J. Phys. Chem. 1985,89, 1531-1537 S*(Ag+) in molten salts, viz., IS*(Ag+,exc)l I0.2R, which is about 5% of [(ea - t)lTrElfor N = 0.5 (about which the excess quantities generally assume their highest value). Hence, one may safely neglect S*(Ag+,exc) and put
-
[ S ( A g + , e ~ c ) ] ~ , , ~ 19.8RN(l - N) [C(Ag+,exc)lT,=,
-
-19.8RTgN(1 - N)
-
[H(Ag+,exc)l~,=~ 0 where G and H are the Gibbs free energy and the enthalpy, respectively. Figure 3 shows the trend of the excess thermodynamic quantities, at T, = 1, vs. N. It is necessary to emphasize that any comparison with analogous representations of excess thermodynamic quantities in regular binary mixtures is conceptually limited by the nonisothermal character of the thermodynamic functions plotted in this figure. As for the exam entropy, one might indeed assume as physically reliable the symmetric trend shown in Figure 3, since, for temperatures close to T, = 1, the thermoelectric power becomes, within the experimental error, practically T independent for each composition (see Figure 1). Nonetheless, the corresponding excess
1531
free energy trend, which is directly affected by the variation of Tg with N, is not symmetric with respect to N = 0.5. Finally, also the third assumption about the excess enthalpy should be restricted to the peculiar low viscosity state attained at Tg, Accordingly, at T, = 1, i.e. under conditions of maximum energy content compatible with the existence of the glass phase, the silver ions may be actually described as a mixture of two main species, those introduced as AgI and those coming from the silver borate. The former kind of silver ions should play a major role in determining some properties of these glasses, such as the conductivity, u, and the glass transition. This statement, which was speculatively reported by one of us1some years ago, can be supported here by the fair straight lines fits, obtainable for room temperature log u, activation energy, E,,, and Tgdata,8 plotted vs. N instead of vs.
x
log u (ohm-' cm-') = -5.34
+ 6.08N
(std dev = 0.1 1)
E,,, (kcal mol-') = 10.395 - 8.567N (std dev = 0.17) Tg (K) = 627.88 - 227.22N (std dev = 4.36) where std dev is the standard deviation. Registry No. AgI, 7783-96-2;silver borate, 13465-88-8.
Solute/Solvent and Solvent/Soivent Interactions in Methanol Solutions: Quantitative Separation by Raman Difference Spectroscopy Keiji Kamogawa and Teizo Kitagawa* Institute for Molecular Science, Okazaki National Research Institutes, Myodaiji, Okazaki, 444 Japan (Received: June 13, 1984; In Final Form: November 26, 1984)
Solute effects in methanol solutions were investigated with Raman difference spectroscopy. Small frequency shifts of the CH3 symmetric stretching vibration of CH30H upon mixing with polar liquids such as H 2 0 and CF,COOH, nonpolar liquids such as CC14 and C6D6,and methanol isotopes such as CH30D and CD30D were observed with the optical multichannel detection system described previously. We propose here a practical method for dividing the total solute effect into contributions from the solvent/solvent interaction and from the solute/solvent interaction. In practice, two quantities, namely, homogeneous and heterogeneous interaction factors, which are indicative of the strength of methanol/methanol and methanol/solute interactions, respectively, are defined and evaluated from the concentration dependence of the frequency shifts. These quantities appeared to reflect specific interactions of CH30H with each liquid.
The effect of the solvent on the spectroscopic properties of the solute has been extensively studied.' When a solute molecule is influenced through its interaction with solvent molecules, conversely the solvent molecules receive a reaction effect from the solute, which may be tentatively called a solute effect. The solute effect has been little investigated hitherto for nonelectrolyte solutions.* Since the replacement of a solvent molecule with a solute implies not only the occurrence of a solute/solvent interaction but also some modification of solvent/solvent interactions, which otherwise are the same as those in neat liquid, quantitative separation of the total solute effect into solute/solvent and solvent/solvent interactions is desired for understanding the solution. A macroscopic approach to this problem was carried out through thermodynamic measurement^.^ Microscopic understanding of the solute effect requires a spectroscopic investigation. Molecular vibrations are sensitive to the intermolecular as well as to the intramolecular potential function. Accordingly, infrared spectroscopy has been applied successfully to study the solvent effect of molecules having particular groups such as the O-H, (1) C. H. Wang, Mol. Phys., 33, 207 (1979). (2) M. L. Josien in "Molecular Spectroscopy for Dense Phases" S. G.
Elkomoss and J. Ringeissen, Eds., Elsevier, New York, 1975, p 583. (3) M.C. A. Donkersloot, J . Solution Chem., 8, 293 (1979).
