NMR measurement of diffusion coefficients by radio-frequency gradients in the case of short relaxation times.

The measurement of translational diffusion coefficients by NMR generally makes use basically of two magnetic field gradient pulses separated by a so-called diffusion interval. The magnetic field gradient arises either from the static magnetic field (denoted by B0 used for polarizing the nuclear spins) or from the radio-frequency field (denoted by B1 used for inducing NMR transitions). The B0 method may be hampered by short effective transverse relaxation times (T2∗), by important gradient rise and fall times or by eddy currents. This does not occur with B1 gradients. Moreover, the effect of short transverse relaxation times during the gradient pulses is reduced by at least a factor of two. However, for B1 gradients, one might face with the limited volume in which the gradient is uniform and with the effect of short relaxation times which imply to reduce the various intervals in the diffusion experiment (this is as well true for the B0 method). Examples will be given for which the measurement of the diffusion coefficient by B0 gradients turned out to be impossible while a proper result was obtained with B1 gradients as far as a correction taking into account the limited volume is applied, together with a correction about the gradient calibration especially when dealing with samples containing paramagnetic species.

Design of a three-loop asymmetric coil producing a homogeneous radiofrequency B1 field gradient along the axis of a vertical sample tube.

A coil system generating a vertical radio-frequency (rf) field gradient (B1 gradient) has been built for surrounding, in a horizontal magnet, a vertical sample (object) of axial symmetry. The system comprises three coaxial loops with an overall shape either spherical or ellipsoidal. The geometry has been theoretically and experimentally devised for producing a very uniform gradient (cancellation of B1 derivatives from second order up to sixth order) in the central region where a vertical receiver/transmitter coil is installed. The latter is of the saddle-shaped type and is geometrically and electrically decoupled from the gradient coil system. This receiver/transmitter coil not only ensures an optimal signal reception but, in addition, is able to deliver perfectly homogeneous rf hard pulses which are mandatory in most NMR experiments. In its present design, the system delivers a uniform gradient in a limited region but could be extended at will. Its main advantages over static field gradients (B0 gradients) appear clearly in the case of very short transverse relaxation times. This property has been emphasized in the case of experiments leading to the measurement of diffusion coefficients. Also, this system would be suitable for chemical shift imaging (CSI) experiments as confirmed by a preliminary test experiment.

On the Observation of 14N Quadrupole Resonance Transitions in Water Proton NMR Relaxometry Dispersion Curves: The Case of a Labile NH Grouping in a Semirigid Molecular Moiety.

The electric field gradient tensor (considered here at the level of a nitrogen nucleus) can be described by two parameters: the largest element in the (X,Y,Z) principal axis system, denoted by VZZ (leading to the nuclear quadrupole coupling), and the asymmetry parameter η = (|VYY| - |VXX|)/|VZZ| with |VZZ| > |VYY| > |VXX|. The frequencies of the three nitrogen-14 nuclear quadrupole resonance (NQR) transitions depend on both parameters but, for sensitivity reasons, their determination may be especially difficult and time consuming. For a partly rigid NH grouping with a labile proton, water nuclear magnetic resonance (NMR) relaxometry curves may exhibit these three transitions (dubbed quadrupolar dips or quadrupole relaxation enhancement (QRE)), provided that the NH grouping belongs to a moiety possessing a sufficient degree of ordering. Their line shape leads to the correlation time describing mainly the motion of the NH grouping (the proton of which being in exchange with water protons), and their amplitude can be interpreted in terms of an effective NH distance. This approach is applied to a hydrogel, where separate NQR lines are observed for the different types of water existing in this system. Furthermore, the analysis of experimental data allows one to determine the nuclear quadrupole coupling in the protonated and deprotonated forms of this molecular moiety involving a labile NH grouping.

