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Tian Z, Jiang P, Xu R. NMR Relaxation of Gas Adsorbed in Microporous Material. J Phys Chem Lett 2024; 15:3023-3028. [PMID: 38465889 DOI: 10.1021/acs.jpclett.4c00221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/12/2024]
Abstract
NMR relaxometry has been widely applied to characterize fluid confined in porous media because of its versatility, chemical selectivity, and noninvasive nature. Here we extend its usage to gas adsorbed in microporous materials by establishing a new quantitative model based on the molecular level NMR relaxation mechanism revealed by the molecular simulation of a prototypical adsorption system, CH4 adsorbed in ZIF-8. The model enables new NMR relaxometry-based characterization methods for thermodynamic, dynamic, and structural properties of adsorption systems, as demonstrated and validated by the experiments where the adsorption capacity and self-diffusivity of H2, CH4, and small alcohols adsorbed in ZIF-8 are deduced from the NMR relaxation data. The findings can serve for a better understanding of the composition-structure-properties relationships of a wide range of adsorption systems which is essential for the development and application of new functional microporous materials.
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Affiliation(s)
- Zijian Tian
- Key Laboratory for CO2 Utilization and Reduction Technology of Beijing, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
| | - Peixue Jiang
- Key Laboratory for CO2 Utilization and Reduction Technology of Beijing, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
| | - Ruina Xu
- Key Laboratory for CO2 Utilization and Reduction Technology of Beijing, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
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2
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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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Asthagiri DN, Beck TL. MD Simulation of Water Using a Rigid Body Description Requires a Small Time Step to Ensure Equipartition. J Chem Theory Comput 2024; 20:368-374. [PMID: 38156881 DOI: 10.1021/acs.jctc.3c01153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2024]
Abstract
In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. We find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation-dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation-dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.
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Affiliation(s)
- Dilipkumar N Asthagiri
- Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37830-6012, United States
| | - Thomas L Beck
- Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37830-6012, United States
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Zill JC, Thompson ES, Nestle N, Valiullin R. Kinetics of Guest-Induced Structural Transitions in Metal-Organic-Framework MIL-53(Al)-NH 2 Probed by High-Pressure Nuclear Magnetic Resonance. J Phys Chem Lett 2023; 14:3391-3396. [PMID: 36996319 DOI: 10.1021/acs.jpclett.3c00155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
A nuclear magnetic resonance (NMR) study of a pore opening in amino-functionalized metal-organic framework (MOF) MIL-53(Al) in response to methane pressure variation is presented. Variations of both NMR signal intensities and transversal relaxation rates for methane are found to reveal hysteretic structural transitions in the MOF material, which are smeared out over broad pressure ranges. Experiments with pressure reversals upon an incomplete adsorption/desorption gave deeper insight into the microscopic transition mechanisms. These experiments have unequivocally proven that the non-stepwise pore opening/closing transitions observed in the experiments are governed by a distribution of the opening/closing pressures over different MOF crystallites, for example, due to a distribution of the crystal sizes or shapes. The slow kinetics of the structural transitions measured in the hysteresis regime revealed a complex free energy landscape for the phase transition process.
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Affiliation(s)
- Jeremias C Zill
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
| | - Emma S Thompson
- BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen am Rhein, Germany
| | - Nikolaus Nestle
- BASF SE, Carl-Bosch-Str. 38, 67056 Ludwigshafen am Rhein, Germany
| | - Rustem Valiullin
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
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Philips A, Autschbach J. Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases. J Phys Chem B 2023; 127:1167-1177. [PMID: 36700851 DOI: 10.1021/acs.jpcb.2c06411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.
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Affiliation(s)
- Adam Philips
- Department of Chemistry, University at Buffalo State University of New York, Buffalo, New York14260-3000, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo State University of New York, Buffalo, New York14260-3000, United States
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Valiya Parambathu A, Chapman WG, Hirasaki GJ, Asthagiri D, Singer PM. Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements. J Phys Chem Lett 2023; 14:1059-1065. [PMID: 36693239 DOI: 10.1021/acs.jpclett.2c03699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nanoconfinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nanoconfinement on the 1H NMR relaxation times T1 and T2 of heptane in kerogen. In the case of T1, we discover the important role of confinement in reducing T1 by ∼3 orders of magnitude from that of bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of T2, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces T2 by ∼5 orders of magnitude from the value for bulk heptane. We use the simulated T2 to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nanopores in kerogen, without additional experimental data.
