Spin Exchange Rate Constants Research Articles

The Chemical Structure of Carbon Nanothreads Analyzed by Advanced Solid-State NMR.

Carbon nanothreads are a new type of one-dimensional sp3-carbon nanomaterial formed by slow compression and decompression of benzene. We report characterization of the chemical structure of 13C-enriched nanothreads by advanced quantitative, selective, and two-dimensional solid-state nuclear magnetic resonance (NMR) experiments complemented by infrared (IR) spectroscopy. The width of the NMR spectral peaks suggests that the nanothread reaction products are much more organized than amorphous carbon. In addition, there is no evidence from NMR of a second phase such as amorphous mixed sp2/sp3-carbon. Spectral editing reveals that almost all carbon atoms are bonded to one hydrogen atom, unlike in amorphous carbon but as is expected for enumerated nanothread structures. Characterization of the local bonding structure confirms the presence of pure fully saturated "degree-6" carbon nanothreads previously deduced on the basis of crystal packing considerations from diffraction and transmission electron microscopy. These fully saturated threads comprise between 20% and 45% of the sample. Furthermore, 13C-13C spin exchange experiments indicate that the length of the fully saturated regions of the threads exceeds 2.5 nm. Two-dimensional 13C-13C NMR spectra showing bonding between chemically nonequivalent sites rule out enumerated single-site thread structures such as polytwistane or tube (3,0) but are consistent with multisite degree-6 nanothreads. Approximately a third of the carbon is in "degree-4" nanothreads with isolated double bonds. The presence of doubly unsaturated degree-2 benzene polymers can be ruled out on the basis of 13C-13C NMR with spin exchange rateconstants tuned by rotational resonance and 1H decoupling. A small fraction of the sample consists of aromatic rings within the threads that link sections with mostly saturated bonding. NMR provides the detailed bonding information necessary to refine solid-state organic synthesis techniques to produce pure degree-6 or degree-4 carbon nanothreads.

Isotope Dependence and Quantum Effects on Atomic Hydrogen Diffusion in Liquid Water.

Relative diffusion coefficients were determined in water for the D, H, and Mu isotopes of atomic hydrogen by measuring their diffusion-limited spin-exchange rate constants with Ni(2+) as a function of temperature. H and D atoms were generated by pulse radiolysis of water and measured by time-resolved pulsed EPR. Mu atoms are detected by muonium spin resonance. To isolate the atomic mass effect from solvent isotope effect, we measured all three spin-exchange rates in 90% D2O. The diffusion depends on the atomic mass, demonstrating breakdown of Stokes-Einstein behavior. The diffusion can be understood using a combination of water "cavity diffusion" and "hopping" mechanisms, as has been proposed in the literature. The H/D isotope effect agrees with previous modeling using ring polymer molecular dynamics. The "quantum swelling" effect on muonium due to its larger de Broglie wavelength does not seem to slow its "hopping" diffusion as much as predicted in previous work. Quantum effects of both the atom mass and the water librations have been modeled using RPMD and a qTIP4P/f quantized flexible water model. These results suggest that the muonium diffusion is very sensitive to the Mu versus water potential used.

Hydrodynamic and nonhydrodynamic contributions to the bimolecular collision rates of solute molecules in supercooled bulk water.

Bimolecular collision rate constants of a model solute are measured in water at T = 259–303 K, a range encompassing both normal and supercooled water. A stable, spherical nitroxide spin probe, perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl, is studied using electron paramagnetic resonance spectroscopy (EPR), taking advantage of the fact that the rotational correlation time, τR, the mean time between successive spin exchanges within a cage, τRE, and the long-time-averaged spin exchange rate constants, Kex, of the same solute molecule may be measured independently. Thus, long- and short-time translational diffusion behavior may be inferred from Kex and τRE, respectively. In order to measure Kex, the effects of dipole–dipole interactions (DD) on the EPR spectra must be separated, yielding as a bonus the DD broadening rate constants that are related to the dephasing rate constant due to DD, Wdd. We find that both Kex and Wdd behave hydrodynamically; that is to say they vary monotonically with T/η or η/T, respectively, where η is the shear viscosity, as predicted by the Stokes–Einstein equation. The same is true of the self-diffusion of water. In contrast, τRE does not follow hydrodynamic behavior, varying rather as a linear function of the density reaching a maximum at 276 ± 2 K near where water displays a maximum density.

