Znd. Eng. Chem. Res. 1994,33, 1355-1362
1366
Spectrofluorometric Measurements of Local Compositions and Comparison to Thermodynamic Models Olivier R. Carre, Daniel J. Phillips, and Joan F. Brennecke. Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
We present measurements of the local composition about the fluorescence probes pyrene and benzo[ghilperylene in binary liquid solvents. The probes provide information about the solvation of the solute on a microscopic scale. The advantage of the fluorescence probes is that they are relatively nonpolar and do not contain functional groups with which to form hydrogen bonds. Actual measurement of local compositions is important as the concept is the basis of a number of useful thermodynamic models. Thus, we compare the measured values with those predicted from both the nonrandom two-liquid (NRTL) equation and the Wilson equation. The standard recommended values of the nonrandomness factor in the NRTL equation generally underestimate the magnitude of the local compositions. Larger nonrandomness factors provide better descriptions of the microscopic environment. On the other hand, the Wilson equation overestimates the magnitude of the local compositions in all cases.
Introduction In the present paper, we are continuing our previous investigation of the local composition of solvent species around a dissolved solute (Phillips and Brennecke, 1993). Local compositions being different from bulk composition is the basis of a number of thermodynamic models, including the NRTL equation (Renon and Prausnitz, 1968) and the Wilson equation (Wilson, 1964). Our objective is to use spectroscopic probes to measure local compositions and compare those measurements to the thermodynamic models. Previously, we reported measurements of local compositions based on the solvatochromic shifts of the absorption probe phenol blue and showed that the measurements matched the predictions from the NRTL equation fairly well (Phillips and Brennecke, 1993). Here, we present the use of two new probes, pyrene (Py) and benzolghil perylene (BPe), and of another spectroscopic technique, fluorescence, which will enable us to gain additional insight into this phenomenon. A detailed summary of theoretical, experimental, and simulation studies on local compositions was given previously (Phillips and Brennecke, 1993). Pyrene is probably the best known of the polyaromatic hydrocarbon (PAH) probes used in fluorescence (Kalyanasundaram and Thomas, 1977;Dong and Winnik, 1982, 1984). In addition, other PAHs (Acree, 1991) have shown selective enhancement of the intensity of their vibronic bands as a function of solvent polarity. In the case of pyrene an increase of the solvent polarity will cause an increase of the intensity of the (0,O)transition commonly denoted as peak I. Through solute-solvent interactions (Hara and Ware, 1980; Kalyanasundaram and Thomas, 1977;Nakajima, 1971,1976)a more polar solvent will cause stronger symmetrylowering perturbations, hence a better mixing of the (0,O)transition with the much stronger (0,2) transition (peak 111). As a result, the ratio of the intensity of peak I to that of peak I11 (11/13) increases (Hartner et al., 1989). However, true quantitative understanding of the phenomena has not yet been achieved. For example, the exact mechanism of the above-mentioned interaction is not well understood (Dong and Winnik, 1982,1984),nor is it understood why some PAHs present this phenomenon while others do not (Acree, 1991). Nevertheless, pyrene
* Author to whom correspondence should be addressed. E-mail:
[email protected]. 0888-588519412633- 1355$04.50/0
has been used to probe microenvironmentsin micelles to compute the critical micelle concentration (Kalyanasundaram and Thomas, 1977; Turro and Kuo, 1986) and to explore solid/liquid interfacial environments (Hartner et al., 19891,as well as measure solvent strengths of liquids (Dong and Winnik, 1982,1984). Benzolghilperylenehas been shown to exhibit solvent-sensitive enhancements of the (0,O)vibronic band, as well (Acree, 1991). Hence, we are interested in using Py and BPe to probe their local environments in binary liquid mixtures.
