Debye Stokes Einstein Equation Research Articles

Conformational states of NADH in water–alcohol solutions studied by molecular dynamics simulations

Redox reactions in living cells involving a coenzyme nicotinamide-adenine-dinucleotide (NAD) are stereospecific and depend on NAD conformation states and on the structure of enzyme binding sites. Therefore, information on NAD conformation states in various environments is important for understanding of the mechanisms of redox reactions. In this paper the structural dynamics of reduced nicotinamide-adenine-dinucleotide (NADH) in water–methanol and water–ethanol solutions was investigated by means of molecular dynamics simulations. The trajectory analysis revealed three stable conformation groups characterized by the distance RNA−AD between adenine and nicotinamide centers of mass: folded (RNA−AD< 5.5 Å), intermediate (5.5 Å <RNA−AD< 12 Å) and unfolded (RNA−AD> 12 Å). It was shown that conformation equilibrium shifted from the folded conformation group at low alcohol concentrations towards the intermediate conformation group at high alcohol concentrations, while the fractional concentration of unfolded conformation group remained almost constant. The nicotinamide and adenine rings were found to be almost parallel in folded conformations and perpendicular in intermediate conformations, while no preferable positions of the rings were found in unfolded conformations. The results obtained were used for the analysis of experimentally determined rotational diffusion times τrexp in NADH in water–methanol and water–ethanol mixtures. Comparison between the calculated and experimental τr values using the generalized Stokes–Einstein–Debye equation allowed for determination of the wettability coefficient C and effective molecular volume Vm as a function of alcohol concentration. The coefficient C was found to be always less than unity and have a minimum at 40% of alcohol which was more pronounced for ethanol than for methanol mixtures. This dependence was attributed to the influence of solution viscosity that has a maximum at 40% of alcohol. The effective molecular volume Vm was found to be practically constant at alcohol concentrations below 60% and rise dramatically at higher alcohol concentrations. This dependence was attributed to the solvation of NADH at high alcohol concentrations.

Fast Dynamics of Difluprednate in Micelles or Swollen-Micelles Revealed by 19F Nuclear Magnetic Resonance Spin Relaxation Rates

Knowledge of molecular rotational dynamics is critical to interpret solution nuclear magnetic resonance (NMR) spectroscopy. The observation of sharp solute NMR signals in micelles contradicted the surfactant viscosity effects noted in the Stokes-Einstein-Debye (SED) equation. Herein, the 19F spin relaxation rates of difluprednate (DFPN) drug dissolved in polysorbate-80 (PS-80) micelles and castor oil swollen micelles (s-micelle) were measured and adequately fit using an isotropic diffusion model based spectral density function. Despite the high viscosity of PS-80 and castor oil, the fitting results revealed fast 4 and 12 ns dynamics of DFPN in both micelle globules. The observation of the fast ns motion in the viscous surfactant/oil micelle phase demonstrated motion decoupling between solute molecules inside micelles and the micelle itself in an aqueous solution. These observations support the role of intermolecular interaction in governing the rotational dynamics of small molecules, versus the viscosity of the solvent molecules as defined in the SED equation.

Heterogeneous Structures of Ionic Liquids as Probed by CO Rotation with Nuclear Magnetic Resonance Relaxation Analysis and Molecular Dynamics Simulations.

The rotational dynamics of carbon monoxide (CO) in ionic liquids (ILs) was investigated by nuclear magnetic resonance (NMR) relaxation measurements and molecular dynamics (MD) simulations. NMR spin-lattice relaxation time measurements were performed for 17O-enriched CO in 10 ILs (four imidazolium-cation-based, four phosphonium-cation-based, and two ammonium-cation-based ILs, all paired with the bis(trifluorosulfonylmethane)imide anion). In combination with previously reported data for five ILs and viscosity data, our results indicated that the obtained rotational relaxation times (τ2R) were much smaller than those predicted using the Stokes-Einstein-Debye (SED) theory. For the same viscosity/temperature values, the τ2R-1 value increased linearly with increasing carbon number of the alkyl group in the cation. The deviation from the SED equation was due to the insensitivity of τ2R to the carbon number, even though a higher carbon number generally leads to higher viscosity values for ILs. To investigate the unique rotational properties of CO in the ILs, MD simulations were performed on five representative ILs (two imidazolium, two phosphonium, and one ammonium) containing CO solutes. From rotational correlation function analyses, the CO rotation mainly occurred in a free rotation-like manner within 1 ps, which explained the relative insensitivity of CO rotation to viscosity. In the subsequent time scale (>1 ps), the minor component of the CO rotation was discriminated among different ILs. It was strongly suggested that, because CO preferably locates in the outer part of the alkyl groups in the cation, the slow CO rotation is correlated with the outer alkyl dynamics, which are decoupled from the whole cation rotation.

