Dynamics of ionic liquids by means of nuclear magnetic resonance relaxation - overview of theoretical approaches.

This paper presents a comprehensive overview of the spin relaxation theory needed for exploring nuclear magnetic resonance (NMR) relaxometry to study the dynamical properties of ionic liquids. The term NMR relaxometry refers to relaxation experiments performed over a wide range of magnetic fields (resonance frequencies). In this way, dynamical processes occurring on timescales from milliseconds to nanoseconds can be studied, including translational and rotational dynamics of both types of ions (cations and anions). In order to take advantage of the remarkable experimental possibilities, appropriate theoretical models linking relaxation properties with ionic motion are needed. With the aim of providing such theoretical tools, 1H and 19F relaxation models for ionic liquids have been reviewed and their applications have been illustrated by several examples. The presented models are valid for an arbitrary magnetic field, include all relevant relaxation pathways and allow to extract detailed information about the translational and rotational dynamics of the ions. On the basis of the theoretical models, formulas allowing a straightforward determination of the translational diffusion coefficients of cations and anions from combined 1H and 19F relaxation studies have been derived and discussed in detail.

Dynamic of binary molecular systems-Advantages and limitations of NMR relaxometry.

1H spin-lattice relaxation studies have been performed for binary systems, including glycerol as the first component and alanine, glycine, and aspartic acid (with different levels of deuteration) as the second one. The relaxation studies have been performed in the frequency range from 10 kHz to 10 MHz vs temperature. A theoretical framework, including all relevant 1H-1H and 1H-2H relaxation pathways, has been formulated. The theory has been exploited for a thorough interpretation of a large set of the experimental data. The importance of the 1H-2H relaxation contributions has been discussed, and the possibility of revealing dynamical properties of individual liquid components in binary liquids has been carefully investigated. As far as the dynamical properties of the specific binary liquids, chosen as an example, are considered, it has been shown that in the presence of the second component (alanine, glycine, and aspartic acid), both molecular fractions undergo dynamics similar to that of glycerol in bulk.

Dynamical properties of solid and hydrated collagen: Insight from nuclear magnetic resonance relaxometry.

1H spin-lattice Nuclear Magnetic Resonance relaxometry experiments have been performed for collagen and collagen-based artificial tissues in the frequency range of 10 kHz-20 MHz. The studies were performed for non-hydrated and hydrated materials. The relaxation data have been interpreted as including relaxation contributions originating from 1H-1H and 1H-14N dipole-dipole interactions, the latter leading to Quadrupole Relaxation Enhancement effects. The 1H-1H relaxation contributions have been decomposed into terms associated with dynamical processes on different time scales. A comparison of the parameters for the non-hydrated and hydrated systems has shown that hydration leads to a decrease in the dipolar relaxation constants without significantly affecting the dynamical processes. In the next step, the relaxation data for the hydrated systems were interpreted in terms of a model assuming two-dimensional translational diffusion of water molecules in the vicinity of the macromolecular surfaces and a sub-diffusive motion leading to a power law of the frequency dependencies of the relaxation rates. It was found that the water diffusion process is slowed down by at least two orders of magnitude compared to bulk water diffusion. The frequency dependencies of the relaxation rates in hydrated tissues and hydrated collagen are characterized by different power laws (ωH-ß, where ωH denotes the 1H resonance frequency): the first of about 0.4 and the second close to unity.

Water Dynamics in Highly Concentrated Protein Systems-Insight from Nuclear Magnetic Resonance Relaxometry.

1H spin-lattice relaxation experiments have been performed for water-Bovine Serum Albumin (BSA) mixtures, including 20%wt and 40%wt of BSA. The experiments have been carried out in a frequency range encompassing three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. The relaxation data have been thoroughly analyzed in terms of several relaxation models with the purpose of revealing the mechanisms of water motion. For this purpose, four relaxation models have been used: the data have been decomposed into relaxation contributions expressed in terms of Lorentzian spectral densities, then three-dimensional translation diffusion has been assumed, next two-dimensional surface diffusion has been considered, and eventually, a model of surface diffusion mediated by acts of adsorption to the surface has been employed. In this way, it has been demonstrated that the last concept is the most plausible. Parameters describing the dynamics in a quantitative manner have been determined and discussed.

Relative Cation-Anion Diffusion in Alkyltriethylammonium-Based Ionic Liquids.

