J. Phys. Chem. C 2008, 112, 18189–18200
18189
Indication of a Very Large Proton Diffusion in Ice Ih. 2. Fluorescence Quenching of Flavin Mononucleotide by Protons 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: June 5, 2008; ReVised Manuscript ReceiVed: September 1, 2008
A time-resolved emission technique was employed to study the effect of excess protons on the fluorescence quenching process of flavin mononucleotide (FMN) in methanol-doped ice samples. We found that an excess of protons in ice has a very large effect on the fluorescence quenching whereas in liquid water the proton fluorescence quenching is rather small. We analyzed the experimental data using the Smoluchowski diffusionassisted binary collision model. Under certain assumptions and approximations, the calculated proton diffusion constant in ice in the range of 245-265 K is about 10 times that of water at 295 K. Introduction Proton transfer reactions, such as autoionization in water, proton conductivity (the von Grotthuss mechanism), acid-base neutralization reactions, and proton pumping through membrane protein channels, are ubiquitous in the fields of chemistry and biology.1-4 The study of the proton reaction in the solid phase, and particularly in ice, is rare and uncommon.5,6 The physics of ice7-10 and its unique properties have interested scientists for a long time, posing many questions that still puzzle us today.8 In the early 1960s it was estimated from the electrical conductivity measurements of Eigen4 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 water11 by about a factor of 2 (when compared to supercooled liquid water12,13 at the same temperature). Ice exhibits a high static relative permittivity which is comparable to that of liquid water. A particularly important issue concerns the role that crystal defects play in the shaping of the ice’s peculiar electrical properties. The theory of Jaccard14 is used to explain the electrical conduction and the dielectric properties of ice. According to this theory, 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 then made possible by means of successive proton jumps. (2) Bjerrum defects,15 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 mechanism of the excess proton transfer in ice was investigated by Ohmine and co-workers16 using the QM/MM method. They proposed that the excess proton is localized in an L-defect in ice. Podeszwa and Buch17 studied the structure and dynamics of orientational defects in ice by molecular dynamics simulations. They found the defect structure to be quite different from the one originally proposed by Bjerrum.15 For the L-defect, one water molecule is displaced at ∼1 Å from the crystal lattice site. Defect jumps occur via vibrational phase coincidence. * Corresponding author: e-mail
[email protected], phone 972-36407012, fax 972-3-6407491.
Over the past two decades,18-23 excited-state intermolecular proton transfer (ESPT) has been studied extensively in the liquid phase. In a recent paper,24 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. 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. When the irradiated sample is in neutral pH, the long-time fluorescence tail decay is nonexponential and arises from the diffusion assisted reversible geminate recombination of the transferred proton with the RO-*, i.e., H+ + RO- f ROH*. When excess protons are present in liquid and in ice, the long-time fluorescence tail decays nearly exponentially with the lifetime of the deprotonated form of the RO*-. We used a 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 a 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. We found that the proton diffusion in ice Ih at 240-263 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 deMaeyer25,26 from about 50 years ago but contradicts conductivity measurements of ice from 1968 to this day. We explained the discrepancy between our results and the conductivity measurements by the difference in the length scale of the proton transport of the two types of measurements. In our study we monitored a small sphere of about 50 nm around a photoacid (which serves as a natural reversible electrode for protons), whereas in the conductance measurements the distances between electrodes were in the range of 1 mm. 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 living cells. Flavin’s ability to absorb blue and near-ultraviolet light leads to several processes in plants. In the present work we use time-resolved and steady state methods to study the quenching properties of flavin mononucleotide (FMN), 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 1 < c < 10 mM. From the analysis of
10.1021/jp804964e CCC: $40.75 2008 American Chemical Society Published on Web 10/23/2008
18190 J. Phys. Chem. C, Vol. 112, No. 46, 2008 SCHEME 1
Uritski et al. of a single (static) donor, an excited flavin molecule, due to its irreversible reaction with a c ) [H+] concentration of proton acceptors (in this study excess proton in liquid and ice) is given by28-30
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) ) kap(a, t) the experimental results and using certain assumptions, we deduce the excess proton diffusion constant. We find that proton diffusion in ice is about 10 times larger than in liquid water at 295 K. The diffusion constants of proton in ice extracted from the current study are in accord with our previous study24 of the effect of excess proton in ice on the reversible photoprotolytic of photoacids. These striking results are in accord with the findings of Eigen and deMaeyer in the late 1950s.25,26 Experimental Section We used the time-correlated single-photon counting (TCSPC) technique to measure the time-resolved emission of flavin mononucleotide (FMN). 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 FMN 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. A flavin mononucleotide (FMN) (Scheme 1) of analytical grade was purchased from Sigma. HCl (1 N) 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 >10 MΩ. Methanol of analytical grade was purchased from Fluka. 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 samples were prepared by first placing the cryogenic sample cell for about 20 min at a supercooled liquid temperature of about 260 K. 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.