0022-3654/85/2089- 1531$01.50/0
N-H, S-H, and C=O groups: although molecules without such functional groups were difficult to treat. Generally, the vibrations which give rise to strong infrared absorption are different from those which give intense Raman lines. The recent development of Raman difference spectroscopy5allowed us to detect very small frequency shifts in the Raman lines and thus to discuss weaker intermolecular interactions between nonpolar groups. Previously we constructed a system to measure Raman difference spectra with high sensitivity.6 Application of this technique to extremely dilute solutions of alkyl sulfates revealed that the Raman line frequencies for C-H stretching modes were affected upon collapse of micelles. To get further insight into the effect of intermolecular interactions on the C-H stretching modes, we chose, in this study, a simple compound (CH,OH) and its binary mixture with polar liquids such as water and trifluoroacetic acid, with nonpolar liquids such as carbon tetrachloride and benzene, and with isotopically substituted methanol. We have (4) C. N. R. Rao and A. S. N. Murthy in "Developments in Applied Spectroscopy", Vol. 7B,E. L. Grove and A. J. Perkins, Eds., Plenum, New York, 1970,p 54. ( 5 ) J. Laane in "Vibrational Spectra and Structure", Vol. 11, J. R. Durig, Ed., Elsevier, Amsterdam, 1983,Chapter 6. (6)K. Kamogawa, K. Tajima, K. Hayakawa, and T. Kitagawa, J . Phys. Chem., 88,2494 (1984).
0 1985 American Chemical Society
1532 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985
Kamogawa and Kitagawa
attempted to separate the total solute effect into solute/methanol and methanol/methanol interactions and to correlate the molecular information with thermodynamic parameters.
A ?
Experimental Procedure Methanol (Nakarai, UV spectroscopic grade), methanol-d, (Merck, 99.5%), methanol-d, (Merck, 99%), and other spectroscopic grade solvents were used without further purification. Water was distilled and deionized. Solutions were prepared by mixing them for several minutes with a teflon-coated stirrer, and they were allowed to stand at 25 O C for 2-18 h before the Raman measurements. Raman spectra were excited at 514.5 nm (50-700 mW) with an Ar+ ion laser (NEC GLG3200). The light path of the incident radiation was fixed by passing it through several irises prior to focussing it on the sample cell. Scattered radiation was passed through a glass filter (Hoya 0-56) to remove the Rayleigh scattering tail, dispersed with single monochromator (Jasco CT-SO,f= 50 cm) at a slit width of 50 pm (Av = 2 cm-'), and then detected with an intensified diode array detector (PAR Model 1420). The data processing system, background subtraction procedures, and computation method to obtain difference spectra were described previously.6 The accuracy of the observed difference spectrum depends on the stability of the excitation light and the temperature of the sample. Samples were kept at 25 f 0.1 O C by circulating thermostatted water into the cell holder. The stability of the laser power and optical path in this experiment were examined by repeated measurements on neat liquid and found to yield a difference peak of A I / Z = 0.008 to 0.02, which corresponds to a 2-5-pm drift in position of the incident laser beam. This indicated the resolution limit of the present measurements to be 0.1 cm-' at 600 nm, which was much smaller than the slit width (2 cm-I).
(1)
where P ( k ) and P ( k ) are the intensities at channel k in the background subtracted spectra,6 and the superscripts denote the mole fraction of methanol. A scaling factor, ,c, was determined so that the band areas of the positive and negative parts of A P ( k ) were nearly equal, although there is no a priori justification for this choice. The intensity change of the Raman lines due to local field effects, if any, is considered to be the same for all Raman lines in the C-H stretching region and accordingly to have little effect on the relative difference intensities of the two (or more) bands. If a single Lorentzian-type band [I = b / ( ( v - vo)2 + a2)Jis shifted by Av, the difference between the shifted and unshifted spectrum would appear to be the derivative of the original spectrum, in which the peak-to-valley intensity difference (AID) and frequency difference (AvD) are given by AZD = (33/2/4)(b/a3)Av and AvD = 2 ~ / 3 ' / ~respectively. , Suppose that the maximum intensity of the band and its full-width a t half-maximum a t e Io and I', respectively. The AID and AvD are expressed in terms of I' and Av as AID
= (33/2Zo/21')A~
(2)
= r/3'I2
(3)
AvD
If the line shape is Gaussian, a similar expression would hold but the numerical coefficients would be different.' In so far as the size of the shift is small, AID is proportional to the frequency shift, the maximum intensity, and the reciprocal of the bandwidth, while AvD is proportional solely to the bandwidth. The proportionality constants depend on the band shape. Note that measurements of the intensity difference, not the frequency difference, provide information about the frequency shift. Since the shape of the C-H stretching band is not given by a simple Lorentzian or Gaussian function and since there are few bands in the spectral region of (7) D.
