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Proton conductivity in supercooled aqueous HCI solutions
Abstract
Measurements of the electrical resistivity of 1, 0.1, and 0.01 M solutions of HCl and KCl in water to-32°C are reported. Values of the proton conductivity λH+ in the HCl solutions are estimated. λH+ is a linear function of temperature in the range -32 to +45°C, λH+ = A(T/Ts - 1), and extrapolates to zero at Ts = 227 K. Implications concerning the structure of water at Ts are discussed.
... Under these conditions, the corresponding experimental diffusion coefficient would be smaller. [32][33][34] That being said, our calculated proton diffusion coefficient is comparable to previously reported proton diffusion coefficients for the similarly over-structured BLYP functional (0.5 to 1.48Å 2 /ps). 13,35,36 In order to obtain results closer to ambient conditions, we ran a second set of simulations at 440 K, which was previously suggested as a temperature at which the PBE functional gives better ambient liquid water properties. ...
The aqueous proton displays an anomalously large diffusion coefficient that is up to 7 times that of similarly sized cations. There is general consensus that the proton achieves its high diffusion through the Grotthuss mechanism, whereby protons hop from one molecule to the next. A main assumption concerning the extraction of the timescale of the Grotthuss mechanism from experimental results has been that, on average, there is an equal probability for the proton to hop to any of its neighboring water molecules. Herein, we present ab initio simulations that show this assumption is not generally valid. Specifically, we observe that there is an increased probability for the proton to revert back to its previous location. These correlations indicate that the interpretation of the experimental results need to be re-examined and suggest that the timescale of the Grotthuss mechanism is significantly shorter than was previously thought.
Proton mobility is traditionally thought to be governed by water molecule rotation. Water rotation times from D2O NMR spinlattice relaxation measurements are compared with proton hopping times from mobility data with and without subtraction of the estimated hydrodynamic mobility. In the latter case the two data agree nicely at high temperatures. It is concluded that the hydrodynamic proton mobility is considerably smaller than previously believed because H3O+ is nearly immobilized by extra-strong hydrogen-bonds to first-shell water ligands, estimated to be about 2 kcal/mol stronger than bulk hydrogen-bonds. Water rotation is slower than proton hopping below 20°C and has a hydrodynamic component to its activation energy. Therefore, proton mobility is not governed by water rotation but rather both processes are controlled by hydrogen-bond dynamics. Comparison with hydrogen-bond lifetimes from depolarized light scattering suggests that two consecutive cleavage events of ordinary hydrogen bonds constitute a single proton hop. This agrees with a recent molecular model for the Grotthuss mechanism.
The rate of excited-state proton transfer from four cyano-substituted 2-naphthols was measured in H2O and D2O by picosecond time-resolved fluorescence. The excited-state acidity constant, pK(a)*, was calculated and compared with previous results and was found to be substitution-dependent, as predicted by the charge-transfer theory. The isotope effect was evaluated for all the compounds of the series. As reported for many other hydroxyaromatic compounds, this effect was more important for the dissociation rate constant than for the recombination rate constant.
A proton transport model is proposed to describe proton diffusion in Nafion/(ZrO 2 /SO 2 - 4 ) nanocomposite membranes. The model considers the water content which could be determined by thermodynamics, dissociation of protons near the acid surface, stabilization of protons in water, and the strength and concentration of acid sites from Nafion as well as ZrO 2 /SO 2 - 4 . The transport of proton occurs via a sluggish hopping process through the membrane surface, and relatively fast structural and ordinary mass diffusion of hydronium ions in the bulk of the membrane pores. The conductivity of the in situ sol-gel prepared Nafion/ (ZrO 2 /SO 2 - 4 ) nanocomposite membranes is accurately predicted as a function of relative humidity without any fitted parameters. Nafion/(ZrO 2 /SO 2 - 4 ) nanocomposite membrane shows higher proton conductivity compared with Nafion at the same temperature and humidity conditions due to the improved water uptake and provision of strong acid sites. The model provides a theoretical framework for understanding proton conduction in nanocomposite membranes and can be successfully used to develop high-conducting membranes for fuel cell applications.
