Liquid Structure of Acetic AcidâWater and Trifluoroacetic AcidâWater

9270

J. Phys. Chem. B 2007, 111, 9270-9280

Liquid Structure of Acetic Acid-Water and Trifluoroacetic Acid-Water Mixtures Studied by Large-Angle X-ray Scattering and NMR Toshiyuki Takamuku,*,† Yasuhiro Kyoshoin,† Hiroshi Noguchi,† Shoji Kusano,† and Toshio Yamaguchi‡ Department of Chemistry and Applied Chemistry, Faculty of Science and Engineering, Saga UniVersity, Honjo-machi, Saga 840-8502, Japan, and AdVanced Materials Institute and Department of Chemistry, Faculty of Science, Fukuoka UniVersity, Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan ReceiVed: March 30, 2007; In Final Form: May 24, 2007

The structures of acetic acid (AA), trifluoroacetic acid (TFA), and their aqueous mixtures over the entire range of acid mole fraction xA have been investigated by using large-angle X-ray scattering (LAXS) and NMR techniques. The results from the LAXS experiments have shown that acetic acid molecules mainly form a chain structure via hydrogen bonding in the pure liquid. In acetic acid-water mixtures hydrogen bonds of acetic acid-water and water-water gradually increase with decreasing xA, while the chain structure of acetic acid molecules is moderately ruptured. Hydrogen bonds among water molecules are remarkably formed in acetic acid-water mixtures at xA e ∼0.4, and water clusters eventually predominate in the mixtures at xA e ∼0.18. The LAXS results have revealed that TFA molecules form not a chain structure but cyclic dimers through hydrogen bonding in the pure liquid. In TFA-water mixtures O‚‚‚O hydrogen bonds among water molecules gradually increase when xA decreases, and hydrogen bonds among water molecules are significantly formed in the mixtures at xA e ∼0.6. It has also been shown that TFA molecules are considerably dissociated to hydrogen ions and trifluoroacetate in the mixtures. 1H, 13C, and 19F NMR chemical shifts of acetic acid and TFA molecules for acetic acid-water and TFA-water mixtures have indicated strong relationships between a structural change of the mixtures and the acid mole fraction. On the basis of both LAXS and NMR results, the structural changes of acetic acid-water and TFA-water mixtures with decreasing acid mole fraction and the effects of fluorination of the methyl group on the structure are discussed at the molecular level.

Introduction Acetic acid is a simple organic acid and an important substance in biochemistry, such as the TCA cycle and metabolism of ethanol with two dehydrogenases. The physicochemical properties of acetic acid have been measured, and their relation to the intermolecular hydrogen-bonded structure has been discussed so far. It is well-known that the relative dielectric constant (6.15) of acetic acid is much lower than that of ethanol (24.3) despite their similar dipole moments (ca. 5.6 × 10-30 Cm). This has often been understood by the formation of cyclic dimers of acetic acid molecules via hydrogen bonding. However, the recent investigation of acetic acid by using both lowfrequency Raman spectroscopy and ab initio calculation1 has suggested that acetic acid molecules form a chain structure by intermolecular hydrogen bonds between the hydroxyl hydrogen atom and the carbonyl oxygen one. The structure of acetic acid in the solid state has been clarified by an X-ray diffraction technique;2 acetic acid molecules form chain structures by hydrogen bonds but do not form cyclic dimers. In the solid state, a weak hydrogen bond C-H‚‚‚OdC between the methyl and carbonyl groups of two acetic acid molecules may stabilize the chain structure. A neutron diffraction experiment on a single crystal of acetic acid has also shown infinite chain structure in * Author to whom all correspondence should be addressed. E-mail: [email protected]. † Saga University. ‡ Fukuoka University.

the solid state.3 Recently, it has thus been understood that the cyclic dimer of acetic acid molecules predominates only in the gas phase. On the other hand, TFA is a much stronger acid than acetic acid due to the high electronegativity of the trifluoromethyl fluorine atoms. TFA has frequently been utilized as a cosolvent for aqueous eluents in a gradient extraction of peptides and proteins by using high performance liquid chromatography. It has been considered that distribution of peptides and proteins between TFA and aqueous eluent phases is a key to the extraction mechanism. A single-crystal X-ray diffraction experiment on TFA has shown that TFA molecules form cyclic dimers via hydrogen bonding.4 There have been a few reports on the structure of liquid acetic acid and acetic acid-water mixtures by using LAXS5,6 and large-angle neutron scattering (LANS)7 techniques. Before the Raman investigation,1 the previous LANS study on liquid acetic acid7 excluded chain structures formed by hydrogen bonding from the fitting analysis on the total radial distribution function by using two models, the chain structure in the crystal2 and a hypothetical structure of a cyclic dimer. The hydration structure of acetate in aqueous sodium acetate solutions has been observed by using LANS with 12C/13C and H/D isotopic substitution.8 This has shown that the carboxylate group is hydrated by 4.0 ( 0.1 of water molecules with the C‚‚‚D distance 2.63 ( 0.01 Å between the carboxylate carbon and water hydrogen atoms. Low-frequency Raman spectroscopic measurements have been

10.1021/jp0724976 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/12/2007

Acetic Acid-Water and Trifluoroacetic Acid-Water made on acetic acid-water mixtures, and the results have revealed the presence of three microscopic phases, acetic acid clusters, water clusters, and acetic acid-water binary ones, in the mixtures.9,10 Molecular dynamics (MD) and Monte Carlo (MC) simulations have been made on pure acetic acid11,12 and acetic acid-water mixtures.13 On one hand, these results suggested that acetic acid molecules prefer a chain structure via hydrogen bonding in the liquid11 and aqueous mixtures,13 as shown by the Raman experiments.1 On the other hand, the liquid structures of TFA and TFA-water mixtures have not yet been clarified at the molecular level by LAXS, LANS, and other spectroscopic techniques. In the present study, LAXS measurements have been made at 298 K on acetic acid, TFA, and their aqueous mixtures over the entire range of acid mole fraction to clarify the structures of both liquids and their aqueous mixtures over the r-range from 0 to ∼6 Å. Moreover, 1H, 13C, and 19F NMR chemical shifts of acetic acid and TFA molecules in their aqueous mixtures have been measured at 298 K as a function of acid mole fraction. In the NMR experiments, an external double reference method has been applied to correct the diamagnetic effect of a sample mixture on a standard substance.14-16 The acid mole fraction dependence of 1H, 13C, and 19F NMR chemical shifts of acetic acid and TFA molecules gives us information on a change in electron distribution within an acid molecule in the mixtures with acid mole fraction, which will strongly reflect the structural change of the mixtures. On the basis of both LAXS and NMR results, plausible structure models of clusters formed in acetic acid-water and TFA-water mixtures are proposed. In addition, effects of fluorination of the methyl group on the structure of the mixtures are discussed at the molecular level. Experimental Section Sample Solutions. Acetic acid (Wako Pure Chemicals, grade for precision analysis) and TFA (Tokyo Chemical Industry, extra grade) were used without further purification. Doubly distilled water was used for all experiments. Sample solutions of acetic acid-water and TFA-water mixtures were prepared by weighing acid and water to the required acid mole fractions. LAXS Measurements. LAXS measurements were made at 298 K on pure acetic acid and acetic acid-water mixtures at acetic acid mole fractions xAA ) 0.05, 0.1, 0.18, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 and on pure TFA and TFA-water mixtures at TFA mole fractions xTFA ) 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9. A rapid liquid X-ray diffractometer (BRUKER AXS, model DIP301) with an imaging plate (IP) (Fuji Film Co.) as a two-dimensional detector was used in the present LAXS experiments. Details of the X-ray diffractometer have been described elsewhere.17,18 Densities for the sample solutions were measured at 298 K by using a densimeter (ANTON Paar K.G., DMA60 and DMA602). X-rays were generated at a rotary Mo anode (Rigaku, RU-300) operated at 50 kV and 200 mA, and then monochromatized by a flat graphite crystal to obtain Mo KR radiation (the wavelength λ ) 0.7107 Å). The sample solutions of acetic acid and TFA systems were sealed into a soda glass capillary (W. Mu¨ller Co.) of 2 mm inner diameter (wall thickness 0.01 mm) with epoxy and vinyl chlorideurethane glues, respectively. X-ray scattering intensities for a sample solution sealed in a capillary were accumulated on the IP for 1 h. The observed range of the scattering angle (2θ) was 0.2-109°, corresponding to the scattering vector s ()4πλ-1 sin θ) of 0.03-14.4 Å-1. X-ray intensities for an empty capillary were also measured as background. Two-dimensional X-ray data, Iobsd(x,y), where x and y are horizontal and vertical coordinates, measured on the IP were

