Measurement of Large Proton Diffusion in Methanol-Doped Ice by

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Measurement of Large Proton Diffusion in Methanol-Doped Ice by Fluorescence Quenching of Riboflavin 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: December 15, 2008; ReVised Manuscript ReceiVed: March 15, 2009

Time-resolved and steady-state emission techniques were employed to study the fluorescence quenching by excess protons of the electrically neutral compound riboflavin in methanol-doped ice samples. We found a very large fluorescence quenching effect by excess protons. This phenomenon has also been observed previously for the negatively charged flavin mononucleotide (FMN) in ice. We assume that the fluorescence quenching rate-determining step is the proton diffusion in the bulk ice. The diffusion-controlled rate constant in recombination reactions for charged molecules depends on the dielectric constant of the medium, whereas for neutral molecules it does not. The theory of the electric properties of ice argues that the dielectric constant depends strongly on the ice doping, and thus the extracted value of the diffusion constant depends on the actual value of the dielectric constant, which was ambiguous in our previous experiments. The current experiments on neutral molecules confirm previous studies based on charged molecules, showing that the proton diffusion constant in methanol-doped ice in the temperature range of 242-262 K is about 10 times that of water at 295 K. Introduction 1-4

The physics of ice and its unique properties have been studied for a long time.2 Ice is the most widespread molecular solid on the surface of the earth and in its atmosphere. In the early 1960s, it was estimated from the electrical conductivity measurements of Eigen5 that the proton mobility in ice is 10-100 times larger than in water. In numerous further measurements, it was found that at about 263 K the proton mobility in ice (0.8 × 10-4 cm2 V-1 s-1) is smaller than in water6 by about a factor of 2 (when compared to supercooled liquid water7,8 at the same temperature). In recent years other techniques were employed to resolve the mystery of proton mobility in ice. However the experimental results of the mobility of protons in ice vary widely; whereas some studies claim that proton mobility in ice crystals is faster than that in liquid water,9 other studies indicate that proton transport is a thermally activated process, which occurs either at a substantially slow rate in ice at low temperatures10-16 or not at all.17 Recent experimental18,19 and computational20 studies on proton translocation along the proton wire of the green fluorescent protein (GFP) indicate that the proton mobility in an ordered protonconductive array consisting of four molecules is ultrafast with a concerted mechanism. The electrical properties of ice are largely due to two types of defects within the crystal structure: (1) Ion defects, which are produced when a proton moves from one end of the bond to the other, thus creating a H3O+, OH- ion pair. Conduction is enabled by means of successive proton jumps. (2) Bjerrum defects,21 which 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 L-defects and the protons are highly mobile, whereas OH- and D-defects are much less so.4 Ohmine and co-workers,22 using the QM/ * Corresponding author. E-mail: [email protected]. Phone: 972-36407012. Fax: 972-3-6407491.

MM method, studied the mechanism of excess proton transfer in ice. They proposed that the excess proton in ice is localized in an L-defect. Podeszwa and Buch23 studied the structure and dynamics of orientational defects in ice by molecular dynamics simulations. They found that L-defect jumps occur via vibrational phase coincidence. In previous studies24,25 we reported that excess protons that were introduced into ice by a strong mineral acid such as HCl in millimolar concentrations react with certain electronically excited molecules within their excited-state lifetime (a few ns). All of the proton-sensitive photoreactive molecules used so far to study the proton diffusion in ice were negatively charged. We used four basic assumptions to analyze the experimental data. Under these assumptions we were able to deduce the proton diffusion constant from the reaction rate. We found that at 258 K the proton diffusion constant in ice is ∼10 times larger than in water. The main assumptions are as follows: 1. Both the proton-sensitive molecules and the protons are homogenously distributed in the bulk of the polycrystalline samples. Methanol molecules serve as a cosolvent that prevents the exclusion of the probe molecule from the bulk ice. For example, the methanol’s hydrophobic CH3 group points toward the heterocyclic rings of flavin in flavin mononucleotide (FMN) (see Scheme 1), whereas the phosphate and the hydroxyl sugar groups form hydrogen bonds with the ice hydrogen bond network structure. For the 2-naphthol-6,8-disulfonate photoacid in ice, the methanol’s CH3 group points toward the aromatic rings. HCl is a strong acid in water, it was also found in recent quantum calculations to be a strong acid in ice,26 and therefore, the degree of acid dissociation is nearly 1. The proton concentration is close to the HCl concentration introduced into the aqueous solution.27 2. The intrinsic reaction of a proton with the molecule in the excited-state is fast, and therefore, the proton diffusion constant in ice is deduced from the diffusion-controlled rate constant that depends on the proton diffusion constant and the dielectric

10.1021/jp811043f CCC: $40.75  2009 American Chemical Society Published on Web 04/13/2009

Measurement of Large Proton Diffusion SCHEME 1

J. Phys. Chem. C, Vol. 113, No. 18, 2009 7871 in living cells in plants. Flavin’s ability to absorb blue and nearultraviolet light leads to several processes.28 Recently we studied the fluorescence quenching of FMN, a negatively charged molecule (shown in Scheme 1) in liquid water and in ice in the presence of small concentrations of the strong mineral HCl acid. We deduced the proton diffusion constant in ice from the fit of the experimental time-resolved emission data by using the irreversible diffusion-assisted recombination model based on the Debye-Smoluchowski equation. We found that the proton diffusion in ice, doped with ∼0.1% mol ratio of methanol at 240-263 K, is about 10 times larger than in liquid water at 295 K. In the present work we use time-resolved and steady-state methods to study the quenching properties of a similar neutral compound riboflavin (B2 vitamin), which is shown in Scheme 1 in ice in the presence of an excess proton introduced by adding a strong mineral acid, HCl, at a small concentration range of 0.5-5 mM. From the analysis of the experimental results and using only two assumptions, rather than three like in our previous studies, we deduce the excess proton diffusion constant. We find that indeed the proton diffusion in ice is about 10 times larger than in liquid water at 295 K. The diffusion constant of proton in ice extracted from the current study is in accord with our previous studies24,25 on the effect of excess proton in ice on the reversible photoprotolytic of photoacids (2-naphthol-6,8disulfonate, 2N68DS)24 and the fluorescence quenching of FMN.25 These striking results are in accord with the findings of Eigen and deMaeyer in the late 1950s.29,30 Experimental Section

