About

Philip Singer is a member of the Singer NMR Lab for Hydrogen & Carbon Geostorage at Rice University. His work is associated with the Department of Chemical & Biomolecular Engineering. The lab focuses on research related to hydrogen and carbon geostorage, contributing to the understanding and development of technologies in this field. Specific details about his background, research focus, or key contributions are not provided in the page text.

Research topics

• Physics
• Chemistry
• Organic chemistry
• Thermodynamics
• Condensed matter physics
• Materials science
• Chemical physics
• Quantum mechanics
• Crystallography
• Nuclear magnetic resonance
• Combinatorics
• Mathematics
• Geometry
• Computational chemistry

Selected publications

• Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

  The Journal of Chemical Physics · 2025-11-12 · 3 citations

  article

  Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, we describe the relative diffusion of the spin dipoles by means of a Fokker-Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker-Planck equation for the diffusion propagator, we estimate dipole-dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)-aqua and Gd(III)-DO3A-butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen-Purcell-Pound, the Solomon-Bloembergen-Morgan, and the Hwang-Freed models. Our implementation is general and publicly available for application to a broad range of systems.

  PublisherDOI

• Molecular-Level Insights into the NMR Relaxivity of Gadobutrol Using Quantum and Classical Molecular Simulations

  Chemical & Biomedical Imaging · 2025-04-09 · 5 citations

  articleOpen accessSenior authorCorresponding

  MRI is an indispensable diagnostic tool in modern medicine; however, understanding the molecular-level processes governing NMR relaxation of water in the presence of MRI contrast agents remains a challenge, hindering the molecular-guided development of more effective contrast agents. By using quantum-based polarizable force fields, the first-of-its-kind molecular dynamics (MD) simulations of Gadobutrol are reported where the 1H NMR longitudinal relaxivity r1 of the aqueous phase is determined without any adjustable parameters. The MD simulations of r1 dispersion (i.e., frequency dependence) show good agreement with measurements at frequencies of interest in clinical MRI. Importantly, the simulations reveal key insights into the molecular level processes leading to r1 dispersion by decomposing the NMR dipole–dipole autocorrelation function G(t) into a discrete set of molecular modes, analogous to the eigenmodes of a quantum harmonic oscillator. The molecular modes reveal important aspects of the underlying mechanisms governing r1, such as its multiexponential nature and the importance of the second eigenmodal decay. By simply analyzing the MD trajectories on a parameter-free approach, the Gadobutrol simulations show that the outer-shell water contributes ∼50% of the total relaxivity r1 compared to the inner-shell water, in contrast to simulations of (nonchelated) gadolinium-aqua where the outer shell contributes only ∼15% of r1. The deviation between simulations and measurements of r1 below clinical MRI frequencies is used to determine the low-frequency electron-spin relaxation time for Gadobutrol, in good agreement with independent studies.

  PublisherDOI

• Characterization of kerogen nanopores using 2D NMR relaxation and MD simulations

  Magnetic Resonance Letters · 2025-05-30 · 2 citations

  articleOpen access1st authorCorresponding

  The characterization of kerogen nanopores is crucial for predicting the geostorage capacity and recoverability of natural gas in unconventional gas shale reservoirs. Towards this end, a powerful technique is presented which integrates 2D NMR T 1 - T 2 relaxation measurements with molecular dynamics (MD) simulations of hydrocarbons confined in the nanopores of kerogen. The integrated NMR-MD technique is demonstrated using T 1 - T 2 measurements of kerogen isolates and organic-rich chalks saturated with heptane, together with MD simulations of heptane completely dissolved in a realistic kerogen model. The NMR-MD results are used to extract the swelling ratio and nanopore size distribution of kerogen as a function of depth in the reservoir. The effects of organic nanoconfinement on the T 1 relaxation dispersion and T 2 residual dipolar coupling of heptane are investigated, as well as the effect of downhole effective stress on the kerogen nanopore size as a function of depth and compaction. Potential applications in partially depleted gas shale reservoirs are discussed, including CO 2 utilization/geostorage, geostorage of green H 2 , and integration of the NMR-MD technique with thermodynamic models for predicting the competitive sorption of gas mixtures in kerogen. • MD simulations calibrate the T 2 surface relaxivity of heptane completely dissolved in kerogen, without any adjustable parameters. • Nanopore size distribution of kerogen determined from T 1 - T 2 measurements of nanopore heptane, without requiring additional experiments. • Swelling ratio of kerogen from nanopore heptane determined as a function of thermal maturity and reservoir depth. • Kerogen nanopore size decreases with reservoir depth due to increase in downhole effective stress and compaction.

  PublisherDOI

• Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids

  The Journal of Physical Chemistry B · 2024-08-09 · 8 citations

  articleOpen accessSenior authorCorresponding

  The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1H–1H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1H NMR T1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

  PublisherOA PDFDOI

• Characterization of kerogen and bitumen in Type II-S organic-rich chalk as a function of maturity using 2D NMR relaxation

  Fuel · 2024-03-16 · 6 citations

  articleSenior authorCorresponding
  PublisherDOI

• Theory and modeling of molecular modes in the NMR relaxation of fluids

  The Journal of Chemical Physics · 2024-02-09 · 9 citations

  articleOpen access

  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.

