Abstract Partially hydrolyzed grades of poly(vinyl alcohol) (PVA), typically with a degree of hydrolysis in the range of 87–90%, are widely used in water-soluble detergent films because of their cold-water solubility, film-forming ability, and biodegradability. Under realistic domestic washing conditions, however, PVA-based detergent capsules can occasionally leave visible gel-like residues, raising questions about whether such materials represent reversible, physically associated PVA–surfactant phases or persistent microplastic-like particles. This study investigates the formation and reversibility of gel-like PVA–surfactant phases representative of commercial detergent capsules, using small-angle X-ray scattering (SAXS), filtration coupled with ATR-FTIR and confocal Raman microscopy, dynamic light scattering (DLS), nuclear magnetic resonance (NMR), and size-exclusion chromatography (SEC). SAXS shows that the formation of the gel-like PVA–surfactant phase under low-water, high-surfactant conditions retains scattering features associated with both the PVA film and the detergent-rich phase, without additional SAXS-detectable features indicative of a distinct mesoscale structure. Upon dilution and filtration, vibrational spectroscopy and DLS reveal no detectable PVA microplastic- or nanoplastic-like particles above or below the 0.45 μm filtration threshold. NMR diffusion measurements show hydrodynamic radii of 8.6–9.2 nm for PVA recovered from washing machine residues, consistent with dissolved single chains, while SEC confirms unchanged molecular-weight distributions and no evidence of degradation or cross-linking (PVA Mp = 85.8 ± 2.4 kDa). Together, these results resolve previous ambiguities about the dissolution behavior of detergent films and provide analytical evidence that detergent-grade PVA remains molecularly dispersed upon dilution. Within the detection limits of the analytical techniques employed, no evidence of particulate PVA species was observed, supporting the conclusion that detergent-grade PVA does not form microplastic- or nanoplastic-like particles under realistic domestic use conditions. This dissolved physical state is consistent with the documented mechanism of biodegradability of detergent-grade PVA in aqueous environments.

The matrix pencil method (MPM) is an approach for quantitative analysis of the multi-exponential time-domain signals from relaxation and diffusion NMR experiments. In contrast to other signal processing methods, MPM relies on solving the generalized eigenvalue problem of a so-called matrix pencil, resulting in discrete values representing the different relaxation species. In this work, the methodology is extended from relaxation experiments towards assessment of NMR self-diffusion studies in micro-porous media on a length scale suitable for determining pore sizes from signal decays. For this, well-defined 3D nano printed micro-capillary structures are introduced as model porous media to correlate the apparent diffusion coefficients derived by MPM from pulsed gradient spin echo (PGSE) experiments to the pore diameter reported by the root-mean-square displacement (RMSD) of molecules diffusing in an array of many regular pores. Due to the high uniformity of the capillaries, the observed signal decay curves are modulated by diffusive diffraction. This phenomenon occurs when the paths of the diffusing spins are confined in an ensemble of identical pores, leading to repeated refocusing of phase coherence in q space. From the q values of the minima, the pore size can be determined for known pore shapes. This can be used as ground truth to validate the results from diffusometry experiments calculated by quantitative analysis methods such as MPM. Results show that MPM algorithm effectively quantifies the diameter within a restricted diffusion experiment. In addition, MPM separates two diffusion components and predicts the correct pore sizes as well as the respective relative contributions.

Spin echoes (SE) refocus chemical shift evolution in weakly coupled homonuclear AX spin systems but leave scalar coupling evolution intact, leading to contamination of the in-phase (IP) echo with anti-phase (AP) coherence. In contrast, the so-called perfect echo (PE), which consists of two SEs flanking a central 90° pulse, can minimize the contribution of AP coherence at the echo, with complete refocusing of homonuclear scalar coupling evolution expected in AX systems based on product operator analysis. However, this precludes the consideration of the effects of differential scalar relaxation (DSR) from the interconversion of IP and AP coherences during a PE or a train of PE echoes (PE-CPMG). In this work, the effects of DSR on an AX spin system subject to a PE or PE-CPMG are considered, and the resulting theoretical spin dynamics are discussed. Exact analytical expressions characterizing the IP and AP coherences of each spin as a function of PE time τPE are derived for a single PE and show relaxation-induced oscillations (RIOs) superimposed onto the decay envelopes of IP coherences along with the concomitant generation of AP coherence, even when pulses are assumed to be ideal, instantaneous, and on-resonance for both spins. Numerical simulations reveal that oscillations in the decay envelop may persist under a PE-CPMG, and that the relaxation of the IP coherences is sensitive to pulse sequence timing in terms of both the repetition rate 1/τPE and total relaxation period. In general, rapid pulsing quenches the AP components and slows down relaxation, though RIOs persist. Notably, specific values of 1/τPE termed dispersion resonances - result in effectively decoupled and non-oscillatory IP decay profiles. We extend our analysis to an AX system undergoing a global two-state exchange process. In direct analogy to DSR, differences between Rex,I and Rex,S - each spin's exchange-induced relaxation enhancements - may induce oscillations in the IP decay profiles and concomitantly generate AP coherence. Moreover, each spin's effective relaxation enhancement is shown to depend on both Rex,I and Rex,S. The analysis of the spin dynamics reported here may be of interest in the further understanding, development, and optimization of PE and PE-CPMG-based pulse sequences, particularly those intended to be used for the accurate measurement and quantification of the underlying dynamics of a homonuclear AX systems undergoing chemical exchange.

