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Jul 11, 2008 - A time-resolved emission technique was employed to study the photoprotolytic cycle of the 2-naphthol-6,8-disulfonate (2N68DS) photoacid...
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J. Phys. Chem. C 2008, 112, 11991–12002

11991

Indication of a Very Large Proton Diffusion in Ice Ih Anna Uritski, Itay Presiado, and Dan Huppert* Raymond and BeVerly Sackler Faculty of Exact Sciences, School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel ReceiVed: February 26, 2008; ReVised Manuscript ReceiVed: April 30, 2008

A time-resolved emission technique was employed to study the photoprotolytic cycle of the 2-naphthol-6,8disulfonate (2N68DS) photoacid in the presence of a low concentration of a strong HCl acid. We found that an excess of protons in ice has a very large and profound effect on the photoprotolytic cycle. The excess proton reacts with the deprotonated form of the photoacid. An analysis of the experimental data reveals that the proton diffusion constant in ice in the temperature range of 240-270 K is much larger than in the liquid state. Under certain assumptions and approximations, the calculated proton diffusion constant in ice is 10 times larger than in water at 295 K, i.e., DHice+ ) 1.2 × 10-3 cm2/s. Introduction Proton transfer has attracted considerable interest in physics, chemistry, and biology, as it is the key process in important reactions1–4 such as autoionization in water, proton conductivity (von Grotthuss mechanism), acid-base neutralization reactions, rearrangement in photostabilizers, and proton pumping through membrane protein channels. Over the past two decades, intermolecular proton transfer in the excited state (ESPT) has been studied extensively in the liquid phase and has provided pertinent information about the mechanisms and parameters controlling acid-base reactions.5–12 In the past, the physics of ice13–16 was studied extensively. The unique properties of ice have interested scientists for hundreds of years. Bacon, Hooke, Faraday, and Kelvin carried out experiments on ice and posed many questions that still puzzle us today.14 Pure ice exhibits a high static relative permittivity that is comparable to that of liquid water. Ice also provides a good example of electrical conduction by transfer of protons that have mobilities of about the same order of magnitude as liquid water.17,18 A particularly important issue concerns the role of crystal defects in the peculiar electrical properties. The theory of Jaccard19 is used to explain the electrical conduction and the dielectric properties of ice. According to Jaccard’s theory, the electrical properties of ice are largely due to two types of defects within the crystal structure. (1) Ion defects are produced when a proton moves from one end of the bond to the other, thus creating a H3O+, OH- ion pair. Conduction is then possible by means of successive proton jumps. (2) Bjerrum defects20 are orientational defects caused by the rotation of a water molecule to produce either a doubly occupied bond (D-defect) or a bond with no protons (L-defect). The mechanism of excess proton transfer in ice was investigated by Ohmine and co-workers21,22 using the QM/MM method. They proposed that the excess proton is localized in an L-defect in ice. Podeszwa and Buch23 studied the structure and dynamics of orientational defects in ice by molecular dynamics simulation. They found the defect structure to be quite different from the one originally proposed by Bjerrum.20 For the L-defect, one water molecule is displaced * Corresponding author. E-mail: [email protected]; phone: 972-36407012; fax: 972-3-6407491.