19F Nuclear Magnetic Resonance spin-lattice relaxation experiments have been performed for a series of ionic liquids including the same anion, bis(trifluoromethanesulfonyl)imide, and cations with alkyl chains of different lengths: triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, dodecyltriethylammonium, decyltriethylammonium, and hexadecyltriethylammonium. The experiments have been carried out in a frequency range of 10 kHz to 10 MHz versus temperature. A thorough analysis of the relaxation data has led to the determination of the cation-anion as a relative translation diffusion coefficient. The diffusion coefficients have been compared with the corresponding cation-cation and anion-anion diffusion coefficients, revealing a correlation in the relative translation movement of the anion and the triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, and dodecyltriethylammonium cations, whereas the relative translation diffusion between the anion and the cations with the longer alkyl chains, decyltriethylammonium and hexadecyltriethylammonium, remains rather uncorrelated (correlated to a much lesser extent).

Relationship between Translational and Rotational Dynamics of Alkyltriethylammonium-Based Ionic Liquids.

1H spin-lattice relaxation experiments have been performed for a series of ionic liquids including bis(trifluoromethanesulfonyl)imide anion and cations of a varying alkyl chain length: triethylhexylammonium, triethyloctylammonium, decyltriethylammonium, dodecyltriethylammonium, triethyltetradecylammonium, and hexadecyltriethylammonium. The relaxation studies were carried out in abroad frequency range covering three orders of magnitude, from 10 kHz to 10 MHz, versus temperature. On the basis of a thorough, quantitative analysis of this reach data set, parameters characterizing the relative, cation-cation, translation diffusion (relative diffusion coefficients and translational correlation times), and rotational motion of the cation (rotational correlation times) were determined. Relationships between these quantities and their dependence on the alkyl chain length were discussed in comparison to analogous properties of molecular liquids. It was shown, among other findings, that the ratio between the translational and rotational correlation times is smaller than for molecular liquids and considerably dependent on temperature. Moreover, a comparison of relative and self-diffusion coefficients indicate correlated translational dynamics of the cations.

Correlated Dynamics in Ionic Liquids by Means of NMR Relaxometry: Butyltriethylammonium bis(Trifluoromethanesulfonyl)imide as an Example.

1H and 19F spin-lattice relaxation experiments have been performed for butyltriethylammonium bis(trifluoromethanesulfonyl)imide in the temperature range from 258 to 298 K and the frequency range from 10 kHz to 10 MHz. The results have thoroughly been analysed in terms of a relaxation model taking into account relaxation pathways associated with 1H-1H, 19F-19F and 1H-19F dipole-dipole interactions, rendering relative translational diffusion coefficients for the pairs of ions: cation-cation, anion-anion and cation-anion, as well as the rotational correlation time of the cation. The relevance of the 1H-19F relaxation contribution to the 1H and 19F relaxation has been demonstrated. A comparison of the diffusion coefficients has revealed correlation effects in the relative cation-anion translational movement. It has also turned out that the translational movement of the anions is faster than of cations, especially at high temperatures. Moreover, the relative cation-cation diffusion coefficients have been compared with self-diffusion coefficients obtained by means of NMR (Nuclear Magnetic Resonance) gradient diffusometry. The comparison indicates correlation effects in the relative cation-cation translational dynamics-the effects become more pronounced with decreasing temperature.

Mechanism of Water Dynamics in Hyaluronic Dermal Fillers Revealed by Nuclear Magnetic Resonance Relaxometry.

1 H spin-lattice nuclear magnetic resonance relaxation experiments were performed for five kinds of dermal fillers based on hyaluronic acid. The relaxation data were collected over a broad frequency range between 4 kHz and 40 MHz, at body temperature. Thanks to the frequency range encompassing four orders of magnitude, the dynamics of water confined in the polymeric matrix was revealed. It is demonstrated that translation diffusion of the confined water molecules exhibits a two-dimensional character and the diffusion process is slower than diffusion in bulk water by 3-4 orders of magnitude. As far as rotational dynamics of the confined water is concerned, it is shown that in all cases there is a water pool characterized by a rotational correlation time of about 4×10-9  s. In some of the dermal fillers a fraction of the confined water (about 10 %) forms a pool that exhibits considerably slower (by an order of magnitude) rotational dynamics. In addition, the water binding capacity of the dermal fillers was quantitatively compared.

Estimation of the magnitude of quadrupole relaxation enhancement in the context of magnetic resonance imaging contrast.

