arXiv subjects

Philip M. Singer

Publications and source records attributed to Philip M. Singer.

15 recordsLinked to original sources

arXiv2023

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

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{\'e}-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

physics.chem-ph↗

arXiv2022

Effect of Nano-Confinement on NMR Relaxation of Heptane in Kerogen from MD Simulations and Measurements

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nano-confinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nano-confinement on the $^1$H NMR relaxation times $T_1$ and $T_2$ of heptane in kerogen. In the case of $T_1$, we discover the important role of confinement in reducing $T_1$ by $\sim$3 orders of magnitude from 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 $T_2$, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces $T_2$ by $\sim$5 orders of magnitude from bulk heptane. We use the simulated $T_2$ to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nano-pores in kerogen, without additional experimental data.

physics.chem-ph↗

arXiv2022

Emergence of the spin polarized domains in the kagome lattice Heisenberg antiferromagnet Zn-barlowite (Zn$_{0.95}$Cu$_{0.05}$)Cu$_{3}$(OD)$_{6}$FBr

Kagome lattice Heisenberg antiferromagnets are known to be highly sensitive to perturbations caused by structural disorder. NMR is a local probe ideally suited for investigating such disorder-induced effects, but in practice large distributions in the conventional one-dimensional NMR data make it difficult to distinguish the intrinsic behavior expected for pristine kagome quantum spin liquids from disorder induced effects. Here we report the development of a two-dimensional NMR data acquisition scheme applied to Zn-barlowite (Zn$_{0.95}$Cu$_{0.05}$)Cu$_{3}$(OD)$_{6}$FBr kagome lattice, and successfully correlate the distribution of the low energy spin excitations with that of the local spin susceptibility. We present evidence for the gradual growth of domains with a local spin polarization induced by 5\% Cu$^{2+}$ defect spins occupying the interlayer non-magnetic Zn$^{2+}$ sites. These spin polarized domains account for $\sim60$\% of the sample volume at 2~K, where gapless excitations induced by interlayer defects dominate the low energy sector of spin excitations within the kagome planes.

cond-mat.str-el↗

arXiv2022

Emergence of spin singlets with inhomogeneous gaps in the kagome Heisenberg antiferromagnets Zn-barlowite and herbertsmithite

The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets. But the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite ZnCu$_{3}$(OD)$_{6}$FBr and herbertsmithite ZnCu$_{3}$(OD)$_{6}$Cl$_2$ do not exhibit long range order, and they are considered the best realizations of the kagome Heisenberg antiferromagnet known to date. Here we use $^{63}$Cu nuclear quadrupole resonance combined with the inverse Laplace transform (ILT) to probe locally the inhomogeneity of delicate quantum ground states affected by disorder. We present direct evidence for the gradual emergence of spin singlets with spatially varying excitation gaps, but even at temperatures far below the super-exchange energy scale their fraction is limited to approximately 60\% of the total spins. Theoretical models need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour.

cond-mat.str-el↗

arXiv2022

Spin excitations of a proximate Kitaev quantum spin liquid realized in Cu$_2$IrO$_3$

Magnetic moments arranged at the corners of a honeycomb lattice are predicted to form a novel state of matter, Kitaev quantum spin liquid, under the influence of frustration effects between bond-dependent Ising interactions. Some layered honeycomb iridates and related materials, such as Na$_{2}$IrO$_{3}$ and $\alpha$-RuCl$_{3}$, are proximate to Kitaev quantum spin liquid, but bosonic spin-wave excitations associated with undesirable antiferromagnetic long-range order mask the inherent properties of Kitaev Hamiltonian. Here, we use $^{63}$Cu nuclear quadrupole resonance to uncover the low energy spin excitations in the nearly ideal honeycomb lattice of effective spin $S = 1/2$ at the Ir$^{4+}$ sites in Cu$_{2}$IrO$_{3}$. We demonstrate that, unlike Na$_{2}$IrO$_{3}$, Ir spin fluctuations exhibit no evidence for critical slowing down toward magnetic long range order in zero external magnetic field. Moreover, the low energy spin excitation spectrum is dominated by a mode that has a large excitation gap comparable to the Ising interactions, a signature expected for Majorana fermions of Kitaev quantum spin liquid.

cond-mat.str-el↗

arXiv2021

Freezing of the Lattice in the Kagome Lattice Heisenberg Antiferromagnet Zn-barlowite ZnCu$_3$(OD)$_6$FBr

