Quantitative interpretation of diffusion-ordered NMR spectra:can we rationalize small molecule diffusion coefficients?

Appealingly simple: A new method is described that allows the diffusion coefficient of a small molecule to be estimated given only the molecular weight and the viscosity of the solvent used. This method makes possible the quantitative interpretation of the diffusion domain of diffusion-ordered NMR spectra (see picture). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fluorinated surfactants in solution: Diffusion coefficients of fluorinated alcohols in water

Intra-diffusion coefficients of three fluorinated alcohols, 2,2,3,3,3-pentafluoropropan-1-ol (PFP), 2,2,3,3,4,4,4-heptafluorobutan-1-ol (HFB) and 2,2,3,3,4,4,5,5,5-nonafluoropentan-1-ol (NFP) in water have been measured by the PFG–NMR spin-echo technique as a function of temperature and composition, focusing on the alcohol dilute region. For comparison, intra-diffusion coefficients of 2,2,2- trifluoroethanol (TFE) and HFB have also been measured in heavy water using the same method and conditions. As far as we know, these are the first experimental measurements of this property for these binary systems. Intra-diffusion coefficients for NFP in water and for TFE and HFB in heavy water have also been obtained by molecular dynamics simulation, complementing those for TFE, PFP and HFB reported in a previous work. The agreement between experimental and simulated results for PFP, HFB and NFP in water is reasonable, although presenting higher deviations than for the TFE/water system. From the dependence of the intra-diffusion coefficients on temperature, diffusion activation energies were estimated for all the solutes in water and heavy water.

Water diffusion in hydroxyethyl methacrylate (HEMA)-based hydrogels formed by gamma-radiolysis

Polymer hydrogels based upon methacrylates are used extensively in the pharmaceutical industry, particularly as controlled release drug delivery systems. These materials are generally prepared by chemically initiated polymerization, but this can lead to the presence of unwanted initiator fragments in the polymer matrix. In the present work, initiation of polymerization by gamma-irradiation of hydroxyethyl methacrylate, with and without added crosslinkers, has been investigated, and the diffusion coefficients for water in the resulting polymers have been measured through mass uptake by the polymers. The diffusion of water in poly(hydroxyethyl methacrylate) at 310 K was found to be Fickian, with a diffusion coefficient of 1.96 +/- 0.1 x 10(11) m(2) s(-1) and an equilibrium water content of 58%, NMR imaging analyses confirmed the adherance to a Fickian model of the diffusion of water into polymer cylinders. The incorporation of small amounts (0.2-0.5 wt%) of added ethyleneglycol-dimethacrylate-based crosslinkers was found to have only a small effect on the diffusion coefficient and the equilibrium water content for the copolymers. (C) 1999 Society of Chemical Industry.

The states, diffusion, and concentration distribution of water in radiation-formed PVA/PVP hydrogels

Hydrogels with various compositions of polyvinyl alcohol (PVA) and poly(1-vinyl-2-pyrrolidinone) (PVP) were prepared by irradiating mixtures of PVA and PVP in aqueous solutions with gamma-rays from Co-60 sources at room temperature. The states of water in the hydrogels were characterized using DSC and NMR T-2 relaxation measurements and the kinetics of water diffusion in the hydrogels were studied by sorption experiments and NMR imaging. The DSC endothermic peaks in the temperature range -10 to +10 degrees C implied that there are at least two kinds of freezable water present in the matrix. The difference between the total water content and the freezable water content was refer-red to as bound water, which is not freezable. The weight fraction of water at which only nonfreezable water is present in a hydrogel with F-VP = 0.19 has been estimated to be g(H2O)/g(Polymer) = 0.375. From water sorption experiments, it was demonstrated that the early stage of the diffusion of water into the hydrogels was Fickian. A curve-fit of the early-stage experimental data to the Fickian model allowed determination of the water diffusion coefficient, which was found to lie between 1.5 x 10(-11) m(2) s(-1) and 4.5 x 10(-11) m(2) s(-1), depending on the polymer composition, the cross-link density, and the temperature. It was also found that the energy barrier for diffusion of water molecules into PVA/PVP hydrogels was approximate to 24 kJ mol(-1). Additionally, the diffusion coefficients determined from NMR imaging of the volumetric swelling of the gels agreed well with the results obtained by the mass sorption method.