Magnetic Resonance Imaging (MRI) is one of the most powerful diagnostic tools providing maps of 1H relaxation times of human bodies. The method needs, however, a contrast mechanism to enlarge the difference in the relaxation times between healthy and pathological tissues. In this work, we discuss the potential of a novel contrast mechanism for MRI based on Quadrupole Relaxation Enhancement (QRE) and estimate the achievable value of QRE under the most favorable conditions. It has turned out that the theoretically possible enhancement factors are smaller than those of typical paramagnetic contrast agents, but in turn, the field-selectivity of QRE-based agents makes them extremely sensitive to subtle changes of the electric field gradient in the tissue. So far, QRE has been observed for solids (in most cases for 14N) as a result of very slow dynamics and anisotropic spin interactions, believed to be necessary for QRE to appear. We show the first evidence that QRE can be achieved in solutions of compounds containing a high spin nucleus (209Bi) as the quadrupole element. The finding of QRE in a liquid state is explained in terms of spin relaxation theory based on the stochastic Liouville equation. The results confirm the relaxation theory and motivate further exploration of the potential of QRE for MRI.

Model - free approach to quadrupole spin relaxation in solid 209Bi-aryl compounds.

Nuclear Quadrupole Resonance (NQR) experiments were performed for deuterated and non-deuterated triphenylbismuth (BiPh3) to inquire into 209Bi relaxation mechanisms. The studies are motivated by the idea of exploiting Quadrupole Relaxation Enhancement (QRE) as a novel contrast mechanism for Magnetic Resonance Imaging. From this perspective relaxation features of nuclei possessing quadrupole moment (quadrupole nuclei) are of primary importance for the contrast effect. Spin-spin relaxation rates associated with the NQR lines were described in terms of the Redfield relaxation theory assuming that the relaxation is caused by fluctuations of the electric field gradient tensor at the position of the quadrupole nucleus that are described by an exponential correlation function. The description referred to as a model-free approach is an analogy of the description used for paramagnetic contrast agents. It was demonstrated that for the deuterated compound this approach captures the essential features of 209Bi relaxation, but it should not be applied for non-deuterated compounds as dipolar interactions between neighbouring protons and the quadrupole nucleus considerably contribute to the relaxation of the last one. Thus, the relaxation scenario for species containing quadrupole nuclei is fundamentally different than for paramagnetic contrast agents and this fact has to be taken into account when predicting contrast effects based on QRE.

Diffusion of Water Molecules on the Surface of Silica Nanoparticles─Insights from Nuclear Magnetic Resonance Relaxometry.

1H spin-lattice nuclear magnetic resonance (NMR) relaxation experiments have been performed for water dispersions of functionalized silica nanoparticles of diameters of 25 and 45 nm. The experiments have been performed in a broad frequency range spanning 3 orders of magnitude, from 10 kHz to 10 MHz, versus temperature, from 313 to 263 K. On the basis of the data, two-dimensional translation diffusion (diffusion close to the nanoparticle surface within a layer of the order of a few diameters of water molecules) has been revealed. The translational correlation times as well as the residence life times on the nanoparticle surface have been determined. It has turned out that the residence lifetime is temperature-independent and is on the order of 5 × 10-6 s for the smaller nanoparticles and by about a factor of 3 longer for the larger ones. The translational correlation time for the case of 25 nm nanoparticles is also temperature-independent and yields about 6 × 10-7 s, while for the dispersion of the larger nanoparticles, the correlation times changed from about 8 × 10-7 s at 313 K to about 1.2 × 10-6 s at 263 K. In addition to the quantitative characterization of the two-dimensional translation diffusion, correlation times associated with bound water molecules have been determined. The studies have also given insights into the population of the bound and diffusing water on the surface water fractions.

Markers of low field NMR relaxation features of tissues.

This work presents an approach to exploiting Nuclear Magnetic Resonance (NMR) relaxometry data (1H spin-lattice relaxation rates covering the frequency range from below 1 kHz to 10 MHz) for the purpose of differentiating between pathological and reference tissues. Characteristic quantities (markers) that can be obtained in a straightforward manner, not resorting to an advanced analysis of 1H spin-lattice relaxation data, have been identified and compared for pathological and reference colon tissues. Moreover, the relaxation data have been parametrised in terms of Lorentzian spectral densities and the possibility of using the obtained dipolar relaxation constants and correlation times as biomarkers to assess the state of tissues has been discussed. It has also been demonstrated that the relaxation data for the reference and the pathological tissues can be attributed to two groups (for each case). The studies are a step towards exploiting the potential of NMR relaxometry for characterisation of pathological changes in tissues.