We use $^{79}$Br nuclear quadrupole resonance (NQR) to demonstrate that ultra slow lattice dynamics set in below the temperature scale set by the Cu-Cu super-exchange interaction $J$~($\simeq160$~K) in the kagome lattice Heisenberg antiferromagnet Zn-barlowite. The lattice completely freezes below 50~K, and $^{79}$Br NQR lineshapes become twice broader due to increased lattice distortions. Moreover, the frozen lattice exhibits an oscillatory component in the transverse spin echo decay, a typical signature of pairing of nuclear spins by indirect nuclear spin-spin interaction. This indicates that some Br sites form structural dimers via a pair of kagome Cu sites prior to the gradual emergence of spin singlets below $\sim30$~K. Our findings underscore the significant roles played by subtle structural distortions in determining the nature of the disordered magnetic ground state of the kagome lattice.

cond-mat.str-el↗

arXiv2021

Molecular dynamics simulations of $^1$H NMR relaxation in Gd$^{3+}$--aqua

Atomistic molecular dynamics simulations are used to investigate $^1$H NMR $T_1$ relaxation of water from paramagnetic Gd$^{3+}$ ions in solution at 25$^{\circ}$C. Simulations of the $T_1$ relaxivity dispersion function $r_1$ computed from the Gd$^{3+}$--$^1$H dipole--dipole autocorrelation function agree within $\simeq 8$\% of measurements in the range $f_0 \simeq $ 5 $\leftrightarrow$ 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 $f_0 \lesssim $ 5 MHz, the simulation overestimates $r_1$ compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting $r_1$ at high frequencies in chelated Gd$^{3+}$ contrast-agents used for clinical MRI.

physics.chem-ph↗

arXiv2021

NMR Investigation on Honeycomb Iridate Ag$_3$LiIr$_2$O$_6$

We investigate the structural and magnetic properties of a Kitaev spin liquid candidate material Ag$_3$LiIr$_2$O$_6$ based on $^7$Li nuclear magnetic resonance line shape, Knight shift and spin-lattice relaxation rate $1/T_1$. The first sample A shows signatures of magnetically ordered spins, and exhibits one sharp $^7$Li peak with FWHM increasing significantly below 14~K. $1/T_1^{stretch}$ of this sample displays a broad local maximum at 40~K, followed by a very sharp peak at $T_N = 9\pm1$~K due to critical slowing down of Ir spin fluctuations, a typical signature of magnetic long range order. In order to shed light on the position-by-position variation of $1/T_1$ throughout the sample, we use Inverse Laplace Transform $T_1$ analysis based on Tikhonov regularization to deduce the density distribution function $P(1/T_1)$. We demonstrate that $\sim 60\%$ of Ir spins are statically ordered at the NMR measurement timescale but the rest of the sample volume remains paramagnetic even at 4.2~K, presumably because of structural disorder induced primarily by stacking faults. In order to further investigate the influence of structural disorder, we compare these NMR results with those of a second sample B, which has been shown by transmission electron microscope to have domains with unwanted Ag inclusion at Li and Ir sites within the Ir honeycomb planes. The sample B displays an additional NMR peak with relative intensity of $\sim 17\%$. The small Knight shift and $1/T_1$ of these defect-induced $^7$Li sites and the enhancement of bulk susceptibility at low temperatures suggest that these defects generate domains of only weakly magnetic Ir spins accompanied by free spins, leading to a lack of clear signatures of long-range order. The apparent lack of long-range order could be easily misinterpreted as evidence for the realization of a spin liquid ground state in highly disordered Kitaev lattice.

cond-mat.str-el↗

arXiv2020

$^1$H-NMR Dipole-Dipole Relaxation in Fluids: Relaxation of Individual $^1$H-$^1$H Pairs versus Relaxation of Molecular Modes

The intra-molecular $^1$H-NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intra-molecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the $^1$H-$^1$H pair and predicts a mono-exponential decay of the $^1$H-$^1$H 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 $^1$H-$^1$H intra-molecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However for the high-symmetry molecule neopentane, the individual $^1$H-$^1$H intra-molecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The inter-molecular autocorrelation functions for $n$-heptane, water, and neopentane also do not admit a mono-exponential behavior of individual $^1$H-$^1$H inter-molecular pairs at distinct initial separations. We suggest expanding the auto-correlation function in terms of molecular modes, where the molecular modes 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.

physics.chem-ph↗

arXiv2020

Elucidating the $^1$H NMR relaxation mechanism in polydisperse polymers and bitumen using measurements, MD simulations, and models

