Classification of Acids and Acidities in Ih Ice II - American Chemical

Jun 24, 2009 - The proton concentration in acidic ice samples was determined by measuring ... ice. Among those photoacids were 2-naphthol-6,8-disulfon...
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J. Phys. Chem. C 2009, 113, 12901–12910

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Classification of Acids and Acidities in Ih Ice II: Reversible Photoacids As a Probe for Proton Concentration Anna Uritski, Itay Presiado, Yuval Erez, Rinat Gepshtein, and Dan Huppert* Raymond and BeVerly Sackler Faculty of Exact Sciences, School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel ReceiVed: March 30, 2009; ReVised Manuscript ReceiVed: May 13, 2009

The proton concentration in acidic ice samples was determined by measuring the time-resolved fluorescence of two photoacids. We found that for a certain concentration of acid the overall proton reaction rate with the deprotonated form of the photoacid (RO-*) to reversibly reform the excited-state photoacid ROH* RO-* + H+ a ROH* depends on the kind of acid used. In strong acid-doped ice samples the rate was larger than in weak acid samples. The experimental results indicate that the acidity scale of commonly used acids in aqueous solutions is also applicable for Ih ice. The weak acids (pKa > 2.5) are weaker in ice, and their pKa increases by bout 2 pKa units. Among the group of weak acids studied, HF (pKa ) 3.2 in water) is a relatively stronger acid in Ih ice and its pKa value is about the same as in water. This finding is in accord with previous electrical conductance measurements in ice. Introduction The physics and chemistry of ice have been studied for a long time.1-4 Ice exhibits a high static relative permittivity, comparable to that of liquid water. There are two types of structural defects that are largely responsible for the ice’s electrical properties: (1) Ion defects, which are the result of proton motion from one end of the bond to the other, thus creating a H3O+, OH- ion pair.5,6 (2) Bjerrum defects,7,8 which are orientational defects caused by the rotation of a water molecule to produce either a doubly protonated bond (D-defect) or a deprotonated bond (L-defect). For many years9-18 excited-state intermolecular proton transfer (ESPT) to a solvent or to a base in a solution has been widely researched in the liquid phase. In recent works19-21 we reported on measurements of the proton diffusion constant in Ih ice, using the photoprotolytic cycle of several photoacids in acid-doped ice. Among those photoacids were 2-naphthol-6,8-disulfonate (2N68DS), 1-naphthol-4-sulfonate (1N4S) and flavin mononucleotide (FMN) in liquid water, and in ice in the presence of small concentrations of a strong mineral acid, HCl. We deduced the proton diffusion constant in ice from the experimental data fit. We found that the value of the proton diffusion constant, DH+, in ice Ih at 240-263 K is about 10 times larger than in liquid water at 295 K. This value is in good agreement with the proton mobility calculations of Pang and co-workers based on a soliton model, where an ionic defect appears as a solitary wave in the proton sublattice.22 The defect concentrations created in pure ice can be influenced by introducing dopant molecules into the lattice. In the past, extrinsic defects were generated by doping the ice with HF. It was assumed that HF and NH3 were of particular interest due to the belief that these molecules substituted H2O molecules with a minimum ice lattice deformation.23-26 In a recent study27 we qualitatively classified the acidity of acids in ice Ih. We used the excited-state deprotonated photoacid, RO-* form of 1N4S, an irreversible photoacid, to monitor the * To whom correspondence should be addressed. E-mail: huppert@ tulip.tau.ac.il. Phone: 972-3-6407012. Fax: 972-3-6407491.

acidity of both weak and strong acids. We found that strong acids in the liquid state are also strong acids in ice and, similarly, weak acids in the liquid phase are also weak acids in ice. In the current study we extend our previous study and qualitatively classify the acidity of mineral and organic acids in ice Ih using two reversible photoacids, 2N68DS and 8-hydroxy-1,3,6-pyrenetrisulfonate (HPTS). We also included an additional acid to the list above, the trifluoroacetic acid (TFA) with an intermediate pKa value of 0.3. The acidity scale of acids, which was determined in this study by observing the time-resolved emission of the ROH* of two reversible acids, is in very good agreement with that of the previous study on 1N4S.27 It is encouraging to find how robust the method is of using photoacids to determine the proton concentration and mobility in the ice phase. Both the previous study and the current one provide similar information on many acids. We also used a buffered solution to determine the pKa value of HF in ice. For that purpose we use an ice sample with equal concentrations of HF and KF. Many objections to this type of measurement may arise from the tendency of guest molecules to be expelled from the bulk ice toward the grain boundaries. We use a small amount of methanol-0.1% mole ratio, to overcome this tendency of ice.19-21 Furthermore, all guest ions and molecules tend to form an inclusion, and severely distort the ice structure. We claim that for an impurity (ions and molecules) concentration of 1 mM, the average distance between these molecules is ∼100 Å. This distance is equivalent to about 40 water molecules in Ih ice. This large distance enables the measuring of the properties of the bulk ice rather than the properties of the local disrupted and amorphous ice close to the probe molecules. The main conclusion of both the current and our previous study is that the acidity scale of commonly used acids in aqueous solutions is also applicable for Ih ice. We also found that weak acids (pKa > 2.5) are even weaker in ice. We estimate that their pKa values in ice are larger by about 2 pKa units than their values in water. We found that, among the group of weak acids studied, HF is a relatively stronger acid, which roughly maintains the