(2)
whose intrinsic proton-recombination rate constant is ka. The pair (FMN/H+) density distribution, p(r,t), is governed by a three-dimensional Smoluchowski equation (diffusion in a potential U(r)).31 For U(r) ) 0, it is possible to solve the above equations analytically for k(t).29 This is no longer true when U(r) * 0. In this case, Szabo30 found an approximate expression for the timedependent rate constant. When a potential is introduced, it behaves correctly at both t ) 0 and t ) ∞
k(0) ) kPTe-βU(a),
k(∞) ) [k(0)-1 + kD-1]-1
(3)
where
kD ) 4πDae
(4)
is the diffusion-control rate constant and ae is an effective radius whose dependence on the dielectric constant is given by23
ae ) RD /(1 - exp(-RD /a)) RD )
ze2 εskBT
(5)
(6)
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.3 RD is the Debye radius, z is the charge of the molecule in electronic units, and e is the charge of the electron. The value of ae for FMN in water with a dielelectric constant of εs ) 78, assuming a negative charge on the phosphate group, is 11 Å. 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 + k(0)/kD. Results
The Smoluchowski Model The Smoluchowski model is used to describe the diffusionassisted 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 time-resolved emission decay of FMN in the presence of an excess proton in the ice sample. We assume that the excess proton transport toward the FMN is the rate-limiting step. The mathematical and computational details of the Smoluchowski model are given elsewhere.27 According to the Smoluchowski model, the survival probability
Figure 1 shows the steady-state emission spectra of FMN excited at 400 nm in several temperatures in the range of 240 < T < 285 K. The neutral pH sample contained 0.5% mole fraction of methanol. The signal intensity at the liquid temperature is larger by a factor of 3 than in ice at 265 K and by a factor of 4 for low temperature ice T < 250 K. The fluorescence band position and shape are identical in liquid and ice in the temperature range shown in the figure. Within the studied temperature range while baring in mind the limited sensitivity of the diode array spectrometer, we did not observe any
Very Large Proton Diffusion in Ice Ih
J. Phys. Chem. C, Vol. 112, No. 46, 2008 18191 rate. The fluorescence quenching decay arises from the reaction of the excess proton in ice with excited-state flavin kq
FMN* + H+ 98 FMN
Figure 1. Steady-state emission spectra of a FMN sample in 0.5% mole ratio of methanol in liquid and in ice phases.