Despite inherent sensitivity constraints, nuclear magnetic resonance (NMR) plays an indispensable role in probing molecular structures and dynamics across scientific disciplines. Remarkably, while extensive efforts have targeted instrumental and experimental sensitivity improvements, comparatively little focus has been dedicated to sensitivity enhancement through signal analysis. Amidst this present gap, the matrix pencil method (MPM) has emerged as a versatile algorithm that offers tunable filtering and phasing capabilities. Extensive prior research has established the MPM as an adept fitting tool in signal analysis. Here, the efficacy of the MPM is investigated by precisely modeling noisy data to separate information-bearing signals from noise, thereby expanding its utility in various magnetic resonance applications. Simulated data is used to confirm the ability of the MPM to discern and separate signals from noise. Comparative analyses against standard Fourier-based filtering methods highlight the superior performance of the matrix pencil filter (MPF) in preserving signal fidelity without introducing aliasing artifacts. A variety of experimental data is then explored to demonstrate the proficiency of the MPF in characterizing signal components and correcting phase distortions. Collectively, these case studies underscore the filtering capacity of the MPM, portending its use for analytical sensitivity improvements in a wide range of NMR applications.

The asymmetry of peak integrals in 2D relaxation maps of exchange between three sites indicates circular flow between the relaxation sites. This disagrees with the detailed balance according to which the exchange between any pair of sites must be balanced in terms of thermodynamic equilibrium. Confined diffusion of particles jumping randomly on a 2D checkerboard grid to any of their eight neighbor positions and confined gas diffusion were modeled in Monte Carlo simulations to explore the impact of topological constraints on particle exchange between three pools. Both models produce density variations across the pore and reveal that up to 1 % of the molecules move in circular paths between the relaxation pools. This motion is driven by different features of either algorithm. It is silent in terms of thermodynamic equilibrium, confirming that multi-site exchange maps are symmetric in this case. The coherent flux is argued to result from stochastic pore resonance related to diffusion eigenmodes. If it can be driven experimentally by external time-varying electric, magnetic, or ultrasonic fields, this may be a way to enhance heterogeneous catalysis.

The matrix pencil method (MPM) is a powerful tool for processing transient nuclear magnetic resonance (NMR) relaxation signals with promising applications to increasingly complex problems. In the absence of signal noise, the eigenvalues recovered from an MPM treatment of transient relaxometry data reduce to relaxation coefficients that can be used to calculate relaxation time constants for known sampling time ∆t. The MPM eigenvalue and relaxation coefficient equality as well as the resolution of similar eigenvalues and thus relaxation coefficients degrade in the presence of signal noise. The relaxation coefficient ∆t dependence suggests one way to improve MPM resolution by choosing ∆t values such that the differences between all the relaxation coefficient values are maximized. This work develops mathematical machinery to estimate the best ∆t value for sampling damped, transient relaxation signals such that MPM data analysis recovers a maximum number of time constants and amplitudes given inherent signal noise. Analytical and numerical reduced dimension MPM is explained and used to compare computer-generated data with and without added noise as well as treat real measured signals. Finally, the understanding gleaned from this effort is used to predict the best data sampling time to use for non-discrete, distributions of relaxation variables.

Abstract. The question is investigated if three-site diffusive relaxation exchange in thermodynamic equilibrium can lead to exchange maps, which are asymmetric for fluids confined to pores. Asymmetry reports circular flow of particles between the relaxation sites which disagrees with detailed balance according to which the particle exchange between any pair of sites must be balanced. Vacancy diffusion and gas diffusion of particles confined to two-dimensional pores were modeled in Monte-Carlo simulations. For each particle move in vacancy diffusion on a 2D checkerboard grid, one of the eight neighboring destination cells was identified on the basis the jump probability calculated from an empirical approximation of the free energy. Gas diffusion was simulated without thermodynamic interaction on a simulation grid which was up to 104 times finer than the particle diameter. It was found that up to 1 % of all particles moves coherently in closed paths. This motion is attributed to pore resonance corresponding to diffusion eigenmodes. The study shows that detailed balance of multi-site exchange does not apply for a small fraction of particles when the exchange is impacted by topological constraints.

