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Rosa E, Gallo E, Sibillano T, Giannini C, Rizzuti S, Gianolio E, Scognamiglio PL, Morelli G, Accardo A, Diaferia C. Incorporation of PEG Diacrylates (PEGDA) Generates Hybrid Fmoc-FF Hydrogel Matrices. Gels 2022; 8:gels8120831. [PMID: 36547355 PMCID: PMC9778368 DOI: 10.3390/gels8120831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 12/12/2022] [Accepted: 12/13/2022] [Indexed: 12/24/2022] Open
Abstract
Generated by a hierarchical and multiscale self-assembling phenomenon, peptide-based hydrogels (HGs) are soft materials useful for a variety of applications. Short and ultra-short peptides are intriguing building blocks for hydrogel fabrication. These matrices can also be obtained by mixing low-molecular-weight peptides with other chemical entities (e.g., polymers, other peptides). The combination of two or more constituents opens the door to the development of hybrid systems with tunable mechanical properties and unexpected biofunctionalities or morphologies. For this scope, the formulation, the multiscale analysis, and the supramolecular characterization of novel hybrid peptide-polymer hydrogels are herein described. The proposed matrices contain the Fmoc-FF (Nα-fluorenylmethyloxycarbonyl diphenylalanine) hydrogelator at a concentration of 0.5 wt% (5.0 mg/mL) and a diacrylate α-/ω-substituted polyethylene-glycol derivative (PEGDA). Two PEGDA derivatives, PEGDA 1 and PEGDA2 (mean molecular weights of 575 and 250 Da, respectively), are mixed with Fmoc-FF at different ratios (Fmoc-FF/PEGDA at 1/1, 1/2, 1/5, 1/10 mol/mol). All the multicomponent hybrid peptide-polymer hydrogels are scrutinized with a large panel of analytical techniques (including proton relaxometry, FTIR, WAXS, rheometry, and scanning electronic microscopy). The matrices were found to be able to generate mechanical responses in the 2-8 kPa range, producing a panel of tunable materials with the same chemical composition. The release of a model drug (Naphthol Yellow S) is reported too. The tunable features, the different topologies, and the versatility of the proposed materials open the door to the development of tools for different applicative areas, including diagnostics, liquid biopsies and responsive materials. The incorporation of a diacrylate function also suggests the possible development of interpenetrating networks upon cross-linking reactions. All the collected data allow a mutual comparison between the different matrices, thus confirming the significance of the hybrid peptide/polymer-based methodology as a strategy for the design of innovative materials.
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Affiliation(s)
- Elisabetta Rosa
- Department of Pharmacy, Research Centre on Bioactive Peptides (CIRPeB), University of Naples “Federico II”, Via Montesano 49, 80131 Naples, Italy
| | - Enrico Gallo
- IRCCS Synlab SDN, Via E. Gianturco 113, 80143 Naples, Italy
| | - Teresa Sibillano
- Institute of Crystallography (IC), CNR, Via Amendola 122, 70126 Bari, Italy
| | - Cinzia Giannini
- Institute of Crystallography (IC), CNR, Via Amendola 122, 70126 Bari, Italy
| | - Serena Rizzuti
- Department of Molecular Biotechnologies and Health Science, University of Turin, Via Nizza 52, 10125 Turin, Italy
| | - Eliana Gianolio
- Department of Molecular Biotechnologies and Health Science, University of Turin, Via Nizza 52, 10125 Turin, Italy
| | | | - Giancarlo Morelli
- Department of Pharmacy, Research Centre on Bioactive Peptides (CIRPeB), University of Naples “Federico II”, Via Montesano 49, 80131 Naples, Italy
| | - Antonella Accardo
- Department of Pharmacy, Research Centre on Bioactive Peptides (CIRPeB), University of Naples “Federico II”, Via Montesano 49, 80131 Naples, Italy
| | - Carlo Diaferia
- Department of Pharmacy, Research Centre on Bioactive Peptides (CIRPeB), University of Naples “Federico II”, Via Montesano 49, 80131 Naples, Italy
- Correspondence: ; Tel.: +39-0812-534-526
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An Investigation of the Sol-Gel Transition of Chitosan Lactate and Chitosan Chloride Solutions via Rheological and NMR Studies. Gels 2022; 8:gels8100670. [DOI: 10.3390/gels8100670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 10/15/2022] [Accepted: 10/17/2022] [Indexed: 11/16/2022] Open
Abstract
In recent years, intensive research has been carried out on the use of hydrogels obtained from natural polymers, mainly chitosan. These products are increasingly replacing solutions based on synthetic materials in medicine. This publication presents the results of studies on the sol-gel transition of chitosan solutions as the base material for the preparation of thermosensitive hydrogels for potential applications in tissue engineering. The measurements were carried out for systems consisting of chitosan lactate and chitosan chloride solutions using β-glycerol phosphate disodium salt pentahydrate and uridine 5′-monophosphate disodium salt as the cross-linking agents. The sol-gel transition point of the solutions was determined based on the rheological measurements in the cone-plate configuration of the rotational rheometer and experiments performed using the method of nuclear magnetic resonance. The obtained results showed a significant influence of the cross-linking agent on the course of the sol-gel transition of chitosan salt solutions, and the systems that consisted of chitosan lactate seemed to be especially interesting for biomedical applications.
