Inhomogeneity of Mixing in Acetonitrile Aqueous Solution Studied by

Small-angle X-ray scattering study on the fluctuations of supercritical aqueous solution of n-pentane along the critical isotherm of water. Takeshi Mo...
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J. Phys. Chem. B 2002, 106, 693-700

693

Inhomogeneity of Mixing in Acetonitrile Aqueous Solution Studied by Small-Angle X-ray Scattering Keiko Nishikawa,* Yasutoshi Kasahara, and Takehiko Ichioka DiVision of DiVersity Science, Graduated School of Science and Technology, Chiba UniVersity, Yayoi, Inage-ku, Chiba 263-8522, Japan ReceiVed: May 22, 2001

Acetonitrile aqueous solution has an upper critical solution temperature (UCST) at 272 K at c ) 0.38 (c represents the mole fraction of acetonitrile). To study quantitatively how the mixing scheme of the solution changes as a function of concentration and temperature, the concentration fluctuation, the Kirkwood-Buff parameters, and individual density fluctuations for acetonitrile and water were obtained by means of smallangle X-ray scattering experiments at 273, 279, and 298 K in the range of 0.0 e c e 0.5. The values of concentration fluctuation became larger close to UCST and exhibit a maximum at c ) 0.38. The mixing scheme of acetonitrile aqueous solution is discussed from the point of view of inhomogeneity of molecular distribution.

Introduction Acetonitrile aqueous solution at various concentrations is widely used in chemical fields such as solvent extraction and organic synthesis.1 The variety in use will originate from the wide change in properties of the solution with changes of concentration and temperature, as well as from the unique properties of acetonitrile itself. Amitage et al. reported that acetonitrile aqueous solution exhibits an upper critical solution temperature (UCST) at 272 K at c ) 0.38 (c represents the mole fraction of acetonitrile).2 It is expected that the microscopic and mesoscopic mixing scheme of the solution changes drastically, dependent on concentration and temperature, especially in the neighborhood of the critical point. A large number of physicochemical measurements for the solution have been carried out; for example, dynamical properties from NMR measurement,3 MD simulation,4,5 and IR absorption spectroscopy by Jomorz et al.6 and by Bertie et al.7 They reported that acetonitrile molecules act as a preferential solvent because a nitrogen in an acetonitrile molecule interacts strongly with the hydrogen in a water molecule through hydrogen bonding. The diffraction studies on pure acetonitrile pointed out that acetonitrile molecules are weakly associated through dipole-dipole interaction.8-11 By a recent X-ray diffraction study combined with IR measurements on pure acetonitrile and the aqueous solution,12 it is pointed out that acetonitrile molecules form zigzag clusters by dipole-dipole interaction, and that, on addition of water, water molecules interact with acetonitrile molecules through dipole-dipole interaction in an antiparallel orientation.12 From mass spectroscopic experiments,13-15 Nishi et al. reported that H+(CH3CN)m(H2O)n species exist in the ionized clusters which are prepared by adiabatic expansion of the aqueous solution. From the macroscopic viewpoint, various thermodynamic studies 2,16-21 pointed out unusual features of acetonitrile aqueous solution * Author to whom correspondence should be addressed. E-mail: [email protected].

and most of them claimed that acetonitrile molecules act as a structure breaker for water. Though many studies on acetonitrile aqueous solution have been performed as mentioned above, there are few reports on temperature dependence of the mixing scheme. Blandamer et al. reported temperature dependence on the fluctuation in the solutions,2,16 which were not so quantitative. Except for Nishi’s reports13-15 and a small-angle neutron scattering (SANS) study by Takamuku et al.,22 many studies focused on one or a few molecules at the most in acetonitrile aqueous solutions, or, on the other hand, discussed macroscopic behaviors of water or acetonitrile molecules. The inhomogeneity of mixing in the solution will grow up with approaching to UCST and then the solution separates into two phases. To investigate the change of the mixing scheme of the solution with a critical point, it is necessary to discuss comprehensively the mixing scheme of the solution from microscopic, mesoscopic, and macroscopic viewpoints. One of the present authors (K.N.) has shown that the information from small-angle X-ray scattering (SAXS) is mesoscopic in size, and that the concentration fluctuation obtained by the SAXS method is a quantitative description of the mixing scheme, and then applied the method to some alcohol aqueous solutions.23-26 In the present report, we apply the method to acetonitrile aqueous solution systems, and study (1) how the mixing state of this solution changes with the change of concentration and temperature, and (2) how the phase separation occurs in the solution. We measured SAXS intensities of the solutions at 273, 279, and 298 K in the range of 0.0 e c e 0.5. Concentration and density fluctuations and cross term of these fluctuations, the Kirkwood-Buff parameters, and individual density fluctuations for acetonitrile and water were obtained by using zero-angle X-ray scattering intensity I(0) and thermodynamic data such as partial molar volumes and isothermal compressibility. The Ornstein-Zernike correlation lengths were also determined for some of the solutions for which it is possible to make the Ornstein-Zernike plot.