phosphorescence or other contributions to the luminescence. We explain the large drop in the fluorescence intensity when the sample freezes by the tendency of the FMN molecules to be excluded from the bulk of the microcrystal ice and aggregate at the grain boundaries and at the edges of the macroscopic sample as well. Figure 2 shows the time-resolved emission of FMN in methanol-doped ice of two samples: that of a neutral pH and that of a sample that contains 4 mM HCl. The methanol doping was of 0.2% mole ratio. The figure shows the time-resolved emission of liquid samples as well as solid samples at several temperatures. The signal’s decay rates of the neutral and the acidic samples differ strongly in ice. In the liquid state the decay rate of the acidic sample is smaller than in ice but larger than the decay rate in neutral pH. From the decay rate of the fluorescence signal of FMN in the acidic sample one can estimate the proton diffusion constant. Figure 3 shows the time-resolved emission of FMN in the presence of 4 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
where FMN* is the excited state of FMN and FMN 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 a large dependence of the proton diffusion constant on the methanol concentration. The methanol molecules probably trap the mobile proton in the bulk ice. When the methanol concentration is about 10% mole ratio, the proton quenching rate is very small and the excited FMN decays almost as if no acid was introduced into the ice sample. Figure 4 shows a comparison between the time-resolved emissions of a FMN sample containing 4 mM, whose methanol doping is 0.2% mole ratio in ice at 263 K acid, a sample of the same composition in the supercooled liquid at 265 K, and ice close to the melting point at 268 K. As seen in the figure, the supercooled liquid sample fluorescence decay rate is small and similar to the signal decay of a liquid sample at temperatures above freezing point, whereas in the solid sample at 263 K the decay rate is more than 10 times larger. The time-resolved emission of FMN in the presence of acid in methanol-doped ice samples at 268 K shows a much smaller quenching rate than ice at temperatures below 263 K. The proton diffusion constant at 268 K is about half of its value in the lower temperatures. This finding was also observed in our previous study on the excess proton effect on the photoprotolytic cycle of 2N68DS. Figure 5 shows the time-dependent fluorescence of FMN in methanol-doped ice (0.2% by mole ratio) at several HCl concentrations in the range of 1 < c < 8 mM. As seen in the figure, in ice at all acid concentrations the signal decay rate 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 2. Time-resolved emission of FMN in 0.2% methanol-doped aqueous sample at several temperatures. Each frame contains two samples: a neutral pH sample and a sample that contains 4 mM HCl.
18192 J. Phys. Chem. C, Vol. 112, No. 46, 2008
Uritski et al.
Figure 3. Time-resolved emission of FMN in 4 mM HCl aqueous solution at various methanol concentrations, displayed at four different temperatures.
basically follows k(∞), and the well-known nonexponential behavior of the Smoluchowski theory is hardly observed. The observed nonexponential fluorescence decay of FMN 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.32 The ice is a disordered system with 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 (FMN) at different times. The parameters of the model fit to the experimental results of 0.1%, 0.2%, 0.5%, and 1% mole fraction of methanol doped ice sample containing 4 mM HCl are given in Tables 1-4. Discussion Figure 4. Time-resolved emission of FMN in 4 mM HCl solution of 0.2% mole ratio of methanol: in the solid phase at 263 and 268 K and in the supercooled liquid phase at 265 K.
Figure 6 shows the fit (solid line) of the experimental results (dots) of the FMN time-resolved fluorescence of a sample containing 4 mM HCl to the diffusion-assisted kinetic model of A + Bf AB, using eqs 1-3. The model fits the short- and long-time signal reasonably well at large doping levels of methanol, i.e., 0.5% mole ratio and at larger values. At lower concentrations of methanol, 220 K, whereas at lower temperatures of T < 220 K it obeys an Arrhenius activation behavior, with a large activation energy of 0.3 eV. Acid Concentration Dependence of the Proton Diffusion. We measured the FMN’s fluorescence intensity in 0.1% mole ratio methanol doped samples in the presence of HCl at a relatively large concentration range of 1 < c < 10 mM. We found that in the temperature range of 230 < T < 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 a particular methanol-doped ice samples. Proton Diffusion Dependence on the Methanol Concentration. In the current study 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% mole ratio. The proton diffusion constant decreases as the methanol concentration increases. We explained 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 methanoldoped ice crystal. The question that subsequently arises then is why to dope ice with methanol? Methanol doping is necessary to incorporate the FMN in the crystal bulk and to prevent the exclusion of the FMN from the bulk and its aggregation at the grain boundaries. At a small methanol concentration of ,0.05%