Measuring macromolecular diffusion using heteronuclear multiple-quantum pulsed-field-gradient NMR

We have previously shown that H-1 pulsed-field-gradient (PFG) NMR spectroscopy provides a facile method for monitoring protein self-association and can be used, albeit with some caveats, to measure the apparent molecular mass of the diffusant [Dingley et al. (1995) J. Biomol. NMR, 6, 321-328]. In this paper we show that, for N-15-labelled proteins, selection of H-1-N-15 multiple-quantum (MQ) coherences in PFG diffusion experiments provides several advantages over monitoring H-1 single-quantum (SQ) magnetization. First, the use of a gradient-selected MQ filter provides a convenient means of suppressing resonances from both the solvent and unlabelled solutes. Second, H-1-N-15 zero-quantum coherence dephases more rapidly than H-1 SQ coherence under the influence of a PFG. This allows the diffusion coefficients of larger proteins to be measured more readily. Alternatively, the gradient length and/or the diffusion delay may be decreased, thereby reducing signal losses from relaxation. In order to extend the size of macromolecules to which these experiments can be applied, we have developed a new MQ PFG diffusion experiment in which the magnetization is stored as longitudinal two-spin order for most of the diffusion period, thus minimizing sensitivity losses due to transverse relaxation and J-coupling evolution.

Laser-induced diffusion decomposition in Fe-V thin-film alloys

We investigate the origin of ferromagnetism induced in thin-film (similar to 20 nm) Fe-V alloys by their irradiation with subpicosecond laser pulses. We find with Rutherford backscattering that the magnetic modifications follow a thermally stimulated process of diffusion decomposition, with formation of a-few-nm-thick Fe enriched layer inside the film. Surprisingly, similar transformations in the samples were also found after their long-time (similar to 10(3) s) thermal annealing. However, the laser action provides much higher diffusion coefficients (similar to 4 orders of magnitude) than those obtained under standard heat treatments. We get a hint that this ultrafast diffusion decomposition occurs in the metallic glassy state achievable in laser-quenched samples. This vitrification is thought to be a prerequisite for the laser-induced onset of ferromagnetism that we observe. 2014 Elsevier B.V. All rights reserved.

Diffusion characteristics of ethylene glycol in skeletal muscle

Part of the optical clearing study in biological tissues concerns the determination of the diffusion characteristics of water and optical clearing agents in the subject tissue. Such information is sufficient to characterize the time dependence of the optical clearing mechanisms—tissue dehydration and refractive index (RI) matching. We have used a simple method based on collimated optical transmittance measurements made from muscle samples under treatment with aqueous solutions containing different concentrations of ethylene glycol (EG), to determine the diffusion time values of water and EG in skeletal muscle. By representing the estimated mean diffusion time values from each treatment as a function of agent concentration in solution, we could identify the real diffusion times for water and agent. These values allowed for the calculation of the correspondent diffusion coefficients for those fluids. With these results, we have demonstrated that the dehydration mechanism is the one that dominates optical clearing in the first minute of treatment, while the RI matching takes over the optical clearing operations after that and remains for a longer time of treatment up to about 10 min, as we could see for EG and thin tissue samples of 0.5 mm.

Application of NMR RDC’s, relaxation and self-diffusion for the study of dynamic processes of small molecules in solution

