The lognormal and gamma distribution models for estimating molecular weight distributions of polymers using PGSE NMR

Molar Mass Determination for Small and Large Molecules Using Diffusion-Ordered Spectroscopy

The development of the most comprehensive universal calibration of molar mass dependences will be presented. For the first time, diffusion-ordered spectroscopy (DOSY) can now provide structure-, solvent-, and temperature-independent molar mass determinations for both small and large molecules. This fundamental theoretical approach provides only one single function which could perfectly describe all molar mass dependences. The new development using DOSY was tested on 477 diffusion coefficients representing altogether 56 molar mass dependences of 30 small molecules in 7 solvents, 5 different polymers in 10 solvents, and 11 temperature dependences of 2 polymers in 2 solvents, respectively. These samples cover a very large range of molar masses varying between 70 g/mol until 1 200 000 g/mol. The derived equation for the molar masses delivered a very good accuracy for all samples and might be one of the best tools for molar mass determinations.

Non-isocyanate polyurethane-co-polyglycolic acid electrospun nanofiber membrane wound dressing with high biocompatibility, hemostasis, and prevention of chronic wound formation

The prevention of chronic wound formation has already been a primary subject in wound management, particularly for deep wounds. The electrospun nanofiber membranes hold tremendous potential in the prevention of chronic wounds due to their micro/nano pore structures. Currently, many natural and synthetic materials have been utilized in the fabrication of nanofiber membranes. However, striking a balance between the structural stability and the biocompatibility remains challenging. It is necessary not only to ensure the long-term durability of nanofiber membranes but also to enhance their biocompatibility for alleviating patients' suffering. In this study, we reported a nanofiber membrane dressing with excellent biocompatibility and mechanical properties, which is potential for the treatment of deep wounds. The basal material chosen for the preparation of the nanofiber membrane was a co-polyester (NI-LPGD5) synthesized by non-isocyanate polyurethane (NIPU) and polyglycolic acid with a dihydroxy structure (LPGD-synthesized from glycolic acid and neopentyl glycol). Moreover, curcumin was also added as a bioactive substance to enhance the pro-healing effect of dressings. The physicochemical properties of the prepared nanofiber membranes were characterized through various physicochemical tools. Our results demonstrated that the NI-LPGD5 co-polymer can be electrospun into smooth fibers. Meanwhile, curcumin-loaded nanofiber membranes (Cur/NI-LPGD5) also exhibited a favorable microscopic morphology. The fabricated membranes exhibited suitable mechanical properties, outstanding hygroscopic-swelling rate and water vapor transmittance. Besides, in vitro cell culturing, the cells on the NI-LPGD5 membrane maintained their maximum viability. The potential of in vivo wound healing was further demonstrated through animal experiments. The experimental results showed that the nanofiber membranes effectively prevented chronic wounds from forming and promoted granulation tissue growth without replacing the dressing throughout the healing process. We also found that these nanofiber membranes could effectively promote the expression of related biomarkers to accelerate wound healing, particularly the Cur/NI-LPGD5 membrane. In conclusion, the fabricated membranes possess suitable physicochemical properties and promising bioactivity. As a result, it effectively prevented the formation of chronic wounds and demonstrated significant potential in reducing the frequency of dressing changes.

The Universal Calibration for Structure- and Solvent-Independent Molar Mass Determinations of Polymers Using Diffusion-Ordered Spectroscopy

It will be shown how diffusion-ordered spectroscopy (DOSY) can produce a universal calibration of molar mass dependences of polymers compared to size exclusion chromatography (SEC) or recently published DOSY methods. Whereas SEC can deliver only structure-independent universal calibrations for a particular solvent, DOSY was used for creating solvent-independent calibrations for a certain polymer. Now, we can demonstrate a universal calibration method that generates both a structure- and solvent-independent molar mass calibration. Only one mathematical function describes the structure- and solvent-independent calibrations for DOSY by implementing the Mark-Houwink approach. The derived equation is tested on polystyrene (PS), poly(ethylene oxide), and poly(methyl methacrylate) of different molar masses and in different solvents. Altogether, 94 diffusion coefficients representing 16 molar mass calibrations of the diffusion coefficients in 10 different solvents could be perfectly matched to one universal calibration function with an average deviation of just 2.5%. It was also found that the Mark-Houwink parameters calculated by DOSY are very close to the SEC data. In any case, this new approach is a very useful tool for the determination of molar masses and new Mark-Houwink parameters via DOSY.

