Dipole Correlation Function Research Articles

Molecular insights into nuclear-magnetic-resonance properties of NaCl solution confined within calcite nanopores

Nuclear magnetic resonance (NMR) relaxation time is an important petrophysical property probing fluid dynamics within pores and providing valuable information to understand solid–fluid interactions and ion-related effects. In this study, we investigate NMR and diffusion properties of confined sodium chloride (NaCl) solutions within calcite nanopores via molecular dynamics (MD) simulations. Density profiles, self-diffusion coefficients, and NMR relaxation times were analyzed as a function of pore size, pore geometry, and NaCl concentration. MD results indicate that the presence of NaCl hinders water movement, resulting in reduced self-diffusion coefficients and relaxation times of water. Nevertheless, the influence of NaCl on water mobility is less than the effects caused by confinement and geometry. Strength of oscillations in water and ion density profiles increases when the slit pore size is reduced to 1 nm, suggesting that water-calcite interactions near pore surfaces are stronger in smaller pore sizes. Analysis of dipole–dipole correlation functions and probability distribution of correlation times shows that ions in aqueous solution have an impact on both intra- and intermolecular interactions. A comprehensive comparison of NMR relaxation times of water in both slit and spherical nanopores reveals that spherical models provide a more accurate representation of the confinement effect induced by pore networks within tight rocks. These findings provide a novel quantitative understanding of the impact of confinement, pore geometry, and ion concentration on the translational and rotational dynamics of confined fluids in calcite nanopores.

Determination of self and cross contributions to the dipole–dipole correlations function from analysis of dielectric measurements

The nonexponential nature of the structural relaxation is one of the most characteristic features of the molecular dynamics in glass-forming liquids. Various experimental techniques can be employed to probe this process; however, broadband dielectric spectroscopy (BDS) is the most frequently used. Based on MD simulations, we provide strong evidence of bi-modal nature of the dielectric loss peak of primary relaxation. Further, we point out that the primary dielectric relaxation process measured at constant displacement D is dominated by the self-correlation term in the dipole–dipole correlation function. In practice, it means that the dielectric spectra should be presented in the dielectric modulus representations to disclose the spectral features of the self mode.

Vibrational spectra of human tissues: Experimental data and density functional theory calculations comparison

Biophotonics techniques enabling molecular sensing of tissues and biological samples of had been widely applied to biomedical problems. Vibrational spectroscopy technologies like Fourier-Transform Infrared (FTIR) spectroscopy is a well-reported example. However, the correct interpretation of measured vibrational spectra of macromolecules and tissues emerging from the complexity of structures is a challenge. Computer simulations can be used as a strategic method to understand interactions between specific parts of a macromolecule. Here we present two implementations of vibrational calculations based on diagonalization of Hessian matrix obtained via Density Functional Theory calculations using Car-Parrinello Molecular Dynamics (CPMD package), Born-Oppenheimer Molecular Dynamics quickstep GPW (CP2K package), and a molecular dynamics calculations based on tight binding (CP2K-TB) was also employed to obtain FTIR spectra via electric dipole correlation function. These calculations were proposed to capture vibrational pieces of information related to FTIR of the human oral mucosa. Eleven models of peptide which represents collagen type I macromolecule including confined water molecules (ranging from 0 to 8 waters), were tested. CPMD and CP2K methods presented an excellent agreement of vibrational bands positions and maximum intensity to experimental data (goodness-of-fit R2 ∼ 0.90). On the other hand, this agreement was very poor for the CP2K-TB case in spite of the correct overall relative spectral intensity with respect to experimental data. We found that the peptide model enclosing eight waters (labeled C8) in CPMD calculations presented the highest value of R2 = 0.99. The CPMD method, despite some limitations, outperformed the CP2K calculation in our case. Here we only used a collagen cutout and confined water, but it is possible to add other molecules such as proteoglycans to investigate and characterize a tissue. The short collagen mimetic peptide has implications for the conformational behavior of native collagen. The method itself can be used for other macromolecules. Furthermore, we assignment of vibrational modes in the high-wavenumber region ( > 2, 000▒cm−1) is also presented.