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Florek-Wojciechowska M. Dynamics of Arabic gum aqueous solutions as revealed by NMR relaxometry. JOURNAL OF THE SCIENCE OF FOOD AND AGRICULTURE 2022; 102:5808-5813. [PMID: 35420169 DOI: 10.1002/jsfa.11930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Revised: 03/15/2022] [Accepted: 04/14/2022] [Indexed: 06/14/2023]
Abstract
BACKGROUND The purpose of this article is to study molecular dynamics through nuclear magnetic relaxation (NMR) dispersion of Arabic gum aqueous solutions analysed in terms of two-fraction exchange model. RESULTS The experiments revealed that relaxation of water molecules was non-monoexponential, which was interpreted in terms of a model describing the magnetization transfer due to exchange of water and polysaccharide protons. The analysis showed that water dynamics decreased slightly with gum content. Polymer-chain dynamics was assigned to regime II of the tube/reptation model. Peculiar temperature dependence of exchange rate was observed in the whole concentration range of Arabic gum solutions. CONCLUSION NMR relaxation probed in a broad frequency and temperature range allows probing of the molecular dynamics of complex food systems. © 2022 Society of Chemical Industry.
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Rosa E, Diaferia C, Gianolio E, Sibillano T, Gallo E, Smaldone G, Stornaiuolo M, Giannini C, Morelli G, Accardo A. Multicomponent Hydrogel Matrices of Fmoc-FF and Cationic Peptides for Application in Tissue Engineering. Macromol Biosci 2022; 22:e2200128. [PMID: 35524744 DOI: 10.1002/mabi.202200128] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Indexed: 11/10/2022]
Abstract
In the last years, peptide based hydrogels are being increasingly used as suitable matrices for biomedical and pharmaceutical applications, including drug delivery and tissue engineering. Recently, we decrived the synthesis and the gelation properties of a small library of cationic peptides, containing a Lys residue at the C-teminus and derivatized with a Fmoc group or with the Fmoc-diphenylalanine (FmocFF) at the N-terminus. Here, we demonstrate that the combination of these peptides with the well known hydrogelator FmocFF, in different weight/weight ratios, allows the achievement of seven novel self-sorted hydrogels, which share similar peptide organization of their supramolecular matrix. Rheological and relaxometric characterization highlighted a different mechanical rigidity and water mobility in the gels as demostrated by the storage modulus values (200 Pa<G'<35000 Pa) and by relaxometry, respectively. In vitro studied demonstrated that most of the tested mixed hydrogels do not disturb significantly the cell viability (>95%) over 72h of treatment. Moreover, in virtue to its capability to strongly favour adhesion, spreading and duplication of 3T3-L1 cells, one of the tested hydrogel may be eligible as sinthetic extracellular matrix. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Elisabetta Rosa
- Department of Pharmacy and Research Centre on Bioactive Peptides (CIRPeB), University of Naples "Federico II", Via Mezzocannone 16, Naples, 80134, Italy
| | - Carlo Diaferia
- Department of Pharmacy and Research Centre on Bioactive Peptides (CIRPeB), University of Naples "Federico II", Via Mezzocannone 16, Naples, 80134, Italy
| | - Eliana Gianolio
- Department of Molecular Biotechnologies and Health Science, University of Turin, Via Nizza 52, Turin, 10125, Italy
| | - Teresa Sibillano
- Institute of Crystallography (IC), CNR, Via Amendola 122, Bari, 70126, Italy
| | - Enrico Gallo
- IRCCS Synlab SDN, Via E. Gianturco 113, Naples, 80143, Italy
| | | | - Mariano Stornaiuolo
- Department of Pharmacy and Research Centre on Bioactive Peptides (CIRPeB), University of Naples "Federico II", Via Mezzocannone 16, Naples, 80134, Italy
| | - Cinzia Giannini
- Institute of Crystallography (IC), CNR, Via Amendola 122, Bari, 70126, Italy
| | - Giancarlo Morelli
- Department of Pharmacy and Research Centre on Bioactive Peptides (CIRPeB), University of Naples "Federico II", Via Mezzocannone 16, Naples, 80134, Italy
| | - Antonella Accardo
- Department of Pharmacy and Research Centre on Bioactive Peptides (CIRPeB), University of Naples "Federico II", Via Mezzocannone 16, Naples, 80134, Italy
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Broche LM, James Ross P, Kennedy BWC, MacEachern CF, Lurie DJ, Ashcroft GP. A new method for investigating osteoarthritis using Fast Field-Cycling nuclear magnetic resonance. Phys Med 2021; 88:142-147. [PMID: 34242886 PMCID: PMC8382587 DOI: 10.1016/j.ejmp.2021.05.034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 05/14/2021] [Accepted: 05/25/2021] [Indexed: 10/25/2022] Open
Abstract
Osteoarthritis in synovial joints remains a major cause of long-term disability worldwide, with symptoms produced by the progressive deterioration of the articular cartilage. The earliest cartilage changes are thought to be alteration in its main protein components, namely proteoglycan and collagen. Loss of proteoglycans bound in the collagen matrix which maintain hydration and stiffness of the structure is followed by collagen degradation and loss. The development of new treatments for early osteoarthritis is limited by the lack of accurate biomarkers to assess the loss of proteoglycan. One potential biomarker is magnetic resonance imaging (MRI). We present the results of a novel MRI methodology, Fast Field-Cycling (FFC), to assess changes in critical proteins by demonstrating clear quantifiable differences in signal from normal and osteoarthritic human cartilage for in vitro measurements. We further tested proteoglycan extracted cartilage and the key components individually. Three clear signals were identified, two of which are related predominantly to the collagen component of cartilage and the third, a unique very short-lived signal, is directly related to proteoglycan content; we have not seen this in any other tissue type. In addition, we present the first volunteer human scan from our whole-body FFC scanner where articular cartilage measurements are in keeping with those we have shown in tissue samples. This new clinical imaging modality offers the prospect of non-invasive monitoring of human cartilage in vivo and hence the assessment of potential treatments for osteoarthritis. Keywords: Fast Field-Cycling NMR; human hyaline cartilage; Osteoarthritis; T1 dispersion; quadrupolar peaks; protein interactions.
