Chain orientation and slow dynamics in elastomers by mixed magic-Hahn echo decays

NMR Longitudinal Rotating Frame Relaxation Time (T1ρ) with a Weak Spin Locking Field as an Approach to Characterize Solid-State Active Pharmaceutical Ingredients: Proof of Concept

Nuclear magnetic resonance (NMR) longitudinal rotating frame relaxation time (T1ρ), rarely used in low-field NMR, can be more effective than conventional T1 and T2 relaxation times to differentiate polymorphic forms of solid pharmaceuticals. This could be attributed to T1ρ sensibility to structural and molecular dynamics that can be enhanced by changing the strength of the oscillating magnetic field (B1) of spinlock pulses. Here, we compared the capacity of T1, T2, and T1ρ to differentiate inactive (A) and active (C) crystalline forms of the World Health Organization essential drug Mebendazole. The results showed that T1 and T2 values of both forms were statistically identical at 0.47 T. Conversely, T1ρ of both forms measured with weak spinlock B1 fields, ranging from 0.08 to 0.80 mT were statistically different in the same spectrometer. The T1ρ also has the limit of detection to detect the presence of at least 10% of inactive A form in the active C form. Therefore, T1ρ, measured with weak spinlock B1 fields can be an effective, streamlined, and complementary approach for characterizing not only solid active pharmaceutical ingredients but other solid-state materials as well.

Real-Time Monitoring Polymerization Reactions Using Dipolar Echoes in 1H Time Domain NMR at a Low Magnetic Field

¹H time domain nuclear magnetic resonance (¹H TD-NMR) at a low magnetic field becomes a powerful technique for the structure and dynamics characterization of soft organic materials. This relies mostly on the method sensitivity to the ¹H-¹H magnetic dipolar couplings, which depend on the molecular orientation with respect to the applied magnetic field. On the other hand, the good sensitivity of the ¹H detection makes it possible to monitor real time processes that modify the dipolar coupling as a result of changes in the molecular mobility. In this regard, the so-called dipolar echoes technique can increase the sensitivity and accuracy of the real-time monitoring. In this article we evaluate the performance of commonly used ¹H TD-NMR dipolar echo methods for probing polymerization reactions. As a proof of principle, we monitor the cure of a commercial epoxy resin, using techniques such as mixed-Magic Sandwich Echo (MSE), Rhim Kessemeier-Radiofrequency Optimized Solid Echo (RK-ROSE) and Dipolar Filtered Magic Sandwich Echo (DF-MSE). Applying a reaction kinetic model that supposes simultaneous autocatalytic and noncatalytic reaction pathways, we show the analysis to obtain the rate and activation energy for the epoxy curing reaction using the NMR data. The results obtained using the different NMR methods are in good agreement among them and also results reported in the literature for similar samples. This demonstrates that any of these dipolar echo pulse sequences can be efficiently used for monitoring and characterizing this type of reaction. Nonetheless, the DF-MSE method showed intrinsic advantages, such as easier data handling and processing, and seems to be the method of choice for monitoring this type of reaction. In general, the procedure is suitable for characterizing reactions involving the formation of solid products from liquid reagents, with some adaptations concerning the reaction model.

Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber

The ¹H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH₂ and CH₃ functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.

Fast-forward approach of time-domain NMR relaxometry for solid-state chemistry of chitosan

Chitosans with different average degrees of acetylation and weight molecular weight were analyzed by time-domain NMR relaxometry using the recently proposed pulse sequence named Rhim and Kessemeier - Radiofrequency Optimized Solid-Echo (RK-ROSE) to acquire ¹H NMR signal of solid-state materials. The NMR signal decay was composed of faster (tenths of μs) and longer components, where the mobile-part fraction exhibited an effective relaxation transverse time assigned to methyl hydrogens from N-acetyl-d-glucosamine (GlcNAc) units. The higher intrinsic mobility of methyl groups was confirmed via DIPSHIFT experiments by probing the ¹H-¹³C dipolar interaction. RK-ROSE data were modeled by using Partial Least Square (PLS) multivariate regression, which showed a high coefficient of determination (R² > 0.93) between RK-ROSE signal profile and average degrees of acetylation and crystallinity index, thus indicating that time-domain NMR consists in a promising tool for structural and morphological characterization of chitosan.