by molar ratio, we noticed large proton quenching of the FMN fluorescence signal of neutral ice samples. The quenching rate depends both on the methanol concentration and on the temperature. Figure 8 shows the time-resolved emission of FMN in several neutral pH methanol-water mixtures of low and intermediate methanol concentrations. As seen in the figure, the emission decay rate of FMN at short times in a frozen solution at low methanol concentration (0.1% and 0.2% mole ratios), and temperature is larger than the decay in the liquid state. At short times in the ice phase the lower the temperature the larger the decay rate. For the intermediate methanol concentration (0.5% and 1% molar ratio) the decay rate in ice at short times (as seen in Figure 8) is somewhat larger than in the liquid state, but for a particular temperature of ice it is much smaller than that of the low methanol concentration. It is also noticeable that at short times the fluorescence decay of FMN in ice is nonexponential at low methanol concentrations. In our previous studies on the photoprotolytic cycle of the 2-naphthol-6,8-disulfonate (2N68DS) photoacid in ice,24 we observed a similar behavior of the time-resolved emission signal of both ROH* and RO- forms. In the case of 2N68DS, the fluorescence quenching effect in pure ice was much smaller than for FMN. The quenching for the RO-* of 2N68DS was observed at methanol concentrations of about c e 0.01% mole ratio, whereas for FMN the quenching is already effective for c e 0.2% mole fraction of methanol. We are not yet certain why the FMN decay in ice and in neutral pH ice consists of nonradiative components. A plausible reason may be that an excited molecule, such as flavin, is a strong photobase and therefore abstracts a proton from a nearby water molecule. Comparison of the Current Results with Our Previous Results. In a recent study we deduced the proton diffusion constant in methanol-doped ice from the reversible photo-
18196 J. Phys. Chem. C, Vol. 112, No. 46, 2008 protolytic cycle of the photoacid 2-naphthol-6,8-disulfonate (2N68DS) kPT
ROH* {\} RO-* + H+ kr
In the absence of excess protons in ice the proton is first transferred to the solution. The proton may geminately recombine with the deprotonated RO-* species of the acid to re-form the excited photoacid ROH*. This recombination process increases the ROH* population, and it therefore affects the profile of the time-resolved emission decay signal of the ROH*. The long time fluorescence profile decays nonexponentially. Excess protons compete with the geminate proton and also recombine with RO-* to re-form the ROH*. In that case the long-time fluorescence decay is exponential rather than nonexponential. The amplitude of the long-time fluorescence tail depends on the excess proton concentration, the proton diffusion constant, and the intrinsic reaction rate constants kPT and kr. In our previous study we assumed that at long times the proton recombination rate with RO- is given by k(∞) (see eq 3) and hence depends on the proton diffusion. The proton diffusion constant in ice deduced from the 2N68DS experiments are similar to the values in the current study. The strong dependence of DH+ on the methanol concentration was also observed in the previous study. The current study on the proton fluorescence quenching of FMN is simpler in its interpretation than in the case of 2N68DS. The fluorescence quenching of FMN by protons fits nicely the well-known diffusion-assisted irreversible recombination theory of Smoluchowski. The fluorescence decay profiles of fluorescence quenching experiments of type A + B f AB are often fitted using the Smoluchowski theory.36 From the current FMN study the values of the diffusion constant of methanol-doped ice are somewhat larger than those of the previous study on 2N68DS.42 The largest value of DH+ in the 2N68DS was 1.3 × 10-3 cm2/s, whereas for the FMN the value of DH+ is ∼1.8 × 10-3 cm2/s. In particular, for 2N68DS this difference may arise from the simplifications and assumptions of modeling the experimental results, since for 2N68DS the geminate proton also participates in the recombination process and thus reduces the probability to find a free RO-* that an excess proton can recombine with. FMN seems to be less soluble in methanol-doped ice than in 2N68DS. The latter is a smaller molecule than FMN, and it is also charged owing to the two negative sulfonate groups. While in case of the 2N68DS we were able to reduce the methanol concentration to 0.02% mole ratio with a minimum reduction of the sample’s fluorescence intensity, in FMN in doped sample the fluorescence intensity is reduced by a factor of 5 when the sample freezes (at 0.1% mole fraction). There are two drawbacks in the experiments on 2N68DS in ice. The first