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Affiliation(s)
- Lionel M Broche
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
| | - P James Ross
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK.
| | - Brett W C Kennedy
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
| | - Campbell F MacEachern
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
| | - David J Lurie
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
| | - George P Ashcroft
- Aberdeen Biomedical Imaging Centre, School of Medicine, Medical Sciences & Nutrition, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
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Kruk D, Florek-Wojciechowska M, Oztop M, Ilhan E, Wieczorek Z. Water dynamics in eggs by means of Nuclear Magnetic Resonance relaxometry. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 327:106976. [PMID: 33901897 DOI: 10.1016/j.jmr.2021.106976] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2020] [Revised: 03/28/2021] [Accepted: 03/29/2021] [Indexed: 06/12/2023]
Abstract
1H Nuclear Magnetic Resonance relaxometry has been applied to reveal dynamical properties of water molecules embedded into egg yolk and white of three species: turkey, chicken and quail. Two fractions of water molecules, referred to as confined-water and free-water fractions, have been revealed. It has been demonstrated that translation diffusion of the confined-water fraction is three-dimensional. The dynamics of the confined-water has been quantitatively described in terms of diffusion coefficients and rotational correlation times. The parameters have been compared for egg yolk and white for all the species. In addition to these quantities, the number of the confined-water molecules per unit volume has been provided for all cases. The obtained parameters provide insight into the dynamics of water in eggs of different origin and allow to identify similarities and differences between them in connection to the structure of the network formed by the macromolecular fraction of egg yolk and white.
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Affiliation(s)
- Danuta Kruk
- Department of Physics & Biophysics, Faculty of Food Sciences, University of Warmia & Mazury in Olsztyn, Michała Oczapowskiego 4, 10-719 Olsztyn, Poland.
| | - Małgorzata Florek-Wojciechowska
- Department of Physics & Biophysics, Faculty of Food Sciences, University of Warmia & Mazury in Olsztyn, Michała Oczapowskiego 4, 10-719 Olsztyn, Poland
| | - Mecit Oztop
- Department of Food Engineering, Middle East Technical University, Ankara, Turkey
| | - Esmanur Ilhan
- Department of Food Engineering, Middle East Technical University, Ankara, Turkey
| | - Zbigniew Wieczorek
- Department of Physics & Biophysics, Faculty of Food Sciences, University of Warmia & Mazury in Olsztyn, Michała Oczapowskiego 4, 10-719 Olsztyn, Poland
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7
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Aiello F, Gerretzen J, Simons MG, Davies AN, Dani P. A multivariate approach to investigate the NMR CPMG pulse sequence for analysing low MW species in polymers. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2021; 59:172-186. [PMID: 32929750 DOI: 10.1002/mrc.5100] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Revised: 09/10/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
Detection and quantification of low molecular weight components in polymeric samples via nuclear magnetic resonance (NMR) spectroscopy can be difficult due to overlapping signal caused by line broadening characteristics of polymers. A way of overcoming this problem could be the exploitation of the difference in relaxation between small molecules and macromolecular species, such as the application of a T2 filter by using the Carr-Purcell-Meiboom-Gill (CPMG) spin-echo pulse sequence. This technique, largely exploited in metabolomics studies, is applied here to material sciences. A Design of Experiments approach was used for evaluating the effect of different acquisition parameters (relaxation delay, echo time and number of cycles) and sample-related ones (concentration and polymer molecular weight) on selected responses, with a particular interest in performing a reliable quantitative analysis. Polymeric samples containing small molecules were analysed by NMR with and without the application of the filter, and analysis of variance was used to identify the most influential parameters. Results indicated that increasing the polymer concentration, hence sample viscosity, further attenuates polymer signals in CPMG experiments because the T2 of those signals tends to decrease with increasing viscosity. The signal-to-noise ratio measured for small molecules can undergo a minimum loss when specific parameters are chosen in relation to the polymer molecular weight. Furthermore, the difference in dynamics between aliphatic and aromatic nuclei, as well as between mobile and stiff polymers, translates into different results in terms of polymer signal reduction, suggesting that the relaxation filter can also be used for obtaining information on the polymer structure.