Experimental Section Materials and Equipment. The spectrofluorometric probes benzotgghilperylene (98%) and pyrene (99%)were used as received from Aldrich. The solvents obtained from Aldrich (cyclohexane, acetophenone, ethyl butyrate, cyclohexanone, acetonitrile (HPLC grade)) and from Fischer (acetone, toluene, cyclohexane (HPLC grade)) were all ACS grade, unless otherwise specified, and used as received. Molecular sieves were used to dry some of the solvents to ascertain that the water content was sufficiently low that it would not influence the fluorescence measurements. The molecular sieves, 4-A 1/8-in. pellets, were obtained from Aldrich and activated at 110 OC for 24 h. Nitrogen, 99.998% prepurified grade, was obtained from Linde and used as received. The steady state fluorescencemeasurementswere made with a modular spectrometer assembly mainly composed of Spectral Energy optical components. The two monochromators (Model GM 252) were equipped with standard 1180grooves/mm gratings. The photomultiplier tube was a Hamamatsu 1P-28 powered by a Keithley Model 247 high-voltage power supply. Verifications of our peak ratio values were made on a FLM Model F 8000 spectrofluorometer. The peak ratios measured were consistently 11% higher than literature values (Acree,1991). However, due to the linearity of eq 7,used to obtain local composition from our peak ratios, this offset cancels out and identical values for the local composition are obtained. The UV spectrophotometer used was a Cary 1 by Varian. The measured absorption spectra fell in the 250-400-nm region, and points were taken at intervals of 0.3 nm. The sample cells for both absorption and fluorescence were clear glass cells with path lengths of 1cm. All mass measurements were performed on a Mettler AE50 digital analytical 0 1994 American Chemical Society
1356 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
balance and were accurate to within O.OOO1 g. All masses measured were of quantities at least 10 mg or higher so that the uncertainty in the measurements was 1% or less. All volumetric measurements were made in Kimax volumetric flasks and are accurate to 0.03 mL (for 2,5,10,25 mL) and to 0.05 mL (for 50 and 100 mL). Procedure. Stock solutions of BPe and Py (3.5 X 10-5 and 2.9 X 104 M, respectively) in cyclohexane were prepared. A 2-mL sample of one of the solutions was taken, and cyclohexane was evaporated. The remaining solid was diluted to 100 mL in each of the pure solvents, so as to obtain dilute probe/solvent solutions of essentially the same probe concentration, and dilute enough to avoid any exciplex formation and/or inner filtering effects due to the solute. Mixtures were obtained by weighing each solvent to produce the desired mole fraction of solvent and cosolvent. Mixtures were examined across the entire concentration range, from pure solvent 1to pure solvent 2, typically in steps of 0.1 mole fraction. Since the solute was so dilute, having a concentration several orders of magnitude smaller than the solvent or cosolvent, solutesolute interactions could be neglected. Thus, we may limit our concerns to the distribution of the two solvents around the solute. The local composition of the two solvents around Py or BPe in various solvent mixtures was obtained from the measurement of the ratio of the intensity of peak I to peak I11 in their respective fluorescence emission spectra. Nitrogen was allowed to bubble through each sample for 15min. This was to remove the oxygen, which will quench the fluorescence intensity (Birks, 1970). The measured peak ratio was taken as the average of five scans. For BPe the fluorescence spectrum was recorded from 400 to 430 nm in steps of 0.1 nm since peak I occurs at ca. 408nm and peak I11occursa t ca. 421 nm, with an excitation wavelength of 380 nm. For Py the fluorescence spectrum was recorded from 365 to 395 nm in steps of 0.1 nm since peak I occurs at ca. 373 nm and peak I11 occurs at ca. 383 nm, with an excitation wavelength of 338 nm. The excitation slit width was 14.8 nm. This width enabled us to use a constant excitation wavelength with all the solvents. Therefore, primary inner filtering, which occurs when the excitation beam is significantly absorbed prior to reaching the interrogation zone (that is, the center of the 1-cm cell), affects both peak intensities by the same factor (Yappert and Ingle, 1989), enabling us to neglect this phenomenon. For example, acetophenone absorbs a significant amount of the light used to excite the BPe, leading to primary inner filtering correction factors as high as 2.4. However, the correction factor is the same for both peaks of interest so the correction factor cancels out when one takes the ratio of peak intensities. The emission slit width was =2.3 nm, which is large enough to avoid diffraction and to obtain a good signal intensity a t low solute concentration, yet small enough to obtain good resolution between the peaks. The use of a small emission slit width was suggested in the literature and the above values are in accordance with those recommended (Acree, 1991). Also, for the binaries considered, secondary inner filtering, which arises when the solution absorbs part of the emission light, was neglected as the absorbances of our mixtures were C0.05 cm-l in the spectral regions considered. For acetophenonelcyclohexane,for example, the correction factor for secondary inner filtering was computed according to the following formula:
where Aw = (w2 - w d = ( y 2 - yl)/b, y2 - y1 being the excitation beam's width, b the cell length path, and T the
transmittance of the solution (Yappert and Ingle, 1989). With absorbances of the solvents at 408 and 421nm ranging from 0.03 cm-l for pure cyclohexane to 0.07 cm-l for pure acetophenone, the secondary inner filtering correction factor for the peak ratio was a t most 1%.The spectra were accumulated at 21 f 1 "C. While ratios for BPe appear to be temperature independent (Acree, 19911,this is not necessarily the case for pyrene. However, the effect of temperature on the Py ratios was neglected since the temperature variation was so small. The spectra of BPe in ACS grade cyclohexane (H2O < 0.01 % ) and in HPLC grade cyclohexane (H2O < 0.004 7% ) or in ethyl butyrate and ethyl butyrate stored over molecular sieves showed no difference in peak ratios. Thus, we used the solvents as received. We will be comparing the measured local composition to those predicted by the NRTL and Wilson equations. In order to obtain interaction parameters, we needed the solubility of Py and BPe in each pure solvent. Except for acetophenone, we obtained the solubilities with UV-vis absorption spectroscopy of a known dilution of a saturated solution of the probe in the pure solvent. An independent calibration curve was prepared for each solute using Beer's law. A maximum of solid was allowed to dissolve under vigorous agitation in each pure solvent. Each sample was centrifuged on a Horiba Capa-300 centrifugal automatic particle analyzer at 3000 rpm for 15 min, to remove solid particles in suspension. Samples of 2 mL of saturated liquid were then diluted and analyzed by UV-vis spectroscopy. Three measurements were taken for each solvent at 24-h intervals. Since acetophenone absorbs in the absorption region of BPe, two samples of 2 mL of acetophenone saturated with BPe were placed for 24 h at 0.01 mmHg and 40 "C and allowed to evaporate. The vapor pressure of BPe is sufficiently low to result in negligible sublimation of the solid. The solid was dissolved in cyclohexane, diluted accordingly, and analyzed by UVvis absorption spectroscopy.
The NRTL and the Wilson Equations The measured values of local composition are compared to two thermodynamic models that are based on local compositions being different than bulk compositions. Using values of the nonrandomness parameter of 0.3 or 0.47 in the NRTL equation, the corresponding interaction parameters between each probe and each pure solvent were computed as previously reported (Phillips and Brennecke, 1993). Basically, the interaction parameters are obtained by independently measuring the solubility of the solid solute in each pure solvent. These parameters are then used in the equation to predict the local composition around the solute in solvent mixtures and compared with the spectroscopic measurements of local compositions. In this study, we also included the nonrandomness parameter as given by the following empirical formula (Mato and Mato, 1989): aij=
1
2 + exp(-aij(zi,
+ T;~))
i,j = 1,2
(2)
In this case we have a three equationslthree unknowns system to solve. The NRTL equation then becomes a true two-parameter equation, like the Wilson equation. When eq 2 is used, the values of a 1 2 and CY32 are not the same so the full expression for the local compositions in this case is
The Wilson equation, for which a12 = a32 = 1 in the above equation, required the value of the molar volume
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1367 Table 1. Peak Ratios of Benzo[ghlperylene (BPe) and Pyrene (Py) BPe in BPe in BPe in BPe in
~
~~
~~
~
BPe in Py in Py in Py in toluene/ cyclohexanone/ acetophenonel ethyl butyrate/ toluene/ bulk mol % acetonel ethyl butyrate/ acetonitrile/ cyclohexane cyclohexane cyclohexane ethyl butyrate of first solvent cyclohexane cyclohexane cyclohexane cyclohexane 0.48 0.48 0.48 0.65 0 0.48 0.48 0.66 1.41 0.57 0.67 0.81 0.84 0.81 0.74 0.73 1.44 10 0.65 0.78 0.97 0.97 0.97 0.80 20 0.88 1.44 0.70 0.86 1.05 1.06 1.09 1.03 30 0.86 1.57 0.76 0.94 1.17 1.10 1.16 1.09 40 0.92 1.68 0.81 0.98 1.23 1.12 50 1.12 1.19 0.98 1.60 0.83 1.03 1.29 1.16 1.20 1.27 60 1.01 1.67 0.88 1.07 1.33 1.17 1.30 1.38 70 1.73 1.09 0.91 1.10 1.21 1.34 1.42 1.33 80 1.11 1.80 1.11 0.92 1.32 1.23 1.37 1.42 90 1.19 1.97O 1.12 1.20 1.40 1.45 0.95 1.21 1.36 100 1.97 a This
data point is not represented in Figure 8,the value of x1z - x 1 being -0.1.