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.

Solvent viscosity induces twisted intramolecular charge transfer state lifetime tunable of Thioflavin-T

Excited-state deactivation dynamics of Thioflavin-T (ThT) in gradual viscosity solvents were investigated. Femtosecond transient absorption spectra and dynamic decay curves both present significant distinction of ThT in different volume ratios binary mixtures solvents. Dynamics fitting lifetime of twisted intramolecular charge transfer (TICT) state is strongly dependent on solvents viscosity. Compared to rotation corresponding time of ThT in low viscosity solvent (0.6 cp) experimentally coincident well with Stokes-Einstein-Debye (SED) equation, the relation between rotation corresponding time and relatively high viscosity (5.9 cp to 1091.2 cp) is more consistent with fractional SED equation. Combined with optimized geometric structures of ThT by density functional theory and time-dependent density functional theory, further understand TICT state lifetime increases with increasing solvents viscosity. Our work provides a comprehensive understanding of fluorescence molecular rotor (FMR) deactivation process in different viscosity solvents and is helpful to design new FMR.

Rational design of sensor for broadband dielectric spectroscopy of biomolecules

Knowledge of electromagnetic properties of biomolecules is essential for a fundamental understanding of electric field interaction with biosystems and for development of novel biomedical diagnostic and therapeutic methods. To enable systematic analysis of the dielectric properties of biomolecule solutions we presented here a method for a rational design of radiofrequency and microwave chip for quantitative dielectric sensing. At first, we estimated the primary frequency band of interest using a relaxation time of targeted molecule via the Stokes–Einstein–Debye equation. Then we proposed a microwave sensing chip for the estimated frequency band and evaluated its performance using both analytical modeling and numerical electromagnetic simulations. We fabricated the chip and experimentally demonstrated that we can extract the complex permittivity (0.5–40 GHz) of the water solution of alanine – one of the most common proteinogenic amino acids – without any calibration liquid and with about 20-fold smaller volume than with commercial methods. The observed dependence of extracted complex permittivity on the alanine concentration was interpreted using molecular dynamics simulations. The procedure we described here can be applied for the development of dielectric sensing method of any polar biomolecule solution.

Intermolecular interactions and molecular dynamics in bovine serum albumin solutions studied by small angle X-ray scattering and dielectric relaxation spectroscopy

We used small angle X-ray scattering (SAXS) and dielectric relaxation spectroscopy (DRS) to clarify static structure and molecular dynamics of bovine serum albumin (BSA) in solution. SAXS allowed us to access spatial correlations of the protein molecules in concentrated solutions at different ionic strength. Using a well-established Fourier inversion technique, called SQ-IFT, we deduced the effective pair correlation functions, g(r)eff, from the effective (or experimental) structure factors, S(q)eff, without assuming any potential models for protein–protein interactions. In terms of S(q)eff and g(r)eff, the mean nearest-neighbor distance, d⁎, the osmotic compressibility, κosm, and the coordination number, NC, were evaluated.The complex dielectric spectra of aqueous BSA solutions measured in the frequency range from 1MHz to 10GHz were able to be decomposed into three relaxation processes having different physical origins. The highest frequency process, whose relaxation time was ca. 8ps, was assigned to cooperative rearrangement of H-bond network of bulk-water. We evaluated the effective hydration number of a BSA molecule, Zhyd, using the bulk-water relaxation amplitude. This approach yielded ca. 1200 hydrated water molecules per a BSA molecule, corresponding to ca. 0.3g hydrated water per 1g protein. The lowest frequency process having a relaxation time of ca. 50ns was assigned to rotational diffusion of the BSA molecule. We confirmed that an effective molar volume of BSA calculated with Stokes–Einstein–Debye equation was identical to that predicted from its molecular weight and specific density. According to the Kirkwood relationship, the dipole–dipole orientational correlation factor decreased with an increase of protein concentration, which indicated the operation of BSA–BSA interaction and favored antiparallel dipolar correlation between the protein molecules.