High-pressure EPR spectroscopy: paramagnetic exchange of organic radicals with iron (III) acetylacetonate

In this work the spin exchange between organic radicals and a paramagnetic transition metal complex is studied as a function of pressure. Spin exchange rate constants of the tetracyanoethene radical anion (TCNE•−) and 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO) with iron (III) acetylacetonate (Fe(acac)3) were measured at elevated pressures with the help of electron paramagnetic resonance (EPR) spectroscopy. As the reactions are diffusion controlled, the effect of pressure on the paramagnetic exchange is examined by comparison of experimental rate constants, determined from line-broadening experiments, with the corresponding theoretical ones. The activation volumes of the reactions were between 4 and 8 mol−1 cm3, consistent with results reported in literature.

Bimolecular Encounters and Re-Encounters (Cage Effect) of a Spin-Labeled Analogue of Cholestane in a Series of n-Alkanes: Effect of Anisotropic Exchange Integral

Electron paramagnetic resonance (EPR) spectra of the nitroxide spin probe 3β-doxyl-5α-cholestane (CSL) are studied as functions of the molar concentration, c, and the temperature, T, in a series of n-alkanes. The results are compared with a similar study of a much smaller spin probe, perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (pDT). The Heisenberg spin exchange (HSE) rate constants, K(ex), of CSL are similar in hexane, octane, and decane and are about one-half of those for pDT in the same solvents. They are also about one-half of the Stokes-Einstein-Perrin prediction. This reduction in HSE efficiency is attributed to an effective steric factor, f(eff), which was evaluated by comparing the results with the Stokes-Einstein-Perrin prediction or with pDT, and it is equal to 0.49 ± 0.03, independent of temperature. The unpaired spin density in CSL is localized near one end of the long molecule, so the exchange integral, J, leading to HSE, is expected to be large in some collisions and small in others; thus, J is modeled by an ideal distribution of values of J = J(0) with probability f and J = 0 with probability (1 - f). Because of rotational and translation diffusion during contact and between re-encounters of the probe, the effective steric factor is predicted to be f(eff) = f(1/2). Estimating the fraction of the surface of CSL with rich spin density yields a theoretical estimate of f(eff) = 0.59 ± 0.08, in satisfactory agreement with experiment. HSE is well described by simple hydrodynamic theory, with only a small dependence on solvent-probe relative sizes at the same value of T/η, where η is the viscosity of the solvent. This result is probably due to a fortuitous interplay between long- and short-range effects that describe diffusion processes over relatively large distances. In contrast, dipole-dipole interactions (DD) as measured by the line broadening, B(dip), and the mean time between re-encounters within the cage, τ(RE), vary significantly with the solvent-probe size ratio at the same value of T/η. For these phenomena, dominated by short-range diffusion, the reciprocal fractional free volume V(0)/V(f) provides a better description of the diffusion. Thus, B(dip) and τ(RE) form common curves when plotted vs V(0)/V(f). As a result, the fractional broadening by DD occurs at an order of magnitude higher values of T/η for CSL compared with pDT.

Rotational and Translational Diffusion of Spin Probes in Room-Temperature Ionic Liquids

We have studied the rotational and translational diffusion of the spin probe 4-hydroxy-2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPOL) in five imidazolium-based room-temperature ionic liquids (RTILs) and glycerol by means of X-band electron paramagnetic resonance (EPR) spectroscopy. Rotational correlation times and rate constants of intermolecular spin exchange have been determined by analysis of the EPR line shape at various temperatures and spin probe concentrations. The model of isotropic rotational diffusion cannot account for all spectral features of TEMPOL in all RTILs. In highly viscous RTILs, the rotational mobility of TEMPOL differs for different molecular axes. The translational diffusion coefficients have been calculated from spin exchange rate constants. To this end, line shape contributions stemming from Heisenberg exchange and from the electron-electron dipolar interaction have been separated based on their distinct temperature dependences. While the Debye-Stokes-Einstein law is found to apply for the rotational correlation times in all solvents studied, the dependence of the translational diffusion coefficients on the Stokes parameter T/η is nonlinear; i.e., deviations from the Stokes-Einstein law are observed. The effective activation energies of rotational diffusion are significantly larger than the corresponding values for translational motion. Effects of the identity of the RTIL cations and anions on the activation energies are discussed.

