Segmental anisotropy in strained elastomers detected with a portable NMR scanner

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.

When the MOUSE leaves the house

Change is inherent to time being transient. With the NMR-MOUSE (MObile Universal Surface Explorer) having matured into an established NMR tool for nondestructive testing of materials, this forward-looking retrospective assesses the challenges the NMR-MOUSE faced when deployed outside a protected laboratory and how its performance quality can be maintained and improved when operated under adverse conditions in foreign environments. This work is dedicated to my dear colleague and friend Geoffrey Bodenhausen on the occasion of his crossing an honorable timeline in appreciation of his ever-continuing success of fueling the dynamics of magnetic resonance.

Fourier and Laplace-like low-field NMR spectroscopy: The perspectives of multivariate and artificial neural networks analyses

Low field Nuclear Magnetic Resonance (LF-NMR) is a rich source of information for a wide range of samples types. These can be hard or soft solids, such as plastics or elastomers; bulk liquids or liquids absorbed in porous materials, and can come from biomaterials, biological tissues, archaeological artifacts, cultural heritage objects. LF-NMR instruments present a significant advance especially for in situ, ex situ and in vivo measurement of relaxation and diffusion. Moreover, high resolution 1D and 2D spectroscopy, as well as magnetic resonance (MR) imaging are available in these fields. In this work we discuss the advanced analysis of the data measured in LF-NMR from the perspectives of tertiary level that implies the analysis on principal components (PCA), and on the quaternary analysis that uses an artificial neural network (ANN). The principles of PCA and ANN are largely discussed. For the PCA analysis, a series of 52 spectra were analyzed, having been recorded in vivo by LF-NMR. Of these spectra, 38 were generated from normal uterus, 7 by uterus tissue with endometrial cancer, and another 7 were obtained from tissues of women with uterine cervical cancer. The PC1 vs PC2 plot was further analyzed using an artificial neural network, and the results are presented as 2D maps of probability. Furthermore, the perspectives of applying an ANN to solve the problem of Laplace-like inversion are discussed. An example of such ANN was presented and the performance was discussed. Finally, a model of complex ANN, capable to sequentially solve this kind of problems specific to LF-NMR is proposed and discussed.

New insights into the thermal behaviour of organic ionic plastic crystals: magnetic resonance imaging of polycrystalline morphology alterations induced by solid–solid phase transitions

Morphology alterations induced by solid–solid phase transitions in Organic Ionic Plastic Crystals (OIPC) elucidate molecular dynamics, micro-structural behaviour and conductive properties of OIPCs.

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.

In situ investigation of leaf water status by portable unilateral nuclear magnetic resonance

A portable unilateral nuclear magnetic resonance (NMR) instrument was used to detect in field conditions the water status of leaves of herbaceous crops (Zea mays, Phaseolus vulgaris), mesophyllous trees (Populus nigra), and natural Mediterranean vegetation characterized by water-spending shrubs (Cistus incanus) and water-saving sclerophyllous trees (Quercus ilex). A good relationship was observed between NMR signal, leaf relative water content, and leaf transpiration in herbaceous leaves undergoing fast dehydration or slowly developing a drought stress. A relationship was also observed between NMR signal and water potential of Populus leaves during the development of a water stress and when leaves recovered from the stress. In the natural vegetation, the relationship between NMR signal and water status was found in Cistus, the species characterized by high transpiration rates, when measured during a drought stress period and after a rainfall. In the case of the sclerophyllous Quercus, the NMR signal, the relative water content, and the transpiration rate did not change at different leaf water status, possibly because a large amount of water is compartmentalized in cellular structures and macromolecules. The good association between NMR signal and relative water content was lost in leaves exposed for 24 h to dehydration or to an osmotic stress caused by polyethylene glycol feeding. At this time, the transverse relaxation time became longer than in leaves maintained under optimal water conditions, and two indicators of membrane damage, the ion leakage and the emission of products of membrane lipoxygenation [(Z)-3-hexenal, (Z)-3-hexenol, and (E)-2-hexenol], increased. These results taken all together give information on the physiological state of a leaf under a developing stress and show the usefulness of the NMR instrumentation for screening vegetation health and fitness in natural and cultivated conditions. It is concluded that the portable unilateral NMR instrument may be usefully employed in field conditions to monitor nondestructively the water status of plants and to assist agricultural practices, such as irrigation scheduling, to minimize stomatal closure and the consequent limitation to plant production.

