate and molecular mass dependence, which resembles the approach to zero of an effective shear rate and molecular mass dependent power-law exponents at sufficiently high shear rates.

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(-7) s-10(-6) s 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.