Stokes-Einstein-Debye Relations Research Articles

The Stokes-Einstein-Debye relation in ortho-terphenyl liquid

The Stokes–Einstein–Debye (SED) relation is proposed to be broken down in supercooled liquids by many studies. However, conclusions are usually drawn by testing some variants of the SED relation rather than its original formula. In this work, the rationality of the SED relation and its variants is examined by performing molecular dynamics simulations with the Lewis–Wahnstrom model of ortho-terphenyl (OTP). The results indicate the original SED relation is valid for OTP but the three variants are all broken down. The inconsistency between the SED relation and its variants is analyzed from the heterogeneous dynamics, the adopted assumptions and approximations as well as the interactions among molecules. Therefore, care should be taken when employing the variants to judge the validity of the SED relation in supercooled liquids.

A Relation between the Formation of a Hydrogen-Bond Network and a Time-Scale Separation of Translation and Rotation in Molecular Liquids.

We study the relation between the translational and rotational motions of liquids, which is anticipated in the framework of the Stokes-Einstein-Debye (SED) treatment. For this purpose, we exploit the fact that 1H field-cycling nuclear magnetic resonance relaxometry and molecular dynamics simulations provide access to both modes of motion. The experimental and computational findings are fully consistent and show that the time-scale separation between translation and rotation increases from the van der Waals liquid o-terphenyl over ethylene glycol to the hydrogen-bonded liquid glycerol, indicating an increasing degree of breakdown of the SED relation. Furthermore, the simulation results for two ethylene glycol models with different molecular conformations indicate that the translation is more retarded than the rotation when the density of intermolecular hydrogen bonds increases. We conclude that an increasing connectivity of a hydrogen-bond network leads to an increasing time-scale separation and, thus, to a stronger SED violation.

Consistent hydrodynamics of ferrofluids

We develop a consistent hydrodynamic theory for ferrofluids that can be concentrated, strongly interacting, and polydisperse. We analyze the dynamics of ferrocolloids under imposed flow and magnetic field, from micro-, meso-, and macroscopic points of view. We settle the long-standing debate on the correct reactive contribution to magnetization dynamics near or far from equilibrium. We obtain a fundamental mesoscopic rotational fluctuation-dissipation relation, linking vortex viscosity and rotational self-diffusivity and with far-reaching consequences on ferrofluid hydrodynamics. It distinguishes from the traditional Stokes–Einstein–Debye relation that only applies to dilute and noninteracting systems. Furthermore, it is used to infer the size of structure units whose rotational diffusion is responsible for the primary Debye peak of water. The characteristic hydrodynamic radius is estimated to be ∼0.18 nm, considerably larger than the geometrical radius of water molecules. This is in contrast to the result obtained by naively employing the Stokes–Einstein–Debye relation. We revisit the magnetoviscous effect in ferrofluids and obtain novel expressions for the rotational viscosity, shedding new light on the effects of inter-particle correlations and particle packing. In particular, previous models usually confuse solvent vorticity with suspension vorticity and do not yield the actual rotational viscosity measured in experiments. We compare our theoretical predictions with recent simulations and find quantitatively good agreements. Our work is to be a cornerstone for understanding ferrofluid dynamics and of considerable importance to various applications. It can be also valuable for studying the hydrodynamics of other structured fluids.

Molecular dynamics simulations vs field-cycling NMR relaxometry: Structural relaxation mechanisms in the glass-former glycerol revisited.

We combine field-cycling (FC) relaxometry and molecular dynamics (MD) simulations to study the rotational and translational dynamics associated with the glassy slowdown of glycerol. The 1H NMR spin-lattice relaxation rates R1(ω) probed in the FC measurements for different isotope-labelled compounds are computed from the MD trajectories for broad frequency and temperature ranges. We find high correspondence between experiment and simulation. Concerning the rotational motion, we observe that the aliphatic and hydroxyl groups show similar correlation times but different stretching parameters, while the overall reorientation associated with the structural relaxation remains largely isotropic. Additional analysis of the simulation results reveals that transitions between different molecular configurations are slow on the time scale of the structural relaxation at least at sufficiently high temperatures, indicating that glycerol rotates at a rigid entity, but the reorientation is slower for elongated than for compact conformers. The translational contribution to R1(ω) is well described by the force-free hard sphere model. At sufficiently low frequencies, universal square-root laws provide access to the molecular diffusion coefficients. In both experiment and simulation, the time scales of the rotational and translational motions show an unusually large separation, which is at variance with the Stokes-Einstein-Debye relation. To further explore this effect, we investigate the structure and dynamics on various length scales in the simulations. We observe that a prepeak in the static structure factor S(q), which is related to a local segregation of aliphatic and hydroxyl groups, is accompanied by a peak in the correlation times τ(q) from coherent scattering functions.

