On the theory of the spin I = 1/2 double quantum NMR: Effects of spins spatial displacements between RF pulses.

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.

On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics.

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.

Segmental dynamics of polyethylene-alt-propylene studied by NMR spin echo techniques.

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.

On the theory of the proton dipolar-correlation effect as a method for investigation of segmental displacement in polymer melts.

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.

Communication: Proton NMR dipolar-correlation effect as a method for investigating segmental diffusion in polymer melts.

A simple and fast method for the investigation of segmental diffusion in high molar mass polymer melts is presented. The method is based on a special function, called proton dipolar-correlation build-up function, which is constructed from Hahn Echo signals measured at times t and t/2. The initial rise of this function contains additive contributions from both inter- and intramolecular magnetic dipole-dipole interactions. The intermolecular contribution depends on the relative mean squared displacements (MSDs) of polymer segments from different macromolecules, while the intramolecular part reflects segmental reorientations. Separation of both contributions via isotope dilution provides access to segmental displacements in polymer melts at millisecond range, which is hardly accessible by other methods. The feasibility of the method is illustrated by investigating protonated and deuterated polybutadiene melts with molecular mass 196 000 g/mol at different temperatures. The observed exponent of the power law of the segmental MSD is close to 0.32 ± 0.03 at times when the root MSD is in between 45 Å and 75 Å, and the intermolecular proton dipole-dipole contribution to the total proton Hahn Echo NMR signal is larger than 50% and increases with time.

NMR relaxation induced by iron oxide particles: testing theoretical models.

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.

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.

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.

Monitoring mass transport in heterogeneously catalyzed reactions by field-gradient NMR for assessing reaction efficiency in a single pellet.

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.

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(-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.

NMR investigations of polymer dynamics in a partially filled porous matrix.

The interior surface of well-defined porous alumina membranes (Anopore) of 20 nm and 200 nm pore diameter, respectively, was coated with polymer layers generated from solution by the solvent evaporation method. Deposits of poly(dimethyl siloxane) (PDMS) with nominal thicknesses ranging from 0.15 to 4.5 nm --corresponding to submonolayer to multilayer films--were investigated, and were compared to poly(butadiene) (PB) as an example for non-wetting polymers. Molecular weights below and above the critical value were studied since the bulk dynamics of such polymers are known to be qualitatively different. First results of NMR relaxation dispersion experiments on these systems are presented, supplemented by transverse relaxation times and double-quantum measurements obtained from high-field NMR. A systematic decrease of relaxation times at low fields with decreasing polymer amount is found for PDMS, but molecules retain a high degree of mobility irrespective of molecular weight. The relaxation dispersion results are supported by T2 data and 1H residual dipolar coupling (RDC) constants, and are discussed in terms of molecular order and reorientational dynamics.

Multiecho sequence for velocity imaging in inhomogeneous rf fields.

The unambiguous determination of velocities with spatial resolution in a multiecho PFG NMR sequence strongly depends on the homogeneity of the B1 field. This affects, in particular, the use of surface coils that bear considerable potential for on-line flow monitoring where a fast-imaging sequence can become vital. However, even with most rf coils dedicated for imaging applications, B1 inhomogeneities are sufficiently large to generate severe problems in performing velocity-imaging experiments. In this paper, the use of a combination of different phase cycles in Carr-Purcell sequences is discussed. The suggested phase cycling scheme tolerates large flip angle imperfections arising in inhomogeneous B1 fields, and thus allows acquisition of a maximum number of echoes within a pulse train. The performance of the velocity-imaging sequence is proven by using phantom samples developing known laminar flow patterns.

Internal fluid dynamics in levitated drops by fast magnetic resonance velocimetry.

Fluid motion inside a levitated drop is determined by the interface properties. Momentum transfer through a highly mobile interface results in stationary vortex patterns inside the drop that dramatically enhance mass transfer between both phases, while immobile interfaces suppress internal dynamics. The presence of small amounts of surface-active substances can result in a partial reduction of interface mobility, the so-called rigid cap. The time dependence of internal flow patterns is presented by means of NMR velocity images of levitated drops, and is compared to fast measurements of the velocity distribution along the three orthogonal coordinates.

Visualizing flow vortices inside a single levitated drop.

The internal flow dynamics in single liquid drops, kept in place through levitation by a counterflowing continuous fluid phase in a suitably designed glass cell, is investigated by PFG NMR techniques. The positional stability of the drops was confirmed from series of one-dimensional profiles and was found to be below the spatial resolution of the experiment. Velocity distribution functions (propagators) along all three coordinates were obtained and demonstrated the long-time stability of the internal dynamics in terms of the velocity magnitudes occurring in the systems. Finally, velocity imaging was applied to visualize the internal vortex patterns in the drops either as projections onto different planes or within thin slices of selected orientations. Two different fluid systems were investigated in order to cover the principal cases of rigid and mobile interfaces. Different fast velocity imaging techniques were employed for monitoring the vastly differing velocity ranges of both cases, and the high sensitivity of the internal three-dimensional motion to the cell geometry is demonstrated.

New approaches to the visualization, quantification and explanation of acid-induced water loss from Ca-alginate hydrogel beads.