10.1021/jp902851c CCC: $40.75  2009 American Chemical Society Published on Web 06/24/2009

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Figure 1. Time-resolved emission of ROH*, the protonated form of 2N68DS measured at 365 nm and excited at 285 nm, in methanol-doped ice of two samples: a neutral pH and a sample that contains 2 mM HCl.

same pKa value in water and in ice. This finding is in accord with previous electrical conductance measurements in ice. Experimental Section We used the time-correlated single-photon counting (TCSPC) technique to measure the time-resolved emission of 2N68DS, HPTS, and 1N4S in water and in ice. For sample excitations we used a cavity dumped Ti:Sapphire femtosecond laser, Mira, Coherent, which provided short, 150 fs, pulses. The laser’s second and third harmonics (SHG and THG), operating over the spectral ranges of 380-430 and 260-285 nm, were used to excite the photoacids in the ice samples. The cavity dumper operated with a relatively low repetition rate of 500 kHz. The TCSPC detection system was 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. 2N68DS and HPTS were purchased from Kodak, and 1N4S was purchased from TCI. HCl (1N), HBr, CF3SO3H, HF, CH2ClCOOH, CF3COOH (TFA), and ClCH2COOH were purchased from Aldrich. HCOOH was purchased from Merck (Germany). For transient measurements the sample concentrations were between 2 × 10-4 and 2 × 10-5 M. HPLC-grade water (Aldrich) had a resistance of >10 MΩ. Methanol of analytical grade was purchased from Fluka. All chemicals were used without further purification. The samples’ pH in the liquid state was measured by a pH meter (Orion). The temperature of the irradiated sample was controlled by placing the sample in a (home-build) liquid N2 cryostat with a thermal stability of ∼ (1.5 K. Ice Sample Preparation. Ice samples were prepared by first placing the cryogenic sample cell for 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 ∼235 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 ∼235 K.

All samples contained 0.1% or 0.2% mole ratio of methanol to prevent the photoacids from aggregating at the grain boundaries of the polycrystalline ice samples.19,20 Reversible and Irreversible Photoprotolytic Cycle of Photoacids. In the present study we used several photoacids to monitor the proton concentration in ice. Both the ROH* and the RO-* conjugate base of the photoacid fluorescence decay are sensitive to proton concentration. Scheme s1 and a detailed explanation on the photoprotolytic cycle are given in the Supporting Information, including proton reversible and irreversible recombination processes. Results Figure 1 shows the time-resolved emission of ROH*, the protonated form of 2N68DS in methanol doped ice of two samples: a neutral pH and a sample containing 2 mM HCl. The methanol doping was 0.1% mole ratio, preventing the aggregation of the photoacid molecules at the grain boundaries of polycrystalline ice. Figure 1 shows the signals of both liquid samples and solid ice samples at several temperatures. In all instances the short time signals are almost identical for both neutral and acidic samples. At intermediate and long times the signals of the neutral and the acidic samples differ strongly in ice, but in the liquid state the difference between signals is much smaller. In both liquid and ice, the neutral sample’s timeresolved signal decays nonexponentially in a very specific time profile. At the short time, the signal decays nearly exponentially and the rate almost exclusively depends on the proton transfer kPT

rate constant kPT, i.e., ROH* 98 RO-* + H+. This part of the signal is almost independent of the proton concentration or of the methanol concentration below 1% mole ratio. In acid free samples the intermediate and long-time parts of the signals strongly depend on the proton geminate recombination process kr

RO-* + H+ 98 ROH*. This process is influenced by the proton diffusion constant DH+, the intrinsic recombination rate constant at the reaction sphere, ka, and the Coulomb potential

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Figure 2. Time-resolved emission of the ROH* form of 2N68DS in weak acid-doped liquid and in ice at four temperatures. Each panel shows five decay curves: an acid-free (neutral pH) solution, and three solutions weak acids of 2 mM of HCOOH, ClCH2COOH, HF, and the strong HCl acid.

V(r). The ROH* emission signal also depends on the excitedstate lifetimes of both ROH* and RO-* and the forward reaction rate constant kPT. The lifetime (τf) corrected long-time asymptotic decay of ROH* is given by

ROH* exp(t/τf) ∝ [K*eq /(4πD)3/2]t-3/2

(1)