10.1021/jp011964v CCC: $22.00 © 2002 American Chemical Society Published on Web 12/27/2001

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Experimental Section Scattering experiments were carried out at BL-15A Station, Photon Factory (PF) at National Laboratory for High Energy Accelerator Research Organization (KEK), Tsukuba, using a SAXS apparatus constructed at the station.27 By a bent mirror and a bent monochromator made of a Si single crystal, X-rays of 1.5 Å in wavelength were selected and the beam was focused to 1.0 × 1.0 mm2 at the position-sensitive proportional counter (PSPC). The camera length was 2100 mm, and the X-ray path was evacuated except at the position where the sample was set. The s region (s ) 4π sin θ/λ; 2θ: scattering angle; λ: X-ray wavelength) ranging from 0.036 to 0.16 Å-1 was covered. The sample was enclosed in a stainless sample cell with diamond windows of 0.1 mm in thickness. The thickness of the sample was ca. 1.0 mm. The temperature of the sample was kept constant by flow of temperature-controlled water through a jacket of the sample cell. The scattering intensities from the solutions of c ) 0.2, 0.3, 0.35, 0.38, 0.4, 0.45, and 0.5 were measured at 273, 279, and 298 K. Intensities from pure water and acetonitrile, and background from the empty cell, were also measured as well as those from the solutions. The intensities from pure water and acetonitrile were used as the standard intensities to calibrate those of the solutions to absolute scale. A beam stopper is made of lead. A hole is bored at the center of the stopper, at which a copper disk of 0.4 mm thickness is stuck. A direct beam passes through the disk and the attenuated beam by it reaches the PSPC. By comparing the attenuated intensity of the direct beam for the case that the sample is in the holder and the one for the case that the holder is empty, the absorption factor µl of the sample (µ: linear absorption coefficient of the sample; l: the path length of the sample) can be obtained experimentally. For all the samples, the absorption factors were determined in this way. The data were corrected for the fluctuation in intensity of incident X-rays, background intensities, and the effects of multiple scattering and absorption.

Figure 1. Scattering intensity of aqueous acetonitrile solutions at (a) 298 K and (b) 273 K. The numbers shows the mole fractions of acetonitrile. The curves refer to the least-squares fitting ones.

Results and Discussion Zero-Angle X-ray Scattering Intensity. The scattered intensities of acetonitrile aqueous solutions at 298 and 273 K after the necessary corrections are shown in Figure 1, parts a and b, respectively. Though the intensities are not converted to absolute scale yet, they are normalized to the intensities from the same volume. At small s-region, the scattering intensities increase as the temperature decreases. Especially, the scattering intensity of c ) 0.38 at 273 K (Figure 1b) is the largest. The scattering intensities of pure water and acetonitrile are much weaker than those of solutions. In the next section, we will show the concentration and density fluctuations that are related to the zero-angle X-ray scattering intensity, I(0). The value of I(0) needs to be obtained for each sample. According to the Ornstein-Zernike theory,28 the scattering intensity near s ) 0 is represented by the following equation for the sample at the neighborhood of the critical point:

I(s) )

I(0) 1 + ξ2s2

(1)

where ξ is the Ornstein-Zernike correlation length. The socalled Ornstein-Zernike plots of 1/I(s) vs s2 for the present solutions formed straight lines for c ) 0.3, 0.35, 0.38, 0.4, 0.45, and 0.5 at 273 and 279 K. As examples, the plots for the solutions at 273 K are shown in Figure 2. From the intensities

Figure 2. The Ornstein-Zernike plots for SAXS intensities of the aqueous acetonitrile at 273 K. The numbers refer to the mole fraction of acetonitrile.

extrapolated to s ) 0 for the plots, the values of I(0) were determined. For the other solutions in which the OrnsteinZernike description is not a good approximation, I(0)’s were obtained from the extrapolation to s ) 0 of least-squares fitting curves which are described by

I(s) ) a + bs2 + cs4 + ds6 The fitting curves are shown in Figure 1, parts a and b.