at ∼1 Å from the crystal lattice site. Defect jumps occur via vibrational phase coincidence. The electrical conductivity measurements of Eigen4 in the early 1960s produced a surprisingly large mobility for the proton in ice. It was estimated4 that the proton mobility in ice is 10-100 times larger than in water. Ice conductance was extensively studied for more than 40 years. Until today, the mobility values of each of the four individual defects is only known within a large uncertainty. The mobility of the L-bonding defect was given by Granicher24 as 2 × 10-4 cm2/(V · s) and later on this was raised25 to 5 × 10-4 cm2/(V · s). The mobility of the ionic defects fluctuated much more, from Eigen’s large value26 of 0.075 to 0.00027 to 0.006 cm2/(V · s).25,27 Takei and Maeno28,29 studied the electrical conductivity and the dielectric properties of HCl-doped ice single crystals grown from HCl liquid solutions of 4 × 10-6 M to 1 × 10-4 M HCl. The concentration of HCl incorporated in the ice is much less, but not directly measurable. The ion conductivity of all samples in Takei and Maeno’s study28,29 is almost temperature independent in the range of 220 < T < 270 K. At lower temperatures, the conductivity decreases with a relatively large activation energy of 0.31 eV. Photoacids are ideal systems to study the proton transfer dynamics in real time. To initiate proton reactions in the liquid and solid phases, protic solvent solutions of photoacids are irradiated by short (femtosecond to picosecond) laser pulses.30,31 Proton transfer is then made possible by the optical trigger pulse. Consequently, the excited-state molecules dissociate very rapidly by transferring a proton to a nearby solvent molecule. The excited-state deprotonated form, RO*-, is negatively charged. Thus, the reversible geminate recombination process is strongly enhanced. The proton transfer rate could be determined either by the initial decay time of the time-resolved fluorescence of the protonated form (RO*H), or by the slow rise time of the emission of the deprotonated species (RO*-). Over the past decade we used a model for an intermolecular ESPT process that accounts for the geminate recombination (GR) of the transferred proton.12,32,33 The study of the proton reaction in the solid phase, and particularly in ice, is rare and uncommon.34,35 Pure ice is known to be a bad solvent. Devlin35,36 studied doped ice samples that were prepared by careful and controlled deposition of water

10.1021/jp801664d CCC: $40.75  2008 American Chemical Society Published on Web 07/11/2008

11992 J. Phys. Chem. C, Vol. 112, No. 31, 2008 molecules on cold surfaces by spraying water and dopants. In many studies they found that the dopants tend to diffuse toward the sample surface. Molecular dynamics simulations by Devlin et al.34 confirm the experimental observation of the tendency of dopants to extract from the bulk and be positioned at the surface. Devlin found that protons stay in the bulk, while the counterion, the chloride in the case of HCl, tends to move to the surface area. In this work we used time-resolved and steady-state methods to study the properties of the photoprotolytic cycle32,33,37–39 of a photoacid in ice in the presence of an excess proton introduced by adding a strong mineral acid, HCl, at a small concentration of c < 5 mM. From the analysis of the experimental results we deduce the excess proton diffusion constant. We found that proton diffusion in ice is about 10 times larger than in liquid water at 295 K. These striking results are in accord with the findings of Eigen and deMaeyer in the late 1950s.26,40 Experimental Section We used the time-correlated single-photon counting (TCSPC) technique to measure the time-resolved emission of the photoacids. For sample excitations we used a cavity dumped Ti:sapphire femtosecond laser (Mira, Coherent), which provides short, 80 fs, pulses. The laser harmonics SHG and THG (third harmonic generation) operate over the spectral range of 380-400 nm, and THG operates in the range of 260-290 nm. The cavity dumper operates with the relatively low repetition rate of 500 kHz. The TCSPC detection system is based on a Hamamatsu 3809U, photomultiplier, and Edinburgh Instruments TCC 900 computer module for TCSPC. The overall instrumental response was about 35 ps (fwhm). The excitation pulse energy was reduced to about 10 pJ by neutral density filters. 2-Naphthol-6,8-disulfonate sodium salt (2N68DS) of analytical grade was purchased from Kodak. HCl (1N) was purchased from Aldrich. For transient measurements, the sample concentrations were between 2 × 10-4 and 2 × 10-5 M. Deionized water had a resistance of 263 K. (4) The proton diffusion constant, DH+, inversely depends on the methanol concentration. The smaller the methanol concentration, the larger DH+.