constant of the medium, when the reaction takes place between charged particles. 3. The high dielectric constant of pure ice is maintained when doped with a range of acid concentrations (0.5-5 mM) of HCl. At freezing point the large dielectric constant of about ε ) 100 further increases when the temperature decreases. The diffusion-controlled reaction constant, kD, strongly depends on whether the reaction takes place between charged particles or neutral reagents. In the case of charged particle reactions, kD also strongly depends on the medium’s dielectric constant. The theory of the electrical properties of ice relates the dielectric constant and the number of ionic defects, n(, or Bjerrum defects, nDL, and their mobilities and charges (see eq 12). The addition of a strong acid at millimolar concentrations may reduce the dielectric constant to about 0.4 of its value in pure ice. In our previous studies we found that proton diffusion in ice is ∼10 times larger than in water. This value was obtained for a dielectric constant of pure ice, i.e., εS ) 100. If the dielectric constant, as predicted by the theory, reduces to ∼44 for ice with n( > nDL as in the case of ice containing c g 1 mM of HCl, then the proton diffusion constant, as evaluated from kD, should reduce by more than a factor of 2. The purpose of the present study is to reduce the number of assumptions and approximations we need in order to determine the value of the proton diffusion constant in ice. By using an uncharged molecule, we eliminate the need for the third assumption in the above list regarding the dielectric constant in acid-doped ice or in methanol-doped ice. Flavin and flavin derivatives are very important in the biological field. Derivatives of riboflavin serve as coenzymes of various flavoproteins in certain oxidation-reduction reactions

In the present study we used the time-correlated single-photon counting (TCSPC) technique to measure the time-resolved emission of riboflavin. For sample excitations we used a cavity dumped Ti:sapphire femtosecond laser, Mira, Coherent, which provides short, 80 fs, pulses. The laser second harmonics (SHG), operating over the spectral range of 380-430 nm, was used to excite the riboflavin ice samples. The cavity dumper operated 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. The actual measurements of the time-resolved emission of riboflavin were conducted by exciting the sample at 430 nm, and the fluorescence was monitored at 550 nm. Riboflavin (Scheme 1) of analytical grade was purchased from TCI. HCl (1N) was purchased from Aldrich. The HCl concentration was in the range of 1-5 mM. For transient measurements the riboflavin concentrations were between 2 × 10-4 and 2 × 10-5 M. Deionized water had a resistance of >10 MΩ. Methanol of analytical grade was purchased from Fluka. The methanol doping of the samples was in the range of 0.1-2.5% mol ratio. Most of the measurements were conducted on samples with 0.1% mol ratio. All chemicals were used without further purification. The temperature of the irradiated sample was controlled by placing the sample in a liquid N2 cryostat with a thermal stability of approximately (1.5 K. Ice Sample Preparation. Ice samples were prepared by first placing the 300 µL cryogenic sample cell for about 20 min at a supercooled liquid temperature of about 260 K. The sealed cryogenic cell was placed under pressure of ∼10-3 torr in a dewar cryostat. The o ring sealing of the optical window

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probably enabled partial degassing of the sample. The second step involved a relatively rapid cooling (5 min) to a temperature of about 240 K. Subsequently, the sample froze within a few minutes. To ensure ice equilibration prior to the time-resolved measurements, the sample temperature was kept for another 10 min at about 240 K. The frozen sample formed a polycrystalline ice sample with unknown microcrystal size. The ice sample strongly scatters the excitation laser pulse. Aging of ice2 is an important parameter that controls its macroscopic properties. In general, the TCSPC time-resolved emission signal of a certain sample at a given temperature was about the same for multiple measurements irrespective of the time elapsed from the moment it was first frozen. So far we found that the signal for a given temperature is insensitive to aging for about 5 h. The Smoluchowski Model. The Smoluchowski model is used to describe the diffusion-assisted irreversible reaction A + B f AB, where the concentration of B is largely in excess over A. In this study it is used to fit the strong, nonradiative, time-resolved emission decay of riboflavin in the presence of an excess proton in the ice sample. We assumed that the excess proton transport toward riboflavin is the rate limiting step. The mathematical and computational details of the Smoluchowski model are given elsewhere.31 According to the Smoluchowski model, the survival probability of a single (static) donor and an excited riboflavin molecule, due to its irreversible reaction with a concentration of protons, c ) [H+], is given by32-35

S(t) ) exp(-c

∫0t k(t') dt')

(1)

where k(t) is the time-dependent rate coefficient for the donor-acceptor pair

k(t) ) k a p(a, t)

(2)

whose intrinsic proton-recombination rate constant is ka. The pair (riboflavin/H+) density distribution, p(r, t), is governed by a three-dimensional Smoluchowski equation. p(a,t) is the probability to find a proton at a contact distance a from the riboflavin molecule. For a spherical symmetry the molecule is placed within a sphere of radius a. The time-dependent reaction rate “constant”, k(t), depends on the probability to find a proton ready for reaction with the molecule. In the absence of an interaction potential the analytical solution is given by

k(t) )

[

]

kDka ka 1 + y(t, γ) kD + ka kD

(3)

Figure 1. Steady-state emission spectra of riboflavin in 0.5% mol ratio of methanol in neutral pH liquid H2O and ice; the sample was excited at 430 nm and the emission was monitored at 550 nm. (a) the relative intensity in arbitrary units and (b) normalized signal.

value for a proton reaction in aqueous solutions.41 The prolate shape of the isoalloxazine three six atoms rings system contains four nitrogen atoms and two oxygen atoms, all of which could be potentially protonated, and lead to fluorescence quenching (see scheme 1). The nonexponentiality in S(t) is a result of a time-dependent rate constant, k(t), as depicted by the ratio k(0)/k(∞) ) 1 + (ka/kD).

where

y(t, γ) ) exp[γ2Dt] erfc[√γ2Dt]

Results

(4)

and where erfc is the complementary error function, and γ is given by

( )

γ ) a-1 1 +

ka kD

(5)

The two limiting values of the time-dependent rate constant, k(t), are at t ) 0 and t ) ∞, i.e.

k(0) ) kak(∞) ) [ka-1 + kD-1]-1

(6)

kD ) 4πDa

(7)

where

is the diffusion-controlled rate constant. a is the actual encounter radius of the specific reaction. a ) 7 Å is a commonly used

Figure 1a shows the steady-state emission spectra of riboflavin excited at 430 nm at several temperatures in the range of 220-300 K. The neutral pH sample contained 0.5% mol fraction of methanol. The signal intensity at the liquid temperature is larger by a factor of 2 than in ice at 265 K and by a factor of 3 for low temperature ice of T < 250 K. The fluorescence band position is identical in liquid and ice in the temperature range shown in the figure. The band shows a blurry vibrational structure in the electronic transition spectrum. The lower the temperature the smaller the bandwidth of the individual band, where the vibration energy difference is ∼1100 cm-1. In low temperature ice the intensity of the second vibrational band increases. We do not have a quantitative explanation for this observation. Qualitatively, it may arise from the difference in the environment of the solvent configuration in close proximity to the flavin ring in ice and in the liquid state. The solute-solvent