Longitudinal relaxation rate measurements for different signals unveiled by nutation spectroscopy: Application to the characterization of two arrangements experienced by water in a clay network.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radiofrequency (rf) field. With an appropriate amplitude of the rf field, the nutation frequency depends on the NMR relaxation times. This property offers the possibility of differentiating species having the same Larmor frequency but differing by their relaxation times. This may occur for the composite proton NMR signal of water in complex systems. Separate nutation signals are thus observed with the possibility of measuring their longitudinal relaxation times by simply applying a saturation hard pulse, followed by an evolution interval, prior to the nutation sequence. This novel experiment has been used for studying the two sites existing for water in two kaolinite samples (one hydrated after stabilization of several months and the other nonhydrated). It turns out that water in these two sites differs essentially by its transverse relaxation time. Moreover, recovery is surprisingly biexponential for these two signals. A proper analysis of results obtained by this saturation-recovery nutation experiment provides not only the specific longitudinal relaxation rates of water in these two sites but also information about the averaging which occurs at long evolution times. This is discussed with regard of the structure and organization of the clay network. In particular, from relaxation rates at short evolution times, it is shown that this network is mainly constituted of ordered platelets, with a relatively weak proportion of randomly distributed platelets.

Proton nutation spectroscopy. Application to the quantitation of water in a kaolinite sample.

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radio-frequency field. Depending on the amplitude of the rf field, the nutation frequency may be sensitive to the two longitudinal and transverse relaxation rates R1 and R2, hence the possibility of differentiating species having the same resonance frequency in the laboratory frame (the Larmor frequency) but differing by their relaxation rates, as it may occur for the composite proton NMR signal of water in complex systems. Thus, Fourier transform of the nutation curve should provide separate peaks associated with the different species involved in a composite classical NMR signal. As nutation peaks may be close to zero frequency (or even at zero frequency), their full observation requires a complex Fourier transform. This implies a second nutation curve, de-phased by 90° with respect to the first one, achieved here by a second nutation experiment preceded by a 90° hard pulse. Eventually, more accurate parameters are obtained by a non-linear least-squares analysis of the simple nutation experiment. This methodology is applied to water in a natural clay (kaolinite) and reveals the unexpected presence of two peaks which can be characterized by the relaxation rates derived from the line-widths of the nutation signals.

Measurement of short transverse relaxation times by pseudo-echo nutation experiments.

Very short NMR transverse relaxation times may be difficult to measure by conventional methods. Nutation experiments constitute an alternative approach. Nutation is, in the rotating frame, the equivalent of precession in the laboratory frame. It consists in monitoring the rotation of magnetization around the radio-frequency (rf) field when on-resonance conditions are fulfilled. Depending on the amplitude of the rf field, nutation may be sensitive to the two relaxation rates R1 and R2. A full theoretical development has been worked out for demonstrating how these two relaxation rates could be deduced from a simple nutation experiment, noticing however that inhomogeneity of the rf field may lead to erroneous results. This has led us to devise new experiments which are the equivalent of echo techniques in the rotating frame (pseudo spin-echo nutation experiment and pseudo gradient-echo experiment). Full equations of motion have been derived. Although complicated, they indicate that the sum of the two relaxation rates can be obtained very accurately and not altered by rf field inhomogeneity. This implies however an appropriate data processing accounting for the oscillations which are superposed to the echo decays and, anyway, theoretically predicted. A series of experiments has been carried out for different values of the rf field amplitude on samples of water doped with a paramagnetic compound at different concentrations. Pragmatically, as R1 can be easily measured by conventional methods, its value is entered in the data processing algorithm which then returns exclusively the value of the transverse relaxation time. Very consistent results are obtained that way.

Direct 1H NMR evidence of spin-rotation coupling as a source of para → ortho-H2 conversion in diamagnetic solvents.