11998 J. Phys. Chem. C, Vol. 112, No. 31, 2008 (5) When the methanol concentration is smaller than 0.01% mole ratio, we observe a quenching of the RO*- fluorescence, causing a reduction in the effective excited-state lifetime of the RO*-. The excited-state lifetime is temperature dependent. The lower the temperature, the shorter the decay time. (6) When comparing the decay curves of the RO*- fluorescence in samples with and without acid, the RO*- signal quenching in the presence of an excess of protons is enhanced by it. This phenomenon is known for many naphthol derivatives, especially for 1-naphthol and its derivatives. (7) In methanol-doped ice samples, in the absence of mineral acid, the proton diffusion constant extracted from the numerical fit of the experimental results by using the reversible diffusion influenced geminate recombination model is rather small and is comparable to supercooled liquid water. When a photoacid is excited in an aqueous solution containing a strong mineral acid like HCl, the excess of homogeneous protons reacts with the RO*- species formed by the photoprotolytic reaction. The overall effect on the time-resolved emission of the RO*H band in the presence of 1 mM of HCl in water and in ice is shown in Figure 1. For reference, the RO*H emission in neutral water and in ice is also shown in the figure. The comparison with the RO*H signal in the neutral sample shows that the RO*H signal is modified by the excess proton reaction with the RO*-. As seen in the figure, at long times the decay of the RO*H band in the presence of an excess of protons in solution is almost exponential with a relatively large amplitude compared to the signal maximum immediately after the pulse excitation. It is also noticeable that the amplitude of the long-time fluorescence tail in ice is larger by about a factor of 30 than in a supercooled water solution. A qualitative analysis of the time-resolved fluorescence of RO*H, based on the importance of proton transport toward the RO*-, relates the relative amplitude of the exponential tail with the proton diffusion constant and the intrinsic reaction rate constants kPT and ka. When the proton concentration is relatively small and the intrinsic recombination rate constant ka is large, the pseudounimolecular recombination rate coefficient is ckD, where c is the acid concentration and kD is the diffusion-controlled reaction rate constant for an excess proton with RO*-. In the case of 2N68DS, the lifetimes of the acid and the conjugate base forms are similar but not equal. For the simpler case of equal lifetimes, 1/k0 ) 1/k′0, the reaction is equivalent to AB a A + B, when we modify the simple kinetic expression to take into account the radiative decay of both the excited-state forms ROH* and RO-* [AB] ) [ROH*] exp(k0t) and [A] ) [RO*-] exp(k0t). From simple chemical kinetics, the time dependence of the RO*H concentration is given by eq 2. According to eq 2, the RO*H fluorescence signal starts from unity and decays to the quasi-equilibrium distribution, cKeq/(1 + cKeq). In general, the overall proton recombination rate constant kr depends on both ka and DH+. When the acid concentration is sufficiently low (c < 10 mM) and the intrinsic recombination rate constant is larger than the kD, the recombination reaction roughly depends only on the transport rate of the excess proton from the bulk ice toward the reaction sphere surrounding the photoacid RO*-. The important finding of this study is that the excess proton diffusion in ice is approximately 20 times larger than the calculated value from the literature mobility. In dc conduction measurements of ice samples, the ion defect current must equal the Bjerrum current. Thus, the two mechanisms effectively act in series. The dc conductivity is therefore chiefly determined by the less effective of the two mechanisms, which for pure ice is the ion defect current.19 At high frequencies, the protons can

Uritski et al. move back and forth along the same path. The interaction between different defect types is small, hence the two processes act independently and in parallel, and the high-frequency conductivity σ∞ is given by

σ∞ ) σi + σB

(14)