of the probe, hence its liquid density at 21 “C. Using Bhirud’s method (Reid et al., 1987)to estimate “saturated” liquid densities, we found 167 cm3/mol for Py and 265 cm3/molfor BPe. The critical data, as well as the boiling temperature, needed in this method were estimated using Joback’s scheme (Reid et al., 1987). The interaction parameters (rij) between the probe and each pure solvent for the Wilson equation are then obtained from the measured values of the solubility of the probe in the pure solvent by solving the following two equations:
with PAHs. The experimental values of the peak ratios in the aforementioned mixtures are reported in Table 1. To compute the local composition from our experimental data, we have assumed a linear contribution of the local mole fraction to the peak ratio in the mixture, as did Nakashima et al. (19921,in the study of microstructure in polystyrenepoly(viny1pyridine)diblock copolymer film:
(7) where (11/13)1and (11/13)3refer to the peak ratios in each of the pure solvents and x12 and x32 are the local compositions of the two solvents around the probe. By modeling the mixture as being made up of two solvational sphere types (probe + pure solvent 1 and probe + pure solvent 2)rather than one (probe + some solvent 1 + some solvent 2), Acree et al. (1993)derived the following:
where
G, = (ui/uj)exp(-rij) and i, j = 1,2
(6)
along with the equations for the solubility of a solid in a liquid given below as eqs 9 and 10. Experimental Results Spectroscopic Measurements. The local compositions in the liquid mixtures were determined from fluorescence measurements. Our previous study used the UVvisible absorption probe, phenol blue, whose absorption wavelength shifts with changing polarity of the solvent. In general, the advantage of fluorescence lies in the sensitivity of the method compared to UV-vis absorption. However, we chose fluorescence probes because they are nearly nonpolar, at least in the ground state. The only UV-visible absorption probes that exhibit large enough shifts to measure local compositionsare highly polar, with functional groups capable of hydrogen bonding. The use of both techniques, fluorescence and UV-visible absorption, and two kind of probes (polar and nonpolar) will, hopefully, lead us to a better insight into preferential solvation in liquid mixtures. Peak ratios of BPe were measured for five binaries (acetone, ethyl butyrate, cyclohexanone, acetophenone, and toluene, each with cyclohexane), and peak ratios of Py were measured for three binaries (toluene/cyclohexane, ethyl butyrate/cyclohexane, acetonitrile/ethyl butyrate). Acetone, cyclohexanone, and acetophenone were not used for P y because these solvents absorbed too strongly in the spectral region of Py, leading to serious primary and secondary inner filtering. Also, triethylamine, which was reported in our previous study using phenol blue (Phillips and Brennecke, 1993) could not be used with the fluorescence probes because it is well-known (Van and Hammond, 1978; Brennecke et al., 1990)that triethylamine forms exciplexes
which yields eq 7 in the case where (1311 = (1313. For our systems, both equations yield similar results, as we shall show below. Thus, we routinely used eq 7 to determine local compositions. It is to be noted that transition energies of phenol blue (Phillips and Brennecke, 1993) correlate linearly with 11/13, within the same binary mixture, with a linear correlation coefficient of at least 0.98 and as high as 0.993for the ethyl butyrate/cyclohexanemixture. Since a linear relationship of absorption transition energies with local composition mole fraction for similarly sized solvent molecules is reasonably well accepted (Kim and Johnston, 1987;Yonker and Smith, 1986; Chatterjee and Bagchi, 1990,1991),the fact that both phenomena (absorption solvatochromic shifts and fluorescence 11/13 values) are correlated leads us to believe that eq 7 is at least a reasonable assumption. It is, however, the major assumption in these analyses. As previously done (Phillips and Brennecke, 1993),we did not attempt to include any factor accounting for solvent size differences (Kim and Johnston, 1987) as the solvents were of somewhat similar molar volumes. Since the solute is dilute, the local compositions in eq 7 must sum to unity. This allows us to determine the experimental local composition of the solvents around the solute. The difference is taken between the local and the bulk compositions of the more polar solvent (x12 - x1) and is plotted versus the bulk mole fraction of the more polar solvent. The measured values of preferential solvation are shown as the large symbols in Figures 1-8. The various curves are model predictions, which will be discussed later. In all but one binary (acetonitrile/ethyl butyrate using pyrene as the probe) the more polar solvent was preferred
1358 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
,."
.
0.8 0.7
-
11p
d3
0.6 0.5
f p-
0.4
0.5 0.4
0.3
B
0.2
0.2
0.1 n "
0.3
0.1
0
.
