Accurate measurements of self-diffusion coefficients with benchtop NMR using a QM model-based approach.

The measurement of self-diffusion coefficients using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy is a well-established method. Recently, benchtop NMR spectrometers with gradient coils have also been used, which greatly simplify these measurements. However, a disadvantage of benchtop NMR spectrometers is the lower resolution of the acquired NMR signals compared to high-field NMR spectrometers, which requires sophisticated analysis methods. In this work, we use a recently developed quantum mechanical (QM) model-based approach for the estimation of self-diffusion coefficients from complex benchtop NMR data. With the knowledge of the species present in the mixture, signatures for each species are created and adjusted to the measured NMR signal. With this model-based approach, the self-diffusion coefficients of all species in the mixtures were estimated with a discrepancy of less than 2 % compared to self-diffusion coefficients estimated from high-field NMR data sets of the same mixtures. These results suggest benchtop NMR is a reliable tool for quantitative analysis of self-diffusion coefficients, even in complex mixtures.

A comparison of non-uniform sampling and model-based analysis of NMR spectra for reaction monitoring.

Nuclear magnetic resonance (NMR) spectroscopy is widely used for applications in the field of reaction and process monitoring. When complex reaction mixtures are studied, NMR spectra often suffer from low resolution and overlapping peaks, which places high demands on the method used to acquire or to analyse the NMR spectra. This work presents two NMR methods that help overcome these challenges: 2D non-uniform sampling (NUS) and a recently proposed model-based fitting approach for the analysis of 1D NMR spectra. We use the reaction of glycerol with acetic acid as it produces five reaction products that are all chemically similar and, hence, challenging to distinguish. The reaction was measured on a high-field 400 MHz NMR spectrometer with a 2D NUS-heteronuclear single quantum coherence (HSQC) and a conventional 1D 1 H NMR sequence. We show that comparable results can be obtained using both 2D and 1D methods, if the 2D volume integrals of the 2D NUS-HSQC NMR spectra are calibrated. Further, we monitor the same reaction on a low-field 43 MHz benchtop NMR spectrometer and analyse the acquired 1D 1 H NMR spectra with the model-based approach and with partial least-squares regression (PLS-R), both trained using a single, calibrated data set. Both methods achieve results that are in good quantitative agreement with the high-field data. However, the model-based method was found to be less sensitive to the training data set used than PLS-R and, hence, was more robust when the reaction conditions differed from that of the training data.

Time-domain signal modelling in multidimensional NMR experiments for estimation of relaxation parameters.

We present a model-based method for estimation of relaxation parameters from time-domain NMR data specifically suitable for processing data in popular 2D phase-sensitive experiments. Our model is formulated in terms of commutative bicomplex algebra, which allows us to use the complete information available in an NMR signal acquired with principles of quadrature detection without disregarding any of its dimensions. Compared to the traditional intensity-analysis method, our model-based approach offers an important advantage for the analysis of overlapping peaks and is robust over a wide range of signal-to-noise ratios. We assess its performance with simulated experiments and then apply it for determination of [Formula: see text], [Formula: see text], and [Formula: see text] relaxation rates in datasets of a protein with more than 100 cross peaks.

Three-dimensional imaging of localized surface plasmon resonances of metal nanoparticles.

The remarkable optical properties of metal nanoparticles are governed by the excitation of localized surface plasmon resonances (LSPRs). The sensitivity of each LSPR mode, whose spatial distribution and resonant energy depend on the nanoparticle structure, composition and environment, has given rise to many potential photonic, optoelectronic, catalytic, photovoltaic, and gas- and bio-sensing applications. However, the precise interplay between the three-dimensional (3D) nanoparticle structure and the LSPRs is not always fully understood and a spectrally sensitive 3D imaging technique is needed to visualize the excitation on the nanometre scale. Here we show that 3D images related to LSPRs of an individual silver nanocube can be reconstructed through the application of electron energy-loss spectrum imaging, mapping the excitation across a range of orientations, with a novel combination of non-negative matrix factorization, compressed sensing and electron tomography. Our results extend the idea of substrate-mediated hybridization of dipolar and quadrupolar modes predicted by theory, simulations, and electron and optical spectroscopy, and provide experimental evidence of higher-energy mode hybridization. This work represents an advance both in the understanding of the optical response of noble-metal nanoparticles and in the probing, analysis and visualization of LSPRs.

