J. Phys. Chem. 1993,97, 6902-6906
6902
Molecular Interactions and Correlation Phenomena between Pressure Shift and Solvent Shift: A Spectral Hole-Burning Study H. Pschierer and J. Friedrich' Physikalisches Institut und Bayreuther Institut fir Makromolek filforschung, Universitbt Bayreuth, 0-8580 Bayreuth, Germany
H. Falk and W. Schmitzberger Institut fir Chemie, Johannes-Kepler- Universitbt, A-4040 Linz, Austria Received: March 4, 1993
We measured the pressure shift of spectral holes for four probe molecules, which differed in size, polarity, and charge, as a function of burn frequency. The solvent was in all cases the same, namely, ethanol/methanol glass. We found that the pressure shift depends in a linear fashion on burn frequency and that the associated slope is uniform despite the variation in the solute-solvent interaction. It seems to be a property of the solvent, solely. These findings can be well understood by assuming that the pressure-induced line shift is proportional to the solvent shift. In this case, the compressibility of the host glass follows directly from the slope of the pressure shift vs frequency data.
Introduction Pressure phenomena in the spectra of guest molecules reflect the structural details of the host lattice and the associated microscopic impurity lattice interaction.! The structural details of the lattice are reflected, for instance, in the solute-solvent pair correlation function and in material parameters .such as the compressibility. For a given structure of the host lattice, the spectral properties of an optical transition, such as its solvent shift or bandwidth, are determined through the microscopic interactions.2-s Under isotropicpressurechanges,the probe lattice interaction is changed and, consequently, an optical transition usually experiences a spectral shift, a line broadening, and a distortionof its line shape. For most organic dye probes in glasses, the inhomogeneousbandwidth is so large that one has to use very high pressures to induce measurable band shifts. An analysis of the associated pressure-induced broadening seems almost impossible. Moreover, all properties determined from spectral changes of the full inhomogeneous band are averages over the whole ensemble of guest molecules. Persistent spectral hole burning, on the other hand, offers the possibility of performing the same type of experiments on lines whose bandwidths can be almost as narrow as the homogeneous width of the transition involved. Correspondingly, extremely low pressure changes are needed to induce measurable line shifts and line-broadening phen~mena.~.'However, the most important aspect of pressure effects on spectral holes lies in the frequency selectivity of the Due to this frequency selectivity, specific subensembles of probe molecules, characterized by specificsolvent shifts, can be selected by tuning the burn frequency over the inhomogeneous band. Thereby, the solvent shift, which is usually considered as a fixed quantity characteristic for the system considered, becomes a parameter of theexperiment. It was shown by Laird and Skinners that the spectral shift of the holes per pressure unit varies in a linear fashion with burn frequency. Moreover, if one assumes that the pressure shift of a frequencyselected ensemble of probe molecules is proportional to its associated solvent shift, then the slope of the pressure shift vs burn frequency is completely determined by the compressibility of the host 1attice.SJ Since the interaction forceswhichdetermine the solvent shift are of rather short range, the compressibility measured this way is essentially a local compressibility. This is of no concern for homogeneous media because one averages over 0022-3654193f 2097-6902$04.00/0
a huge variety of local compressibilities,thereby measuring the bulk compressibility. But it is a very important aspect for nonhomogeneous media. Because of the local character, the technique can be used to measure in a straightforward way the compressibilities of mesoscopic particles such as globular chromoproteins.lO-l3 It was this aspect which triggered the present study. There are a rich variety of microscopic interactions between an organic dye impurity molecule and its surrounding solvent. There are short-range as well as long-range interactions and attractive as well as repulsive interactions. Not all of them contribute to the solvent shift or pressure shift, but they may, on the other hand, contribute to the line broadening. Hence, although theassumption of a proportionality between pressure shift and solvent shift seems to be rather plausible, it is nevertheless a strong restriction because of the variety of forces involved. The present work is aimed at checking the reliability of the pressure shift-solvent shift model. Our experimental approach is straightforward: We chose four very different probe molecules. They differ in size, shape, charge, symmetry, and polarity. These probe molecules were investigated by pressure-tuning hole burning spectroscopy in the same host glass, namely, in ethanol/methanol glass. The quantity on which we focused is the slope of the pressure shift vs burn frequency. It was our goal to find out whether this slope is significantly influenced by the probe-lattice interaction or whether this slope is a property of the host lattice, solely, as predicted by the simple pressure shift-solvent shift model. Experimental Section
The four probe molecules are shown in Figure 1: hypericin, protoporphyrin IX, resorufin, and dimethyl-s-tetrazine. They were dissolved in a 3:l ethano1:methanol mixture. The concentrations varied between 2 X 10-5 and 5 X 10-5 mol/L. At these concentrations, the optical density in the pressure cell could be kept between 0.3 and 0.6 in the maximum of the long-wavelength band. For the four molecules considered, this band is located between 15 900 cm-l (protoporphyrin IX) and 17 600 cm-l (dimethyl-s-tetrazine). Hole burning was performed in this red edge band. Since the solubility of protoporphyrin IX in ethanol/ methanol is extremely low, we dissolved it in dimethylformamide first. Then, this solution was diluted to 1:lOO with the ethanol/ methanol mixture. 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6903
Pressure Shift of Spectral Holes
pressure
4%
Hc
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/ MPa 1
2
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Figure 1. Probe molecules.