Measurements of σ and σ∞ enable the estimation of the relative effectiveness of the two processes. The value of the proton diffusion constant in ice as deduced from our photoacid experiments is about 20 times larger than the value µH3O+ ≈ 10-7 m2 V-1 s-1 estimated from ice conductance measurements.16 The electrical conductivity measurements of Eigen4 in the early 1960s resulted in a surprisingly large mobility value for the proton in ice. The results of this study show that the proton mobility in ice is indeed larger than that in water, at least on a nanometric distance scale. Already in 1983 Nagle53 advocated the existence of proton wires in ice and in enzymatic systems in which the proton transport is carried out via a concerted mechanism (Grotthuss mechanism) on a limited length scale. Ice conductance was extensively studied for more than forty years. To date, the mobility values of each of the four individual defects is only known within a large uncertainty. Jaccard19 argued that the dielectric constant in ice is very sensitive to the number of charged OH- and H+ carriers, as well as to the D and L orientational defects. The effective dielectric constant next to an impurity might be strongly affected by the impurity, as well as by the procedure of ice preparation. In a separate section we will discuss the possible implications of the change in the dielectric constant in acid-doped ice on our results and interpretations. Figure 8 shows a summary of the main result of this study. It shows a plot of the proton diffusion of several samples as a function of temperature in liquid and in ice containing several methanol concentrations. At a very low methanol concentration of 0.001% (mole ratio), the proton diffusion constant reaches a value of ∼1.2 × 10-3 cm2/s at about 260 K. As the methanol concentration increases, the diffusion constant decreases. In 1% mole ratio of methanol, the diffusion constant drops by a factor of 9 to a value of 1.35 × 10-4 cm2/s. The value of the proton diffusion constant in pure water at 295 K is about 0.9 × 10-4 cm2/s. From the AB reversible dissociation-recombination model fitting, we extract a diffusion constant for the supercooled liquid at 260 K of about 0.35 x10-4 cm2/s. The value of proton diffusion in an ice sample, doped with 0.001% mole ratio of methanol, is roughly 34 times larger than the supercooled liquid sample’s value, and it is about 13 times larger than the value of proton diffusion in water at 298 K.

Figure 8. Proton diffusion constant of both liquid and ice samples as a function of temperature at several methanol concentrations.

Very Large Proton Diffusion In Ice Ih The analysis of the emission signals of ice at several temperatures shows that the diffusion constant is the largest between 250-260 K. In large methanol concentrations, it decreases at both higher and lower temperatures. At about 268 K and 1% mole ratio of methanol, the proton diffusion constant decreases by about a factor of 2 from its maximum value at 260 K. At very low temperatures (T < 220 K), the slow rate of the proton transfer prevents the accurate determination of the proton diffusion constant from the long-time fluorescence tail. We estimate that the proton diffusion constant at 220 K is about half-that of its maximum value. Explaining the Discrepancy in the Diffusion Constant Extracted from Experiments with Acid and without It. The experiments of the photoprotolytic cycle of 2N68DS in methanoldoped ice in the absence of a mineral acid indicate that the diffusion constant of the geminate proton is not large, but rather similar to the supercooled water values. In contrast to this observation, we found that, in ice samples that contain mineral acid, the proton diffusion constant is rather large. In samples with a small methanol concentration, the proton diffusion constant of an excess proton is about an order of a magnitude larger than that of water at 295 K. The discrepancy between these two results may be bridged by the following explanation: The ice structure surrounding the photoacid is far from an ideal Ih ice. The relatively large photoacid causes a large mismatch between the structure of the solvation shells of methanol doped water surrounding the photoacid and the actual Ih crystalline structure at a further distance from the photoacid. We suggest that the solvent next to the photoacid is organized in a vitreous ice (amorphous ice) structure rather than in a crystalline Ih structure. If such an assumption holds, than the proton diffusion in the amorphous region is more likely to have a value similar to that of a supercooled liquid, rather than that of pure Ih ice. For a value of DH+ ≈ 2 × 10-5 cm2/s, the proton diffusion length at time t, LD ) (6Dt)1/2, is rather small; for 1 ns, LD ) 34 Å. The GR model for excited-state proton transfer based on the DSE predicts a large effect of the diffusion constant on the amplitude of the RO*H time-resolved emission at intermediate and long times. As the value of DH+ becomes smaller, the amplitude of the fluorescence tail becomes larger. Thus, most of the geminaterecombination process arises from protons that are close to the photoacid, and consequently they are also influenced by the strong Coulomb interaction of the triply charged RO*-. When the diffusion is large the GR probability is reduced and the experimental long-time fluorescence intensity drops. In methanoldoped samples, containing a small amount of mineral acid, the average distance of an excess proton from a photoacid is large. For an acid concentration of about 1 mM, the average distance is about 100 Å. We propose that, at such a distance from the photoacid, the ice structure is of an Ih phase. The excess proton motion in the Ih structure is of a Grotthuss-like mechanism. The distance that the proton can cover in a synchronized fashion is unknown, but may include an average long jump of about three water molecules. Such long jump mechanism is the basis of a large proton diffusion constant in ice. We assume that the proton moves with a large diffusion constant unitl it reaches the region of amorphous ice next to the photoacid. That region might overlap with the Coulomb cage given by the RO*- · · · H+, Debye radius, RD. For ice at T ≈ 260 K, with a dielectric constant of  ) 100 RDice ) 17 Å. The diffusion controlled rate constant kD is given by kD ) 4πN′DA+RD, where N′ ) NA/1000 and RD ) ze2εkBT. NA is Avogadro’s number, z is the RO*charge in electronic unit, and e is the electronic charge. The