Rotational and Translational Mobility of Nitroxide Spin Probes in Ionic Liquids and Molecular Solvents

Rotational and translational movements of 1-oxyl-2,2,6,6-tetramethyl-4-oxypiperidine (TEMPOL) spin probe in the room temperature ionic liquid (RTIL) 1-octyl-3-methylimidazolium tetrafluoroborate (omimBF4) and in two molecular solvents, 1-propanol and isopropyl benzene (cumene), have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Rotational correlation times τ c of spin probes and the intermolecular spin exchange rate constants k e were measured from EPR spectra at different temperatures and TEMPOL concentrations, and compared with the published data. The τ c values were calculated both by known equations and from the EPR spectra simulation. Rotation movements of TEMPOL in omimBF4 cannot be described by the model of the isotropic Brownian diffusion, which is valid for conventional solvents. The correct modeling of EPR spectra in RTIL can be achieved with the assumption of different rotational mobility of the spin probe around different molecular axes. The rotational, D rot, and translational, D tr, diffusion coefficients were calculated from τ c and k e values. The Debye–Stokes–Einstein law is valid in all three solvents while the dependence of D tr on T/η is not linear in Stokes–Einstein coordinates. The effective activation energy E rot a of the rotational movements in omimBF4 is noticeably higher than the corresponding values for conventional solvents, while the effective activation energies E tr a of the translational movements are comparable in all solvents studied.

Measurement of the spin-exchange and chemical ionization rate constants in collisions of polarized metastable 23 S 1 helium atoms with 32 S 1/2 sodium atoms

Experimental data on the spin-exchange rate constants for the He(23S1)-Na(32S1/2) system are reported for the first time. Measurements show that the spin-exchange rate constant is Cse = (23 ± 11) × 10−10 cm3 s−1 and the chemical ionization rate constant is Csi = (29 ± 14) × 10−10 cm3 s−1 at a temperature of 420 K. The results are compared with the data calculated from the rate constants.

Effect of Viscosity on the Spin Exchange of TCNE and TEMPO Radicals with Iron(III) Acetylacetonate

The spin exchange of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and the radical anion of tetracyanoethene (TCNE), with iron acetylacetonate, Fe(acac)3, was investigated as a function of solvent viscosity and temperature by X-band EPR spectroscopy. Acetone, methanol, ethanol, 1-propanol, 1-pentanol, 1-hexanol, 1-octanol, and chloroform were used as solvents because they provide a wide range of viscosity. The spin exchange rate constants measured in the different solvents ranged from 3 × 108 to 8 × 109 M−1 s−1, and from 7 × 108 to 1 × 1010 M−1 s−1 for the TEMPO/Fe(acac)3 and the TCNE/Fe(acac)3 systems, respectively. The spin exchange rate constants, k e, are compared with the corresponding diffusion rate constants. It was found that the k e values correlate well with those of diffusion and hence the intermolecular spin exchange is strongly diffusion-controlled. The activation energies and pre-exponential factors are calculated from the Arrhenius plots.

Collision-induced spin exchange of alkali-metal atoms withH3e: Anab initiostudy

We present a rigorous quantum study of spin-exchange transitions in collisions of the alkali-metal atoms with $^{3}\text{H}\text{e}$ in the presence of an external magnetic field. Using accurate ab initio interaction potentials, we obtain refined estimates for the Fermi contact interaction constants for complexes of Na, K, and Rb atoms with $^{3}\text{H}\text{e}$. Ab initio calculations show that the Fermi contact interaction in $\text{Li-}^{3}\text{H}\text{e}$ varies more slowly with internuclear distance than predicted by the atomic model [R. M. Herman, Phys. Rev. 37, A1062 (1965)]. The calculated spin-exchange rate constants for Na, K, and Rb atoms in a gas of $^{3}\text{H}\text{e}$ are in good agreement with experimental data. Our calculations demonstrate that at a temperature of 0.5 K, collision-induced spin exchange of the alkali-metal atoms occurs at a very slow rate of $\ensuremath{\sim}{10}^{\ensuremath{-}22}\text{ }{\text{cm}}^{3}/\text{s}$, suggesting potential applications in cryogenic cooling, precision spectroscopy, and quantum optics.

Probing molecular geometry of solids by nuclear magnetic resonance spin exchange at the n=0 rotational-resonance condition

Exploration of the molecular geometry in rotating powder solids on the basis of magnetization exchange between spins with identical isotropic chemical shifts but differing chemical shielding tensor orientations is demonstrated experimentally. For this we take advantage of the potential of the ODESSA (one-dimensional exchange spectroscopy by sidebands alternation) experiment for the accurate measurement of spin exchange rate constants. We also report the observation of oscillatory behavior of the rotor-driven magnetization exchange at this so-called n=0 rotational-resonance condition which, in contrast to n=1,2,3,… rotational-resonance conditions, takes place at nearly arbitrary magic-angle spinning frequencies. The sensitivity of the longitudinal exchange decays to the relevant physical parameters of the spin system under conditions of rotor-driven and proton-driven magnetization exchange is discussed theoretically and demonstrated experimentally. Several C13 and P31 spin-exchange measurements have been performed on a series of model compounds covering a broad range of internuclear distances between carboxyl carbon atoms, and on a series of phosphorylated amino acids with different internuclear distances between phosphorus sites. The capacity of the ODESSA experiment for an unambiguous recognition of distinct internuclear distances is demonstrated. Potential applications of such measurements involve the exploration of intermolecular distances and the determination of the mutual orientation of neighboring molecular fragments in polycrystalline and noncrystalline solids.