  PublisherOA PDFDOI

• Theory and modeling of molecular modes in the NMR relaxation of fluids

  arXiv (Cornell University) · 2023-10-09

  preprintOpen access

  Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display 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 autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational 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 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 Pad{é}-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

  PublisherOA PDFDOI

• Effect of Nanoconfinement on NMR Relaxation of Heptane in Kerogen from Molecular Simulations and Measurements

  The Journal of Physical Chemistry Letters · 2023-01-24 · 15 citations

  articleOpen accessSenior authorCorresponding

  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.

  PublisherOA PDFDOI

• Estimation of Permeability Anisotropy and Depositional Cycles in Organic-Rich Chalk by NMR Restricted Diffusion

  2023-06-10 · 1 citations

  article

  We present a new method for studying permeability anisotropy and paleo-depositional cycles by combining NMR anisotropic restricted diffusion measurements and scanning electron microscope (SEM) images on the core. In particular, the method is applied to measuring a depositional cycle from the Tethys Sea in the late Cretaceous period in the Ghareb Formation, which appears to be equivalent to the present-day El Nino-Southern Oscillation cycle. The NMR anisotropic restricted diffusion measurements were made with a 2.3-MHz NMR core analyzer on adjacent 1-in. core plugs drilled parallel (horizontal) and perpendicular (vertical) to the bedding plane. The cores at connate water saturation were then saturated with methane at 1,200 psi and then saturated with decane for NMR measurements using unipolar stimulated-echo pulse sequences. Different values of diffusion time were used to probe both the short L_D (diffusion length) regime with decane to determine surface-to-volume ratio S/V and the long L_D regime with methane to determine 1/tau, where tau is the diffusive tortuosity. Pore size and tortuosity were estimated based on the NMR restricted diffusion vs. diffusion length data and then used in a modified Carman-Kozeny model to predict the permeability anisotropy. The figure shows NMR anisotropic restricted diffusion measurements (restricted diffusivity (D/D_0) vs. diffusion length (L_D)) on decane-saturated cores with connate water (C10(H2O)) and methane-saturated cores with connate water in horizontal and vertical directions. The S/V is the same for horizontal and vertical directions, indicating the pore size is the same in the two samples. The permeabilities, computed from a modified Carman-Kozeny model, show that tortuosity is the main factor in the anisotropy of the measured core permeabilities. The diffusive tortuosity is much greater in the vertical direction than in the horizontal direction due to the additional diffusional restriction from the depositional laminations. We find that the L_D at which the vertical core reaches its tortuosity limit is significantly shorter than in the horizontal direction. We interpret the value of L_D ~100 µm, where the vertical diffusion reaches the asymptotic limit, as the half-spacing between laminations due to the depositional cycle. SEM images of the organic-rich chalk in this zone show several layers of shell fragments with the half-spacing between laminations of about 100 µm, which is consistent with NMR restricted diffusion results. We propose a new method to measure the permeability anisotropy using NMR restricted diffusion and the Carman-Kozeny model. This method can reduce the diffusive coupling using hydrocarbon saturation on cores with connate water and make a more accurate permeability estimation. The Ghareb Formation has been carefully dated in this region, and the rate of deposition is known. Thus, the laminations shown in the NMR restricted diffusion enable us to estimate the duration of the depositional cycle in this late Cretaceous period (~69 Mya). Surprisingly, we find that the timing of this paleo-depositional cycle was very close to the present-day El Nino-Southern Oscillation cycle.

  PublisherDOI

• Thermal and concentration effects on ¹H NMR relaxation of Gd³⁺-aqua using MD simulations and measurements

  Physical Chemistry Chemical Physics · 2022-01-01 · 9 citations

  articleOpen accessSenior author

  ) in terms of molecular modes and determine the thermal activation energies of the two largest modes, both of which are consistent with the range of literature values for rotational diffusion. We also determine the activation energies for translational diffusion and low-field electron-spin relaxation, both of which are consistent with the literature. Furthermore, we validate the MD simulations at human body temperature and concentrations of the paramagnetic ion used in clinical MRI, and we quantify the uncertainties in both simulations and measurements.

  PublisherOA PDFDOI

Frequent coauthors

• George J. Hirasaki

  Rice University

  38 shared

• Takashi Imai

  McMaster University

  31 shared

• H. Alloul

  24 shared

• D. Asthagiri

  20 shared

• Walter G. Chapman

  19 shared

• Péter Matus

  Comenius University Bratislava

  17 shared

• V. Brouet

  Université Paris-Saclay

  15 shared

• Zeliang Chen

  National Medical Products Administration

  15 shared

Labs

• Singer NMR Lab for Hydrogen & Carbon GeostoragePI

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Education

• PhD, Physics

  Massachusetts Institute of Technology

  2003

• MPhys, Physics

  University of Oxford

  1997