Raman Determination of Equilibrium Constants
Determination of Equilibrium Constants for Electron Donor-Acceptor Complexes by Resonance Raman Spectroscopy' Kirk H. Mlchaelian,2 Klaus E. Rleckhoff, and Eva-Marla Volgt* Departments of Chemistry and Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 (Received August 9, 1976; Revised Manuscript Received May 16, 1977) Publication costs assisted by the National Research Council of Canada
We describe a new method for the measurement of equilibrium constants for electron donor-acceptor complexes in solution which makes quantitative use of resonance Raman intensity effects in one of the components of the complex. This procedure was evaluated through its application to tetracyanoethylene complexes having methylbenzenes and methoxybenzenes as electron donors. The equilibrium constants calculated from resonance Raman intensities agree well with published data obtained by previously established methods, where comparative data are available, thus confirming the usefulness of the new method.
Introduction We present in this paper a new method for the determination of equilibrium constants (Kcm)for the formation of electron donor-acceptor (EDA) complexes in solution. In this technique, relative intensities in the Raman spectra of EDA complexes are used to calculate the degree of complexation of one of the components in solutions where initial concentrations are known; once the intensity changes with complexation have been determined for the component under consideration, each solution which is analyzed yields a value for KcAD. The change in the relative intensities of the C=C and CEN stretching bands in the Raman spectrum of tetracyanoethylene (TCNE) on complexation with aromatic electron which is a consequence of preresonance or resonance Raman (RR) ~ c a t t e r i n g ,arises ~ $ ~ from the proximity of the Raman excitation frequencies to the charge transfer absorption bands. TCNE EDA complexes having methyl or methoxy substituted benzenes as electron donors display large intensity changes in the TCNE v c e and Y C = ~bands with complexation when an argon laser is used for excitation; these bands are also red-shifted up to 20 cm-l with respect to their positions in the spectrum of uncomplexed TCNE.3 Since the intensity changes are more easily related to the degree of complexation of TCNE, they were chosen as the basis for the Raman determination of KCAD.TCNE complexes which have comparatively small equilibrium constants and show smaller intensity effects upon complexation (e.g., benzeneTCNE) were not examined, since the uncertainties in the Kcm for such complexes as calculated from the Raman spectra are of the same order of magnitude as the equilibrium constants themselves. The principal solvent used for the Raman determination of KcA"was CH2C1,; the reasons for selection of this solvent are given in the Results section. Other solvents used for dibromomethane and the Raman determination of KCAD, 1,2-dichloroethane, were chosen for similar reasons. Equilibrium constants for TCNE complexes in nonpolar solvents were not included in the present study, because of circumstances described below.
476,5,488.0, and 514.5 nm were used for excitation of the spectra. Excitation power was kept below 250 mW to avoid heating the solutions and affecting the equilibrium constants. Experimental equipment was the same as previously describedS6 Solutions which were used for Kcm determination had a total TCNE concentration of about 0.05 M. The concentration of complexed TCNE was generally between 5 X M, i.e., about 1-10% of the acceptor and 5 X was complexed in each solution. This meant that the intensity ratio of the vc=c band with respect to the v c E N band for each sample was intermediate between the complexed value and the uncomplexed value, and could be used to calculate the fraction of TCNE present which was complexed (see below). Solutions were prepared with concentrations [D] [A] in order to keep the occurrence of termolecular complexes to a minimum. The intensity ratios which appear in eq 2 were obtained as follows: Izu/Il, came from the spectrum of uncomplexed TCNE, the subscripts 1 and 2 referring to the Y C = ~and v * ~ vibrations, respectively. IzC/Ilc was obtained for each complex by examining solutions which contained a large excess of donor, and thus had most of the TCNE comin general depends on donor and on exciplexed; 12,/11, tation wavelength, so it was measured with all of the above-mentioned laser lines for every donor used. The other ratios were calculated as the products I2,/IlC = U2U/Il") ( I l u / I l c ) and I k / I I u = U 2 c / I l c ) ( I l c / I l J 9 where I l c / I h is the relative increase in V C intensity ~ on complexation. This intensity increase was determined by comparison of the VC=C intensity with that of a strong solvent band for a TCNE solution before and after the addition of sufficient donor to cause complexation of virtually all of the TCNE present. This use of a solvent band as internal standard compensated for the loss in overall intensity resulting from the absorption of the excitation light by the EDA complex formed in this process. The intensities of the bands were measured as peak heights. RepresentatiGe data of measured and calculated intensity ratios and their dependence on excitation wavelength described above are shown in Table I.