Measurement of Large Proton Diffusion interaction determines the emission position with respect to the vacuum position, the spectral width of the vibrational components and the Huang Ryss factors, which determine the relative intensity of the individual vibrational bands. Figure 1b shows the steady-state emission spectra shown in figure 1a, normalized to their peak intensity. An increase of the second vibrational band is clearly seen in the spectra of samples below 263 K. Within the studied temperature range, while bearing in mind the limited sensitivity of the diode array spectrometer, we did not observe any phosphorescence or other contributions to the luminescence. We attribute the large drop in the fluorescence intensity upon sample freezing to the tendency of the riboflavin molecules to be excluded from the bulk of the microcrystal ice and aggregate at the grain boundaries as well as at the edges of the macroscopic sample. A similar reduction in the fluorescence intensity upon freezing of a sample was also found in our previous study on FMN in ice.25 Figure 2 shows the time-dependent fluorescence of riboflavin in methanol doped ice (0.1% by mol ratio) at several HCl concentrations in the range of 0.5-5 mM. As seen in the figure, the signal decay rate, in ice at all acid concentrations, is much larger than in the liquid phase. The decay rate depends on the acid concentration in both liquid and ice samples. The larger the acid concentration, the larger the quenching rate. Figure 3 shows the time-resolved emission of riboflavin in the presence of 5 mM HCl acid in methanol-doped ice samples that differ in their methanol concentrations. As seen in the figure, the lower the methanol concentration, the larger the quenching rate. The fluorescence quenching decay arises from the reaction of the excess proton in ice with excited-state riboflavin, (riboflavin is B2 vitamin)

J. Phys. Chem. C, Vol. 113, No. 18, 2009 7873 kq

B2* + Η+ 98 Β2

(8)

where B2* is the excited-state of riboflavin and B2 is its ground state. The overall rate constant depends on both the proton diffusion rate and the intrinsic proton recombination rate. We attribute the large dependence on the methanol concentration to the large dependence of the proton diffusion constant on the methanol concentration. Methanol molecules probably trap the mobile proton in the bulk ice. Similar results were observed for FMN in ice doped with methanol at similar concentrations. Upon freezing the methanol molecules tend to surround the riboflavin molecule at its hydrophobic sites. This phenomenon is known in liquids as a preferential solvation of large molecules in binary mixture solvents.36-38 The large methanol concentration surrounding the riboflavin may also reduce the intrinsic rate constant ka (eqs 2-6) of proton quenching. Figure 4a shows the fit (solid line) of the experimental results (dots) on a linear scale of the riboflavin time-resolved fluorescence of a sample containing 0.5, 1, 2.5, and 5 mM HCl, respectively, and doped with 0.1% mol ratio of methanol to the diffusion assisted kinetic model of A + B f AB, using eqs 2-6. The model fits the short- and the long-time signal reasonably well at large doping levels of methanol, i.e., at 0.5% mol ratio and at larger values. At lower concentrations of methanol, i.e., < 0.2% mol ratio, we find that the signal at short times consists of an additional short-time component of about 0.3 ns < τ < 0.6 ns depending on the sample’s temperature, with a relative amplitude of about 0.15. Such a component is observed in neutral pH samples of riboflavin and FMN as well. In general, the lower the temperature and the methanol doping level, the larger the nonexponential character of the experimental

Figure 2. Time-resolved emission of riboflavin in 0.1% mol ratio of methanol at several HCl concentrations in the range of 0.5-5 mM. The sample was excited at 430 nm and the emission was monitored at 550 nm.

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Figure 3. Time-resolved emission of riboflavin in 5 mM HCl solution at various methanol concentrations, displayed at four different temperatures. The sample was excited at 430 nm and the emission was monitored at 550 nm.

results. Figure 4b shows on a semilogarithmic plot the timeresolved emission (dots) and the computer fit (solid line) of the data shown in Figure 4a at longer times. The semilog plot shows a much better resolution of both the data and the fit at long times, where the signal intensity is less than 10% of its initial value. The time dependent rate constant k(t) of the Smoluchowski model varies from the initial value of k(0) at time zero to k(∞) at longer times. The model’s calculated fit is almost exponential at times longer than 50 ps. Since in ice kD is large because D ) 10-3 cm2/s,24,25 the switching between k(0) and k(∞) occurs in a very short time span. The survival probability, S(t), also depends on the proton concentration c, which in our experiments is low. Under such conditions S(t) basically follows k(∞) and the well-known non exponential behavior of the Smoluchowski theory is hardly observed. To account for a residual nonexponential long-time fluorescence tail, which does not fit the Smoluchowski model, we added to the computational fit a small amplitude stretched exponent component, a exp[ -(t/ τ)R], where a ∼ 0.005, τ ∼ 4 ns, and R ) 0.75. Another source of unexpected fluorescence components may arise from the finite purity of the sample as purchased from the supplier (98%), which we used without further purification. In addition, longtime irradiation during the time-resolved emission experiments can also influence the measured signal by adding fluorescent photochemical products. We estimate that photochemistry is marginal, since riboflavin is excited at a rather long wavelength, 430 nm, and at a low energy of ∼10 pJ per pulse of 500 kHz source. The observed nonexponential fluorescence decay of riboflavin at a low methanol doping level is likely to arise from a large dispersion in the transport properties of the protons. Ordered proton wires of various lengths promote large diffusion constants.39 Ice is a disordered system with respect to the hydrogen position1-16 and therefore, it has a large concentration of defects.