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Affiliation(s)
- Federica Aiello
- ECG-MAS, Expert Capability Group - Measurement and Analytical Science, Nouryon Chemicals B.V., Deventer, The Netherlands
| | - Jan Gerretzen
- ECG-MAS, Expert Capability Group - Measurement and Analytical Science, Nouryon Chemicals B.V., Deventer, The Netherlands
| | - Marcel G Simons
- ECG-MAS, Expert Capability Group - Measurement and Analytical Science, Nouryon Chemicals B.V., Deventer, The Netherlands
| | - Antony N Davies
- ECG-MAS, Expert Capability Group - Measurement and Analytical Science, Nouryon Chemicals B.V., Deventer, The Netherlands
- SERC, Sustainable Environment Research Centre, Faculty of Computing Engineering and Science, University of South Wales, Pontypridd, UK
| | - Paulo Dani
- ECG-MAS, Expert Capability Group - Measurement and Analytical Science, Nouryon Chemicals B.V., Deventer, The Netherlands
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8
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Ostrovskaya IK, Fatkullin NF, Körber T, Rössler EA, Lozovoi A, Mattea C, Stapf S. On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics. J Chem Phys 2020; 152:184904. [PMID: 32414263 DOI: 10.1063/5.0005049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times. With an increase in observation time, the contribution from end effects to the FID increases. In the regime of incoherent reptation, contributions to the FID from central segments yield an exponent of 1/4 for the stretched decay and contributions from end segments yield an exponent of 3/16. In the regime of coherent reptation, the central segments generate a stretching exponent of 1/2, whereas the end segments contribute with an exponent of 1/4. These predictions are shown to be in qualitative agreement with the experimental FIDs of perdeuterated poly(ethylene oxide) with molecular masses of 132 kg/mol and 862 kg/mol.
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Affiliation(s)
- I K Ostrovskaya
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - N F Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - T Körber
- Inorganic Chemistry III and Northern Bavarian NMR Centre, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - E A Rössler
- Inorganic Chemistry III and Northern Bavarian NMR Centre, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - A Lozovoi
- Department of Physics, CUNY-The City College of New York, New York, New York 10031, USA
| | - C Mattea
- Department of Technical Physics II/Polymer Physics, TU Ilmenau, P.O. Box 100 565, D-98684 Ilmenau, Germany
| | - S Stapf
- Department of Technical Physics II/Polymer Physics, TU Ilmenau, P.O. Box 100 565, D-98684 Ilmenau, Germany
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Lo Meo P, Mundo F, Terranova S, Conte P, Chillura Martino D. Water Dynamics at the Solid-Liquid Interface to Unveil the Textural Features of Synthetic Nanosponges. J Phys Chem B 2020; 124:1847-1857. [PMID: 32069049 PMCID: PMC7997571 DOI: 10.1021/acs.jpcb.9b11935] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
![]()
A fast-field-cycling
NMR investigation was carried out on a set
of polyurethane cyclodextrin nanosponges, in order to gain information
on their textural properties, which have been proven to be quite difficult
to assess by means of ordinary porosimetric techniques. Experiments
were performed on both dry and wet samples, in order to evaluate the
behavior of the “nonexchangeable” C-bound 1H nuclei, as well as the one of the mobile protons belonging to the
skeletal hydroxyl groups and the water molecules. The results acquired
for the wet samples accounted for the molecular mobility of water
molecules within the channels of the nanosponge network, leading back
to the possible pore size distribution. Owing to the intrinsic difficulties
involved in a quantitative assessment of the textural properties,
in the present study we alternatively propose an extension to nanosponges
of the concept of “connectivity”, which has been already
employed to discuss the properties of soils.