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frequency /cm-l Figure 2. (a) Absorption spectrum of hypericin in EtOH/MeOH. Temperature: 1.5 K. (b) Holes under pressure. The burn frequency is indicated by an arrow. Temperature: 1.5 K. In order to ensure isotropic pressure conditions, the solutions were sealed in small plastic bags. Pressure was transmitted via He gas. At 1.5 K, the temperature at which our experiments were carried out, the maximum pressure is 2.5 MPa. At higher pressures, He solidifies. The accuracy of the pressure control was about 10-3 MPa. Hole burning was performed with a ring dye laser or with a pulsed dye laser (dimethyl-s-tetrazine). In both cases, the holes were detected in transmission by scanning the laser over the spectral range where burning was performed. In pressure-tuning hole-burning spectroscopy,the initial hole shape is of no concern since it is only the pressure-induced shift and broadening which are measured. Hence, the initial holes were burnt to relative depths of 10-30% in order to ensure a good signal to noise quality. Figure 2b shows a hole as it broadens and shifts under increasing pressure. In all cases, the initial holes (0 MPa) could be well fitted to Lorentzian line shapes. The holes under pressure were fitted to
wavenumbers Figure 3. (a) Pressure shift of a spectral hole for three burn frequencies. Probe: hypericin. Temperature: 1.5 K. (b) Shift per pressure as a function of burn frequency. The inhomogeneous line is shown, too. Probe: hypericin. Temperature: 1.5 K.
a Voigtian shape. From this fit procedure, the parameters of interest, namely, the central frequency of the holeand the pressureinduced broadening, were determined. Repeated reversibility checks at the beginning and at the end of the whole pressuretuning procedure of a hole made sure that plastic distortions of the lattice did not occur and that the scanning procedure did not affect the hole shape. Protoporphyrin IX and resorufin were purchased from Aldrich and used without further purification. Dimethyl-s-tetrazine was purified by repeated recrystallization from solution. Hypericin was isolated from Hypericum perforatum L. and purified by droplet countercurrent chromatography according to ref 14. ReSdtS
Figures 2 and 3 show, for hypericin as an example, how the holes shift under increasing pressure as a function of burn frequency. Figure 2a is a survey absorption spectrum. All holeburning experiments were carried out in the prominent red edge band. A specific hole, burnt at the frequency indicated by an arrow, is shown in Figure 2b as it broadens and shifts under pressure. The pressure shift is to the red. In Figure 3a, we plotted the frequency shift as a function of pressure for three positions within the inhomogeneous band. We stress that the shift is perfectly linear with pressure. The shift per pressure unit increases as one goes from the blue to the red side. Figure 3b summarizes the pressure shift data: plotted is the shift per pressure unit as a function of burn frequency. The inhomogeneousband is also shown. The three arrows correspond to the data in Figure 3a. Clearly, the shift per pressure unit follows a linear frequency dependence. Figure 4 gives an overview of the frequency dependence of the pressure shift for the four dye impurity molecules. For representation purposes, the data of the various samples are vertically displaced. The frequency in this representation is measured with respect to the so-called vacuum absorption frequency v,, of the dye probes involved.15 vvacis characterized through the fact that, right at vvao the pressure shift vanishes. As can be seen in Figure 4, for dimethyl-s-tetrazine and resorufin, vvac is within the inhomogeneous band and can be measured directly. Also note
Pschierer et al.