0.4 0.6 Bulk mole fraction of toluene
0
0.2
0.8
1
Figure 1. Difference in local and bulk composition of toluene in cyclohexane around BPe. (-) Wilson equation;(- -) NRTL equation with a12 = 0.47;(- - -) NRTL equation with a12 = 0.3;(- - -) NRTL equation with calculated a;(a) experimental values using eq 7.
I 0
0.2
0.4
0.6 Bulk mole frwion of cyclohexanone
0.8
1
Figure 4. Differencein local and bulk composition of cyclohexanone in cyclohexane around BPe. (-) Wilson equation; (--) NRTL equation with a12 = 0.47;(- - -1 NRTL equation with a12 = 0.3;(- - -) NRTL equation with calculated a;(H) experimental values using eq I.
-
1
p I
H 4
0'4
P
0.3
v
I
0.2
2 0.1
0 0.2
0
0.4
0.6
Bulk mole fraction of ethyl butyrate
0.8
1
I
0
Figure 2. Differencein local and bulk compositionof ethyl butyrate in cyclohexane around BPe. (-) Wilson equation; (-3 NRTL equation with 4 1 2 = 0.47;(- - -) NRTL equation with a12 = 0.3;(- - -) NRTL equation with calculated a;(a)experimental values using eq 7; (E) experimental values using eq 8. 0.35
0.2
0.4 0.6 Bulk mole fraction ofacetophenone
0.8
Figure 5. Differencein local and bulk cornposition of acetophenone in cyclohexane around BPe. (-) Wilson equation; (--) NRTL equation with a12 = 0.47;(- - -) NRTL equation with a12 = 0.3;(- - -) NRTL equation with calculated a;(B) experimental values using eq 7.
-I
0
02
0.4 0.6 Bulk mole fraction of netone
0.8
1
I
1
Figure 3. Difference in local and bulk composition of acetone in cyclohexanearound BPe. (-) Wilsonequation;(- -) NRTL equation with a12 = 0.47;(- - -) NRTL equation with 4 1 2 = 0.3 and 72 given by eq 10; NRTL equation with a12 = 0.3 and 72 given by eq 9; (- - -) NRTL equation with calculated a;(H) experimental values using eq 7. (-e)
around the solute. In general, this is the expected trend for solvents of approximately the same size, as observed in the case of phenol blue (Phillips and Brennecke, 1993). Thistrend was observed by molecular dynamics simulation for Lennard-Jones liquid mixtures by Narusawa and
0
0.2
0.4 0.6 Bulk mole fraction of toluene
0.8
1
Figure 6. Difference in local and bulk composition of toluene in cyclohexane around Py. (-1 Wilson equation; (- -) NRTL equation with a12 = 0.47;(- - -) NRTL equation with alp = 0.3;(- - -) NRTL equation with calculated a;(a)experimental values using eq 7.Note that NRTL predictions with a12 = 0.47 and with calculated a are essentially identical.
Nakanishi (1980) in the case where both solvents were of equal size but of different interaction energies. Also,they observed that the higher the interaction parameter ratio
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1359 Table 2. Physical Properties of Solvents at 26 O C pure solvent cyclohexane toluene ethyl butyrate acetone cyclohexanone acetophenone acetonitrile
0
0.2 0.4 0.6 Bulk mole W o n of ethyl butyrate
0.8
1
Figure 7. Difference in local and bulk composition of ethyl butyrate in cyclohexane around Py. (-) Wilson equation; (--) NRTL equation with a12 = 0.47;(- - -1NRTL equationwith a12 = 0.3;(- - -) NRTL equation with calculated a;(la) experimental values using eq 7. Note that NRTL predictions with a12 = 0.47and with calculated a are essentially identical.
I
0.35+
dipole moment (D) 0.0 0.45 1.74 2.88 3.01 3.02 3.92
molar volume (cm*/mol) 108.1 106.3 132.3 73.5 103.5 116.9 52.4
Table 3. Solubility Data for Benzo[ghi]perylene (BPe) and Pyrene (Py) in Each Pure Solvent at 21 O C solubility of BPe pure solvent (mole fraction) errop ( % ) cyclohexane 1.49 X lo-' 9.5 acetone 6.34 X lo-' 0.7 ethyl butyrate 1.16 X 1O-S 6.5 toluene 2.04 X 103 1.4 cyclohexanone 4.00 x 10-9 5.1 acetophenone 6.40 X 103 4.6 pure solvent acetonitrile cyclohexane6 ethyl butyrate toluene
solubility of Py (mole fraction) 0.00574 0.0114 0.0540 0.0665
erroP ( % ) 0.6 2.4 6.0 1.5
a Error = standard deviation/averagevalue.b Thevalueof 0.01089 was reported at 25 "C (Judy et al., 1987).