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Affiliation(s)
- Paolo Lo Meo
- Department of Biological, Chemical and Pharmaceutical Sciences and Technologies (STEBICEF), University of Palermo, V.le delle Scienze ed. 17, 90128 Palermo, Italy
| | - Federico Mundo
- Department of Biological, Chemical and Pharmaceutical Sciences and Technologies (STEBICEF), University of Palermo, V.le delle Scienze ed. 17, 90128 Palermo, Italy
| | - Samuele Terranova
- Department of Biological, Chemical and Pharmaceutical Sciences and Technologies (STEBICEF), University of Palermo, V.le delle Scienze ed. 17, 90128 Palermo, Italy
| | - Pellegrino Conte
- Department of Agricultural, Food and Forest Sciences (SAAF), University of Palermo, V.le delle Scienze ed. 4, 90128 Palermo, Italy
| | - Delia Chillura Martino
- Department of Biological, Chemical and Pharmaceutical Sciences and Technologies (STEBICEF), University of Palermo, V.le delle Scienze ed. 17, 90128 Palermo, Italy
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Sheveleva NN, Dolgushev M, Lähderanta E, Markelov DA. NMR Relaxation of Functionalized Dendrimers. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01427] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Nadezhda N. Sheveleva
- St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
- Department of Physics, LUT University, Box 20, Lappeenranta 53851, Finland
| | - Maxim Dolgushev
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Paris 75005, France
| | - Erkki Lähderanta
- Department of Physics, LUT University, Box 20, Lappeenranta 53851, Finland
| | - Denis A. Markelov
- St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
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Flämig M, Hofmann M, Lichtinger A, Rössler EA. Application of proton field-cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2019; 57:805-817. [PMID: 30604576 DOI: 10.1002/mrc.4823] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2018] [Revised: 12/19/2018] [Accepted: 12/20/2018] [Indexed: 06/09/2023]
Abstract
With the availability of commercial field-cycling relaxometers together with progress of home-built instruments nuclear magnetic resonance relaxometry has gained new momentum as a method of investigating the dynamics in viscous liquids and polymer melts. The method provides the frequency dependence of the spin-lattice relaxation rate. In the case of protons, one distinguishes intramolecular and intermolecular relaxation pathways. Whereas the intramolecular contribution prevails at high frequencies and reflects rotational dynamics, the often ignored intermolecular relaxation contribution dominates at low-frequency and provides access to translational dynamics. A universal low-frequencies dispersion law holds which in pure systems allows determining the diffusion coefficient in a straightforward way. In addition, the rotational time constant is extracted from the high-frequency relaxation contribution. This is demonstrated for simple and ionic liquids and for polymer melts.
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Affiliation(s)
- Max Flämig
- Experimentalphysik and Nordbayerisches NMR-Zentrum, Universität Bayreuth, Bayreuth, Germany
| | - Marius Hofmann
- Experimentalphysik and Nordbayerisches NMR-Zentrum, Universität Bayreuth, Bayreuth, Germany
| | - Anne Lichtinger
- Experimentalphysik and Nordbayerisches NMR-Zentrum, Universität Bayreuth, Bayreuth, Germany
| | - Ernst A Rössler
- Experimentalphysik and Nordbayerisches NMR-Zentrum, Universität Bayreuth, Bayreuth, Germany
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12
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Mikac U, Sepe A, Gradišek A, Kristl J, Apih T. Dynamics of water and xanthan chains in hydrogels studied by NMR relaxometry and their influence on drug release. Int J Pharm 2019; 563:373-383. [DOI: 10.1016/j.ijpharm.2019.04.014] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2018] [Revised: 03/21/2019] [Accepted: 04/06/2019] [Indexed: 12/12/2022]
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13
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Lozovoi A, Mattea C, Fatkullin N, Stapf S. Segmental Dynamics of Entangled Poly(ethylene oxide) Melts: Deviations from the Tube-Reptation Model. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Lozovoi
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - C. Mattea
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, 420008 Kazan, Tatarstan, Russia
| | - S. Stapf
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
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14
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McKenzie I, Chai Y, Cortie DL, Forrest JA, Fujimoto D, Karner VL, Kiefl RF, Levy CDP, MacFarlane WA, McFadden RML, Morris GD, Pearson MR, Zhu S. Direct measurements of the temperature, depth and processing dependence of phenyl ring dynamics in polystyrene thin films by β-detected NMR. SOFT MATTER 2018; 14:7324-7334. [PMID: 29796450 DOI: 10.1039/c8sm00812d] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
There is indirect evidence that the dynamics of a polymer near a free surface are enhanced compared with the bulk but there are few studies of how dynamics varies with depth. β-Detected nuclear spin relaxation of implanted 8Li+ has been used to directly probe the temperature and depth dependence of the γ-relaxation mode, which is due to phenyl rings undergoing restricted rotation, in thin films of atactic deuterated polystyrene (PS-d8) and determine how the depth dependence of dynamics is affected by sample processing, such as annealing, floating on water and the inclusion of a surfactant, and by the presence of a buried interface. The activation energy for the γ-relaxation process is lower near the free surface. Annealing the PS-d8 films and then immersing in water to mimic the floating procedure used to transfer films had negligible effects on the thickness of the region near the free surface with enhanced mobility. Measurements on a bilayer film indicate enhanced phenyl ring dynamics near the buried interface compared with a single film at the same depth. PS-d8 films annealed with the surfactant sodium dodecyl sulfate (SDS) deposited on the surface show enhanced dynamics in the bulk compared with a pure PS-d8 film and a PS-d8 film where the SDS was washed away. There is less contrast between the surface and bulk in the SDS-treated sample, which could account for the elimination of the Tg confinement effect observed in films containing SDS [Chen and Torkelson, Polymer, 2016, 87, 226].