Derivation of the stationary fluorescence spectrum formula for molecular systems from the perspective of quantum electrodynamics

Numerical simulations of stationary fluorescence spectra of molecular systems usually rely on the relation between the photon emission rate and the system’s dipole–dipole correlation function. However, research papers usually take this relation for granted, and standard textbook expositions of the theory of fluorescence spectra also tend to leave out this important relation. In order to help researchers with less theoretical training gain a deeper understanding of the emission process, we perform a step-by-step derivation of the expression for the fluorescence spectrum, focusing on rigorous mathematical treatment and the underlying physical content. Right from the start, we employ quantum description of the electromagnetic field, which provides a clear picture of emission that goes beyond the phenomenological treatment in terms of the Einstein A coefficient. Having obtained the final expression, we discuss the relation of the latter to the present level of theory by studying a simple two-level system. From the technical perspective, the present work also aims at familiarizing the reader with the density matrix formalism and with the application of the double-sided Feynman diagrams.

Dipole distortions in the intergalactic medium

Abstract Baryonic feedback can significantly modify the spatial distribution of matter on small scales and create a bulk relative velocity between the dominant cold dark matter and the hot gas. We study the consequences of such bulk motions using two high-resolution hydrodynamic simulations, one with no feedback and one with very strong feedback. We find that relative velocities of order $100\ {\rm km}\, {\rm s}^{-1}$ are produced in the strong feedback simulation, whereas it is much smaller when there is no feedback. Such relative motions induce dipole distortions to the gas, which we quantify by computing the dipole correlation function. We find halo coordinates and velocities are systematically changed in the direction of the relative velocity. Finally, we discuss potential to observe the relative velocity via large-scale structure, Sunyaev–Zel’dovich and line emission measurements. Given the non-linear nature of this effect, it should next be studied in simulations with different feedback implementations/strengths to determine the available model space.

An experimental and theoretical investigation on relaxor behavior and local correlations in xBi(Zn0.5Ti0.5)O3-(1-x)BaTiO3 ceramics

Relaxor behavior and local correlations in perovskite structured xBi(Zn0.5Ti0.5)O3-(1-x)BaTiO3 (xBZT-(1-x)BT,0.30 ≥x ≥ 0.10) ceramics are investigated by both experimental and theoretical Ab initio molecular dynamics calculations. For 0.30 ≥x ≥ 0.10, xBZT-(1-x)BT ceramics show typical relaxor behavior. For x ≥ 0.20, the J-E loops show “whale” shape and no saturated P-E loops are observed even near the polar nanoregions (PNRs) freezing temperature Tf (135 K–146 K), indicating that long range polar order (ferroelectric domian) does not exist in these samples, and the PNRs locate at nonergodic state with temperature decreasing. The partial pair distribution function (PDF) results show that Bi atoms are very sensitive to the local B site occupancy and have pronounced trend to displace toward neighboring Zn atoms. The Bi-Zn displacement coupling will enhance the local polarization and stabilize the PNRs even at higher temperature. The dipole correlation function (DCF) results show that the Bi dipoles only correlate with their nearest Ti neighbors and the polarization correlation with the second-nearest Ti neighbors is negligible. No existence of long range polar order in xBZT-(1-x)BT (x ≥ 0.20) can be attributed to the Bi displacement influenced highly by the random distribution of Zn atoms and the dominated Bi-Ti dipole correlations only existing within the nearest Bi-Ti neighbors.

A time-correlation function approach to nuclear dynamical effects in X-ray spectroscopy.

Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking nuclear dynamics and the associated nuclear correlations into account may be of importance for X-ray spectroscopy. Recently, we have developed an efficient protocol to account for nuclear dynamics in X-ray absorption and resonant inelastic X-ray scattering spectra [Karsten et al., J. Phys. Chem. Lett. 8, 992 (2017)], based on ground state molecular dynamics accompanied with state-of-the-art calculations of electronic excitation energies and transition dipoles. Here, we present an alternative derivation of the formalism and elaborate on the developed simulation protocol using gas phase and bulk water as examples. The specific spectroscopic features stemming from the nuclear motions are analyzed and traced down to the dynamics of electronic energy gaps and transition dipole correlation functions. The observed tendencies are explained on the basis of a simple harmonic model, and the involved approximations are discussed. The method represents a step forward over the conventional approaches that treat the system in full complexity and provides a reasonable starting point for further improvements.