drawback is that the first step in the photoprotolytic cycle is a proton transfer from the photoacid to the ice, and only then protons from the bulk can react with the RO-. Thus, there is a time lag from excitation until the ROH* molecules convert to RO-*. At low temperatures the rate of proton transfer is slow (about 1 ns), and hence the information on the diffusion-assisted proton recombination at short times is unattainable. The second drawback concerns the participation of the geminate proton in the recombination of RO- with excess protons in the bulk. In FMN proton quenching experiments these two complications are avoided. We assume that the proton quenching is a single step reaction. An excess proton reacts with an excited FMN, and the outcome is a groundstate FMN. The flavin segment of FMN contains four hetero-
Uritski et al. cyclic nitrogens and two oxygens linked to ring carbons. Except for one nitrogen that is bonded to the ribitol, the three other nitrogens and the two oxygens can react with the excess proton. This reaction leads to a radiationless process. Connection between the Determination of the Diffusion Constant and the Dielectric Properties of Ice. The FMN molecule consists of three molecular segments: flavin, sugar ribitol, and a phosphate group. In a neutral pH solution and probably also in neutral pH ice, the only charged segment of FMN is the phosphate group. In water the largest acid dissociation equilibrium constant of the phosphate is Ka ) 7.1 × 10-3. The temperature dependence of the low pK of the phosphate moiety is 0.0044 pK/deg. Thus, upon cooling, the pK of the first ionization may decrease by 0.1 or more units, with subsequent change in the proportion between the two states of the FMN. Consequently, a phosphate group is almost fully protonated in an aqueous solution with a strong acid concentration of about 0.1 M. Our FMN quenching experiments are performed at lower concentrations of up to 10-2 M. In a low FMN concentration solution with a strong acid of 7 × 10-3 M, half of the phosphate molecules in the aqueous solution are uncharged because of the protonation (neutralization reaction). As described in the previous section, the level of protonation affects the effective radius ae. For the uncharged FMN molecule the diffusion-controlled rate constant (eq 4) depends on a, with the contact radius being 7 Å rather than ae ≈ 11 Å. For any given value of kD, the extracted value of DH+ is inversely proportional to ae (see eq 4). We do not know the pKa values of the phosphate group in FMN and particularly in ice. Usually acidic groups attached to molecules have their acidic quality diminished compared with the acid itself. In that case the phosphate group might be fully protonated under the experimental condition currently employed. Equations 4-6 show that the proton recombination rate strongly depends on the dielectric constant. The large acid effect 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 present study. It was previously reported that the dielectric constant of ice strongly decreases with an HF acid concentration.39 According to Jaccard’s theory14 and Hubmann’s corrections,37 the static dielectric constant εs is given by
(
σDL σ( e eDL ( 1 εs - ε∞ ) σDL ε0Φ σ( + 2 2 e( eDL
(
)
)
2
2
(7)
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 the thermal energy kBT. The behavior of the static dielectric constant as a function of an HF impurity concentration is complicated (see Figure 9.7 in ref 7). 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/ cm3 (0.1 mM). At about 3 × 1017 molecules/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 and reaches a value of εs ) 25 at 1018-1019 molecules/cm3. In pure ice the number of Bjerrum defects is much larger than the ionic defects and σDL > σ(. For HF, a weak acid in an
Very Large Proton Diffusion in Ice Ih aqueous solution (pKa = 3), the H+ concentration in doped ice is small, and nH+ is proportional to nHF. In that case the value of the dielectric constant oscillates as a function of an HF concentration. At a very low HF concentration, εs ) 100, whereas for nHF ) 3 × 1017 molecules/cm3,39 σ( ) 1/2σDL and εs ) ε∞. As the HF concentration continues to increase, so does εs since σ( . σDL. HCl is a very strong acid, and therefore we assume that all the HCl molecules dissociated in the small concentration range we explored (1 < c e 10 mM), and in that case σ( . 