Jérôme Hirschinger

A nuclear magnetic resonance answer to the Boltzmann–Loschmidt controversy?

A unique experimental tool to deepen into the Boltzmann–Loschmidt controversy is provided by the NMR polarization echoes (PE). These appear when a local spin excitation, evolving with a many-body “diffusive” spin dynamics, is reversed. The attenuation of the PEs represents a progresive failure of the quantum interferences to rebuild the local excitation. Our results indicate that, in the absence of detectable environmental interactions, the characteristic time of this attenuation is determined by the reversible dynamics itself, i.e., spin–spin interaction time. This supports the Boltzmanns hypothesis of molecular “chaos”.

19F/29Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

19F/29Si Hartmann-Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated 29Si-19F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si-F internuclear distance, r = 2.62 +/- 0.05 A, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69 +/- 0.04 A recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of approximately 14 kHz is shown to be necessary for an effective suppression of 19F-19F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.

A 13C solid-state NMR study of the structure and auto-oxidation process of natural and synthetic melanins.

This paper presents a 13C CP/MAS NMR study of the melanin pigments obtained through natural and synthetic origins: sepia-melanin from squid ink and three synthetic 5,6-dihydroxyindole-melanins prepared using different non-enzymatic oxidation pathways. The synthetic pigments can be distinguished from natural melanin by the absence of aliphatic carbons, thereby confirming the unreacted 3,4-dihydroxyphenylalanine and the proteinaceous origins of the aliphatic resonances in natural eumelanin. The spectra of selected non-protonated carbon resonances and those with only protonated carbon signals led to a quantitative analysis. An auto-oxidative experiment using a synthetic melanin, over a period of 130 h, has shown an unusually slow disappearance of hydrogen peroxide formed in situ. The 13C-NMR spectrum of the insoluble oxidized synthetic melanin compared to that before auto-oxidation clearly demonstrates that the oxidation process is associated with chemical changes within the pigment; i.e., carbonyl functional group formation and an increase of the non-protonated carbons fraction.

Molecular dynamics as studied by static-powder and magic-angle spinning 2H NMR.

The 2H NMR magic-angle spinning (MAS) technique is compared to the static-powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The linewidth of individual spinning sidebands of the one-dimensional MAS spectra are observed to be characteristic of the correlation time from approximately 10(-2) to approximately 10(-8) s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS 2H NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon lineshape distortions due to anisotropic T2 and T1Q relaxation, respectively. All these results are demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the alpha-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound.

Cross-polarization dynamics and proton dipolar local field measurements in some organic compounds

Hartmann–Hahn inversion–recovery cross‐polarization magic‐angle spinning experiments were performed for all types of protonated carbons (CHn with n=1, 2 and 3). The resulting non‐exponential decays were analyzed using both a simple memory function approach and density matrix calculations. Although the memory function approach provides a useful analytical description of the cross‐polarization dynamics, the density matrix method is required to account better for the details of the spin dynamics. 13C‐detected dipolar local fields of protons were measured using the wideline separation experiment. It was observed that the resulting local free induction decays may be quantitatively described by their local second moment. Moreover, the local spin diffusion process controlling the second stage of the cross‐polarization dynamics is directly related to the strength of the local dipolar field of protons.

Cross-polarization dynamics and spin diffusion in some aromatic compounds

The inversion-recovery cross-polarization (IRCP) magic-angle spinning experiment has been applied to study the 13C-1H cross-polarization dynamics of protonated aromatic carbons in ferrocene, 5,6-dimethoxyindole (DMI) and some indole derivatives. Using the 13C-detected proton spin diffusion (SD) experiment recently developed by Zhang et al. [Solid State Nucl. Magn. Reson., 1 (1992) 313], the slow decaying or incoherent stage of the IRCP experiment is shown to be controlled by the spin diffusion process at the directly bound proton. Moreover, a simple phenomenological model treating spin diffusion as a relaxation process provides an excellent agreement with both the IRCP and SD experimental data for all the different C-H pairs of DMI and its derivatives. The resulting time constants of the non-exponential spin diffusion decays are related to the local intra- and intermolecular network of dipolar interactions. This model is nevertheless found to be inadequate for ferrocene because intramolecular spin diffusion then has an inhomogeneous character.

Many-spin quantum dynamics during cross polarization in 8CB

We analyze theoretically and experimentally the quantum dynamics of a three-spin-1/2 system during cross polarization (CP). Our analysis takes into account a Hamiltonian behavior for a carbon 13C coupled to two protons 1H while the coupling to a spin bath is treated in the fast fluctuation approximation. This model is applied to the methylene and biphenyl groups of the smectic and nematic phases of the liquid crystal 4-n-octyl-4′-cyanobiphenyl (8CB). Experimental data from standard CP, combined with our theoretical results, allow us to separate the homonuclear 1H–1H and heteronuclear 1H–13C residual dipolar couplings. These values are in good agreement with those obtained by using a combination of CP under Lee–Goldburg conditions and standard CP data. A well differentiated relaxation behavior among the two phases seems to indicate that while the extreme narrowing approximation is appropriate for the nematic phase, the description of the smectic phase requires consideration of the slow-motion limit.

NMR polarization echoes in a nematic liquid crystal.

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson-Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.

59Co, 23Na NMR and electric field gradient calculations in the layered cobalt oxides NaCoO2 and HCoO2

59Co and 23Na NMR has been applied to the layered cobalt oxides NaCoO(2) and HCoO(2) at three different magnetic field strengths (4.7, 7.1 and 11.7T). The 59Co and 23Na quadrupole and anisotropic shift tensors have been determined by iterative fitting of the NMR line shapes at the three magnetic field strengths. Due to the large 59Co quadrupole interaction in NaCoO(2), a frequency-swept irradiation procedure was used to alleviate the limited bandwidth of the excitation. While the 59Co and 23Na shift and quadrupole coupling tensors in NaCoO(2) are found to be coincident and axially symmetric in agreement with the crystal symmetry requirements, the fits of the 59Co NMR spectra clearly show the presence of structural disorder in HCoO(2). The 23Na chemical shift anisotropy can be reproduced by shift tensor calculations using a point dipole model and considering that the magnetic susceptibility in NaCoO(2) is due to Van Vleck paramagnetism for Co(3+). Electric field gradient calculations using either the empirical point charge model or the ab initio full potential-linearized augmented plane wave method are compared with the experimental NMR data.