Less is more: how compressed sensing is transforming metrology in chemistry.

Mathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways. With the advent of the digital age, the subject of information theory has grown hugely in importance. In particular, over the last two decades significant advances in our understanding of sampling and function reconstruction have culminated in the development of an idea known as compressed sensing. What seems like an abstract idea is now having a profound impact throughout the scientific world-from enabling high-resolution imaging of pediatric patients in clinical medicine through to advancing 3D electron tomography images of nanoparticle catalysts and NMR spectroscopy studies of proteins. In this Minireview, we summarize these applications and provide an outlook on how the principles of compressed sensing are leading to entirely new approaches to measurement throughout the physical and life sciences.

Quantitative examination of the anatomy of the juvenile sugar maple xylem.

New methodologies have enabled viable sap yields from juvenile sugar maple trees. To further improve yields, a better understanding of sap exudation is required. To achieve this, the anatomy of the xylem must first be fully characterised. We examine juvenile maple saplings using light optical microscopy (LOM) and scanning electron microscopy (SEM), looking at sections cut along differing orientations as well as macerations. From this we measure various cell parameters. We find diameter and length of vessel elements to be 28 ± 8 µm and 200 ± 50 µm, for fibre cells 8 ± 3 µm and 400 ± 100 µm, and for ray parenchyma cells 8 ± 2 µm and 50 ± 20 µm. We also examine pitting present on different cell types. On vessel elements we observe elliptical bordered pits connecting to other vessel elements (with major axis of 2.1 ± 0.7 µm and minor 1.3 ± 0.3 µm) and pits connecting to ray parenchyma (with major axis of 4 ± 2 µm and minor 2.0 ± 0.7 µm). We observe two distinct pit sizes on fibres with circular pits 0.7 ± 0.2 µm in diameter and ellipsoidal pits 1.6 ± 0.4 µm by 1.0 ± 0.3 µm. We do not observe distinct pitting patterns on different fibre types. The various cell and pit measurements obtained generally agree with the limited data available for mature trees, with the exception of vessel element and fibre length, both of which were significantly smaller than reported values.

Detection of honey adulteration using benchtop 1H NMR spectroscopy.

High magnetic field NMR spectroscopy featuring the use of superconducting magnets is a powerful analytical technique for the detection of honey adulteration. Such high field NMR systems are, however, typically housed in specialised laboratories, require cryogenic coolants, and necessitate specialist training to operate. Benchtop NMR spectrometers featuring permanent magnets are, by comparison, significantly cheaper, more mobile and can be operated with minimal expertise. The lower magnetic fields used in such systems, however, result in limited spectral resolution, which diminishes their ability to perform quantitative composition analysis. These limitations may be overcome by implementing a recently developed field-invariant model-based fitting method which is defined by the underlying quantum mechanical properties of the nuclear spin system; this method is applied here to quantify the sugar composition of honey using benchtop 1H NMR (43 MHz) spectroscopy. The detection of adulteration of 26 honey samples with brown rice syrup is quantitatively demonstrated to a minimum adulterant concentration of 5 wt%. Honey adulteration with corn syrup, glucose syrup and wheat syrup was also quantitatively detected using this approach. Our NMR detection of adulteration was shown to be invariant with time over 60 days of storage.

Examination of embolisms in maple and birch saplings utilising microCT.

We demonstrate the application of synchrotron x-ray microtomography (microCT) to non-invasively examine the internal structure of a maple and birch sapling. We show that, through the use of standard image analysis techniques, embolised vessels can be extracted from reconstructed slices of the stem. By combining these thresholded images with connectivity analysis, we map out the embolisms within the sapling in three dimensions and evaluate the size distribution, showing that large embolisms over 0.005 mm3 in volume compose the majority of the saplings' total embolised volume. Finally we evaluate the radial distribution of embolisms, showing that in maple fewer embolisms are present towards the cambium, while birch has a more uniform distribution.

Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins.

