Anal. Chem. 1002, 64, 1763-1768
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Quantitative Resolution of Dual Fluorescence Spectra in Molecules Forming Twisted Intramolecular Charge-Transfer States. Toward Establishment of Molecular Probes for Medium Effects in Supercritical Fluids and Mixtures Ya-Ping Sun,?Gerald Bennett> Keith P. Johnston3 and Marye Anne Fox'*+ Department of Chemistry and Biochemistry and Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1167
A thermodynamlc equlllbrlum between tho locally exclted state and the twisted Intramolecular charge-transfer (TICT) state In p(dknethylamlno)benronltrlle and ethyl p(dlmethylamlno)benzoate Is used to probe unusual solute-solvent InteracttomIn supercrltlcal trlnuoromdhaneandcarbon dioxide mlxturer. WelI-deflned locally exclted state fluorescence spectra of the two moleculesare obtalnedthrough appllcatlon of prlnclpal component analyrlr. Ouantltatlve resolution of dual fluorescence spectra of the locally exclted date and the TICT state b accomplished by udng a comblnatlon of nonIlnear leastsquarer flttlng and prlnclpal component analysisselfmodellng, In whlch a new selfmodellng constraint Is Introduced.
INTRODUCTION Fluorescent probes have been widely used in the characterization of medium properties such as polarity and polarizability. Molecules forming twisted intramolecular chargetransfer (TICT) states are particularly useful in this regard. It is well established'-3 that in a polar medium p-(N,N-dimethy1amino)benzonitrile (DMABN) and ethyl p-(NJV-dimethy1amino)benzoate (DMAEB) form twisted intramolecular charge-transfer (TICT) states whose presence is signalled by a second fluorescence band red-shifted from the fluorescence band of the locally excited (LE) state. The relative fluorescencequantum yields of the two emissionsare dictated by a thermodynamic equilibrium between the two emitting states. LE s TICT Since the TICT state is more polar than the LE state, this equilibrium strongly depends on medium polarity and polarizability. The spectral maxima of the two emission bands are also polarity and polarizability dependent, making DMABN and DMAEB particularly amenable to be used as molecular probes in supercritical fluids. A unique feature of supercritical fluids is that their solvation properties can be continuouslyvaried over a wide range, from gaslike to liquidlike, making it possible to vary solutemedium interaction without changing the solvent. This property has found valuable applications in extraction4 and 'Department of Chemistry and Biochemistry. Department of Chemical Engineering. (1) Rettig, W. Angew. Chem., Int. Ed. Engl. 1986, 25, 971. (2) Lippert, E.; Rettig, W.; BonaEiC-Kouteck9, V.; Heisel, F.; MiehB, J. A. Adv. Chem. Phys. 1987,68, 1. (3) Sun, Y.-P.; Fox, M. A,; Johnston, K. P. J. Am. Chem. SOC.1992, 114, 1187. (4) McHugh, M.; Krukonis, V. Supercritical Fluid Extractions; Buttenvorths: Boston, 1986.
*
chr~matography.~In the density region near the critical density, solute-solvent interactions are much stronger than what would be expected from the dielectric continuum the0ry.~+8 Such unusual behavior is attributed to clustering of solvent molecules about the solute, creating a local environment where the effective solvent density is significantly higher than the bulk density. Because of this, prediction of solute-solvent interactions in supercritical fluids from existing theoretical models is very difficult. A quantitative experimental characterization of commonly employed supercritical fluids would therefore be very rewarding,consideringtheir wide range of existing and potential applications. An understanding of supercritical fluid mixtures or supercritical fluids containing cosolventa is particularly important. For example, mixtures of supercritical carbon dioxide with a polar cosolvent have been widely used in extraction and c h r ~ m a t o g r a p h y In . ~ ~many ~ cases, the presence of a cosolvent greatly improves the solubility of a solute, but it also introduces additional complexity to the interpretation of results. Clearly, characterization of solute-solvent interactions in these supercritical mixtures remains a challenge to modern solution theory, and well-established molecular probes are required for this task. In DMABN and