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.

Study of order and dynamic processes in tendon by NMR and MRI

Tendons are composed of a parallel arrangement of densely packed collagen fibrils that results in unique biomechanical properties of strength and flexibility. In the present review we discuss several advanced magnetic resonance spectroscopy (MRS) and imaging (MRI) techniques that have allowed us to better understand the biophysical properties of tendons and ligaments. The methods include multiple quantum and T(2) filtering combined with NMR and MRI techniques. It is shown in detail how these techniques can be used to extract a number of useful parameters: 1) the (1)H-(1)H and (1)H-(2)H dipolar interactions; 2) the proton exchange rates between water and collagen, and between water molecules; 3) the distribution of fibril orientations; and 4) the anisotropy of diffusion. It is shown that relaxation data as a function of angular dependence can be obtained in vivo using mobile NMR sensors. Finally, this article describes how double quantum filtered (DQF) MRI can be used to image and monitor the healing process in injured tendons.

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.

An analytical methodology for magnetic field control in unilateral NMR

Traditionally, unilateral NMR systems such as the NMR-MOUSE have used the fringe field between two bar magnets joined with a yoke in a 'U' geometry. This allows NMR signals to be acquired from a sensitive volume displaced from the magnets, permitting large samples to be investigated. The drawback of this approach is that the static field (B0) generated in this configuration is inhomogeneous, and has a large, nonlinear, gradient. As a consequence, the sensitive volume of the instrument is both small and ill defined. Empirical redesign of the permanent magnet array producing the B0 field has yielded instruments with magnetic field topologies acceptable for varying applications. The drawback of current approaches is the lack of formalism in the control of B0. Rather than tailoring the magnet geometry to NMR investigations, measurements must be tailored to the available magnet geometry. In this work, we present a design procedure whereby the size, shape, field strength, homogeneity, and gradients in the sensitive spot of a unilateral NMR sensor can be controlled. Our design uses high permeability pole pieces, shaped according to the contours of an analytical expression, to control B0, allowing unilateral NMR instruments to be designed to generate a controlled static field topology. We discuss the approach in the context of previously published design techniques, and explain the advantages inherent in our strategy as compared to other optimization methods. We detail the design, simulation, and construction of a unilateral magnet array using our approach. It is shown that the fabricated array exhibits a B0 topology consistent with the design. The utility of the design is demonstrated in a sample nondestructive testing application. Our design methodology is general, and defines a class of unilateral permanent magnet arrays in which the strength and shape of B0 within the sensitive volume can be controlled.

NMR relaxation dispersion of vulcanized natural rubber

The dependence of the 1H spin-lattice relaxation time on the magnetic field strength has been determined for linear and cross-linked polyisoprene for Larmor frequencies between 5 kHz and 20 MHz. Universal power-law relations are found for all temperatures and cross-link densities under investigation and are compared to published results of rotating-frame experiments on similar natural rubber samples. The shape of the individual dispersion functions can be superposed into a master curve using appropriate shift factors. While addition of filler particles even at large weight fractions has only a minor effect on the relaxation times, uniaxial deformation and swelling are demonstrated to alter the molecular dynamics significantly.

Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.

Self-diffusion measurements by a constant-relaxation method in strongly inhomogeneous magnetic fields

The simple pulse sequence thetax-tau1-2thetay-tau1+tau2-2thetay-tau2-Hahn echo used to measure the self-diffusion coefficient D under constant-relaxation condition, i.e., for tau1+tau2=const. was investigated in the presence of strongly inhomogeneous static as well as radiofrequency magnetic fields. The encoding of the Hahn-echo amplitude by the pulse flip angle and diffusion was evaluated by taking into account the spatial distribution of the off-resonance field, the strength and orientation of the local field gradients, and the pulse flip angles by a computer simulation program. As input files, this program uses maps of static and radiofrequency fields, and the D coefficient can be evaluated from the time dependence of the Hahn-echo amplitude. The method was applied to a mobile one-sided NMR sensor, NMR-MOUSE with a bar magnet by measuring D for a series of liquids with different viscosities. The method was shown to be particularly useful for measuring D of solvents in elastomers without the need for measurements of the transverse relaxation rates. The self-diffusion coefficient of toluene in a series of crosslinked natural rubber samples was measured and correlated with the crosslink density. Finally, the method was applied to measure the diffusion anisotropy of free water in bovine Achilles tendon.