Molecular Weight Distribution of Branched Polymers: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory

It is challenging to predict the molecular weight distribution (MWD) for a polymer with a branched architecture, though such information will significantly benefit the design and development of branched polymers with desired properties and functions. A Monte Carlo (MC) simulation method based on the Gillespie algorithm is developed to quickly compute the MWD of branched polymers formed through step-growth polymerization, with a branched polyetherimide from two backbone monomers (4,4′-bisphenol A dianhydride and m-phenylenediamine), a chain terminator (phthalic anhydride), and a branching agent (tris[4-(4-aminophenoxy)phenyl] ethane) as an example. This polymerization involves four reactions that can be all reduced to a condensation reaction between an amine group and a carboxylic anhydride group. A comparison between the MC simulation results and the predictions of the Flory-Stockmayer theory on MWD shows that the rates of the reactions are determined by the concentrations of the functional groups on the monomers involved in each reaction. It further shows that the Flory-Stockmayer theory predicts MWD well for systems below the gel point but starts to fail for systems around or above the gel point. However, for all the systems, the MC method can be used to reliably predict MWD no matter if they are below or above the gel point. Even for a macroscopic system, a converging distribution can be quickly obtained through MC simulations on a system of only a few hundred to a few thousand monomers that have the same molar ratios as in the macroscopic system.

Self-assembled Ru(bda) Coordination Oligomers as Efficient Catalysts for Visible Light-Driven Water Oxidation in Pure Water

Water-soluble multinuclear complexes based on ruthenium 2,2'-bipyridine-6,6'-dicarboxylate (bda) and ditopic bipyridine linker units are investigated in three-component visible light-driven water oxidation catalysis. Systematic studies revealed a strong enhancement of the catalytic efficiency in the absence of organic co-solvents and with increasing oligomer length. In-depth kinetic and morphological investigations suggest that the enhanced performance is induced by the self-assembly of linear Ru(bda) oligomers into aggregated superstructures. The obtained turnover frequencies (up to 14.9 s^-1 ) and turnover numbers (more than 1000) per ruthenium center are the highest reported so far for Ru(bda)-based photocatalytic water oxidation systems.

Investigation of the surfactant distribution in oil-in-water emulsions during the crystallization of the dispersed phase via nuclear magnetic resonance relaxometry and diffusometry

The crystallization of melt emulsions is of great interest to the food, cosmetic, and pharmaceutical industries. Surfactants are used in emulsions and suspensions to stabilize the dispersed phase; thus, questions arise about the liquid-liquid and solid-liquid interfaces of the droplets or particles and the distribution of the surfactant in the different phases (continuous and dispersed phase, interface). Nuclear magnetic resonance relaxation and diffusion measurements revealed that the internal and rotational mobility of surfactant molecules at the liquid-liquid interface decreases with increasing droplet sizes. Additionally, solid-liquid interfaces have fewer surfactants than liquid-liquid interfaces as a result of the desorption of the surfactant molecules during the crystallization of the droplets. Relaxation rates of surfactant molecules in aqueous solution as single molecules, micelles, and at the liquid-liquid and solid-liquid interface are analyzed for the first time.

Rapid Online Analysis of Photopolymerization Kinetics and Molecular Weight Using Diffusion NMR

Online, high-throughput molecular weight analysis of polymerizations is rare, with most studies relying on tedious sampling techniques and batchwise postanalysis. The ability to track both monomer conversion and molecular weight evolution in real time could underpin precision polymer development and facilitate study of rapid polymerization reactions. Here, we use a single time-resolved diffusion nuclear magnetic resonance (NMR) experiment to simultaneously study the kinetics and molecular weight evolution during a photopolymerization, with in situ irradiation inside the NMR instrument. As a model system, we used a photoinduced electron transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization. The data allow diffusion coefficients and intensities to be calculated every 14 s from which the polymer size and monomer conversion can be extracted. Key to this approach is (1) the use of shuffled gradient amplitudes in the diffusion NMR experiment to access reactions of any rate, (2) the addition of a relaxation agent to increase achievable time resolution and, (3) a sliding correction that accounts for viscosity changes during polymerization. Diffusion NMR offers a uniquely simple, translatable handle for online monitoring of polymerization reactions.