Experimental Section Raman spectra were measured in the VC=C (about 1560 cm-') and V C ~ N(about 2230 cm-l) regions for the TCNE EDA complexes in solution; all measurements were made at room temperature. The argon ion laser lines at 457.9,
Results The complexation of TCNE results in an increase in the from the value for unintensity ratio I(vc=~)/~(v~...N) complexed TCNE (about 0.5) to a larger value characteristic of the complex and of the excitation frequency
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The Journal of Physical Chemistry, Vol. 6 1, No. 15, 1977
K. H. Michaelian, K. E. Rieckhoff, and E. M. Voigt
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TABLE I: Intensity Ratios Used for the Calculation of KOADfor TCNE EDA Complexes in CH,Cl, Solutionsapb Excitation wavelength, I2ul Izcl I,cl Izcl Donor nm IIU IlU I1 c - I,, Durene 488.0 0.26 0.031 15 59 514.5 0.23 0.019 22 96 Isodurene 488.0 0.33 14 43 0.043 514.5 0.30 17 58 0.032 Pentamethyl488.0 0.31 0.016 36 115 benzene 514.5 0.32 0.010 188 61 Hexamethyl488.0 0.012 62 150 0.41 benzene 0.0068 110 275 514.5 0.41 a Uncertainties in the intensity ratios are less than 10% of their magnitudes. Subscripts 1 and 2 signify TCNE VC=C and ag v C = ~bands, respectively; c and u denote complexed and uncomplexed TCNE, respectively.
~ s e d In . ~a solution ~ ~ where a small fraction y of the TCNE is complexed, the vc=C and vcsN intensities originate both from complexed and from uncomplexed TCNE and an intensity ratio somewhere between the two limiting values occurs. This fraction is given by the ratio y = [AD]/[A],, where [AD] is the equilibrium concentration of the complex and [A], is the initial acceptor concentration. For the TCNE vc=c and ag VC-N intensities we thus have
*
0
Flgure 1. Intensity ratio of TCNE v m and vwN bands as a function of relative donor concentration for durene (+) and mesitylene (0and 0). The uncertainty in the observed I,/& is f0.2 or less. The excitation wavelength was 514.5 nm (+ and 0)or 488.0 nm (0).The curves show 11/12calculated from eq 2 and 3 for the following conditions: (a) KcAD= 3.3, excitation at 514.5 nm; (b) KcAD= 1.6, excitation at 514.5 nm; (c) K,AD = 1.6, excitation at 488.0 nm.
TABLE 11: Equilibrium Constants for TCNE EDA Complexes in CH2C12Solutions at Room Temperature ( - 21 O C)
+
1-Y Y (Izc / I l u ) + (1- Y N I 2 U /I,,
(2
where 11,and IZC are intensities per mole of complexed are intensities per mole of unTCNE, and 11,and IZu complexed TCNE. The equilibrium constant for the formation of the complex according to the relation D A + AD can be written
+
(3) where [D], is the initial donor concentration. When y is much less than 1, eq 3 reduces to y iz: K,ADID]O. The solvents used for Raman studies of EDA complexes must be chosen so that they satisfy certain criteria. The most important of these are the following: that the solvent dissolve both of the components of the complex in sufficient concentration that the Raman bands of interest are of reasonable intensity over a range of concentrations; that the solvent does not have Raman bands which interfere with the component bands to be analyzed; and finally; that the solvent does not interact strongly with either of the components. Since dichloromethane meets all the above criteria, it was chosen as the principal solvent for this investigation; moreover, equilibrium constants determined by other methods have been reported for many TCNE EDA complexes in CH2C12,so that a comparison of some of the Raman results with other published results is possible. In Figure 1 the dependence of 11/12on [DIo/[A]o for several different TCNE EDA complexes is shown. The infigure shows that for low donor concentrations 11/12 The Journal of Physical Chemistry, Voi. 8 1, No. 15, 1977
Donor
KCAD,M-'
l,c/I,&~b
o-Xylene m-Xylene p-Xylene Mesitylene Durene Isodurene Pentamethylbenzene Hexamethylbenzene Anisole o-Dimethoxybenzene m-Dimethoxybenzene p-Dimethoxybenzene 1,2,3-Trimethoxybenzene 1,2,4-Trimethoxybenzene 1,3,5-Trimethoxybenzene
0.42 i 0.15 0.50 i 0.18 0.52 i 0.19 1.6 i 0.6 3.3 i 0.4 4.7 -i. 0.7 7.4 i 0.6 17 i 2 0.52 i 0.14 1.0 t 0.3 1.0 i 0.3 1.0 t 0.3 0.84 i 0.30 1.2 t 0.3 1.3 t 0.3
75 i 75 i 75 i 75i 96 58 188 275 20 i 12i 30i 9 i 30 i 12t 45 i
25 25 25 25
5 3 10 3 10 3 10
a Intensity increase of the TCNE v c Z c band on complexation; excitation wavelength 514.5 nm. b Values quoted with uncertainties are estimated (see text).