On the microscopic origins of relaxation processes in aqueous peptide solutions undergoing a glass transition

We combine broadband dielectric spectroscopy (BDS) with ¹H and ²H nuclear magnetic resonance (NMR) to study molecular dynamics in mixtures of ε-polylysine with H₂O or D₂O. In BDS, four relaxation processes can be attributed to molecular dynamics. While the fastest process P1 obeys the Arrhenius law, the slowest process P4 shows prominent non-Arrhenius behavior typical of structural α relaxation. For the intermediate processes P2 and P3, the temperature dependence changes at the glass transition temperature T_g. The ¹H and ²H NMR results yield insights into the molecular origins of these relaxation phenomena. In these NMR analyses, we exploit, in addition to the isotope selectivity of the method, the possibility to distinguish between various types of motion based on their respective line-shape effects and the capability to single out specific molecular moieties based on different spin-lattice relaxation behaviors. In this way, we reveal that process P1 results from the rotation of side and end groups of the peptide, while process P2 is caused by a reorientation of essentially all water molecules, which are quasi-isotropic and survive well below T_g. As for the peptide backbone dynamics, we find evidence that rotational motion of polar groups is involved in process P3 and that nonpolar regions show a dynamical process, which is located between P3 and P4. Thus, the NMR analyses do not yield evidence for coexisting fast peptide-decoupled and slow peptide-coupled water species, which contribute to BDS processes P2 and P3, respectively, but minor bimodality of water motion may remain undetected. Finally, it is demonstrated that the proton/deuteron exchange needs to be considered when interpreting experimental results for molecular dynamics in aqueous peptide solutions.

Crystallinity of polyolefins with large side groups by low-field 1H NMR T2 relaxometry: Isotactic Polybutene-1 with form II and I crystals

Phase composition and molecular mobility were studied using ¹H NMR T₂ relaxometry in isotactic polybutene-1 (iPB-1) with two polymorphs - form I and II crystals. Several types of NMR relaxation methods and data analysis were evaluated for determining the most reliable way for studying physical phases in iPB-1. Three-phase model provided the most appropriate description of the phase composition in iPB-1, i.e., a crystal-amorphous interface separates the crystalline and the amorphous phases. Due to complex molecular mobility in iPB-1, the amount of rigid fraction should be considered as NMR crystallinity number. Two types of chain segments are present in the amorphous phase: (1) chain segments with anisotropic mobility due to chain anchoring to crystals and chain entanglements; and (2) highly mobile chain end segments. The polymorphic phase II to I transition causes significant immobilization of polymer chains in the crystalline and the amorphous phases. Molecular weight of iPB-1 largely influences phase composition and molecular mobility in crystalline and amorphous phases.

Power-optimized, time-reversal pulse sequence for a robust recovery of signals from rigid segments using time domain NMR

Time domain NMR (TD-NMR) has been widely used on the analysis of liquids or liquid components in heterogeneous materials such as food, biological tissues, synthetic and bio polymers, oil-bearing rocks, biomasses and cement-based materials. The use of TD-NMR for studying solid and soft mater has been growing in number and variety of applications, mostly for organic systems where the detection of ¹H signals is highly advantageous. However, the strong ¹H-¹H dipolar interactions in solids make the ¹H FID to decay in the same order of the dead time of most commercially available NMR probe heads. Thus, solid echoes are often used for recovering signals from solid components. In this article we reinvestigate the time-reversal solid-echo pulse sequence proposed by Rhim and Kessemeier, seeking for optimal pulse power and timing conditions that maximize its efficiency on recovering ¹H signals from rigid segments. We show that under these optimized conditions, which we denote as Rhim and Kessemeier - Radiofrequency Optimized Solid-Echo (RK-ROSE), the experiment can be more efficient than its most popular counterparts Solid-Echo (SE) and mixed-Magic Sandwich Echoes (mixed-MSE). Our results also suggest that, despite the finite pulse power, with current probe technology the RK-ROSE experiment is potentially able to provide an accurate estimation of rigid components, without relying on an external calibration using multiple standard samples, as usually done in SFC analysis of the FID signal. At last, we demonstrate that RK-ROSE can be adapted as a simple filter to supress signals from mobile segments in heterogeneous materials.