Macromolecular dynamics of sulfonated poly(styrene- b-ethylene- ran-butylene- b-styrene) block copolymers by broadband dielectric spectroscopy

Macromolecular dynamics of sulfonated poly(styrene- b-ethylene- ran-butylene- b-styrene) (sSEBS) triblock copolymers were investigated using broadband dielectric spectroscopy (BDS). Two main relaxations corresponding to the glass transitions in the EB and S block phases were identified and their temperature dependences were VFT-like. T g for the S block phase shifted to higher temperature due to restrictions on chain mobility caused by hydrogen bonded SO 3H groups. While the EB block phase T g appeared to remain constant with degree of sulfonation in DMA experiments, it shifted somewhat upward in BDS spectra. A low temperature relaxation beneath the glass transition of the EB block phase was attributed to short range chain motions. The Kramers–Krönig integral transformation was used to calculate conductivity-free loss permittivity spectra from real permittivity spectra to enhance true relaxation peaks. A loss permittivity peak tentatively assigned to relaxation of internal S-EB interfacial polarization was seen at temperatures above the S block phase glass transition, and the temperature dependence of this relaxation was VFT-like. The fragilities of the EB and S block domains in sulfonated SEBS decreased after sulfonation. The temperature dependence of the dc conduction contribution to sSEBS loss spectra also followed VFT-like behavior and S block segmental relaxation time correlated well with conductivity according to the fractional Debye–Stokes–Einstein equation.

Orientational and Translational Dynamics of Polyether/Water Solutions

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments and pulsed field-gradient spin-echo NMR (PFGSE-NMR) experiments were performed to measure the rotational and translational diffusion constants of a polyether, tetraethylene glycol dimethyl ether (TEGDE), in binary mixtures with water over concentrations ranging from pure TEGDE to approaching infinite dilution. In addition, hydrodynamic calculations of the rotational and translational diffusion constants for several rigid TEGDE conformations in the neat liquid and in the infinitely dilute solution were performed to supplement the experimental data. The rotational relaxation data follow the Debye-Stokes-Einstein (DSE) equation within experimental error over the entire water concentration range. The agreement with the DSE equation indicates that there is no significant structural change of the polyether as the water content is changed. In contrast to the rotational dynamics, the translational diffusion data show a distinct deviation from Stokes-Einstein (SE) behavior. As the water content of the mixture is reduced, the translational diffusion rate decreases less rapidly than the increase in viscosity alone predicts until the water/TEGDE mole ratio of 7:1 is reached. Upon further reduction of water content, the translational diffusion tracks the viscosity. Comparison of the translational data with the rotational data and the hydrodynamic computations shows that the translational dynamics cannot be explained by a molecular shape change and that the low water fraction solutions are the ones that deviate from hydrodynamic behavior. A conjecture is presented as a possible explanation for the different behaviors of the rotational and translational dynamics.

Structure-Dependent DC Conductivity and Relaxation Time in the Debye−Stokes−Einstein Equation

The basis for a modification of the Debye-Stokes-Einstein (DSE) equation between the dc conductivity, sigma(dc), and dielectric relaxation time, tau, has been examined by using broad-band dielectric spectroscopy of LiClO4 solutions in 5-methyl-2-hexanol and 1-propanol and of pure liquids. According to the DSE equation, the log sigma(dc)-log tau plots should have a slope of -1. We find that sigma(dc) begins to depend upon the structure of an electrolytic solution when a variation of solvent's equilibrium dielectric permittivity, epsilon(s), with temperature causes the ion population to vary. As a consequence of this intrinsic dependence, the log sigma(dc)-log tau plots do not obey the DSE equation. Inclusion of the effect of change in epsilon(s) on the DSE equation may be useful in analyzing the measured quantities in terms of Brownian diffusion of both ions and molecules in ultraviscous liquids. Proton translocation along a hydrogen bond contributes little to sigma(dc), which appears to be predominantly determined by the ion population in the two alcohols and the solutions. The effect is briefly discussed in the potential energy landscape paradigm of structure fluctuations, and it is suggested that the high-frequency shear modulus measurements of ionic solutions would help reveal the temperature-dependent deviation from the DSE equation.