Violation of Stokes–Einstein and Stokes–Einstein–Debye relations in polymers at the gas-supercooled liquid coexistence

Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations near the mode coupling theory transition temperature T c at three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation near T c in both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.

Confinement Effects on Glass-Forming Aqueous Dimethyl Sulfoxide Solutions.

Combining broadband dielectric spectroscopy and nuclear magnetic resonance studies, we analyze the reorientation dynamics and the translational diffusion associated with the glassy slowdown of the eutectic aqueous dimethyl sulfoxide solution in nano-sized confinements, explicitly, in silica pores with different diameters and in ficoll and lysozyme matrices at different concentrations. We observe that both rotational and diffusive dynamics are slower and more heterogeneous in the confinements than in the bulk but the degree of these effects depends on the properties of the confinement and differs for the components of the solution. For the hard and the soft matrices, the slowdown and the heterogeneity become more prominent when the size of the confinement is reduced. In addition, the dynamics are more retarded for dimethyl sulfoxide than for water, implying specific guest-host interactions. Moreover, we find that the temperature dependence of the reorientation dynamics and of the translational diffusion differs in severe confinements, indicating a breakdown of the Stokes–Einstein–Debye relation. It is discussed to what extent these confinement effects can be rationalized in the framework of core-shell models, which assume bulk-like and slowed-down motions in central and interfacial confinement regions, respectively.

Molecular size and shape effects: Rotational diffusion and the Stokes-Einstein-Debye relation

Formulation of rotational diffusion coefficient and the Stokes-Einstein-Debye (SED) relation is presented for diatomic molecular liquids by molecular dynamics simulation with two-center Lennard-Jones (2CLJ) potentials. Shear viscosity ηsv and rotational diffusion coefficient Dr are expressed as a function of molecular mass and number density N/V, or moment of inertia, packing fraction, temperature T, interaction energy, and molecular elongation l∗ ≡ l/σ, where N is the number of molecules included in the system volume V, l the bond length in the diatomic molecules, and σ the size parameter used in the LJ potentials. The packing fraction and elongation are the variables expressing molecular size and shape, respectively. These results produce directly a molecular-basis SED relation as Drηsv/T ∝ vm∗1/3l∗−3(N/V), where vm∗ is the dimensionless molecular volume expressed as an analytical function only of elongation l∗. That is, this SED equation depends not on the size but on the shape. This is highly contrasted with the original SED relation based on the size, which suggests overall reconsideration of the relation on a molecular scale. The shape term accounts for a paradox that more spherical molecules such as N2 deviate more strongly from the original SED equation based on a spherical particle. In addition, the SED relation without the size is consistent with the Stokes-Einstein relation for both the Lennard-Jones and 2CLJ liquids expressed as Dηsv/T ∝ (N/V)1/3, where D is the translational self-diffusion coefficient.

On the relation between reorientation and diffusion in glass-forming ionic liquids with micro-heterogeneous structures.

We investigate complex structure-dynamics relations in glass-forming ionic liquids comprising 1-alkyl-3-methylimidazolium cations and bis(trifluoromethylsulfonyl)imide anions. In doing so, we exploit the microheterogeneous structures emerging when the alkyl length is increased in the range n = 1-12 and use that 1H and 2H NMR give information about cation dynamics, while 19F NMR reports on anion motions. Furthermore, we combine spin-lattice relaxation analysis, including field-cycling relaxometry, with stimulated-echo experiments to follow reorientation dynamics related to structural relaxation in wide dynamic ranges and we apply static field gradients to probe translational diffusion. The resulting correlation times τ and diffusion coefficients D show Vogel-Fulcher-Tammann temperature dependence. Moreover, they indicate a moderate slowdown of both cation and anion dynamics with increasing alkyl length n. However, the relative diffusivities of the ionic species depend on the cation size, where cations are more mobile for n < 6 and anions for n > 6. Finally, we relate rotational and translational motions in the framework of the Stokes-Einstein-Debye (SED) approach. We find that the SED relation is obeyed for anion dynamics in all samples, while it breaks down for cation dynamics when n is increased. The origin of this SED breakdown is shown to differ fundamentally from that reported previously for conventional glass formers. We argue that an emergence of cation clusters causes a retardation of cation diffusion relative to cation reorientation upon cooling, i.e., the studied ionic liquids show a complex interplay of structural and dynamical properties.