When comparing the ROH* signals of samples with and without acid we can see that the relative amplitude of both the intermediate and long-time signals of the acidic sample increases with respect to the neutral sample. In the liquid state, the longtime signal intensity increases only slightly, whereas in ice the amplitude of the long-time signal increases by more than an order of magnitude. We explain the large increase in the amplitude of the long-time component by a large increase in the value of the proton diffusion constant in ice, DH+. Our previous studies19-21 indicate that the value of DHice+ is 10 time larger than in water. Figure 2 shows the time-resolved emission of the ROH* form of 2N68DS in ice at four different temperatures. Each panel shows five decay curves: an acid-free (neutral pH) solution, three solutions of weak acids of 2 mM of HCOOH, ClCH2COOH, HF, and the fifth sample contains HCl, which is a strong acid in water. The three weak acids in the liquid phase have pKa values of 2.9, 3.2, and 3.75 for ClCH2COOH, HF, and HCOOH, respectively. For each temperature the signals are almost identical at short times. At long times, however, the amplitude and decay times depend on the particular acid. The short-time decay rate signifies the proton transfer rate to the solvent (water kPT or ice), i.e., ROH* a RO-* + H+. The long-time fluoreskr cence tail arises from the repopulation of ROH* by the reverse reaction. The amplitude of the long-time signal depends on the proton concentration and on the reversible recombination process (Scheme s1 provides an illustration of the process). Figure 3 shows the time-resolved emission of ROH* form of 2N68DS in several strong acid samples at four temperatures

in both liquid and ice. The concentration of the strong acid samples of HCl (pKa ) -7), HBr (pKa ) -9), and CF3SO3H (pKa ) -15) was 2 mM. For comparison, the figure also shows the signals of a neutral pH sample and of a weak HF acid sample. The short-time ROH* signals of the strong acids are similar to those of the weak acids shown in Figure 2. The shorttime decay is independent of the acid. The amplitude of the long-time fluorescence tail depends on the proton concentration, which in turn depends on the acid’s strength and concentration. The figure also includes the ROH* signal in a sample that contains an acid of intermediate strength, TFA (pKa ) 0.3). As seen in the figure, the time-resolved ROH* signal of a 2 mM TFA ice sample is similar to the signals of the much stronger acids. Figure 4 shows the time-resolved emission of the ROH* form of HPTS measured in liquid and in ice at four different temperatures. Each panel shows four decay curves: an acidfree (neutral pH) solution and three solutions of 2 mM of weak acids: HCOOH, ClCH2COOH, and HF. HPTS (pK* ≈ 1.3) like 2N68DS (pK* ≈ 0.7) is also a reversible photoacid. As in the case of 2N68DS (see Figure 2) the time-resolved ROH* emission signal of both photoacids consists of short- and longtime components. For each temperature the signals are almost identical at short times. At long times, however, the amplitude and decay times depend on the acid’s strength. Figure 5 shows the time-resolved emission of the ROH* form of HPTS in several strong acid samples at four temperatures in both liquid and ice phases. The strong HCl and HBr acid samples contained 2 mM of acid. For comparison, the figure also shows the signals of a neutral pH sample and a weak HF acid sample. The short-time ROH* signals of the strong acids are similar to those of the weak acids shown in Figure 4. This component’s decay rate mainly arises from the proton transfer to the surrounding water molecules with an intrinsic constant, kPT, which is unaffected by the acid’s presence at low concentrations. The amplitude of the long-time fluorescence tail depends on the acid’s strength, which is why it is much larger than in the weak acid samples signals shown in Figure 4. Since

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Figure 3. Time-resolved emission of the ROH* form of 2N68DS in neutral pH and in four strong acid samples: TFA (pKa ) 0.3), HCl (pKa ) -7), HBr (pKa ) -9), and CF3SO3H (pKa ) -15).

Figure 4. Time-resolved emission of the ROH* form of HPTS measured at 440 nm in weak acid-doped liquid and in ice at four temperatures. Each panel shows four decay curves: an acid-free (neutral pH) solution and three weak acid solutions of 2 mM of HCOOH, ClCH2COOH, and HF.

strong acids almost completely dissociate the amplitude of the long-time fluorescence tail of the three acids is nearly the same. Figure 6a shows the time-resolved emission of the ROH* form of 1N4S measured at 360 nm in four samples at different temperatures. In our previous study we used 1N4S, where we classified the acidity of weak and strong acids in ice.27 In the current study we again use 1N4S, this time to classify an additional acid, TFA, which has a moderate pKa value of 0.3. We compared the experimental results of 1N4S and the reversible photoacids 2N68DS and HPTS. In general, we find that for samples with a few mM of TFA, the proton concentration in water is very close to that of strong acids with negative values of pKa. Each panel in Figure 6a shows the ROH* decay of acid-free, 2 mM of HCl and TFA ice samples. The ROH*

fluorescence signals of 1N4S (an irreversible photoacid) are different from those of the reversible photoacids shown in Figure 3 for 2N68DS and Figure 5 for HPTS. The proton’s reaction with the RO-* of 1N4S to reform the protonated ROH mainly produces the ground state ROH(g). As a result, the excited state ROH* signals in Figure 6a are only slightly affected by the excess protons of the acidic samples. For the reversible photoacids 2N68DS and HPTS, the amplitude of the long-time fluorescence component of the ROH* strongly increases in strong acid ice samples. Figure 6b shows the time-resolved emission of the RO-* form of 1N4S measured at 450 nm of the samples shown in Figure 6a. The decay of the RO-* emission of 1N4S strongly depends on the proton concentration of the sample, especially in the ice