Interrogating the relationship between the microstructure of amphiphilic poly(ethylene glycol-b-caprolactone) copolymers and their colloidal assemblies using non-interfering techniques

Understanding the microstructural parameters of amphiphilic copolymers that control the formation and structure of aggregated colloids (e.g., micelles) is essential for the rational design of hierarchically structured systems for applications in nanomedicine, personal care and food formulations. Although many analytical techniques have been employed to study such systems, in this investigation we adopted an integrated approach using non-interfering techniques - diffusion nuclear magnetic resonance (NMR) spectroscopy, dynamic light scattering (DLS) and synchrotron small-angle X-ray scattering (SAXS) - to probe the relationship between the microstructure of poly(ethylene glycol-b-caprolactone) (PEG-b-PCL) copolymers [e.g., block molecular weight (MW) and the mass fraction of PCL (f_PCL)] and the structure of their aggregates. Systematic trends in the self-assembly behaviour were determined using a large family of well-defined block copolymers with variable PEG and PCL block lengths (number-average molecular weights (M_n) between 2 and 10 and 0.5-15 kDa, respectively) and narrow dispersity (Ð < 1.12). For all of the copolymers, a clear transition in the aggregate structure was observed when the hydrophobic f_PCL was increased at a constant PEG block M_n, although the nature of this transition is also dependent on the PEG block M_n. Copolymers with low M_n PEG blocks (2 kDa) were observed to transition from unimers and loosely associated unimers to metastable aggregates and finally, to cylindrical micelles as the f_PCL was increased. In comparison, copolymers with PEG block M_n of between 5 and 10 kDa transitioned from heterogenous metastable aggregates to cylindrical micelles and finally, well-defined ellipsoidal micelles (of decreasing aspect ratios) as the f_PCL was increased. In all cases, the diffusion NMR spectroscopy, DLS and synchrotron SAXS results provided complementary information and the grounds for a phase diagram relating copolymer microstructure to aggregation behaviour and structure. Importantly, the absence of commonly depicted spherical micelles has implications for applications where properties may be governed by shape, such as, cellular uptake of nanomedicine formulations.

Characterization of Polymer Molecular Weight Distribution by NMR Diffusometry: Experimental Criteria and Findings

NMR diffusometry finds useful applications in characterizing molecular weight (M) and molecular weight distribution (MWD) for polymers due to its unique advantages in generic detection, chemical selectivity, and quantitation. Here, we present a fundamental study to explore how the condition of diffusion measurement impacts the determined MWD. We use the critical dilute concentration C_dilute^* to explicitly delineate the boundary of the sufficiently dilute condition, below which chain interactions have a negligible impact on polymer diffusion. We present solid evidence to validate the postulated theory that links C_dilute^* to molecular weight, polydispersity, and chain conformation. Quantitative analysis reveals the consequence of violating the sufficiently dilute condition with M/MWD characterization. These findings provide useful guidance for M/MWD characterization by NMR diffusion and help to rationalize the data disparity that exists in the literature. The results further provide new insights into the interplay between chain conformations and diffusion for globular structure, such as proteins, and provide a different approach toward characterizing polymer architecture and molecular weight.

Perspectives in process analytics using low field NMR

Low field NMR is a powerful analytical tool which creates an enormous added value in process analytics. Based on specific applications in process analytics and perspectives for low field NMR in form of spectroscopy, relaxation, diffusion, and imaging in quality control, diverse applications and technical realizations like spectrometers, time domain NMR, mobile NMR sensors and MRI will be discussed.

Flexible modeling of ratio outcomes in clinical and epidemiological research

In medical studies one frequently encounters ratio outcomes. For modeling these right-skewed positive variables, two approaches are in common use. The first one assumes that the outcome follows a normal distribution after transformation (e.g. a log-normal distribution), and the second one assumes gamma distributed outcome values. Classical regression approaches relate the mean ratio to a set of explanatory variables and treat the other parameters of the underlying distribution as nuisance parameters. Here, more flexible extensions for modeling ratio outcomes are proposed that allow to relate all the distribution parameters to explanatory variables. The models are embedded into the framework of generalized additive models for location, scale and shape (GAMLSS), and can be fitted using a component-wise gradient boosting algorithm. The added value of the new modeling approach is demonstrated by the analysis of the LDL/HDL cholesterol ratio, which is a strong predictor of cardiovascular events, using data from the German Chronic Kidney Disease Study. Particularly, our results confirm various important findings on risk factors for cardiovascular events.