Classification of mobile- and immobile-molecule timescales for the Stokes–Einstein and Stokes–Einstein–Debye relations in supercooled water

Molecular dynamics simulations have been performed on TIP4P/2005 supercooled water to investigate the molecular diffusion and shear viscosity at various timescales and assess the Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations. For this purpose, we calculated various time correlation functions, such as the mean-squared displacement, stress relaxation function, density correlation function, hydrogen-bond correlation function, rotational correlation function of molecular orientation, non-Gaussian parameter, and four-point correlation function. Our study of the SE and SED relations indicates that the transport coefficients and timescales obtained using these time correlation functions may be classified into two distinct classes: those governed by either mobile or immobile molecules, due to dynamical heterogeneity. In particular, we show that the stress relaxation time, hydrogen-bond lifetime, and large-angle rotational relaxation time are coupled with translational diffusion, and are characterized by mobile molecules. In contrast, the structural -relaxation time, small-angle rotational relaxation time, and characteristic timescales of four-point correlation functions are decoupled with translational diffusion, and are governed by immobile molecules. This decoupling results in a violation of the SE relation. These results indicate that the identification of timescales that appropriately characterize transport coefficients, such as translational diffusion constant and shear viscosity, provides a deep insight into the violation of the SE and SED relations in glass-forming liquids.

Spurious violation of the Stokes\u2013Einstein\u2013Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the {boldsymbol{ell }}-th degree Legendre polynomials {{boldsymbol{tau }}}_{{boldsymbol{ell }}}, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, {{boldsymbol{tau }}}_{{boldsymbol{ell }}}kBT/η and Dt{{boldsymbol{tau }}}_{{boldsymbol{ell }}}, where Dt is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values are decoupled with η/T, but are coupled with the translational diffusion constant Dt. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

On the hydrogen-bond network and the non-Arrhenius transport properties of water

We study the structural and dynamic transformations of SPC/E water with temperature, through molecular dynamics (MD), and discuss the non-Arrhenius behavior of the transport properties and orientational dynamics, and the magnitude of the breakdown of the Stokes–Einstein (SE) and the Stokes–Einstein–Debye (SED) relations, in the light of these transformations. Our results show that deviations from Arrhenius behavior of the self-diffusion at low temperatures cannot be exclusively explained by the reduction of water defects (interstitial waters) and the increase of the local tetrahedrality, thus, suggesting the importance of the slowdown of collective rearrangements. Interestingly we find that at high temperatures (T ⩾ 340 K) water defects lead to a slight increase of the tetrahedrality and a decrease of the self-diffusion, opposite to water at low temperatures. The relative magnitude of the breakdown of the SE and the SED relations is found to be in accord with recent experiments (Dehaoui et al 2015 Proc. Natl Acad. Sci. USA 112 12020) resolving the discrepancy with previous MD results. Further, we show that SPC/E hydrogen-bond (HB) lifetimes deviate from Arrhenious behaviour at low temperatures in contrast with some previous MD studies. This deviation is nevertheless much smaller than that observed for the orientational dynamics and the transport properties of water, consistent with the relaxation times measured by several experimental methods. The HB acceptor exchange dynamics defined here by the acceptor switch and reform (librational dynamics) frequencies exhibit similar Arrhenius deviations, thus explaining to some extent the non-Arrhenius behavior of the transport properties and of the orientational dynamics of water. Our results also show that the fraction of HB switches through a bifurcated pathway follow a power law with the temperature decrease. Thus, at low temperatures HB acceptor switches are less frequent but occur on a faster time scale consistent with the temperature dependence of the ratio of the rotational relaxation times for the different Legendre polynomial ranks.

Reorientational Relaxation of Small Solutes in Viscoelastic Liquids.