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15
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Zhukov IV, Kiryutin AS, Yurkovskaya AV, Grishin YA, Vieth HM, Ivanov KL. Field-cycling NMR experiments in an ultra-wide magnetic field range: relaxation and coherent polarization transfer. Phys Chem Chem Phys 2018; 20:12396-12405. [PMID: 29623979 DOI: 10.1039/c7cp08529j] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An experimental method is described allowing fast field-cycling Nuclear Magnetic Resonance (NMR) experiments over a wide range of magnetic fields from 5 nT to 10 T. The method makes use of a hybrid technique: the high field range is covered by positioning the sample in the inhomogeneous stray field of the NMR spectrometer magnet. For fields below 2 mT a magnetic shield is mounted on top of the spectrometer; inside the shield the magnetic field is controlled by a specially designed coil system. This combination allows us to measure T1-relaxation times and nuclear Overhauser effect parameters over the full range in a routine way. For coupled proton-carbon spin systems relaxation with a common T1 is found at low fields, where the spins are "strongly coupled". In some cases, experiments at ultralow fields provide access to heteronuclear long-lived spin states. Efficient coherent polarization transfer is seen for proton-carbon spin systems at ultralow fields as follows from the observation of quantum oscillations in the polarization evolution. Applications to analysis and the manipulation of heteronuclear spin systems are discussed.
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Affiliation(s)
- Ivan V Zhukov
- International Tomography Center SB RAS, Novosibirsk, 630090, Russia.
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16
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Galiceanu M, Tota de Carvalho L, Mülken O, Dolgushev M. Dynamics of Dual Scale-Free Polymer Networks. Polymers (Basel) 2017; 9:E577. [PMID: 30965880 PMCID: PMC6418598 DOI: 10.3390/polym9110577] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Revised: 10/29/2017] [Accepted: 10/31/2017] [Indexed: 01/31/2023] Open
Abstract
We focus on macromolecules which are modeled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding a link between non-neighboring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameters' set ( γ , p ) , we encounter for these dynamical properties regions of constant in-between slope.
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Affiliation(s)
- Mircea Galiceanu
- Departamento de Fisica, Universidade Federal do Amazonas, Manaus 69077-000, Brazil.
| | | | - Oliver Mülken
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
| | - Maxim Dolgushev
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
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17
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Lozovoi A, Petrova L, Mattea C, Stapf S, Rössler EA, Fatkullin N. On the theory of the proton dipolar-correlation effect as a method for investigation of segmental displacement in polymer melts. J Chem Phys 2017; 147:074904. [DOI: 10.1063/1.4998184] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- A. Lozovoi
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - L. Petrova
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - C. Mattea
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - S. Stapf
- Department Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - E. A. Rössler
- Department Experimentalphysik II, University of Bayreuth, 95440 Bayreuth, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
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18
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Lozovoi A, Mattea C, Hofmann M, Saalwaechter K, Fatkullin N, Stapf S. Segmental dynamics of polyethylene-alt-propylene studied by NMR spin echo techniques. J Chem Phys 2017; 146:224901. [PMID: 29166039 DOI: 10.1063/1.4984265] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Segmental dynamics of a highly entangled melt of linear polyethylene-alt-propylene with a molecular weight of 200 kDa was studied with a novel proton nuclear magnetic resonance (NMR) approach based upon 1H → 2H isotope dilution as applied to a solid-echo build-up function ISE(t), which is constructed from the NMR spin echo signals arising from the Hahn echo (HE) and two variations of the solid-echo pulse sequence. The isotope dilution enables the separation of inter- and intramolecular contributions to this function and allows one to extract the segmental mean-squared displacements in the millisecond time range, which is hardly accessible by other experimental methods. The proposed technique in combination with time-temperature superposition yields information about segmental translation in polyethylene-alt-propylene over 6 decades in time from 10-6 s up to 1 s. The time dependence of the mean-squared displacement obtained in this time range clearly shows three regimes of power law with exponents, which are in good agreement with the tube-reptation model predictions for the Rouse model, incoherent reptation and coherent reptation regimes. The results at short times coincide with the fast-field cycling relaxometry and neutron spin echo data, yet, significantly extending the probed time range. Furthermore, the obtained data are verified as well by the use of the dipolar-correlation effect on the Hahn echo, which was developed before by the co-authors. At the same time, the amplitude ratio of the intermolecular part of the proton dynamic dipole-dipole correlation function over the intramolecular part obtained from the experimental data is not in agreement with the predictions of the tube-reptation model for the regimes of incoherent and coherent reptation.