J. Phys. Chem. C, Vol. 112, No. 31, 2008 11999 proton first diffuses and reaches a sphere of RD. Once the proton is within the Coulomb cage, the proton recombination reaction with the conjugate base RO*- is immediate. Assumptions and Approximations in the Determination of the Proton Diffusion Constant. The main assumptions are as follows: (1) Both the photoacid molecules and the protons are homogenously distributed in the bulk of the polycrystalline samples. HCl is a strong acid, hence the degree of acid dissociation is almost 1. The proton concentration is close to the HCl concentration introduced into the aqueous solution.54 (2) The methanol molecules serve as a cosolvent that prevents the exclusion of the photoacid from the ice. The methanol hydrophobic CH3 group points toward the aromatic rings of 2-naphthol, whereas the sulfonates and the hydroxyl groups form hydrogen bonds with the ice hydrogen network structure. (3) The high dielectric constant of pure ice is also maintained when doped with a range of acid concentrations 0.2 e c e 5 mM of HCl. The large dielectric constant of about ε ) 100 at freezing point further increases when the temperature decreases. The main approximation in the fitting is the use of a rather simple kinetic model that provides only a good fit to the timeresolved emission of the RO*H form of the photoacid at short and long times. The model completely fails to fit the intermediate times. These depend strongly on the proton geminate recombination process as well as on the intrinsic finite recombination constant ka, and are not included in our fitting models. There are much more sophisticated models that provide a reasonable fit for the intermediate times as well. The second approximation is the use of a diffusion-controlled rate constant kD as the overall proton recombination rate constant kr, i.e., kr = kD. Such an assumption is a good approximation when the intrinsic recombination rate constant is much larger than kD. 2N68DS exhibits a very large intrinsic recombination rate constant ka in both liquid and in ice states. From the timeresolved measurements of 2N68DS in neutral pH samples in both liquid and in ice, the intrinsic rate constant in liquid and ice at to 260 K is about 2 × 1011 M-1 s-1. The long-time asymptotic expression for the irreversible rate constant takes into account both the diffusion-controlled rate constant and the intrinsic rate constant k(∞)-1 ) [kr-1 + kD-1]-1 (see eq 11). The long-time overall rate constant is always smaller than kD. Thus, the actual diffusion constant in ice may be larger than the one we extract from the fit of the experimental results. The Temperature Dependence of the Proton Diffusion. The temperature dependence of the diffusion constant is rather small in the relatively narrow temperature range of 220 < T < 270 K that was studied. Figure 8 shows the temperature dependence of the diffusion constant for several doping levels of methanol. In the liquid state, the diffusion decreases linearly with a decrease in the temperature. The supercooled liquid region behaves as if the diffusion constant value has a continuous temperature dependence functional form extrapolated from the liquid dependence at T < 273 K. The solid-state proton diffusion constant is very large in comparison with the supercooled liquid values. The methanol doping dependence of the diffusion constant in the liquid state is small. In contrast to the liquid state, the diffusion constant depends strongly on the methanol concentration. At a large methanol concentration of >0.125% mole ratio, the diffusion constant in ice at T < 253 K decreases as the temperature increases. Close to the melting point, the diffusion constant value is about half of the maximum value at 253 K. The diffusion