DMAEB, the LE and TICT emission bands severelyoverlap. Therefore, a quantitative resolution of their spectral mixtures becomes a major task in the employment of these molecules as probes. With a successful spectral resolution, either spectral shifts in the LE or TICT bands or changesin the relative contributions of the two emission bands could be used as indicators for characterization of microscopic solvation. Spectral resolution has been recognized as one of the most difficult, but most useful, techniques in chemometrica.9 Leastsquares spectral resolution and principal component analysisself-modelingspectral resolution are among the most widely (5) Chester, T. L.; Pinketon, J. D. Anal. Chem. 1990, 62, 394R. Futakami, M.; Kobayashi, T.; Yamasaki, K. J. (6) (a) Kajimoto, 0.; Phys. Chem. 1988,92,1347. (b)Morita, A.; Kajimoto, 0.J. Phys. Chem. 1990, 94, 6420. (7) (a) Johnston, K. P.; Kim, S.;Combes, J. ACS Symp. Ser. 1989,406, 52. (b) Kim, S.;Johnston, K. P. Ind. Eng. Chem. Res. 1987,26,1206. (c) Kim, S.;Johnston, K. P. AIChE J. 1987,33,1603. (d) Johnston, K. P.; McFann, G . J.; Peck, D. G.; Lemert, R. M. Fluid Phase Equilib. 1989, 52, 337. (8) (a) Yonker, C. R.; Smith, R. D. J . Phys. Chem. 1988,92,235. (b) Frye, S. L.; Yonker, C. R.; Kalkwarf, D. R.; Smith, R. D. ACS Sym. Ser. Symp. 1987,329,27. (c) Brennecke, J. F.; Eckert, C. A. Am. Chem. SOC. Ser. 1989, 406, 52. (d) Brennecke, J. F.; Tomasko, D. L.; Peshkin, J.; Eckert, C. A. Ind.Eng. Chem. Res. 1990,29,1682. (e)Betta, T. A.; Bright, F. V. Appl. Spectrosc. 1990,44,1196,1203. (0Betta, T. A.; Zagrobelny, J.; Bright, F. V. Am. Chem. SOC.Symp. Ser. 1991, in press. (9) (a) Ramos, L. S.;Beebe, K. R.; Carey, W. P.; Sanchez, E. M.; Erickson, B. C.; Wilson, S. E.; Wangen, L. E.; Kowalski, B. R. Anal. Chem. 1986,58,294R. (b) Brown, S. D.; Barker, T. Q.;Larivee, R. J.; Monfre, S. L.; Wilk, H. R. Anal. Chem. 1988,60, 252R. (c) Brown, S. D. Anal. Chem. 1990, 62, 84R.
0003-2700/92/0364-1763$03.00/0 0 1992 American Chemical Society
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applied methods. In this paper, we report a quantitative resolution of spectral mixtures composed of the LE and TICT emissions of DMABN and DMAEB in mixed supercritical fluids based on a combination of principal component analysis-self-modeling and nonlinear least-squares spectral resolution methods, toward establishment of well-characterized molecular probes. A new self-modeling boundary condition based on photophysical properties of the studied systems is introduced and evaluated. The very unusual properties of supercritical CHF3-COz mixtures, as probed by the dual fluorescence of DMABN and DMAEB, are also discussed. EXPERIMENTAL SECTION Materials. DMABN (Aldrich 98 % ) and DMAEB (Aldrich 99 % ) were both repeatedly recrystallized from ethanol-water before being stored under vacuum for at least 12 h. Carbon dioxide (Liquid Carbonic 99.99%) and trifluoromethane (MG industry) were purified on a freshly packed column of activated carbon. Measurements. Fluorescence spectra of DMABN and DMAEB were measured on a computer-interfacedSLM Aminco SPF-5OOC emission spectrophotometer equipped with a 300-W Xe lamp using a right-angle geometry. All measurements were conducted in a high-pressure optical cell described elsewhere.1° A hexane solution of DMABN or DMAEB with known optical density was loaded into the cell. The hexane solvent was then evaporated carefully under a slow purge of nitrogen. The cell was then sealed and maintained at the required temperature. Fluorescence spectra of DMABN or DMAEB vapor in the cell were recorded using the multiple-averagingmode of the instrument. The experimentalapparatus is essentially the same as the one reported previously3 except that two syringe pumps filled with CHF3 and COz, respectively, were used. At the beginning of a measurement, CHF3 is gradually added to the optical cell until a certain pressure is reached. During this process, fluorescence spectra were measured. The CHF3 pump is then closed and COz is added with the second pump to create a series of supercritical CHF34302mixtures,to a total pressureof 5000psia. Fluorescence spectra of the sample DMABN or DMAEB were measured in these mixtures at a series of total pressures. All measurements were carried out at 40 "C.