Effect of Pressure on Molecular and Ionic Motions in Ultraviscous Acetaminophen–Aspirin Mixture

Effect of pressure and temperature on molecular motions and dc conductivity in ultraviscous, 50 wt% acetaminophen–aspirin melt has been studied by dielectric relaxation spectroscopy. The spectra obtained over the pressure range, 5–300 MPa and temperature range, 295–320 K show a distribution of relaxation times greater than found in pure acetaminophen. The equilibrium dielectric permittivity and relaxation time, τ, of the melt increase with increase in pressure and decrease in temperature and the dc conductivity, σdc, decreases. The pressure and temperature variation of the limiting high frequency permittivity shows significant contribution from infrared polarization. The volumes of activation for σdc and τ vary with both the pressure and temperature, indicating that there is also a structural effect that determine σdc. This effect would add a non-linear term to the Debye–Stokes–Einstein equation for variation of σdc with τ. The ultraviscous liquid remains stable with time, and with change in temperature and pressure, suggesting that a more stable glassy state of a pharmaceutical may be obtained by mixing a second component.

Orientational diffusion of n-alkyl cyanides

Ultrafast optical Kerr effect spectroscopy has been used to study thetemperature-dependent orientational dynamics of a series of nitriles withn-alkyl chains ranging from one to 11 carbons in length. In all cases the orientationaldiffusion is found to be described by a single-exponential decay. Analysis of theorientational correlation times using the Debye–Stokes–Einstein equation suggests that themolecules adopt extended configurations and reorient as rigid rods. The liquids withshorter alkyl chains undergo an apparent ordering transition as they are cooled.

Test of the fractional Debye-Stokes-Einstein equation in low-molecular-weight glass-forming liquids under condition of high compression.

From temperature studies at ambient pressure, it was pointed out for several glass-forming liquids that the alpha-relaxation time (tau) can be related to the dc-ionic conductivity (sigma) through the phenomenological fractional Debye-Stokes-Einstein (DSE) equation. In the present paper we test the validity of fractional DSE equation for relaxation data obtained from pressure variable experiments. To this end we carried out broadband dielectric measurements (10 mHz-10 MHz) in a wide range of pressures (0.1-300 MPa). The material under study were N,N-diglycidyl-4-glycidyloxyaniline and N,N-diglycidylaniline. As a result we found that the fractional DSE equation is also obeyed for pressure pathways.

Ultrafast Raman-induced Kerr-effect of water: Single molecule versus collective motions

The ultrafast optical Kerr-response of water and heavy water has been measured at 1 bar in the temperature range between 273 and 373 K. The nuclear Kerr response of the liquid exhibits a pronounced double exponential decay on longer time scales after dephasing of impulsively perturbed acoustic modes is completed. The time constant, τ2, characterizing the slowly decaying exponential component of the Kerr-response function is in quantitative agreement with rotational diffusion time constants of the water molecules obtained form nuclear magnetic resonance (NMR) spin-lattice relaxation rates. A detailed comparison with THz time domain spectroscopy demonstrates that the reorientational dynamics responsible for the long time tail of the Kerr response are due to single molecule as opposed to collective effects. Furthermore, a good agreement between the single molecule rotational diffusion and the Stokes–Einstein–Debye equation is found in the temperature range of thermodynamic stability of the liquid. The time constant, τ1, characterizing the fast exponential component of the Kerr-response of water is found to be in qualitative agreement with central Lorentzian linewidths obtained from frequency-domain, depolarized Raman scattering experiments. The temperature dependence of τ2 does not follow an Arrhenius-type behavior, which was previously taken as evidence for thermally activated crossing of a librational barrier with concomitant hydrogen-bond breakage. Instead, the temperature dependence of the fast relaxation time constant can be represented adequately by the Speedy–Angell relation which has been shown to accurately describe a number of transport parameters and thermodynamic properties of water.