TABLE 111: Equilibrium Constants for TCNE EDA Complexes in Solvents Other Than CH2Clzat Room Temperature ( - 21 C) Donor
Solvent
p-Dimethoxybenzene Hexamethylbenzene Hexamethylbenzene
CH2Br, CHzBr2 C,H,Cl,
KCAD,M-' 1.0 i 0.3 23 i 2 19 i 3
I,c/Ilua 9 f 3b 206 153
a Intensity increase of the TCNE v c Z c band on complexation; excitation wavelength 514.5 nm. b Estimated value (see text).
creases linearly with relative concentration, which follows from eq 2 and 3 when y l ~ results of the Raman and absorption methods for obtaining KcADare greatly a t variance with those derived from a calorimetric method.ll The equilibrium constants calculated from the Raman spectra, for solutions with [D] [A] (column 2, Table IV) agree well with those obtained from absorption spectra for solutions have [Dl >> [A] (column 3). Since only 1:l complexes are likely to occur when the donor concentration is comparable to that of the acceptor and the overall concentration is low, the consistency of these results affirms the assumption that only 1:l complexes occur under the condition [D] >> [A] for the complexes studied. Thus we conclude that the KcAD calculated from the Raman intensity ratios are the true equilibrium constants for the 1:l complexes. Further comment on the accuracy of the KcADdetermined from Raman spectra is possible in view of the results of NMR measurements of KcADfor 7r-a EDA complexes using, however, acceptors other than TCNE. The KcAD calculated from absorption spectra for solutions with [D] = [A] agree well with the NMR results, which are inde-
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Jerry E. Solomon
pendent of the relative concentration [D]/[A].12 The lack of relative concentration dependence in the NMR data implies that the same kind of complex is detected in each solution; by inference, that is the 1:1 complex. This indicates that the K:” determined by absorption spectroscopy for solutions with [D] = [A] are accurate equilibrium constants for the formation of 1:l complexes. Since the absorption and Raman results tend to agree, the Raman intensity ratio method is thus supported by the NMR method as well. Since the Raman method for K$” determination was not applied to TCNE complexes in nonpolar solvents (see above), we are unable to extend further the comparison of Raman results with published Kc-”’’.On the basis of the good results which we obtained for the TCNE complexes in CH2C12and similar solvents, we expect the Raman intensity ratio method to also prove successful for EDA complexes in nonpolar solvents. A verification of this prediction should be the next test of the Raman method for measuring equilibrium constants.