The methanol doping introduces proton traps in the bulk ice. Trapped protons may be released at a large time spread and thus protons may hit the target molecules (riboflavin) at different times. Another plausible contribution to the fast nonexponential component at a low methanol concentration may arise from riboflavin molecules being expelled from the bulk ice and aggregating at the grain boundaries. In pure ice-riboflavin samples (undoped with methanol) the signal intensity is very small, roughly 0.01 of the intensity of methanol-doped ice with 1% mol ratio of methanol, and the fluorescence is nonexponential. It could be fitted to a stretched exponent a exp[-(t/ τ)R], where t ) 0.3 ns and R ) 0.55. Similar results were found in pure ice FMN samples.25 A detailed description of riboflavin in a pure ice sample is given in a subsequent subsection. Table 1 gives the parameters of the Smoluchowski model fit to the experimental results of 0.1% mol fraction of a methanol doped ice sample containing 2.5 mM of HCl at several temperatures. The Smoluchowski model predicts nonexponential decay curves because k(t) (eq 6) is time-dependent. It is difficult to differentiate between ka and DH+ in our case since DH+ is very large and comparable to ka. Thus, the error in the values of DH+ and ka may be large. The error in the value of k(∞) obtained from the best fit, on the other hand, is only ( 10%. Figure 5a shows on a linear scale the intensity of the timeresolved emission (dots) of several riboflavin samples of methanol-doped ice at 258 K. The samples contain 5 mM of HCl and the methanol’s mol ratio varies from 0.1% to 1%. A computer fit based on the Smoluchowski model is also plotted (solid line). The fitting parameters are given in Table 2. Figure 5b shows the same information as Figure 5a on a semilogarithmic scale. As seen in both panels, the computer fit is rather good. From the best fit we determine the proton diffusion constant, which strongly depends on the methanol doping level. It is reduced by more than an order of magnitude when the

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kD ) 4πDae

(9)

where ae is an effective radius, which replaces the contact radius a given in eqs 2 and 7, and whose dependence on the dielectric constant is given by40

ae ) RD ⁄ (1 - exp(-RD ⁄ a))

(10)

and

RD )

ze2 εskBT

(11)

where a is the actual encounter radius of the specific reaction. a ) 7 Å is a commonly used value for a proton reaction in aqueous solutions.41 RD is the Debye radius, z is the charge of the molecule in electronic units, and e is the charge of the

Figure 4. Experimental data (dot) and computer fits using the DebyeSmoluchowski irreversible model (solid line) of the time-resolved emission of riboflavin in 0.1% mol ratio of methanol-doped ice containing several acid concentrations; (a) on a linear scale and (b) on a semilogarithmic scale.

TABLE 1: Fitting Parameters of the Smoluchowski Model for Riboflavin in 2.5 mM HCl, 0.1% mol Fraction of Methanol Doped Water and Icea phase

T [K]

ka [1011 M-1 s-1]

D [10-4 cm2 s-1]

liquid liquid super-cooled liquid solid solid solid solid solid solid

295 281 268 271 266 261 256 250 245

0.6 0.6 0.6 7.0 7.0 7.0 7.0 7.0 7.0

0.9 0.8 0.6 1.4 8.5 15 16 15 18

a The excited-state lifetime of riboflavin, τ ) 5.4 ns. The contact radius a ) 7 Å. The estimated error in the determination of k(∞) is (10% (see text).

methanol concentration increases from 0.1% to ∼1% mol ratio. The fitting parameters are given in table 2. Discussion In recent studies,24,25 we measured the reaction rate of excess protons introduced in ice by adding a strong mineral acid, HCl, with molecules that are proton-sensitive in their first excited singlet state. All of the molecules used in the previous studies were negatively charged. Using uncharged probe molecules, such as riboflavin, in ice is of great importance in determining the proton diffusion with more certainty. The diffusioncontrolled rate constant for the charged particles is given by

Figure 5. Experimental data (dot) and computer fits using the DebyeSmoluchowski irreversible model (solid line) of the time-resolved emission of riboflavin in a 5 mM HCl solution at several doping levels of methanol and measured at 258 K; (a) on a linear scale and (b) on a semilogarithmic scale.

TABLE 2: Fitting Parameters of the Smoluchowski Model for Riboflavin in 5 mM HCl-Doped Ice with Several Methanol Doping Levels mol fraction of MeOH (%)

ka [1011 M-1 s-1]

D [10-4 cm2 s-1]

aa

τa [ns]

0.1 0.2 0.5 1.0

7.0 4.0 2.0 1.4

18.0 8.0 3.0 1.4

0.15 0.10 0.10

0.25 0.50 1.00

a

A short time decay component was added in order to produce the best fit (see text).

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electron. The diffusion-controlled rate constant, kD, of a negatively charged molecule with a proton strongly depends on the dielectric constant The value of ae for a negatively charged molecule like FMN in water with a dielelectric constant of water, εs ) 78, assuming a single negative charge on the phosphate group is 11 Å. The smaller the dielectric constant, the larger RD, and consequently, ae increases as well. For a given experimental measurement of the proton reaction rate with a photoreactive molecule, kD is calculated and DH+ is determined. A large value of kD may arise from a large DH+ and/or a large ae, which depends on both εs and the amount of negative charge on the photoreactive molecule. The large acid effect on the nonradiative decay of FMN in ice may be the outcome of a drop in the value of the dielectric constant as a consequence of doping the ice with HCl, rather than of a large diffusion constant as proposed in the previous studies. It was previously reported that the dielectric constant of ice strongly decreases with an HF acid concentration.42 According to Jaccard’s theory1 and Hubmann’s corrections,4,43 the static dielectric constant εs is given by

(

)

σ( σDL 2 1 e( eDL εs - ε∞ ) σDL 2 ε0Φ σ( + e(2 eDL2

(

)

(12)

where σ( and σDL are the conductivity of the ionic and Bjerrum defects respectively. e(2 and eDL2 are the effective electrical charges of the ionic and Bjerrum defects respectively, and Φ is the product of a geometrical factor and of the thermal energy kBT.12 The behavior of the static dielectric constant as a function of an HF impurity concentration is complicated. As the number density of HF molecules, nHF, increases, εs falls from a value of nearly 100 that is characteristic of a pure ice (at freezing point) to about 25 at 5 × 1016 molecules per cm3 (0.1 mM). At about 3 × 1017 molecules per cm3 it further drops to a minimum value of ∼3.2 (the high frequency value, ε∞, of ice). At higher concentrations, the dielectric constant rises again. According to eq 12, εs is expected to be ∼44 in the HCl doping level of our experiments, assuming n( . nDL. The main findings of this study and of the previous studies on charged molecules24,25 are as follows: 1. An excess of protons introduced in ice by adding a strong mineral acid reacts with the excited riboflavin and, as a result, the fluorescence lifetime is strongly reduced in the ice phase. From the decay rate we calculate the diffusion-controlled rate constant kD and the proton diffusion constant DH+. 2. The proton diffusion constant in ice is about 10 times larger than in water. The temperature dependence of the proton diffusion constant in ice is in the range of 220-263 K, which is rather small. Similar value of the proton diffusion constant in ice was deduced in previous studies with several negatively charged proton-sensitive molecules.24,25 Our findings of large DH+ are qualitatively in agreement with the electrical measurements of Eigen and deMaeyer29,30 from about 50 years ago. They found that proton mobility in ice is 10-100 times larger than in water, but their values contradicted experiments conducted from 1968 to this day on electrical conductivity measurements of ice. We explained the discrepancy between the results of the present study and the electrical d.c. conductivity measurements by the length scale of the two types of measurements. In our measurements, we monitored a small sphere of about 50 nm around our excited probe molecules, whereas in the conductance