1/2σDL. According to Hubmann’s expression, which is derived from Jaccard’s theory, εs is expected to be ∼44 in the HCl doping level of our experiments. Takei and Maeno34,35,38 studied the electrical conductivity and the dielectric properties of HCl-doped ice in single crystals grown from an HCl liquid solutions of 4 × 10-6-1 × 10-4 M HCl. The concentration of HCl incorporated in the ice is rather small, although not directly measurable. For a mother solution of 10-5 M the concentration of HCl in bulk single ice crystal was estimated as 2.5 × 10-7 M from the dc conductivity assuming a mobility of positive ionic defect (2.7 × 10-8 m2/(V s)).38 The ion conductivity σ( of all samples in Takei and Maeno’s study34,35 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. As in Takei and Maeno’s experiments, we also found that the proton diffusion constant is almost temperature independent (within a factor of 2) in the range of 240-265 K. The conductivity of the ion defects is given by σ( ) ∑2i)1niµi|ei|, where ni is the ion defect number density, |ei| is the ion effective charge, and µi 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, then the diffusion-controlled rate constant will be strongly affected. The Debye radius RD scales inversely with the dielectric constant RD ) ze2/εskBT (eq 6). The diffusioncontrolled rate constant depends on RD, i.e., kD = 4πN′DH+RD/ (1 - exp(-RD/a)). The large increase in the fluorescence quenching of FMN in ice arises not only because of a large increase in DH+ but partially also from the large increase of RD. The study of Steinmann39 showed that the dielectric constant of HF-doped ice strongly depends on the acid concentration. However, in our experiments, the value of the proton diffusion constant extracted from the fit of the experimental results by using the diffusion-assisted kinetic model is independent of the proton concentration in the range of 1 < c < 10 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. In the extreme case, where the dielectric constant decreases to εs ) 44 and kD = 4πN′DH+RD, RD should nearly double, whereas the proton diffusion constant that we calculated from the experimental time-resolved emission results should, in fact, be halved from the value we deduced for εs ) 100. In that case, proton diffusion in ice should only be 5 times larger than in water at 295 K or about 15 times larger than in super cooled liquid at ∼265 K. In dc electrical conduction the ion defect current must equal the Bjerrum current.10 Thus, the two mechanisms effectively
J. Phys. Chem. C, Vol. 112, No. 46, 2008 18197 act in series and the relation between the dc conductivity σ, the ion defect conductivity σ(, and the Bjerrum defect conductivity σDL is well represented by
1 1 1 + = σ σ( σDL
(8)
The dc conductivity is therefore chiefly determined by the less effective of the two mechanisms, which for pure ice is the ion defect current because the ion concentration is much lower than the Bjerrum defect. At high frequencies the protons can move back and forth along the same path. The interaction between different defect types is small, and hence the two processes act independently in parallel; the high-frequency conductivity σ∞ is given by
σ∞ ) σ( + σDL
(9)
Measurement of σ and σ∞ enables the relative effectiveness of the two processes to be estimated. The current experiments of photoactive molecules that are sensitive to protons like FMN (in this study) or photoacids (in our previous study) determine the value of the proton diffusion that is associated with σ∞ rather than σ. The proton reaction occurs only once; consequently, the slow orientational motion of the water molecules to correct the position of the hydrogens is not important. Proton Reaction at Grain Boundaries and Characterization of the Ice Sample. The second possible explanation to the strikingly large acid effect on the quenching rate of FMN in doped ice is along the lines of other observations,6,40 suggesting that dopants tend to exclude from the ice bulk and aggregate on grain boundaries. If that is the case, then the FMN molecules in our experiments are not incorporated in the bulk of a microcrystal of ice; rather, the FMN position is at the grain boundaries. The proton reaction with the RO*- 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 FMN molecules are located. We assume 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 FMN molecules themselves are at the grain boundaries, as are the counterions (sodium ions from the phosphate as the chlorides from the HCl), while the protons stay inside the bulk of the microcrystals. In that case, the FMN 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 we adopted in our previous study using 2N68DS and implemented also in the present work is the dimensionality of the problem. The proton diffuses with a three-dimensional bulk diffusion constant to a surface nearby and reacts with the FMN only at the grain boundaries. The proper description of the diffusion toward the surface may be regarded as one-dimensional. In a recent paper42 we characterized the position of a photoacid in methanol-doped ice polycrystalline 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. The Fo¨rster’s EET