At ambient temperature, conversion from 100% enriched para-hydrogen (p-H2; singlet state) to ortho-hydrogen (o-H2; triplet state) leads necessarily to the thermodynamic equilibrium proportions: 75% of o-H2 and 25% of p-H2. When p-H2 is dissolved in a diamagnetic organic solvent, conversion is very slow and can be considered as arising from nuclear spin relaxation phenomena. A first relaxation mechanism, specific to the singlet state and involving a combination of auto-correlation and cross correlation spectral densities, can be retained: randomly fluctuating magnetic fields due to inter-molecular dipolar interactions. We demonstrate here that (i) this dipolar mechanism is not sufficient for accounting for the para→ortho conversion rate, (ii) spin-rotation interaction, an intra-molecular mechanism, behaves similarly to random-field interaction and, thus, may be involved in the singlet relaxation rate. Also, as the para→ortho conversion is monitored by proton nuclear magnetic resonance (NMR) of dissolved o-H2 (p-H2 is NMR-silent), one has to account for H2 exchange between the liquid phase and the gas phase within the NMR tube, as well as for dissolution effects. Experimental evidence of the above statements is brought here in the case of two organic solvents: acetone-d6 and carbon disulfide. The observed temperature dependence of the para→ortho conversion rate shows that spin-rotation can be the dominant contribution to the p-H2 relaxation rate in the absence of tangible dipolar interactions. Our findings shed new light on the "mysterious" mechanism of the para→ortho conversion which has been searched for several decades.

Toward nitrogen-14 nuclear quadrupole resonance imaging by nutation experiments performed with a radio-frequency field gradient.

Until now, NQR imaging has been considered mainly in the case of Chlorine-35. This is a spin 3/2 resonating at relatively high frequency (around 30MHz) thus affording a favorable sensitivity. Conversely, Nitrogen-14 (spin 1) NQR is much less sensitive because its resonances frequencies are below 6MHz. In contrast to already existing methodologies for object localization by 14N NQR, we present here a new, more straightforward, approach and the principles of space dependent 14N Quadrupole Resonance are laid down. The method is based on nutation curves obtained with an inhomogeneous radio-frequency field produced by a dedicated transmit-receive coil. The gradient created that way does not need to be uniform although more accurate results would be obtained with a uniform gradient. Nutation curves have been simulated by a specially designed algorithm which takes into account the 14N Quadrupole Resonance particularities including the so-called powder average. Preliminary experiments were carried out with the highest resonance frequency (4.64MHz) of sodium nitrite (NaNO2). A cylindrical sample of powder sodium nitrite containing a spacer was used. Simulations of the corresponding nutation curves not only demonstrate the existence of this spacer but, in addition, provide its position and its thickness. This clearly ascertains the feasibility of 14N Quadrupole Resonance imaging.

Electron Spin Polarization Transfer to ortho-H2 by Interaction of para-H2 with Paramagnetic Species: A Key to a Novel para → ortho Conversion Mechanism.

We report that at ambient temperature and with 100% enriched para-hydrogen (p-H2) dissolved in organic solvents, paramagnetic spin catalysis of para → ortho hydrogen conversion is accompanied at the onset by a negative ortho-hydrogen (o-H2) proton NMR signal. This novel finding indicates an electron spin polarization transfer, and we show here that this can only occur if the H2 molecule is dissociated upon its transient adsorption by the paramagnetic catalyst. Following desorption, o-H2 is created until the thermodynamic equilibrium is reached. A simple theory confirms that in the presence of a static magnetic field, the hyperfine coupling between unpaired electrons and nuclear spins is responsible for the observed polarization transfer. Owing to the negative electron gyromagnetic ratio, this explains the experimental results and ascertains an as yet unexplored mechanism for para → ortho conversion. Finally, we show that the recovery of o-H2 magnetization toward equilibrium can be simply modeled, leading to the para → ortho conversion rate.

¹4N Quadrupole Resonance line broadening due to the earth magnetic field, occuring only in the case of an axially symmetric electric field gradient tensor.