Effect of stable and metastable dimers on collision-induced rototranslational spectra: Carbon dioxide – rare gas mixtures

The role of stable and metastable dimers as well as of free collisions in the collision-induced rototranslational absorption by the compressed CO2–Ar and CO2–Xe gas mixtures is elucidated using the classical three-dimensional trajectories method. The contribution from the stable dimers is obtained via Fourier transform of the dipole correlation function. The spectral bandshape due to the unbound trajectories (metastable dimers and free collisions) is calculated as an averaged Fourier spectrum of the collision-induced dipole moment. The mean lifetimes of metastable dimers have been estimated as 3.8 ps for CO2–Ar and 5.9 ps for CO2–Xe pairs. Trajectory computations are complemented by calculations of zero spectral moments using pair distribution functions. The stable and metastable dimer contribution to the zero spectral moment is shown to be comparable with that from free collisions.

Nuclear-magnetic-resonance relaxation due to the translational diffusion of fluid confined to quasi-two-dimensional pores.

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.

Dynamics of a Paradigmatic Linear Polymer: A Proton Field-Cycling NMR Relaxometry Study on Poly(ethylene–propylene)

The dynamics of melts of linear poly(ethylene-alt-propylene) (PEP) of different molar masses (M) is investigated by 1H field-cycling (FC) NMR relaxometry. Employing a commercial and a home-built relaxometer the spin-lattice relaxation rate R1(ω) is measured in the frequency range of 200 Hz to 30 MHz and the temperature range of 200–400 K. Transforming the FC NMR relaxation data to the susceptibility representation and applying frequency–temperature superposition, master curves for the dipolar correlation function CDD(t/τα) (containing intra- and intermolecular contributions) are constructed which extend up to six decades in amplitude and eight in time. Here, τα is the time scale of the structural (α-) relaxation, which is obtained over several decades. Comparison with previously reported FC data for polybutadiene (PB) discloses very similar CDD(t). Depending on M, all the five relaxation regimes of a polymer melt are covered: in addition to the α-process (0) and the terminal relaxation (IV), which are imm...

Motional narrowing under diffusion of two spin sub-lattices in LiNaSO4

An expression for the dipolar correlation function characterizing the fluctuations of the Hamiltonian under uncorrelated diffusion of two cationic sub-lattices in a solid has been obtained. A corresponding formula, which can be used for fitting the two-step temperature dependencies of the NMR line width, has been deduced. We also considered the case of a distribution of correlation times and deduced a corresponding analytical fitting function. Elaborated expressions have been applied to the NMR line width analysis of LiNaSO4 in the temperature range 295–788K.

Classical Description of the Vibrational Spectroscopy, Structure, and Electrostatics of the Halide Solvation Shell with the POLIR Potential.

POLIR (POLarizable for IR) (J. Chem. Phys. 2008, 129, 034504) is a polarizable, flexible, and transferable water potential which describes the IR spectrum in the O-H stretch region via the classical dipole correlation function with simple quantum corrections. POLIR also reproduces experimental spectral shifts in solutions of Ca(2+), Mg(2+), and Cu(2+) (J. Am. Chem. Soc. 2011, 133, 9441-9450). Here we present an extended investigation of POLIR water in the solvation shell of the halides F(-), Cl(-), Br(-), and I(-) using various interaction potentials, polarizabilities, and short-range electrostatic damping parameters. Our results indicate that the correlation of the first solvation shell dipoles produces IR spectra that are in agreement with experiment; that is, vibrational spectral shifts may be obtained with classical mechanics and simple corrections. Calculated ion induced dipoles agree with quantum simulations. Further analysis shows that ion-dependent shifts in the spectra may be attributed to the hydrogen bond O···O-H angle distribution within the first solvation shell, decomposed into ion-water and water-water contributions.