RESULTS A N D DISCUSSION Principal Component Analysis. As one of the most widely employed methods in factor analysis, principal component analysis makes it possible to represent m experimental spectra in a k-dimensional vector coordinate ( k I m),if each of the m spectra is a linear combination of k pure-component spectra.11 In practice, the vector coordinate is constructed by k significant eigenvectors, V , (p = 1, k ) , and the other eigenvectors represent primarily experimental noise.12 Since an experimental spectrum in data matrix Di can be written as k
Di =
apiVp+ R,
p=l
where Ri is a residual vector, within experimental uncertainties, it can be characterized by a set of combination coefficients up (p = 1, k) in the k-dimensional eigenvector coordinate. Self-Modeling Spectral Resolution. Although k eigenvectors obtained from the principal component analysis for a k-component sysem allow m experimental spectra to be characterized by m sets of combination coefficients, neither (10)Yazdi, P.; McFann, G. J.; Fox, M. A.;Johnston, K. P. J. Phys. Chem. 1990,94,7224. (11)Malinowski,E. R.;Howery, D. G. Factor Analysis in Chemistry; Wiley: New York, 1980. (12)Beebe, K.R.;Kowalski, B. R. Anal. Chem. 1987,59,1007A.
S.C. 0.3
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al of combination coefficlents (a, and az)for DMAEB in CHF3-COZ mixtures (A).The limit for the TICT band (0) is determined using the Gaussian boundary condition. A plot of the standard devletlon (0)forfitting the constructed spectrum (based on a pair of combinatlon coefficients)to a Gaussian curve is also shown, and its minimum COTresponds to the limit. Flgure 1. Plot
the eigenvectors nor the combination coefficients have physical meaning. The physically meaningful solution for spectral resolution is the determination of k pure-component spectral vectors. A self-modeling spectral resolution is thus to determine k sets of combination coefficients that generate k pure-component spectra. For a two-component system ( k = 2), the most commonly used method for self-modeling is due to Lawton and Sylvestre.l3 The coefficients a1 and a2 will fall on a normalization line (Figure l),if each experimental spectrum is normalized so that the spectral area is set to unity. Obviously, the two sets of combination coefficients for the two pure-component spectra also fall on the line, corresponding to two points on the two out extremes. Determination of these two points, often called limits, requires two boundary conditions. If the two pure-component spectra do not totally overlap over the entire wavelength range, Le., if there is a t least one wavelength where component 1 has a contribution and component 2 does not and there is at least one other wavelength where the reverse applies, they constitute two boundary conditions for the two pure-component spectra. It is noteworthy that the two conditions, each determining a pure component, are independent of each other. In practice, determination of the limits can be somewhat ambiguous because of uncertainties in the experimental spectra. The introduction of additional boundary conditions, particularly those based on chemical properties of the system,14 is very helpful. In many cases, there is only one Lawton-Sylvestre type of condition present, which determines one pure component, and the other one has to be obtained on the basis of one or more other condition(s). Chemical properties such as the Stern-Volmer fluorescence quenching behavior have been applied in this regard.15 For dual fluorescence spectra of DMABN and DMAEB, the two underlying pure components are the LE and TICT emission bands. The boundary condition for finding the LE band is clearly available because there is a wavelength range a t the red onset where the LE band does not contribute. (13)(a) Lawton, W.H.; Sylvestre, E. A. Technometrics 1971,13,617. (b) Borgen, 0.S.; Kowalski, B. R. Annl. Chim. Acta 1985,174,1. (14)(a) Sun, Y.-P.; Sears, D. F., Jr.; Saltiel, J. Anal. Chem. 1987,59, 2515. (b) Sun, Y.-P.; Sears, D. F., Jr.; Saltiel, J.J. Am. Chem. SOC.1988, 110, 6277. ( c ) Sun, Y.-P.; Sears, D. F., Jr.; Saltiel, J.; Mallory, F. B.; Mallory, C. W.; Buser, C. A.J . A m Chem. SOC.1988,110,6974.(d) Sun, Y.-P.; Sears, D. F., Jr.; Saltiel, J. J. Am. Chem. SOC.1989,111, 706. (15)Saltiel, J.; Sears, D. F., Jr.; Choi, J.-0.;Sun, Y.-P.; Eaker, D. W.; Mallory, F. B.; Mallory, C. W. Unpublished results.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
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7
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aI
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Figure 2. Eigenvectors associated wlth the two large eigenvalues for the matrix of LE spectra of DMABN. The first eigenvector (A) corresponds to the smoothed LE band of DMABN and the second elgen-
vector (6) conslsts almost exciuslvely of reslduai experimental noise.