The mechanism behind the $^1$H NMR frequency dependence of $T_1$ and the viscosity dependence of $T_2$ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies ($f_0 = 0.01 \leftrightarrow$ 400 MHz) and viscosities ($η= 385 \leftrightarrow 102,000$ cP) using $T_{1}$ and $T_2$ in static fields, $T_{1}$ field-cycling relaxometry, and $T_{1ρ}$ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times $T_{1LM} \propto f_0$ and $T_{2LM} \propto (η/T)^{-1/2}$ with a phenomenological model of $^1$H-$^1$H dipole-dipole relaxation which includes a distribution in molecular correlation times and internal motions of the non-rigid polymer branches. We show that the model also accounts for the anomalous $T_{1LM}$ and $T_{2LM}$ in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the $T_{1} \propto f_0$ dispersion and $T_2$ of similar polymers simulated over a range of viscosities ($η= 1 \leftrightarrow 1,000$ cP) are in good agreement with measurements and the model. The $T_{1} \propto f_0$ dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under confinement, without the need to invoke paramagnetism.

physics.chem-ph↗

arXiv2020

Molecular Dynamics Simulations of NMR Relaxation and Diffusion of Heptane Confined in a Polymer Matrix

The mechanism behind the NMR surface relaxation and the large $T_1$/$T_2$ ratio of light hydrocarbons confined in the nano-pores of kerogen remains poorly understood, and consequently has engendered much debate. Towards bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of $^1$H NMR relaxation and diffusion of heptane in a polymer matrix, where the high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. We calculate the autocorrelation function $G(t)$ for $^1$H-$^1$H dipole-dipole interactions of heptane in the polymer matrix and use this to generate the NMR frequency ($f_0$) dependence of $T_1$ and $T_2$ relaxation times as a function of $ϕ_{C7}$. We find that increasing molecular confinement increases the correlation time of the heptane molecule, which decreases the surface relaxation times for heptane in the polymer matrix. For weak confinement ($ϕ_{C7} > 50$ vol%), we find that $T_{1S}/T_{2S} \simeq 1$. Under strong confinement ($ϕ_{C7} \lesssim $ 50 vol%), we find that the ratio $T_{1S}/T_{2S} \gtrsim 4$ increases with decreasing $ϕ_{C7}$, and that the dispersion relation $T_{1S} \propto f_0$ is consistent with previously reported measurements of polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism, but our studies suggests that $^1$H-$^1$H dipole-dipole interactions enhanced by organic nano-pore confinement dominates the NMR response in saturated organic-rich shales, without the need to invoke paramagnetism.

physics.chem-ph↗

arXiv2018

NMR Spin-Rotation Relaxation and Diffusion of Methane

The translational-diffusion coefficient $D_T$ and the spin-rotation contribution to the $^1$H NMR relaxation time $T_{1J}$ for methane (CH$_4$) are investigated using MD (molecular dynamics) simulations, over a wide range of densities $ρ$ and temperatures $T$, spanning the liquid, supercritical, and gas phases. The simulated $D_T$ agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular-velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function $G_{\!J}(t)$ for spin-rotation interactions. With increasing $D_T$ (i.e. decreasing $ρ$), $G_{\!J}(t)$ shows increasing deviations from the single-exponential decay predicted by the Langevin theory for hard spheres, and the deviations are quantified using inverse Laplace transforms of $G_{\!J}(t)$. $T_{1J}$ is derived from $G_{\!J}(t)$ using the kinetic model "km" for gases ($T_{1J}^{km}$), and the diffusion model "dm" for liquids ($T_{1J}^{dm}$). $T_{1J}^{km}$ shows better agreement with $T_1$ measurements at higher $D_T$, while $T_{1J}^{dm}$ shows better agreement with $T_1$ measurements at lower $D_T$. $T_{1J}^{km}$ is shown to dominate over the MD simulated $^1$H-$^1$H dipole-dipole relaxation $T_{1RT}$ at high $D_T$, while the opposite is found at low $D_T$. At high $D_T$, the simulated spin-rotation correlation-time $τ_J$ agrees with the kinetic collision time $τ_K$ for gases, from which a new relation $1/T_{1J}^{km} \propto D_T$ is inferred, without any adjustable parameters.

physics.chem-ph↗

arXiv2018

Role of Internal Motions and Molecular Geometry on the NMR Relaxation of Hydrocarbons