J. Phys. Chem. B, Vol. 111, No. 31, 2007 9271 integrated into one-dimensional data, Iobsd(θ), after correction for polarization as previously reported.17 The observed intensities for the samples and empty capillary were also corrected for absorption.18 The contribution of the sample solution alone was obtained by subtracting the intensity for the empty capillary from that for the sample. The corrected intensities were normalized to absolute units by conventional methods.19-21 The structure function, i(s), was calculated by using eq 1 in ref 22. In the data treatment the stoichiometric volume V was chosen to contain one O atom from acetic acid or TFA and water in the systems. The structure function was Fourier transformed into the radial distribution function, D(r), in the usual manner.22 To perform a quantitative analysis of the X-ray data, a comparison between the experimental structure function and the theoretical one, which was calculated on a structure model with eq 5 in ref 22, was made by a least-squares refinement procedure by using eq 4 in ref 22. The present X-ray diffraction data were treated by programs KURVLR23 and NLPLSQ.24 1H, 13C, and 19F NMR Measurements. 1H and 13C NMR spectra of acetic acid-water and TFA-water mixtures were measured at 298 K over the entire xA range on an FT-NMR spectrometer (JEOL, JNM-AL300). Moreover, 19F NMR measurements for TFA-water mixtures were made by using the same spectrometer. The sample solution was kept in a 5-mm sample tube (Shigemi, PS-001). An external double reference tube (Shigemi), whose dimension is a capillary of 1.5 mm outer diameter with a blown-out sphere of 3 mm at the bottom, was placed at the center of the 5-mm sample tube containing a sample solution. Hexamethyldisiloxane (HMDS) (Wako Pure Chemicals, the first grade) was sealed into the external double reference tube as a reference substance for 1H and 13C NMR measurements, while trifluoromethlybenzene (Tokyo Chemical Industry, extra grade) was utilized for 19F NMR measurements. The observed chemical shifts for acetic acid and TFA molecules in the mixtures were corrected for the volume magnetic susceptibility of the sample solutions by an external double reference method as follows.14-16 Two peaks assigned to the reference substance at the sphere and capillary parts of the reference tube, respectively, are observed in an NMR spectrum. The difference in the chemical shift between the two peaks, ∆δref, in the units of ppm is related to volume magnetic susceptibilities (χs and χr, respectively) of a sample solution and the reference substance through

∆δref ) κ(χs - χr) × 106

(1)

where κ is the shape factor for the reference tube. Before measurements on a sample solution the κ value was determined by the ∆δref measured for five deuterated liquids, CDCl3, (CD3)2SO, C6D12, C6D6, and (CD3)2CO, at 298 K, whose χ’s are available in the literature.14 The corrected chemical shift of a sample solution, δcorr, referred to the reference substance in the capillary is given by

δcorr ) δobs - (4π/3)(χs - χr) × 106 ) δobs - (4π/3κ)∆δref (2) where δobs represents the observed chemical shifts and 4π/3 is the shape factor for the capillary part of the reference tube. Consequently, the diamagnetic effect of a sample solution on the reference substance can be corrected for the observed chemical shift through eq 2. In the present NMR experiments, the sample temperature was controlled at 298.2 ( 0.1 K by a mixture of hot air and dry

9272 J. Phys. Chem. B, Vol. 111, No. 31, 2007

Figure 1. Structure functions i(s) weighted by s for acetic acid, water,25 and acetic acid-water mixtures at various xAA. Dotted lines represent experimental values, and solid lines are theoretical ones.

Figure 2. RDFs in the D(r) - 4πr2F0 form for acetic acid, water,25 acetic acid-water mixtures at various xAA. Dotted lines represent experimental values, and solid lines are theoretical ones.

nitrogen stream generated from liquid nitrogen. The digital resolutions of the chemical shifts for 1H, 13C, and 19F NMR measurements were (0.0012, (0.017, and (0.0013 ppm, respectively. Results and Discussion LAXS for Acetic Acid-water Mixtures. Figure 1 shows the structure function i(s) weighted by s for pure acetic acid and the acetic acid-water mixtures at various mole fractions of acetic acid xAA. For comparison, that for pure water (xAA ) 0) measured in the previous investigation25 is also depicted in the figure. The corresponding radial distribution functions (RDFs) in the form of D(r)-4πr2F0 are shown in Figure 2. In the RDF for pure acetic acid (xAA ) 1), two sharp peaks at 1.3 and 2.4 Å are ascribed to intramolecular interactions within an acetic acid molecule, such as C1-C2 and C1-O bonds and nonbonding C2‚‚‚O and O1‚‚‚O2, respectively (the notation of atoms is depicted in Figure 3). A tail of the 2.4 Å peak at the long-range side arises from an O‚‚‚O hydrogen bond between acetic acid molecules. Three large peaks centered at 3.5, 5.0, and 8.5 Å are attributed to intermolecular interactions between acetic acid molecules. To elucidate the liquid structure of acetic acid, a peak fit by using plausible structure models was made on the observed RDF for acetic acid in the range of 0 e r/Å e 6. In the fit, structure parameters of intramolecular interactions for an acetic acid molecule were used by slightly modifying the crystal structure of acetic acid.2 Four structure models for intermolecular interactions, a hydrogen-bonded cyclic dimer, a hydrogen-bonded chain observed in the solid state, a dipoledipole interaction, and a side-on dimer by bifurcated hydrogen