However, severe overlap between the LE band and the TICT band at the blue onset makes determination of the latter rather ambiguous. The Lawton-Sylvestre type boundary condition is therefore apparently not completely reliable in this case. Since the 0,Otransition at the twisted geometry of DMABN and DMAEB is very weak, the TICT state fluorescence is a hot emission in nature,' and its spectrum can be best approximated as a Gaussian function. This constitutes an additional boundary condition for the determination of the TICT emissionband. In our self-modelingspectral resolution, finding the limit for the TICT band is equivalent to finding a set of combination coefficients associated with a spectrum that can be best fitted by a Gaussian function. The calculational procedure can be explained by the results shown in Figure 1. By stepping along the normalization line a t the end corresponding to the TICT emission band, a spectrum is generated for each pair of combination coefficients. This spectrum is then fitted by a Gaussian function, and the fitting standard deviation is computed. Apparently, the minimum deviation (Figure 1)corresponds to the pair of combination coefficients from which the correct TICT emission band can be generated. L E Emission Bands of DMABN and DMAEB Vapor. Although the experimental spectra that we want to resolve are two-component systems, one of the components, the LE emission band, can actually be determined separately. Fluorescence spectra of DMABN and DMAEB vapor with 1 atm of COz as buffer gas were measured at 40 "C. It is conceivable that these spectra consist only of emissions from DMABN and DMAEB locally excited states. Because the vapor pressures of DMABN and DMAEB under the experimental conditions are very low and consequently because the fluorescence measurements had to be carried out near the sensitivity limit of our spectrometer, these spectra are quite noisy. Smoothing of the spectra was accomplished through the application of the principal component analysis. A data matrix composed of 30 experimental spectra of DMABN vapor, obtained by repeating the measurement 30 times, was prepared. Principal component analysis of the data matrix yielded three large eigenvalues 0.425, 0.124 X 10-3, and 0.110 X 10-3. Clearly, these values are consistent with the expectation of a one-component system. Shown in Figure 2 are the eigenvectors associated with the largest and the second largest eigenvalues. The first eigenvector is
Flgurs 3. Representativeexperimental spectra of DMAEB, normalized for the LE band, in pure CHFI (solld lines, in the order of increasing TICT band Intensity, P = 441 and 528 psia) and in CHF3-C02 mlxtures (dashed lines, in the order of decreasing TICT band intensity, total pressure P = 1060, 1136, 1441, 2232, and 4832 psia).
therefore the best estimate, in the least-squares sense, of the single-component LE emission band of DMABN vapor,lZ and the rest of the calculated eigenvectors are caused by experimental noise and can be discarded. For the second eigenvector, an almost exclusive contribution of random experimental uncertainties is evident (Figure 2). The smoothed LE emission band of DMAEB vapor was determined in a similar fashion. The data matrix for the principal component analysis was also constructed of 30 spectra and yielded three large eigenvalues of 0.362,0.211 X and 0.141 X 10-3. Again, the principal eigenvector corresponds to the smoothed LE emission band of DMAEB vapor. DMAEB in Supercritical CHFJ-CO~Mixtures. Fluorescence spectra of DMAEB were measured in pure CHFS, with the COZsyringe pump closed, at 40 "C at pressures up to 530 psia. The CHF3 pump was then shut off, and the second pump was used to gradually add COz to the fluorescence cell. Supercritical mixtures of COZ and CHF3 were prepared in the cell, and the mole fraction of CHF3 decreased as more and more COZwas added. Fluorescence spectra of DMAEB in these mixtures were recorded at a series of total pressures up to 5000 psia. Shown in Figure 3 are spectra obtained at representative pressures. A data matrix composed of 36 spectra of DMAEB, both in pure CHF3 (up to 530psia) and in CHF3-C02mixtures, treated by the principal component analyis, yielded the four large eigenvalues of 0.445,0.487 X lO-l, 0.196 X and 0.236 X 10-3. Because of the significant nonlinear effect from spectral shifts of both the LE and TICT emission bands, the third eigenvector clearly contains more than just experimental uncertainty, and the matrix is not a well-defined twocomponent system. Although there are few practical systems in which nonlinear effects are totally absent, the effect in this case is substantial,to the extent that the experimental matrix can no longer be reasonably treated as a two-component system. A quantitative application of the self-modeling spectral resolution method then becomes impossible. Nonlinear Least-Squares Spectral Resolution. Since the LE band of DMAEB vapor is available and the TICT band is known to be Gaussian, an experimental spectrum of DMAEB can, a t least in principle, be fitted by the following equation if the shape of the LE emission band does not change with pressure: 'T ,u'T ,J + + (1- xLE)G(;,~u
z(;) = xLdLE(;
(2)
where G(;,A;T,;*,,J is a Gaussian function with A;T and ;Tm being the TICT band full width at half-maximum (fwhm) and the band maximum, respectively,ILE(;) is the LE emission