18198 J. Phys. Chem. C, Vol. 112, No. 46, 2008 experiment, described below, 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. We used 2N68DS in its deprotonated form, RO*-, as the EET donor and fluorescein disodium salt as the acceptor. We compared the experimental results of the time-resolved emission EET of samples in an aqueous liquid state with the results in ice. The EET process at a concentration of 0.2 < c < 1 mM showed a small, but similar, energy transfer rate for both liquid and ice samples (the critical radius being R0 ) 56 Å). 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 donor and acceptors. For a 10 µm cubic crystal with a bulk concentration of 1 mM of acceptors, the average distance between adjacent photoacid 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 should 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 the donor decay time is a few picoseconds. The actual donor decay measured in the experiments of our previous study42 was close to its radiative rate, τ ) 12 ns. We therefore concluded that 2N68DS tends to stay in the methanol-doped polycrystalline ice bulk. Solubility of FMN in Methanol-Doped Ice Samples. Pure ice is known to be a poor solvent. Devlin et al.6,40 studied doped ice samples which were prepared by careful and controlled deposition of water 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.40 confirmed the experimental observation that dopants tend 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 our previous studies41-43 we noticed that photoacids tend to be excluded from the bulk, and aggregate at the grain boundaries of the polycrystalline ice. In the present study we noticed that the same is true for FMN. A small amount of methanol helps to prevent the segregation of dopants from ice and its aggregation at the grain boundaries. This aggregation of FMN may lead to dimerization and consequently to fluorescence intensity reduction. In a recent work Grajek et al.44 studied by time-resolved emission the consequences of large concentrations of FMN in aqueous solution. From absorption spectra measurements they found an efficient formation of FMN dimers with simultaneous absence of higher order aggregates even at highest concentrations. It was found that fluorescence intensity decays are strongly accelerated in the presence of dimers, due to excitation energy trapping, and then become nonexponential. Figure 9a shows the time-resolved emission of solid FMN powder taken from the container as purchased from Sigma (no solvent was added) along with the signal of FMN in pure ice sample (methanol-free). The intensity of FMN fluorescence signal of undoped ice is roughly 200 times smaller than the signal of methanol-doped samples. We attribute this low fluorescence yield not only to the increase in the decay rate but also to migration of expelled FMN molecules from the center of the macroscopic sample where the excitation takes place with a laser beam of 300 µm size spot to the edge of the sample (outside the irradiated spot). For both samples the fluorescence decay rate is very large at short times and generally decays nonexponentially. Figure 9b shows on a log-log plot the time-
Uritski et al.
Figure 9. Time-resolved emission of FMN powder and of FMN in an undoped-ice sample. (a) A semilog plot along with a fit to a stretched exponent (see text). (b) A log-log plot of the data shown in frame a and a fit to a power law decay function of t-1 (see text).
resolved emission of solid FMN powder shown in Figure 9a. The signal of the excited-state is corrected for the natural radiative decay by means of multiplication by exp(t/τf), where τf ) 5 ns is the excited-state lifetime. As seen in Figure 9b, the decay of FMN approximately obeys a power law of t-1. The decay of the solid FMN powder sample could also be reasonably fit to a stretched exponent of exp-(t/τ)0.5, where τ ) 0.27 ns (solid line in Figure 9a). In the study of proton fluorescence quenching of FMN we found that the FMN fluorescence intensity depends to a much greater extent on the methanol concentration than on the photoacids used in previous ice studies. For 2N68DS samples we were able to reduce the methanol concentration to 0.01% mole ratio and maintain the photoacid fluorescence intensity close to that of the liquid state. For FMN samples whereas at 0.1% mole ratio of methanol the fluorescence intensity (at 268 K) reduced by a factor of 5 compared to that in the liquid state. This large reduction in the fluorescence intensity, which is probably due to aggregation at the grain boundaries, did not affect the time-resolved emission that was collected from the 20% of the total FMN molecules that are positioned in the ice bulk. Penzkofer et al.45 studied the fluorescence quenching of flavins in aqueous solutions by reducing compounds. They used three flavin derivatives, one of which was FMN, and three reducing agents. The fluorescence quantum yields and fluorescence lifetimes are determined as a function of the reducing compound concentration. It was found that the dynamics of the fluorescence quenching is diffusion controlled, and it is proposed that the fluorescence quenching is governed by an electron
Very Large Proton Diffusion in Ice Ih
J. Phys. Chem. C, Vol. 112, No. 46, 2008 18199 transfer theories relate the electron transfer rate constant to the donor acceptor distance46
ket ) k0 exp[-β(x - x0)]
Figure 10. Time-resolved emission of FMN in aqueous solution in the presence of a reduction agent DTT. The DTT concentrations are 12.5, 25, and 50 mM.