Central to structural studies of biomolecules are multidimensional experiments. These are lengthy to record due to the requirement to sample the full Nyquist grid. Time savings can be achieved through undersampling the indirectly-detected dimensions combined with non-Fourier Transform (FT) processing, provided the experimental signal-to-noise ratio is sufficient. Alternatively, resolution and signal-to-noise can be improved within a given experiment time. However, non-FT based reconstruction of undersampled spectra that encompass a wide signal dynamic range is strongly impeded by the non-linear behaviour of many methods, which further compromises the detection of weak peaks. Here we show, through an application to a larger α-helical membrane protein under crowded spectral conditions, the potential use of compressed sensing (CS) l (1)-norm minimization to reconstruct undersampled 3D NOESY spectra. Substantial signal overlap and low sensitivity make this a demanding application, which strongly benefits from the improvements in signal-to-noise and resolution per unit time achieved through the undersampling approach. The quality of the reconstructions is assessed under varying conditions. We show that the CS approach is robust to noise and, despite significant spectral overlap, is able to reconstruct high quality spectra from data sets recorded in far less than half the amount of time required for regular sampling.

Exploring the origins of turbulence in multiphase flow using compressed sensing MRI.

Ultrafast magnetic resonance imaging, employing spiral reciprocal space sampling and compressed sensing image reconstruction, is used to acquire velocity maps of the liquid phase in gas-liquid multiphase flows. Velocity maps were acquired at a rate of 188 frames per second. The method enables quantitative characterization of the wake dynamics of single bubbles and bubble swarms. To illustrate this, we use the new technique to demonstrate the role of bubble wake vorticity in driving bubble secondary motions, and in governing the structure of turbulence in multiphase flows.

Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces. A compressed sensing-electron tomography (CS-ET) approach.

In this paper, we apply electron tomography (ET) to the study of the three-dimensional (3D) morphology of iron oxide nanoparticles (NPs) with reactive concave surfaces. The ability to determine quantitatively the volume and shape of the NP concavity is essential for understanding the key-lock mechanism responsible for the destabilization of gold nanocrystals within the iron oxide NP concavity. We show that quantitative ET is enhanced greatly by the application of compressed sensing (CS) techniques to the tomographic reconstruction. High-fidelity tomograms using a new CS-ET algorithm reveal with clarity the concavities of the particle and enable 3D nanometrology studies to be undertaken with confidence. In addition, the robust performance of the CS-ET algorithm with undersampled data should allow rapid progress with time-resolved 3D nanoscale studies, 3D atomic resolution imaging, and cryo-tomography of nanoscale cellular structures.

A numerical investigation of the hydrodynamic dispersion in triply periodic chromatographic stationary phases.

3D printed custom chromatographic stationary phases have recently been demonstrated. Using the Lattice Boltzmann Method, we compared the model-predicted chromatographic performance of random packing of monodisperse spheres, open tubular columns (OTC) and stationary phases based on three triply periodic minimal surfaces (TPMS): Schwarz Diamond (SD), Schoen Gyroid (SG) and Schwarz Primitive (SP). Three performance metrics were employed in this comparison: i) reduced plate height, ii) Darcy number, iii) kinetic performance factor. Each simulated geometry was unconfined with an impermeable stationary phase to remove wall effects and pore diffusion. The performance was studied for macro-porosities in the range 0.2 to 0.8, depending on the geometry. OTCs were found to have superior permeability to both random sphere packing and TPMS structures across the entire porosity range. At porosity greater than 0.366, the Schwarz Diamond medium achieved the lowest levels of band broadening and greatest kinetic performance. The reduced plate height of all stationary phase geometries was shown to increase with bed porosity. The kinetic performance was found to increase with porosity for TPMS structures, decrease with porosity for random packing and be independent of porosity for OTCs. This work illustrates that chromatographic stationary phase geometries based on TPMS structures are theoretically competitive with random packing and open tubular columns and their feasibility for practical chromatography should continue to be explored.

Quantification of mixtures of analogues of illicit substances by benchtop NMR spectroscopy.