L. Rousseau, J. Raman Spectrosc., 10, 94 (1981).
I
3000
1
I
1
1
2800 z)/cm-l
Figure 1. The C-H stretching Raman spectrum of neat liquid methanol (A) and the difference spectra, Pll,O(k,f~),between the unshifted and the uniformly shifted by K = +5 (B) and = -5 channels (C). One channel
Quantitative Analysis of Difference Spectra The difference spectrum, A P y ( k ) , is defined by
AP'(k ) = P ( k ) - c,P( k )
I
corresponds to 0.94 cm-I in this experiment. Io denotes the maximum intensity of the us band. AI denotes a peak-to-valley height of the us mode in the difference spectrum.
interest, an empirical calibration curve corresponding to eq 2 was obtained as described below. The background subtracted spectrum of pure methanol, Z'.O(k), was measured and digitally shifted by f~channels to yield I',O(k f K ) . The difference, AZ1.O(k,f K ) , was defined by AZ'.'(k, f K ) = Z'.'(k f
K)
- Z'.'(k)
(4)
Figure 1 illustrates this procedures by subtracting the Raman spectrum of neat C H 3 0 H (A) and the difference AI'.o between the unshifted and uniformly shifted spectra by K = +5 channels (B) or K = -5 channels (C) (nearly equal to f5 cm-' shift). As expected, a derivative pattern appears. The peak-twalley intensity difference of the 2834-cm-' band, which is represented simply by AI hereafter, is almost twice as large as that of the 2944-cm-I band for the uniform shift, and this pattern was unaltered until the size of shift becomes as large as 30 cm-I. Figure 2 exhibits plots of AZ/Zo vs. the assumed shift for the 2834-cm-' band. AI/Zo is linearly proportional to Av when Av is small, but it deviates from a straight line as Av becomes large. This deviation is different for positive and negative shifts due to the presence of other bands. Hereafter this curve serves as a calibration curve for evaluating the size of the frequency shift, Av, from the observed intensity difference, AZ. When the shift becomes larger than 50 cm-', the increase in AZ/Io is not monotonic with regard to Av, but for such a large shift, a difference spectrum is unnecessary. Results The Raman spectrum in the C-H stretching region of liquid C H 3 0 H (Figure 1A) consists of four bands at 2837,2914,2942, and 2987 cm-l. The assignment of the 2837-cm"' line to the totally symmetric CH, stretching mode (vs) is undoubted.' The next intense line at 2942 cm-I is polarized and considered to be an
Raman Difference Spectra of MeOH Solutions
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1533
I
io
io
io o -io -io -30 Figure 2. The empirical curve for the correlation between the peak-tovalley height and the assumed frequency shifts. The ordinate stands for the ratio of AI to loof the us band (see Figure 1). in-plane component of an asymmetric CH3 stretching mode (u,). This mode is degenerate in C3, symmetry and its Raman line is very weak for CH3CN with C3, symmetry. Therefore, the intrinsic Raman intensity of this mode is presumably weak. The strong intensity of the u, mode observed in CH30H may be attributed to a lowering of the molecular symmetry, which allows its vibrational mixing with u,, with the 0-H stretching, and with other in-plane vibrations. Indeed, the splitting of u, between the in-plane and out-of-plane components is observed with infrared spectra.8a Accordingly, the intensity increase of this line is considered to be due to vibrational mixing. The two other lines are a combination and an overtone of deformation modes of the CH3group or possibly an out-of-plane component of the split v, modessb Mixing with Polar Liquid. Difference spectra of the polar solute/methanol solutions vs. the neat liquid CH30H are shown in Figure 3, where A, B, and C represent solutions with mole fractions of methanol (XMaH)of 0.90 in HzO, 0.10 in H 2 0 , and 0.95 in CF3COOH, respectively. Although the spectra shown in Figure 3 were obtained without the half-wave plate, the polarization measurements of the difference spectra6 revealed that those differences arise from the parallel component and therefore from the polarized modes of methanol. Figure 3A was well reproduced by the simulated curves illustrated in Figure lB, indicating that a uniform shift of the spectrum from the neat liquid took place when X M a H was large. In contrast, the difference spectrum for a dilute solution could not be well reproduced by the simulations. W e notice that the relative intensity of the positive peaks of the u, and u, lines is different in Figure 3B from that observed in Figure 1B. This may be caused by different frequency shifts for the us and u, lines. To test this hypothesis we tried to fit the difference spectrum in Figure 3B by assuming a larger shift for u, than for us, but the fit was still unsuccessful. The broken line in Figure 3B depicts the hypothetical curve which would appear if the u, shifted by 10 cm-' without a change of intensity. The failure to fit the experimental spectrum for u, is ascribed to imbalance between the height of the positive peak and the depth of the trough. This strongly suggests that the frequency shift is accompanied by an intensity increase for the u, mode, whereas for us simply the frequency shift occurs. A spectral change similar to that for X M a H = 0.10 in H 2 0 was observed for the difference spectrum of AI for X M a H = 0.95 in CF3COOH as shown in Figure 3C. This implies that the effect of dissolving 0.05 mole fraction of CF,COOH in C H 3 0 H is as
large as the effect of dissolving 0.90 mole fraction of H20. Although the strength of the methanol/solvent interaction varies, depending on the concentration, we stress that mixing with polar liquids always yields an increase of the C-H stretching frequencies of CH3OH. Isotopic Dilution. C H 3 0 H and CD30Dare consideied to have identical chemical properties and thus to form an ideal ~ o l u t i o n . ~ Unexpectedly, when CH30H was diluted with CD30D, the spectrum of C H 3 0 H was clearly affected as shown in Figure 4, where the difference AI for X M a H = 0.1 is shown by trace B. The difference pattern observed correspands to an upward shift of both Raman lines upon dilution with CD30D. To clarify the reason for the frequency shifts, two other combinations were examined, namely, C H 3 0 H / C H 3 0 Dand CH30D/CD30D. The difference spectra between pure CH30H and C H 3 0 D and between the = 0.1 and pure C H 3 0 D C H 3 0 D / C D 3 0 D mixture with XMeOD are shown by traces C and D, respectively, which exhibit shifts by -2 and 0.9 cm-', respectively. Therefore, it became clear that the shifts are nearly additive and that a significant part of the frequency shift observed for the CH30H/CD30Dpair could be explained by the shifts for the C H 3 0 H / C H 3 0 Dpair. This result indicates that an exchange between the 0-H and 0-D groups causes the frequency shift occurring upon mixing of C H 3 0 H with CDSOD. However, it is stressed that, although relatively small, a 0.9-cm-I shift does take place upon mixing of CH30D with CD30D. Since
(8) (a) A. Stnallach, R. Meyer, and Hs.H.Glinthard, J . Mol. Spcrrosc., 52, 94 (1974); (b) P. D. Mallinson, J . Mol. Spectrosc., 58, 194 (1975).