The water loss of Ca-alginate hydrogels at pHs below 4.0 was visualized with 1HNMR-imaging by covering a single alginate bead with cyclohexane-d12 in a specially equipped NMR-tube and adding propionic acid at defined concentrations. The exact amount of water expelled from the beads was calculated from their weight loss and correlated with the acid concentrations and pHs within the hydrogel matrix. The maximum water loss of 52% (w/w) occurred at pH 1.0, while only 5% (w/w) of the initial water content were lost at pH 3.6. The analysis of the water collected from several alginate beads for Ca2+ -ions and free polysaccharides led to the assumption that, due to the acid-induced protonation of the carboxyl functions, the ionotropic network is gradually converted to an alginic acid gel structured by H-bonds. This contradicts existing theories explaining the pH-induced water loss by a lower solubility of the alginate chains and decreased repulsion between protonated carboxyl functions, but explains previously reported pH-dependent alterations of mass transport and drug retention of Ca-alginate gels. Thus, the presented experiments enable a more precise and complete view of the acid-induced process within Ca-alginate hydrogels. The transfer to the characterization of other hydrogels is possible and should be advantageous, especially if a calibration of the NMR-measurement could be achieved.

Molecular dynamics of n-dodecylammonium chloride in aqueous solutions investigated by 2H NMR and 1H NMR relaxometry.

Molecular dynamics in n-dodecylammonium chloride/water solutions for concentrations of 34 and 45 wt% was studied by 2H NMR and by 1H NMR dispersion of spin-lattice relaxation in the 2 kHz-90 MHz frequency range. The system exhibits a number of lyotropic liquid crystalline phases, which differ in symmetry and involve motions characterized by a wide frequency scale. The analysis of 2H NMR lineshapes of selectively deuterated DDACl molecules gave us an evidence for local trans-gauche conformational changes in the chains, whereas the dispersion of spin-lattice relaxation times T1 explored by fast field cycling method revealed fast local motions, translational diffusion and collective molecular dynamics of the chains. In particular, we have found that the order director fluctuation mechanism in smectic and nematic phases dominates spin-lattice relaxation below 1 MHz and that local motions and translational diffusion are responsible for the spin-lattice relaxation in the higher Larmor frequency range.

Spectrally resolved velocity exchange spectroscopy of two-phase flow.

The Velocity EXchange SpectroscopY (VEXSY) technique, which provides a means to correlate macroscopic molecular displacements measured during two intervals separated by a variable mixing period, has been applied for the first time to a system of two-phase flow. The chemical shift difference between water and methyl protons has been exploited to simultaneously determine the probability of displacements, or propagator, of both components in a water/silicone oil mixture flowing through a glass bead pack. The joint two-time probability densities as well as the conditional probabilities of velocities show a clearly distinct dispersion behaviour of both fluids which is a consequence of the different wetting properties of the fluids with respect to the glass surface of the bead pack.

NMR velocimetry of falling liquid films.

First results on NMR velocimetry of falling liquid films are presented. A film of average thickness 1 mm and width 40 mm is sustained by a continuous flow of silicon oil over a vertical plate made from PMMA. The spatial distribution of velocities is measured using a double spin--echo imaging pulse sequence supplemented by a bipolar velocity encoding gradient. Spin density and velocity images as well as two-dimensional velocity maps of different situations, i.e., undisturbed and disturbed falling film flow, are discussed. Experimental and theoretical velocity data for undisturbed film flow are compared.

NMR visualization of displacement correlations for flow in porous media.

The temporal correlations of velocities for both water and a water-glycerol mixture flowing through a random packings of monodisperse spherical particles have been investigated using two-dimensional nuclear magnetic resonance methods. By combining various flow rates, fluid viscosities, and bead sizes, a wide range of flow parameters has been covered, the dimensionless Peclet number ranging from 100 to 100 000. The velocity exchange spectroscopy (VEXSY) technique has been employed to measure the correlation between velocities during two intervals separated from each other by a mixing time tau(m). This time is made both large and small compared with the time constant tau(c), required for a fluid element possessing the average flow velocity to cover a distance equal to the characteristic size in the system, the bead diameter. The two-dimensional conditional probability of displacement resulting from the VEXSY method reveals the existence of different "subensembles" of molecules, including a slow moving pool whose displacement is dominated by Brownian motion, an intermediate ensemble whose velocities change little over the mixing time, and a fast flowing ensemble which loses correlation due to mechanical dispersion. We find that that the approach to asymptotic dispersion, as tau(c)/tau(m) increases, depends strongly on the Peclet number, the deviation of the velocity autocorrelation function from a monoexponential Ornstein-Uhlenbeck process becoming more pronounced with increasing Peclet number.

NMR imaging of falling water drops.

The falling water drop is a simple model for studying phenomena related to chemical extraction, where two immiscible phases are dynamically blended to promote the transport of solute molecules from one phase to the other. Convective motion inside the drop significantly influences the extraction efficiency. Whereas optical and tracer methods are model bound or invasive, NMR imaging is noninvasive, direct, and applicable to nontransparent media. The first NMR measurements of a water drop falling through air are reported. It is shown that, in drops from pure water, large-scale convection rolls are observed in contrast to drops with the surface tension lowered by surfactants.