Heisenberg spin exchange and molecular diffusion in liquid crystals

Solute Diffusion into Polymer Swollen by Supercritical CO2 by High-Pressure Electron Paramagnetic Resonance Spectroscopy and Chromatography

High-pressure electron paramagnetic resonance (EPR) was used to measure translational diffusion coefficients (D_tr) of a TEMPONE spin probe in poly(D,L-lactide) (PDLLA) and swollen in supercritical CO₂. D_tr was measured on two scales: macroscopic scale (>1 μm), by measuring spin probe uptake by the sample; and microscopic scale (<10 nm), by using concentration-dependent spectrum broadening. Both methods yield similar translational diffusion coefficients (in the range 5-10 × 10^-12 m²/s at 40-60 °C and 8-10 MPa). Swollen PDLLA was found to be homogeneous on the nanometer scale, although the TEMPONE spin probe in the polymer exhibited higher rotational mobility (τ_corr = 6 × 10^-11 s) than expected, based on its D_tr. To measure distribution coefficients of the solute between the swollen polymer and the supercritical medium, supercritical chromatography with sampling directly from the high-pressure vessel was used. A distinct difference between powder and bulk polymer samples was only observed at the start of the impregnation process.

Influence of the Electric Charge of Spin Probes on Their Diffusion in Room-Temperature Ionic Liquids

The rotational and translational diffusion of negatively charged and uncharged spin probes in five imidazolium-based room-temperature ionic liquids (RTILs), 1-ethyl-3-methylimidazolium tetrafluoroborate, emimBF₄, 1-butyl-3-methylimidazolium tetrafluoroborate, bmimBF₄, 1-octyl-3-methylimidazolium tetrafluoroborate, omimBF₄, 1-octyl-3-methylimidazolium hexafluorophosphate, omimPF₆, and 1-octyl-3-methylimidazolium chloride, omimCl, has been studied by means of electron paramagnetic resonance spectroscopy. Detailed analyses of the spin-Hamiltonian parameters and spin exchange interactions have been carried out. The temperature dependences of the line broadening induced by the electronic dipole-dipole interaction and the electron spin exchange coupling are determined. The translational mobility of spin probes is semiquantitatively characterized and successfully explained in the framework of a hypothesis based on the assumption of polar and unpolar domains within the RTILs.

Field-cycling NMR and DNP - A friendship with benefits

Field-cycling relaxometry, or rather its electronic version with a resistive magnet which requires signal detection at a field strength of 1 Tesla or below, remains an inherently insensitive technique due to the construction compromise that goes along with the need for a fast-switching, low-inductance magnet. For the same reasons, signal lifetime is short and frequency resolution is typically not given, at least for the predominantly used hydrogen nuclei. Dynamic Nuclear Polarization (DNP) bears the potential to circumvent these disadvantages: not only has it been demonstrated to enhance magnetization by up to three orders of magnitude beyond its thermal value, but it also provides the possibility to address particular parts of a molecule, thus generating selectivity even in the absence of spectral resolution. At the same time, DNP requires the introduction of stable radicals giving rise to additional relaxation contributions. This article presents a straightforward way to recover the native relaxation rates of the undisturbed system, and shows examples in different research fields where field-cycling relaxometry is traditionally used for refining models of molecular dynamics and interactions.

Continuous Diffusion Model for Concentration Dependence of Nitroxide EPR Parameters in Normal and Supercooled Water

Electron paramagnetic resonance (EPR) spectra of radicals in solution depend on their relative motion, which modulates the Heisenberg spin exchange and dipole-dipole interactions between them. To gain information on radical diffusion from EPR spectra demands both reliable spectral fitting to find the concentration coefficients of EPR parameters and valid expressions between the concentration and diffusion coefficients. Here, we measured EPR spectra of the 14N- and 15N-labeled perdeuterated TEMPONE radicals in normal and supercooled water at various concentrations. By fitting the EPR spectra to the functions based on the modified Bloch equations, we obtained the concentration coefficients for the spin dephasing, coherence transfer, and hyperfine splitting parameters. Assuming the continuous diffusion model for radical motion, the diffusion coefficients of radicals were calculated from the concentration coefficients using the standard relations and the relations derived from the kinetic equations for the spin evolution of a radical pair. The latter relations give better agreement between the diffusion coefficients calculated from different concentration coefficients. The diffusion coefficients are similar for both radicals, which supports the presented method. They decrease with lowering temperature slower than is predicted by the Stokes-Einstein relation and slower than the rotational diffusion coefficients, which is similar to the diffusion of water molecules in supercooled water.

Multiple scale investigation of molecular diffusion inside functionalized porous hosts using a combination of magnetic resonance methods

Diffusion in organo-functionalized porous hosts could be tracked by evaluation of spin exchange processes using EPR spectroscopy.