The reversible proton dissociation and geminate recombination of photoacids was studied as a function of temperature in neat water, binary water mixture containing 0.6 mol% glycerol, and doped ice containing 0.6 mol% glycerol. The deuterium isotope effect on both condensed phases was also studied. 8-hydroxypyrene-1,3,6 trisulfonate trisodium salt was used as the electronically-excited-state proton emitter. The experimental data are analyzed by the Debye–Smoluchowski equation solved numerically with boundary conditions to account for the reversibility of the reaction. We propose a qualitative model to describe the unusual temperature dependence of the proton transfer rate in the liquid phase. We also propose a model for proton transfer in solid ice based on L-defects transport as proton acceptors. While in the liquid phase at t > 10°C the proton dissociation rate constant is almost temperature independent, in glycerol-doped ice we find a large temperature dependence.
An earlier study on the properties of supercooled water and some solutes obtained by simple graphical extrapolation of data available in the literature, determined above the freezing point, led to the hypothesis that water could have a temperature of structural arrest at t0 =-30 °C for H2 O and -22 °C for D2 O. From the present investigation of many more properties of a widely varied nature, this discovery is confirmed throughout. The method is compared with the classical logarithmic Arrhenius and van't Hoff methods that predict t0 always to occur at 0 K, and with the more recently used power law dependence method. With the latter, extrapolated plots intersect the temperature axis at or near to a value of ts =-45 °C, that is, systematically more negative than t0 . It is argued that this ts value, which is the so-called singularity temperature, is likely to be an artefact. It is suggested that, instead of using modified van 't Hoff or Arrhenius relationships to describe temperature dependences in the full temperature range, polynomials in (t-t0 ) should be used.
A fundamental understanding of the relationship between the nanoscale structure of proton exchange membranes (PEMs) and their proton conductivity would be exceedingly useful in optimizing existing and designing new materials. In this work, a set of structural descriptors, accounting for nanopore size, functionalization and connectivity are employed to predict proton conductivities in PEMs. The model reproduces experimentally determined conductivities in two PEMs. The model is applied to water-filled cylindrical nanopores functionalized on their interior surface with acid groups. It is demonstrated that for cylindrical nanopores of a given radius there is an optimal surface coverage of acid groups. The optimum can be sharply peaked, indicating that non-optimal surface coverages (either too low or too high) drastically reduce the conductivity of the pore. The theoretical maximum conductivity through a cylindrical nanopore is calculated to be about 0.70 S/cm at 300 K.
When two ions of opposite charge in an aqueous solution form an ion pair, the hydration shells of the individual ions become partly destroyed because of the weakened interaction between the ions and the water molecules. The reaction A–+ K⁺⇌ AK +hFH2O is considered, where A– is the hydrated free anion and K⁺ the cation, and AK the less hydrated contact ion pair. The equilibrium concentrations are calculated, taking into account the excess Gibbs energies that arise from ion–ion and ion–dipole interactions. The concentration of the bulk water also affects the equilibrium.
Combining this chemical model with the MSAT (mean spherical approximation transport) equations for the electrolytic conductivity, very precise fits with an rms better than 0.05% of conductivity data are obtained, up to high concentrations (e.g. 12 mol dm–3 for HCI at 25 °C).
Using the equilibrium concentrations obtained from conductivity data, density and vapour pressure data can be reproduced quantitatively. Using this approach, molar volumes of free hydrated ions, contact ion pairs and bulk water are independent of the concentration.
In a concentrated acid or salt solution the amount of solvent molecules bound in the ionic solvation layers is an appreciable fraction of the total amount of solvent available. Some of the bound solvent molecules are released upon contact-ion-pair formation. The participation of the solvent is taken into account in the calculation of ion-pair formation by explicitly balancing the mixing entropy change with the standard and excess energy changes. The latter are taken from the mean spherical approximation theory for ion-ion interaction, augmented with a term for electrostatic ion-ion-pair interaction. A least-squares global optimization applied to a large body of available literature data on conductivities of univalent electrolytes over the concentration range up to saturated solutions is used for obtaining consistent values for ionic hydration numbers, standard free energies of ion-pair formation and electrostatic interaction parameters. With these values the measured conductivity data can be reproduced over the whole concentration range with an accuracy approaching that of the measurements themselves. As an example, the results for HCl and CsCl are presented and compared.
