Ketocyanine Dye in Methanol + Acetone + Water and Metha

Jan 29, 2008 - ReceiVed: October 8, 2007; In Final Form: NoVember 8, 2007 ... differs significantly from the mole fraction average of the E values in ...
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J. Phys. Chem. B 2008, 112, 2056-2062

UV-Visible Spectroscopic Study of Solvation in Ternary Solvent Mixtures: Ketocyanine Dye in Methanol + Acetone + Water and Methanol + Acetone + Benzene Angshuman Maitra Department of Chemistry, Burdwan UniVersity, Burdwan 713104, India

Sanjib Bagchi* Department of Chemistry, Indian Institute of Science Education and Research, Kolkata, 700106, India ReceiVed: October 8, 2007; In Final Form: NoVember 8, 2007

Solvation characteristics of a ketocyanine dye have been studied in completely miscible ternary solvent mixtures, namely, methanol + acetone + water and methanol + acetone + benzene, by monitoring the solvatochromic absorption band of the dye. The maximum energy of absorption (E) of the solute in a ternary solvent mixture differs significantly from the mole fraction average of the E values in the component solvents. Results in the corresponding binary solvent mixtures also show a deviation of the E value from the mole fraction averaged E values. The results have been explained in terms of preferential solvation using a two phase model of solvation. The excess or deficit over the bulk composition of a solvent component in the vicinity of the solute molecule in a ternary solvent mixture has been estimated using the knowledge of solvation in the corresponding binary mixtures.

Introduction The chemical physics of solvation in solvent mixtures is of current interest.1-8 Experimental evidence suggests that a solute may induce a change in the composition of the solvation sphere compared with that in the bulk. The phenomenon, known as preferential solvation, has been studied in recent years for binary solvent mixtures both experimentally9-12 and theoretically13-17 in terms of solute-solvent and solvent-solvent interactions. While solvation in a binary solvent mixture has been studied extensively, systemic study of solvation in a ternary mixture is scanty. In the case of binary solvation, it has been indicated that besides solute-solvent interaction solvation characteristics depend on solvent nonideality. It is thus instructive to investigate the role of solvent-solvent interaction in ternary solvation. Measurements of equilibrium properties of ternary solvent mixtures reveal that the observed property deviates from the mole fraction average in most of the cases18-19 indicating the existence of solvent-solvent interaction in a ternary solvent system. In the event of ideal solvation, an observed property (P) of an indicator solute is given by the average of the property of the component solvents weighted by the mole fraction of the solvents.14,20 Thus,

P)

∑xiPi

(1)

monitoring the solvatochromic charge-transfer absorption band of the solute.21 A systematic study using other indicator solutes is required to draw a general conclusion. In the present paper we have studied the solvation of a ketocyanine dye as shown in Figure 1(dye I). The longest wavelength absorption band of the dye originates because of an intramolecular charge transfer (ICT) from the N atom of the amino group to the carbonyl O atom.22 Absorption and the corresponding fluorescence band show significant solvent sensitivity. Electronic spectral properties of the dye have been studied in mixed binary solvents.22 The objective of the present work is to study the role of solutesolvent and solvent-solvent interactions on the solvation characteristics of the dye in mixed ternary solvents by monitoring the absorption band of the solute as a function of solvent composition. Two solvent mixtures, namely, methanol + acetone + water and methanol + acetone + benzene have been included in the present study. The solvation characteristics in the corresponding binary solvent mixtures have also been studied. Information about the knowledge of binary solvation has been utilized to analyze the results on ternary solvation using a two-phase model of solvation. To test the generality of results, experiments were also performed in the two solvent mixtures using a structurally similar ketocyanine dye (dye II in Figure 1). Experimental Section

where xi denotes the mole fraction of ith solvent. Any deviation from eq 1 would indicate the existence of solute-solvent and solvent-solvent interactions. Electronic spectroscopy provides a suitable method for studying solvation. It has been observed that maximum energy of electronic transition of various solutes depends to a great extent on the local environment around the solute. Recently, we have studied the solvation characteristics of Reichardt’s ET(30) betaine dye in ternary mixtures by * Corresponding author. E-mail: [email protected].