6904 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 1
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Figure 4. Shift per pressure unit as a function of burn frequency for the four probe molecules studied. Note that the burn frequency is measured relative to vvSc,the frequency where the pressure shift vanishes. that the pressure shift changes sign as the burn frequency is tuned across vvac. We stress that for the four data series the dependence of the pressure shift on burn frequency is linear. The slopes of the associated straight lines are practically identical. Figure 5 shows how the pressure-induced broadening depends on burn frequency. Although the broadening differs significantly for the various dye probes, there is no significant frequency dependence.
Discussion There is a thorough theoretical treatment of pressure effects on spectral holes in the literature: The quantities of interest are the line shift, the pressure-inducedbroadening, and the associated line shape. We assumed, in agreement with the experiments, that the latter is Gaussian. The shift s and the broadening u are given by
u = [ N (a2(R))( 1 - p')] "'1ApI
(2)
respectively. Here, v(R) is the perturbation of the transition frequency of the dye probe by a solvent molecule at a distance Rand a(R)Ap is the changeof v(R) when the pressure ischanged by Ap: (3) K is the isothermal compressibility. The brackets indicateensemble averages, for instance
-
v(R) Putting this into eq 1 yields
-
1/R"
(5)
= (nK/3)(vb - V ~ a c ) ~ p
(6) A reasonable choice for n is 6 , as is the case for dispersion or higher order electrostatic interactions. Then, it is directly possible to determine the compressibility from the slope of the pressure shift as a function of burn frequency. Note that there is a sharp frequency where the pressure shift goes through zero and changes sign, when the burning laser is tuned through this frequency. Within the frame of eq 6 , this frequency is interpreted as the vacuum frequency vvac of the probe dye. Per definition, the difference V b - vvBcis the solvent shift of the subensembleof guest molecules selected with the laser frequency vb. Hence, eq 6 states that the pressure shift of a molecule absorbing at Vb is proportional to its solvent shift. We call this simple relation the pressure shift-solvent shift model. The conditions under which it holds are given by eq 5 or, equivalently, by the condition p2 1. At this point, we draw attention to the fact that pz 1 implies u = 0 (eq 2). Hence, under this condition, one would not expect any pressure broadening of the holes. We stress that, on a qualitative basis, eq 6 describes the experiments very well: The slopes of the pressure shift vs frequency data are perfectly linear, and for two dye probes, namely, resorufin and dimethyl-s-tetrazine, vvac can be directly measured because it falls into the frequency range of the inhomogeneousband. Indeed, we get pressure shifts to the red as well as to the blue. It is a very interesting observation that eq 6 seems to hold in a quantitative fashion, too. This follows from the fact, that, despite the differences in the microscopic forces between probe and solvent, the slope is constant. Hence, it has to be a property of the host material, as is reflected in the compressibility K. In the following, we will characterize the four probe molecules used and their specific interactions. Then, we will try to find arguments why, despite the variety of interactions and despite the fact that the holes broaden under pressure, eq 6 still holds.