Towards applying NMR relaxometry as a diagnostic tool for bone and soft tissue sarcomas: a pilot study.

This work explores what Fast Field-Cycling Nuclear Magnetic Resonance (FFC-NMR) relaxometry brings for the study of sarcoma to guide future in vivo analyses of patients. We present the results of an ex vivo pilot study involving 10 cases of biopsy-proven sarcoma and we propose a quantitative method to analyse 1H NMR relaxation dispersion profiles based on a model-free approach describing the main dynamical processes in the tissues and assessing the amplitude of the Quadrupole Relaxation Enhancement effects due to 14N. This approach showed five distinct groups of dispersion profiles indicating five discrete categories of sarcoma, with differences attributable to microstructure and rigidity. Data from tissues surrounding sarcomas indicated very significant variations with the proximity to tumour, which may be attributed to varying water content but also to tissue remodelling processes due to the sarcoma. This pilot study illustrates the potential of FFC relaxometry for the detection and characterisation of sarcoma.

Slow dynamics of solid proteins - Nuclear magnetic resonance relaxometry versus dielectric spectroscopy.

1H Nuclear Magnetic Resonance (NMR) relaxometry and Dielectric Spectroscopy (DS) have been exploited to investigate the dynamics of solid proteins. The experiments have been carried out in the frequency range of about 10 kHz-40 MHz for NMR relaxometry and 10-2Hz-20 MHz for DS. The data sets have been analyzed in terms of theoretical models allowing for a comparison of the correlation times revealed by NMR relaxometry and DS. The 1H spin-lattice relaxation profiles have been decomposed into relaxation contributions associated with 1H-1H and 1H-14N dipole - dipole interactions. The 1H-1H relaxation contribution has been interpreted in terms of three dynamical processes of time scales of 10-6s, 10-7s and 10-8s. It has turned out that the correlation times do not differ much among proteins and they are only weakly dependent on temperature. The analysis of DS relaxation spectra has also revealed three motional processes characterized by correlation times that considerably depend on temperature in contrast to those obtained from the 1H relaxation. This finding suggest that for solid proteins there is a contribution to the 1H spin-lattice relaxation associated with a kind of motion that is not probed in DS as it does not lead to a reorientation of the electric dipole moment.

Dynamics of Solid Proteins by Means of Nuclear Magnetic Resonance Relaxometry.

1H Nuclear magnetic resonance (NMR) relaxometry was exploited to investigate the dynamics of solid proteins. The relaxation experiments were performed at 37 °C over a broad frequency range, from approximately 10 kHz to 40 MHz. Two relaxation contributions to the overall 1H spin-lattice relaxation were revealed; they were associated with 1H-1H and 1H-14N magnetic dipole-dipole interactions, respectively. The 1H-1H relaxation contribution was interpreted in terms of three dynamical processes occurring on timescales of 10-6 s, 10-7 s, and 10-8 s, respectively. The 1H-14N relaxation contribution shows quadrupole relaxation enhancement effects. A thorough analysis of the data was performed revealing similarities in the protein dynamics, despite their different structures. Among several parameters characterizing the protein dynamics and structure (e.g., electric field gradient tensor at the position of 14N nuclei), the orientation of the 1H-14N dipole-dipole axis, with respect to the principal axis system of the electric field gradient, was determined, showing that, for lysozyme, it was considerably different than for the other proteins. Moreover, the validity range of a closed form expression describing the 1H-14N relaxation contribution was determined by a comparison with a general approach based on the stochastic Liouville equation.

Thermodynamic consequences of the kinetic nature of the glass transition.

In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.

Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling.

To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we have extended the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, τα(T, V). We also employ the thermodynamic scaling idea reflected in the density scaling power law, τα = f(T(-1)V(-γ)), recently acknowledged as a valid unifying concept in the glass transition physics, to differentiate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time τα and the configurational entropy SC, giving evidence that also SC(T, V) = g(T(-1)V(-γ)) with the exponent γ that enables to scale τα(T, V). This important findings have meaningful implications for the connection between thermodynamics and molecular dynamics near the glass transition, because it implies that τα can be scaled with SC.