Mechanism of relaxation enhancement of spin labels in membranes by paramagnetic ion salts: dependence on 3d and 4f ions and on the anions.

Progressive saturation EPR measurements and EPR linewidth determinations have been performed on spin-labeled lipids in fluid phospholipid bilayer membranes to elucidate the mechanisms of relaxation enhancement by different paramagnetic ion salts. Such paramagnetic relaxation agents are widely used for structural EPR studies in biological systems, particularly with membranes. Metal ions of the 3d and 4f series were used as their chloride, sulfate, and perchlorate salts. For a given anion, the efficiency of relaxation enhancement is in the order Mn(2+) > or = Cu(2+) > Ni(2+) > Co(2+) approximately Dy(3+). A pronounced dependence of the paramagnetic relaxation enhancement on the anion is found in the order ClO(-)(4) > Cl(-) > SO(2-)(4). This is in the order of the octanol partition coefficients multiplied by spin exchange rate constants that were determined for the different paramagnetic salts in methanol. Detailed studies coupled with theoretical estimates reveal that, for the chlorides and perchlorates of Ni(2+) (and Co(2+)), the relaxation enhancements are dominated by Heisenberg spin exchange interactions with paramagnetic ions dissolved in fluid membranes. The dependence on membrane composition of the relaxation enhancement by intramembrane Heisenberg exchange indicates that the diffusion of the ions within the membrane takes place via water-filled defects. For the corresponding Cu(2+) salts, additional relaxation enhancements arise from dipolar interactions with ions within the membrane. For the case of Mn(2+) salts, static dipolar interactions with paramagnetic ions in the aqueous phase also make a further appreciable contribution to the spin-label relaxation enhancement. On this basis, different paramagnetic agents may be chosen to optimize sensitivity to different structurally correlated interactions. These results therefore will aid further spin-label EPR studies in structural biology.

Impact of theRb87singlet scattering length on suppressing inelastic collisions

A computation of $^{87}\mathrm{\ensuremath{-}}^{87}$Rb spin-exchange rate constants as functions of the two-body singlet scattering length ${\mathrm{a}}_{\mathrm{s}}$ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for ${\mathrm{a}}_{\mathrm{s}}$. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the $^{87}\mathrm{Rb}$ singlet scattering length (74--102 a.u.).

Time-Resolved ESR Study of Spin Exchange Processes in the Photoreduction of 9,10-Anthraquinone-1,5-disulfonate

The photoreduction of 9,10-anthraquinone-1,5-disulfonate by 2,2,6,6-tetramethlypiperdine in aqueous solution was studied on the nanosecond and microsecond time scales using time-resolved optical and ESR measurements. The lifetime of the 9,10-anthraquinone-1,5-disulfonate triplet in aqueous solution was determined to be 135 ns and the electron transfer rate constant from 2,2,6,6-tetramethlypiperidene to be k{sub N}=5.7 x 10{sup 8}M{sup -1} s{sup -1}. This system allowed both radicals of the pair, the anthraquinone anion and (for the first time) the aminyl radical, to be studied by ESR. The radicals are spin polarized (CIDEP) by both the triplet and geminate radical pair mechanisms. Time-resolved ESR experiments were carried out with the transient nutation and Fourier transform techniques. Because of steric hindrance, the recombination reaction in the quinone-piperidine system is suppressed and, therefore, the spin dynamics are dominated by spin polarization, relaxation, and spin exchange. A quantitative analysis by modified Bloch equations allowed polarization factors (triplet mechanism and radical pair mechanism), spin relaxation times (T{sub 1} and T{sub 2}), and the spin exchange rate constants between the anthraquinone anion and aminyl radicals to be obtained. The spin exchange rate constants between quinone-aminyl radical pairs and between aminyl-aminyl radical pairs are identical and are in the diffusion-controlled limit (k{submore » ex} = 4.5 x 10{sup 9} M{sup -1} s{sup -1}). 30 refs., 9 figs., 3 tabs.« less

