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Pinheiro Dos Santos TJ, Orcan-Ekmekci B, Chapman WG, Singer PM, Asthagiri DN. Theory and modeling of molecular modes in the NMR relaxation of fluids. J Chem Phys 2024; 160:064108. [PMID: 38341792 DOI: 10.1063/5.0180040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2023] [Accepted: 01/18/2024] [Indexed: 02/13/2024] Open
Abstract
Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.
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Affiliation(s)
| | | | - Walter G Chapman
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
| | - Philip M Singer
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
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Faux DA, Istók Ö, Rahaman AA, McDonald PJ, McKiernan E, Brougham DF. Nuclear spin relaxation in aqueous paramagnetic ion solutions. Phys Rev E 2023; 107:054605. [PMID: 37328976 DOI: 10.1103/physreve.107.054605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Accepted: 04/20/2023] [Indexed: 06/18/2023]
Abstract
A Brownian shell model describing the random rotational motion of a spherical shell of uniform particle density is presented and validated by molecular dynamics simulations. The model is applied to proton spin rotation in aqueous paramagnetic ion complexes to yield an expression for the Larmor-frequency-dependent nuclear magnetic resonance spin-lattice relaxation rate T_{1}^{-1}(ω) describing the dipolar coupling of the nuclear spin of the proton with the electronic spin of the ion. The Brownian shell model provides a significant enhancement to existing particle-particle dipolar models without added complexity, allowing fits to experimental T_{1}^{-1}(ω) dispersion curves without arbitrary scaling parameters. The model is successfully applied to measurements of T_{1}^{-1}(ω) from aqueous manganese(II), iron(III), and copper(II) systems where the scalar coupling contribution is known to be small. Appropriate combinations of Brownian shell and translational diffusion models, representing the inner and outer sphere relaxation contributions, respectively, are shown to provide excellent fits. Quantitative fits are obtained to the full dispersion curve of each aquoion with just five fit parameters, with the distance and time parameters each taking a physically justifiable numerical value.
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Affiliation(s)
- David A Faux
- Department of Physics, University of Surrey, Guildford, GU2 7XH, United Kingdom
| | | | | | | | - Eoin McKiernan
- School of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland
| | - Dermot F Brougham
- School of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland
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Singer PM, Parambathu AV, Pinheiro Dos Santos TJ, Liu Y, Alemany LB, Hirasaki GJ, Chapman WG, Asthagiri D. Predicting 1H NMR relaxation in Gd 3+-aqua using molecular dynamics simulations. Phys Chem Chem Phys 2021; 23:20974-20984. [PMID: 34518855 DOI: 10.1039/d1cp03356e] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Atomistic molecular dynamics simulations are used to predict 1H NMR T1 relaxation of water from paramagnetic Gd3+ ions in solution at 25 °C. Simulations of the T1 relaxivity dispersion function r1 computed from the Gd3+-1H dipole-dipole autocorrelation function agree within ≃8% of measurements in the range f0 ≃ 5 ↔ 500 MHz, without any adjustable parameters in the interpretation of the simulations, and without any relaxation models. The simulation results are discussed in the context of the Solomon-Bloembergen-Morgan inner-sphere relaxation model, and the Hwang-Freed outer-sphere relaxation model. Below f0 ≲ 5 MHz, the simulation overestimates r1 compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting r1 at high frequencies in chelated Gd3+ contrast-agents used for clinical MRI.
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Affiliation(s)
- Philip M Singer
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
| | - Arjun Valiya Parambathu
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
| | | | - Yunke Liu
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
| | - Lawrence B Alemany
- Shared Equipment Authority and Department of Chemistry, Rice University, 6100 Main St., Houston, TX 77005, USA
| | - George J Hirasaki
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
| | - Walter G Chapman
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
| | - Dilip Asthagiri
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main St., Houston, TX 77005, USA.