Takamuku et al. bonds, were examined to explain the RDF for acetic acid. However, each model alone could not reproduce the interactions in the RDF; in particular, the models of the hydrogen-bonded cyclic dimer, the dipole-dipole interaction, and the side-on dimer could not explain the large peaks at 3.5 and 5.0 Å because they contribute mainly to the short-range of r e 3.2 Å. On the other hand, the hydrogen-bonded chain could explain the interactions in the range of 3 e r/Å e 6 because the interatomic distances in the chain fall into this range. Nevertheless, the 3.5 Å peak could still not be reproduced by the model of the hydrogen-bonded chain. Thus, the dipole-dipole interactions between acetic acid molecules were adopted as other contributions to explain the 3.5 Å peak. The combination of the two models gave a good reproducibility for the interactions at r e ∼5 Å. Furthermore, the longer-range interactions at 4.5 e r/Å e 6 could be explained by assuming interactions between two chains layered with the distance of ∼4.2 Å. Thus, the present analysis suggests that a chain structure of acetic acid by hydrogen bonds is mainly formed in pure acetic acid, accompanied by that from the dipole-dipole interaction. Here, it should be emphasized that cyclic dimers by hydrogen bonds are scarcely formed in the liquid. The important interatomic distances obtained from the present analysis are shown in Figure 3. A large peak centered at 8.5 Å can be assigned to longerrange interactions, such as the fourth neighbor interactions in the chain structure of acetic acid, which were not analyzed in the present study. A least-squares refinement procedure was applied to the structure function for acetic acid in the s-range from 0.1 to 14.4 Å-1 by using the structure model consisting of the chain structure and the dipole-dipole interaction moiety of acetic acid molecules built in the model fit. The structure parameters of intramolecular interactions within an acetic acid molecule listed in Table 1 were fixed during the least-squares refinement. The important intermolecular interactions optimized are summarized in Table 2. All the structure parameters obtained are listed in Table S2 in the Supporting Information. As seen in Figures 1 and 2, the theoretical si(s) and RDF calculated by using the structure parameters in Tables 1 and S2 well reproduce the observed ones, except for the longer-range interactions at s e ∼1.6 Å-1 and r g 6 Å, respectively, which were not taken into account due to complexity; instead, continuum electron distributions were assumed in the longer range. Table 2 shows that the distance of the O‚‚‚O hydrogen bond between acetic acid molecules is estimated to be 2.656 ( 0.004 Å. This is comparable with those determined from the previous LAXS5 and LANS7 investigations (2.626 and 2.70 Å, respectively). However, the distance of O‚‚‚O hydrogen bond between acetic acid molecules is much shorter than those for other protic solvents, such as water (2.826 ( 0.002 Å) and methanol (2.771 ( 0.004 Å),25 due probably to the acidity of the hydroxyl group of the acetic acid molecule. As shown in Table 2, the number (0.85 ( 0.01) of an O‚‚‚O hydrogen bond estimated for one oxygen atom within an acetic acid is smaller than unity which is expected from formation of a cyclic dimer or an infinite chain of all acetic acid molecules. It is suggested that hydrogen bonds of many cyclic dimers would be broken even if dimers were formed in the liquid. Therefore, the chain structure of acetic acid by hydrogen bonding is mainly formed in pure acetic acid; the hydroxyl and carbonyl groups of an acetic acid molecule play roles as proton donor and acceptor, respectively, to other molecules in the chain structure. Moreover, acetic acid molecules released from the chain structure may form the dipoledipole interaction between them in the liquid.

Acetic Acid-Water and Trifluoroacetic Acid-Water

J. Phys. Chem. B, Vol. 111, No. 31, 2007 9273

Figure 3. Structure models of chain structure by hydrogen bonds, dipole-dipole interaction, and side-on dimer of acetic acid molecules. The dotted lines represent hydrogen bonds.

TABLE 1: Intramolecular Interactions for Acetic Acid and Water Moleculesa 103b

n

C1-C2 C1-O1 C1-O2 O2-H C2-H C2‚‚·O1 C2‚‚·O2 C1‚‚·H O1‚‚·O2

Acetic Acid 1.480 1.210 1.310 1.000 1.260 2.380 2.340 2.190 2.210

1 1 1 2 1 2 2 10 2

1 1 1 1 3 1 1 3 1

O-H H‚‚·H

Waterb 0.970 1.555

2 10

2 1

r

b

a The distance r (Å), temperature factor b(Å2), and number n. Reference 29.

In the RDFs of the acetic acid-water mixtures in the mole fraction range of 0.3 e xAA e 0.9 (Figure 2), the features observed for pure acetic acid remain, although the intensities of the interactions gradually decrease with decreasing xAA. However, a valley at 2.8 Å observed in the RDF for the pure liquid acetic acid becomes shallower when the mole fraction decreases, and a new peak at 2.8 Å appears in the RDF at xAA ) 0.4. The 2.8 Å peak is assigned mainly to O‚‚‚O hydrogen bonds among water molecules as observed in other aqueous mixtures.22,25,26 Furthermore, O‚‚‚O hydrogen bonds between acetic acid and water molecules may also contribute to the peak at 2.8 Å, although the hydrogen bonds might appear at the shorter distance of 2.65 Å because of the acidity of the hydroxyl group of the acetic acid molecule, as the hydrogen bonds between acetic acid molecules in the liquid. As shown in Figure 4 a, the fact that the O‚‚‚O hydrogen bonds at 2.65 Å disappear in the RDFs for the mixtures at xAA e 0.1 despite 10 mol % of acetic acid remaining in the mixtures indicates the validity of the assignment for the 2.8 Å peak. Thus, the 2.8 Å peak suggests an increase in O‚‚‚O hydrogen bonds of acetic acid-water and water-water in the mixtures with decreasing xAA. In the range of xAA e 0.18, the 2.8 Å peak of O‚‚‚O hydrogen bonds is significantly grown with decreasing xAA, whereas the interactions observed for pure acetic acid gradually disappear. The RDFs for the mixtures at xAA ) 0.05 and 0.1 bear resemblance to that for pure water (xAA ) 0), i.e., three peaks at 2.8, 4.5, and 7 Å for the first, second, third neighbor interactions of the tetrahedral-

like structure of water25,27,28 are observed in the RDFs. Thus, the change in the RDFs for the acetic acid-water mixture with decreasing xAA indicates that the chain structure of acetic acid is gradually ruptured in the mixtures when the mole fraction decreases from xAA ) 0.9 to 0.4 and that water clusters dominate in the mixtures at xAA e 0.18. It is probable that both chain structures of acetic acid and water clusters coexist in the mixtures in the range of 0.18 < xAA < 0.4. To clarify the structural change of the acetic acid-water mixtures, first, a model fit was made on the RDFs for the mixtures by using the structure parameters of the chain structure and the dipole-dipole interaction of acetic acid molecules obtained above and a hydrogen bond between acetic acid and water molecules, accompanied by those of the tetrahedral-like structure of water with nonbonding interstitial molecules of water determined in the previous investigation.25 The model parameters of a linear hydrogen bond between acetic acid and water molecules, such as C1‚‚‚O, were built by setting the distance between the carboxyl oxygen and water oxygen atoms at ∼2.8 Å. Moreover, addition of the interactions in the sideon dimer of acetic acid by bifurcated hydrogen bonds (Figure 3) could give better reproduction of the RDFs for the mixtures in the range of 0.18 e xAA e 0.6. The bifurcated hydrogen bonds between acetic acid and water molecules were also taken into account to explain the RDFs in the water-rich mixtures at xAA ) 0.05 and 0.1. The intramolecular interactions within an acetic acid used in the analysis for the pure liquid and those within a water molecule determined from the previous LANS experiment29 were adopted in the fits on the RDFs for the mixtures. The intramolecular interactions for both molecules are listed in Table 1. The RDFs for the mixtures could be explained by slight modifications for the structure parameters of the models, depending on the composition of the mixtures. Finally, a leastsquares refinement was made on the structure functions of the mixtures in the range of 0.1 e s/Å-1 e 14.4 to optimize the structure parameters. The structure parameters for the intramolecular interactions of acetic acid and water molecules were not allowed to vary during the least-squares refinement fit. The important optimized structure parameters for the acetic acidwater mixtures are summarized in Table 2, together with those for pure water determined in the previous investigation.25 All the optimized structure parameters for the mixtures are listed in Table 2S in the Supporting Information. Figures 1 and 2 show good reproduction for the observed si(s) and RDFs by the

χAA interactions

parameter

0b

2.829(1) 17 3.41(3)

0.10

0.70

0.80

0.90

Linear Hydrogen Bonds of Water-Water and Acetic Acid-Water 2.822(2) 2.822(2) 2.824(3) 2.834(5) 2.843(8) 2.837(12) 17 17 17 17 17 17 3.06(3) 2.41(3) 1.58(3) 1.07(3) 0.77(4) 0.52(4)

0.18

0.30

0.40

0.50

0.60

1

2.849(19) 17 0.33(4)

2.861(23) 17 0.30(4)

2.866(29) 17 0.24(4)

Linear Hydrogen Bonds of Acetic Acid-Acetic Acid 2.635(0) 2.634(6) 2.654(5) 2.658(5) 10 10 10 10 0.20(1) 0.38(1) 0.50(1) 0.60(1)

2.658(4) 10 0.71(1)