Basic principles of static proton low-resolution spin diffusion NMR in nanophase-separated materials with mobility contrast

We review basic principles of low-resolution proton NMR spin diffusion experiments, relying on mobility differences in nm-sized phases of inhomogeneous organic materials such as block-co- or semicrystalline polymers. They are of use for estimates of domain sizes and insights into nanometric dynamic inhomogeneities. Experimental procedures and limitations of mobility-based signal decomposition/filtering prior to spin diffusion are addressed on the example of as yet unpublished data on semicrystalline poly(ϵ-caprolactone), PCL. Specifically, we discuss technical aspects of the quantitative, dead-time free detection of rigid-domain signals by aid of the magic-sandwich echo (MSE), and magic-and-polarization-echo (MAPE) and double-quantum (DQ) magnetization filters to select rigid and mobile components, respectively. Such filters are of general use in reliable fitting approaches for phase composition determinations. Spin diffusion studies at low field using benchtop instruments are challenged by rather short (1)H T1 relaxation times, which calls for simulation-based analyses. Applying these, in combination with domain sizes as determined by small-angle X-ray scattering, we have determined spin diffusion coefficients D for PCL (0.34, 0.19 and 0.032nm(2)/ms for crystalline, interphase and amorphous parts, respectively). We further address thermal-history effects related to secondary crystallization. Finally, the state of knowledge concerning the connection between D values determined locally at the atomic level, using (13)C detection and CP- or REDOR-based "(1)H hole burning" procedures, and those obtained by calibration experiments, is summarized. Specifically, the non-trivial dependence of D on the magic-angle spinning (MAS) frequency, with a minimum under static and a local maximum under moderate-MAS conditions, is highlighted.

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.

Probing α-relaxation with nuclear magnetic resonance echo decay and relaxation: a study on nitrile butadiene rubber

One dimensional (1)H NMR measurements have been performed to probe slow molecular motions in nitrile butadiene rubber (NBR) around its calorimetric glass transition temperature Tg. The purpose is to show how software aided data analysis can extract meaningful dynamical data from these measurements. Spin-lattice relaxation time, free induction decay (FID) and magic sandwich echo (MSE) measurements have been carried out at different values of the static field, as a function of temperature. It has been evidenced how the efficiency of the MSE signal in reconstructing the original FID exhibits a sudden minimum at a given temperature, with a slight dependence from the measuring frequency. Computer simulations performed with the software SPINEVOLUTION have shown that the minimum in the efficiency reconstruction of the MSE signal corresponds to the average motional frequency taking a value around the inter-proton coupling. The FID signals have been fitted with a truncated form of a newly derived exact correlation function for the transverse magnetization of a dipolar interacting spin pair, which allows one to avoid the restriction of the stationary and Gaussian approximations. A direct estimate of the conformational dynamics on approaching the Tg is obtained, and the results are in agreement with the analysis performed via the MSE reconstruction efficiency. The occurrence of a wide distribution of correlation frequencies for the chains motion, with a Vogel-Fulcher type temperature dependence, is addressed. A route for a fruitful study of the dynamics accompanying the glass transition by a variety of NMR measurements is thus proposed.

Molecular dynamics parameter maps by 1H Hahn echo and mixed-echo phase-encoding MRI

Residual dipolar couplings and averaged correlation time maps in soft matter were obtained by mixed echo phase-encoding solid imaging (MIPSI). Use of the mixed echo in soft matter NMR imaging experiments has two crucial advantages: the signal intensity is recovered with a weak incoherence losses, and second, the intervals during which the phase-encoding evolution due to the magnetic field gradients takes place can be chosen to be much larger than with all other spin echo experiments and hence, a higher special resolution can be achieved. The parameter maps are compared to those obtained by the Hahn-echo phase-frequency encoding method. For both MRI methods the density operator formalism is applied in the average Hamiltonian approximation to describe the encoding of the spin echoes by the molecular motions. The results of preliminary experiments are presented.

The heterogeneity of segmental dynamics of filled EPDM by (1)H transverse relaxation NMR

Residual second moment of dipolar interactions M(2) and correlation time segmental dynamics distributions were measured by Hahn-echo decays in combination with inverse Laplace transform for a series of unfilled and filled EPDM samples as functions of carbon-black N683 filler content. The fillers-polymer chain interactions which dramatically restrict the mobility of bound rubber modify the dynamics of mobile chains. These changes depend on the filler content and can be evaluated from distributions of M(2). A dipolar filter was applied to eliminate the contribution of bound rubber. In the first approach the Hahn-echo decays were fitted with a theoretical relationship to obtain the average values of the (1)H residual second moment <M(2)> and correlation time <τ(c)>. For the mobile EPDM segments the power-law distribution of correlation function was compared to the exponential correlation function and found inadequate in the long-time regime. In the second approach a log-Gauss distribution for the correlation time was assumed. Furthermore, using an averaged value of the correlation time, the distributions of the residual second moment were determined using an inverse Laplace transform for the entire series of measured samples. The unfilled EPDM sample shows a bimodal distribution of residual second moments, which can be associated to the mobile polymer sub-chains (M(2) ≅ 6.1 rad (2) s(-2)) and the second one associated to the dangling chains M(2) ≅ 5.4 rad(2) s(-2)). By restraining the mobility of bound rubber, the carbon-black fillers induce diversity in the segmental dynamics like the apparition of a distinct mobile component and changes in the distribution of mobile and free-end polymer segments.