The solutes were synthesized by a procedure described previously.22,32 Methanol, acetone, and benzene were purified and dried by standard procedures.23-24 All three solvents were distilled from calcium hydride prior to experiment. Triply distilled water was used for the experiments. Mixed solvents were prepared by carefully mixing the components by weight. Spectral measurements were taken on a Shimadzu UV 2101 spectrophotometer. Temperature was controlled to 298 ( 0.1 K by circulating water from a thermostat. The position of the

10.1021/jp709819n CCC: $40.75 © 2008 American Chemical Society Published on Web 01/29/2008

Solvation in Ternary Solvent Mixtures

J. Phys. Chem. B, Vol. 112, No. 7, 2008 2057

Figure 1. Ketocyanine dyes used in the present study.

band maximum (λm) was determined by using the peak-finding software on the instrument. Band maximum in a particular solvent mixture was measured in a number of replicate measurements. The precision of the replicate measurements was (1 nm. The energy of maximum absorption (E) was calculated from the wavelength maximum (λm) according to the following formula:

E (kcal mol-1) ) 28590 (λm/nm)

(2)

An inaccuracy of (1nm in the measurement of λm leads to inaccuracy in the E value of (0.1 kcal mol-1. Concentrations of the solute in the solutions were in the range 10-5 to 10-4 M. Results The ICT absorption band of the solutes in a mixed solvent appears broad and structureless. Solvatochromism of the ICT band is continuous, reversible, and independent of the concentration of the solute in the range studied. The bandwidth and shape practically remain unchanged and no isosbestic point is observed in the spectrum. All of these facts indicate that the shift of band maximum is not caused by change of equilibria between different chemical species in solution. Figure 2 shows the experimental solvent compositions for the ternary solvent mixtures on triangular plot. Values of maximum energy absorption in a ternary solvent mixture, E123, at various compositions at 298 K for dye I have been listed in Tables 1 and 2. For ideal solvation behavior, the value of a solvent-sensitive property of a solute in a mixed solvent is supposed to be given by the mole fraction average of the property in pure component solvents.14,20 Thus, the value of maximum energy of absorption in a ternary mixture in an ideal case will be given by the following equation:

E123 (ideal) ) x1E1 + x2E2 + x3E3

(3)

Figure 2. Solvent composition used in the present study for methanol + acetone + water (A) and methanol + acetone + benzene (B).

TABLE 1: Energy of Absorption Band Maximum of Dye I, E123, and Other Related Parameters as a Function of Solvent Composition of the Ternary Solvent Mixture Water (1) + Methanol (2) + Acetone (3) at 298 K x1

x2

E123a,b

E123(id)a,b

∆a,b

δ1a,b

δ2a,b

δ3a,b

0.60 0.30 0.40 0.50 0.30 0.35 0.45 0.35 0.55 0.60 0.65 0.70 0.70 0.75 0.80 0.80 0.20 0.20 0.30 0.40 0.40 0.10

0.20 0.30 0.30 0.25 0.20 0.35 0.35 0.30 0.25 0.30 0.10 0.15 0.20 0.10 0.10 0.15 0.40 0.60 0.50 0.10 0.50 0.80

64.23 65.98 65.07 64.71 65.69 65.20 64.51 65.27 64.46 63.89 64.64 64.03 63.69 63.96 63.48 63.08 65.69 65.20 64.99 65.69 64.44 65.13

63.32 64.86 64.28 63.80 65.06 64.47 63.89 64.57 63.51 63.12 63.23 62.84 62.74 62.65 62.36 62.26 65.24 64.84 64.46 64.68 63.88 65.02

0.91 1.12 0.79 0.91 0.63 0.73 0.62 0.70 0.95 0.77 1.41 1.19 0.95 1.31 1.12 0.82 0.45 0.36 0.53 1.01 0.56 0.11