"W
0
I
I
0.2
0.4
I
0.6 bulk mole fractionof ethyl butyrate
I
+
0.8
1
Figure 8. Difference in local and bulk composition of acetonitrile in ethyl butyrate around Py. (-) Wilson equation; (--) NRTL equation with a12 = 0.47;(- - -) NRTL equationwith a12 = 0.3;(- - -) NRTL equation with calculated a; (a) experimental values using eq 7.
the greater the difference in the radial distribution function. Careful examination of the experimental results also reveals this trend. For BPe the deviation of x12 from X I is greater, the greater the dipole moment difference between the solvents: (x12 - XI)~ 0 . 2for toluene/ 3 acetone/cyclohexane; ~ 0 . 3 for 5 ethyl cyclohexane;~ 0 .for butyrate/cyclohexane; =0.4 cyclohexanone/cyclohexane; ~ 0 . 4 acetophenone/cyclohexane. 8 This was also observed for Py in the case of toluene/cyclohexane (0.1) and ethyl butyrate/cyclohexane (0.25). The differences between local and bulk mole fractions were somewhat smaller for pyrene than benzo[ghilperylene. This may be due to the fact that BPe is asymmetric and, as a result, slightly polar, which may result in stronger interactions with the more polar solvent. The dipole moments of the solvents are given in Table 2 to give an idea of the magnitude of the interactions with the various solvents. However, it must be remembered that the possible interactions are dipole/ dipole, dipole/induced dipole, as well as van der Waals interactions. We purposely tried to avoid solvents with the potential of creating specificchemical interactions with themselves, with each other, or with the solute (for example, alcohols). Interestingly, for Py in ethyl butyrate/ acetonitrile, although acetonitrileis the more polar solvent, ethyl butyrate was enhanced around the solute. Therefore,
in Figure 8 the difference reported is the increase in the local composition of ethyl butyrate around the pyrene. If one knows that acetonitrile/cyclohexane are immiscible while ethyl butyrate and cyclohexane are miscible, this result seems more reasonable. As one might then expect, the solubility of Py is lower in acetonitrile than in ethyl butyrate, demonstrating that van der Waals interactions can make a significant contribution to the strength of a solvent, in addition to dipole/induced dipole forces. Solubilities. Solubilities of the probes in the pure solvents are shown in Table 3. They follow the expected trend except for toluene and acetonitrile. That is, in general, solubility increases with dipole moment and polarizability of the solvent. The high solubility of the probes in toluene is probably due to some specific electron donor/electron acceptor complex involvingthe ?r-electrons of the probes. Pyrene has been reported (Takemura, 1976) to form such complexes with various aromatics, such as trinitrobenzene, although the specific case of toluene or acetophenone was not addressed. In the case of acetophenone, it is harder to say if such interaction does take place since it possesses a very large dipole moment and would be expected to have a high solubility, as observed, even in the absence of specific interactions. A detailed explanation of the possible specific chemical interactions between aromatic probes and solvents was given previously (Phillipsand Brennecke, 1993). The other exception to the increasing solubility with increasing solvent polarity trend is acetonitrile. While acetonitrile possessesthe highest dipole moment, its solubility is barely larger than that of cyclohexane in moles per liter and is the smallest in mole fraction, reemphasizing that the magnitude of van der Waals forces can be as large as dipole/ induced dipole forces.
Comparison to the NRTL and Wilson Equations The solubility measurements taken above allowed the computation of the activity coefficient of the probes in the pure solvents (72)through either of the following t,wo
1360 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 Table 4. NRTL and Wilson Interaction Parameters of Each Pure Solvent with Benzo[gh]perylene (BPe)
NRTL interaction param (112) pure solvent cyclohexane acetone ethyl butyrate toluene cyclohexanone acetophenone
= 0.3' all = 0.3 4.565 6.467 2.811 4.867 2.210 4.270 1.673 3.722 3.065 1.001 0.569 2.612
a12
= 0.47 4.719 3.260 2.657 2.100 1.429 0.964
a12
Wilson Param
a12 = eq 2b (712) 4.738(0.490) 4.436 3.282(0.480) 2.990 2.665(0.472) 2.114 2.092 (0.465) 1.097 1.396(0.454) 0.273 0.913(0.448) -0.021
a Using eq 9 with Ac,, while the next column is using eq 10 to compute 72. The numbers in parentheses are the a12 as given when using eq 2.