1977, Chapter 5.
, 3100 3000 2900 2800 2700 !
V/crn-' Figure 3. Concentration differencespectra of binary mixtures of methanol with polar liquids: (A) ( X M a H = 0.9 in water) - (neat methanol), (B) ( X M ~=H0.1 in water) - (neat methanol), (C) ( X M ~=H0.95 in trifluoroacetic acid) - (neat liquid). The dotted line in (B) represents the difference spectrum expected for a simple shift of the spectrum of neat liquid by -10 cm-I.
(9) Y.Marcus in "Introduction to Liquid State Physics", Wiley, London,
Kamogawa and Kitagawa
1534 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 I
> t-
zz W t-
z I
03100 3000 2900 2800 2700 WAVE NUMBER/C~-’
3000
2800
Figure 5. Concentration difference spectra of binary mixtures of methanol with nonpolar liquid: (A) ( X M ~=H0.9 in CCI,) - (neat liquid); (B) (X,,, = 0.1 in CCI,) - (neat liquid), (C) (X,,, = 0.01 in CCI,) - (neat liquid); and D (A’,,, = 0.95 in C6D6)- (neat liquid). In (c), d , and dl are defined as the larger and smaller values in valley depths of the difference band of us, respectively, and AI, denotes the larger value of the peak-to-valley height.
1
I
3100 3000 2900 2800 2700 Wm-’
Figure 4. Concentration difference spectra N ( u ) of methanol in isotopic mixtures: (A) absolute spectra at X,,, = 0.1 in CD30D (solid line) and of neat methanol (broken line) (the ordinate scale is arbitrary); (B) (X,,, = 0.9 in CD30D) - (neat liquid); (C) (pure CH30H) - (pure CH30D); (D) (X,,,o, = 0.1 in CD30D) - (pure CH3OD).
the vibrational coupling between the 0-D and C-H stretching modes is negligible for CH,OD, this shift should be attributed to an intermolecular interaction between the CH3 group and the surroundings. Similar frequency shifts are also reported for isotopic dilution of liquids containing nonexchangeable protons, such as CHC13/CDC13” and C6H6/C&6.” These shifts presumably arise from so-called intermolecular resonance coupling of molecular vibrations. 2 ~ 1 Mixing with Nonpolar Liquids. Both carbon tetrachloride and benzene are miscible with methanol in any proportion and can serve as nonpolar solutes or solvents. However, the excess functions of mixing suggest that C H 3 0 His solvated in a cluster form instead of a molecular mixture.14 Collapse of the CH30H cluster upon dilution is also suggested by results from ‘H NMRI5 and lightscattering studies,I6 although there has been no information about the CH, group. Figure 5 shows the difference spectra of C H 3 0 H in CC14 with X M a H = 0.90 (A), X M a H = 0.10 (B), and X M a H = 0.01 (C) and (IO) J. Laane and W. Kiefer, J . Chem. Phys., 73, 4971 (1980).
J. Laane and W. Kiefer, Appl. Spectrosc., 35, 428 (1981). C. H. Wang and J. McHale, J . Chem. Phys., 72, 4039 (1980). J. L. McHale, J . Chem. Phys., 75, 30 (198 1). J. S. Rowlinson in “Liquid and Liquid Mixtures”, 2nd ed, Butterworth, London, 1977, p 165. (IS) (a) J. C.Davis, Jr., K. S. Pitzer, and C. N. R. Rao, J . Phys. Chem., 64, 1744, (1960); (b) W. B. Dixon, J . Phys. Chem., 74, 1396 (1970). (16) T. Kato, T. Nakanishi, and T.Fujiyama, Bull. Chem. SOC.Jpn., 53, (1 1) (12) (13) (14)
2173 (1980).