-0.19 -0.22 -0.16 -0.19 -0.12 -0.15 -0.14 -0.14 -0.20 -0.18 -0.27 -0.25 -0.21 -0.26 -0.23 -0.19 -0.09 -0.08 -0.12 -0.18 -0.14 -0.03

0.09 0.09 0.08 0.09 0.03 0.08 0.08 0.06 0.11 0.13 0.08 0.12 0.14 0.11 0.12 0.14 0.03 0.06 0.08 0.03 0.11 0.02

0.10 0.14 0.09 0.10 0.09 0.08 0.05 0.08 0.09 0.05 0.19 0.12 0.07 0.16 0.12 0.05 0.06 0.03 0.04 0.16 0.02 0.01

Ei and xi in the above equation represent respectively the maximum energy of absorption and mole fraction of ith solvent. Values of E123 (ideal) and its difference from E123 (∆ ) E123 E123 (ideal)) have been listed in Tables 1 and 2. A significant deviation of E123 from the ideal value has been observed in all cases. The deviation from the ideal value is always positive for the methanol + water + acetone mixture while it is always negative for the methanol + acetone + benzene mixture. The following equation has been used in earlier studies to represent the composition dependence of the solute property, E123, in a ternary solvent mixture.6-8,21

a Units are in kilocalories per mole. b Uncertainity in E123, E123(id), ∆, δ is (0.1, (0.1, (0.2, (0.02, respectively.

E123 ) E123 (ideal) + x1x2x3 (A + Bx1 + Cx2)

where A, B, and C are constants for a particular ternary mixture and the solute. It may be mentioned that similar expressions

(4)

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TABLE 2: Energy of Absorption Band Maximum, E123, of Dye I and Other Related Parameters as a Function of Solvent Composition of the Ternary Solvent Mixture Methanol (1) + Acetone (2) + Benzene (3) at 298 K x1

x2

E123a,b

E123(id)a,b

∆a,b

δ1a,b

δ2a,b

δ3a,b

0.20 0.20 0.30 0.30 0.50 0.25 0.20 0.40 0.45 0.35 0.35 0.25 0.30 0.35 0.25 0.30 0.25 0.10 0.15 0.20 0.10 0.10 0.15 0.40 0.60 0.50 0.10 0.50 0.25 0.25 0.45 0.35 0.15 0.25 0.20 0.30 0.10 0.40 0.55

0.20 0.60 0.30 0.40 0.25 0.50 0.30 0.30 0.10 0.35 0.45 0.45 0.35 0.15 0.55 0.60 0.65 0.65 0.70 0.70 0.75 0.80 0.80 0.20 0.20 0.30 0.40 0.40 0.25 0.35 0.45 0.10 0.15 0.20 0.15 0.10 0.15 0.40 0.20

65.72 66.42 65.64 65.95 65.41 66.26 65.95 65.57 65.04 65.8 66.12 66.12 65.87 65.26 66.26 66.34 66.65 66.81 66.73 66.65 66.89 66.97 66.89 65.34 65.19 65.49 66.58 65.80 65.72 65.95 65.80 65.19 65.87 65.49 65.80 65.11 66.18 65.72 65.19

67.10 66.90 66.80 66.75 66.33 66.83 67.05 66.55 66.53 66.65 66.60 66.85 66.78 66.75 66.80 66.65 66.75 67.13 66.98 66.85 67.08 67.05 66.93 66.60 66.10 66.30 67.25 66.25 66.95 66.90 66.35 66.78 67.25 66.98 67.13 66.90 67.38 66.50 66.23

-1.38 -0.48 -1.16 -0.80 -0.92 -0.57 -1.10 -0.98 -1.49 -0.85 -0.48 -0.73 -0.91 -1.49 -0.54 -0.31 -0.10 -0.32 -0.25 -0.20 -0.19 -0.08 -0.04 -0.26 -0.91 -0.81 -0.67 -0.45 -1.23 -0.95 -0.55 -1.59 -1.38 -1.49 -1.33 -1.79 -1.20 -0.78 -1.04