Fluorescence anisotropy of ketocyanine dyes in homogeneous and heterogeneous media. Estimation of micellar microviscosity

Fluorescence anisotropies (r) of two ketocyanine dyes have been determined in homogeneous solvents (pure and mixed binary) and in micellar media. For pure solvents the rotational reorientation times have been calculated and compared with the values calculated using the modified Stokes–Einstein–Debye equation. The discrepancy between the two values has been discussed in terms of dielectric factors. Ethanol–water and ethanol–octan-1-ol binary mixtures exhibit ideal solvation behaviour and the anisotropy values are well represented by Perrin's equation. For a protic–aprotic solvent mixture, non-ideal solvation behavior is observed which has been explained as due to solute–solvent as well as solvent–solvent interaction for the two component solvents. The microviscosity around a micellar region and the related activation energy has been measured from the r values in these media at various temperatures.

Microscopic Viscosity and Rotational Diffusion of Proteins in a Macromolecular Environment

The Stokes–Einstein–Debye equation is currently used to obtain information on protein size or on local viscosity from the measurement of the rotational correlation time. However, the implicit assumptions of a continuous and homogeneous solvent do not hold either in vivo, because of the high density of macromolecules, or in vitro, where viscosity is adjusted by adding viscous cosolvents of various size. To quantify the consequence of nonhomogeneity, we have measured the rotational Brownian motion of three globular proteins with molecular mass from 66 to 4000 kD in presence of 1.5 to 2000 kD dextrans as viscous cosolvents. Our results indicate that the linear viscosity dependence of the Stokes–Einstein relation must be replaced by a power law to describe the rotational Brownian motion of proteins in a macromolecular environment. The exponent of the power law expresses the fact that the protein experiences only a fraction of the hydrodynamic interactions of macromolecular cosolvents. An explicit expression of the exponent in terms of protein size and cosolvent's mass is obtained, permitting definition of a microscopic viscosity. Experimental data suggest that a similar effective microviscosity should be introduced in Kramers’ equation describing protein reaction rates.

An Evaluation of the Overall Rotational Correlation Times of Tetraalkylammonium Ions in Solution. 13C NMR Relaxation Study

Abstract The 13C NMR spin-lattice and spin–spin relaxation times (T1 and T2), and the nuclear Overhauser effect (NOE) were measured for tetraalkylammonium ions (R4N+, R = C2H5 (Et), n-C3H7 (n-Pr), n-C4H9 (n-Bu), and n-C5H11 (n-Pen)) in the concentrated aqueous solutions of their bromides or chlorides. A minimum was observed in the temperature dependence of T1 for the α-carbon in each solution. The value was 1.2—1.4 times higher than that predicted assuming only the isotropic overall rotation of the R4N+ ion. This increase in the T1 minimum values was ascribed to the rotations around the N–α-C bonds with an restriction in the azimuthal angle for each bond. The ranges where the N–α-C bonds could rotate with the time scales much less than those for the overall rotations were determined by the values of the T1 minima for the corresponding R4N+ ions as ±20°, ±17°, ±20°, and ±20° centering the gauche conformations, respectively, for Et4N+, n-Pr4N+, n-Bu4N+, and n-Pen4N+. These values well reproduced the T2 and NOE values observed at various temperatures in the concentrated aqueous solutions of the R4N+ halides. By using the thus obtained ranges of the azimuthal angles, the overall rotational correlation times in the dilute aqueous solutions (0.01 mol kg−1) were also determined. The obtained rotational correlation times were compared with those calculated using the Stokes–Einstein–Debye equation and the effect of the hydrophobic hydration was discussed.