12000 J. Phys. Chem. C, Vol. 112, No. 31, 2008 constant at T > 253 K decreases linearly with the decrease in temperature. At about 220 K, its value is half of that at 253 K. The small temperature dependence of the diffusion constant is also seen in the conductivity of the ion defect σ( /e( of the HCl doped sample measured by Takei and Maeno.28,29 The results show that the conductivity is almost constant in the high temperature range of T > 220 K, whereas at lower temperatures of T < 220 K it obeys an Arrhenius activation behavior, with an activation energy of 0.3 eV. Acid Concentration Dependence on the Proton Diffusion. We measured the photoprotolytic cycle of 2N68DS in 1% mole ratio methanol-doped samples in the presence of HCl at a relatively large concentration range of 0.25 < c < 5 mM. We found that in the large temperature range of 220 < T < 298 K, the diffusion constant obtained from the fit of the experimental data by the AB kinetic dissociation recombination model is independent of the acid concentration in 1% methanol-doped ice samples. In doped ice samples with lower methanol concentration, we used only a few acid concentrations: The analysis of the experimental results of those samples also provides the same conclusion; the proton diffusion constant derived from the fit to the experimental data is independent of the HCl concentration. Proton Diffusion Dependence on the Methanol Concentration. Pure ice is known to be a bad solvent.16 Upon slowly controlled freezing, most of the dopants are extracted from of the crystal and consequently concentrate at the grain boundary. In our initial experiments on the photoprotolytic cycle of the photoacid in pure ice,55–57 we noticed that the frozen samples are nonfluorescent, while in the liquid samples the fluorescence is at least 3 orders of magnitude more intense. We explained the lack of fluorescence of the photoacid in “pure” ice samples by the aggregation of the photoacid molecules at the grain boundary. Dimerization of two photoacid molecules causes the annihilation of the overall transition dipole moment, which will lead to the reduction of the fluorescence intensity. We found a procedure to overcome the aggregation of the photoacid molecules upon freezing. To prevent the aggregation, we added 1% of methanol (mole ratio) to a pure aqueous solution. The methanol probably serves as a mediator between the hydrophobic aromatic rings of the photoacid with the ice water molecules. In numerous experiments we found that the fluorescence intensity of the frozen methanol-doped ice sample containing the photoacid is “behaving properly”. In this study we found that the proton diffusion constant of ice strongly depends on the methanol concentration. It varies by a factor of 10 when the methanol concentration decreases by a factor of 1000. Figure 9 shows on a log-log scale the proton diffusion constant at 258 K in methanol-doped ice as a function of the methanol mole ratio. The proton diffusion constant decreases as the methanol concentration increases. We explain this effect by the ability of methanol to capture the proton with a fast rate and to release it at a much slower rate. Thus, methanol serves as a proton trap within the experimental time window. The overall effect is a reduction in the effective diffusion constant within the methanol-doped ice crystal. The question that arises then is why dope the ice with methanol? Methanol doping is necessary to incorporate the photoacid in the crystal bulk, and to prevent the exclusion of the photoacid from the bulk and its aggregation at the grain boundaries. At a small methanol concentration of σ(. For HF, a weak acid in an aqueous solution (pKa = 3), the H+ concentration in doped ice is small, and nH+ is proportional to (nHF)1/2. In such a case, the value of the dielectric constant oscillates as a function of an HF concentration. At a very low HF concentration, εs ) 100, whereas at nHF ) 3 × 1017 molecules,58 σ( ) (1/2)σDL and εs ) ε∞. As the HF concentration continues to increase, so does εs since σ( . σDL. Unlike the weak acid HF, HCl is a very strong acid, and therefore we consider that all the HCl molecules dissociated in the small concentration range we explored (0.25 < c e 5 mM), and in such a case σ( . (1/2)σDL. According to Jaccard’s theory, εs is expected to be 21 in the HCl doping level of our experiments. Takei and Maeno28,29 studied the electrical conductivity and the dielectric properties of HCl-doped ice single crystals grown from HCl liquid solutions of 4 × 10-6 M to 1 × 10-4 M HCl. Two out of three samples described in that work30 behave similarly to HF. The concentration of HCl incorporated in the ice is much less, but not directly measurable. The static dielectric constant decreases with temperature, and crosses the minimum point twice: at -45 °C and at -85 °C. One sample (sample E, grown from a 4 × 10-6 M solution, (see Figure 4 in reference 52) shows a similar temperature dependence of the dielectric constant of the pure ice sample, namely, the static dielectric constant increases as the temperature decreases. The static dielectric constant of the two extreme samples ranges between 80 and 100 in the high temperature range of 253 < T < 270 K. The ion conductivity σ( of all samples in Takei and Maeno’s study28,29 is almost temperature independent in the range of 220 < T < 270 K. At lower temperatures, the σ( conductivity decreases with a relatively large activation energy of 0.31 eV. Comparing the behavior of our samples with the data of the study of Takei and Maeno strengthens our assumption regarding the dielectric constant and the degree of dissociation of HCl in the sample. We assumed that the dielectric constant is close to 100 and that the degree of acid dissociation is almost 1. We also found that the proton diffusion constant is only slightly temperature dependent (within a factor of 2) in the range of 220-270 K. The conductivity of the ion defects is given by 2