(2)

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TABLE 1: Zero-Angle X-ray Scattering Intensities and Fluctuations of Aqueous Acetonitrile Solutions c

I(0) (1023 e.u./cm3)

N h 〈(∆c)2〉

〈(∆N)2〉/N h

〈(∆c)(∆N)〉

3.34 7.52 8.63 8.08 7.77 6.67 4.55

-2.37 -6.00 -7.27 -7.04 -6.90 -6.23 -4.45

298 K 0.00 0.20 0.30 0.35 0.38 0.40 0.45 0.50 1.00

2.06 13.5 27.5 30.3 28.0 26.7 22.5 15.7 3.02

0.00 0.20 0.30 0.35 0.38 0.40 0.45 0.50 1.00

1.94 19.7 62.7 79.7 79.9 69.7 52.2 30.0 2.83

1.7 4.82 6.17 6.17 6.17 5.86 4.4 279 K 3.4 12.6 18.6 20.5 18.8 16.2 10.3

6.2 19.1 25.3 26.0 23.0 17.8 10.3

-4.55 -15.5 -21.6 -23.0 -20.7 -16.9 -10.3

273 K 0.00 0.20 0.30 0.35 0.38 0.40 0.45 0.50 1.00

1.9 28.0 108 206 252 170 113 48.2 2.8

5.0 22.1 49.0 65.9 46.8 39.1 17.0

8.97 33.4 66.4 83.4 57.0 39.1 17.0

-6.66 -27.1 -56.9 -74.1 -51.6 -37.3 -17.0

The obtained I(0)’s must be converted into absolute scale. For a one component system, I(0) is related to the isothermal compressibility given by

()

N2 I (0) ) Z κk T V T B TD

2

Figure 3. Zero-angle X-ray scattering intensity of aqueous acetonitrile solutions against the mole fraction of acetonitrile, c. The errors in the intensities caused by the extrapolation procedure are estimated to be less than 1%.

fitting are less than 1%. The I(0) values have a maximum near c ) 0.38 for all isotherms and increase remarkably at decreasing temperature. Fluctuations. Bhatia and Thornton gave a theoretical relation between the fluctuations and intensity of X-ray scattering.30 Applying their theorem actually, Nishikawa obtained the fluctuations of some binary mixtures by SAXS experiments and discussed their mixing states.23-26 The concentration and density fluctuations and cross term of these fluctuations are presented by N h 〈(∆c)2〉, 〈(∆N)2 〉/N h and 〈(∆c)(∆N)〉, respectively. The brackets and lines above letters mean the averages. The relation between the zero-angle intensity, I(0), and concentration fluctuation, N h 〈(∆c)2〉, is given by30

I(0)/N h )Z h 2(N/V)kBTκT + {Z h δ - (ZR - Zβ)}2N h 〈(∆c)2〉 (4) (3)

where superscript “TD” at I(0) means the zero-angle X-ray scattering intensity calculated from thermodynamic values, Z is the number of electrons in a molecule, and N is the number of molecules in the corresponding volume V. T is the thermodynamic temperature, kB the Boltzmann constant, and κT is the isothermal compressibility. IWTD(0) and IANTD(0) of water and acetonitrile are calculated from eq 3 by use of the values of κT which were reported by Grant-Taylor et al., namely, 451 for water and 1154 TPa-1 for acetonitrile at 298 K.29 Zero-angle intensities ITD(0)’s of water and acetonitrile obtained from eq 3 are 2.06 × 1023 and 3.02 × 1023 e.u./cm3 respectively, where “e.u.” means electron unit. The ratio of IANTD(0)/IWTD(0) is 1.47. The ratio of IAN(0)/IW(0), where IAN(0) and IW(0) are the obtained values from the present SAXS experiments, is 1.48. It can be concluded that SAXS experiments and some corrections for data were made adequately, because the ratio of the intensities by experiments was in good agreement with that by calculation. By comparing IW(0) and IWTD(0), I(0)’s of all solutions were converted into absolute scales. The temperature dependence of I(0)’s is listed in Table 1 and shown in Figure 3, where the values are normalized to the intensities per cm3. The largest errors in determination of each I(0) value will originate from the extrapolation of experimental scattering intensity to s ) 0. As shown in Figure 1 for the polynominal fitting or in Figure 2 for the Ornstein-Zernike fitting, the experimental intensities are well reproduced by eq 2 or eq 1. The errors of determined values for I(0)’s by the