Determination of very rapid molecular rotation by using the central electron paramagnetic resonance line

Picosecond rotational correlation times of perdeuterated tempone (PDT) are found in alkane and aromatic liquids by directly using the spectral width of the central electron paramagnetic resonance line. This is done by mathematically eliminating the nonsecular spectral density from the spectral parameter equations, thereby removing the need to assume a particular form for it. This is preferable to fitting a constant correction factor to the spectral density, because such a factor does not fit well in the low picosecond range. The electron-nuclear spin dipolar interaction between the probe and solvent is shown to be negligible for the very rapid rotation of PDT in these liquids at the temperatures of the study. The rotational correlation times obtained with the proposed method generally agree to within experimental uncertainty with those determined by using the traditional parameters. Using the middle line width offers greater precision and smoother trends. Previous work with the central line width is discussed, and past discrepancies are explained as possibly resulting from residual inhomogeneous broadening. The rotational correlation time almost forms a common curve across all of the solvents when plotted with respect to isothermal compressibility, which shows the high dependence of rotation on liquid free volume.

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.

Experimental method to measure the effect of charge on bimolecular collision rates in electrolyte solutions

A stable, monoprotic nitroxide spin probe is utilized as a model to study molecular collisions in aqueous electrolyte solutions. The rate constants of bimolecular collisions, K(col) for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (CP) when it is uncharged (at low pH) and K(col)⁻ when it is charged (CP⁻; at high pH), are measured as functions of temperature and ionic strength. The ratio f* ≡ K(col)⁻/K(col) is a direct measure of the effect of charge on the collision rate. Neglecting the small differences in size and diffusion coefficients of CP and CP⁻, f* is the fractional change in collision rate due to Coulomb repulsion which was treated theoretically in Debye's classic paper [Trans. Electr. Chem. Soc. 1942, 82, 265]. K(col) and K(col)⁻ are determined from EPR spectral changes due to spin-spin interactions which are dominated by Heisenberg spin exchange under the conditions of these experiments. Values of f* vary linearly with values of κ · d in the range 0.4 < κ · d < 1.8, where κ and d are the inverse Debye screening length and the distance at closest approach, respectively. Values of d obtained in two independent ways, (1) from rotational correlation times measured by EPR and (2) by insisting that the experimental results be consistent with the Debye theory at infinite dilution, yield similar results. As the ionic strength is increased (κ increased), the screening effect reduces the effect of the Coulomb barrier more slowly than predicted by the Debye theory. While values of K(col) and K(col)⁻ vary substantially with T, approximately following the Stokes-Einstein-Smoluchowski equation, values of f* depend only slightly on temperature at a given value of κ · d, as is predicted by Debye's theory.

Nitroxide spin exchange due to re-encounter collisions in a series of n-alkanes

Bimolecular collisions between perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-l-oxyl molecules in three alkanes have been studied by measuring the electron paramagnetic resonance (EPR) spectral changes induced by spin exchange. We define an "encounter" to be a first-time collision followed by a series of re-encounters prior to the diffusing pair's escaping each other's presence. The present work stems from a recent proposal [B. L. Bales et al., J. Phys. Chem. A 107, 9086 (2003)] that an unexpected linear dependence of the spin-exchange-induced EPR line shifts on spin-exchange frequency can be explained by re-encounters of the same probe pair during one encounter. By employing nonlinear least-squares fitting, full use of the information available from the spectral changes allows us to study encounters and re-encounters separately. The encounter rate constants appear to be dominated by hydrodynamic forces, forming a common curve for hexane, decane, and hexadecane when plotted against T/eta, where eta is the shear viscosity. Unexpectedly, encounters are not dependent on the ratio mu = a/a(s), where a and a(s) are the van der Waals radii of the nitroxide probe and the solvent, respectively. It is argued that the near coincidence of the resulting encounter rate constant with the hydrodynamic prediction is likely due to a near cancellation of terms in the general diffusion coefficient. Thus, the semblance of hydrodynamic behavior is coincidental rather than intrinsic. In contrast, the mean times between re-encounters do depend on the relative sizes of probe and solvent. For hexane at lower temperatures, the Stokes-Einstein equation apparently describes re-encounters well; however, at higher temperatures and for decane and hexadecane, departures from the hydrodynamic prediction become larger as mu becomes smaller. This is in qualitative agreement with the theory of microscopic diffusion of Hynes et al. [J. Chem. Phys. 70, 1456 (1979)]. These departures are well correlated with the free volume available in the solvent; thus, the mean times between re-encounters form a common curve when plotted versus the free volume. Because free volume is manifested macroscopically by the isothermal compressibility, it is expected and observed that the re-encounter rate also forms a common curve across all three solvents when plotted with respect to compressibility. The existence of a common curve for alkanes raises the prospect of using EPR to determine the compressibility of substances such as fossil fuels and biological membranes.

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated 14N- and 15N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DII is reduced by a factor of between six and thirty compared to the value for T = 295 K is given by (1.3 +/- 0.6) x 10 -10m2s-1 greater than or equal to DII greater than or equal to (2.4 +/- 0.3) x 10-11M2s-1.