equations (Prausnitz et al., 1986):
(10)
once the solubility mole fraction is measured, since Tt, Ac,, and Ahfare known or can be estimated. Equation 10 is just an approximation of the preceding one, where the Ac, terms have been neglected and the triple point temperature has been replaced with the normal melting point, and possesses the advantage that measured values of ASf and Tmare available for the probes used. We used the following values: for BPe, ASf = 7.48 cal/(mol K), Tt Tm = 554 K (Casellato et al., 1973); for Py, ASf = 9.8 cal/(mol K), Tt T , = 423.8 K (Wong and Westrum, 1971). We estimated the liquid and solid heat capacities of the probes (Hurst and Harrison, 1992) as no values were available for these properties except for the solid heat capacity ofPy (Wongand Westrum, 1971). We found that for BPe cpa= 79 cal/(mol K) and cpl = 95 cal/(mol K). For Py the values are cps = 59.7 cal/(mol K), which compares nicely with the value of Wong and Westrum (1971 (cps = 54.9 cal/(mol K)), and cpl = 72 cal/(mol K). We computed the interaction parameters in the NRTL and Wilson equations using both the full equation (9) and its simplified version (10). Although including the Ac,'s changes the activity coefficients of the probes in the pure solvents,by a factor of approximately 8 for BPe, the activity coefficientsare changed by the same amount in allsolvents. Hence, both sets of interaction parameters for the NRTL or Wilson equation are highly correlated. Since, in calculating local composition, we are only interested in the difference of the interaction parameters, the effect of including or neglecting the Ac, terms on the prediction of local compositions is insignificant. This is shown in Figure 3. The values of 712 in the NRTL equation computed for a = 0.3 with and without the Ac, terms are shown in the first two columns of Table 4 and are correlated, as expected. Thus, had we included the Ac, terms in our previous work (Phillips and Brennecke, 19931, it would not have changed the predictions of the local compositions at all. However, it could give dramatically different values of the interaction parameters. Since our objective in this paper is to examine the measurements and predictions of local compositions, we continued the practice of using the simplified version. The interaction parameters were obtained from solubilities determined by UV-vis absorption spectroscopy with an independently determined Beer-Lambert law. Besides examining various values of a in the NRTL equation, there are no fit parameters in the thermodynamic models so they provide true predictions of the local compositions. We tested both eqs 7 and 8 for obtaining the local composition from experimental data. Acree's method (eq
-
-
Table 5. NRTL and Wilson Interaction Parameters of Each Pure Solvent with Pyrene (Py) NRTL interaction param ( ~ ~ 2 ) wilson pure solvent a12 = 0.3 a12 = 0.47 a12 = eq 2O param (712) acetonitrile 1.784 2.252 2.249 (0.467) 0.875 cyclohexane 1.117 1.572 1.543 (0.457) 0.910 ethyl butyrate -0.507 0.017 -0.057 (0.442) -0.487 toluene -0.695 -0.245 -0.374 (0.417) -0.927 a
The numbers in parentheses are the a12 a~ given when using eq
2.