As demonstrated before, the application of a weak static B0 magnetic field (less than 10 G) may produce definite effects on the ¹4N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. Here, we address more precisely the problem of the relative orientation of the two magnetic fields (the static field and the radio-frequency field of the pure NQR experiment). For a field of 6G, the evolution of the signal intensity, as a function of this relative orientation, is in very good agreement with the theoretical predictions. There is in particular an intensity loss by a factor of three when going from the parallel configuration to the perpendicular configuration. By contrast, when dealing with a very weak magnetic field (as the earth field, around 0.5 G), this effect drops to ca. 1.5 in the case Hexamethylenetetramine (HMT).This is explained by the fact that the Zeeman shift (due to the very weak magnetic field) becomes comparable to the natural line-width. The latter can therefore be determined by accounting for this competition. Still in the case of HMT, the estimated natural line-width is half the observed line-width. The extra broadening is thus attributed to earth magnetic field. The latter constitutes therefore the main cause of the difference between the natural transverse relaxation time (T2) and the transverse relaxation time derived from the observed line-width (T2(⁎)).

Effect of a weak static magnetic field on nitrogen-14 quadrupole resonance in the case of an axially symmetric electric field gradient tensor.

The application of a weak static B0 magnetic field (less than 1 mT) may produce a well-defined splitting of the (14)N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B0, (ii) the amplitude and pulse duration of the radio-frequency field, B1, used for detecting the NQR signal, and (iii) the relative orientation of B0 and B1. For instance, when B0 is parallel to B1 and regardless of the B0 value, the signal intensity is three times larger than when B0 is perpendicular to B1. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained.

NMR relaxometry study of the interaction of water with a Nafion membrane under acid, sodium, and potassium forms. Evidence of two types of bound water.

Through (1)H NMR relaxometry techniques (determination of the spin-lattice relaxation time as a function of the NMR measurement frequency), we have investigated, on a molecular scale, the water behavior in Nafion NRE 212 under acid, sodium, and potassium forms, the latter arising from different chemical treatments (with and without EDTA). Quantitatively, it turns out that (i) EDTA removes unwanted cations that may affect water mobility and (ii) the natural countercations (sodium and potassium) also affect water mobility according to their size. In order to go further, we have developed a new methodology that rests on the comparison between samples prepared with H2O and D2O. For the latter, residual protons allow us to exclusively access intermolecular contribution to proton relaxation and, thus, enable us to deduce the intramolecular contribution of proton relaxation in H2O. The analysis of this contribution reveals, for the first time, two types of bound water in Nafion.

New application of proton nuclear spin relaxation unraveling the intermolecular structural features of low-molecular-weight organogel fibers.

Proton nuclear spin relaxation has been for the first time extensively used for a structural and dynamical study of low-molecular-weight organogels. The gelator in the present study is a modified phenylalanine amino acid bearing a naphthalimide moiety. From T(1) (spin-lattice relaxation time in the laboratory frame) and T(1ρ) (spin-lattice relaxation time in the rotating frame) measurements, it is shown that the visible gelator NMR spectrum below the liquid-gel transition temperature corresponds to a so-called isotropic compartment, where gelator molecules behave as in a liquid phase but exchange rapidly with the molecules constituting the gel structure. This feature allows one to derive, from accessible parameters, information about the gel itself. Nuclear Overhauser effect spectroscopy (NOESY) experiments have been exploited in view of determining not only cross-relaxation rates but also specific longitudinal rates. The whole set of relaxation parameters (at 25 °C) leads to a correlation time of 5 ns for gelator molecules within the gel structure and 150 ps for gelator molecules in the isotropic phase. This confirms, on one hand, the flexibility of the organogel fibers and, on the other hand, the likely presence of clusters in the isotropic phase. Concerning cross-relaxation rates, a thorough theoretical investigation in multispin systems of direct and relayed correlations in a NOESY spectrum allows one to make conclusions about contacts (around 2-3 Å) not only between naphtalimide moieties of different gelator molecules but also between the phenyl ring and the naphtalimide moiety again of different gelator molecules. As a result, not only is the head-to-tail structure of amino acid columns confirmed but also the entangling of nearby columns by the naphthalimide moieties is demonstrated.