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Zhan S, Su Y, Jin Z, Wang W, Cai M, Li L, Hao Y. Molecular insight into the boundary conditions of water flow in clay nanopores. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113292] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Faux D, Kogon R, Bortolotti V, McDonald P. Advances in the Interpretation of Frequency-Dependent Nuclear Magnetic Resonance Measurements from Porous Material. Molecules 2019; 24:E3688. [PMID: 31614973 PMCID: PMC6832834 DOI: 10.3390/molecules24203688] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Revised: 09/27/2019] [Accepted: 10/08/2019] [Indexed: 11/24/2022] Open
Abstract
Fast-field-cycling nuclear magnetic resonance (FFC-NMR) is a powerful technique for non-destructively probing the properties of fluids contained within the pores of porous materials. FFC-NMR measures the spin-lattice relaxation rate R 1 ( f ) as a function of NMR frequency f over the kHz to MHz range. The shape and magnitude of the R 1 ( f ) dispersion curve is exquisitely sensitive to the relative motion of pairs of spins over time scales of picoseconds to microseconds. To extract information on the nano-scale dynamics of spins, it is necessary to identify a model that describes the relative motion of pairs of spins, to translate the model dynamics to a prediction of R 1 ( f ) and then to fit to the experimental dispersion. The principles underpinning one such model, the 3 τ model, are described here. We present a new fitting package using the 3 τ model, called 3TM, that allows users to achieve excellent fits to experimental relaxation rates over the full frequency range to yield five material properties and much additional derived information. 3TM is demonstrated on historic data for mortar and plaster paste samples.
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Affiliation(s)
- David Faux
- Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK.
| | - Rémi Kogon
- Department of Physics and Astronomy, Viale Berti Pichat 6/2, 40127 Bologna, Italy.
| | - Villiam Bortolotti
- Department of Civil, Chemical, Environmental, and Materials Engineering, Via Terracini 28, 40126 Bologna, Italy.
| | - Peter McDonald
- Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK.
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Liu C, Min F, Liu L, Chen J. Density Functional Theory Study of Water Molecule Adsorption on the α-Quartz (001) Surface with and without the Presence of Na +, Mg 2+, and Ca 2. ACS OMEGA 2019; 4:12711-12718. [PMID: 31460393 PMCID: PMC6682150 DOI: 10.1021/acsomega.9b01570] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/28/2019] [Accepted: 07/12/2019] [Indexed: 06/10/2023]
Abstract
Adsorption of the single water molecule on the α-quartz (001) surface with and without the presence of Na+, Mg2+ and Ca2+ was analyzed utilizing the density functional theory method. Our results demonstrate that the optimal adsorption configuration of the single water molecule on the α-quartz (001) surface lies in the bridge being configured with two formed hydrogen bonds. These were Os-Hw and Hs-Ow (s and w represent, respectively, surface and water molecules), while the main hydrogen bond is Hw-Os. Furthermore, the corresponding adsorption energy was ∼-72.60 kJ/mol. In this study, the presence of metal ions helped to deflect the spatial position of the water molecule, and the distance between Ow and Hs was altered significantly. Furthermore, the charge transfer between the interacting atoms increased in the presence of metal ions, wherein the effects of Ca2+ and Na+ proved to be significant compared to Mg2+. Finally, it emerged that metal ions interacted with the water molecule and were subsequently adsorbed on the α-quartz (001) surface. This occurred due to the electrostatic attraction, consequently impacting the hydration characteristics of the quartz surface.
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Nascimento M, Chencarek B, Souza AM, Sarthour RS, Coutinho B, Correia MD, Oliveira IS. Enhanced NMR relaxation of fluids confined to porous media: A proposed theory and experimental tests. Phys Rev E 2019; 99:042901. [PMID: 31108641 DOI: 10.1103/physreve.99.042901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2018] [Indexed: 06/09/2023]
Abstract
We propose a theory to account for the NMR relaxation of water protons in situations in which the fluid is confined to porous structures exhibiting a scarce distribution of paramagnetic centers on their surface. Though much of what is stated and assumed concerns the response of water, the model has sufficiently general features to be able to explain proton relaxation of other polar fluids under similar conditions. One of the main results of the paper is to show that the local anisotropy introduced by the dominant dipolar coupling in the relaxation rates of active surface elements induces a measurable dependence on sample orientation in the overall relaxation rates of the saturating fluid provided its confining structure is not statistically isotropic. Measurements of T_{1} proton relaxation on water saturating microcapillary tubes are performed to reveal the effect.