2.655(4) 10 0.77(1)

2.659(4) 10 0.80(1)

2.656(4) 10 0.85(1)

O‚‚·O

r 103b n

O2‚‚·O1

r 103b n

O2‚‚·O1,2

r 103b n

O‚‚·O

r 103b n

O1‚‚·O1′

r 103b n r 103b n

First Neighbor Interactions in Chain Structure of Acetic Acid Molecules 3.53 3.55 3.55 3.55 3.55 10 10 10 10 10 0.30 0.40 0.50 0.60 0.70 5.54 5.54 5.54 5.54 5.54 20 20 20 20 20 0.30 0.40 0.50 0.60 0.70

3.55 10 0.75 5.54 20 0.75

3.55 10 0.85 5.54 20 0.85

3.55 10 0.85 5.54 20 0.85

3.55 10 0.90 5.54 20 0.90

O2‚‚·O1′′

r 103b n

Second Neighbor Interaction in Chain Structure of Acetic Acid Molecules 5.85 5.85 5.85 5.85 5.85 20 20 20 20 20 0.15 0.20 0.25 0.30 0.35

5.85 20 0.38

5.85 20 0.43

5.85 20 0.43

5.85 20 0.45

C1‚‚·C1

r 103b n

3.24 20 0.50

3.24 20 0.50

3.24 20 0.50

3.24 20 0.50

C1‚‚·O2

r 103b n

C2‚‚·C2′

2.826(2) 17 3.43(3)

0.05

3.075 20 0.36 3.35 15 1.00

3.35 15 1.00

3.24 20 0.10

2.659(4) 10 0.67(1)

Bifurcated Hydrogen Bonds for Side-On Dimer of Acetic Acid Molecules and Acetic Acid-Water 3.035(34) 3.003(15) 3.002(9) 2.999(15) 3.002(16) 3.020(41) 20 20 20 20 20 20 0.84 1.11 1.41(8) 0.71(7) 0.61(6) 0.22(6) 3.35 15 0.90

3.24 20 0.25

3.35 15 0.80


TABLE 2: Important Optimized Parameter Values of the Interactions in Water, Acetic Acid, and Their Mixtures Obtained by Least-Squares Fitsa

Interstitial Water Molecules 3.35 3.35 3.35 15 15 15 0.30 0.20 0.20

Dipole-Dipole Interaction between Acetic Acid Molecules 3.24 3.24 3.24 3.24 3.24 20 20 20 20 20 0.50 0.50 0.50 0.50 0.50 Interaction in Side-On Dimer Interactions of Acetic Acid Molecules 3.35 3.35 3.35 3.35 3.35 20 20 20 20 20 0.25 0.50 0.30 0.20 0.10

Takamuku et al.

a The interatomic distance r (Å), the temperature factor b (Å2), the number of interactions n. The values in parentheses are standard deviations of the last figure. The parameters without standard deviations were not allowed to vary in the calculations. b Reference 25.


Figure 4. Coordination numbers per oxygen atom for (a) acetic acidwater and (b) TFA-water mixtures as a function of acid mole fraction. Filled circles give the numbers for interaction between acid molecules, and open circles represent the sum of those of acid-water and waterwater. The standard deviations σ are indicated as error bars.

theoretical ones calculated by using the structure parameters in Tables 1 and 2S, except for the long-range interactions at s e ∼2 Å-1 and r g ∼5.5-6 Å not considered in the present analysis. As shown in Table 2, three types of O‚‚‚O hydrogen bonds formed in the acetic acid-water mixtures. Hydrogen bonds between acetic acid molecules in the chain structure, linear hydrogen bonds of acetic acid-water and water-water, and bifurcated hydrogen bonds of acetic acid-acetic acid and acetic acid-water could be individually estimated from the RDFs because the respective peaks at 2.6, 2.8, and 3.0 Å of O‚‚‚O hydrogen bonds were distinguishable in the RDFs. The distances of O‚‚‚O hydrogen bonds of acetic acid-water and water-water in the mixtures are estimated in the range from 2.822 ( 0.002 to 2.866 ( 0.029 Å, not depending on the mole fraction. However, their numbers gradually increase with decreasing xAA (increasing water content) due mainly to enhancement of hydrogen bonds among water molecules in the mixtures. On the other hand, the distances of O‚‚‚O hydrogen bonds between acetic acid molecules fall into the range from 2.634 ( 0.006 to 2.659 ( 0.004 Å. Their numbers gradually decrease when the xAA decreases, showing that the chain structure of acetic acid molecules by hydrogen bonding is disrupted in the mixtures with decreasing xAA. The distance of bifurcated O‚‚‚O hydrogen bonds is estimated to be ∼3.00 Å. The numbers of bifurcated O‚‚‚O hydrogen bonds suggest that the side-on dimers of acetic acid-acetic acid and acetic acid-water are formed in the mixtures in the range of 0.05 e xAA e 0.6 with a maximum at xAA ) 0.3. In Figure 4a, the number of O‚‚‚O hydrogen bonds for acetic acid-acetic acid in the chain structure and the sum of those for acetic acid-water and water-water are depicted as a function of xAA. The number (filled circles) of O‚‚‚O hydrogen bonds between acetic acid molecules in the chain structure gradually decreases with decreasing xAA, whereas that (open circles) for acetic acid-water and water-water increases. In the range of 0.5 < xAA < 1, the former is larger than the latter, suggesting that the chain structure of acetic acid predominates in the mixtures. In the range of 0.18 e xAA e 0.4, the latter remarkably increases when the xAA decreases, but the former shows that the chain structure of acetic acid molecules remains. Thus, the chain structure of acetic acid molecules and water clusters coexists in the mixtures in this range. However, the predominant structure of the mixtures changes from the chain structure of acetic acid to water clusters at xAA ≈ 0.4. At xAA < 0.18, the number of O‚‚‚O hydrogen bonds for acetic acid-


Figure 5. Structure functions i(s) weighted by s for TFA, water,25 and TFA-water mixtures at various xTFA. Dotted lines represent experimental value, and solid lines are theoretical ones.

Figure 6. RDFs in the D(r) - 4πr2F0 form for TFA, water,25 TFAwater mixtures at various xTFA. Dotted lines represent experimental values, and solid lines are theoretical ones.

water and water-water is close to that for bulk water. Hence, the water structure is predominantly formed in the mixtures. In the water-rich range of xAA < 0.18, acetic acid molecules may be hydrated in the water structure. LAXS for TFA-Water Mixtures. Figures 5 and 6 show the structure function i(s) weighted by s for pure TFA and TFA-water mixtures at various TFA mole fractions xTFA and the corresponding RDFs in the form of D(r) - 4πr2F0, respectively. In addition, those for pure water are depicted in each figure, for comparison.25 In the RDF for pure TFA (xTFA ) 1), two dominant peaks at 1.4 and 2.3 Å are assigned to C1-O, C1-C2, and C2-F bonds and nonbonding interactions, such as C2‚‚‚O, C1‚‚‚F, and F‚‚‚F, within a TFA molecule, respectively (Figure 7 shows the notation of atoms). A small hump at 2.8 Å arises from O‚‚‚O hydrogen bonds between TFA molecules. A broad and large peak centered at 5.5 Å is attributed to intermolecular interactions between TFA molecules. However, intermolecular interactions in the longer-range above ∼7 Å are not significantly observed in the RDF for TFA, whereas those centered at 8.5 Å arising from the fourth-neighbor interactions in the chain structure appear in the RDF for acetic acid (Figure 2). To clarify the structure of pure TFA, a model fit based on the crystal structure of TFA4 was performed on the RDF for TFA in the range of 0 e r/Å e 6.5. The structure parameters of intramolecular interactions within a TFA molecule were obtained by modifying those determined from single-crystal X-ray diffraction experiment4 and listed in Table 3. The structure parameters for the cyclic dimer of TFA molecules determined by the crystal-


Takamuku et al.