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Affiliation(s)
- Arjun Valiya Parambathu
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas77005, United States
- Department of Chemical and Biomolecular Engineering, University of Delaware, 150 Academy Street, Newark, Delaware19716, United States
| | - Walter G Chapman
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas77005, United States
| | - George J Hirasaki
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas77005, United States
| | - Dilipkumar Asthagiri
- Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee37830-6012, United States
| | - Philip M Singer
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas77005, United States
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Ok S, Gautam S, Liu KH, Cole DR. Surface Interactions and Nanoconfinement of Methane and Methane plus CO 2 Revealed by High-Pressure Magic Angle Spinning NMR Spectroscopy and Molecular Dynamics. MEMBRANES 2022; 12:1273. [PMID: 36557180 PMCID: PMC9785918 DOI: 10.3390/membranes12121273] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 12/02/2022] [Accepted: 12/10/2022] [Indexed: 06/17/2023]
Abstract
This study explores the fundamental, molecular- to microscopic-level behavior of methane gas confined into nanoporous silica proxies with different pore diameters and surface-to-volume (S/V) ratios. Surfaces and pore walls of nanoporous silica matrices are decorated with hydroxyl (-OH) groups, resembling natural heterogeneity. High-pressure MAS NMR was utilized to characterize the interactions between methane and the engineered nanoporous silica proxies under various temperature and pressure regimes. There was a change in the chemical shift position of confined methane slightly in the mixtures with nanoporous silica up to 393 K, as shown by high-pressure 13C-NMR. The 13C-NMR chemical shift of methane was changed by pressure, explained by the densification of methane inside the nanoporous silica materials. The influence of pore diameter and S/V of the nanoporous silica materials on the behaviors and dynamics of methane were studied. The presence of CO2 in mixtures of silica and methane needs analysis with caution because CO2 in a supercritical state and gaseous CO2 change the original structure of nanoporous silica and change surface area and pore volume. According to simulation, the picosecond scale dynamics of methane confined in larger pores of amorphous silica is faster. In the 4 nm pore, the diffusivity obtained from MD simulations in the pore with a higher S/V ratio is slower due to the trapping of methane molecules in adsorbed layers close to the corrugated pore surface. In contrast, relaxation measured with NMR for smaller pores (higher S/V) exhibits larger T1, indicating slower relaxation.
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Affiliation(s)
- Salim Ok
- School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA
| | - Siddharth Gautam
- School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA
| | - Kao-Hsiang Liu
- Shull Wollan Center—A Joint Institute for Neutron Science Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - David R. Cole
- School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA
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Yang K, Sadeghi Pouya E, Liu L, Li M, Yang X, Robinson N, May EF, Johns ML. Low‐Field NMR Relaxation Analysis of High‐Pressure Ethane Adsorption in Mesoporous Silicas. Chemphyschem 2022; 23:e202100794. [DOI: 10.1002/cphc.202100794] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 12/20/2021] [Indexed: 12/11/2022]
Affiliation(s)
- Kaishuo Yang
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Ehsan Sadeghi Pouya
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Libin Liu
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Ming Li
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Xiaoxian Yang
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Neil Robinson
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Eric F. May
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
| | - Michael L. Johns
- Department of Chemical Engineering The University of Western Australia 35 Stirling Highway (M050) Perth WA 6009 Australia
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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: 1] [Impact Index Per Article: 0.3] [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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Madhavi WM, Weerasinghe S, Momot KI. Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2020.114727] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Asthagiri D, Chapman WG, Hirasaki GJ, Singer PM. NMR 1H- 1H Dipole Relaxation in Fluids: Relaxation of Individual 1H- 1H Pairs versus Relaxation of Molecular Modes. J Phys Chem B 2020; 124:10802-10810. [PMID: 33185099 DOI: 10.1021/acs.jpcb.0c08078] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The intramolecular 1H NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the 1H-1H pair and predicts a monoexponential decay of the 1H-1H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n-heptane and water this is not the case. In particular, the autocorrelation function of individual 1H-1H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual 1H-1H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual 1H-1H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.
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Affiliation(s)
- D Asthagiri
- Rice University, Department of Chemical and Biomolecular Engineering, 6100 Main Street, Houston, Texas 77005, United States
| | - Walter G Chapman
- Rice University, Department of Chemical and Biomolecular Engineering, 6100 Main Street, Houston, Texas 77005, United States
| | - George J Hirasaki
- Rice University, Department of Chemical and Biomolecular Engineering, 6100 Main Street, Houston, Texas 77005, United States
| | - Philip M Singer
- Rice University, Department of Chemical and Biomolecular Engineering, 6100 Main Street, Houston, Texas 77005, United States
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Valiya Parambathu A, Singer PM, Hirasaki GJ, Chapman WG, Asthagiri D. Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of n-Heptane in a Polymer Matrix Revealed by MD Simulations. J Phys Chem B 2020; 124:3801-3810. [PMID: 32267690 DOI: 10.1021/acs.jpcb.0c00711] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The mechanism behind the NMR surface-relaxation times (T1S,2S) and the large T1S/T2S ratio of light hydrocarbons confined in the nanopores of kerogen remains poorly understood and consequently has engendered much debate. Toward bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of 1H NMR relaxation and diffusion of n-heptane in a polymer matrix. The high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. Diffusion of n-heptane shows a power-law dependence on the concentration of n-heptane (ϕC7) in the polymer matrix, consistent with Archie's model of tortuosity. We calculate the autocorrelation function G(t) for 1H-1H dipole-dipole interactions of n-heptane in the polymer matrix and use this to generate the NMR frequency (f0) dependence of T1S,2S as a function of ϕC7. We find that increasing molecular confinement increases the correlation time, which decreases the surface-relaxation times for n-heptane in the polymer matrix. For weak confinement (ϕC7 > 50 vol %), we find that T1S/T2S ≃ 1. Under strong confinement (ϕC7 ≲ 50 vol %), we find that T1S/T2S ≳ 4 increases with decreasing ϕC7 and that the dispersion relation T1S ∝ f0 is consistent with previously reported measurements of polydisperse polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism; instead, our studies suggests that 1H-1H dipole-dipole interactions enhanced by organic nanopore confinement dominate the NMR response in saturated organic-rich shales.
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Affiliation(s)
- Arjun Valiya Parambathu
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
| | - Philip M Singer
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
| | - George J Hirasaki
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
| | - Walter G Chapman
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
| | - Dilipkumar Asthagiri
- Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
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