In equations for the partial volume, dilatability, heat capacity, and adiabatic compressibility of aqueous urea, the properties
are “fitted” to the singular temperature T
s of overcooled water T
s = 227.15 K (R. J. Speedy, J. Phys. Chem., 91, 3354 (1987)). The equations for the characteristics of D2O-(ND2)2CO and T2O-(NT2)2CO systems were obtained by scaling the temperature to 6 and 9.4 K, respectively. The properties of infinitely dilute solutions
did not reveal the sign reversal of the isotope effect. The isoconcentrates of the partial volumes and dilatability form wagging
lines in the region of low temperatures. The temperature dependences of the properties have extrema and inflection points,
while the isotope effects in solutions of finite concentrations experience sign reversal. The maximum density temperature
(MDT) of the solution decreases as the urea concentration increases, and also on passing from D2O-(ND2)2CO to H2O-(NH2)2CO. Thus, for the 8m solution, the MDT is 259.6 K (protium system) and 266.7 K (deuterium system). The difference is almost equal to the shift
of the MDT after the H2O → D2O transition (7.2 K).
Dynamical properties of water and protons in Nafion with an equivalent weight of 1144 are studied using the recently developed reactive molecular dynamics (RMD) algorithm at various water contents. The structural diffusion of a proton along the aqueous domains is modeled via a mechanism similar to that observed in bulk aqueous systems. The algorithm implements reactivity in classical MD simulations by three steps: (i) satisfaction of the trigger, (ii) instantaneous reaction, and (iii) local equilibration. Two different schemes (Method 1 and Method 2) of execution of the algorithm are investigated, which differ in terms of the range of the local environment involved in the reaction. Both methods are parametrized to the experimental rate constant of proton transport in bulk water. The mean lifetime of the protons increased with the water content in Nafion. Water diffusivities of the reactive systems using the two schemes increased with the hydration level and were higher than the diffusion coefficients in the nonreactive system. The more detailed scheme in Method 2 which included the relaxation of the extended hydrogen bonding network around the proton-hopping reaction lowered the water diffusivity compared to that of Method 1 and also affected both the structural and vehicular components of diffusion. The total charge diffusion, vehicular component, and structural component increased with water content, and the two components of the charge diffusion were found to be negatively correlated. The negative correlation is due to preferential structural diffusion of the proton toward the sulfonate group, whereas vehicular diffusion tends to move the H3O+ ion away from the sulfonate group.
We present a model that incorporates the structural diffusion of a proton into a classical molecular dynamics simulation using a reactive molecular dynamics (RMD) algorithm. The transition state for proton transfer obtained from ab initio calculations is mapped onto a set of geometric and energetic triggers to describe the structural diffusion of the proton in the simulation. Numerical values of these triggers are parametrized to satisfy the experimental values of rate constant and activation energy in order to capture the molecular and macroscopic features of structural diffusion. The algorithm partitions the structural diffusion of a proton into three steps: (i) satisfaction of the triggers, (ii) instantaneous reaction, and (iii) local equilibration. The final step ensures that the ending point of the reaction provides the correct structure and heat of reaction. Hence, the reactivity is incorporated by the algorithm rather than through the development of a reactive potential. We have applied this scheme to study proton transport in bulk water and solutions of HCl. Total charge diffusion along with the structural and vehicular decomposition is studied as a function of temperature (280−320 K). The two components are found to be uncorrelated and the structural diffusion contributes 60−70% of the total charge diffusion in bulk water. The method is applied to HCl solutions (0.22−0.83 M) to study the effect of concentration on proton transport. The reduction in the total diffusivity of the charge with an increase in concentration is due to the reduction in structural diffusion.
High proton conductivity in aqueous solutions has been known for a long time and is attributed to the Grotthus mechanism. In this study, we calculated the proton-transfer rate constant associated with prototropic mobility in water as a function of temperature. We found a strong correlation between the proton-transfer rate constant at low temperatures, T < 290 K, and the dielectric relaxation time. The model that we used to calculate the proton-transfer rate constant is based on diffusive propagation of the solvent configuration along a generalized solvent coordinate from the reactant potential surface toward the crossing point with the product potential surface. The proton transfer occurs at the crossing point, and the rate is calculated by a sink term placed at the crossing point. The sink term includes the solvent velocity and the Landau−Zener transmission coefficient. Both the diffusion constant and the Landau−Zener transmission coefficient depend on the dielectric relaxation of the solvent. The calculations are compared with the proton mobility data and an interpolation expression that bridges the nonadiabatic limit and the solvent-controlled limit.