Figure 7. Structure model of cyclic TFA dimers by hydrogen bonds. The dotted lines represent hydrogen bonds.

TABLE 3: Intramolecular Interactions for TFA Moleculea trifluoroacetic acid

r

103b

n

trifluoroacetic acid

r

103b

n

C1-C2 C1-O1 C1-O2 O2-H C2-F1 C2-F2 C2-F3 C2‚‚·O1 C2‚‚·O2 O1‚‚·O2 C1‚‚·F1

1.526 1.213 1.303 0.900 1.340 1.324 1.331 2.381 2.342 2.263 2.361

2 3 3 2 2 2 2 10 10 5 10

1 1 1 1 1 1 1 1 1 1 1

C1‚‚·F2 C1‚‚·F3 O1‚‚·F1 O1‚‚·F2 O1‚‚·F3 O2‚‚·F1 O2‚‚·F2 O2‚‚·F3 F1‚‚·F2 F1‚‚·F3 F2‚‚·F3

2.371 2.327 2.674 3.424 3.064 3.445 2.596 2.982 2.150 2.166 2.159

10 5 10 10 10 10 10 10 5 5 5

1 1 1 1 1 1 1 1 1 1 1

a

The distance r(Å), temperature factor b(Å2), and number n.

lographic experiment4 were employed as a structure model of intermolecular interactions. Moreover, the structure between two cyclic dimers in the unit cell of the crystal, where the dimers are close to each other with a tilt angle ∼90°, was considered as a model of the long-range interactions. In Figure 7, the structure model of the cyclic dimer of TFA molecules is exhibited with the important interatomic distances. An open structure of a TFA dimer, where only one hydrogen bond is formed between two molecules, was also adopted as a structure model due to the weak hydrogen bond between the hydroxyl hydrogen and the carbonyl oxygen atoms as described below. These structure parameters could well explain the observed RDF for TFA in the range of 0 e r/Å e 6.5. In addition, a continuum electron distribution was assumed for the individual atoms instead of the longer-range interactions at r > 6.5 Å. A leastsquares refinement procedure was made on the structure function for TFA in the range of 0.1 e s/Å-1 e 13.4 by using the structure parameters modeled. The important optimized structure parameters are summarized in Table 4, and all the structure parameters obtained for TFA were listed in Table 4S in the Supporting Information. The theoretical si(s) and RDF calculated by using the structure parameters in Tables 3 and 4S well reproduce the observed ones as shown in Figures 5 and 6, although the long-range interactions at s e ∼2 Å-1 and r g ∼6.5 Å were not taken into account in the present analysis. Thus, the present results suggest that TFA molecules form cyclic and open dimers via hydrogen bonding in the liquid, whereas the hydrogen-bonded chain structure of acetic acid molecules predominates in pure acetic acid. The steric hindrance of the larger trifluoromethyl group of TFA molecule may be one of the reasons for the different structure between TFA and acetic acid. Table 4 shows that the distance of O‚‚‚O hydrogen bonds between TFA molecules is estimated to be 2.817 ( 0.009 Å. This distance for the TFA dimer is much longer than that (2.656

( 0.004 Å) for the hydrogen-bonded chain of acetic acid molecules because the hydrogen-bond acceptability of the carbonyl oxygen atom in a TFA molecule is much lower than that in an acetic acid molecule due to the electron withdrawing of the three fluorine atoms. The number (0.61 ( 0.03) of O‚‚ ‚O hydrogen bonds between TFA molecules is smaller than that (0.85 ( 0.01) between acetic acid molecules in the chain. It is suggested that ∼15% of TFA molecules do not form hydrogen bonds with any other molecule. This is also due to the lower hydrogen-bond acceptability of a TFA molecule compared to that of an acetic acid one. In Figure 6, the RDFs for the TFA-water mixtures in the wide range of 0.2 e xTFA e 0.9 are comparable with that for pure TFA, although the amplitude of the peaks is gradually weakened when the xTFA decreases. Hence, TFA dimers are formed in the mixtures in this mole fraction range. However, the 2.8 Å peak for O‚‚‚O hydrogen bonds in the RDFs is gradually strengthened when the xTFA decreases from xTFA ) 0.4. At xTFA ) 0.1, the large peak at 5.5 Å assigned mainly to interactions in the cyclic dimer becomes very weak. Finally, the RDF for the mixture at xTFA ) 0.05 has a feature similar to that for pure water (xTFA ) 0), revealing that the tetrahedrallike structure of water by hydrogen bonding is dominantly formed in the mixture. In the RDFs for the acetic acid-water mixtures, the 2.65 Å peak for O‚‚‚O hydrogen bonds of acetic acid-acetic acid is distinguishable from the peaks of acetic acid-water and waterwater hydrogen bonds. However, one peak at 2.8 Å related to O‚‚‚O hydrogen bonds is observed in the RDFs for the TFAwater mixtures over the entire mole fraction range. Thus, the 2.8 Å peak in the RDFs for the mixtures arises from all the O‚‚‚O hydrogen bonds of TFA-TFA, TFA-water, and waterwater. The O‚‚‚O hydrogen bond longer for TFA-TFA than for acetic acid-acetic acid despite the stronger acidity of TFA may be ascribed to the lower hydrogen-bond acceptability of the carbonyl oxygen atom of the TFA molecule due to the electron withdrawing of the trifluoromethyl group as mentioned above. A quantitative analysis was made on the RDFs for the TFAwater mixtures to clarify the structural change of the mixtures with TFA mole fraction. The structure parameters of the intramolecular interactions for water and TFA molecules were fixed to those in Tables 1 and 3, respectively. The RDFs for the mixtures in the range of 0 e r/Å e 6.5 were fitted by using a structure model consisting of both cyclic and open TFA dimers, hydrogen-bonded structures between TFA and water molecules, and the hydrogen-bonded water structure, together with a nonbonding interstitial water molecule.25 The structure parameters of a hydrogen bond between TFA and water molecules are the same as those between a TFA molecule and an oxygen atom of other molecules in the dimer structure. Figure 8 shows an example of the model fit on the RDF for the TFA-water mixtures at xTFA ) 0.2. The dotted and solid lines represent respectively the observed RDF and the theoretical one calculated by using the structure parameters of the intramolecular interactions and the above model (Table 4). The chain line gives the residual curve obtained by subtracting the theoretical values from the observed ones. As seen, two peaks at 2.4 and 3.2 Å remain in the residual curve, meaning that other interactions should contribute to the observed RDFs for the mixture. The new interactions may arise from the hydration structure of oxonium ion and trifluoroacetate because TFA is a strong acid, whereas such interactions are hardly observed in the RDF for the aqueous mixtures of weak acetic acid.