Field-Cycling NMR Relaxometry Probing the Microscopic Dynamics in Polymer Melts

Field-cycling (FC) 1H and 2H NMR relaxometry is applied to linear polybutadiene (PB) of different molar mass (M) in order to test current polymer theories. Applying earth field compensation, five decades in the frequency dependence of the spin–lattice relaxation rate T1–1(ν) = R1(ν) are accessed (200 Hz - 30 MHz), and we focus on the crossover from Rouse to entanglement dynamics. A refined evaluation is presented, which avoids application of frequency–temperature superposition as well as Fourier transformation. Instead, the power-law exponent e in the entanglement regime is directly determined from the susceptibility representation χNMR″(ω) = ω/T1(ω) ∝ ωe by a derivative method. Correspondingly, a power-law t–e characterizes the decay in the time domain, i.e., the dipolar correlation function. For the total 1H relaxation, comprising intra- and intermolecular relaxation, a high-M exponent etotal = 0.31 ± 0.03 is found. An isotope dilution experiment, which yields the intramolecular relaxation reflecting so...

Polar nanoregions in water: A study of the dielectric properties of TIP4P/2005, TIP4P/2005f and TTM3F

We present a critical comparison of the dielectric properties of three models of water-TIP4P/2005, TIP4P/2005f, and TTM3F. Dipole spatial correlation is measured using the distance dependent Kirkwood function along with one-dimensional and two-dimensional dipole correlation functions. We find that the introduction of flexibility alone does not significantly affect dipole correlation and only affects ɛ(ω) at high frequencies. By contrast the introduction of polarizability increases dipole correlation and yields a more accurate ɛ(ω). Additionally, the introduction of polarizability creates temperature dependence in the dipole moment even at fixed density, yielding a more accurate value for dɛ/dT compared to non-polarizable models. To better understand the physical origin of the dielectric properties of water we make analogies to the physics of polar nanoregions in relaxor ferroelectric materials. We show that ɛ(ω, T) and τD(T) for water have striking similarities with relaxor ferroelectrics, a class of materials characterized by large frequency dispersion in ɛ(ω, T), Vogel-Fulcher-Tammann behaviour in τD(T), and the existence of polar nanoregions.

Local-field approximation of homonuclear dipolar interactions in 7Li-NMR: Density-matrix calculations and random-walk simulations tested by echo experiments on borate glasses

NMR echo techniques have proven to be important to study dynamics in ion conductors and other solid materials. Using the spin-3/2 nucleus 7Li as a probe, both the quadrupolar and the often neglected homonuclear dipolar interactions modulate the NMR frequency as the ion performs jump processes. Retaining only the local-field term of the many-body Hamiltonian, the impact of the dipolar interaction on various echo experiments was studied using spin dynamics calculations yielding products of dipolar and quadrupolar correlation functions. Using a simple stochastic model these functions were simulated with particular emphasis on the impact of ionic motions and on the conditions under which the dipolar and quadrupolar contributions factorize. The results of the computations and of the random-walk simulations are compared with experimental data obtained for various lithium borate and lithium borophosphate glasses. It is concluded that the local-field approximation is a useful means of treating the Li–Li dipole interactions and that the simple model that we introduce is capable of describing many experimentally observed features. Furthermore, because the dipolar and quadrupolar contributions essentially factorize, a selective determination of the corresponding correlation functions becomes possible.

Dynamics of Linear Polybutadienes in Solution Studied by Field Cycling 1H NMR.

Field cycling 1H NMR relaxometry is utilized to investigate dynamics in solutions of monodisperse polybutadienes of different molecular mass (M) and deuterated toluene. Broad temperature and polymer mass fraction ranges (c = 5-100%) are studied. By applying frequency-temperature superposition, susceptibility master curves χ″DD(ωτs) are constructed. They cover the segmental relaxation and polymer chain dynamics, and provide the concentration dependence of the segmental time constant τs(T). The relaxation strength of polymer dynamics is reduced similarly for all M with decreasing c; for the lowest c, almost no polymer dynamics shows up, that is, the dipolar correlation function obtained via Fourier transform decays almost completely due to segmental dynamics. The dipolar correlation function is decomposed into contributions of segmental and polymer dynamics. Its long-time power-law exponent associated with entanglement dynamics is increased from its bulk value with reduced c. This is interpreted as a continuous increase of the effective entanglement molecular mass.