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Figure 5. Time-resolved emission of the ROH* form of HPTS in two strong acid samples at four temperatures in both liquid and ice phases. The strong HCl and HBr acid samples contained 2 mM of acid.

phase. An excess proton reacts with the RO-* to form the ground state ROH(g), thus decreasing the population of the RO-*, which leads to a large increase in the emission decay rate of the RO-*. The RO-* decay rate of reversible photoacids is independent of the excess proton concentration. The decay rate of the RO-* form of 1N4S in the 2 mM HCl is only slightly larger than that of TFA in the ice samples. The pKa values of the two acids in the liquid state differ by about 7 orders of magnitude. Equation 2 shows that when the samples are doped with only a few mM of the strong HCl acid, or with the moderately strong TFA acid, the proton concentration should be close to the acid concentration. A calculation we performed shows that when the TFA (pKa ≈ 0.3) concentration is 100 times larger, c > 100 mM, the proton concentration is lower than the acid concentration (see Figure s1 in the Supporting Information). Introducing large impurity concentrations around 100 mM into the ice samples probably modifies the pure ice’s qualities such as the dielectric constant, the dielectric relaxation time, τD, proton mobilities and Bjerum defects mobilities and concentrations. The small difference in the decay rates of HCl and TFA arises either from the difference in their pKa values or from the local environment (imperfections) in the ice structure next to the larger TFA molecule. As expected from our previous studies, the fluorescence decay rate of the acidic samples in liquid water is much smaller than in ice. Our explanation for this observation is that there is a large difference between the values of DH+ in liquid water and in ice, since DH+ in ice is 10 times larger than in the liquid state.

acidity of both weak and strong acids by measuring the timeresolved emission of the RO-* of 1N4S (an irreversible photoacid) reacting with the excess proton in both liquid water and ice to form the ground state ROH. The reaction with the proton quenches the fluorescence of the RO-* of 1N4S. The decay time of the time-resolved emission signal of the RO-* depends on the proton concentration. Thus, the proton fluorescence quenching rate is an excellent tool for determination of the proton concentration introduced in a sample that contains a known acid concentration. The main conclusion of our previous study was that the acidity scale of commonly used acids in aqueous solutions is also applicable for Ih ice. We found one exception to the general rule. HF, which is a weak acid in water, is stronger than other weak acids in ice. This finding is in accord with previous electrical conductance measurements in ice.4,28 As mentioned above, in the current study we used two reversible photoacids as a nanoprobe for proton concentration in ice, thus enabling the classification of an acid’s strength in ice. For the purpose of making such a classification we used several mineral and organic acids which are known to be weak, intermediate and strong in aqueous solutions. The fluorescence of the ROH* form of the reversible photoacids is sensitive to proton reactions, whereas the fluorescence of the deprotonated RO-* form is sensitive to the proton reaction in the case of irreversible photoacids such as 1N4S, which was used in the previous study. In the reversible case, the proton reacts with the RO-* to reform the ROH* in the excited state, RO-* +

Discussion

H+ {\} ROH*. The time-resolved emission signal of the

In the current study we want to confirm the results procured in our previous studies and to demonstrate the possible use of photoacids in determination of acidities of acids in ice and also excess proton concentrations over 10-4 M. In the current study we extended our previous results27 and qualitatively classify the acidity of strong acids and quantitatively classify the acidities of acids with pKice a > 2 in ice Ih using two reversible photoacids, 2N68DS and HPTS. In the previous study27 we monitored the

reversible photoacids in the ROH* form consists of two timeresolved contributions. The short-time component is mainly determined by the rate of proton transfer to the solvent, kPT, whereas the long-time fluorescence tail depends on all the parameters involved in the reversible scheme. For an acid-free sample the main parameters are ka, DH+, kPT, and the radiative lifetimes of both the ROH* and the RO-*. In an acid-doped sample the excess proton concentration released by the acid

kr

kPT

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Figure 6. Time-resolved emission of 1N4S in neutral pH, HCl, and TFA acid samples at four temperatures. (a) ROH* measured at 360 nm. (b) RO-* measured at 450 nm. Ka

dissociation, HA {\} A- + H+, plays a major role in the longtime fluorescence amplitude of the ROH* signal. The larger the proton concentration the larger the amplitude. In the Supporting Information we provide the computational model to analyze the time-resolved ROH* signals of reversible photoacids in the presence of excess protons in ice. In general, the findings of the current study, which were attained by using the reversible photoacids, are in very good agreement with the previous study, in which we employed irreversible photoacids. Strong acids in water are also strong in ice and similarly, weak acids in water are also weak in ice. Both the previous and the current studies provided almost the same information on many acids.