σ( ) ∑ ni µi|ei| i)1

where n is the ion defects number density, |ei| is the ion effective charge, and µ is the mobility that scales linearly with the diffusion constant by the Stokes-Einstein relation, µ( ) (e/ kBT)DH+. If the dielectric constant decreases with temperature in the presence of HCl, the diffusion-controlled rate constant is strongly affected. The Debye radius RD scales inversely with the dielectric constant RD ) (ze2)/(εkBT). The diffusioncontrolled rate constant depends on RD, i.e., kD ) 4πN′DH+RD. The large increase in the amplitude of the fluorescence tail in ice arises not only because of a large increase in DH+, but is partially arises from the large increase of RD.

The study of Steinmann58 shows that the dielectric constant of HF-doped ice strongly depends on the acid concentration. In our experiments, the value of the proton diffusion constant extracted from the fit of the experimental results by using the kinetic model is independent of the proton concentration in the range of 0.25 < c < 5 mM. This finding suggests that the effective dielectric constant in the acid-doped ice studied in this work was almost constant at all acid concentrations, whereas some of the measurements of Takei and Maeno29 show a large reduction in εs. In the extreme case where the dielectric constant decreases to εs ) 21 according to equation 16 and kD = 4πN′RDDH+, RD should increase by a factor of about 5, whereas the proton diffusion constant that we calculated from the experimental time-resolved emission results should, in fact, be reduced by a factor of 5 from the value we deduced for εs ) 100. If this was the situation, then proton diffusion in ice should only be 2.7 times larger than in water at 295 K or about 9 times larger than in super cooled liquid at ∼265 K. Proton RO-* Recombination at the Polycrystalline Grain Boundaries. The second possible explanation to the strikingly large acid effect on the amplitude of the long-time exponential fluorescence tail in ice is along the lines of many other observations,35,36 suggesting that dopants tend to exclude from the ice bulk and to aggregate on grain boundaries. If that is the case, then the photoacid molecules in our experiments are not incorporated in the bulk of a microcrystal of ice, rather the photoacid position is at the grain boundaries. The proton reaction with the RO*- is taking place at the grain boundaries rather than in the bulk. Devlin35,36 studied acid-doped ice samples, where a controlled deposition of water molecules was achieved through spraying water and HCl on cold surfaces. They found that protons stay in the bulk, while the counterion, the chloride in the case of HCl, tends to move to the surface area. Let us assume that the photoacids themselves are at the grain boundaries, as are the counterions (sodium ions from the sulfonates of 2N68DS as well as the chlorides from the HCl), while the protons stay inside the bulk of the microcrystals. In that case, the photoacid concentration is very large at the surface, whereas the excess proton concentration is small. The photoprotolytic cycle takes place at the surface of the polycrystalline ice. The experimental results then are still indicative of a very large proton diffusion constant in the bulk ice, and it is much larger than in liquid water. The proton transport toward the surface is by diffusion in the bulk. The proton recombination occurs at the grain boundaries where the photoacid molecules tend to situate. The overall process can be described by a one-dimensional diffusion controlled reaction rate constant. In a recent paper59 we characterized the position of the photoacid in methanol doped ice samples by employing the Fo¨rster electronic energy transfer (EET) process between two chromophores. We used the EET process to estimate the average distance between two large aromatic compounds in polycrystalline samples. For a 10 µm cubic crystal with a bulk concentration of 1 mM, the average distance between adjacent photoacid molecules at the grain boundaries of a microcrystal with a size of 10 µM should be equivalent to about 5 Å. We used 2N68DS in its deprotonated form, RO*- as the EET donor, and fluorescien disodium salt as the acceptor. We compared experimental results of the time-resolved emission EET of samples in aqueous liquid state with the results in ice. The EET process at a concentration of 0.2 < c < 1 mM for the acceptor showed a small and similar energy transfer rate for both liquid