Glassy, Rouse, and Entanglement Dynamics As Revealed by Field Cycling1H NMR Relaxometry

Poly(propylene glycol), poly(isoprene), and poly(dimethlyl siloxane) (PDMS) of different molecular masses M are investigated by field-cycling 1H NMR relaxometry to monitor the crossover from segmental dynamics, to Rouse and entanglement dynamics. The spin–lattice relaxation dispersions T1(ω) obtained at different temperatures (160 K – 400 K) are converted to the susceptibility representation χ″DD (ω) = ω/T1(ω). Applying frequency–temperature superposition, the data are merged to provide master curves χ″DD (ωτs) with τs = τs(T) being the segmental correlation times. Combining them with those from dielectric spectroscopy about 12 decades in time are covered. A similar M dependence of χ″DD (ωτs) is observed for all polymers (t ≫ τs) and comparison with dielectric normal mode spectra is carried out. In the case of PDMS showing particularities at t ≈ τs we attempt to separate intra- and intermolecular relaxation contributions. Transformation into time domain yields the dipolar correlation function CDD(t/τs) wh...

The effect of the spatial nonlocality of the Kirkwood g-factor on the determination of the long wavelength dielectric functions in dipolar fluids

The Kirkwood g-factor that determines the long wavelength dielectric constant of a simple, isotropic, translationally invariant dipolar fluid is given by an integral of a dipole-dipole correlation function over a spherical region of a nonzero radius R(K) chosen such that any further increase in the radius leads to no change in the value of the integral, thereby defining a Kirkwood correlation length R(K). For radii less than the correlation length the integral defines a radius dependent (nonlocal) Kirkwood g-factor, implying a nonlocal dielectric function. The nonlocal nature of these quantities has important consequences for the determination of the long wavelength dielectric function from dipole fluctuations via the Kirkwood-Fröhlich connection. The dipole-dipole correlation function (the volume dipole auto-correlation function) commonly used in this determination involves particles residing solely within a sphere of radius R, unlike the correct correlation function which involves either a single particle with those particles in a spherical volume of radius R(K) or those particles in a spherical volume of radius R with those residing within a spherical volume of radius R+R(K). A procedure is suggested for extracting the infinite system dipole-dipole correlation function from results of simulations performed on finite spherical samples. Using some results reported in the recent literature, relative to the accurate correlation function the commonly used correlation function ranges from 27% too small for a sphere having a radius comparable to the Kirkwood correlation length to 4% too small at a radius of seven times that correlation length. As a result, the apparent dielectric constants, as determined by the conventional procedure of using the fluctuations of the sum of dipoles in a finite fixed volume, are also too small. This suggests that a dielectric constant extracted from computer simulations using a total dipole-total dipole correlation function in a given volume with other geometries and/or boundary conditions will result in similar errors.

Protracted Crossover to Reptation Dynamics: A Field Cycling1H NMR Study Including Extremely Low Frequencies

The segmental dynamics of 1,4-polybutadiene is investigated by means of electronic field cycling 1H NMR. The frequency dependence (dispersion) of the spin–lattice relaxation time is probed over a broad range of temperature (223–408 K), molecular mass (355 ≤ M (g/mol) ≤ 441 000), and frequency (200 Hz–30 MHz). The extremely low frequencies are accessed by employing a home-built compensation for earth and stray fields extending prior reports about 2 decades to lower frequencies. Applying frequency–temperature superposition yields master curves over 10 decades in frequency (or time), and after Fourier transform the full dipolar correlation function is traced over up to 8 decades in amplitude. Several relaxation regimes can be identified, and their power-law exponents are compared to the predictions of the Doi–Edwards tube-reptation model, namely the free Rouse (I) and the constrained Rouse regime (II). Whereas the predicted value of the power-law exponent of regime II is 0.25, we find that it depends on M an...

Magnetic reversal of an artificial square ice: dipolar correlation and charge ordering

Magnetic reversal of an artificial square ice pattern subject to a sequence of magnetic fields applied slightly off the diagonal axis is investigated via magnetic force microscopy of the remanent states that result. Sublattice independent reversal is observed via correlated incrementally pinned flip cascades along parallel dipolar chains, as evident from analysis of vertex populations and dipolar correlation functions. Weak dipolar interactions between adjacent chains favour antialignment and give rise to weak charge ordering of ‘monopole’ vertices during the reversal process.