This paper investigates the possibility of using benchtop NMR spectroscopy for quantification of illicit drugs (methamphetamine) in binary and ternary mixtures with impurities and cutting agents (N-isopropylbenzylamine, phenethylamine and dimethylsulfone). To avoid handling regulated substances, methamphetamine in our experiments is substituted with amino-2-propanol, which has similar functional groups and chemical structure to methamphetamine and hence a related NMR spectrum. Binary and ternary mixtures at concentrations from 30 mmol/L up to 500 mmol/L for each of these species were measured using a 60 MHz benchtop spectrometer. The spectra were analysed using both integration and a model-based algorithm that relies on a full quantum mechanical description of the studied spin systems. Both techniques were able to quantify the composition of the mixtures. The root mean squared error in the measured concentration using the model-based algorithm was < 10 mmol/L, whereas the error using integration was typically > 20 mmol/L. Thus, we conclude benchtop NMR is viable for quantitative measurements of mixtures of illicit substances, particularly when coupled with a quantum mechanical model for the analysis.

Quantitative frother analysis on coal mine process water with a benchtop NMR spectrometer.

This paper investigates the use of a benchtop NMR for quantification of a commonly used frothing agent, methyl isobutyl carbinol (MIBC) in the process water of a coal preparation facility. Solid phase extraction is used to increase the concentration of MIBC in the sample so that it is quantifiable by a benchtop NMR. A polymeric, reversed phase column with methanol as solvent gives a MIBC recovery rate of 67 ± 4% as determined using 400 MHz high-field NMR. The recovery rate consistently falls in the above narrow range even in the presence of diesel and inorganic electrolytes which are likely present as background chemicals in the process water. Using the average MIBC recovery rate, we use a quantum mechanical model to analyse the intensity of MIBC in the benchtop spectra. The quantum mechanical modelling algorithm effectively excludes the effect of the diesel on the measured NMR signal. The quantification error when the inlet concentration of MIBC is between 1 and 12 mg/L (1.2-15 ppm v/v), is within 0.5 mg/L (0.6 ppm v/v).

Quantitative analysis of wine and other fermented beverages with benchtop NMR.

We present a fully automated approach for quantitative compositional analysis of fermented beverages using benchtop nuclear magnetic resonance (NMR) spectroscopy. NMR spectroscopy, renowned for its applications in chemical structure elucidation, is gaining attention as a quantitative analytical technique due to its inherent linearity and the ability to obtain comprehensive quantitative information with a single simple experiment. Recently developed benchtop NMR spectrometers offer the quantitative capabilities of NMR to a wide range of potential users in industry, but their applicability has been limited by the reduced effective spectral resolution and the need for more advanced data processing. We address this problem with a model-based algorithm that hinges on the well-understood description of quantum mechanical phenomena in NMR spectroscopy. We demonstrate the effectiveness of our approach on a challenging problem of analysing the composition of wine and related fermented beverages - an important potential niche application of quantitative NMR. We successfully quantify more than 15 major components in the wine matrix and enable the quantification of species whose analysis is generally not possible with established methods. The average discrepancy of the obtained concentrations, when compared to the traditional methods of analysis, usually does not exceed 10% and is lower for the most abundant species (e.g. below 5% for ethanol).

Quantitative analysis using external standards with a benchtop NMR spectrometer.

This paper investigates the use of benchtop NMR spectrometers for quantitative analysis with external standards. Specifically, it focuses on the measurement of aqueous samples with analyte concentrations ranging from 30 mM to 1.7 M and electrical conductivity of up to 84mScm-1 using a 43 MHz instrument. It is demonstrated that measurements using the PULCON method cannot achieve an average error in quantification of <4% with the benchtop NMR tested here unless the standard and analyte are very similar. Our analysis indicates that this comparatively large error arises from the fixed tuning and matching of the benchtop spectrometer. We confirm that for moderately dilute samples (less than 0.2 M), the integral area of the solvent peak is suitable for use as an internal standard to mitigate this error. Furthermore, a round robin study demonstrates that the second major source of uncertainty in these measurements arises from the manual processing of the spectra by different analysts. Here we propose heuristics for manual baseline and phase correction to reduce this analyst-dependent error to about 3 %. We also demonstrate that semi-automated quantification using qGSD is able to achieve similar accuracy of integration, but with reduced sensitivity to the processing of the operator.

Improving the accuracy of model-based quantitative nuclear magnetic resonance.