0.46 0.11 0.38 0.25 0.33 0.16 0.33 0.34 0.57 0.28 0.15 0.21 0.29 0.55 0.14 0.08 0.02 0.04 0.04 0.04 0.01 -0.01 -0.01 0.46 0.34 0.29 0.13 0.15 0.41 0.29 0.18 0.60 0.46 0.51 0.46 0.67 0.36 0.26 0.39

0.48 0.42 0.40 0.36 0.18 0.36 0.54 0.27 0.13 0.30 0.22 0.43 0.37 0.24 0.37 0.21 0.11 0.45 0.31 0.22 0.32 0.19 0.11 0.24 0.12 0.18 0.67 0.14 0.43 0.44 0.20 0.18 0.48 0.43 0.36 0.22 0.58 0.28 0.14

-0.94 -0.53 -0.78 -0.61 -0.51 -0.52 -0.87 -0.61 -0.70 -0.58 -0.37 -0.67 -0.66 -0.79 -0.51 -0.29 -0.13 -0.49 -0.35 -0.26 -0.33 -0.18 -0.10 -0.70 -0.46 -0.47 -0.80 -0.29 -0.84 -0.73 -0.38 -0.78 -0.94 -0.94 -0.82 -0.89 -0.94 -0.54 -0.53

a

Units are in kilocalories per mole. b Uncertainity in E123, E123(id), ∆, δ is (0.1, (0.1, (0.2, (0.02, respectively.

have been used earlier to describe the composition dependence of a solvent property in a ternary solvent mixture in absence of any solute.18.19,25-27 In the present case also, eq 4 represents the experimental data points with the best-fit values of the coefficients A, B, and C (within an uncertainty limit ca. 10%) are -31.3, 167.4, and -2.81 respectively for the methanol + water + acetone mixture and -106.5, 84.8, and 120.2 for the methanol + acetone + benzene mixture. Figure 3 shows the computed iso-∆ lines for the ternary systems. Note that the iso-∆ lines are closed curves. The area enclosed by the curve decreases as the value of ∆ increases. The estimated solvent composition, (x1, x2, x3), where the value ∆ is maximum may be found as (0.56, 0.22, 0.22) and (0.25, 0.25, 0.50) respectively for the ternary mixture water (1) + methanol (2) + acetone (3) and methanol (1) + acetone (2) + benzene (3). In this context, it may be noted that a study of excess properties of the binary solvent mixture shows that the maximum deviation from ideality is observed in approximately equimolar binary composition of acetone + methanol, and this has been explained in terms of hydrogen bond interaction between methanol and acetone.18 In the case of a ternary solvation, the maximum deviation is observed where the ratio of mole fraction of methanol and acetone is approximately unity. The ratio of mole fraction of methanol and acetone remains unchanged but the absolute value

Figure 3. Curves of constant 4 value for methanol + acetone + water (upper) and methanol + acetone + benzene (lower). 4 values in kcal mol-1 for iso 4 curves (from outermost to innermost) are 0.3,0.8 and 1.5 (upper) and -0.6, -1.0, -1.3, and -1.45 (lower).

changes when water in the mixture water + methanol + acetone is replaced by benzene. This is because water and benzene interact differently with the cosolvents and also with the solute. We have also studied the solvation characteristics of dye I in the corresponding mixed binary solvents. Values of E12, the energy of maximum absorption in a binary solvent mixture (1 + 2), are summarized in Table 3. In the event of ideality, the spectroscopic property (E12) will be given by the mole fraction average, and eq 3 reduces to the following:

E12 (ideal) ) x1E1 + x2E2

(5)