The reorientational relaxation times of some small aromatic solutes are determined with nuclear magnetic resonance spectroscopy and time-resolved fluorescence anisotropy measurements in various solvents that exhibit viscoelasticity in the megahertz region. All the reorientational relaxation times in viscoelastic liquids are shorter than those predicted by the hydrodynamic Stokes-Einstein-Debye (SED) relation using the steady-state shear viscosity. The deviation from the SED relation becomes larger in solvents whose shear relaxation is slower. When the reorientational relaxation times in a solvent are compared, the deviation from the SED relation tends to decrease when the reorientational relaxation time increases. From a comparison with the shear relaxation spectra, it is demonstrated that the deviation from the SED relation can be ascribed to the effective reduction of the viscous friction on fast reorientation, reflecting the decrease in shear viscosity with increasing frequency.

Shape of dynamical heterogeneities and fractional Stokes-Einstein and Stokes-Einstein-Debye relations in quasi-two-dimensional suspensions of colloidal ellipsoids.

We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.

Electron spin-lattice relaxation mechanisms of nitroxyl radicals in ionic liquids and conventional organic liquids: temperature dependence of a thermally activated process.

During the past two decades, several studies have established a significant role played by a thermally activated process in the electron spin relaxation of nitroxyl free radicals in liquid solutions. Its role has been used to explain the spin relaxation behavior of these radicals in a wide range of viscosities and microwave frequencies. However, no temperature dependence of this process has been reported. In this work, our main aim was to investigate the temperature dependence of this process in neat solvents. Electron spin-lattice relaxation times of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and 4-hydroxy-TEMPO (TEMPOL), in X-band microwave frequency, were measured by the pulse saturation recovery technique in three room-temperature ionic liquids ([bmim][BF4], [emim][BF4], and [bmim][PF6]), di-isononyl phthalate, and sec-butyl benzene. The ionic liquids provided a wide range of viscosity in a modest range of temperature. An auxiliary aim was to examine whether the dynamics of a probe molecule dissolved in ionic liquids was different from that in conventional molecular liquids, as claimed in several reports on fluorescence dynamics in ionic liquids. This was the reason for the inclusion of di-isononyl phthalate, whose viscosities are similar to that of the ionic liquids in similar temperatures, and sec-butyl benzene. Rotational correlation times of the nitroxyl radicals were determined from the hyperfine dependence of the electron paramagnetic resonance (EPR) line widths. Observation of highly well-resolved proton hyperfine lines, riding over the nitrogen hyperfine lines, in the low viscosity regime in all the solvents, gave more accurate values of the rotational correlation times than the values generally measured in the absence of these hyperfine lines and reported in the literature. The measured rotational correlation times obeyed a modified Stokes-Einstein-Debye relation of temperature dependence in all solvents. By separating the contributions of g-anisotropy, A-anisotropy and spin-rotation interactions from the observed electron spin-lattice relaxation rates, the contribution of the thermally activated process was obtained and compared with its expression for the temperature dependence. Consistent values of various fitted parameters, used in the expression of the thermal process, have been found, and the applicability of the expression of the thermally activated process to describe the temperature dependence in liquid solutions has been vindicated. Moderate solvent dependence of the thermally activated process has also been observed. The rotational correlation times and the spin-lattice relaxation processes of nitroxyls in ionic liquids and in conventional organic liquids are shown to be explicable on a similar footing, requiring no special treatment for ionic liquids.

Change of translational-rotational coupling in liquids revealed by field-cycling 1H NMR.

Applying the field-cycling nuclear magnetic resonance technique, the frequency dependence of the (1)H spin-lattice relaxation rate, R1ω=T1(-1)ω, is measured for propylene glycol (PG) which is increasingly diluted with deuterated chloroform. A frequency range of 10 kHz-20 MHz and a broad temperature interval from 220 to about 100 K are covered. The results are compared to those of experiments, where glycerol and o-terphenyl are diluted with their deuterated counter-part. Reflecting intra- as well as intermolecular relaxation, the dispersion curves R1ω,x (x denotes mole fraction PG) allow to extract the rotational time constant τrot(T, x) and the self-diffusion coefficient D(T, x) in a single experiment. The Stokes-Einstein-Debye (SED) relation is tested in terms of the quantity D(T, x) τrot(T, x) which provides a measure of an effective hydrodynamic radius or equivalently of the spectral separation of the translational and the rotational relaxation contribution. In contrast to o-terphenyl, glycerol and PG show a spectral separation much larger than suggested by the SED relation. In the case of PG/chloroform mixtures, not only an acceleration of the PG dynamics is observed with increasing dilution but also the spectral separation of rotational and translational relaxation contributions continuously decreases. Finally, following a behavior similar to that of o-terphenyl already at about x = 0.6; i.e., while D(T, x) τrot(T, x) in the mixture is essentially temperature independent, it strongly increases with x signaling thus a change of translational-rotational coupling. This directly reflects the dissolution of the hydrogen-bond network and thus a change of solution structure.