How do molecules move near T g? Molecular rotation of six probes in o-terphenyl across 14 decades in time

Time resolved optical spectroscopy was used to observe molecular rotation over more than 14 decades in time for six probes in o-terphenyl (OTP). In contrast to previous studies, probe rotation times are found to depend significantly upon probe size in the deeply supercooled regime. Systematic deviations from the temperature dependence of the Debye–Stokes–Einstein equation are observed, however, these deviations are relatively small. These observations are inconsistent with some models of cooperative molecular motion near Tg which invoke rigid aggregates or locally liquidlike regions. The width of the relaxation spectrum (characterized by the KWW β parameter) systematically decreases with increasing probe size. Near Tg, the largest probe (rubrene) rotates with nearly a single exponential correlation function. Based on the observed trend in β, it is estimated that OTP is homogeneous on length scales greater than 2.5 nm at Tg.

Dynamics of the glass-forming liquid di-2-ethylhexyl phthalate (DOP) as studied by light scattering and neutron scattering

Dynamic light scattering (depolarized Rayleigh and polarized Rayleigh–Brillouin) and quasielastic neutron scattering are employed to study the dynamics of the glass-forming liquid di-2-ethylhexyl phthalate (DOP) (Tg=184 K). The depolarized Rayleigh scattering measurements were made in the temperature range from 303 to 433 K, the polarized Rayleigh–Brillouin measurements in the range from 263 to 433 K, and the quasielastic neutron-scattering measurements in the range from 37 to 312 K and in the Q range from 0.33 to 1.84 Å−1. The orientation times for DOP, obtained from a single Lorentzian fit to the experimental depolarized spectra at high T, are in good agreement with recent dielectric data for the primary (α) relaxation. However, at lower T, the viscosity increases more strongly than the orientation times and the Stokes–Einstein–Debye equation which can adequately describe the dynamics in the high-T range is insufficient at temperatures close to Tg. The relaxation time obtained from the Rayleigh–Brillouin experiment is about 1 order of magnitude faster than the orientation times. In the neutron-scattering experiment we find a strong decrease of the elastic intensity and a corresponding increase of the quasielastic intensity around Tg. The data analysis with respect to the dynamics (from a two Lorentzian fit) revealed the existence of three processes affecting the high-frequency range: (i) a ‘‘fast’’ (τ2∼10 ps) Q-independent motion with weak T dependence (E2=1.54 kcal/mol), (ii) a ‘‘slow’’ Q-dependent motion, and (iii) a flat background increasing with T and Q. The fast process is discussed in terms of a very localized motion of the phenyl group (β relaxation) and, as such, as a precursor of the the primary (α) relaxation. The relaxation time of this process (τ2) was found to compare nicely with the time τmax from the Rayleigh–Brillouin (RB) experiment suggesting that the latter is caused by fast localized motions. The slow process is discussed in terms of the jump-diffusion model. The activation energy associated with the jump-diffusion times is 6.1 kcal/mol and it is associated with large-scale diffusional motion of the DOP molecule. The relaxation times obtained from this process are compared with the relaxation times obtained from the depolarized and dielectric techniques for the primary relaxation. Finally, the background can be identified with fast local motions and/or low-frequency excitations relaxing outside the energy window of our experiment.

Erratum: Solvent structure effects on solvated electron reactions in mixed solvents: Negative ions in 1-propanol–water and 2-propanol–water

In models of the kinetics of chemical reactions in solution the solvent is commonly assumed to be a uniform continuum. An example is the Smoluchowski–Debye–Stokes–Einstein equation for the rate constant k2 of a bimolecular reaction between charged or polar species: k2 = κRTfrr/1.5ηrd where κ = probability that a reactant encounter pair will react, R = gas constant, T = temperature, f = Coulombic interaction factor, rr = effective radius for reaction, η = solvent viscosity, and rd = effective radius for mutual diffusion. The equation is useful in evaluating effects of bulk-fluid properties on reaction rates. Residual effects are attributed to more specific solvent behaviour. Rate constants and activation energies E2 of reactions of solvated electrons with and ions vary with the composition of 1-propanol–water and 2-propanol–water mixed solvents. Plots of k2η/fT against solvent composition are nonlinear and change with solvent pair and with reactant pair. Measured molar conductivities Λ0(Li+, ) and Λ0(2Li+,...