Thus, for ideal solvation in a binary solvent mixture, a plot of the observed E12 values will be linear in mole fraction over the entire range. Figure 4 shows the plots of E12 as a function of mole fraction of a component solvent along with the ideal lines. It appears that the experimental data points deviate significantly from the ideal line for methanol + water, water + acetone, and methanol + benzene mixtures. The deviation from ideality of the observed spectroscopic transition energy has often been explained in terms of preferential solvation of indicator solute by a component solvent.9-15 The nature of deviation indicates that organic cosolvents are always preferred by dye I over water in an aqueous binary mixture. For methanol + benzene system, the solute is preferentially solvated by the more polar component, namely, methanol. For the methanol + acetone mixture, there is a small deviation from ideal behavior. For acetone +

Solvation in Ternary Solvent Mixtures

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Figure 4. Plots of E(A), the energy of maximum absorption of the ketocyanine dye I as a function of solvent composition in mixed binary solvents. (A) methanol + water, (B) acetone + water, and (C) methanol + benzene.

TABLE 3: Energy of Maximum Absorption (Kilocalorie per Mole) of the Ketocyanine Dye I in Mixed Binary Solvents at 298 K mole fraction of component 1 solvent mixture (1 + 2)

0. 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

water +methanol water + acetone methanol + acetone methanol + benzene acetone + benzene

65.2 67.2 67.2 67.7 67.7

65.0 66.9 67.0 66.2 67.6

64.7 66.6 66.8 65.3 67.6

64.5 66.4 66.6 65.3 67.4

64.2 65.9 66.3 64.9 67.5

63.9 65.6 66.2 65.0 67.3

63.6 65.1 65.9 64.9 67.4

63.1 64.3 65.8 64.6 67.2

62.7 63.8 65.7 64.6 67.2

62.1 62.7 65.4 64.7 67.6

61.4 61.4 65.2 65.2 67.2

benzene mixed solvent, the cosolvents have E values very close to each other and no appreciable deviation from ideal behavior is observed. Discussions In a mixed solvent system, the indicator solute will be solvated by the component solvent molecules. Because of solute-solvent and solvent-solvent interaction, the composition in the immediate neighborhood of the solute may however differ from the bulk composition. The equilibrium composition in the immediate neighborhood of the solute molecule will be determined by the criterion of minimum Gibbs free energy of the solute solvent system. Solvation in binary solvents has been extensively studied. In our earlier work with binary solvent systems, we showed that a positive deviation of the measured spectroscopic transition energy (E) from the ideal line indicates PS of the solute by the solvent component having higher E

values and vice versa. Thus, Figure 4 indicates that the solute (dye I) prefers methanol over benzene in methanol + benzene mixture. This is intelligible in terms of higher polarity of methanol. The preference of organic cosolvents by the solute in aqueous organic solvent mixture, however, needs special mention. In spite of greater polarity of water compared to that of methanol or acetone, the latter components are present in excess over water in the vicinity of the solute molecule. We have also observed similar preferential solvation behavior in these solvent mixtures by monitoring a different polarity (viz, solubility) of the indicator solute.28 We have explained this behavior in terms of the presence of hydrophobic wings in the molecule. To describe solvation in a solvent mixture, we have used the two phase model of solvation. In this model, solvent molecules are assumed to be partitioned in two regions. The region in the neighborhood of the solute molecule, where the solvent

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molecules experience the field due to the solute, is the local region, while solvent molecules outside the local region are said to be in the bulk. If NiL and Ni are the number of solvent molecules of ith type in the local and the bulk region, respectively, the Gibbs free energy, G, for the solute-solvent system is given by the following expression for a ternary solvent mixture:

G ) [N1Ls1L + N2Ls2L + N3Ls3L] + [N1L(N1L - 1)11L/2 + N2L(N2L - 1)22L/2 + N3L(N3L - 1)33L/2 + N1L N2L12L + N3L N2L23L + N1L N3L31L] + [N1(N1 - 1)11/2 + N2(N2 - 1)22/2 + N3(N3 - 1)33 /2 + N1 N212 + N2 N323 + N3 N113 ] [ kT ln[(N1L + N2L + N3L)!/(N1L!N2L!N3L!)] + kTln[(N1 + N2 + N3)!/(N1!N2!N3!)]] (6) In the above equation, si and sj are the energies of solute-i solvent and i solvent-j solvent interactions. The superscript L indicates the local phase. The first term in the square bracket on the right-hand side of eq 6 represents solute-solvent interaction, the second and third term in bracket represent solvent-solvent interaction in the local and bulk region, respectively. The fourth term represents the entropy term. NiL and Ni are related by particle number conservation as follows:

NiL + Ni ) total number of i solvent molecules (i ) 1, 2, 3) (7) Values of N1L, N2L, and N3L vary with solvent composition. We assume that the total number of molecules in the local region (cybotactic zone; N1L + N2L + N3L) is constant. If we consider the first layer of solvent molecules as constituting local (cybotactic) region, the constancy of the total number of solvent molecules is valid when the molecules have the same size.17 With this assumption the number of independent composition variables in the expression for G reduces to two. Values of NiL at equilibrium can be obtained by minimizing G with respect to the two independent variables. Thus, taking N1L and N2L as two independent variables, we get the following two conditions for equilibrium solvation:

kT ln K13 ) kT ln [(N1LN3)/(N1N3L)] ) [s3L - s1L] + [ N111 - N1L11L - N333 + N3L33L + (N1L - N3L)31L (N1 - N3)31 + N212 - N2L12L - N213 + N2L23L + (11L - 33L)/2 - (11 - 33)/2] (8) and

kT ln K23 ) kT ln [(N2LN3)/(N2N3L)] ) [s3L - s2L] + [ N211 - N2L22L - N323 + N3L23L + (N2L - N3L)32L (N2 - N3)32 + N112 - N2L12L - N131 + N1L31L + (22L - 33L)/2 - (22 - 33)/2] (9) The term Kij, defined as [(NiLNj)/(Ni NjL)] ) [(xiLxj)/(xixjL)] may be looked upon as the equilibrium constant for the following solvent exchange equilibrium:

jı + j ) i + jj

(10)

where jı and jj represent component solvent molecules in the local region, while i and j represent those in the bulk. Equations 8 and 9 indicate that the value of Kij is dependent on solutesolvent interaction and solvent-solvent interaction or solvent nonideality effect (terms in the first and second square bracket respectively in the right-hand side of eqs 8 and 9). Moreover, the solvent-solvent interaction or the solvent nonideality effect is dependent on the composition of the solvent mixture. When all  values are equal and ijL ) ij, which is equivalent to ideality of the solvent behavior, terms in the second square bracket of eqs 8 and 9 vanish. Similar expressions for the equilibrium constant for the solvent exchange equilibrium can derived for binary solvation.29-31 In that case, the value of Kij * 1 indicates that xiL * xi, meaning that the composition of the solvent mixture in the local region is different from that in the bulk. The maximum transition energy per mole, E, under these conditions, may be written as

E ) Σ NiLEi/Σ NiL

(11)

In the above equation, Σ NiL represents the total number of solvent molecules in the local region and, for solvent molecules having almost equal size, may be assumed to be constant. Thus, defining the local mole fraction as xiL ) NiL/Σ NiL; i ) 1, 2, 3, we have the following

E12 ) x1LE1 + x2LE2 E123 ) x1LE1 + x2LE2 + x3LE3

: binary mixture

(12)

: ternary mixture

(13)

Note that according to eqs 8 and 9 the value of xiL is in general different from that of xi. This is because of differential solutesolvent interaction and solvent-solvent interaction. To calculate the excess or deficiency of a solvent component in the cybotactic region over that in the bulk for a ternary solvent mixture, we proceed as follows. From eqs 3 and 13, we write

∆ ) E123 - E123 (ideal) ) Σ(xiL - xi)Ei

(14)

Defining a quantity δi ) (xiL - xi), which is a measure of the excess or deficit of the i solvent in the local region compared to that in the bulk and noting that Σδi ) 0, we have

∆ ) δ1(E1 - E3) + δ2(E2 - E3)

(15)