In this study we also added TFA to the list of acids. The pKa of this acid is the largest among organic acids with a value of ∼0.3 in water. We found that for a few mM of acid, the timeresolved emission signal of the ROH* is similar to the strong acids (pKa < -7 in water), leading to the conclusion that the degree of dissociation of a few mM of TFA in ice is more than 90%, thus making the proton concentration in ice similar to that produced by introduction of strong acids like HBr (pKa ) -9) and HCl (pKa ) -7). The Lowry-Brønstead definition of an acid suggests that a strong acid has a great tendency to transfer a proton to another molecule and that a strong base has a large affinity for protons. The quantitative measure of an acid’s strength is the acid

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dissociation constant, Ka, which is the equilibrium constant for the acid dissociation reaction in water

[H3O+][A-] Ka ) [HA]

(2)

Strong and Weak Acid Classification in Ice Ih. In the previous and in the current study we found that weak acids with a pKa in the range of 2.0-3.75 show that their degree of dissociation in ice samples with an acid concentration of a few mM is smaller than strong acids, i.e., pKa < 0. HCOOH (formic acid) with a pKa of ∼3.75 in water exhibits the smallest acid effect on the time-resolved emission of the RO-* form of 1N4S27 and of the ROH* of 2N68DS and HPTS in both liquid water and ice. In our current experiment we used several computational fitting parameters that were also used in our previous experiment.19,27 The Supporting Information describes the computational models, which are based on the mechanism illustrated in Scheme s1 enabling the semiquantitative fit of the experimental results shown in Figures 1-6. The kinetic models incorporate the acid effect and the proton diffusion’s contribution. Below we will shortly list our assumptions and values of the parameters that are relevant for our current experiment. For the reversible photoacids, 2N68DS and HPTS, the intrinsic rate constant for proton recombination, ka in eq s2, is replaced by Smoluchowski model’s time-dependent rate constant, k(t) (eq s8), enabling the incorporation of the diffusion process into the simple kinetic equations, which totally ignore the transport of reactants to form an encounter pair prior to the actual chemical reaction. The long-time asymptotic expression, k(∞), for the irreversible time-dependent rate constant, k(t), takes into account both the diffusion-controlled rate constant, kD, and the intrinsic rate constant, k(0) ) ka exp[-βU(a)], k(∞) ) [k(0)-1 + kD-1]-1 (eq s9). Here, β ) 1/kBT and U(a) is the Coulomb potential at the contact distance a. This approximation is valid only at long times. The long-time fluorescence tail of the ROH* of 2N68DS decays nearly exponentially, and has almost the same lifetime as that of the RO-*, τf′ ) 12.5 ns. The ROH* signal at the intermediate time range is strongly influenced by the proton geminate recombination, and as a consequence, the signal is nonexponential. At longer times the signal tends to decay exponentially. We monitor this long-time fluorescence tail for about 50 ns. From the time-resolved measurements of the ROH* of 2N68DS and HPTS in ice, the second-order, intrinsic, reversible recombination constant ka (eq s2) in ice at 260 K is about 7 × 1011 and 4 × 1011 M-1 s-1, respectively. The proton diffusion constant in ice, DH+, strongly depends on the methanol doping level: the smaller the methanol concentration the larger DH+. It more or less varies inversely with the methanol concentration. For the HPTS samples we used 0.2% mole ratio of methanol so that DH+ ) 5 × 10-4 cm2/s. A combination of the four negative charges on the RO-* of HPTS and a large dielectric constant (ε ) 100) results in a second order diffusioncontrolled rate which is also 4 × 1011 M-1 s-1. Thus, the overall rate constant, k(∞), is about half of both k(0) and kD. In all the various acid ice samples in this study a diffusion constant with a value of 10-3 cm2/s was used in the analysis of 2N68DS samples that contained 0.1% mole ratio of methanol. We used the proton concentration as the only adjustable parameter in the fitting of the time-resolved emission of the ROH* form of the two photoacids. The strong acids show that in acid-doped ice, with a proton concentration of 2 mM (i.e., cH+ ) cacid) and

Figure 7. Time-resolved emission of the ROH* form of 2N68DS in ice doped with 2 mM of weak acid at 258 K and a computer fit (solid line) to the kinetic model described in the Supporting Information.

with the above-mentioned value for the proton diffusion constant, the data fit is rather good in the temperature range of 247-263 K. Figure 7 shows the fit (solid line) of the experimental results of the ROH* time-resolved fluorescence of 2N68DS ice samples with 2 mM of several acids at 258 K by using the simple chemical kinetics model of AB a A + B using eqs s3-s6. The acids used are HCl, HF, ClCH2COOH, and HCOOH. The model nicely fits the short- and the long-time signal. The intermediate time depends strongly on the reversible proton geminate recombination process. The AB reversible kinetic dissociation model is inapplicable for the intermediate time region. The short time is mainly determined by the rate of the proton transfer from the photoacid to the ice. The transferred proton can recombine geminately with the RO-* to reform the ROH*. This process increases the ROH* population, and hence the ROH* luminescence is larger than expected. At a sufficiently long time, the reversible geminate recombination process is less efficient since the proton moves away as time progresses from the close vicinity of the photoacid to longer distances and escapes the large Coulomb potential, hence the probability to recombine decreases. The long-time fluorescence tail in an acidfree sample decreases as a power law of t-3/2. In samples containing acid, the excess protons in the sample compete with the geminate proton to recombine with the RO-*. At the intermediate time, the geminate proton is close to the photoacid, thus making the recombination probability larger for the geminate proton than for the excess proton, which has an average distance of about 100 Å at 1 mM of acid. At a long time, the situation changes and the recombination probability of an excess proton is comparable to or larger than that of the geminate proton. Furthermore, the AB model predicts that at long times there is an exponential decay of the fluorescence tail with a lifetime close to the excited-state lifetime of the RO*-. At temperatures higher than 263 K or lower than 247 K the diffusion constant decreases.19-21 As expected from eq 2, we found that for the three strong acids (HCl, HBr, and CF3SO3H), the acid and the proton concentrations are the same within an experimental error of (10%. For the weak acids, the actual proton concentration is smaller than the acid concentration. It is also significantly smaller than the calculated concentration according to their pKa value in water at room temperature. For the weakest acid used in this study, HCOOH (pKa ) 3.75 in