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Affiliation(s)
- M Nascimento
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ. CEP 22290-180, Brazil
- Centro de Pesquisas e Desenvolvimento Leopoldo Américo Miguez de Mello-CENPES/PETROBRAS, Av. Horácio Macedo, 950, Cidade Universitária, Rio de Janeiro, RJ 21941-915, Brazil
| | - B Chencarek
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ. CEP 22290-180, Brazil
| | - A M Souza
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ. CEP 22290-180, Brazil
| | - R S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ. CEP 22290-180, Brazil
| | - B Coutinho
- Centro de Pesquisas e Desenvolvimento Leopoldo Américo Miguez de Mello-CENPES/PETROBRAS, Av. Horácio Macedo, 950, Cidade Universitária, Rio de Janeiro, RJ 21941-915, Brazil
| | - M D Correia
- Centro de Pesquisas e Desenvolvimento Leopoldo Américo Miguez de Mello-CENPES/PETROBRAS, Av. Horácio Macedo, 950, Cidade Universitária, Rio de Janeiro, RJ 21941-915, Brazil
| | - I S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150 Ed. Cesar Lattes, Urca, Rio de Janeiro, RJ. CEP 22290-180, Brazil
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Faux DA, McDonald PJ. Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics. Phys Rev E 2017; 95:033117. [PMID: 28415374 DOI: 10.1103/physreve.95.033117] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Indexed: 01/20/2023]
Abstract
Nuclear-magnetic-resonance (NMR) spin-lattice (T_{1}^{-1}) and spin-spin (T_{2}^{-1}) relaxation rate measurements can act as effective nondestructive probes of the nanoscale dynamics of ^{1}H spins in porous media. In particular, fast-field-cycling T_{1}^{-1} dispersion measurements contain information on the dynamics of diffusing spins over time scales spanning many orders of magnitude. Previously published experimental T_{1}^{-1} dispersions from a plaster paste, synthetic saponite, mortar, and oil-bearing shale are reanalyzed using a model and associated theory which describe the relaxation rate contributions due to the interaction between spin ensembles in quasi-two-dimensional pores. Application of the model yields physically meaningful diffusion correlation times for all systems. In particular, the surface diffusion correlation time and the surface desorption time take similar values for each system, suggesting that surface mobility and desorption are linked processes. The bulk fluid diffusion correlation time is found to be two to five times the value for the pure liquid at room temperature for each system. Reanalysis of the oil-bearing shale yields diffusion time constants for both the oil and water constituents. The shale is found to be oil wetting and the water T_{1}^{-1} dispersion is found to be associated with aqueous Mn^{2+} paramagnetic impurities in the bulk water. These results escalate the NMR T_{1}^{-1} dispersion measurement technique as the primary probe of molecular-scale dynamics in porous media yielding diffusion parameters and a wealth of information on pore morphology.
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Affiliation(s)
- D A Faux
- Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
| | - P J McDonald
- Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
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Faux DA, McDonald PJ, Howlett NC. Nuclear-magnetic-resonance relaxation due to the translational diffusion of fluid confined to quasi-two-dimensional pores. Phys Rev E 2017; 95:033116. [PMID: 28415296 DOI: 10.1103/physreve.95.033116] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Indexed: 01/09/2023]
Abstract
Nuclear-magnetic-resonance (NMR) relaxation experimentation is an effective technique for nondestructively probing the dynamics of proton-bearing fluids in porous media. The frequency-dependent relaxation rate T_{1}^{-1} can yield a wealth of information on the fluid dynamics within the pore provided data can be fit to a suitable spin diffusion model. A spin diffusion model yields the dipolar correlation function G(t) describing the relative translational motion of pairs of ^{1}H spins which then can be Fourier transformed to yield T_{1}^{-1}. G(t) for spins confined to a quasi-two-dimensional (Q2D) pore of thickness h is determined using theoretical and Monte Carlo techniques. G(t) shows a transition from three- to two-dimensional motion with the transition time proportional to h^{2}. T_{1}^{-1} is found to be independent of frequency over the range 0.01-100 MHz provided h≳5 nm and increases with decreasing frequency and decreasing h for pores of thickness h<3 nm. T_{1}^{-1} increases linearly with the bulk water diffusion correlation time τ_{b} allowing a simple and direct estimate of the bulk water diffusion coefficient from the high-frequency limit of T_{1}^{-1} dispersion measurements in systems where the influence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surface-to-bulk desorption rates for a thin pore. G(t) is found to decorrelate when spins move from the surface to the bulk, display three-dimensional properties at intermediate times, and finally show a bulk-mediated surface diffusion (Lévy) mechanism at longer times. The results may be used to interpret NMR relaxation rates in hydrated porous systems in which the paramagnetic impurity density is negligible.
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Affiliation(s)
- D A Faux
- Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
| | - P J McDonald
- Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
| | - N C Howlett
- Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
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