Theoretical aspects of chemically induced magnetic polarization

The role of theory in guiding and simplifying interpretation of electron spin resonance experiments on photochemical and other reactions involving free radical intermediates is surveyed. Emphasis is on models which provide a physical picture as well as quantitative estimates for such phenomena as the radical pair mechanism of chemically induced electron spin polarization (CIDEP), the closely related process of spin exchange during radical-radical encounters, and spin lattice relaxation. Some specific topics discussed are: 1) an improved quantitative model of STo CIDEP combining an initial stage of polarization development followed partial loss of this polarization to spin exchange, 2) the relation between the spin exchange and recombination rate constants, and 3) simplification of spin-lattice relaxation in the common case of spin-rotation relaxation. The modification of the polarization processes in two-dimensional and closed three-dimensional systems is also discussed

Addition and spin exchange rate constants by longitudinal field μSR: The Mu+NO reaction

The addition reaction Mu+NO+M→MuNO+M and the spin exchange reaction Mu(↑) +MO(↓)→Mu(↓)+NO(↑) have been measured by longitudinal field μSR at room temperature in the presence of up to 58 atm of N2 as inert collider. The pressure dependence of the longitudinal relaxation rate due to the addition reaction (λc) demostrates that the system is still in the low pressure regime in this pressure range. The corresponding termolecular rate constant has been determined ask0,Mu=(1.10±0.25)×10−32 cm6 molecules−2 s−1, almost 4 times smaller than the corresponding H atom reactionk0,H=3.90×10−32 cm6 molecules−2 s−1 [I.M. Campbell et al., J. Chem. Soc. Faraday Trans. 1.71 (1975) 2097]. The average value of the spin exchange rate constants in the 2.5–58 atm pressure range,kSE=(3.16±0.06)×10−10 cm3 molecule−1 s−1, is in good agreement with previous values obtained by transverse field μSR [D.G. Fleming et al., J. Chem. Phys. 73 (1980) 2751].

Spin-polarized deuterium in magnetic traps.

We have calculated the spin-exchange two-body rate constants associated with the population dynamics of the hyperfine levels of atomic deuterium as a function of magnetic field in the Boltzmann zero-temperature limit. Results indicate that a gas of low-field--seeking deuterium atoms trapped in a static magnetic field minimum decays rapidly into an ultrastable gas of doubly spin-polarized deuterium. We also discuss the temperature dependence of various effects.

Spin-Polarized Deuterium: Stabilization in Magnetic Traps

We report on a calculation of the spin-exchange two-body rate constants associated with the population dynamics of the hyperfine levels of atomic deuterium as a function of magnetic field in the Boltzmann zero temperature limit. We find that a gas of low field seeking deuterium atoms trapped in a static magnetic field minimum decays rapidly into an ultra stable gas of doubly spin-polarized deuterium.

EPR investigation of the intermediate spin exchange regime

The electron paramagnetic resonance spectra of di-tert butylnitroxide (DTBN) are studied as a function of the nitroxide concentration in three hydrocarbon solvents at constant temperature. In the concentration range studied, DTBN undergoes electron spin exchange which leads to broadening, shifting, and eventual collapse of the lines forming the 19-line proton hyperfine pattern. Particular emphasis is given to the spin exchange frequencies ωHE in the region in which they are comparable with the proton hyperfine coupling constants—the intermediate spin exchange regime. Both linewidths and line shapes are found to be in full accord with theory in the intermediate exchange regime which completes the demonstration that theory and experiment are in agreement, the slow and fast exchange regimes having been studied many times in the past. Modeling the spectral lines as Lorentzian–Gaussian convolutions allows a detailed exposition of the collapse of the hyperfine structure as ωHE increases and this collapse, too, is well described by theory. Bimolecular spin exchange rate constants are compared with the prediction of simple hydrodynamic theory.

Electron spin resonance study of spin exchange in a nematic solvent

Spin-exchange rate constants have been measured from the concentration dependence of the e.s.r. linewidths of two nitroxide radicals, TANONE (4-oxo-2,2,6,6-tetramethylpiperidino-oxy) and M-DOXYL [2-hexyl-2-(10′-methoxycarbonyldecyl)-4,4-dimethyloxazolidinyl-3-oxyl], in the isotropic and nematic phases of MBBA. Strong exchange is observed for TANONE in both phases and for M-DOXYL in the isotropic phase but the latter radical exhibits weak exchange in the nematic phase. A qualitative discussion of the nature of the radical–radical encounters affords an explanation of the observations.