The matrix pencil method (MPM) is tested as an approach to quantitatively process multiexponential low-field nuclear magnetic resonance T1 relaxometry data. The data is obtained by measuring T1 saturation recovery curves in the highly inhomogeneous magnetic field of a stray-field sensor. 0.9% brine solutions, doped with different concentrations of a Gd3+ containing contrast agent, serve as test liquids. Relaxation-times as a function of contrast-agent concentration along with the T1 relaxation curves for combinations of multiple different test liquids are measured, and the results from processing using MPM as well as inverse Laplace transformation as a benchmark are compared. The relaxation-time resolution limits of both procedures are probed by gradually reducing the difference between the relaxation-times of two liquids measured simultaneously. The sensitivity to quantify the relative contribution of each component to the magnetization build-up curve is explored by changing their volume ratio. Furthermore, the potential to resolve systems with more than two components is tested. For the systems under test, MPM shows superior performance in separating two or three relaxation components, respectively and effectively quantifying the time constants.

Maximizing standoff distance by direct placement of probe coils on magnet bodies, while maximizing signal-to-noise is critical to the successful application of unilateral NMR. Two types of radio frequency (rf) coils for linear array, unilateral magnets are described: ''simple fringe" and "split fringe coils." These coils are designed to fully exploit the standoff distance of the unilateral magnet by placement directly on the magnet surface. Such placement fails for normal surface coils used for magnetic resonance due to eddy current induced shielding by the conductive magnet surface. The coil design strategy includes a rectangular cross section solenoid coil, either continuous or split in the center, mounted with the center axis of the coil parallel to the magnet surface. These geometries, when placed on a conducting surface, enhance the rf field produced in the sample region, outside of the solenoid coil. The spatial homogeneity of both rf coils are characterized using the ANSYS (TM) finite element modelling software. ANSYS (TM) modeled coil geometries led to homogeneous, surface displaced rf fields. These coils were then constructed and characterized with magnetic resonance imaging. Finally, two experiments that use these coils to perform large standoff relaxation measurements are described. (C) 2022 Elsevier Inc. All rights reserved.

High pressure assisted infusion of nutrients into food was in situ monitored with magnetic resonance imaging (MRI). Modification of an off-the-shelf pressure reactor with an MRI detection circuit provided a large enough volume to accommodate food. The model food used here was peeled apple flesh as it is considered as a good mimic for fibrous food. The nuclear spin relaxation properties of the water surrounding the apple flesh were enhanced by adding paramagnetic manganese cations. In this way, MRI relaxation contrast can be used to monitor the location of doped bulk water in and around the apple flesh during pressurization. This work tracked the efficiency of pressure induced nutrient infusion in situ, demonstrating that pressure gating and ramping offer no nutrient mass transport advantage over operation at constant pressure and that the presence of a peel expectedly disrupts solute transport into the fruit. High pressure assisted infusion, with all pressurization strategies shown here, yielded nearly 100-fold faster infusion times than at ambient pressure.

We introduce an optimized design for a three-magnet array unilateral magnetic resonance (MR) device. The sensitive spot is 0.5 cm3, and begins roughly 0.5 cm from the magnet surface with a field variation of less than 1.5% of the B0 resonant frequency. 3D simulation was used in conjunction with a trust-region optimization method to determine the optimal magnet geometry to achieve a large sensitive spot. A standard surface coil was used to excite and detect the MR signal from the sensitive spot. The array has dimensions of 8.4 × 7.4 × 4.1 cm and a mass of 0.74 kg. The surface of the magnets are shielded with a thin layer of copper tape to avoid acoustic ringing. Attenuation of the B1-field due to eddy currents in the copper sheet was reduced by displacing the coil from the surface, at the cost of working distance. The quality factor and B1-field attenuation due to eddy currents are explored experimentally by incrementally displacing the coil from the magnet surface. A minor reduction in working distance increases the sensitivity of the measurement. To assess device performance, T1, T2, T1–T2, and diffusion measurements were undertaken with a cod liver oil phantom.

The matrix pencil method (MPM) is explored for stable, reproducible data processing in nuclear magnetic resonance (NMR) relaxometry. Data from one-dimensional and two-dimensional relaxometry experiments designed to measure transverse relaxation T2, longitudinal relaxation T1, diffusion coefficient D values, and their correlations in a standard olive oil/water mixture serve as a platform available to any NMR spectroscopist to compare the performance of the MPM to the benchmark inverse Laplace transform (ILT). The data from two practical examples, including the drying of a solvent polymer system and the enzymatic digestion of polysialic acid, were also explored with the MPM and ILT. In the cases considered here, the MPM appears to outperform the ILT in terms of resolution and stability in the determination of fundamental constants for complex materials and mixtures.