of CH,OH in C6D6 with X M ~ O=H 0.95 (D). In contrast to the two previous cases, the Raman lines are shifted to lower frequency in Figure 5. This tendency is the same as that found for the C-H stretching modes Of C6H6 upon dilution with C6D6 or cS2.l’ The difference pattern of Figure 5D is nearly the same as that of Figure lC, indicating a uniform downward shift of the C-H Raman lines for methanol dissolved in C&. In cc14(Figure 5A), on the other hand, the positive peak of the u, mode is remarkably large, indicating an appreciable intensity increase of the u, mode when methanol is mixed with CC14. The difference between the spectra for XMeOH = 0.90 in CC14 and X M e O H = 0.95 in C6D6 is noteworthy. The pattern of the difference spectrum for the CH30H/CC14 mixture remained unaltered on dilution until X M e o H = 0.1, but at lower methanol concentrations it began to change. The difference spectrum for X M a H = 0.01 (Figure 5C) suggests that both the vs and va lines narrow and increase frequency slightly from pure liquid methanol. As illustrated in Figure 3C, the depths of the two satellite troughs on either side of a central positive peak are designated by d , and d2 (here d l > d 2 ) . We define an asymmetry factor,f= ( d , - d 2 ) / ( d l+ d2),which is equal to zero if a band changes in width, and is equal to unity when the change is simply a frequency shift (since d2 = 0). The frequency shift for the difference spectrum in Figure 5C was obtained from Figure 2 by putting A I = fA11.5Substitution of the observed values for XMeOH = 0.01 gave Av = -0.8 cm-’. The same type of spectral change as in Figure 5C was observed for the CH30H/C6D6 mixture when XMeOH 5 0.1. Frequency Shifts. The frequency shifts of the u, line of C H 3 0 H in various binary mixtures are plotted against XMeOH in Figure 6. The shifts for isotopic dilution are linear in X M d H . The similar linear dependence was also observed for other isotopic mixtures including C6H6/C6D6, (CH3)2CO/(CD3)2C0,and CH3CN/ CD3CN.I7 For the aqueous solutions of CH30H, the plot of Au vs. X M a H is linear only at X M a H > 0.6 and increases more rapidly toward more dilute solutions. On the other hand, the plot of Av vs. XM~OH in Cc1, and that in C6D6 are nonlinear at high mole fractions of CH,OH and the former exhibits a sharp upturn at XMeOH 5 0.1. The magnitude of Av in an aqueous solution is several times larger than the frequency shifts in isotopic solutions, and those for solutions in cc14and C6D6 were rather small with negative sign. The shifts for methanol in the C c l 4 and C6D6 solutions were similar to each other, although the profiles of difference spectra for the v, mode were different. If the intensity of the u, mode is determined by the local symmetry of the CH3 group, a direct interaction of a guest molecule with one of three ~
~~~
~
( 1 7 ) K. Kamogawa and T. Kitagawa, paper in preparation
The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 1535
Raman Difference Spectra of MeOH Solutions
12
10
8
Figure 7. Schematic illustration of the meaning of eq 6 . Right: painvise interaction between a central molecule and every other molecule in pure solvent. This is the standard state in this treatment and therefore Avow = 0. Left: the pairwise interaction in a binary solution where the shaded circles denote the solute molecules. Av, reflects the difference in the magnitude of the interaction of the central molecule with ith molecule between solution and pure liquid.
A%i1 6
summation is over the number (N,) of probe molecules. Then it can be regarded that each probe molecule undergoes the same frequency shift Avobsdas the time average. Since Avobsdis defined as a shift from the pure liquid state, it reflects the difference in the intermolecular interactions between the probe molecules in the solution and in the pure liquid. If the total intermolecular interactions are the sums of the pairwise potentials, Avobsdcan also be represented as the sum of contributions from the individual pairs: that is
4
2
0
-2 Figure 6. The plots of the observed frequency shifts of the vI band vs. mole fractions of methanol in the solutions: (A) aqueous solution; (0) isotopic solution (CD,OD); (0)CCll solution. The solid lines were obtained in the following way: A second-order polynomial was assumed to reproduce the five successive observed points, in which three parameters were determined by the least-squares fitting. The values of this function in the region of the three central points were adopted. The five points were moved in succession. At both ends where the number of points is not sufficient, the weight of one point was adjusted in the least-squares fitting.
C-H bonds may lower the local symmetry of the CH3group and cause an increase of the vibrational coupling of the v, mode with other vibrations. If this is the case, the present experiments suggest that CC14 and CF3COOH interact directly with the CH3 group = of methanol even when present at high dilution (X,,, 0.9-0.95). A possible change of vibrational mixing of v, with v, may cause a frequency shift of the v, mode.