Figure 6. Proton diffusion constant in both water and ice as a function of temperature for a sample doped with 0.1% mol ratio of methanol.

measurements the distances between electrodes were much larger, i.e., in the range of 1 mm. 3. To prevent the exclusion of the guest molecules (riboflavin) from the bulk ice we dope the ice with a fraction of a percent (mol ratio) of methanol. When the methanol concentration is smaller than 0.1% mol ratio, we observe a large quenching of the riboflavin fluorescence in ice in neutral pH solutions, causing a large reduction in the effective excited-state lifetime of the riboflavin. The excited-state lifetime is temperature dependent. The lower the temperature, the shorter the decay time. The proton diffusion constant, DH+, in methanol doped ice inversely depends on the methanol concentration; the smaller the methanol concentration the larger DH+. Figure 6 shows a plot of the evaluated proton diffusion constant as deduced from the time-resolved emission of riboflavin samples as a function of temperature in liquid and in ice containing 0.1% mol ratio of methanol. At a very low methanol concentration of 0.1% (mol ratio), the proton diffusion constant reaches a value of ∼1.8 × 10-3 cm2/s at about 258 K. The value of the proton diffusion constant in pure water at 295 K is about 0.9 × 10-4 cm2/s. From the diffusion-assisted Smoluchowski irreversible recombination model fitting, we were able to deduce a rather small diffusion constant of about 0.35 × 10-4 cm2/s for the supercooled liquid at 260 K. The value of proton diffusion in an ice sample, doped with 0.1% mol ratio of methanol, is roughly 40 times larger than the value of the supercooled liquid sample, and it is about 20 times larger than the value of proton diffusion in water at 298 K. The analysis of the signals of ice at several temperatures shows that the diffusion constant is the largest at 250-260 K, and it decreases at both higher and lower temperatures. At about 263 K, the proton diffusion constant abruptly decreases by about a factor of 2 from its maximum value at 253 K. At 268 K the diffusion constant further decreases to a value over six times smaller than 253 K. In our previous work on FMN the decrease of the proton diffusion in methanol-doped ice at high temperatures (T > 263 K) was much smaller. We attributed this phenomenon to the local solvent structure surrounding the guest molecule. Riboflavin is less miscible in water than FMN as it is uncharged. The methanol-doped ice structure next to riboflavin is less ordered at high ice temperatures. The steady-state emission spectra, shown in figure 1, present the emission spectra of riboflavin in ice at high temperatures, exhibiting similar shape and intensity as the liquid water samples. At very low temperatures (T < 220 K), the large fluorescence quenching of


Figure 7. The proton diffusion constant in methanol-doped ice, DH+, as a function of the methanol mole ratio. The slope of the least mean squares fit is 1.1.

riboflavin in neutral pH samples at low methanol concentrations and low temperatures prevents the accurate determination of the proton diffusion constant. We estimate that the proton diffusion constant at 220 K is about half-that of its maximum value. We measured riboflavin’s fluorescence intensity in 0.1% mol ratio methanol doped samples in the presence of HCl at a relatively large concentration range of 0.5-5 mM (see Figure 2). We found that in the temperature range of 230-298 K, the diffusion constant obtained from the fit of the experimental data by the diffusion-assisted Smoluchowski irreversible recombination model is independent of the acid concentration in specific methanol-doped ice samples. In the current and in the previous studies24,25 we found that the proton diffusion constant of methanol-doped ice strongly depends on the methanol concentration. It varies by a factor of 25 when the methanol concentration decreases from 2.5% to 0.1% mol ratio (see table 2 for DH+ at several methanol concentrations). The proton diffusion constant decreases as the methanol concentration increases. We explained this effect by the ability of methanol to capture the proton at 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 subsequently arises is why to dope ice with methanol. Methanol doping is necessary to incorporate the riboflavin in the crystal bulk, and to prevent the exclusion of the riboflavin from the bulk and its aggregation at the grain boundaries. At a small methanol concentration of ,0.05% by mol ratio we noticed large proton quenching of the riboflavin fluorescence signal of neutral ice samples. The quenching rate depends both on the methanol concentration and on the temperature. Figure 7 shows on a log-log plot, the value of DH+ at 258 K versus the methanol mol fraction in the ice sample. As seen in the figure, DH+ decreases linearly with the methanol concentration. Figure 8 shows the time-resolved emission of riboflavin in several neutral pH (acid-free) methanol-water mixtures at low and intermediate methanol concentrations. As seen in the figure, the emission decay rate of riboflavin at short times in a frozen solution at low methanol concentrations (0.1% and 0.2% mol ratio) and low temperatures is larger than the decay in the liquid state. At short times the lower the temperature in the ice phases the larger is the decay rate. For the intermediate methanol

J. Phys. Chem. C, Vol. 113, No. 18, 2009 7877 concentration (0.5%, 1% mol ratio) the decay rate in ice at short times is somewhat larger than in the liquid state, but for a particular ice temperature it is much smaller than that of the low methanol concentration. It is also noticeable that at short times the fluorescence decay of riboflavin in ice is nonexponential at low methanol concentrations. We are still investigating why the riboflavin decay in ice and in neutral pH ice consists of nonradiative components. A plausible reason may be that an excited molecule, such as isoalloxazine, is a strong photobase and therefore abstracts a proton from a nearby water molecule. An additional reasonable explanation is based on the observation that a large fraction of the riboflavin molecules aggregates at the grain boundaries of the polycrystalline sample. This fraction depends on the concentration of methanol; the smaller the methanol’s mol ratio the larger the riboflavin’s fraction at the grain boundaries. In pure ice the fluorescence intensity of riboflavin decreases by about a factor of 100. The time-resolved emission signal is nonexponential with a long-time tail. Proton Reaction at Grain Boundaries and Characterization of the Ice Sample. Pure ice is known to be a poor solvent. Devlin et al.44,45 studied doped ice samples, which were prepared by careful and controlled deposition of water molecules on cold surfaces by spraying water and dopants. They found that as time progresses after sample preparation the dopants tend to diffuse toward the sample surface. Molecular dynamics simulations by Buch and co-workers45 confirmed the experimental observation that dopants tend to extract from the bulk and be positioned at the surface. There is another possible explanation for the extraordinarily large acid effect on the quenching rate of riboflavin and the proton reactivity with excited molecules used in our previous studies of 2N68DS and FMN in doped ice.24,25 This explanation is based on Devlin, Buch and their co-workers’ observations,44,45 suggesting that dopants tend to be excluded from the ice bulk and aggregate at the grain boundaries. If that is the case, then the riboflavin molecules in our experiments are not incorporated in the bulk of the ice microcrystal but are rather at the grain boundaries. The proton reaction then takes place at the grain boundaries rather than in the bulk. The proton may diffuse from the bulk toward the grain boundaries where the riboflavin molecules are located. The protons are positioned either in the bulk of a microcrystal or at the grain boundaries. A careful study of the equilibrium solubility of HCl in Ih ice as a function of temperature and partial pressure of HCl between -8° and -35 °C was conducted by Thibert and Domine´46 by doping large, single ice crystals for several weeks with gaseous HCl. Their results indicate that the solubility of HCl in the bulk of large single ice crystals is very low. In our experiments the freezing process occurs under conditions that are very far from thermodynamic equilibrium. The entire acidic liquid sample freezes (300 µL) in a time period of less than two minutes after the onset of the freezing process. The temperature gradient between the supercooled liquid at 265 K and the colder surroundings of the cryostat is approximately ∆T ) 10 K (see the Experimental Section). We find that the reaction rate of the proton quenching of riboflavin and the other molecules previously studied, depends linearly on the HCl concentration in the range of 0.5-10 mM. The value of kD evaluated from the pseudo first order rate constant ckD is independent of the acid concentration. The above evidence indicates that under the experimental condition of a relatively fast freezing process the HCl is incorporated in the bulk of the microcrystal, and its degree of dissociation to protons is close to unity.