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water) we found from the fit of the experimental data (see figure ) 5.9. For 7) a rather large drop in the acidity: pKice a ClCH2COOH (pKa ) 2.9 in water) we calculate pKice a ) 4.6. These findings indicate that in general, the pKa values of acids in ice are significantly larger than in water. For HF (pKa ) 3.2 27 we in water) we find pKice a ) 3.4. In the previous study value of ∼3.6, which is in a good estimated for HF a pKice a agreement with the current study. The HCl-doped ice results show that k(∞) for 2N68DS is nearly independent of the temperature in the relatively narrow temperature range of 243-263 K and that at T ) 258 K it yields a maximum value of 3 × 1011 M-1 s-1.21 Furthermore, k(∞)(cH+/ cacid) is independent of the acid concentration in the range of 1.0-10 mM, which is an expected behavior from a strong acid. For the weak HCOOH acid-doped ice the situation is different: k(∞)(cH+/cacid) varies with the temperature. The dependence of the cH+/cacid ratio on the temperature shows that at low temperatures the degree of dissociation is smaller than at high temperatures. We attribute this finding to the large temperature dependence of Ka (the acid’s equilibrium constant). In general, the temperature dependence of a chemical equilibrium constant can be approximated by29

d(ln Keq) ∆H =d(1/T) R

(3)

where ∆H is the enthalpy of the chemical reaction. The temperature dependence of Ka in endothermic reactions (weak acids) is positive, and the equilibrium constant decreases as the temperature decreases. For strong acids the reaction is exothermic; consequently, Ka increases as the temperature decreases. In conclusion, weak acids (except HF) with pKa values of around 3 dissociate in ice, at low concentrations of roughly 1 mM with a smaller degree of dissociation than in water. The weak acid degree of dissociation is in the rang of 10-30%, while that of strong acids at 1 mM reaches >90%. The difference in the proton concentration in ice between HF and a strong acid, such as HCl, at a millimolar concentration range, is not measured in orders of magnitude but by a mere factor of 2. If the proton concentration is mainly responsible for the ice conductivity (at high acid doping levels), then conductivity measurements, similar to those preformed by Takei and Maeno30,31 in the 80s, with an acid doping level below 10-4 M will probably not show a large difference between the results of HCl and HF at temperatures above 235 K. Since we used a relatively high acid concentration range of 1-5 mM, as compared with the concentrations used in the conductivity measurements (c < 10-4 M), the historical debate regarding the preferential use of HF over strong acids, such as HCl or HBr, in ice might not be relevant since HF at these low concentrations is expected to fully dissociate. Minot and co-workers32 used quantum mechanical calculations to study HCl and HF interactions in ice. According to the results of their calculations two things happen: first, HCl inside the ice bulk structure is completely dissociated, and second, a hydrogen atom is transferred to a second water molecule, which results in a separate ion pair. On the other hand, HF does not seem to dissociate. Our results on acidity classification show that the HF dissociation equilibrium constant is Ka ≈ 10-3. This low value is enough for a millimolar concentration of HF to undergo 30% of dissociation in ice. Such a small Ka value might be out of Minot et al. calculation range. Experiments in “Buffered” Samples. Another test for the degree of acidity of an acid is the ability of a weak acid and its

conjugate base to form a buffer solution. The equilibriumconstant expression for the dissociation of weak acids suitable for buffers is often written in logarithmic form:

pH ) pKa + log

[conjugate base] [weak acid]

(4)