where ZR and Zβ is the number of electrons in an R molecule and a β molecule, respectively. Z h is given by

Z h ) c R ZR + c β Zβ

(5)

where cR and cβ are mole fractions of R and β. The concentration and density fluctuations and cross term of these fluctuations are related to some thermodynamics parameters, as shown in following equations:30

N h 〈(∆c)2〉 ) N h kBT/

( ) ∂2G ∂c2

(6)

T,P,N

〈(∆N)2〉/N h ) (N h /V)kBTκT + δ2[N h 〈(∆c)2〉]

(7)

〈(∆N)(∆c)〉 ) -δ[N h 〈(∆c)2〉]

(8)

where G is the Gibbs free energy. The notation of δ is the term correcting the size difference of R and β molecules, which is given by

h /V δ ) (VR - Vβ)N

(9)

where VR and Vβ are partial molar volumes of R and β molecules, respectively. The partial molar volumes for the acetonitrile-water mixtures were obtained from the reported excess molar volumes of the solution at 298 and 279 K.2 The partial molar volumes at 273 K, whose values were not reported, were substituted for by those

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Figure 5. Contour curves (broken curves) of the concentration fluctuation of aqueous acetonitrile solutions. The numbers on the curve show the values of the concentration fluctuation. Solid curve refers to the miscibility curve. 2 Open circles are the measured points of the present study. The solid line a refers to the locus of the maxima in the isotherms for the density fluctuation of acetonitrile, and the line b refers to the loci for the ones of water and of undistinguished particles. The dotted area shows the Ornstein-Zernike region.

Figure 4. Fluctuations of aqueous acetonitrile solutions. (a) Concentration fluctuation, (b) density fluctuation, and (c) cross term.

at 279 K. The isothermal compressibilities, κT, of acetonitrile aqueous solution were obtained at a few concentrations in the range of 0 e c e 1 at 298 K by Grant-Taylor et al.29 The values of isothermal compressibility for the solution at the concentration necessary to the analyses were obtained by extrapolation. The isothermal compressibilities at 273 and 279 K were substituted for by those at 298 K because of small temperature dependence of the values in solution. The concentration fluctuations for the solutions were calculated from eq 4 with I(0) values obtained by the present experiment and thermodynamic data of κT, VW, and VAN. The density fluctuations and the cross term of these fluctuations were also calculated from eqs 7 and 8. The concentration and density fluctuations and the cross term of these fluctuations are shown in Figure 4 , parts a, b, and c, respectively. The values are also listed in Table 1. The absolute

values of these parameters for fluctuations have maxima or minima around c ) 0.38, whose trends resemble the I(0) behavior shown in Figure 3. The concentration fluctuation for the binary ideal solution is given by c(1 - c). Here, the ideal solution means the one where the volumes of the component molecules are the same and they are mixed randomly. The maximum value of the concentration fluctuation for the ideal solution is given by 0.25 at c ) 0.5. In the neighborhood of UCST, the fluctuation for acetonitrile solution is several hundred times larger than that of the ideal solution, which shows the extremely large inhomogeneity of mixing in the solution. The concentration fluctuations were obtained quantitatively and reported only for the aqueous solutions of ethanol,26 n-propanol and 2-propanol,25 and tertbutyl alcohol,23,24 which are miscible with water in any proportion and at any temperature. The values of acetonitrile solutions are much larger than the ones of these alcohol solutions. As mentioned above, the partial molar volumes of VAN and VW for the solutions at 273 K were substituted by those at 279 K. We expect that the values of fluctuation at 273 K will become larger than the present values by use of the VAN, VW, and κT values at the temperature. The present work is the first report for the concentration fluctuation of the solution which has the critical point. The contour lines of the concentration fluctuation are drawn in Figure 5, with the miscibility curve by Amitage et al.2 The numbers on the broken curves represent the values of the concentration fluctation. This is a rough map, because the measured points are not sufficient enough to draw contour lines. However, the map is a useful sketch, which directly shows the inhomogeneity of molecular distribution for the solution in the phase diagram of concentration and temperature. The Kirkwood-Buff Parameters. The Kirkwood-Buff parameters are defined by31

