The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments

Håkansson, Björn; Nydén, Magnus; Söderman, Olle

doi:10.1007/s003960050532

Cited by 96 publications

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“…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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confidence: 99%

“…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%

“…Many distribution models exist, and the estimation of the distribution is an inverse problem for which there is no unique solution. We are physically motivated to use the lognormal distribution [14,29,30],…”

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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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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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“…The diffusion time was set to ∆ = 100 ms and 128 scans were accumulated at 17 different gradient strengths. As described by Håkansson et al (2000), Garver andCallaghan (1991), andFleischer (1985), the resulting self-diffusion coefficients of the lignin samples could be obtained after fitting the intensity decays (I(k, D)) to a lognormal distribution function where D m denotes the fitted mass-weighted median selfdiffusion coefficient, σ describes the distribution width, k is defined from the experimental settings as and γ is the nuclear magnetogyric radius for protons. Sodium polystyrene sulfonate standards were used to obtain the scaling parameters (K = 1.62 x 10 -8 m 2 /s and α = -0.58) needed to calculate the mass-weighted molar mass distribution by applying the Mark-Houwink relationship between the self-diffusion coefficient (D) and the molar mass (M), i.e.…”

Section: Analysesmentioning

confidence: 99%

Effects of biological treatment on the chemical structure of dissolved lignin-related substances in effluent from thermomechanical pulping

Andersson

Pranovich

Norgren

et al. 2008

Nordic Pulp &Amp; Paper Research Journal

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SUMMARY:Effluent from a TMP-based pulp and paper mill was collected at the inlet and outlet of the mill's biological treatment plant and fractionated by sorption on XAD-8 resin and MTBE precipitation. Fractionation indicated that the refractory dissolved organic material in biologically treated effluent was mainly composed of lignin-related substances. Characterisation of the lignin-related substances by chromatographic and spectrometric methods confirmed the similarities of the isolated material and milled wood lignin. Fractionation and characterisation of alkali-extracted material from solids (biosludge) in biologically treated effluent found evidence of lignin-related material. Results indicated that biological treatment had altered the chemical structure and molar-mass distribution of dissolved lignin-related substances.

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“…As a result, a multiple detection configuration is usually required to reach reliable molecular weight data by SEC, since the intensity of the response obtained in each detection mode does not only depend on molecular weight but also on parameters that are a function of the macromolecule composition [16,17]. Pulsed gradient spin echo (PGSE) [18 -20] NMR can be used to estimate the weight average molecular weight (M w ) of a synthetic homopolymer from the measurement of its molecular self-diffusion coefficient [21][22][23][24]. For block copolymers, we have recently shown that such estimation not only requires properly recorded calibration curves for each of the polymers constituting the blocks, but also a hydrodynamic model to correctly interpret the diffusion data [25].…”

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Analytical strategy for the molecular weight determination of random copolymers of poly(methyl methacrylate) and poly(methacrylic acid)

Giordanengo

Viel

Hidalgo

et al. 2010

J. Am. Soc. Mass Spectrom.

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Molecular weight characterization of random amphiphilic copolymers currently represents an analytical challenge. In particular, molecules composed of methacrylic acid (MAA) and methyl methacrylate (MMA) as the repeat units raise issues in commonly used techniques. The present study shows that when random copolymers cannot be properly ionized by MALDI, and hence detected and measured in MS, one possible analytical strategy is to transform them into homopolymers, which are more amenable to this ionization technique. Then, by combining the molecular weight of the so-obtained homopolymers, as measured by MS, with the relative molar proportion of the MMA and MMA units, as given by 1 H NMR spectrum, one can straightforwardly estimate the molecular weight of the initial copolymer. A methylation reaction was performed to transform MAA-MMA copolymer samples into PMMA homopolymers, using trimethylsilyldiazomethane as a derivatization agent. Weight average molecular weight (M w ) parameters of the MAA-MMA copolymers could then be derived from M w values obtained for the methylated MAA-MMA molecules by MALDI, which were also validated by pulsed gradient spin echo (PGSE) NMR. An alkene function in one of the studied copolymer end-groups was also shown to react with the methylation agent, giving rise to MMA-like polymeric by-products characterized by tandem mass spectrometry and which could be avoided by adjusting the amount of the trimethylsilyldiazomethane in the reaction medium. (J Am Soc Mass Spectrom 2010, 21, 1075-1085) © 2010 American Society for Mass Spectrometry P olymers based on weak acids such as poly-(methacrylic acid) (PMAA) have attracted considerable attention because of the ability of the system to change strongly upon variations in the pH and ionic strength of the solution [1]. For example, amphiphilic PMAA-based block copolymers were reported to efficiently adsorb uranyl ions [2] or to selfassemble to produce dynamic micelles sensitive to different stimuli [3][4][5][6]. In particular, block copolymers containing PMAA and poly(methyl methacrylate) (PMMA) segments were the subject of intensive research activities [7][8][9][10]. However, interesting properties were also demonstrated for copolymers containing random MAA-MMA segments [11][12][13][14]. Performance of such materials highly depends on structurally-related parameters but also on molecular weight distribution.Determination of molecular weight parameters is not a trivial task for copolymers. Liquid state nuclear magnetic resonance (NMR) is the most commonly used technique for this purpose but only allows the number average molecular weight (M n ) parameter to be obtained. Size exclusion chromatography (SEC) requires calibration with narrow standards of the same chemical nature and structure as the analyte. Alternatively, one can use calibration which relies on Mark-HouwinkKuhn-Sakurada (MHKS) parameters being known for the standards and the analyte [15], since these parameters depend on both the nature of co-monomers and their relative proportion with...

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The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments

Cited by 96 publications

References 0 publications

Scaling exponent and dispersity of polymers in solution by diffusion NMR

Scaling exponent and dispersity of polymers in solution by diffusion NMR

Effects of biological treatment on the chemical structure of dissolved lignin-related substances in effluent from thermomechanical pulping

Analytical strategy for the molecular weight determination of random copolymers of poly(methyl methacrylate) and poly(methacrylic acid)

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