In the biological literature this is called the HendersonHasselbalch equation. When the acid concentration equals the conjugate base concentration [A-], then pH ) pKa. Thus, the pKa value of a weak acid in ice may simply be determined by using a buffer solution with equal concentrations of acid and its conjugate base salt. For HF, we use KF as the salt that provides the conjugate base, F-. Figure 8 shows on a semilogarithmic scale the time-resolved emission of the ROH* form of 2N68DS in solutions containing HF and KF, which is a salt composed of the acid’s conjugate base, F-, at several temperatures in liquid and in ice. There are four samples in each frame: neutral pH (without KF or HF), 2 mM HF, 2 mM KF, and a buffered sample that contains both 2 mM HF and 2 mM KF. The signal of the liquid samples at 291 K and at a short-time is almost insensitive to the relatively small HF and KF concentrations. In the solid state, the shortand the long-time components depend on both HF and KF. Figure 8 shows that in ice, the fastest decay rate of the shorttime component of the ROH* form is attributed to a sample that contains 2 mM of KF. We found a similar effect in previous studies on the photophysics and photochemistry of reversible photoacids in ice in the presence of KF. In an ice sample which contains F- ions, the ROH* decay rate of HPTS or 2N68DS19 is larger than for pure ice samples. Our explanation was that the immobile F- anion in ice is able to create mobile L-defects. L-defect mobility is known to be large.4 The mobile L-defect may react with an acidic group such as an excited ROH* and remove a proton: L- + ROH* f RO-* + LH. Thus, the reaction with an L-defect increases the decay rate of the ROH* form of the photoacid in ice. In the previous classification study27 we also observed the same effect on the ROH* of 1N4S. The amplitude of the long-time fluorescence tail of the buffered solution sharply decreases in comparison to the 2 mM HF ice sample. This nicely fits the concept of weak acids forming a buffered solution with a low and controlled proton concentration, and the use of the Henderson-Hasselbalch equation (eq 4) to determine the proton concentration. Figure 9 shows the time-resolved emission of the ROH* form of 2N68DS in the presence of 2 mM KCl, 2 mM HCl and a sample containing both 2 mM HCl and 2 mM KCl. In the liquid state, the long-time fluorescence tail’s amplitude of the acidic samples is moderate, whereas in the ice samples the amplitude is large because the proton diffusion constant in ice is 10 times larger than in liquid water. The addition of 2 mM of KCl, a salt with the weak conjugate base Cl-, only slightly decreases the large amplitude of the long time fluorescence tail ROH* in ice in the presence of a strong acid such as HCl. The relatively small decrease in the amplitude of the ROH* long-time fluorescence tail in the presence of both 2 mM HCl and 2 mM KCl is attributed to the kinetic salt effect and to a small reduction of DH+. The additional ions, introduced by adding KCl into the solution, form an ionic atmosphere surrounding the charged photoacid, which partially screens the Coulomb attraction between H+ and RO-*, ultimately reducing the effective proton recombination rate to reform the ROH*. Moreover, ions in liquid water (especially cations) tend to form a solvation shell. Consequently, the hexagonal ice structure that provides excess

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Figure 8. Time-resolved emission of the ROH* form of 2N68DS in an acid-free solution, in solutions containing 2 mM HF, 2 mM KF, and in a buffer solution containing both 2 mM HF and 2 mM KF.

Figure 9. Time-resolved emission of the ROH* form of 2N68DS in the presence of 2 mM KCl, 2 mM HCl and in a sample containing both 2 mM HCl and 2 mM KCl.

mobility to the proton is ruptured by ions and impurities, thus causing the proton diffusion constant to decrease. The important point to stress here is that the fluorescence decay curve of the ROH* in the presence of the strong acid, HCl, behaves differently than in the presence of a weak acid like HF. Adding a weak conjugate base (Cl-) to a strong acid (HCl) does not affect the proton concentration. The proton recombination is almost unaffected, hence the much smaller change in the amplitude of the long-time fluorescence tail in

the case of HCl. In contrast, in weak acid (HF) solutions, the addition of a relatively strong conjugate base (F-) strongly decreases the amplitude of the long-time fluorescence tail, which is an indication (as expected from a weak acid) of the reduction in the proton concentration (see Figure 8 and eq 4). At the beginning of the Discussion we stated that the pH of a weak acid in water can also be adjusted using an acidic solution treated with a salt containing the acid’s conjugate base, in our case HF and KF. Thus, the pH could be set at a fixed

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value and acidic or basic impurities in the solution could be neutralized within the so-called buffer capacity. According to eq 4, when [KF] ) [HF], the pH equals the pKa, and thus, the pKa of the acid in ice could be determined. The experimental results shown in Figure 8, in which 2 mM KF was added to 2 mM HF, allowed us to estimate the proton concentration from the large decrease in the amplitude of the ROH* long-time tail fluorescence of 2N68DS when compared to a neutral pH sample. We found that [H+] = 2.0 × 10-4 M, which corresponds to a pKa value of ∼3.5. This value is larger by 0.3 pKa units than the pKa value of HF in liquid water. Summary We studied the time-resolved emission of two reversible photoacids, 2N68DS and HPTS, in liquid water and in methanoldoped ice in the presence of small concentrations of strong and weak acids. We used a time-resolved emission technique to monitor the modification of the protonated ROH* fluorescence by excess protons in both liquid water and in ice. In the previous study27 we used the 1N4S irreversible photoacid to classify the acidity of weak and strong acids in ice. For irreversible photoacids the proton reaction with the RO-* reform the ground state ROH(g) and the observation of the reaction is carried out by monitoring the time-resolved emission of the RO-*. In general, we found that for reversible photoacids the rate of excess proton to reform the ROH* in ice depends both on the acid concentration and on the strength of the acid. In the milimolar concentrations employed in this study, the proton concentration released into the bulk ice by a weak acid with a pKa value of ∼3.5 or larger, is smaller by only about a factor of 10 than that of a strong acid. We found in the current and in previous27 studies that strong and weak acids in liquid water are also strong and weak acids in ice. In the current study we found that the pKa values of the weak HCOOH and ClCH2COOH acids in ice increase by about 2 pKa units from their liquid water values. HF (pKa ≈ 3.2 in water) is significantly stronger in ice than other weak acids with even smaller pKa values (stronger acids in liquid than HF). We used the chemical concept of pH control by preparing a buffer solution of the weak HF acid. We determined the pKa of HF in a buffered solution containing equal amounts of HF and KF. These findings provide further support for ice researchers, who maintain that enhanced electrical conductivity in ice is best achieved by doping it with HF. The experimental results show once again that the pKa value of HF in ice is roughly the same as in water. Acknowledgment. This work was supported by grants from the Israel Science Foundation and from the James-Franck German-Israelı¨ Program in Laser-Matter Interaction.