transfer process from the donor, the reducing agent, to flavin. We used the fluorescence quenching of FMN by the reducing agent, dithiothreitol (DTT), to further explore and characterize the position of this proton-sensitive molecule in the methanoldoped ice sample. Figure 10 shows the time-resolved emission of FMN in aqueous solution containing large concentrations of DTT. The fluorescence quenching by DTT is indicated by the shorter decay times of the FMN fluorescence. The larger the DTT concentration the faster the decay rate becomes. The experimental data could be fitted using the diffusion-assisted irreversible reaction model based on the DSE (see eqs 1-6). The larger the DTT concentration, the larger the nonexponential character of the fluorescence decay curves, as expected from the condition k(0) > kD (see eq 3). The diffusion-controlled rate constant depends on D, the mutual diffusion constant, which is in this case (large molecules in viscous media) small; it is of the order magnitude of 10-5 cm2/s, and kD = 5 × 109 M-1 s-1. Nonadiabatic electron
(10)
k0 is the rate constant at a known distance denoted by x0. β for electron transfer reaction is of the order of magnitude of 1 Å-1. In ice the donor-acceptor are immobile; therefore, the excited donor-acceptors distances are fixed in time, whereas both the donor (the reducing agents) and the acceptor molecules in the liquid state can diffuse and approach each other while in the excited state. Thus, if both FMN and DTT molecules positions in ice are in the bulk, the fluorescence quenching should be slightly reduced compared to its level in the liquid state. On the other hand, if both donor and acceptor are expelled from the bulk and their position is at the grain boundaries, we expect the donor-acceptor distances to shorten dramatically for polycrystalline ice. As mentioned above, for 1 mM bulk concentration and crystals of about 10 µm in size, the average distance between donor and acceptor molecules is ∼100 Å in the bulk, while only 5 Å in the grain boundaries. The electron transfer rate, according to eq 9, should increase by many orders of magnitude at the grain boundaries. Figure 11 shows time-resolved emission of FMN in water-methanol mixtures containing 5 mM DTT at several temperatures. In the liquid state, the decay is almost exponential at samples with methanol concentration of 0.5-2.5% mole ratio, and the rate of quenching is small compared to the radiative decay rate. In ice, the decay rate in the presence of 5 mM DTT is slightly higher than the decay rate in a DTT-free FMN sample. We explain these results as 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 is large, and the average distances between donor and acceptor should decrease more than 10-fold. The expected rate of electron transfer should be
Figure 11. Time-resolved emission of FMN in two methanol concentrations of methanol-doped ice in the presence and absence of 5 mM DTT. Each panel shows the data of three samples: 5 mM DTT in 1% and 0.5% mole ratio of methanol and a sample of only FMN.
18200 J. Phys. Chem. C, Vol. 112, No. 46, 2008 ultrafast, probably a few picoseconds. The actual increase of the rate is only a fraction of a nanosecond. It may indicate that only a small fraction of the fluorescence signal arises from FMN molecules that are at the grain boundaries, whereas the main portion of the fluorescence signal is originated from FMN molecules positioned in the bulk ice. Summary We studied the fluorescence quenching of flavin mononucleotide (shown in Scheme 1) in liquid water and in ice in the presence of small concentrations of the strong mineral acid HCl. We used a time-resolved emission technique to monitor the fluorescence quenching 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 ice Ih 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 study,24 where we used the 2-naphthol-6,8-disulfonate (2N68DS) photoacid instead of the flavin mononucleotide used in this study. Ice conductance was extensively studied for more than 40 years. The mobility of the proton in ice fluctuated, from Eigen’s large value25 of 0.075 to 0.000 27 and to 0.006 cm2/(V s).47,48 Our findings are commensurate with the electrical measurements of Eigen and deMaeyer25,26 from about 50 years ago but contradict electrical conductivity measurements of ice from 1968 to this day. We explained the discrepancy between the results of the present study and the electrical dc conductivity measurements by the length scale of the two types of measurements as well as that ours provide the high-frequency proton mobility. In our measurements, we monitored a small sphere of about 50 nm around our excited probe molecules, whereas in the conductance measurements the distances between electrodes were in the range of 1 mm. Acknowledgment. We thank Prof. John F. Nagle and Prof. M. Gutman for helpful discussions. This work was supported by grants from the Israel Science Foundation and the JamesFranck 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) Z. Phys. Chem. (Muenchen, Ger.) 1958, 17, 224. (4) (a) Eigen, M. Proton Transfer. Angew. Chem., Int. Ed. 1964, 3, 1. (b) Eigen, M.; Kruse, W.; Maass, G.; De Maeyer, L. Prog. React. Kinet. 1964, 2, 285. (5) Uras-Aytemiz, N.; Joyce, C.; Devlin, J. P. J. Phys. Chem. A 2001, 105, 10497.
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