Optimising magnetic resonance sampling patterns for parametric characterisation

Sampling strategies are often central to experimental design. Choosing efficiently which data to acquire can improve the estimation of parameters and reduce the acquisition time. This work is focused on designing optimal sampling patterns for Nuclear Magnetic Resonance (NMR) applications, illustrated with respect to the best estimate of the parameters characterising a lognormal distribution. Lognormal distributions are commonly used as fitting models for distributions of spin-lattice relaxation time constants, spin-spin relaxation time constants and diffusion coefficients. A method for optimising the choice of points to be sampled is presented which is based on the Cramér-Rao Lower Bound (CRLB) theory. The method's capabilities are demonstrated experimentally by applying it to the problem of estimating the emulsion droplet size distribution from a pulsed field gradient (PFG) NMR diffusion experiment. A difference of <5% is observed between the predictions of CRLB theory and the PFG NMR experimental results. It is shown that CLRB theory is stable down to signal-to-noise ratios of ∼10. A sensitivity analysis for the CRLB theory is also performed. The method of optimizing sampling patterns is easily adapted to distributions other than lognormal and to other aspects of experimental design; case studies of optimising the sampling scheme for a fixed acquisition time and determining the potential for reduction in acquisition time for a fixed parameter estimation accuracy are presented. The experimental acquisition time is typically reduced by a factor of 3 using the proposed method compared to a constant gradient increment approach that would usually be used.

Clear distinction between CAC and CMC revealed by high-resolution NMR diffusometry for a series of bis-imidazolium gemini surfactants in aqueous solutions

The aggregation behavior in the transition region was studied for a series of dicationic surfactants 3,3′-[α,ω-(dioxaalkane)]bis(1-dodecylimidazolium)dichlorides with varied spacer length from two to twelve carbon atoms. We employed Nuclear Magnetic Resonance diffusometry and Bayesian DOSY analysis to obtain the aggregate size distribution in the transition region. The critical concentrations CC were independently obtained from surface tension, electric conductivity, UV-Vis and NMR methods. The micelle aggregation numbers were estimated from the self-diffusion coefficients and were independently confirmed using steady-state fluorescence quenching. The morphology of the aggregates was characterized by small-angle scattering of synchrotron radiation and molecular dynamics simulations. The obtained CC values are identified as critical aggregation concentrations CAC. A broad transition region was observed, and stable micelles were obtained at much higher concentrations than CAC. The accurate CMC values could not be identified for the systems in the study. We indicated that the distribution of aggregate size becomes small and the system becomes homogeneous at much larger concentrations than CAC (typically 15–20 mM). The existence of a slow exchange between two environments, an aggregate and aqueous environment, was confirmed by ¹H NMR and 2D HSQC NMR spectroscopy.

The aggregation behavior in the transition region was studied for a series of dicationic surfactants 3,3′-[α,ω-(dioxaalkane)]bis(1-dodecylimidazolium)dichlorides with varied spacer length from two to twelve carbon atoms.

PALMA, an improved algorithm for DOSY signal processing

NMR is a tool of choice for the measurement of diffusion coefficients of species in solution.

Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation model

We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.

The Power of Heterogeneity: Parameter Relationships from Distributions

Complex scientific data is becoming the norm, many disciplines are growing immensely data-rich, and higher-dimensional measurements are performed to resolve complex relationships between parameters. Inherently multi-dimensional measurements can directly provide information on both the distributions of individual parameters and the relationships between them, such as in nuclear magnetic resonance and optical spectroscopy. However, when data originates from different measurements and comes in different forms, resolving parameter relationships is a matter of data analysis rather than experiment. We present a method for resolving relationships between parameters that are distributed individually and also correlated. In two case studies, we model the relationships between diameter and luminescence properties of quantum dots and the relationship between molecular weight and diffusion coefficient for polymers. Although it is expected that resolving complicated correlated relationships require inherently multi-dimensional measurements, our method constitutes a useful contribution to the modelling of quantitative relationships between correlated parameters and measurements. We emphasise the general applicability of the method in fields where heterogeneity and complex distributions of parameters are obstacles to scientific insight.