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Figure 8. Time-resolved emission of riboflavin at several temperatures in a number of neutral pH methanol-water mixtures.

Let us now assume that the protons stay in the bulk and that the riboflavin molecules are locked at the grain boundaries. In that case, the riboflavin concentration is very large at the surface, whereas the excess proton concentration is small. The proton fluorescence quenching takes place at the surface of the polycrystalline ice. The experimental results are then indicative of proton diffusion from the bulk toward the grain boundaries. The main difference between this description and the pure bulk reaction, where both the acid and the molecules are in the bulk, is the dimensionality of the problem. The proton diffuses with a three-dimensional bulk diffusion constant to a nearby surface and reacts with the riboflavin only at the grain boundaries. The proper description of the diffusion toward the surface may be simulated by a one-dimensional diffusion grid, where the fluorescence quenching reaction takes place only at the boundary of the grid. A similar diffusion problem was solved for timeresolved emission of semiconductor photoluminescence of a single bulk crystal, where the surface is activated by a large density of surface states and large surface recombination velocities that capture the mobile electrons or holes.47 A qualitative analysis of the experimental riboflavin data using the formalism from the field of semiconductors provides about the same value for the proton diffusion constant as the quantitatively analyzed Smoluchowski-based case, where both the riboflavin and the proton are considered to be in the bulk. In the case where both the proton and the photoreactant molecules are on the surface of the ice microcrystals, proton diffusion happens on the surface. The surface concentrations of both the protons and the photoreactive molecules are large, and the expected reaction rates are supposedly large as well, since they linearly depend on the proton concentration. Qualitatively, the experimental results of the sample with 0.1% mol ratio of methanol indeed show a 10-fold increase in the overall

reaction rate as compared to liquid water. Let us assume that the microcrystal size is 10 µm and the proton diffusion constant + on the surface is the same as of water, i.e. kDH = 5 × 1010 M-1 -1 s . Simple kinetic estimation that take into account the large effective proton concentration on the surface of the grain boundaries yield a calculated rate constant, which is smaller by a factor of 10 than the liquid water diffusion-controlled reaction rate constant. Thus, in the case described above, where both protons and acids are at the grain boundaries, the calculated diffusion-controlled reaction rate is supposedly smaller than the value for protons in liquid H2O at 298 K, and the deduced < Dliq. surface proton diffusion constant remains Dsurface ice Riboflavin in Pure Ice. Figure 9 shows the time-resolved emission of riboflavin in pure water and ice samples (undoped with methanol). Each panel shows the signals of three samples: a sample at neutral pH and samples with 2.5 mM and 5 mM HCl. In the liquid state, the decay rate of the signal depends on the acid concentration, as expected from the nearly diffusioncontrolled rate of the proton quenching reaction. In neutral pH ice, at temperatures below 260 K, the time-integrated fluorescence rate decreases by a factor of 100 from that of the liquid sample signal. The decay of the time-resolved emission signal of the neutral pH samples is nonexponential. The average decay time is calculated in the following manner:

〈τ 〉 )

∫0∞ f(t)dt

where f(t) is the normalized experimental time-resolved signal. Table 3 shows 〈τ〉 values of neutral pH samples at several temperatures. The value of 〈τ〉 in ice slightly depends on the temperature; the lower the temperature the larger the〈τ〉. For 258 K, 〈τ〉) 1.71 ns. The lifetime of riboflavin in the liquid state is 5.3 ns and the decay is nearly a single exponential. By


J. Phys. Chem. C, Vol. 113, No. 18, 2009 7879

Figure 9. Time-resolved emission of riboflavin in pure water and ice samples (undoped with methanol) at several temperatures and also in acid ice samples.

TABLE 3: Average Lifetime of Riboflavin Fluorescence (a) in Pure H2O; MeOH and Acid-Free and (b) in the 5 mM HCl-Doped Sample; Methanol-Freea phase

T [K]

〈τ〉 [ns]

liquid liquid solid solid solid solid solid

(a) 291 265 268 263 258 247 227

5.16 5.31 4.49 1.47 1.71 1.81 2.55

liquid liquid liquid solid solid solid solid solid solid solid

(b) 291 276 265 242 247 253 258 263 265 268

3.99 4.20 4.33 0.51 0.32 0.30 0.29 0.33 0.46 0.56

a Sample excitation and emission wavelengths are 430 and 550 nm, respectively.