The component solvents of the ternary mixture in the present investigation have been chosen such that E1 > E2 > E3. The overall sign of ∆ thus depends on the sign of δ1 and δ2. Equation 14 for a binary solvent mixture reduces to

∆ ) δ1(E1 - E2)

(16)

Note that, unlike the case of binary solvation, the apparent deviation from ideality, ∆ ) 0, does not necessarily mean the equality of local and bulk mole fraction (δi ) 0). Rather, the local composition of all the components differ from that in the bulk in such a way that the value of the parameter E123 calculated according to eq 15 equals the ideal value. To calculate δ1 and δ2, we need another equation between δ1 and δ2. From the definition of K12, it follows that K12 ) [(x1+ δ1)x2]/[x1(x2 + δ2)], which on rearrangement gives the following equation:

(δ1/x1) - (δ2K12)/x2 ) (K12 - 1)

(17)

Note that eqs 15 and 17 indicate a relationship between ∆ and K12. Thus, eqs 4 and 6 are related in some way, indicating that

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J. Phys. Chem. B, Vol. 112, No. 7, 2008 2061

TABLE 4: Energy of Absorption Band Maximum E123 of the Indicator Dye II in the Ternary Solvent Mixture Methanol (1) + Acetone (2) + Benzene (3) at 298 K x1

x2

(E123)observeda,b

(E123)calculateda,b,c

0.20 0.50 0.35 0.25 0.20 0.25 0.20 0.55

0.20 0.25 0.35 0.55 0.70 0.35 0.15 0.20

57.9 57.4 57.9 58.9 59.8 58.3 58.1 56.7

57.8 57.2 58.0 58.9 59.7 58.3 58.0 56.8

a Units are in kilocalories per mole. b Uncertainity in (E123)observed ) (0.1. c Calculated using eq 20; E1 ) 56.9, E2 ) 60.9, E3 ) 62.2.

TABLE 5: Energy of Absorption Band Maximum E123 of the Indicator Dye II in the Ternary Solvent Mixture Water (1) + Methanol (2) + Acetone (3) at 298 K x1

x2

(E123)observeda,b

(E123)calculateda,b,c

0.60 0.30 0.15 0.20 0.40

0.20 0.30 0.35 0.60 0.50

56.3 59.1 58.4 57.6 56.0

56.2 59.3 58.4 57.8 55.6

a Units are in kilocalories per mole. b Uncertainity in (E123)observed ) (0.1. c Calculated using eq 20; E1 ) 52.3, E2 ) 56.9, E3 ) 60.9.

the empirical parameters A, B, C are related to the model parameters. The actual relationship is not obtainable at the present state of development of the model. It appears from eqs 15 and 17 that a knowledge of equilibrium constant for solvent exchange equilibrium, K12 (or in general, Kij), would lead to evaluation of individual δ values. Values of Kij cannot, however, be obtained from studies of solvation in a ternary solvent mixture. In our studies with binary solvent mixtures, it has been noted that electron spectroscopic studies provide a method for estimation of K12. The local mole fraction of component solvents in a binary solvent mixture (1 + 2) is given by:29-31

X1L ) (E12 - E2)/(E1 - E2)

(18)

K12 ) ((E12 - E2)/(E1 - E2))‚(x2/x1)

(19)

and

We have calculated K value for methanol + acetone system for dye I at various compositions. As discussed earlier, solvation in this mixture shows only a small deviation from ideality. Thus, K12 values for the binary solvent mixture are close to unity. It has been found that K12 values are smooth functions of the ratio of mole fraction of solvent components, x1/x2. K12 ) 0.9970.0295 (x1/x2), where the subscripts 1 and 2 represent acetone and methanol, respectively. We have assumed that the preferential solvation parameter K12 (which is a measure of excess solute property) obtained in binary solvent mixture is transferable to ternary solvation for the same solute. Similar procedure for explaining excess solvent properties in a ternary mixture has been reported in the literature.18,19,25 In our present work, we have assumed that the value of K12 in a ternary solvent mixtures depends similarly on the ratio of mole fraction of acetone and methanol as that observed for binary solvation of the solute involving solvents. Thus, in our calculation for a particular ternary solvent composition (x1, x2, x3), we have taken the value of K12 as obtained from the binary solvation of the solute for the same (x1/x2) ratio. Values of δ1 and δ2 were then calculated using eqs 15 and 17. The values have been listed in Tables 1 and 2. For the two solvent mixtures, the value of δ