GRβ )

∫(gRβ(r) - 1)dV

(10)

where gRβ(r) is the partial distribution function. Ben-Naim pointed out the importance of the Kirkwood-Buff parameters for solution chemistry and interpreted that the parameters are a measure of the affinity of R molecules around a β molecule and vice versa.32 For a binary solution system, he showed that

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the Kirkwood-Buff parameters are obtained from three kinds of thermodynamic parameters, (∂2G/∂c2)T,P,N, Vi (i ) R or β) and κT, and then discussed the mixing state in ethanol aqueous solution.32 After his paper, some papers were published, reporting the Kirkwood-Buff parameters of various solutions by using of thermodynamic data only.33,34 However, there were some questions in accuracy, because it is difficult to obtain accurate values from the second derivatives for the Gibbs free energy with respect to concentration. The concentration fluctuation obtained by SAXS is directly related to the Kirkwood-Buff parameters,35

Vβ2n 1 GRR ) - + κTkBT + 2 [N h 〈(∆c)2〉] nR c

(11)

VR2n 1 h 〈(∆c)2〉] Gββ ) - + κTkBT + 2 [N nβ c

(12)

R

β

GRβ ) κTkBT -

VRVβn [N h 〈(∆c)2〉] cRcβ

(13)

where nR and nβ are the number densities of species R and β, and n is the one when molecules are not distinguished. Three Kirkwood-Buff parameters, GRβ are obtained separately from the combination of κT, Vi, and I(0) from SAXS experiments; namely, the values of the second derivative of the Gibbs free energy by concentration can be substituted for by the SAXS intensity which is possible to be directly measured. The concentration and temperature dependence of these Kirkwood-Buff parameters for acetonitrile aqueous solutions are shown in Figure 6 , parts a, b, and c, and listed in Table 2. Though values of the GAN,AN exhibit a maximum at c ) 0.30 and 298 K, the position of maximum shifts to c ) 0.38 as the temperature decreases. The maxima of GW,W show inverse shift, namely, at c ) 0.45 for 298 K and at c ) 0.38 for 273 K. Even at 30 K higher than UCST, the affinities of same kinds of molecules are considerably large and are increasing as approaching the critical temperature. There are reports on the Kirkwood-Buff parameters of the solution by Matteoli et al. (at 303 K),33 and by Blandamer et al.,34 both of which were obtained by thermodynamic values only. The agreement of the present data with these data is not quantitative but qualitative. It is predicted that the disagreement originates from not the difference between mesoscopic probe (SAXS data) and macroscopic one (thermodynamic data) but the data treatments especially in the second derivative of the Gibbs free energy. Satoh and Nakanishi also reported the parameters by Monte Carlo simulation at 298 K and 1 atm with a NPT ensemble.36 The values are much smaller than the present results and the maximum and minimum positions are not in agreement. It is thought that the system size (216 molecules in total) of the simulation is too small to investigate the mesoscopic fluctuations. Moreover, it is regrettable that the simulation for the solution in the neighborhood of c ) 0.38 is missing. With the average number density nR of molecule R, the quantities nRGRβ are obtained, the physical meaning of which is the fluctuation of the particle numbers of each component. Namely, for R ) β, the quantity (nRGRR + 1) is the fluctuation of the particle number of R molecules and for R * β the quantity nRGRβ is the cross fluctuation between the particle number of R molecules and β molecules.24-26 The number fluctuation (density fluctuation) of each component is shown in Figure 7, parts a and b. Note that the density fluctuation 〈(∆N)2〉/N h given

Figure 6. The Kirkwood-Buff parameters of aqueous acetonitrile solutions. (a) GAN,AN, (b) GW,W, and (c) GAN,W.