comparing the time integrated signal intensity and the average lifetime of liquid and ice, while bearing in mind the time resolution of the TCSPC instrumentation (IRF of 35 ps), we find that about 97% of the molecules in ice do not fluoresce with a lifetime longer than ∼20 ps. We explain this fact as a manifestation of the very small solubility of large molecules in pure ice. Most of the riboflavin molecules probably aggregate at the grain boundaries or are even pushed away altogether from

the bulk ice, and situated at the edge of the macroscopic sample. In the previous study we found that the time-resolved emission of solid powder samples of FMN (no solvent) shows a weak signal of about 0.01 of that of a solution and a nonexponential decay with an average lifetime similar to the one found for riboflavin in pure ice.25 Upon dimerization and oligomerization of aromatic and heterocyclic compounds the fluorescence intensity tends to diminish drastically. Thus, the pure ice sample’s low intensity indicates that the riboflavin molecules are indeed excluded from the bulk ice and their position is either at the grain boundaries or even at the edge of the macroscopic sample. When acid is added to a sample of riboflavin in pure water ice the fluorescence decay rate is much faster than in a neutral pH sample. The decay rate of ice samples with 2.5 mM and 5 mM HCl is almost the same. In methanol-doped ice the decay rate linearly depends on the acid concentration (see Figure 2). The decay rate of acidic samples in pure ice is larger by about a factor of 5 than in 0.1% methanol-doped ice. The results of riboflavin in pure water samples can be explained in several ways. According to experiments conducted by Devlin, Buch and co-workers44,45 HCl also tends to be positioned at the surface layer of a thin-film of ice. Thibert and Domine´46 found that HCl gas is immiscible in large single crystal ice as well. Let us assume that HCl is better dissolved in methanol-doped ice. Thus, in pure ice the riboflavin molecules and the protons are at the grain boundaries. The reaction rate with protons is larger than in methanol-doped samples since the effective surface concentration of the protons on the microcrystal surface is much larger hence the large pseudo first order rate constant, cH+kD. A qualitative analysis shows that the value of the proton diffusion constant on pure ice microcrystal surfaces at temperatures above 230 K is comparable to its value in liquid water at 298 K. A

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second explanation of the experimental results, which is not yet quantitatively analyzed, assumes that the protons are in the bulk of the pure ice whereas the riboflavin molecules are on the microcrystal surface. The proton diffusion and the bulk ice diffusion constants are the same, but the recombination rate depends on the coverage of the surface by riboflavin. In general, the surface recombination velocity depends on the surface coverage by riboflavin. From the experimental results of the fast fluorescence decay of riboflavin in pure ice samples we then conclude that the surface coverage is large, and hence most of the riboflavin molecules in pure ice are at the grain boundaries. The third explanation for the large fluorescence quenching rate by protons in pure ice is that proton diffusion in the bulk of pure ice is much larger than in methanol-doped ice. From experiments with methanol-doped ice we find that the fluorescence quenching rate depends on the methanol concentration (see Figure 3); the larger the mol ratio of methanol the smaller the quenching rate. Thus, we expect the proton diffusion constant in pure ice to be the largest. Characterization of Methanol-Doped Ice. In a recent paper48 we characterized the position of a photoacid (2N68DS) in methanol-doped ice polycrystalline samples by employing the Fo¨rster electronic energy transfer (EET) process between two chromophores. We used 2N68DS in its deprotonated form, RO*-, as the EET donor, and fluorescein disodium salt as the acceptor. To demonstrate how the strength and sensitivity of the EET method determine where the dopants are positioned in ice samples, we calculated the average distance for the bulk and surface positions of the donors and acceptors. For a 10 µm cubic microcrystal with a bulk concentration of 1 mM of acceptors, the average distance between adjacent donor-acceptor molecules at the grain boundaries should be equivalent to about 5 Å. However, in the bulk ice the distance between a donor and an acceptor is supposed to be more than 20 times larger, i.e., ∼100 Å. In the case of an average distance of 5 Å, the EET process for an interaction of R0 ) 56 Å,49 the donor decay time is a few picoseconds. The actual donor decay time measured in the ice characterization experiments of our previous studies24,25 was rather long and close to its radiative lifetime, τ ) 12 ns. We therefore concluded that 2N68DS tends to stay in the methanol-doped polycrystalline ice bulk, rather than aggregate at the grain boundaries. In another experiment we used the electron transfer process to evaluate the position of FMN in methanol-doped ice samples.25 Electron transfer, unlike proton transfer, occurs fast and efficiently in water and in other liquids over very long distances of tens of angstroms. The electron donor was dithiothretiol (DTT) and the acceptor was the FMN molecule. For the electron transfer experiments in ice, the decay rate in the presence of 5 mM DTT was slightly higher than the decay rate in a DTT-free FMN sample. We explained that these results were a consequence of a small lowering of the average distance between FMN and DTT in ice. In the case of total expulsion of both FMN and DTT from the bulk of the methanol-doped ice in polycrystalline samples, the surface concentration of both DTT and FMN was large and the average distances between donor and acceptor should have decreased more than 10-fold. The expected electron transfer rate should be ultrafast, probably in the order of 1012 s-1. The actual increase of the rate was only by 109 s-1 (close to the radiative rate). The experimental results may indicate that only a small fraction of the fluorescence signal arose from FMN molecules that were at the grain boundaries, whereas the main portion of the fluorescence signal originated from FMN molecules positioned in bulk ice. The

Uritski et al. characterization experiments described above provide further reassurance that in methanol-doped ice at methanol concentrations of 0.1%-1% mol ratio a large fraction of proton-sensitive electronically excited molecules are positioned in the bulk of an ice microcrystal of a polycrystalline ice sample. The steadystate and time-resolved emission experiments showed that these molecules embedded in the bulk of a neutral pH ice sample and exhibited a similar behavior as in the liquid state. In samples doped with HCl at low concentrations of 0.5-5 mM, the molecules react with protons with a nearly diffusion-controlled reaction rate constant, kD. The value of the proton diffusion constant of ice in the current and on previous studies is about the same. Summary The diffusion-controlled recombination reaction rate of charged species depends on the dielectric constant of the solvent. The dielectric constant of pure ice is εS ) 100, whereas in aciddoped ice the theory predicts a reduction to εS ) 44 when n( . nDL. The diffusion-controlled rate constant, kD, for neutral species is independent of the dielectric constant. In a previous contribution we used FMN (see Scheme 1), a negatively charged molecule, to determine the proton constant in methanol-doped ice.25 In order to decrease the number of assumptions and approximations needed in the determination of the proton diffusion constant we used in this study a similar compound to FMN, riboflavin, which is a neutral flavin compound (Scheme 1) that also reacts with a proton in water and ice with a nearly diffusion-controlled rate. We used a time-resolved emission technique to monitor the fluorescence quenching of riboflavin by excess protons, introduced by adding a small concentration of HCl. In the presence of an excess of protons in both liquid water and ice, we deduced the proton diffusion constant in ice from the fit to the experimental data by using the irreversible diffusion-assisted recombination model based on the Debye-Smoluchowski equation. We found that the proton diffusion in methanol-doped ice at 240 - 263 K is about 10 times larger than in liquid water at 295 K. This large proton diffusion is in accord with our previous studies,24,25 where we used negatively charged molecules such as 2-naphthol-6,8-disulfonate (2N68DS) photoacid, which is triply charged, and the flavin mononucleotide, which is charged ice once. The large difference in DH+ values found in the current 24,25 and the accepted value deduced study and in previous works from electrical conductivity measurements may be explained by the length scale of the two types of measurements. In our measurements, we onitored a small sphere of about 50 nm around our excited probe molecules, whereas in the conductance measurements the distances between electrodes were much larger, i.e., in the range of 1 mm. Acknowledgment. This work was supported by grants from the Israel Science Foundation and the James-Franck GermanIsrael Program in Laser-Matter Interaction. References and Notes (1) Fletcher N. H. The Chemical Physics of Ice; Cambridge University Press: London, 1970. (2) Hobbs. P. V. Ice Physics; Clarendon Press; Oxford. U.K. 1974. (3) Von Hippel, A.; Runck, A. H.; Westphal, W. B. Physics and Chemistry of Ice; Walley, E., Jones, S. J., Gold, L. W. Eds.; Royal Society of Canada: Ottawa, 1973. (4) Petrenko, V. F.; Whitworth, R. W. The Physics of Ice; Oxford University, Press: Oxford, U.K., 1999. (5) (a) Eigen, M. Angew. Chem. 1964, 3, 1. (b) Eigen, M.; Kruse, W.; Maass, G.; De Maeyer, L. Prog. React. Kinet. 1964, 2, 285.