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Affiliation(s)
- A Lozovoi
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - C Mattea
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - M Hofmann
- Department of Chemistry, Louisiana State University, 70803 Baton Rouge, Louisiana, USA
| | - K Saalwaechter
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle (Saale), Germany
| | - N Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan, Russia
| | - S Stapf
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
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19
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Lozovoi A, Mattea C, Herrmann A, Rössler EA, Stapf S, Fatkullin N. Communication: Proton NMR dipolar-correlation effect as a method for investigating segmental diffusion in polymer melts. J Chem Phys 2016; 144:241101. [PMID: 27369489 DOI: 10.1063/1.4954664] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- A. Lozovoi
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - C. Mattea
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - A. Herrmann
- Department of Experimentalphysik II, University of Bayreuth, 95440 Bayreuth, Germany
| | - E. A. Rössler
- Department of Experimentalphysik II, University of Bayreuth, 95440 Bayreuth, Germany
| | - S. Stapf
- Department of Technical Physics II, Technische Universität Ilmenau, 98684 Ilmenau, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, Kazan, 420008 Tatarstan, Russia
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20
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Steele RM, Korb JP, Ferrante G, Bubici S. New applications and perspectives of fast field cycling NMR relaxometry. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2016; 54:502-9. [PMID: 25855084 DOI: 10.1002/mrc.4220] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Revised: 12/17/2014] [Accepted: 01/19/2015] [Indexed: 05/08/2023]
Abstract
The field cycling NMR relaxometry method (also known as fast field cycling (FFC) when instruments employing fast electrical switching of the magnetic field are used) allows determination of the spin-lattice relaxation time (T1 ) continuously over five decades of Larmor frequency. The method can be exploited to observe the T1 frequency dependence of protons, as well as any other NMR-sensitive nuclei, such as (2) H, (13) C, (31) P, and (19) F in a wide range of substances and materials. The information obtained is directly correlated with the physical/chemical properties of the compound and can be represented as a 'nuclear magnetic resonance dispersion' curve. We present some recent academic and industrial applications showing the relevance of exploiting FFC NMR relaxometry in complex materials to study the molecular dynamics or, simply, for fingerprinting or quality control purposes. The basic nuclear magnetic resonance dispersion features are outlined in representative examples of magnetic resonance imaging (MRI) contrast agents, porous media, proteins, and food stuffs. We will focus on the new directions and perspectives for the FFC technique. For instance, the introduction of the latest Wide Bore FFC NMR relaxometers allows probing, for the first time, of the dynamics of confined surface water contained in the macro-pores of carbonate rock cores. We also evidence the use of the latest field cycling technology with a new cryogen-free variable-field electromagnet, which enhances the range of available frequencies in the 2D T1 -T2 correlation spectrum for separating oil and water in crude oil. Copyright © 2015 John Wiley & Sons, Ltd.
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Affiliation(s)
| | - Jean-Pierre Korb
- Physique de la Matière Condensée, Ecole Polytechnique-CNRS, 91128, Palaiseau, France
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21
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Hansen MR, Graf R, Spiess HW. Interplay of Structure and Dynamics in Functional Macromolecular and Supramolecular Systems As Revealed by Magnetic Resonance Spectroscopy. Chem Rev 2015; 116:1272-308. [DOI: 10.1021/acs.chemrev.5b00258] [Citation(s) in RCA: 91] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Michael Ryan Hansen
- Max Planck Institute for Polymer Research, P.O. Box 3148, 55021 Mainz, Germany
| | - Robert Graf
- Max Planck Institute for Polymer Research, P.O. Box 3148, 55021 Mainz, Germany
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22
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McKenzie I, Daley CR, Kiefl RF, Levy CDP, MacFarlane WA, Morris GD, Pearson MR, Wang D, Forrest JA. Enhanced high-frequency molecular dynamics in the near-surface region of polystyrene thin films observed with β-NMR. SOFT MATTER 2015; 11:1755-1761. [PMID: 25605007 DOI: 10.1039/c4sm02245a] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
β-detected nuclear spin relaxation of (8)Li(+) has been used to probe the depth dependence of molecular dynamics in high- and low-molecular-weight deuterated polystyrene. The average nuclear spin-lattice relaxation rate, 1/T(avg)(1), is a measure of the spectral density of the polymer motion at the Larmor frequency (41 MHz at 6.55 T). In both samples, 1/T(avg)(1) is depth independent below ∼200 K but above this temperature it decreases approximately exponentially with distance from the free surface, returning to bulk behavior for depths greater than ∼10 nm. This is direct evidence for a region near the free surface with enhanced molecular dynamics compared with the bulk. The effective thickness of the surface region increases with increasing temperature and is finite even above the glass transition. These results present challenges for the current understanding of dynamics near the surface of polymer glasses.