Dynamics of methanol in ionic liquids: validity of the Stokes-Einstein and Stokes-Einstein-Debye relations.

The validity of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations for methanol in the physical environment of the ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide is studied by means of nuclear magnetic resonance (NMR) relaxation time experiments, viscosity measurements and molecular dynamics (MD) simulations. The reorientational correlation times of the hydroxyl groups of pure methanol and of methanol in the IL/methanol mixtures were determined. For that purpose an approach for estimating NMR deuteron quadrupole coupling constants, presented by Wendt and Farrar (Mol. Phys. 1998, 95, 1077-1081), was confirmed. The self-diffusion coefficients of methanol were taken from the MD simulations. The viscosities of all systems were then measured and the SE and SED relations validated. For pure methanol both relations are valid, whereas they become increasingly invalid with increasing IL concentration, as indicated by effective volumes and radii that are too low. The deviation from the SE and SED relations could be related to dynamical heterogeneities described by the non-Gaussian parameter α(t) obtained from MD simulations. For pure methanol, α(t) is close to zero in accord with the validity of both relations. With increasing IL concentration the dynamical heterogeneities of methanol increase strongly. The times t* at the maximum of α(t) increase linearly with the relative number of methanol monomers in the mixtures. Thus, the dynamical heterogeneities are largest for single methanol molecules fully embedded in the IL environment. In their own environment methanol molecules are highly mobile, whereas in the IL-rich region the mobility is strongly reduced leading to the non-validity of SE and SED relations.

Stokes–Einstein–Debye Failure in Molecular Orientational Diffusion: Exception or Rule?

The Stokes-Einstein-Debye (SED) expression is used routinely to relate orientational molecular diffusivity quantitatively to viscosity. However, it is well-known that Einstein's equations are derived from hydrodynamic theory for the diffusion of a Brownian particle in a homogeneous fluid and examples of SED breakdown and failure for molecular diffusion are not unusual. Here, using optical Kerr-effect spectroscopy to measure orientational diffusion for solutions of guanidine hydrochloride in water and mixtures of carbon disulfide with hexadecane, we show that these two contrasting systems each show pronounced exception to the SED relation and ask if it is reasonable to expect molecular diffusion to be a simple function of viscosity.

A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.

Fractional Stokes–Einstein–Debye relation and orientational entropy effects in strongly hydrogen-bonded liquid amides

The impedance spectroscopy studies performed for two strongly hydrogen-bonded liquid amides: N-methylpropionamide (NMP, CH(3)·NH·CO·C(2)H(5)) and N-ethylacetamide (NEA, C(2)H(5)·NH·CO·CH(3)) have shown that the two centers of the peptide linkage, -NH·CO-, active in the C=OH-N hydrogen bonds formation, exhibit quite different sensibilities to the steric screening effects. In contrast to the oxygen atom, a relatively small change (CH(3)- to C(2)H(5)-) in the screening of the hydrogen atom leads to an essential decrease of the degree of the amide self-association. As a consequence, both the static dielectric permittivity and the orientational entropy increment of NEA are essentially lower than those of NMP. However, it was found that the dynamic processes studied are only weakly influenced (in the case of dc conductivity, σ(DC)) or totally not influenced (the dielectric relaxation time, τ(D)) by the different degrees of NMP and NEA self-association. The experiment shows that for both the amides, the logσ(DC) vs. logτ(D) dependence is nonlinear and can be described with the fractional Stokes-Einstein-Debye relation, σ(DC)τ ≅ const, with the exponent s varying from about -0.8 to about -0.6 in the temperature range from 5 °C to 110 °C.

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in the neat ionic liquid (IL) [C(2)mim][NTf(2)] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)--H bond in the cation C(2)mim(+), and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non-Gaussian parameter alpha(t). If alpha(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.