by eq 7 and shown in Figure 4b refers to the fluctuation of numbers of molecules when the acetonitrile and water molecules are not distinguished. While the density fluctuation in the undistinguished case and that for water have maxima at c ) 0.38 for all isotherms, the peak for acetonitrile has temperature dependence; namely it is positioned at lower concentration at higher temperature and shifts to c ) 0.38 as it approaches the critical temperature. The loci of the peaks of the density fluctuations are shown by lines in Figure 5. The magnitude of the fluctuation of water molecules is much larger than that of acetonitrile molecules. Therefore, the contribution of the fluctuation of water is dominant in the total particle number fluctuation and the concentration fluctuation in the system. The same behaviors are found in some alcohol aqueous solutions.24-26

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TABLE 2: The Kirkwood-Buff Parameters and Density Fluctuations of Acetonitrile (nANGAN,AN + 1) and Water (nWGW,W + 1) of Aqueous Acetonitrile Solutions c

GAN,AN (Å3 molecule-1)

GW,W (Å3 molecule-1)

0.20 0.30 0.35 0.38 0.40 0.45 0.50

698 829 730 573 496 321 137

433 1527 2155 2299 2397 2566 2206

0.20 0.30 0.35 0.38 0.40 0.45 0.50

1634 2440 2500 2226 1795 1112 486

869 4013 6491 7619 7298 7060 5192

0.20 0.30 0.35 0.38 0.40 0.45 0.50

2483 4376 6799 7444 4648 2592 879

1294 7056 17188 24660 18259 15668 8678

GAN,W (Å3 molecule-1) 298 K

279 K

273 K

nANGAN,AN + 1

nWGW,W + 1

-656 -1247 -1389 -1292 -1242 -1080 -759

4.44 6.36 6.18 5.27 4.80 3.61 2.18

9.53 24.2 29.6 29.0 28.7 26.7 19.9

-1295 -3248 -4158 -4256 -3763 -2964 -1777

9.12 16.9 18.9 17.8 14.9 10.2 5.3

18.3 62.6 88.3 95.2 86.6 72.9 46.4

-1896 -5675 -10940 -13686 -9356 -6534 -2948

13.3 29.6 49.8 57.2 37.1 22.4 8.69

26.7 109.2 232.3 306.0 215.3 160.7 76.9

TABLE 3: The Correlation Lengths of the Ornstein-Zernike for Aqueous Acetonitrile Solutions c

273 K

279 K

0.20 0.30 0.35 0.38 0.40 0.45 0.50

21.3 Å 28.8 31.9 25.5 21.6 13.6

14.4 16.7 16.6 15.3 13.9 10.0

known that the Ornstein-Zernike description is suitable. The relation between the SAXS intensity and the Ornstein-Zernike correlation length ξ is given by eq 1. The length is related to the correlation function of the density as given by28

r ∝ exp - /r ξ

( )

Figure 7. Density fluctuations of (a) acetonitrile and (b) water of aqueous acetonitrile solutions.

Correlation Length. From SAXS experiments, other information can be obtained; it is the correlation length which shows inhomogeneity of the system from the viewpoint of size. In the case of the system which is near the critical point, it is well-

(14)

where n(r) and nj are the one-body density function at r and its average value, respectively. Equation 14 indicates that there is no aggregate with the characteristic size, and that the number of aggregates decreases exponentially with increase of their size and the correlation length ξ is the parameter of the decrease. In the present aqueous acetonitrile solution, the function (n(r) - nj) will refer to the difference of mean electron density for the aggregates made of acetonitrile and water molecules and that for surroundings. We obtained the lengths for the solutions at some concentrations and temperatures where the OrnsteinZernike description is a good approximation and listed them in Table 3. The values of ξ for the solutions, of course, increase with approach to the UCST and reach 30 several Å at the thermodynamic state of 1 K higher than the critical point. A rough sketch of the Ornstein-Zernike region for the solution is shown as a dotted area in Figure 5. The Ornstein-Zernike region means the thermodynamic states in the phase diagram where the Ornstein-Zernike description is realized. Recently, Takamuku et al.22 have carried out SANS experiments on the solutions at 298 K and reported the Debye