Low spectral resolution and extensive peak overlap are the common challenges that preclude quantitative analysis of nuclear magnetic resonance (NMR) data with the established peak integration method. While numerous model-based approaches overcome these obstacles and enable quantification, they intrinsically rely on rigid assumptions about functional forms for peaks, which are often insufficient to account for all unforeseen imperfections in experimental data. Indeed, even in spectra with well-separated peaks whose integration is possible, model-based methods often achieve suboptimal results, which in turn raises the question of their validity for more challenging datasets. We address this problem with a simple model adjustment procedure, which draws its inspiration directly from the peak integration approach that is almost invariant to lineshape deviations. Specifically, we assume that the number of mixture components along with their ideal spectral responses are known; we then aim to recover all useful signals left in the residual after model fitting and use it to adjust the intensity estimates of modelled peaks. We propose an alternative objective function, which we found particularly effective for correcting imperfect phasing of the data - a critical step in the processing pipeline. Application of our method to the analysis of experimental data shows the accuracy improvement of 20 %-40 % compared to the simple least-squares model fitting.

Bayesian approach for automated quantitative analysis of benchtop NMR data.

Low-cost, user-friendly benchtop NMR instruments are often touted as a "one-click" solution for data acquisition, however insufficient peak dispersion in their spectra often reduces the accuracy of quantification and requires user expertise with sophisticated processing tools. Our work aims to facilitate the wide acceptance of benchtop NMR instruments as a viable and effective substitute for cryogenic magnets. We propose an algorithmic approach that completely automates the routine analysis of sets of samples with similar compositions - the problem that often underlies many industrial applications concerned with reaction and process monitoring and quality control. Our solution is rooted in the idea of parametric modelling formulated in terms of Bayesian statistics, which effectively incorporates prior knowledge about the studied system (such as concentration-dependent chemical shift changes) that is usually available in industrial applications. Furthermore, the use of quantum mechanical models for chemical species makes our approach invariant to the spectrometer field strength - a necessary prerequisite for the successful analysis of benchtop data. We demonstrate the performance of our method with two representative sets of samples: mixtures of alcohols and acetates, and aqueous mixtures of biologically relevant species. In these examples, our fully automated analysis of benchtop spectra achieves average errors in concentrations of 0.01 mol/mol and 0.02 mol/mol respectively. Our method is competitive with the traditional processing approaches of well resolved high-field data and has the potential to bring the benefits of NMR even to a small chemistry laboratory.

A field-invariant method for quantitative analysis with benchtop NMR.

Recently developed benchtop instruments have the potential of bringing the benefits of NMR spectroscopy to the wide variety of industrial applications. Unfortunately, their low spectral resolution poses significant challenges for traditional quantification approach. Here we present a novel model-based method designed to overcome these challenges. By defining our models in terms of quantum mechanical properties of the underlying spin system, we make our approach invariant to the spectrometer field strength and especially suitable for analyzing benchtop data. Our experimental results on prepared samples and natural fruit juices confirm the applicability of our method for quantitative analysis of medium-field 1H NMR spectra. The developed method succeeds in accurately separating the spectra of glucose anomers and even monitoring their interconversion in non-deuterated water. Furthermore, the compositions of unbuffered natural fruit juices estimated using data from 43 MHz to 400 MHz spectrometers are in good agreement with each other and with the reference values from nutrition databases.

On the influence of rotational motion on MRI velocimetry of granular flows - Theoretical predictions and comparison to experimental data.

Continuum dynamics of granular materials are known to be influenced by rotational, as well as translational, motion. Few experimental techniques exist that are sensitive to rotational motion. Here we demonstrate that MRI is sensitive to the rotation of granules and that we can quantify its effect on the MRI signal. In order to demonstrate the importance of rotational motion, we perform discrete element method (DEM) simulations of spherical particles inside a Couette shear cell. The variance of the velocity distribution was determined from DEM data using two approaches. (1) Direct averaging of the individual particle velocities. (2) Numerical simulation of the pulsed field gradient (PFG) MRI signal acquisition based on the DEM data. Rotational motion is found to be a significant effect, typically contributing up to 50% of the signal attenuation, thus amplifying the calculated velocity variance. A theoretical model was derived to relate an MRI signal to the angular velocity distribution. This model for the signal was compared to previously published experimental data as well as simulated MRI results and found to be consistent.