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band observed for DMAEB vapor, and a; is the bathochromic shift of the LE band with increasing pressure. Each experimental spectrum is normalized in such a way that CIEXP(;)A; = 1
(3)
and so does the LE band. F?r a given is value, eq 2 has three parameters, XLE, A;T, and uT,. Among them XLE is a linear parameter, which can be separated from the other two (nonlinear) parameters in a nonlinear least-squares fitting. This separation greatly increases the stability of the regression. By minimizing the target function
i
(4) for XLE only, XLE can be written as
Combining eqs 2 and 5, we obtain
For a given is,eq 6 depends on two parameters Ah;T and ;Tm, which can be determined through a nonlinear regression employing eq 4 as the target function. The standard deviation corresponding to this target function is computed for each given value of us until a minimum is found, which corresponds to the best fit of the overall least-squares regression. As shown in Figure 4A, the LE band of DMAEB red-shifts with increasing pressure in pure CHF3 and then remains nearly constant as increasing amounts of COZare added. The shift of the TICT band follows a somewhat different pattern (Figure 4B). It red-shifts significantly with increasing pressure in pure CHF3 and then shifts back somewhat when increasing amounts of COZ are added. After the total pressure reaches 1350 psia, however, the TICT band maximum remains unshifted despite the continually increasing mole fraction of COz. The same pattern applies to the dependence of the relative contribution of TICT emission on the total pressure (Figure 4C). The accuracy of the regression procedures described above depends on how well the TICT band is defined. Spectral noise can be significant at low pressures because the contribution of the TICT emission is small, which in tucns causes too much flexibility in the regression for AvT and uTm and a rather slow convergence in the iteration (a too shallow minimum). It is therefore favorable to determine the TICT emission band from experimental spectra observed a t high pressures and then to use the obtained LE and TICT bands to fit those spectra ,to low pressures by assuming that the TICT band fwhm AUT is nearly pressure independent. Determination of the TICT band a t high pressures can be best accomplished by application of the self-modeling spectral resolution discussed in previous sections. A data matrix which consists of experimental spectra of DMAEB at high pressures (1400-5000 psia) and the LE band of DMAEB vapor (8nm red-shifted) was treated by principal component analysis. The four large eigenvalues are 0.164, 0.146 X 10-l)0.120 X and 0.159 X 10-5, indicating a welldefined two-component system. A plot of the combination coefficients is shown in Figure 1,where the TICT band limit was determined by the newly introduced boundary condition, namely minimizing the fitting standard deviation of the spectrum generated by the limiting combination coefficients
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Figure 4. LE band bathochromic shift (A), TICT band bathochromic shift (B), and the relative contributlon of the TICT band xTiCT(C) as a function of pressure for DMAEB in pure CHF3 (the left side of the dashed line) and In CHF3-C02 mixtures (the right side of the dashed Ilne), determined through a dlrect nonlinear least-squares fit (0)and by fixing the TICT band wldth (A).
to a Gaussian function (Figure 1). The TICT band obtained from the resolution is indeed a well-defined Gaussian with fwhm A;T of 6000 cm-l. That the data matrix composed of the shifted LE band of DMAEB vapor and mixture spectra of DMAEB observed at high pressures can be treated successfullyas a two-component system and resolved into a LE band and a Gaussian TICT band clearlydemonstrates that the LE emission band is indeed pressure independent, as assumed in the nonlinear leastsquares spectral resolution (eq 2). By fixing A i T in eq 6, a nonlinear regression of the experimental spectra of DMAEB discussed above becomes easier. The results, also shown in Figure 4, are in good agreement with those obtained previously by direct regression of both A;T and iTm.
DMABN in CHF3-COz Mixtures. Fluorescence spectra of DMABN in supercritical CHFB-CO~mixtures similar to those discussed above were measured a t 40 "C. In pure CHF3, the contribution of the TICT emission increases with increasing pressure, up to 500 psia. After that, the CHF3 pump was shut off and COZ was added to the fluorescence cell gradually up to a total pressure of 5000 psia. Since the formation of a TICT state in DMABN is somewhat more difficult than in DMAEB because of differences in their
ANALYTICAL CHEMISTRY, VOL. 84, NO. 17, SEPTEMBER 1, 1992 0
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is added. Again, this is not the case for the TICT band shifts of DMABN: in pure CHFB, the TICT band maximum redshifts with increasing pressure, and the further addition of COZthereafter causes the band maximum to shift to lower wavelengths (blue-shift). Such blue-shifts ceased a t a total pressure of 1350psia. The relative contribution of the TICT band to the total emission in DMABN depends on pressure (Figure 5C) in a somewhat different fashion from that in DMAEB (Figure 4C). In the low-pressure region (