Theory The difference spectra reported here have provided qualitatively a new kind of information about the structure of binary solutions. However, there is no established way to make it more quantitative. Therefore, we propose the following new correlation of spectroscopic information with the thermodynamic properties of nonelectrolyte solutions. It is obvious that individual methanol molecules in solution undergo different degrees of intermolecular interaction and hence frequency shift, depending on their microenvironments. For such a heterogeneous system, it is postulated that the observed frequency shifts are the ensemble averages of all the individual shifts which the probe molecules undergo: NP
AVobsd = ( 1 / N p ) x A v O ’ ) J=
1
(5)
Here AVO’)is the frequency shift of the j t h molecule and the
Here the summation goes over all the molecules of the solvent (A) and of the solute (B), and Aut is the shift in the probe frequency due to pair interaction of the probe molecule with every other molecule. This is illustrated schematically in Figure 7. If the interaction between the ith molecule and the probe molecule were identical with that in the pure liquid, Avi would be zero for this particular pair. Suppose that we measure a frequency shift of one of the vibrations of the A species in a binary solution composed of NA and N Bmolecules of the A and B species, respectively. The frequency shift which occurs upon addition of one molecule of the A or B species is represented by AvAA or AvAB, respectively
Here AvAA is the increase of AVobsd due to an increase of the interactions between the same type of molecule due to the increase in NA, and accordingly it is called the homogeneous interaction factor. On the other hand, AvAB indicates an increase of AvObsd due to an increase of the interactions between the different type molecules (AB) and accordingly it is called the heterogeneous interaction factor. Since SAvobsdis an increase of Avobaddue to addition of SNA and SNB moleculs of the A and B species, respectively, when both species are changed, it should obey the following relation: SAv0M = AvaSNA
+ AvABSNB
(9)
Both Ava and AvAB are functions of concentration, but in so far as the ratio, NA/NB is kept constant, both remain constant.” Keeping a given ratio for NA/NB, we integrate eq 9 with regard to NA and N B to obtain NOAVobsd = AvAANA + AvABNB where No = NA
+ N E . Equation
10 can be rewritten as
Avow = AvAAXA + A V A ~ B (18) Reference 14, Chapter 4.2.
(10)
(11)
1536 The Journal of Physical Chemistry, Vol. 89, No. 8, 1985 where XA
+ X B = 1.
(6Av0,/SXA)
Therefore = -(6Av0,/6X~)
15
=
AvAA
- AVAB (12)
Equation 12 implies that a unit change of mole fraction, which actually means a substitution of 1 mol of B with 1 mol of A, brings about the frequency shift equivalent to the difference between AvM and A v A B . Substitution of eq 12 into eq 1 1 yields
+ (1 - X A ) ( f i A V o b s d / a X A ) A ~ A= B AV0bs.d - xA(6Avobsd/6xA)
AVAA=
Kamogawa and Kitagawa
AVOW
IO
AUSd
4 nl+
(13) 5
(14)
When the observed shift is linearly proportional to the mole fraction, that is, Avo, = axA 6, it must satisfy a + 6 = 0 because the frequency shift should be zero at XA = 1.0 (pure solvent). In such a case the following relations should hold:
+
A v =~0
(15)
=b
(16)
AvAB
Discussion The frequency shifts of the vibrational spectra have been discussed in terms of the first momentI2 defined by M(') = s v Z ( v ) d v / s Z ( u ) dv
(17)
If the spectrum, Z(v), is completely symmetric with regard to the band center, the first moment is exactly the same as the peak shift. When the band is asymmetric, the first moment gives the frequency shift of the spectral center. On the other hand, the present method for evaluating the shift emphasizes the shift of the peak frequency. Since the Raman line of the vs mode is symmetric, the moment analysis would give the same results as the present one if the base line and band shape of the individual spectra were determined correctly. In the following we assign methanol to species A and the other component to species B, and the homogeneous and heterogeneous interaction factors are represented as A v M ~ Hand Avsol, respectively. A U M a H and AvM reflect the strength of methanol/methanol and methanol/solute interactions, respectively, and can be evaluated through eq 13 and 14, with XA= X M a H and the curves shown in Figure 6. The values of A v M ~ Hand Avsol thus determined are plotted against X M a H in Figure 8 for the H20/MeOH, CD30D/MeOH, and CC14/MeOH solutions. For the isotopic dilution of CH30H with CD30D, Avsol is positive and constant (4 cm-I) and AvMcOH is zero over almost the entire concentration region. It means that the substitution of methanol by CD30D influences only the molecules in contact with C D 3 0 D but not the molecules in the CH30H-rich region. Thus it seems reasonable that a major part of the shift is attributed to the H / D exchange which occurs for only the molecules in contact. Also for the intermolecular resonance coupling of molecular vibration^,^^^'^ probably only the first neighbor has a significant effect. In the case of dilution with H 2 0 , the limiting value of Avsol for X M a H = 1 is 5 cm-I and the value increases nonlinearly as X M a H decreases. This result probably implies that methanol molecules in contact with the first H 2 0 molecule undergo an additional interaction from the second H 2 0 molecule added. On the other hand, for X M a H from 1 .O to 0.7, A v M ~ H= 0, implying that the methanol-rich domain is little influenced by addition of a small fraction of H20. Destruction of the liquid structure of methanol in the methanol-rich domain starts around X M a H = 0.7 and proceeds until X M a H = 0.3, where another change takes place. The excess heat and excess entropy of mixing also exhibit their minima at X M a H = 0.3.19 Presumably the dilution process with HzO can be classified into two parts; the first is the region of ideal mixing (XMeOH = 1.0-0.3) and the second is the region of formation of a new aggregated assembly below X M e O H = 0.3. The formation of a micelle-like assembly at X M a H = 0.05 was previously predicted based on theoretical calculations.z0 (19) A. G. Mitchell and W. F. K. Wynne-Jones, Discuss. Faraday Soc., 161 (1953).