Inhomogeneity of Mixing in Acetonitrile Solution correlation length LD.37 The correlation length is defined on the assumption that there are aggregates with a dimension as an averaged size, while the Ornstein-Zernike correlation length corresponds to the parameter of the exponential decay of the size distribution for aggregates. Namely, the Ornstein-Zernike region is more inhomogeneous in the distribution of the molecules. As shown in Figure 5, the solutions at 298 K are not included in the Ornstein-Zernike region. Takamuku et al. reported that the fitting by the Debye correlation are not so good for the solutions in the range of c ) 0.25-0.40 and supposed that the aggregates of several dimension are probably formed. The Debye correlation lengths for the present SAXS data at 298 K are consistent with the SANS ones.22 The inhomogeneity becomes large as growth of aggregates with various size. The generation of aggregates with macroscopic size corresponds to the phase separation. Mixing State. For acetonitrile-water mixtures, we obtained temperature and concentration dependence of the concentration fluctuation, density fluctuation, divided density fluctuations of acetonitrile and water, and correlation length. The fluctuations of density and concentration and correlation length represent directly the inhomogeneity of the distribution of molecules in mesoscopic region. The fluctuations give information on the inhomogeneity from the viewpoint of number of each molecule, and the correlation length gives that on the inhomogeneity in the viewpoint of size of aggregates. Koga et al. have also reported a comprehensive thermodynamic study on the solution by measuring excess chemical potentials and the second derivatives of the Gibbs free energy such as partial molar enthalpies, entropies, and volumes.21 They divided the solution into three composition regions in each of which the mixing scheme is quantitatively different from those of other regions. The composition region of the present SAXS study corresponds to Mixing Scheme 2 of Koga’s definition.21,38 In the region, there is no hydrogen bond network of water molecules perfectly connected in the system (i.e., bondpercolation), and the solution consists of two kinds of clusters, each rich in acetonitrile or water. Except for the regions far from the critical point, there are no aggregations with a characteristic size. The clusters grow rapidly with a decrease of temperature and separated at 272 K at c ) 0.38 when the clusters reach the macroscopic size. Koga et al. compared the mixing behavior in the aqueous acetonitrile with those of aqueous alcohols, and concluded that the thermodynamic behavior of aqueous acetonitrile resembles that of aqueous 1-propanol rather than that of ethanol or methanol despite the fact that the molar volume of acetonitrile (52.9 cm3 mol-1) is close to that of methanol (40.8 cm3 mol-1) or that of ethanol (58.7 cm3 mol-1). This behavior will be caused by the difference of the effect of CN group in a acetonitrile molecule and OH group in a methanol or ethanol molecule. The present author (K.N.) carried out comprehensive studies on the mixing schemes of some aqueous alcohols by SAXS measurements,23-26 being short of aqueous methanol. For aqueous tert-butyl alcohol solution, the characteristic factor determining the mixing state seems to be the formation of the cage structure of water molecules around a tert-butyl alcohol, such as clathrate-hydrate-like structure.23,24 For aqueous 1-propanol, the prominent factor is probably the formation of micelle by hydrophobic interaction.25 For aqueous ethanol, the factor will be the balance of hydrogen bonding energies between ethanol-ethanol and water-ethanol.26 The inhomogeneity of aqueous alcohols becomes smaller in order of 1-propanol, tertbutyl alcohol, and ethanol. The inhomogeneity of aqueous