χTFA interaction

parameter

0

b

0.05

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1

2.820(4) 6 1.29(3)

2.820(5) 5 1.07(3)

2.808(6) 5 0.90(3)

2.817(9) 5 0.61(3)

3.222(8) 10 2.89(10)

3.223(9) 10 2.42(10)

3.237(12) 10 1.71(10)

3.241(23) 10 1.00(10)

2.512(18) 20 0.95(6)

2.482(22) 20 0.76(6)

2.496(30) 20 0.55(6)

2.414(84) 20 0.18(7)

r 103b n

2.826(2) 17 3.43(3)

2.828(1) 16 3.35(3)

O‚‚·O

r 103b n

3.35 15 1.00

3.35 15 0.90

3.35 15 0.80

3.35 15 0.60

C‚‚·O

r 103b n

3.195(20) 10 3.85(36)

3.196(13) 10 3.85(23)

Hydration for Trifluoroacetate CF3COO3.190(8) 3.192(7) 3.197(6) 3.221(7) 10 10 10 10 3.95(16) 3.85(13) 3.84(12) 3.28(11)

O‚‚·O

r 103b n

2.461(15) 10 2.90(17)

2.524(13) 15 2.67(12)

2.507(10) 20 2.57(9)

C1‚‚·O

r 103b n

3.53 10 1.00

3.53 10 0.90

3.53 10 0.70

Interactions of TFA-TFA and TFA-Water 3.53 3.53 3.53 10 10 10 0.50 0.50 0.50

3.53 10 0.45

3.53 10 0.45

3.53 10 0.40

3.53 10 0.40

3.53 10 0.35

C1‚‚·C1′

r 103b n r 103b n r 103b n

3.88 20 0.15 6.02 35 0.15 6.94 35 0.15

3.88 20 0.20 6.02 35 0.20 6.94 35 0.20

Interactions in TFA Dimer 3.88 3.88 3.88 20 20 20 0.25 0.25 0.25 6.02 6.02 6.02 35 35 35 0.25 0.25 0.25 6.94 6.94 6.94 35 35 35 0.25 0.25 0.25

3.88 20 0.28 6.02 35 0.28 6.94 35 0.28

3.88 20 0.28 6.02 35 0.28 6.94 35 0.28

3.88 20 0.30 6.02 35 0.30 6.94 35 0.30

3.88 20 0.30 6.02 35 0.30 6.94 35 0.30

3.88 20 0.35 6.02 35 0.35 6.94 35 0.35

r 103b n r 103b n

4.18 20 0.15 3.34 10 0.15

4.18 20 0.20 3.34 10 0.20

Interactions between TFA Dimers 4.18 4.18 4.18 20 20 20 0.23 0.23 0.25 3.34 3.34 3.34 10 10 10 0.23 0.23 0.25

4.18 20 0.25 3.34 10 0.25

4.18 20 0.28 3.34 10 0.28

4.18 20 0.28 3.34 10 0.28

4.18 20 0.30 3.34 10 0.30

4.18 20 0.35 3.34 10 0.35

C1‚‚·F1′ C2‚‚·C2′

C1‚‚·C1′′ O1‚‚·F1′′

Interstitial Water Molecules 3.35 3.35 3.35 15 15 15 0.60 0.30 0.20

Hydration for Oxonium Ion H3O+ 2.523(11) 2.529(11) 2.528(16) 20 20 20 2.09(7) 1.87(7) 1.20(6)

a The interatomic distance r(Å), the temperature factor b(Å2), the number of interactions n. The values in parentheses are standard deviations of the last figure. The parameters without standard deviations were not allowed to vary in the calculations. b Reference 25.


O‚‚·O

Linear Hydrogen Bonds of Water-Water, TFA-Water, and TFA-TFA 2.829(2) 2.829(2) 2.825(3) 2.824(3) 2.831(4) 2.829(4) 15 11 8 8 8 6 3.08(3) 2.54(3) 1.98(3) 1.74(3) 1.62(4) 1.44(3)


TABLE 4: Important Optimized Parameter Values of the Interactions in Water, Trifluoroacetic Acid and Their Mixtures Obtained by Least-Squares Fitsa


Takamuku et al.

Figure 8. Result of a model fit on the RDF for TFA-water mixture at xTFA ) 0.2. Dotted line represents experimental values, solid line theoretical ones, and dashed line residual ones.

According to the previous LAXS and LANS investigations on hydrochloric acid30 and aqueous sodium acetate solutions,8 respectively, the 2.4 Å peak is assigned to three shorter O‚‚‚O hydrogen bonds in the distorted tetrahedral structure of hydrated oxonium ion, and the 3.2 Å peak is attributed to the C‚‚‚O interaction between the carboxyl carbon and water oxygen atoms in the hydrated structure of the carboxyl group. Finally, the observed RDFs for the TFA-water mixtures could be explained by the addition of the hydration structure of oxonium ion and trifluoroacetate to the above model, depending on the TFA mole fraction. A least-squares refinement procedure was made on the structure functions for the mixtures in the range of 0.1 e s/Å-1 e 13.4 by employing the structure parameters of these models, together with continuum electron distributions. In Table 4, the important optimized structure parameters for the TFA-water mixtures are summarized. All the structure parameters for the mixtures are available in Table 4S in the Supporting Information. Figures 5 and 6 indicate the good reproducibility of the theoretical si(s) and RDF calculated by using the structure parameters summarized in Tables 1, 3, and 4S for the observed ones. Table 4 shows that the distances of O‚‚‚O hydrogen bonds for the TFA-water mixtures do not drastically change beyond the uncertainties with decreasing TFA mole fraction. On the other hand, the numbers of O‚‚‚O hydrogen bonds for the mixtures gradually increase when the TFA mole fraction decreases, suggesting that hydrogen bonds among water molecules are evolved in the mixtures. For comparison with the acetic acid-water mixtures, the total numbers of O‚‚‚O hydrogen bonds determined directly from the RDFs were separated into those for TFA-TFA and the sum of those for TFA-water and water-water by subtracting the numbers of C1‚‚‚C1′ and C1‚‚‚O interactions in respective cyclic and open TFA dimers regarded as those for TFA-TFA hydrogen bonds from the total numbers. Figure 4b shows the mole fraction dependence of the number of O‚‚‚O hydrogen bonds for TFATFA and the sum of those for TFA-water and water-water. The numbers of O‚‚‚O hydrogen bonds for TFA-TFA moderately decrease with decreasing xTFA in the range of xTFA > 0.3 and significantly decrease below xTFA ) 0.3. On the other hand, the sum of the numbers of O‚‚‚O hydrogen bonds for TFA-water and water-water gradually increases with decreasing xTFA from 0.9 to 0.3. Hence, the sum becomes larger than the numbers of O‚‚‚O hydrogen bonds for TFA-TFA in the range of xTFA e 0.6, suggesting that hydrogen bonds among water molecules are evolved in the mixtures in this range. When the mole fraction further decreases from 0.3, the sum of the numbers of O‚‚‚O hydrogen bonds for TFA-water and waterwater sharply increase and approach the number for bulk water. These changes in the numbers of the O‚‚‚O hydrogen bonds for the mixtures indicate that in the range of xTFA > 0.6 TFA

Figure 9. Degrees of dissociation for TFA molecules in TFA-water mixtures as a function of xTFA. Filled circles give those estimated from hydration structure of oxonium ion and open circles those estimated from hydration structure of trifluoroacetate. The standard deviations σ are indicated as error bars.

dimers are mainly formed in the mixtures, in the range of 0.3 e xTFA e 0.6 both TFA dimers and water clusters coexist in the mixtures, and in the range of xTFA < 0.3 water clusters markedly evolve as the predominant structure in the mixtures. In the structural change of the TFA-water mixtures with decreasing xTFA, a strong acid of TFA molecule dissociates to hydrogen ion and trifluoroacetate as mentioned above. The degrees of dissociation for TFA molecules in the TFA-water mixtures were estimated from the concentration of oxonium ion and trifluoroacetate determined from the 2.4 and 3.2 Å peaks, respectively, in the residual curve of the RDFs for the mixtures. In Figure 9, the degrees of dissociation for TFA molecules are plotted as a function of xTFA. Both plots show that TFA molecules gradually dissociate in the TFA-water mixtures with increasing water content (decreasing xTFA). In particular, those for TFA molecules significantly increase at xTFA ) 0.4 and reach a plateau at ∼100% in the range of xTFA e 0.2-0.3. The difference between the values estimated from the 2.4 and 3.2 Å peaks beyond the statistical errors may be caused by the difficulty of peak separation for the interactions of the hydration structure of oxonium ion and trifluoroacetate from the other interactions in the RDFs. Moreover, the degrees of dissociation estimated from the RDFs at xTFA ) 0.2 and 0.3 are larger by a factor of ∼3 than that determined by Raman peaks of the TFA molecule31 due to the uncertainties of the coordination numbers estimated for oxonium ion and trifluoroacetate. Nevertheless, both plots give the same results that dissociation of TFA molecules significantly occurs in the TFA-water mixtures at xTFA < ∼0.4. The dissociation of TFA molecules may be one of the reasons why TFA molecules scarcely form a chain structure by hydrogen bonding, together with the steric hindrance between the trifluoromethyl groups. NMR Chemical Shifts. Figure 10 a and b show 1H, 19F, and 13C NMR chemical shifts for the methyl and trifluoromethyl groups of acetic acid and TFA molecules in the acetic acidwater and TFA-water mixtures as a function of acid mole fraction xA. The 1H and 19F NMR chemical shifts for the methyl and trifluoromethyl groups moderately increase (change toward a low field) when the xA decreases to ∼0.3 and then drastically increase with the further decrease in xA, resulting in an inflection point at xA ≈ 0.3 in both plots. The 13C NMR chemical shifts for the trifluoromethyl group of a TFA molecule change with decreasing xA in a similar manner to the 19F NMR chemical shifts; an inflection point at xA ≈ 0.3 appears. Those for the methyl group of an acetic acid molecule also change to a low



