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

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes

Spin-lattice relaxation rates R₁(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R₁(T) vs the spin-spin relaxation rate R₂(T) and (ii) a plot of R₁(T) vs an independently measured reference time τ_ref(T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < β_K ≤ 0.67. Plots of the spin-spin relaxation rate R₂─rescaled by the NMR coupling constant─as a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the site-specific dynamics is found to merge, suggesting that near T_g the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to T_g. Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.

Glassy and Polymer Dynamics of Elastomers by 1H-Field-Cycling NMR Relaxometry: Effects of Fillers

1H spin-lattice relaxation rate (R1) dispersions were acquired by field-cycling (FC) NMR relaxometry between 0.01 and 35 MHz over a wide temperature range on polyisoprene rubber (IR), either unfilled or filled with different amounts of carbon black, silica, or a combination of both, and sulfur cured. By exploiting the frequency-temperature superposition principle and constructing master curves for the total FC NMR susceptibility, χ″(ω) = ωR1(ω), the correlation times for glassy dynamics, τs, were determined. Moreover, the contribution of polymer dynamics, χpol″(ω), to χ″(ω) was singled out by subtracting the contribution of glassy dynamics, χglass″(ω), well represented by the Cole-Davidson spectral density. Glassy dynamics resulted moderately modified by the presence of fillers, τs values determined for the filled rubbers being slightly different from those of the unfilled one. Polymer dynamics was affected by the presence of fillers in the Rouse regime. A change in the frequency dependence of χpol″(ω) at low frequencies was observed for all filled rubbers, more pronounced for those reinforced with silica, which suggests that the presence of the filler particles can affect chain conformations, resulting in a different Rouse mode distribution, and/or interchain interactions modulated by translational motions.

Dynamics of poly(vinyl butyral) studied using dielectric spectroscopy and 1H NMR relaxometry

Dielectric Spectroscopy (DS) and ¹H Fast Field-Cycling (FFC) NMR relaxometry were applied for understanding the dynamic behavior of the amorphous ter-polymer poly(vinyl butyral) (PVB) across the glass transition temperature (T_g = 70 °C by Differential Scanning Calorimetry). Above T_g, main chain segmental motions (α relaxation) were detected and characterized using both DS and FFC NMR relaxometry. The correlation times extracted by the analysis of DS and FFC NMR relaxometry data agreed within a factor of three and showed a Vogel-Fulcher-Tammann temperature dependence, with an associated T_g of 69 °C and a fragility of 155 for PVB glass. Below T_g, a secondary process (β relaxation) was revealed by DS, and was ascribed to reorientations of the vinyl alcohol dipoles due to local twisting motions with an associated activation barrier of 11 kcal mol^-1. The β process was also found to contribute to ¹H NMR relaxation above T_g.

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

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.

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 I^SE(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.

New applications and perspectives of fast field cycling NMR relaxometry

The field cycling NMR relaxometry method (also known as fast field cycling (FFC) when instruments employing fast electrical switching of the magnetic field are used) allows determination of the spin-lattice relaxation time (T1 ) continuously over five decades of Larmor frequency. The method can be exploited to observe the T1 frequency dependence of protons, as well as any other NMR-sensitive nuclei, such as (2) H, (13) C, (31) P, and (19) F in a wide range of substances and materials. The information obtained is directly correlated with the physical/chemical properties of the compound and can be represented as a 'nuclear magnetic resonance dispersion' curve. We present some recent academic and industrial applications showing the relevance of exploiting FFC NMR relaxometry in complex materials to study the molecular dynamics or, simply, for fingerprinting or quality control purposes. The basic nuclear magnetic resonance dispersion features are outlined in representative examples of magnetic resonance imaging (MRI) contrast agents, porous media, proteins, and food stuffs. We will focus on the new directions and perspectives for the FFC technique. For instance, the introduction of the latest Wide Bore FFC NMR relaxometers allows probing, for the first time, of the dynamics of confined surface water contained in the macro-pores of carbonate rock cores. We also evidence the use of the latest field cycling technology with a new cryogen-free variable-field electromagnet, which enhances the range of available frequencies in the 2D T1 -T2 correlation spectrum for separating oil and water in crude oil. Copyright © 2015 John Wiley & Sons, 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.

Intermolecular spin relaxation and translation diffusion in liquids and polymer melts: insight from field-cycling 1H NMR relaxometry

With the advent of commercial field-cycling (FC) spectrometers, NMR relaxometry has gained new momentum as a method of investigating dynamics in liquids and polymers. The outcome of FC NMR experiments is spin-lattice relaxation time versus frequency (relaxation dispersion). In the case of protons, due to the intra- and intermolecular origin of dipolar interactions, the relaxation dispersion reflects rotational as well as translational dynamics. The latter shows a universal dispersion law at low frequencies, which allows determination of the diffusion coefficient D(T) in addition to the rotational correlation time τ(rot)(T), that is, FC (1)H NMR becomes an alternative to field-gradient NMR spectroscopy. Subdiffusive translation found in polymers can be accessed by singling out the intermolecular relaxation through isotope dilution experiments, and the mean square displacement can then be revealed as a function of time, thus complementing neutron scattering experiments. Likewise, information on reorientational dynamics is provided by the intramolecular relaxation. Assuming frequency-temperature superposition the corresponding correlation functions can be monitored up to eight decades in amplitude and time, which allows thorough testing of current polymer theories.

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.