Water behavior in mesoporous materials as studied by NMR relaxometry.

Water in mesoporous materials possessing a two-dimensional hexagonal structure has been studied by the variation of its NMR longitudinal relaxation time T(1) as a function of the static magnetic field value, or equivalently of the NMR measurement frequency. This technique, dubbed relaxometry, has been applied from 5 kHz (measurement frequency) up to 400 MHz with various instruments including a variable-field spectrometer operating between 8 and 90 MHz. Moreover, the range 0-5 kHz could be investigated by transverse relaxation, T(2) denoting the corresponding relaxation time, and relaxation in the rotating frame, T(1ρ) denoting the corresponding relaxation time. Measurements of proton relaxation rates (inverse of relaxation times) have been performed with H(2)O and HOD (residual protons of heavy water) at water volumes of 80%, 60%, and 40% relative to the porous volume. Comparison between H(2)O and HOD shows clearly that, above 1 MHz where both sets of data are superposed, relaxation is purely intermolecular and due to paramagnetic relaxation (dipolar interactions of water protons with unpaired electrons of paramagnetic entities). Below 1 MHz, it is possible to subtract the intermolecular contribution (given by HOD data) from H(2)O data so that one is left with intramolecular relaxation which is solely due to water reorientational motions. The analysis of these low-frequency data (in terms of Lorentzian functions) reveals two types of water within the pores: one interacting strongly with the surface and the other corresponding to a second layer. High-frequency data, which arise from paramagnetic relaxation, exhibit again two types of water. Due to their correlation times, one type is assigned to relatively free water within the pores while the other type corresponds to bulk (interparticular) water. Their proportions, given as a function of the volume fraction, are consistent with the above assignments.

Creation and evolution of net proton hyperpolarization arising from para-hydrogenation.

When a hydrogenation reaction is carried out with gaseous hydrogen enriched in its para- isomer in the earth magnetic field (prior to adiabatic insertion of the sample in the NMR magnet), enhanced proton longitudinal order (represented by 2I(z)(A)I(z)(B)) is created but also difference of enhanced polarizations (I(z)(A)-I(z)(B)). In a first part, it is shown theoretically and experimentally that the longitudinal relaxation time of this polarization difference is roughly twice the ones of individual polarizations. The second part is devoted to a pulse sequence designed for transforming this difference into net hyperpolarization. The evolution of this global hyperpolarization is studied experimentally in a third part and it is observed that a fraction of hyperpolarization possesses an effective longitudinal relaxation time similar to the one of the initial polarization difference. Those experimental results are interpreted by numerical calculations based on Solomon-type equations including the longitudinal order and possibly dipolar-csa cross correlation rates.

Solvent dynamical behavior in an organogel phase as studied by NMR relaxation and diffusion experiments.

An organogelation process depends on the gelator-solvent pair. This study deals with the solvent dynamics once the gelation process is completed. The first approach used is relaxometry, i.e., the measurement of toluene proton longitudinal relaxation time T(1) as a function of the proton NMR resonance frequency (here in the 5 kHz to 400 MHz range). Pure toluene exhibits an unexpected T(1) variation, which has been identified as paramagnetic relaxation resulting from an interaction of toluene with dissolved oxygen. In the gel phase, this contribution is retrieved with, in addition, a strong decay at low frequencies assigned to toluene molecules within the gel fibers. Comparison of dispersion curves of pure toluene and toluene in the gel phase leads to an estimate of the proportion of toluene embedded within the organogel (found around 40%). The second approach is based on carbon-13 T(1) and nuclear Overhauser effect measurements, the combination of these two parameters providing direct information about the reorientation of C-H bonds. It appears clearly that reorientation of toluene is the same in pure liquid and in the gel phase. The only noticeable changes in carbon-13 longitudinal relaxation times are due to the so-called chemical shift anisotropy (csa) mechanism and reflect slight modifications of the toluene electronic distribution in the gel phase. NMR diffusion measurements by the pulse gradient spin-echo (PGSE) method allow us to determine the diffusion coefficient of toluene inside the organogel. It is roughly two-thirds of the one in pure toluene, thus indicating that self-diffusion is the only dynamical parameter to be slightly affected when the solvent is inside the gel structure. The whole set of experimental observations leads to the conclusion that, once the gel is formed, the solvent becomes essentially passive, although an important fraction is located within the gel structure.