Figure 10. Acid mole fraction xA dependence of (a) 1H, 19F, and (b) 13 C NMR chemical shifts, which were corrected for magnetic susceptibilities of sample solutions, for the methyl and trifluoromethyl groups of acetic acid and TFA molecules. HMDS was used as a reference for 1 H and 13C NMR, and trifluoromethlybenzene was adopted for 19F NMR. The standard deviations σ are indicated as error bars.

Figure 11. Acid mole fraction xA dependence of 13C NMR chemical shifts, which were corrected for magnetic susceptibilities of sample solutions, for the carboxyl group of acetic acid (filled circles) and TFA (open circles) molecules. HMDS was used as a reference. The standard deviations σ are indicated as error bars.

field with decreasing xA, but an inflection at xA ≈ 0.3 is not significant. The inflection points at xA ≈ 0.3 observed in the NMR data coincide with that for the numbers of O‚‚‚O hydrogen bonds obtained by the LAXS experiments; water clusters are markedly formed in both acetic acid-water and TFA-water mixtures at xA ≈ 0.3, whereas the inherent structures of acetic acid and TFA are considerably disrupted in the mixtures. In the range of xA e ∼0.3, thus, acetic acid and TFA molecules may be accommodated to water clusters by hydrogen bonds between acid and water molecules in both mixtures. The lowerfield shifts of the 1H, 19F, and 13C NMR data for the methyl and trifluoromethyl groups are ascribed to the decrease in the electron density of the groups, i.e., the significant shifts at xA < ∼0.3 are caused by electrons on the methyl and trifluoromethyl groups being markedly drawn to the carboxyl group due to hydrogen bonding between acid and water molecules in water clusters. The difference in the 13C NMR chemical shifts between acetic acid and TFA molecules may be attributed to the higher intrinsic electron density of the trifluoromethyl group than that of the methyl one because of the high electronegativity of the fluorine atoms. In addition, most of TFA molecules release hydrogen ions in the mixtures at xA e ∼0.3 as shown in the degrees of dissociation for TFA molecules; thus, the electrons are strongly drawn to the carboxylate group. These are probably the reasons why the 13C NMR chemical shifts for the trifluoromethyl group of the TFA molecule more markedly increase than those for the methyl group of the acetic acid molecule. Figure 11 shows the 13C NMR chemical shifts for the carboxyl group of acetic acid and TFA molecules as a function of xA. As seen in the figure, both values decrease (change toward a high field) with decreasing xA from 1 to ∼0.4 and then increase (toward a low field again) with further decreasing xA. Thus, a minimum of the 13C NMR chemical shifts for the carboxyl group of acetic acid and TFA molecules is found at xA ≈ 0.4. The change in the 13C NMR chemical shifts can be explained as follows. The high-field shift with decreasing xA from 1 to ∼0.4 originates from hydrogen bonds between acid and water molecules. As discussed above, the electrons of the methyl and trifluoromethyl groups partly move to the carboxyl group by hydrogen bonding with water molecules, leading to the higher electron density on the carboxyl carbon atoms. With further decreasing xA from ∼0.4 the dissociation of TFA molecules considerably takes place in the mixtures, as shown in Figure 9. Hence, the electron density for the carbon atoms of carboxylate decreases because a negative charge may be spread on the

resonance structure of the carboxylate. Consequently, the 13C NMR chemical shifts for the carboxyl group of TFA molecules in the TFA-water mixtures sharply increase again when the xA decreases from ∼0.4. The 13C NMR chemical shifts for the carboxyl group of acetic acid molecules in the mixtures also increase again with decreasing xA, but less significantly than those for TFA molecules due to the less dissociation of weak acetic acid. Structure of Acetic Acid-Water and TFA-Water Mixtures. On the basis of all the present results, structural changes of the acetic acid-water and TFA-water mixtures with decreasing acid mole fraction can be concluded as follows. In the pure liquid, acetic acid molecules mainly form the chain structure by hydrogen bonds, where the hydroxyl and carbonyl groups of a molecule play roles as proton donor and acceptor to other molecules, respectively. This liquid structure is comparable with the structure of the solid state. Additionally, an acetic acid molecule may interact with another by dipoledipole interaction in the liquid, but scarcely forms a cyclic dimer as observed in the gas phase. In both chain and dipole-dipole structures, the dipole moments of molecules are arranged to an antiparallel direction among them, which may yield the low relative dielectric constant. As shown in the numbers of O‚‚‚O hydrogen bonds as a function of xAA, when the water content increases, water molecules are hydrogen-bonded with acetic acid molecules and among them. In fact, the low-field shift of the 1H and 13C NMR data for the methyl group of acetic acid reveals the moderate increase in hydrogen bonds between acetic acid and water molecules with increasing water content to xAA ≈ 0.3. On the other hand, the chain structure of acetic acid molecules is gradually disrupted in the mixtures with decreasing xAA. The mole fraction dependence of the numbers of O‚‚‚O hydrogen bonds shows that water clusters significantly increase in the mixtures at xAA ≈ 0.4 and eventually predominate in the range of xAA < ∼0.18. This is clearly reflected in the 1H NMR chemical shifts of the methyl group of acetic acid; i.e. the values sharply change toward the low field with decreasing xAA from ∼0.3 because acetic acid molecules are hydrated in the evolved water clusters. In the pure liquid, TFA molecules mainly form cyclic and open dimers by hydrogen bonding, but hardly form a long-chain structure as observed in acetic acid. This may be caused by steric hindrance of the trifluoromethyl group of the TFA molecule that is larger than the methyl group of acetic acid one. In addition, the low hydrogen-bond acceptability of the carbonyl oxygen atom of the TFA molecule due to the electron-