References and Notes (1)This research was supported by grants from the National Research Council of Canada to K. E. Rieckhoff and E. M. Voigt. (2) Present address: Department of Chemistry, Universlty of Toronto, Toronto, Ontario, Canada M5S 1Al. (3) K. H. Michaelian, K. E. Riikhoff, and E. M. Voigt, Chem. phys. Lett., 23, 5 (1973). (4) The bands in the Raman spectra of TCNE EDA complexes whlch in ref 3 were described as shifted or new donor bands have recently been found to be experimental artifacts. (5) K. H. Michaellan, K. E. Rieckhoff, and E. M. Voigt, Chem. Phys. Lett.,
30, 480 (1975). (6) K. H. Mlchaelian, K. E. Rieckhoff, and E. M. Voigt, Proc. Mtl. Acad. Sci. U . S . A . , 72, 4196 (1975). (7) R. X. Ewall and A. J. Sonnessa, J. Am. Chem. Soc., 92, 2845 (1970). (8) R. E. Merrifield and W. D.Phillips, J . Am. Chem. Soc.,80, 2778
(1958). (9) P. J. Trotter and D. A. Yphantis, J . Phys. Chem., 74, 1399 (1970). (10) R. Foster and I. B. C. Matheson, Spectrochim. Acta, Part A , 23, 2037 (1967). (11) W. C. Herndon, J. Feuer, and R. E. Mitchell, Chem. Commun., 435 (1971). (12) R. Foster, “Organic Charge Transfer Complexes”, Academic Press, London, 1969.
Raman Measurements of Temperature Effects on Self-Association in Glycerol Jerry E. Solomon Department of Physics, San Diego State University, San Diego, California 92182 (Received March 11, 1977) Publication costs assisted by the Department of Physics, San Diego State University
The effect of temperature on intermolecular hydrogen bonding in glycerol is studied by use of the OH Raman stretching band. The value of av,/aT for glycerol is found to be 3.4 f 0.3 cm-l/K as compared to 0.63 f 0.08 cm-l/K for methanol. The results are discussed in terms of the functionality of various alcohols and their relative glass-formingtendencies. An interpretation of the results is presented based on the “configurationalentropy” theory of glass formation.
I. Introduction The glycerol system represents an important class of hydrogen bonded glass formers, and we are currently carrying out measurements aimed at elucidating the role of hydrogen bonding in the glass formation process. Although the monofunctional alcohols such as methanol and ethanol form glasses fairly readily, there appears to be a significant difference in the glass-forming tendency of these simple alcohols and polyfunctional alcohols such as glycerol. In fact, glycerol forms a glass so readily that it is extremely difficult to crystallize this substance. As is well known,lp2 the OH stretching band, which appears in the infrared and Raman spectra of systems containing OH groups, is an extremely useful indicator in studies of hydrogen bonding, and our current studies utilize measurements of the shift in the peak of the OH stretching band, us, as a function of temperature to probe the role of hydrogen bonding in glass formation. In this article we wish to report some early results which we feel lend support to the notion that there are readily measurable quantitative differences in the glass-forming tendencies of mono-, di-, and polyfunctional alcohol^.^ 11. Experimental Section The measurements reported here were made in the standard 90° Raman scattering geometry using a Spectra-Physics argon-ion laser as the excitation source, and The Journal of Physical Chemistry. Vol. 8 1, No. 15, 1977
a Spex 1704 l-m monochromator. Both photon-counting and dc anode current measurements with an ITT FW130 photomultiplier tube were used in detecting the Raman signals. The samples are contained in a l-cm diameter tubing cross which is fused inside a dewar and cooled by flowing cold nitrogen gas. The glycerol samples were prepared by filtering and distillation to remove particulates and H20. The sample temperature was measured using a copper-constantan thermocouple and a digital voltmeter. The temperature measurement accuracy of the data presented here is f 2 K. The Raman spectra obtained with this system were wavelength calibrated using a lowpressure mercury discharge source, and wavenumber calibrated against standard spectra of spectroquality dimethyl sulfoxide (DMSO), CC14, and benzene. 111. Results and Discussion The results which we wish to report are shown in Figure 1, where we have plotted Y , as a function of temperature for both glycerol and methanol. Although infrared results for methanol have been reported previously,4 we felt it necessary to have a comparison based on samples run in the same system under the same conditions. The striking difference in behavior of the two systems is readily apparent from the figure. From our data we find the temperature dependence of v,, av,/aT, to be 0.63 f 0.08 cm-l/K for methanol and 3.4 f 0.3 crn-l/K for glycerol. In contrast with these results, Fishman and Chen5 find