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), ß-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, ß-HMX and α-NTO are explosive compounds.

Behavior of cesium and thallium cations inside a calixarene cavity as probed by nuclear spin relaxation. Evidence of cation-pi interactions in water.

We have studied the complexes formed between the p-sulfonatocalix[4]arene and cesium or thallium metal cation, first by carbon-13 longitudinal relaxation of the calixarene molecule at two values of the magnetic field B(0). From the longitudinal relaxation times of an aromatic carbon directly bonded to a proton, thus subjected essentially to the dipolar interaction with that proton, we could obtain the correlation time describing the reorientation of the CH bond. The rest of this study has demonstrated that it is also the correlation time describing the tumbling of the whole calixarene assembly. From three non-proton-bearing carbons of the aromatic cycles (thus subjected to the chemical shift anisotropy and dipolar mechanisms), we have been able to determine the variation of the chemical shift anisotropy when going from the free to the complex form of the calixarene. These variations not only provide the location of the cation inside the calixarene cavity but also constitute a direct experimental proof of the cation-pi interactions. These results are complemented by cesium and thallium relaxation measurements performed again at two values of the magnetic field B(0). An estimation of the mean distance between the cation and the calixarene protons could be obtained. These measurements have also revealed an important chemical shift anisotropy of thallium upon complexation.

Effect of the static magnetic field strength on parahydrogen induced polarization NMR spectra.

Spin polarization transfer from parahydrogen (p-H(2)) to another molecular entity is generally thought to be mediated by longitudinal spin order (represented by the operator product I(z)(A)I(z)(B), A and B being the two hydrogen nuclei which originate from p-H(2) after a hydrogenation reaction). The longitudinal spin order leads to antiphase patterns in the proton NMR spectrum. In addition to these antiphase patterns, in-phase patterns, arising from polarization differences (represented by (I(z)(A)-I(z)(B))), have been experimentally observed. A complete theory, based on a density operator treatment, has been worked out and applied to the two types of parahydrogen induced polarization experiments: PASADENA (PArahydrogen and Synthesis Allow Dramatically Enhanced Nuclear Alignment; hydrogenation reaction inside the NMR magnet) and (ALTADENA) (Adiabatic Longitudinal Transport After Dissociation Engenders Nuclear Alignment; hydrogenation reaction outside the NMR magnet). It is shown that polarization differences are always created in the case of a PASADENA experiment but that their amplitude depends critically on the ratio of the J coupling over the frequency difference between A and B. In the case of an ALTADENA experiment, if the sample is slowly transferred toward the NMR magnet, polarization differences are definitely created and their amplitude can be larger than the amplitude of the longitudinal spin order. Some test experiments demonstrate the validity of the proposed theory.

Self-diffusion coefficients obtained from proton-decoupled carbon-13 spectra for analyzing a mixture of terpenes.

In the limit of sufficient sensitivity, natural abundance 13C offers a much better spectral resolution than proton NMR. This is due to an important chemical shift range and to proton-decoupling conditions that yield one peak per carbon with practically no overlap. However, pulsed gradient spin echo experiments, which lead to the diffusion coefficient associated with each peak, have scarcely been employed. In this article, we present and compare different ways to access this quantity and we have effectively verified that, without any precaution, diffusion coefficients cannot be properly determined from standard procedures. The cause of such a failure is decoupling during the gradient pulses. We have used a very simple remedy that proved to be very successful on a model mixture of three monoterpenes and that appears as being of general applicability.