Although blood plasma water content (PWC) is a relevant metric for many medical diagnostic procedures, the routine clinical measurement of PWC has remained elusive. Portable nuclear magnetic resonance (NMR) offers one way to nondestructively and quickly measure PWC. Contrived pseudoplasma samples that mimic blood plasma while also allowing rigorous control over water content are used to demonstrate the role of NMR in this work. Calibration curves relating measured NMR relaxation time constants (T-2 and T-1) to gravimetric PWC values for a set of human lyophilized plasma samples are used to predict the PWC in porcine and model human blood plasma from respective NMR T-2 and T-1 values. It is shown that the T-2 and T-1 decay constants measured with low field NMR relaxometry correlate with the PWC values for pseudoplasma and human lyophilized plasma samples. Statistical testing of the NMR-PWC correlation model demonstrated a prediction accuracy exceeding 98%. The PWC obtained in this way was used to correct sodium cation concentrations reported from direct ion-selective electrode tests. The accuracy of PWC determination with NMR is comparable to that of the gravimetric method that requires sample lyophilization. The rapid turnaround time, non-destructive nature, and portable footprint of the NMR-PWC measurement makes rapid, point-of-care clinical electrolyte estimates possible.

The chemical shift difference, Δσ, between the methylene and hydroxyl protons in the high resolution 1 H nuclear magnetic resonance spectrum of ethylene glycol is shown to be pressure dependent. The equilibrium Δσ values for ethylene glycol are reported as a function of temperature and pressure between ambient conditions, 323 K and 2 kbar, respectively. This surface is used along with Δσ values measured in response to a rapid pressure increase to calculate a temperature rise that is used to infer a temperature change for water that is consistent with theoretical estimates. This work implies that compression heating and decompression cooling are not significant enough to interfere with pressure induced protein folding studies.

Solid-state nuclear magnetic resonance (NMR) spectroscopy is used to study heavily Yb3+ and Er3+ doped, fluorescent NaY1–x–yYbxEryF4 nanoparticles. An understanding of the 19F wide line NMR response suggests that the 0 ppm portion of the 19F NMR spectrum can be used as a probe of trivalent lanthanide content via spin–lattice relaxation time changes. A Yb3+ and Er3+ magnetic interaction is manifest as a cooperative contribution to the 19F spin–lattice relaxation rate in heavily co-doped nanoparticle samples. The results from this study will aid in the understanding of the mechanism of enhanced optical up-conversion among these well-known nanostructures.

Introduction: Recent advances have made portable nuclear magnetic resonance (NMR) spectroscopy economically and practically feasible. The ease with which it can be customized makes portable NMR an extremely desirable analytical technique. However, portable NMR obtains a weaker signal with decreased resolution compared to traditional NMR. As such, one typically measures exponential decay constants at low field rather than frequencies. Here, the matrix pencil method (MPM) is explored for stable, reproducible data processing in low field NMR. Currently, the inverse Laplace transform (ILT) is the conventional method for processing data in low field NMR. However, the ILT is hindered by sensitivity to noise, poor resolution, and high computational requirements that make it difficult to apply in non-laboratory environments. Improving the efficiency of data processing could expand the applications of portable NMR and enhance the quality of information gained from correlation experiments. The MPM fits in a broad category of filter diagonalization methods for digital signal analysis, and was developed for use in radar, antenna, and acoustics technologies. The success of the MPM in other areas of signal processing makes its application to low field NMR promising.

A low cost, portable, high volume, stainless steel pressure reactor is modified to easily perform magnetic resonance relaxometry at industrially relevant pressures. Unlike existing pressurization strategies common to nuclear magnetic resonance (NMR) spectroscopy, this approach is amenable to realistic samples that feature heterogeneity and have traditionally escaped NMR study at pressure. This pressure reactor/NMR probe combination is easily accommodated by most single-sided and other low magnetic field permanent magnet assemblies. The performance of the probe is demonstrated by accomplishing NMR relaxometry on polydimethylsiloxane at different pressures with two types of unilateral magnets.

Low frequency nuclear magnetic resonance (NMR) is used to noninvasively and nondestructively detect spoiled tomato concentrate stored in >200 L metal-lined containers. It is shown that longitudinal and transverse NMR relaxation times change as the tomato concentrate spoils. A rapid, viscosity-dependent spoilage detection method that takes advantage of the inherent inhomogeneity in single-sided NMR instruments is proposed. Here, the effective transverse magnetization decay rate is used as a parameter to determine tomato concentrate spoilage. Three different low frequency, single-sided NMR instruments are described and compared to determine the optimum sensor for spoiled tomato concentrate detection in large-format, metal-lined, aseptic containers. The most effective NMR sensor for this application is temperature stable and has large magnetic field gradients and a homogeneous magnetic field region offset >0.5 cm from the magnet surface. Practical Application This manuscript describes a noninvasive and nondestructive tomato concentrate spoilage detector for application to large-format, sealed, commercial storage bins.