The translational self-diffusion coefficients of supercooled water at atmospheric pressure were examined using pulsed-gradient spin-echo NMR diffusion measurements down to 238 K. As the temperature decreased, the diffusion behavior became distinctly non-Arrhenius. It was found that the diffusion behavior when plotted in an Arrhenius form was well-described by a Vogel-Tamman-Fulcher-type relationship in the temperature range from 298 to about 242 K. However, a fractional power-law-type equation was found to provide a better fit that extended over the entire measured temperature range. Below this temperature range, the diffusion coefficient decreased rather steeply, and at 238 K, the diffusion coefficient was 1.58 × 10
An analytical model for water and charge transport in highly acidic and highly confined systems such as proton exchange membranes of fuel cells is developed and compared to available experimental data. The model is based on observations from both experiment and multiscale simulation. The model accounts for three factors in the system including acidity, confinement, and connectivity. This model has its basis in the molecular-level mechanisms of water transport but has been coarse-grained to the extent that it can be expressed in an analytical form. The model uses the concentration of H(3)O(+) ion to characterize acidity, interfacial surface area per water molecule to characterize confinement, and percolation theory to describe connectivity. Several important results are presented. First, an integrated multiscale simulation approach including both molecular dynamics simulation and confined random walk theory is capable of quantitatively reproducing experimentally measured self-diffusivities of water in the perfluorinated sulfonic acid proton exchange membrane material, Nafion. The simulations, across a range of hydration conditions from minimally hydrated to fully saturated, have an average error for the self-diffusivity of water of 16% relative to experiment. Second, accounting for three factors-acidity, confinement, and connectivity-is necessary and sufficient to understand the self-diffusivity of water in proton exchange membranes. Third, an analytical model based on percolation theory is capable of quantitatively reproducing experimentally measured self-diffusivities of both water and charge in Nafion across a full range of hydration.
The anomalous behavior of liquid water is apparent from the temperature dependence of many experimental properties. Among these are the abnormal high limiting ionic conductivities λ(0) of protons and hydroxyl ions, which in a previous paper we found to depend linearly on the square root of the absolute temperature T(1/2). Here we describe a further study of these conductivities in both light and heavy water, together with the remarkable transition temperature T(0) [242.7 K in H(2)O and 250.5 K in D(2)O], where the supercooled liquid becomes inert and, for example, restricted water molecule rotation is arrested. From T(0) the rotation barrier heights for the two solvents are determined. The conductivity data enable to obtain experimentally the zero point energies of H(+) and D(+) in liquid water, with results in the right order of magnitude as compared to values estimated along quantum mechanical routes. Contrary to general opinion, the isotope effect λ(0)(H(+))/λ(0)(D(+)) is temperature dependent, its value being close to 2(1/2) only near 20 °C. The isotope effect λ(0)(OH(-))/λ(0)(OD(-)) also takes temperature dependent values, substantially higher than 2(1/2). Still, the linear relationships with T(1/2) sustain a model based on water rotation control for the conductivity mechanism. For a quantitative analysis, the rotation frequency ω is expressed by a simple linear function of T(1/2) in terms of the moment of inertia I and the quantity T(0)(1/2). This "ab initio" calculation is found to be in perfect agreement with theoretical and experimental data in the literature, when ω is identified with the reciprocal of the so-called single molecule relaxation time τ(s). The data analysis eventually leads to the conclusion that the hydrogen ion transfer between water molecules proceeds via two parallel pathways. Next to the rotation controlled hopping mechanism there exists a temperature independent transfer controlled by tunnelling, occurring at all relative orientations of the participating water molecules. The applicability of the excess conductivity concept for hydrogen and hydroxyl ions is critically discussed.
