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

Williamson, Nathan H.; Nydén, Magnus; Röding, Magnus

doi:10.1016/j.jmr.2016.04.007

Cited by 39 publications

(40 citation statements)

References 30 publications

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“…Uniform penalty inversion (UPEN) [32,33] reduces the line broadening and pearling effects in non-parametric models. Parametric models on the other hand are based on physically motivated information and use a pre-defined number of components involving a commensurate number of pre-defined functions to form [28,[34][35][36][37]. The user is able to utilize prior knowledge by specifying the number of components.…”

Section: Numerical Inverse Laplace Transformmentioning

confidence: 99%

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

Williamson

Röding

Galvosas

et al. 2016

Journal of Magnetic Resonance

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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.

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Section: Numerical Inverse Laplace Transformmentioning

confidence: 99%

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

Williamson

Röding

Galvosas

et al. 2016

Journal of Magnetic Resonance

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“…However, the scaling parameters of Eq. (1) specific to that polymersolvent system must be found by measuring ⟨D⟩ on fractionated samples of the polymer with known M. Therefore, currently all PGSE NMR-based methods which convert from D to M cannot independently measure the absolute molecular mass distribution [12,13,14,15,16,17,18,19,20,21,22,23,24,25].In this paper we show that ν in Eq.(1) can be directly estimated from a single PGSE experiment in which the extremity (end-group) polymer signal can be spectrally resolved by a chemical shift from the polymer main-chain signal. The scaling exponent, ν, is a measure of the polymer conformation as well as solvent quality [3,26], with bounds of ν = 1/3 for a perfectly coiled, impenetrable, polymer ball and ν = 1 for a perfectly straight polymer rod [17].…”

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confidence: 99%

“…In this way, M n and M w of each mixture are known. In the following, we introduce PGSE NMR and reproduce equations [24] for the application of the lognormal [29,30,14] and gamma [21,31] distribution models. We then explain sample preparation and outline the procedure for obtaining ν, M w /M n , and the molecular mass distribution.…”

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Scaling exponent and dispersity of polymers in solution by diffusion NMR

Williamson

Röding

Miklavcic

et al. 2017

Journal of Colloid and Interface Science

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Molecular mass distribution measurements by pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) spectroscopy currently require prior knowledge of scaling parameters to convert from polymer self-diffusion coefficient to molecular mass. Reversing the problem, we utilize the scaling relation as prior knowledge to uncover the scaling exponent from within the PGSE data. Thus, the scaling exponent-a measure of polymer conformation and solvent quality-and the dispersity (M w /M n ) are obtainable from one simple PGSE experiment. The method utilizes constraints and parametric distribution models in a two-step fitting routine involving first the mass-weighted signal and second the number-weighted signal. The method is developed using lognormal and gamma distribution models and tested on experimental PGSE attenuation of the terminal methylene signal and on the sum of all methylene signals of polyethylene glycol in D 2 O. Scaling exponent and dispersity estimates agree with known values in the majority of instances, leading to the potential application of the method to polymers for which characterization is not possible with alternative techniques. Keywords:Pulsed gradient spin echo, pulsed field gradient, Nuclear Magnetic Resonance spectroscopy, Molecular weight distribution, Polymers, DOSY, Polydispersity Index, Self-diffusion, Molar mass, Flory exponent, Lognormal distribution, Gamma distribution, End-group analysis, Scaling law Synthetic polymers have distributions of molecular masses determined by their synthesis [1]. Measuring the molecular mass distribution rather than its average is important because the dispersity can influence polymer properties [2]. Absolute as opposed to relative measurements are needed when using polymer physics to fully realize the potential applications of a polymer [3]. Only a handful of techniques can measure the absolute molecular mass distribution [3]. The gold standard is size exclusion chromatography (SEC) using universal calibration [4], which does not always work [5,6]. New techniques must be developed to aid in the advancement of polymer science.Pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) [7,8] is a powerful technique for obtaining the distribution of polymer self-diffusion coefficients D [9], from which the distribution of molecular masses M can be obtained by the scaling law [10] ration give PGSE NMR a competitive edge with respect to SEC. Chemical shift information [7], e.g. in a diffusion ordered spectroscopy (DOSY) plot [11], provides the ability to observe chemical heterogeneity and impurity. Sample preparation generally does not require filtration because contaminates from large particles such as dust do not impact the experiment. However, the scaling parameters of Eq. (1) specific to that polymersolvent system must be found by measuring ⟨D⟩ on fractionated samples of the polymer with known M. Therefore, currently all PGSE NMR-based methods which convert from D to M cannot independently measure the absolute molecular mass distribution [...

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“…The question arose whether K and α are unique given that the diffusion was measured at lowest concentrations. To extend previous work, some dilute polymer solutions in CDCl 3 are summarized and the diffusion coefficients of the decamer in solution are added ( Figure ). Data are distributed around a trend line with α = 0.51.…”

Section: Resultsmentioning

confidence: 99%

¹H PFG‐NMR Diffusion Study on a Sequence‐Defined Macromolecule: Confirming Monodispersity

Guo

Wetzel

Solleder

et al. 2019

Macro Chemistry & Physics

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A monodisperse decamer bearing ten different side chains, obtained via the iterative Passerini three‐component reaction and subsequent deprotection, is investigated by 1H pulsed field gradient (PFG) NMR. Both the stimulated echo (PFG‐STE) and a fast spin‐echo pulse sequence (β‐PFG‐SE) are applied to explore the translational diffusion properties of the sequence‐defined decamer in solution at different concentrations with the aim of establishing an independent and new method to confirm its monodispersity. The signals decay according to the expectation of monodisperse molecules in solution with a high experimental accuracy, indeed verifying the monodispersity of these decamers. The diffusion coefficients can further be interpreted in terms of molecular weight. Both NMR methods result in comparable diffusion coefficients, while the β‐PFG‐SE reduces the experimental time by a factor of about 18.

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

Cited by 39 publications

References 30 publications

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

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

Scaling exponent and dispersity of polymers in solution by diffusion NMR

¹H PFG‐NMR Diffusion Study on a Sequence‐Defined Macromolecule: Confirming Monodispersity

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

Cited by 39 publications

References 30 publications

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

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

Scaling exponent and dispersity of polymers in solution by diffusion NMR

1H PFG‐NMR Diffusion Study on a Sequence‐Defined Macromolecule: Confirming Monodispersity

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Product

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¹H PFG‐NMR Diffusion Study on a Sequence‐Defined Macromolecule: Confirming Monodispersity