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG (1)H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T(2,short) and 1/T(2,long) were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T(1)/T(2) ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T(2)/T(2,eff) is derived as a function of the T(1)/T(2) ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T(1)-T(2) correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T(1)-T(2) experimental correlations maps were corrected for the T(1)/T(2) effect using the derived T(2)/T(2,eff) correction factor.

Surface UV aging of elastomers investigated with microscopic resolution by single-sided NMR

Depth profiles taken from the surface of UV irradiated natural rubber sheets have been measured with microscopic resolution using a Profile NMR-MOUSE. An NMR observable related to the sum of the spin echoes in the Carr-Purcell-Meiboom-Gill pulse sequence was used to characterize the cross-link density changes produced by the action of UV radiation in each sheet. The aging process was investigated as function of irradiation time and penetration depth. An exponential attenuation law with a space dependent absorption coefficient describes the change in the NMR observable with penetration depth. An Avrami model is used to describe the dependence of the absorption coefficient on the aging time. The method can be applied to investigate the effect of various aging agents on the surfaces of elastomers.

Segmental order in end-linked polymer networks: a Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.

Multispin moments edited by multiple-quantum NMR: application to elastomers

The spin system response to the five-pulse sequence used for measurements of double-quantum and triple-quantum buildup curves is evaluated in the initial excitation/reconversion regime. The multispin dipolar network that is present also in many soft solids like elastomers was considered. It is proved rigorously that the relevant quantity for analysis of double-quantum build-up curves in the initial regime is the second van Vleck moment. The higher-order moments edited by double-quantum as well as higher-order coherences in the multiple-quantum build-up experiments are different from van Vleck moments. These results can be applied to compare (1)H residual moments edited by double-quantum and triple-quantum experiments with those measured by other NMR methods. The sensitivity of multiple-quantum coherences to the changes in the values of residual dipolar couplings for cross-linked natural rubber under uniaxial elongation is also discussed. Under such conditions (1)H second van Vleck moments were measured for different elongation ratios of a cross-linked natural rubber. Moreover, (1)H triple-quantum edited moments were also measured for the same sample under uniaxial compression. The dependence of the second van Vleck moment and the time of the maximum of the double-quantum buildup curve on the cross-link density of natural rubber measured at low magnetic field was also investigated.

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.

1H multiple-quantum nuclear magnetic resonance investigations of molecular order in polymer networks. II. Intensity decay and restricted slow dynamics

We present an approach towards the analysis of the intensity decay in proton multiple-quantum experiments on polymeric networks in terms of slow fluctuations of the residual dipole-dipole coupling tensor. Solutions for individual spin pairs as well as the three-spin system of methyl groups are derived, and the influence of the cycle time of the multiple-quantum pulse sequence is evaluated. The multiple-quantum strategy discussed herein features the advantage that the magnitude of the fluctuating part of the residual dipole-dipole coupling constant and the correlation time of the slow process can be determined independently of the integral residual coupling constant as well as its distribution. The theory is applied to experiments on end-linked poly(dimethylsiloxane) model networks with mono- and bimodal chain length distributions, where it is found that, for all samples, correlation times of the slow processes average to about 1 ms, and that the magnitude of the fluctuating part of the dipole-dipole coupling is significantly smaller than the average dipole-dipole coupling constant. This observation is interpreted in terms of considerably restricted reorientations of topological constraints.

Parameter maps of 1H residual dipolar couplings in tendon under mechanical load

Proton multipolar spin states associated with dipolar encoded longitudinal magnetization (DELM) and double-quantum (DQ) coherences of bound water are investigated for bovine and sheep Achilles tendon under mechanical load. DELM decay curves and DQ buildup and decay curves reveal changes of the 1H residual dipolar couplings for tendon at rest and under local compression forces. The multipolar spin states are used to design dipolar contrast filters for NMR 1H images of heterogeneous tendon. Heterogeneities in tendon samples were artificially generated by local compression parallel and perpendicular to the tendon plug axis. Quotient images obtained from DQ-filtered images by matched and mismatched excitation/reconversion periods are encoded only by the residual dipolar couplings. Semi-quantitative parameter maps of the residual dipolar couplings of bound water were obtained from these quotient images using a reference elastomer sample. This method can be used to quantify NMR imaging of injured ordered tissues.