J. Phys. Chem. B, Vol. 106, No. 3, 2002 699 ethanol is several tens times smaller than that of aqueous acetonitrile. In the case of aqueous methanol, which was not studied, the fluctuation will be less compared with aqueous ethanol, and the mixing scheme is expected to be close to the ideal mixing. The methyl group in acetonitrile is too small to form aggregations by hydrophobic interaction. Then, it is expected that the acetonitrile molecules aggregate with dipoledipole interaction of CN groups. In fact, it is dominant interaction to form the structure of neat liquid acetonitrile.8-12 In the aqueous solution, of course, the hydrogen bonding between the CN group and the OH group exists. However, the bonding will be weaker than the one between OH and OH. Consequently, water molecules aggregate with themselves and acetonitrile molecules do. This will be the mechanism of large inhomogeneity of the mixing in the solution and at last reach to the phase separation. The important factor which determines the mixing scheme of the acetonitrile-water system is expected to be strong hydrogen bonding of water molecules, weak one of water and acetonitrile molecules, and dipole-dipole interaction of acetonitrile molecules. Acknowledgment. The authors are grateful to the Photon Factory (PF) at the High Energy Accelerator Research Organization (KEK) for giving us the opportunity to perform the experiments. References and Notes (1) Riddick, J. A.; Bungh, W. B.; Sakano, T. K. Organic SolVents; John Willey & Sons: New York, 1986. (2) Armitage, D. A.; Blandamer, M. J.; Foster, M. J.; Hidden, N. J.; Morcom, K. W.; Symons, M. C. R.; Wootten, M. J. Trans. Faraday Soc. 1968, 64, 1193. (3) Easteal, A. J. Aust. J. Chem.1979, 32, 1379. (4) Kovacs H.; Laaksonen, A. J. Am. Chem. Soc. 1991, 113, 5596. (5) Bergman, D. L.; Laaksonen, A. Phys. ReV. E 1998, 58, 4706. (6) Jomorz, D.; Stangret, J.; Lingdren, J. J. Am. Chem. Soc. 1993, 115, 6165. (7) Bertie, J. E.; Lan, Z. J. Phys. Chem. B 1997, 101, 4111. (8) Kratochwill, A.; Weidner, J. U.; Zimmermann, H. Ber. Buns. Ges. Phys. Chem. 1973, 77, 408. (9) Bertagnolli, H.; Zeidler, M. D. Mol. Phys. 1978, 35, 177. (10) Steinhauser, O.; Bertagnolli, H. Chem. Phys. Lett. 1981, 78, 555. (11) Radnai, T.; Itoh, S.; Ohtaki, H. Bull. Chem. Soc. Jpn. 1988, 61, 3845. (12) Takamuku, T.; Tabata, M.; Yamaguchi, A.; Nishimoto, J.; Kumamoto, M.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998, 102, 8880. (13) Nishi, N.; Yamamoto, K.; Shinohara, H.; Nagashima, U.; Okuyama, T. Chem. Phys. Lett. 1985, 122, 599. (14) Wakisaka, A.; Shimizu, Y.; Nishi, N.; Tokumaru, K.; Sakuragi, H. J. Chem. Soc., Faraday Trans. 1992, 88, 1129. (15) Wakisaka, A.; Takahashi, S.; Nishi, N. J. Chem. Soc., Faraday Trans. 1995, 91, 4063. (16) Blandmer, M. J.; Foster, M. J.; Waddington, D. A. Trans. Faraday Soc. 1970, 66, 1369. (17) Cunningham, G. P.; Vidulich, G. A.; Kay, R. L. J. Chem. Eng. Data 1967, 12, 336. (18) Moreau, C.; Douheret, G. J. Chem. Thermodyn. 1976, 8, 403. (19) Benson, G. C.; D’arcy, P. J.; Handa, Y. P. Thermochim. Acta 1981, 46, 295. (20) Handa, Y. P.; Benson, G. C. J. Solution Chem. 1981, 10, 291. (21) Nikolova, P. V.; Duff, A. J. B.; Westh, P.; Haynes, C. A.; Kasahara, Y.; Nishikawa, K.; Koga, Y. Can. J. Chem. 2000, 78, 1553. (22) Takamuku, T.; Matsuo, D.; Yamaguchi, A.; Tanabe, M.; Yoshida, K.; Yamaguchi, T.; Nagao, M.; Ootomo, T.; Adachi, T. Chem. Lett. 2000, 878. (23) Nishikawa, K.; Kodera, K.; Iijima, T. J. Phys. Chem. 1987, 91, 3694. (24) Nishikawa, K.; Hayashi, H.; Iijima, T. J. Phys. Chem. 1989, 93, 6559. (25) Hayashi, H.; Nishikawa, K.; Iijima, T. J. Phys. Chem. 1990, 94, 8334. (26) Nishikawa, K.; Iijima, T. J. Phys. Chem. 1993, 97, 10824. (27) Wakabayashi, K.; Amemiya, Y. Handbook on Synchrotron Radiation; Ebashi, S., Koch, M., Rubinstein, E., Eds.; North-Holland: Amsterdam, 1991; Chapter 19.

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