Measurement of Large Proton Diffusion (6) Kelly, I. J.; Salomon, R. R. J. Phys. Chem. 1969, 50, 75. (7) Camplin, G. C.; Glen, J. W. Physics and Chemistry of Ice; Walley, E., Jones, S. J., Gold, L. W. Eds.; Royal Society of Canada: Ottawa, 1973; p 256. (8) Kunst, M.; Warman, J. M. J. Phys. Chem. 1983, 87, 4093. (9) Eigen, M.; de Maeyer, L. In The Structure of Electrolytic Solutions; Wiley: New York, 1959; p 64, et seq. (10) Wooldridge, P. J.; Devlin, J. P. J. Chem. Phys. 1988, 88, 3086. (11) Fisher, M.; Devlin, J. P. J. Phys. Chem. 1995, 99, 11584. (12) Uras-Aytemiz, N.; Joyce, C.; Devlin, J. P. J. Chem. Phys. 2001, 115, 9835. (13) Everest, M. A.; Pursell, C. J. J. Chem. Phys. 2001, 115, 9843. (14) Geil, B.; Kirschgen, T. M.; Fujara, F. Phys. ReV. B: Condens. Matter Mater. Phys. 2005, 72, 014304. (15) Kang, H. Acc. Chem. Res. 2005, 38, 893. (16) Moon, E.; Lee, C.; Kang, H. Phys. Chem. Chem. Phys. 2008, 10, 4814. (17) Cowin, J. P.; Tsekouras, A. A.; Iedema, M. J.; Wu, K.; Ellison, G. B. Nature (London) 1999, 398, 405. (18) Stoner-Ma, D.; Melief, E. H.; Nappa, J.; Ronayne, K. L.; Tonge, P. J.; Meech, S. R. J. Phys. Chem. B 2006, 110, 22009. (19) van Thor, J. J.; Zanetti, G.; Ronayne, K. L.; Towrie, M. J. Phys. Chem. B 2005, 109, 16099. (20) Vendrell, O.; Gelabert, R.; Moreno, M.; Lluch, M. J. Phys. Chem. B 2008, 112, 5500. (21) Bjerrum, N. Science 1952, 115, 385. (22) Kobayashi, C.; Saito, S.; Ohmine, I. J. Chem. Phys. 2001, 115, 4742. (23) Podeszwa, R.; Buch, V. Phys. ReV. Lett. 1999, 83, 4570. (24) Uritski, A.; Presiado, I.; Huppert, D. J. Phys. Chem. C 2008, 112, 11991. (25) Uritski, A.; Presiado, I.; Huppert, D. J. Phys. Chem. C 2008, 112, 18189.

J. Phys. Chem. C, Vol. 113, No. 18, 2009 7881 (26) Calatayud, M.; Courmier, D.; Minot, C. Chem. Phys. Lett. 2003, 369, 287. (27) Devlin, J. P. J. Chem. Phys. 1988, 89, 5967. (28) Singer T. P. FlaVins and FlaVoproteins; Elsevier Scientific Publishing Company: Amsterdam, 1976. (29) Eigen, M.; deMaeyer, L.; Spatz, H. Ber. Bunsen-Ges. Phys. Chem. 1964, 68, 19. (30) Eigen, M.; deMaeyer, L. Proc. R. Soc. London 1958, 247, 505. (31) Cohen, B.; Huppert, D.; Agmon, N. J. Phys. Chem. A 2001, 105, 7165. (32) Von Smoluchowski, M. Z. Phys. Chem. 1917, 92, 129. (33) Tachiya, M. Radiat. Phys. Chem. 1983, 21, 167. (34) Szabo, A. J. Phys. Chem. 1989, 93, 6929. (35) Agmon, N.; Szabo, A. J. Chem. Phys. 1990, 92, 5270–5284. (36) Suppan, P. J. Chem. Soc., Faraday Trans. 1 1987, 83, 495. (37) Khajehpour, M.; Kauffman, J. F. J. Phys. Chem. A 2000, 104, 7151. (38) Molotsky, T.; Huppert, D. J. Phys. Chem. A 2003, 107, 2769. (39) Nagle, J. F. J. Phys. Chem. 1983, 87, 4086. (40) Agmon, N. J. Phys Chem. A 2005, 109. (41) (a) Weller, A. Prog. React. Kinet. 1961, 1, 189109. (b) Weller, A. Z. Phys. Chem. N. F. 1958, 17, 224. (42) Steinemann, S. HelVetica Physica Acta 1957, 30, 581. (43) Hubmann, M. Z. Physics B 1979, 32, 127. (44) Devlin, J. P.; Gulluru, D. B.; Buch, V. J. Phys. Chem. B 2005, 109, 3392. (45) Devlin, J. P.; Uras, N.; Sadlej, J.; Buch, V. Nature (London) 2002, 417, 269. (46) Thibert, E.; Domine´, F. J. Phys. Chem. B 1997, 101, 3554. (47) Rosenwaks, Y; Thacker, B. R.; Nozik, A. J.; Shapira, Y; Huppert, D. J. Phys. Chem. 1993, 97, 10421. (48) Uritski, A.; Huppert, D. J. Phys. Chem. A 2008, 112, 3066. (49) Speiser, S. Chem. ReV. 1996, 96, 1953.

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Measurement of Large Proton Diffusion in Methanol-Doped Ice by

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