The role of internal motions and molecular geometry on $^1$H NMR relaxation times $T_{1,2}$ in hydrocarbons is investigated using MD (molecular dynamics) simulations of the autocorrelation functions for in{\it tra}molecular $G_R(t)$ and in{\it ter}molecular $G_T(t)$ $^1$H-$^1$H dipole-dipole interactions arising from rotational ($R$) and translational ($T$) diffusion, respectively. We show that molecules with increased molecular symmetry such as neopentane, benzene, and isooctane show better agreement with traditional hard-sphere models than their corresponding straight-chain $n$-alkane, and furthermore that spherically-symmetric neopentane agrees well with the Stokes-Einstein theory. The influence of internal motions on the dynamics and $T_{1,2}$ relaxation of $n$-alkanes are investigated by simulating rigid $n$-alkanes and comparing with flexible (i.e. non-rigid) $n$-alkanes. Internal motions cause the rotational and translational correlation-times $τ_{R,T}$ to get significantly shorter and the relaxation times $T_{1,2}$ to get significantly longer, especially for longer-chain $n$-alkanes. Site-by-site simulations of $^1$H's along the chains indicate significant variations in $τ_{R,T}$ and $T_{1,2}$ across the chain, especially for longer-chain $n$-alkanes. The extent of the stretched (i.e. multi-exponential) decay in the autocorrelation functions $G_{R,T}(t)$ are quantified using inverse Laplace transforms, for both rigid and flexible molecules, and on a site-by-site bases. Comparison of $T_{1,2}$ measurements with the site-by-site simulations indicate that cross-relaxation (partially) averages-out the variations in $τ_{R,T}$ and $T_{1,2}$ across the chain of long-chain $n$-alkanes. This work also has implications on the role of nano-pore confinement on the NMR relaxation of fluids in the organic-matter pores of kerogen and bitumen.

physics.chem-ph↗

arXiv2009

Numerical Modeling of Complex Porous Media For Borehole Applications

The diffusion/relaxation behavior of polarized spins of pore filling fluid, as often probed by NMR relaxometry, is widely used to extract information on the pore-geometry. Such information is further interpreted as an indicator of the key transport property of the formation in the oil industry. As the importance of reservoirs with complex pore geometry grows, so does the need for deeper understanding of how these properties are inter-related. Numerical modeling of relevant physical processes using a known pore geometry promises to be an effective tool in such endeavor. Using a suite of numerical techniques based on random-walk (RW) and Lattice-Boltzmann (LB) algorithms, we compare sandstone and carbonate pore geometries in their impact on NMR and flow properties. For NMR relaxometry, both laboratory measurement and simulation were done on the same source to address some of the long-standing issues in its borehole applications. Through a series of "numerical experiments" in which the interfacial relaxation properties of the pore matrix is varied systematically, we study the effect of a variable surface relaxivity while fully incorporating the complexity of the pore geometry. From combined RW and LB simulations, we also obtain diffusion-convection propagator and compare the result with experimental and network-simulation counterparts.

cond-mat.soft↗

arXiv2006

Influence of local fullerene orientation on the electronic properties of A3C60 compounds

We have investigated sodium containing fullerene superconductors Na2AC60, A = Cs, Rb, and K, by Na-23 nuclear magnetic resonance (NMR) spectroscopy at 7.5 T in the temperature range of 10 to 400 K. Despite the structural differences from the Rb3C60 class of fullerene superconductors, in these compounds the NMR line of the tetrahedrally coordinated alkali nuclei also splits into two lines (T and T') at low temperature. In Na2CsC60 the splitting occurs at 170 K; in the quenched cubic phase of Na2RbC60 and Na2KC60 we observe split lines at 80 K. Detailed investigations of the spectrum, spin-spin and spin-lattice relaxation as well as spin-echo double resonance (SEDOR) in Na2CsC60 we show that these two different tetrahedral sites are mixed on a microscopic scale. The T and T' sites differ in the orientation of first-neighbor C60 molecules. We present evidence that the orientations of neighboring molecules are uncorrelated. Thermally activated molecular reorientations cause an exchange between the T and T' sites and motional narrowing at high temperature. We infer the same activation energy, 3300 K, in the temperature range 125 to 300 K. The spin lattice relaxation rate is the same for T and T' down to 125 K but different below. Both the spin-lattice relaxation rate and Knight shift are strongly temperature dependent in the whole range investigated. We interpret this temperature variation by the effect of phonon excitations involving the rigid librational motion of the C60 molecules. By extending the understanding of the structure and molecular dynamics of C60 superconductors, these results may help in clarifying the effects of the structure on the superconducting properties.

cond-mat.supr-con↗