for methanol and acetone are positive while those of water and benzene are negative. The negative value of δ for a solvent component indicates that the local region is deficient with respect to that component relative to the average composition. Thus results in the present case indicate that methanol and acetone are preferred over benzene or water in the local region. Benzene and acetone have similar value of spectroscopic transition energy and the preference of acetone over benzene cannot be explained in terms of solute-solvent interaction. On the other hand, benzene-methanol and benzene-acetone interaction is weaker than methanol-acetone interaction. Deficiency of benzene possibly arises due to differential solventsolvent interaction. In the case of ternary mixtures of methanol and acetone containing water, the deficiency of water is intelligible in terms of strong water-water interaction due to hydrogen bond formation. Moreover, the presence of hydrophobic wing in the solute molecule repels water molecules in the local region. As a result, water remains self-associated, and the number of water molecules in the local region is less than the average value. The obtained δ values have been used to fit experimental data on E123 ((E123)obs) in the studied solvent mixtures with a structurally similar probe (dye II, Figure 1) having similar properties.32 Thus, we have calculated E123 values according to the following equation

(E123)calculated ) (x1 + δ1)E1 + (x2 + δ2)E2 + (x3 + δ3)E3 (20) The observed and calculated values are given in Tables 4 and 5. Note that the calculated values of E123 for the dye II using the δ values for the dye I agree well with the experimentally observed values. Conclusion Information about the local region around a solute in a ternary solvent mixture can be obtained by monitoring the ICT band of a ketocyanin dye. The composition of the local region differs from the average composition due to differential solute-solvent and solvent-solvent interaction. The excess or deficit of a solvent component in the local region can be estimated from a knowledge of binary solvation. Acknowledgment. Financial support from UGC, India under DSA programme in Chemistry (Phase III) is being acknowledged. References and Notes (1) Aznarez, S.; Katz, M.; Arancibia, E. L. J. Solution Chem. 2002, 31, 639. (2) Segura, H.; Wisniak, J.; Galindo, G.; Reich, R. Phys. Chem. Liq. 2002, 40, 67. (3) Acosta, J.; Arce, A.; Rodil, E.; Soto, A. Fluid Phase Equilib. 2002, 203, 83. (4) Lotfollahi, M. N.; Modarress, H. J. Chem. Phys. 2002, 116, 2487. (5) Garcia, B.; Alcalde, R.; Aparicio, S.; Leal, J. M.; Matos, J. S. Phys. Chem. Chem. Phys. 2001, 3, 2866. (6) Ray, N.; Pramanik, R.; Das, P. K.; Bagchi, S. Chem. Phys. Lett. 2001, 341, 255. (7) Ray, N.; Bagchi, S. Chem. Phys. Lett. 2002, 364, 621. (8) Ray, N.; Bagchi, S. J. Mol. Liq. 2004, 111, 19. (9) Dawber, J. G.; Ward, J.; Williams, R. A. J. Chem. Soc., Faraday Trans. 1 1988, 84, 713. (10) Chatterjee, P.; Laha, A. K.; Bagchi, S. J. Chem. Soc., Faraday Trans. 1992, 88, 1675. (11) Covington, A. K.; Dunn, M. J. Chem. Soc., Faraday Trans. 1 1989, 85, 2835. (12) Suppan, P. J. Chem. Soc., Faraday Trans. 1 1987, 83, 495. (13) Marcus, Y. J. Chem. Soc., Faraday Trans. 1 1988, 84, 1465. (14) Ben-Naim, A. J. Phys. Chem. 1989, 93, 3809.

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