8) seemed to yield similar but slightly higher values of preferential solvation, as shown in Figure 2. We concluded that for our systems, where the absolute intensity of the fluorescence did not change significantly from one solvent to another, eq 7 was adequate. Moreover, we preferred the equation using peak ratios since the peak ratios are easier to reproduce than absolute intensity. In general, it may be seen (Figures 1-8) that the Wilson equation dramatically overpredicts local composition in all cases, except for acetone/cyclohexane (Figure 3). In this case one should note that the size difference between the two solvents is the greatest (see Table 2) of the BPe binaries investigated here. More importantly, the smaller solvent in this mixture is also the more polar one; thus both its size and polarity are working to increase the local composition of the acetone around the probe. Since size differences are not taken into account in the analysis of the fluorescence data, this results in an apparent better fit by the Wilson equation. For the ethyl butyrate/ cyclohexane system (Figure 2) the somewhat smaller cyclohexane molecule is the less polar one. Since size effects are not taken into account in the spectroscopic measurements, this results in an apparent even greater overprediction by the Wilson equation. The qualitative trends of these observations of the influence of size differences are in agreement with those obtained by Narusawa and Nakanishi (1980) and by Gierycz and Nakanishi (1983)for molecules of equal and different sizes, using molecular dynamics simulation of Lennard-Jones mixtures. For the NRTL equation the value of a = 0.3, recommended for polar liquids (Renon and Prausnitz, 1968) and used previously (Phillips and Brennecke, 1993), did not yield good predictions. The choice of CY is somewhat arbitrary, and it appears that higher (0.47) values of a yield better predictions for the systems investigated in this study. In four cases (bothethyl butyrate/cyclohexane mixtures; cyclohexane/cyclohexanone; cyclohexane/acetophenone) the use of the a value given by eq 2 gave a very close prediction of the measured values. This equation consistently gave values of a close to 0.47, as can be seen in Tables 4 and 5, and it is remarkable that it worked relatively well since eq 2 was only recommended for miscible liquid systems. The only case were the NRTL overpredicts the local composition is for Py in the toluene/ cyclohexane mixture. This may be due to some specific interaction as extensivelydetailed previously. The NRTL equation mildly overpredicts the local composition of the toluene around BPe in the toluene/cyclohexane system, but it is harder to draw the conclusion of specific chemical interaction of toluene with the BPe based solely on the local composition measurements. However, like Py, the solubility of BPe in toluene is higher than expected, supporting the idea of specific chemical interaction between the toluene and BPe. For the acetonitrile/ethyl butyrate mixture, the preferred solvent is predicted by the models to be ethyl butyrate, as could be anticipated from the measurements of solubilities. This was confirmed
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1361 experimentally from the peak ratios, as mentioned above, although the preferred solvent was not the more polar solvent. Finally, the BPe and the Py probes yield very similar results for the toluene/cyclohexane and ethyl butyrate/cyclohexane mixtures, with the NRTL equation giving reasonably good predictions of the experimental results when eq 2 was used for the nonrandomness factors. As mentioned previously, the local composition enhancements around BPe are a bit higher than around Py. This is probably due to stronger solute-solvent interactions. Unfortunately the ground-state dipole moment of the probes are not known, but if Py was a flat molecule then it would have a zero dipole moment. One would expect the asymmetric BPe to be slightly polar. It turns our that Py is a folded molecule (slightly bent out of the plane) whose folding angle is thought to vary with the solvent (Waris et al., 1988),thus having a small groundstate dipole moment. Therefore, on the basis of these measurements, one might conclude that BPe is slightly more polar than Py, resulting in a larger preferential solvation of the more polar component around the BPe.
Conclusion In this study we have developed the use of fluorescence spectroscopy to obtain experimental estimates of local compositions around solutes in liquid solvent mixtures. The experimental results have been compared with both the NRTL equation and the Wilson equation. The following points can be made: 1. The extent of preferential solvation by the more polar solvent around the fluorescenceprobe benzouhil perylene followed the same order as for the absorption probe phenol blue: toluene/cyclohexane < acetone/cyclohexane < ethyl butyrate/cyclohexane < cyclohexane/cyclohexanone < cyclohexane/acetophenone. Since the fluorescence and absorption probes measure solvent strength by very different physical mechanisms, this emphasizes the usefulness of a variety of spectroscopic probes to provide information about the micro environment in mixtures. 2. The local composition of the more polar solvent was as much as 2.3 times that of the bulk. 3. In all but one binary the more polar solvent was preferred around the solute. The one exception, the acetonitrile/ethyl butyrate binary, demonstrates the important contribution of van der Waals forces to overall solvent strength. 4. The Wilson equation overpredicted the local compositions in all cases. 5. The NRTL equation provided better predictions of the local compositions, especially when a value of 0.47was used for the nonrandomness factor.
Acknowledgment is made to the National Science Foundation (GrantsNSF-CTS 90-09562and NSF-CTS 91-57087)for support of this work. Nomenclature G = NRTL or Wilson equation energy parameter R = gas constant T = absolute temperature Tt = triple point temperature T, = melting point temperature u = molar volume x i = bulk mole fraction of component i x i j = local mole fraction of component i around central molecule j Acp = difference in heat capacity between liquid and solid Ahf = enthalpy of fusion ASf = entropy of fusion
a = NRTL nonrandomness factor y = activity coefficient 7
= NRTL or Wilson equation energy parameter
Superscripts and Subscripts i = component i j = component j 1 = liquid s = solid max = maximum mixt = mixture
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Received for review October 26, 1993 Accepted February 8, 1994. Abstract published in Advance ACS Abstracts, March 15, 1994. @