Spin-lattice Relaxation, self-Diffusion coefficients and Residual Dipolar Couplings (RDC’s) are the basis of well established Nuclear Magnetic Resonance techniques for the physicochemical study of small molecules (typically organic compounds and natural products with MW < 1000 Da), as they proved to be a powerful and complementary source of information about structural dynamic processes in solution. The work developed in this thesis consists in the application of the earlier-mentioned NMR techniques to explore, analyze and systematize patterns of the molecular dynamic behavior of selected small molecules in particular experimental conditions. Two systems were chosen to investigate molecular dynamic behavior by these techniques: the dynamics of ion-pair formation and ion interaction in ionic liquids (IL) and the dynamics of molecular reorientation when molecules are placed in oriented phases (alignment media). The application of NMR spin-lattice relaxation and self-diffusion measurements was applied to study the rotational and translational molecular dynamics of the IL: 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4]. The study of the cation-anion dynamics in neat and IL-water mixtures was systematically investigated by a combination of multinuclear NMR relaxation techniques with diffusion data (using by H1, C13 and F19 NMR spectroscopy). Spin-lattice relaxation time (T1), self-diffusion coefficients and nuclear Overhauser effect experiments were combined to determine the conditions that favor the formation of long lived [BMIM][BF4] ion-pairs in water. For this purpose and using the self-diffusion coefficients of cation and anion as a probe, different IL-water compositions were screened (from neat IL to infinite dilution) to find the conditions where both cation and anion present equal diffusion coefficients (8% water fraction at 25 ºC). This condition as well as the neat IL and the infinite dilution were then further studied by 13C NMR relaxation in order to determine correlation times (c) for the molecular reorientational motion using a mathematical iterative procedure and experimental data obtained in a temperature range between 273 and 353 K. The behavior of self-diffusion and relaxation data obtained in our experiments point at the combining parameters of molar fraction 8 % and temperature 298 K as the most favorable condition for the formation of long lived ion-pairs. When molecules are subjected to soft anisotropic motion by being placed in some special media, Residual Dipolar Couplings (RDCs), can be measured, because of the partial alignment induced by this media. RDCs are emerging as a powerful routine tool employed in conformational analysis, as it complements and even outperforms the approaches based on the classical NMR NOE or J3 couplings. In this work, three different alignment media have been characterized and evaluated in terms of integrity using 2H and 1H 1D-NMR spectroscopy, namely the stretched and compressed gel PMMA, and the lyotropic liquid crystals CpCl/n-hexanol/brine and cromolyn/water. The influence that different media and degrees of alignment have on the dynamic properties of several molecules was explored. Different sized sugars were used and their self-diffusion was determined as well as conformation features using RDCs. The results obtained indicate that no influence is felt by the small molecules diffusion and conformational features studied within the alignment degree range studied, which was the 3, 5 and 6 % CpCl/n-hexanol/brine for diffusion, and 5 and 7.5 % CpCl/n-hexanol/brine for conformation. It was also possible to determine that the small molecules diffusion verified in the alignment media presented close values to the ones observed in water, reinforcing the idea of no conditioning of molecular properties in such media.

Single molecule simulation of diffusion and enzyme kinetics

This work presents a molecular-scale agent-based model for the simulation of enzymatic reactions at experimentally measured concentrations. The model incorporates stochasticity and spatial dependence, using diffusing and reacting particles with physical dimensions. We developed strategies to adjust and validate the enzymatic rates and diffusion coefficients to the information required by the computational agents, i.e., collision efficiency, interaction logic between agents, the time scale associated with interactions (e.g., kinetics), and agent velocity. Also, we tested the impact of molecular location (a source of biological noise) in the speed at which the reactions take place. Simulations were conducted for experimental data on the 2-hydroxymuconate tautomerase (EC 5.3.2.6, UniProt ID Q01468) and the Steroid Delta-isomerase (EC 5.3.3.1, UniProt ID P07445). Obtained results demonstrate that our approach is in accordance to existing experimental data and long-term biophysical and biochemical assumptions.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Diffusion-weighted MR imaging of the spine at 3-T: feasibility, optimization of b-value and utility to differentiate benign from pathological vertebral compression fractures

Purpose: To evaluate the feasibility, determine the optimal b-value, and assess the utility of 3-T diffusion-weighted MR imaging (DWI) of the spine in differentiating benign from pathologic vertebral compression fractures.Methods and Materials: Twenty patients with 38 vertebral compression fractures (24 benign, 14 pathologic) and 20 controls (total: 23 men, 17 women, mean age 56.2years) were included from December 2010 to May 2011 in this IRB-approved prospective study. MR imaging of the spine was performed on a 3-T unit with T1-w, fat-suppressed T2-w, gadolinium-enhanced fat-suppressed T1-w and zoomed-EPI (2D RF excitation pulse combined with reduced field-of-view single-shot echo-planar readout) diffusion-w (b-values: 0, 300, 500 and 700s/mm2) sequences. Two radiologists independently assessed zoomed-EPI image quality in random order using a 4-point scale: 1=excellent to 4=poor. They subsequently measured apparent diffusion coefficients (ADCs) in normal vertebral bodies and compression fractures, in consensus.Results: Lower b-values correlated with better image quality scores, with significant differences between b=300 (mean±SD=2.6±0.8), b=500 (3.0±0.7) and b=700 (3.6±0.6) (all p<0.001). Mean ADCs of normal vertebral bodies (n=162) were 0.23, 0.17 and 0.11×10-3mm2/s with b=300, 500 and 700s/mm2, respectively. In contrast, mean ADCs were 0.89, 0.70 and 0.59×10-3mm2/s for benign vertebral compression fractures and 0.79, 0.66 and 0.51×10-3mm2/s for pathologic fractures with b=300, 500 and 700s/mm2, respectively. No significant difference was found between ADCs of benign and pathologic fractures.Conclusion: 3-T DWI of the spine is feasible and lower b-values (300s/mm2) are recommended. However, our preliminary results show no advantage of DWI in differentiating benign from pathologic vertebral compression fractures.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.