0
-5
Figure 8. Experimental values of the homogeneous and heterogeneous inteructionfuctors, Avsol (A) and AvMaH (B), obtained from the data of Figure 6 and eq 13 and 14. The derivative was calculated from the polynomials obtained (see the caption of Figure 6): (A)aqueous solution; ( 0 )isotopic solution (CD,OD); (0)CC1, solution.
For the CC14/CH30H solution, Avsol for X M a H = 1 is ca. -4 cm-I. The direction of the shift is opposite that for the H20/ CH30H solution, but the magnitudes of the shifts are similar. The low-frequency shifts upon the mixing of CH30H with CC14 may possibly be caused by the dispersion forces of more polarizable CC14 on the C H 3 group,21 but it would not explain the overall behavior, that is, while PVm increases gradually as X M a H becomes smaller, A U M a H is almost zero until X M a H is less than 0.4, where a new trend begins. The concentration of X M a H = 0.4 is the same as that where the excess volume of mixing changes sign.22 Presumably, reorganization of methanol clusters either in their sizes15or in the orientational order in each cluster,21proceeds at concentrations below X M a H = 0.4. It is interesting to compare A v M ~ Hwith the Kirkwood-Buff parameter, G22.3 The paGZ2value (here pa is the number density of the CH30H) is a measure of the local concentration of CH30H around a central CH30H molecule, in this case, and it is given by integrating the excess amount of radial distribution function for solvent molecules over,the bulk average. For the H20/CH30H solution, GZ2exhibited a broad maximum at X M a H = 0.3: where A v M ~ Hhas its minimum in Figure 8. For the CC14/CH30H pair, Gz2exhibited a monotonic increase and the increment becomes increasingly larger as XMaH becomes smaller.23 These behaviors of G22as a function of X M a H seem qualitatively similar to those in the corresponding cwes of A U M a H vs. X M a H , although there is no obvious reason for the similarity. The present study provided some idea about the sizes of the individual terms of the intermolecular potential in liquid methan0l.~3'~The intramolecular C-H/O-H vibrational coupling is as large as 2 cm-' while the intermolecular C-H/C-H resonance coupling term is at most 1 cm-'. These are much smaller than the shift of 12 cm-I observed for the H 2 0 / C H 3 0 H solution. The remaining contribution might be attributed to the linear term in the intermolecular potential f u n c t i ~ n . ~This ~ . ~shift ~ is close to that for the vs mode observed upon an increase in pressure to 12 kbar . In conclusion, Avsol and A Y M ~ Hare parameters which may be indicative of the strength of solute/methanol and methanol/ methanol interactions. Analysis of Raman difference spectra in terms of the homogeneous and heterogeneous interaction factors (20) S . Okazaki, H. Touhara, and K. Nakanishi, J. Chem. Phys., 81,890 (1984). (21) 2. Kecki, Specrrochirn. Acra, 18, 1155 (1962). (22) G. C. Paraskevopoulos and R.W. Missen, Trans.Faraday Soc., 58, 869 (1962). (23) T. Kato, T. Fujiyama, and H. Nomura, Bull. Chem. SOC.Jpn., 55, 3368 (1982). (24) K. S.Schweizer and D. Chandler, J. Chem. Phys., 76,2296 (1982). (25) W. Schindler and J. Jonas, J. Chem. Phys., 73, 3547 (1980). (26) J. F. Mammone and S . K. Sharma, J. Phys. Chem., 84, 3130 (1980).
J. Phys. Chem. 1985,89, 1537-1541 allows quantitative treatment of the frequency shifts upon mixing of two liquids and, as a result, enables us to discuss the solute effect spectroscopically. Acknowledgment. The authors express their gratitude to Prof.
1537
Willis B. Person of University of Florida for discussions and a critical reading of this paper. _ _ Registry NO. CH,OH, 67-56-1; CCI4, 56-23-5; C6H6, 71-43-2; CF3COOH, 76-05-1.
Evidence for Aggregates of Cationic Surfactants in Dilute Methanollc Solution of Benzene Arun Kumar Chattopadhyay, Maurice Drifford, Departement de Physico- Chimie, CEN-Saclay, 91 -Gif-sur- Yvette, France
and Claude Treiner* Laboratoire d'Electrochimie, Universite Pierre et Marie Curie, Bat.- F 4, Place Jussieu, 75005 Paris, France (Received: May 17, 1984; In Final Form: November 21, 1984) Static light-scattering and total vapor pressure techniques have been applied to the study of the behavior of trimethyl-nalkylammonium bromide (decyl, dodecyl, tetradecyl, hexadecyl, and octadecyl) surfactants in methanol + benzene mixtures. Both experimental techniques provide evidence that, in presence of at least 2 wt % benzene, surfactant aggregates are formed most probably of the direct type with 3 to 5 monomers per aggregate. At a given benzene concentration, the critical aggregation concentration is a linear function of the number of carbon atoms in the linear hydrocarbon chain. It is also shown from precise vapor pressure measurements that the cationic surfactants salt-in benzene at concentrations below the critical aggregation concentration, as in the classical case of aqueous solutions;however, the salting-in constant of benzene in methanolic surfactant solutions becomes less negative with the increase in hydrocarbon chain length in opposition to the trend observed in aqueous solutions.