Uritski et al. Supporting Information Available: Reversible and irreversible excited-state proton transfer process computational models for the analysis of time-resolved emission data in the presence of excess protons in the sample. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fletcher N. H. The Physics and Chemistry of Ice; Cambridge University Press: London, 1970. (2) Hobbs. P. V. Ice Physics; Clarendon Press; Oxford, UK, 1974. (3) 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, UK, 1999. (5) Jaccard, C. Ann. N.Y. Acad. Sci. 1965, 125, 390. (6) Kobayashi, C.; Saito, S.; Ohmine, I. J. Chem. Phys. 2001, 115, 4742. (7) Bjerrum, N. Science 1952, 115, 385. (8) Podeszwa, R.; Buch, V. Phys. ReV. Lett. 1999, 83, 4570. (9) Ireland, J. E.; Wyatt, P. A. AdV. Phys. Org. Chem. 1976, 12, 131. (10) (a) Gutman, M.; Nachliel, E. Biochem. Biophys. Acta 1990, 391, 1015. (b) Pines, E.; Huppert, D. J. Phys. Chem. 1983, 87, 4471. (11) Tolbert, L. M.; Solntsev, K. M. Acc. Chem. Res. 2002, 35, 19. (12) (a) Rini, M.; Magnes, B. Z.; Pines, E.; Nibbering, E.T. J. Science 2003, 301, 349. (b) Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. J. Science 2005, 310, 5745. (13) Tran-Thi, T. H.; Gustavsson, T.; Prayer, C.; Pommeret, S.; Hynes, J. T. Chem. Phys. Lett. 2000, 329, 421. (14) Agmon, N. J. Phys. Chem. A 2005, 109, 13. (15) Spry, D. B.; Fayer, M. D. J. Chem. Phys. 2008, 128, 084508. (16) Siwick, B. J.; Cox, M. J.; Bakker, H. J. J. Phys. Chem B 2008, 112, 378. (17) Buch, V.; Milet, A.; Va´cha, R.; Jungwirth, P.; Devlin, P. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 7342. (18) Mondal, S. K.; Sahu, K.; Sen, P.; Roy, D.; Ghosh, S.; Bhattacharyya, K. Chem. Phys. Lett. 2005, 412, 228. (19) Uritski, A.; Presiado, I.; Huppert, D. J. Phys. Chem. C 2008, 112, 11991. (20) Uritski, A.; Persiado, I.; Huppert, D. J. Phys. Chem. C 2008, 112, 18189. (21) Uritski, A.; Persiado, I.; Huppert, D. J.Phys. Chem. A 2009, 113, 959. (22) Pang, X. F.; Feng, Y. P. Chem. Phys. Lett. 2003, 373, 392. (23) Nagle, J. F. J. Phys. Chem. 1983, 87, 4086. (24) Hubmann, M. Z. Physik B 1979, 32, 127. (25) Steinemann, A. HelV. Phys. Acta 1957, 30, 581. (26) von Hippel, A.; Mykolajewycz, R.; Runck, A. H.; Westphal, W. B. J. Chem. Phys. 1972, 57, 2560. (27) Uritski, A.; Presiado, I.; Gepshtein, R.; Erez, Y.; Huppert, D. J. Phys. Chem. C 2009, 113, 7342. (28) Camplin, G. C.; Glen, J. W. Physics and Chemistry of Ice, 5th ed.; Walley, E., Jones, S. J., Gold, L. W., Eds.; Royal Society of Canada: Ottawa, 1973; p 256. (29) Atkins P. W. Physical Chemistry 5th ed.; Oxford University Press: Oxford, UK, 1994. (30) Takei, I.; Maeno, N. J. Phys. Chem. 1984, 81, 6186. (31) Takei, I.; Maeno, N. J. Phys. (Paris) 198748, 121 (Colloque C1). (32) Calatayud, M.; Courmier, D.; Minot, C. Chem. Phys. Lett. 2003, 369, 287.

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