12002 J. Phys. Chem. C, Vol. 112, No. 31, 2008 and ice samples (the critical radius being R0 ) 56 Å). We concluded that both the donor (the photoacid) and the acceptor at these low concentrations are situated in the bulk of the ice microcrystal rather than at the grain boundaries of the microcrystal, where the distances between donor and acceptor are suppose to be much shorter than R0, and hence the EET process will be very efficient. Fo¨rster’s EET experiment indicates that, in methanol-doped ice, the photoacid molecules tend to stay in the bulk of the microcrystal rather than aggregate at the grain boundaries upon freezing of the sample. Summary We studied the photoprotolytic cycle of the photoacid 2-naphthol-6,8-disulfonate (2N68DS) in liquid water and in ice in the presence of small concentrations of a strong mineral acid HCl. We used a time-resolved emission technique as well as a steady-state emission to monitor the excess proton effect on the photoprotolytic cycle. In the presence of an excess of protons in both liquid water and ice, we found an increase of the longtime fluorescence tail of the protonated form RO*H. The longtime fluorescence tail decays nearly exponentially with the lifetime of the deprotonated form of the RO*-. We used a simple kinetic model to analyze the experimental time-resolved data. In ice in the presence of HCl, we found that the exponential fluorescence long-time tail had surprisingly large amplitude, even in an excess proton concentration as low as a fraction of 1 mM. We deduced the proton diffusion constant in ice from the experimental data fit by using a simple kinetic model. We found that the proton diffusion in ice Ih at 250-260 K is about 10 times larger than in liquid water at 295 K. This large proton diffusion is in accord with the findings of Eigen and deMaeyer from about 50 years ago, but contradicts conductivity measurements of ice from 1968 to this day. We explained the discrepancy between the results of this study and the conductivity measurements by the length scale of the two types of measurements. In our measurement, we monitored a small sphere of about 50 nm around a photoacid, whereas in the conductance measurements, the distances between electrodes were in the range of 1 mm. Acknowledgment. This work was supported by a grant from the James-Franck German-Israel Program in Laser-Matter Interaction. References and Notes (1) Bell, R. P. The Proton in Chemistry, 2nd ed; Chapman and Hall: London, 1973. (2) Proton Transfer Reaction Caldin, E.F., Gold, V., Eds.; Chapman and Hall: London, 1975. (3) (a) Weller, A. Prog. React. Kinet. 1961, 1, 189. (b) Weller, A. Z. Phys. Chem. N. F. 1958, 17, 224. (4) (a) Eigen, M. Proton transfer. Angew. Chem., 1964, 3, 1. (b) Eigen, M.; Kruse, W.; Maass, G.; De Maeyer, L. Prog. React. Kinet. 1964, 2, 285. (5) Ireland, J. E.; Wyatt, P. A. AdV. Phys. Org. Chem. 1976, 12, 131. (6) (a) Gutman, M.; Nachliel, E. Biochem. Biophys. Acta 1990, 391, 1015. (b) Pines, E.; Huppert, D. J. Phys. Chem. 1983, 87, 4471. (7) Kosower, E. M.; Huppert, D. Annu. ReV. Phys. Chem. 1986, 37, 127. (8) Tolbert, L. M.; Solntsev, K. M. Acc. Chem. Res. 2002, 35, 19. (9) (a) Rini, M.; Magnes, B. Z.; Pines, E.; Nibbering, E.T. J. Science 2003, 301, 349. (b) Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. J. Science 2005, 310, 5745.

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