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23
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Hofmann M, Kresse B, Privalov AF, Willner L, Fatkullin N, Fujara F, Rössler EA. Field-Cycling NMR Relaxometry Probing the Microscopic Dynamics in Polymer Melts. Macromolecules 2014. [DOI: 10.1021/ma501520u] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
- M. Hofmann
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - B. Kresse
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - A. F. Privalov
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - L. Willner
- Institute of Complex
Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - N. Fatkullin
- Institute of Physics, Kazan Federal University, Kazan 420008, Tatarstan Russia
| | - F. Fujara
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany
| | - E. A. Rössler
- Experimentalphysik
II, Universität Bayreuth, D-95440 Bayreuth, Germany
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24
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Interactions of poly(dimethylsiloxane) with nanosilica and silica gel upon cooling–heating. J Colloid Interface Sci 2014; 426:48-55. [DOI: 10.1016/j.jcis.2014.03.055] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2014] [Revised: 03/21/2014] [Accepted: 03/25/2014] [Indexed: 11/21/2022]
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25
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Fatkullin N, Mattea C, Stapf S. On the theory of double quantum NMR in polymer systems: the second cumulant approximation for many spin I = 1/2 systems. J Chem Phys 2013; 139:194905. [PMID: 24320353 DOI: 10.1063/1.4830410] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
General analytical expressions for Double Quantum Nuclear Magnetic Resonance (DQ NMR) kinetic curves of many-spin I = 1∕2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the initial part of the kinetic curves and provide a reasonable approximation up to times of about the effective spin-relaxation time. For the case when the system contains two isolated spins, this result exactly reproduces known expressions. In the case of polymer melts, the intermolecular magnetic dipole-dipole interactions significantly influence the time dependence of the DQ NMR kinetic curves.
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Affiliation(s)
- N Fatkullin
- Institute of Physics, Kazan Federal University, Kazan, 420008 Tatarstan, Russia
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26
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Meier R, Kruk D, Rössler EA. Intermolecular spin relaxation and translation diffusion in liquids and polymer melts: insight from field-cycling 1H NMR relaxometry. Chemphyschem 2013; 14:3071-81. [PMID: 23881836 DOI: 10.1002/cphc.201300257] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2013] [Indexed: 11/11/2022]
Abstract
With the advent of commercial field-cycling (FC) spectrometers, NMR relaxometry has gained new momentum as a method of investigating dynamics in liquids and polymers. The outcome of FC NMR experiments is spin-lattice relaxation time versus frequency (relaxation dispersion). In the case of protons, due to the intra- and intermolecular origin of dipolar interactions, the relaxation dispersion reflects rotational as well as translational dynamics. The latter shows a universal dispersion law at low frequencies, which allows determination of the diffusion coefficient D(T) in addition to the rotational correlation time τ(rot)(T), that is, FC (1)H NMR becomes an alternative to field-gradient NMR spectroscopy. Subdiffusive translation found in polymers can be accessed by singling out the intermolecular relaxation through isotope dilution experiments, and the mean square displacement can then be revealed as a function of time, thus complementing neutron scattering experiments. Likewise, information on reorientational dynamics is provided by the intramolecular relaxation. Assuming frequency-temperature superposition the corresponding correlation functions can be monitored up to eight decades in amplitude and time, which allows thorough testing of current polymer theories.
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Affiliation(s)
- Roman Meier
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth (Germany)
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27
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Meier R, Herrmann A, Hofmann M, Schmidtke B, Kresse B, Privalov AF, Kruk D, Fujara F, Rössler EA. Iso-Frictional Mass Dependence of Diffusion of Polymer Melts Revealed by 1H NMR Relaxometry. Macromolecules 2013. [DOI: 10.1021/ma400881c] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- R. Meier
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
| | - A. Herrmann
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
| | - M. Hofmann
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
| | - B. Schmidtke
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
| | - B. Kresse
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt,
Germany
| | - A. F. Privalov
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt,
Germany
| | - D. Kruk
- Faculty of Mathematics & Computer Science, University of Warmia & Mazury in Olsztyn, 10710 Olsztyn, Poland
| | - F. Fujara
- Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt,
Germany
| | - E. A. Rössler
- Experimentalphysik II, Universität Bayreuth, 95440 Bayreuth, Germany
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