Introduction In the course of a study of the free energy of interaction between inorganic and organic electrolytes with benzene in methanol by a vapor pressure method,' it was observed that the activity of the mixed solvent (benzene + methanol) after an initial decrease upon addition of a cationic surfactant, remained constant above a critical concentration. Sudden change in the slope of the variation of total vapor pressure vs. surfactant concentration, which was specific to surfactants, could not be observed in the absence of benzene. This observation could be attributed as evidence for the formation of aggregates comparable to micelle formation in aqueous or nonaqueous solvents. The aggregation of ionic surfactants in nonaqueous solvents is a well-established field of research with applications particularly for the catalysis of chemical reactiom2 It has eventually been studied in nonaqueous solvents of very low dielectric constant such as aliphatic and aromatic hydrocarbons and chlorinated solvents. Evidence for ionic aggregation in nonaqueous solvents of high dielectric constant is scarce and their nature not known. Micelle formation of amphiphatic compounds in water is assumed to be the consequence of the specific physicochemical properties of the solvent; in solvents of low dielectric constant so-called inverse micelles seem to be favored by dipole-dipole interactions between the ionic surfactants associated in ion pairs and stabilized by small quantities of water molecule^.^ Neither phenomena can be advocated in nonaqueous solvents of high dielectric constant; ionic surfactants are essentially dissociated into free ions and the hydrophobic phenomenon is ruled out. Nevertheless, aggregation of ionic surfactants has been observed in ethylene glycol4 (e = 40.7) dimethyl sulfoxide5 (e = 46.7), and ( I ) C. Treiner and A. K. Chattopadhyay, J. Chem. SOC.,Faraday Trans. I , 79,2915 (1983). ( 2 ) J. H.Fendler and E. J. Fendler in "Micellar and Macromolecular Catalysis", Academic Press, New York, 1975. (3) H.F. Eicke in "Topics in Current Chemistry", Springer-Verlag,Berlin, 1979. ~. (4) L. G. Ionescu and D. S. Fung, J. Chem. SOC.,Faraday Trans. 1, 77, 2907 -. . (19811. --, ( 5 ) E.J. Fendler, V. G. Constien, and J. H.Fendler, J. Phys. Chern., 79, 917 (1978). \ - -
hydrazine6 (e = 51.7). There is no evidence in the literature for such aggregates in methanol (e = 32.7), in fact it has been shown that aggregates of barium dinonylnaphthalenesulfonate in toluene are destabilized by the addition of small quantities of methanol.' There is an indication that alcohols such as 1-pentanol*might favor this type of association with dialkylsulfosuccinate electrolytes such as AOT. In view of this scattered information on ionic aggregation of surfactants in these solvents, it was deemed worthwhile to investigate the origin of such thermodynamic observations on methanol + benzene surfactant solutions with a more specific technique such as light scattering; furthermore, as the role of benzene in the stabilization of the aggregates was not known, attempts were made to restrict the investigationsto the low benzene concentration range needed for the existence of such aggregates and investigate the effect of the series of ionic surfactants on the aggregation phenomenon. We present in this report static vapor pressure and light scattering measurements on the behavior of the alkyltrimethylammonium series ranging from decyl- to octadecyltrimethylammonium bromide in methanol in presence of a low concentration of benzene. Vapor pressure measurements are essential to study the behavior of low surfactant concentrations where only monomer ions are present. The interaction of these surfactant monomer with benzene may be measured by a salting (Setchenov) constant just as in aqueous solutions and, consequently, it may help in understanding the behavior of the more complicated aggregates formed at higher surfactant concentration; light scattering measurements provide information on the aggregates themselves. The essential conclusion which may be drawn from this preliminary study is that small aggregates of about 3 to 5 surfactant monomers are definitely stabilized in methanol by benzene molecules. A critical micelle concentration reflected by a neat break in the vapor presence of intensity of light vs.
+
(6) M. S.Ramadan, D. F. Evans, and R. Lumry, J. Phys. Chem., 87,4538 (1983). (7)A.J. Fryer and S . Kaufman, J. Colloid Interface Sci., 29,444(1969). ( 8 ) (a) J. B. Peri, J. Colloid Interface Sci., 29,6 (1969). (b) A. S. Kertes and H.Gutman in "Surface and Colloid Science", Vol. VIII, E. Matijevic, Ed., Wiley-Interscience, New York, 1976.
0022-3654/85/20S9-1537$01.50/00 1985 American Chemical Society