9280 J. Phys. Chem. B, Vol. 111, No. 31, 2007 withdrawing of the trifluoromethyl fluorine atoms is disadvantageous for formation of a hydrogen-bonded chain despite the high hydrogen-bond donicity of the hydroxyl hydrogen atom due to the same. With decreasing xTFA, hydrogen bonds among water molecules significantly increase in the TFA-water mixtures in the range of xTFA e ∼0.6. Water clusters are remarkably formed in the mixtures in the range of xTFA < ∼0.3, while TFA dimers are significantly ruptured with decreasing xTFA. It is likely that TFA molecules dissociated from the dimers may be embedded into water clusters in the mixtures. The 19F and 13C NMR data of the trifluoromethyl group of TFA molecule are consistent with the structural changes of the TFAwater mixtures with decreasing xTFA. Thus, the formation of hydrogen bonds between TFA and water molecules in the TFAwater mixtures leads to the electron-withdrawing from the trifluoromethyl group to the carboxyl one. Actually, the 19F and 13C NMR chemical shifts of the trifluoromethyl group change toward the low field, in particular, sharply increasing at xTFA e ∼0.3 because water clusters are significantly evolved in the mixtures. In the range of ∼0.4 e xTFA e 1, the high-field shift of the 13C NMR data for the carboxyl group of TFA molecule with decreasing xTFA demonstrates the electrons withdrawing to the carboxyl group by hydrogen bonding between TFA and water molecules. Although TFA molecules are hydrogen-bonded with water molecules in the TFA-water mixtures in the range of xTFA e ∼0.4, the 13C NMR chemical shifts for the carboxyl group of the TFA molecules increase again with decreasing xTFA in this range. This arises mainly from dissociation of TFA molecules in the water-rich mixtures at xTFA e ∼0.4. In fact, the present LAXS results show the formation of hydrated oxonium ion and trifluoroacetate in the mixtures. For the acetic acid-water mixtures, the 13C NMR chemical shifts for the carboxyl group of acetic acid molecules change with decreasing xAA in a similar way to the TFA-water mixture changes. However, the increase in the values for acetic acid molecules with decreasing xAA is less significant than for TFA molecules because of less dissociation of acetic acid. The remarkable dissociation of TFA molecules in the mixtures may influence the numbers of O‚‚‚O hydrogen bonds estimated from the RDFs for the TFA-water mixtures by the following. One can predict that the larger hydrophobic trifluoromethyl group of the TFA molecule more easily disrupts the tetrahedrallike structure of water in the mixtures at lower acid mole fractions than the smaller methyl group, as shown in a comparison between mixtures of ethanol-water32,33 and trifluoroethanol-water.34 In Figure 4, however, the decreases in the numbers of O‚‚‚O hydrogen bonds for both mixtures with increasing xA are comparable to each other, suggesting that disruption of the water structure in the TFA-water mixtures occurs similarly to that in the acetic acid-water ones. This may be caused by both oxonium ion and trifluoroacetate formed in the TFA-water mixtures; i.e. water molecules may easily form hydrogen bonds around both ions in the mixtures. It is thus likely that the hydrogen bonds among water molecules around the hydration structure of the ions compensate for the disruption of the water structure by the large trifluoromethyl group. Indeed, the numbers of O‚‚‚O hydrogen bonds estimated from the RDFs for the TFA-water mixtures involve the longer hydrogen bond of a water molecule in the hydration shell of oxonium ion due to the distance of 2.90 Å.30 This may be the reason for the moderate decrease in the numbers of O‚‚‚O hydrogen bonds for the mixtures with increasing TFA content.

Takamuku et al. Acknowledgment. This work was supported partly by Grants-in-Aid (No. 15550016 and 19550022 (T.T.) and 15076211 (T.Y.)) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The density measurements and NMR experiments for the sample solutions were carried out at Analytical Research Center for Experimental Sciences of Saga University. Supporting Information Available: All the optimized structure parameters obtained from the present LAXS experiments (Tables S2 and S4). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Nakabayashi, T.; Kosugi, K.; Nishi, N. J. Phys. Chem. A 1999, 103, 8595. (2) Nahringbauer, I. Acta Chem. Scand. 1970, 24, 453. (3) Jonsson, P. G. Acta Crystallogr., Sect. B 1971, 27, 893. (4) Nahringbauer, I.; Lundgren, J.-O.; Andersen, E. K. Acta Crystallogr., Sect. B 1979, 35, 508. (5) Gorbunova, T. V.; Shilov, V. V.; Batalin, G. I. Zh. Strukt. Khim. 1973, 14, 424. (6) Gorbunova, T. V.; Zakharova, I. K.; Batalin, G. I. Zh. Fiz. Khim. 1981, 55, 2969. (7) Bertagnolli, H. Chem. Phys. Lett. 1982, 93, 287. (8) Kameda, Y.; Sasaki, M.; Yaegashi, M.; Tsuji, K.; Oomori, S.; Hino, S.; Usuki, T. J. Solution Chem. 2004, 33, 733. (9) Kosugi, K.; Nakabayashi, T.; Nishi, N. Chem. Phys. Lett. 1998, 291, 253. (10) Nishi, N.; Nakabayashi, T.; Kosugi, K. J. Phys. Chem. A 1999, 103, 10851. (11) Briggs, J. M.; Nguyen, T. B.; Jorgensen, W. L. J. Phys. Chem. 1991, 95, 3315. (12) Chen, B.; Siepmann, J. I. J. Phys. Chem. B 2000, 104, 8725. (13) Chocholousˇova´, J.; Vacek, J.; Hobza, P. J. Phys. Chem. A 2003, 107, 3086. (14) Mizuno, K.; Tamiya, Y.; Mekata, M. Pure Appl. Chem. 2004, 76, 105. (15) Momoki, K.; Fukazawa, Y. Anal. Chem. 1990, 62, 1665. (16) Momoki, K.; Fukazawa, Y. Anal. Sci. 1994, 10, 53. (17) Yamanaka, K.; Yamaguchi, T.; Wakita, H. J. Chem. Phys. 1994, 101, 9830. (18) Ihara, M.; Yamaguchi, T.; Wakita, H.; Matsumoto, T. AdV. X-Ray Anal. Jpn. 1994, 25, 49; Yamaguchi, T.; Wakita, H.; Yamanaka, K. Fukuoka UniV. Sci. Rep. 1999, 29, 127. (19) Furukawa, K. Rep. Progr. Phys. 1962, 25, 395. (20) Krogh-Moe, J. Acta Crystallogr. 1956, 2, 951. (21) Norman, N. Acta Crystallogr. 1957, 10, 370. (22) Takamuku, T.; Tabata, M.; Yamaguchi, A.; Nishimoto, J.; Kumamoto, M.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998, 102, 8880. (23) Johanson, G.; Sandstro¨m, M. Chem. Scr. 1973, 4, 195. (24) Yamaguchi, T. Doctoral Thesis, Tokyo Institute of Technology, Tokyo, Japan, 1978. (25) Takamuku, T.; Yamaguchi, T.; Asato, M.; Matsumoto, M.; Nishi, N. Z. Naturforsch. 2000, 55a, 513. (26) Matsugami, M.; Takamuku, T.; Otomo, T.; Yamaguchi, T. J. Phys. Chem. B 2006, 110, 12372. (27) Narten, A. H.; Levy, H. A. J. Chem. Phys. 1971, 55, 2263. (28) Narten, A. H. J. Chem. Phys. 1972, 56, 5681. (29) Ichikawa, K.; Kameda, Y.; Yamaguchi, T.; Wakita, H.; Misawa, M. Mol. Phys. 1991, 73, 79. (30) Lee, H.-G.; Matsumoto, Y.; Yamaguchi, T.; Ohtaki, H. Bull. Chem. Soc. Jpn. 1983, 56, 443. (31) Strehlow, H.; Hildebrandt, P. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 173. (32) Matsumoto, M.; Nishi, N.; Furusawa, T.; Saita, M.; Takamuku, T.; Yamagami, M.; Yamaguchi, T. Bull. Chem. Soc. Jpn. 1995, 68, 1775. (33) Nishi, N.; Matsumoto, M.; Takahashi, S.; Takamuku, T.; Yamagami, M.; Yamaguchi, T. In Structures and Dynamics of Clusters; Kondow, T., Kaya, K., Terasaki, A., Eds.; Universal Academy Press, Inc. and Yamada Science Foundation: 1996; pp 113-120; Matsumoto, M. Masters Thesis, Kyushu University, 1996. (34) Takamuku, T.; Kumai, T.; Yoshida, K.; Yamaguchi, T.; Otomo, T. J. Phys. Chem. A 2005, 109, 7667.

Liquid Structure of Acetic AcidâWater and Trifluoroacetic AcidâWater

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