Bond-order analysis is introduced to facilitate the study of cooperative many-molecule effects on proton mobility in liquid water, as simulated using the multistate empirical valence-bond methodology. We calculate the temperature dependence for proton mobility and the total effective bond orders in the first two solvation shells surrounding the H(5)O(2) (+) proton-transferring complex. We find that proton-hopping between adjacent water molecules proceeds via this intermediate, but couples to hydrogen-bond dynamics in larger water clusters than previously anticipated. A two-color classification of these hydrogen bonds leads to an extended mechanism for proton mobility.
The reversible proton dissociation and geminate recombination of a photoacid is studied as a function of temperature in water electrolyte solutions and binary water-methanol mixtures, containing 0.1 and 0.2 mole fractions of methanol. 8-Hydroxypyrene-1,3,6-trisulfonate trisodium salt (HPTS) is used as the photoacid. The experimental data are analyzed by the reversible geminate recombination model. We found that the slope of the logarithm of the proton-transfer rate constant as a function of the inverse of temperature (Arrhenius plot) in the liquid phase of these samples are temperature-dependent, while in the solid phase, the slope is nearly constant. The slope of the Arrhenius plot in frozen electrolyte solution is larger than that of the water-methanol mixtures, which is about the same as in pure water. Careful examination of the time-resolved emission in ice samples shows that the fit quality using the geminate recombination model is rather poor at relatively short times. We were able to get a better fit using an inhomogeneous kinetics model assuming the proton-transfer rate consists of a distribution of rates. The model is consistent with an inhomogeneous frozen water distribution next to the photoacid.
Time-resolved emission was used to measure the photoprotolytic cycle of an excited photoacid as a function of temperature, both in liquid water and in ice, in the presence of an inert salt. The inert salt affects the geminate recombination between the transferred proton with the conjugate base of the photoacid. We used the Debye-Hückel theory to express the screening of the Coulomb electrical potential by the inert salt. We find that in the liquid phase the measured screening effect is small and the Debye-Hückel expression slightly overestimates the experimental effect. In ice, the screening effect is rather large and the Debye-Hückel expression under estimates the measured effect. We explain the large screening in ice by the "salting-out" effect in ice that tends to concentrate the impurities to confined volumes to minimize the ice crystal energy.
The vitrification of pure water is compared with that of molecular solutions rich in water, and gross differences are noted.
Thermodynamic reasoning and direct observations on noncrystallizing nanoconfined water indicate that the glass transition
in ambient-pressure water is qualitatively distinct from that found in the usual molecular liquids. It belongs instead to
the order-disorder class of transition seen in molecular and ionic crystalline materials. The distinctive “folding funnel”
energy landscape for this type of system explains the extreme weakness of the glass transition of water as well as the consequent
confusion that has characterized its scientific history; it also explains the very small excess entropy at the glass transition
temperature. The relation of confined water behavior to that of bulk is discussed, and the “fragile-to-strong” transition
for supercooled water is interpreted by adding a “critical point–free” scenario to the two competing scenarios for understanding
supercooled bulk water.
A new multistate empirical valence bond model (MS-EVB3) is developed for proton solvation and transport in aqueous solutions. The new model and its quantum version (qMS-EVB3) are based on the MS-EVB2 model [Day et al., J. Chem. Phys. 2002, 117, 5839] and recently developed flexible water models-the SPC/Fw model [Wu et al. J. Chem. Phys. 2006, 124, 24503] and the qSPC/Fw model [Paesani et al. J. Chem. Phys. 2006, 125, 184507]-for classical and quantum simulations, respectively. Using ab initio data as benchmarks, the binding energies and optimized geometries calculated with the new model for protonated water clusters, as well as the potential energy surface for proton shuttling between water molecules in a cluster environment, are improved in comparison to the MS-EVB2 model. For aqueous solutions, classical and quantum molecular dynamics simulations with the MS-EVB3 model yield a more accurate description of the solvation structure and diffusive dynamics of the excess proton. New insight is also provided into the proton solvation and hopping dynamics in water, as well as the "amphiphilic" nature of the hydrated proton that has been predicted to give rise to its enhanced concentration at aqueous interfaces and an effectively lower pH of the air-water interface [Petersen et al. J. Phys. Chem. B 2004, 108, 14804].
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