- -
Characteristic Features of the Systems Investigated
(a)= i J d & g(R) a(R)
with g(R) being the radial dye-solvent two-particle correlation function. Vis the volume of the sample, and N is the number of solvent molecules. Accordingly, N ( v2(R)) is the square of the inhomogeneous width r and v, = N ( v(R)) is the average solvent shift, Le., the differencebetween thevacuum absorption frequency of the probe and the maximum vo of the inhomogeneous band. An important quantity is the so-called degree of correlation, p , defined as8J5 (4) = 1 if a and v are proportional, i.e., fully correlated, and p = 0 if there is no correlation. p can be interpreted as a measure of similarity between theinteraction patterns of probeand solvent molecules with and without pressure. p2
Within the frame of this model, there is a series of approximations involved: (i) The N-particle density correlation function can be factorized in a product of pair correlation functions involving the solute-solvent interaction only. (ii) The perturbation v(R) of the transition through the solvent molecules is pairwise additive. (iii) The density of the solvent is sufficiently high. A high density implies a Gaussian line shape for the inhomogeneous band as well as for the pressure-induced broadening kernel of the hole. The interestingcase, on which we focus in this paper, is obtained when p 1. Then, -R 6vJ6R v, and it follows immediately that
With the exceptionof dimethyl-s-tetrazine,the probe molecules lack inversion symmetry and hence have a dipole moment. However, even in the case of dimethyl-s-tetrazine, it can be concluded from the absorption spectrum that the symmetry of the ?r-electron system is lower than D2h and that the molecule is distorted in alcohol glass. Hence, it has a dipole moment, too. The distortioncomes from hydrogenbonding between the alcoholic solvent and the nitrogen atoms of the aromatic ring. Indeed, the spectrum in alcohol glass shows two origins, quite in contrast to the dimethyl-s-tetrazine in n-octane.l6 Then, since the solvent is polar too, there is, in all cases, a dipolar coupling between solvent and probe molecules. In addition to the dipolar coupling, all probe molecules are subject to the dispersion interaction. The dispersioninteraction dependson the polarizability of the molecule in its respective electronic state. Since the polarizability is higher in the excited state, the dispersion interaction leads always to a red shifta4 It falls off with distance as R-6. The dipole-dipole
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6905
Pressure Shift of Spectral Holes interaction, on the other hand, has different features. If the orientation of the matrix dipoles is random,there is no contribution to the line shift, but there is a contribution to the line broadening. The range of the dipolar forces in homogeneous solutions is long. However, in its immediate environment, the probe molecule may polarizethe solvent dipoles to some extent. The polarization gets frozen in as the liquid is cooled through the glass transition. This shell of polarized molecules then contributes to the line shift. The corresponding forces fall off as R6, too. Depending on the respective change of the dipole moment in the excited state, the line shift can be to the red or to the blue.213 If the shift is to the blue, these higher order electrostatic forces counteract the dispersion forces and the average solvent shift may be small. In such a case, vvrc may fall into the inhomogeneous band.1s Note that a corresponding compensation in the inhomogeneous line width is unlikely to take place. It is the square of the interaction which determines the inhomogeneous width, and cancellation effects can only occur if electrostatic and dispersive forces are strongly correlated." As for resorufin, it is charged, and, hence, it is subject to an ion-dipole interaction, in addition to the dispersive force and the various kinds of dipolar forces. Again, for random solvent dipoles, the ion-dipole interaction makes no contribution to the pressureinduced line shift, but it may contributeto the pressure broadening. However, as mentioned above, polarization of tbe solvent dipoles may occur through a combined interaction with charge and dipole moment of the impurity molecule. Yet, if the configuration of the solvent molecules is not changed through the probe excitation, there still will not be any contribution to a spectral shift because the charge remainsunaffected during such a process. A situation like this occurs when the dipole moment experiences a change in magnitudeonly, but not in its direction. These kinds of transitions do not couple to the lattice very strongly; hence, they are characterized by intense zero phonon lines and low intensities in the phonon wing. This seems to be the case for resorufin. Finally, apart from the various electrostatic forces and from the dispersive force, there is the short-range repulsive interaction. It seems that this interaction is the same for all probe molecules considered. However, as was argued by Laird and Skinner, this is not the case. There is a length scale involved which takes into account the different sizes of probe and solvent molecules. This length scale parameter affects not only the interaction but also the two-particle radial correlation function g(R). Hence, we considered it important to vary the size of the probe molecules, in order to get an impression of how this may influence the slope factor of the pressure shift vs burn frequency. Regarding the variety of interactions and their diversity in the various probe systems, we have to answer two questions: Why do the experimental results for the pressure shift so convincingly support a single type of interaction, 1/R*?And if so, how can we explain the pressure broadening?
-
Conclusions The most important parameter in eqs 1 and 2 is p, the degree of correlation. p determines, via the correlation function ( a v ) , the slope of the frequencydependenceof the pressure shift as well as the pressure-inducedbroadening. All relevant probe-solvent interactions are supposed to influence p. We have argued in the preceding section that the molecular interactions in our guest host systems arevery different. Yet we observe a constant slope. The only reasonable explanation seems that p is close to 1 and that the slope is determinedby a property of the host glass, namely, the compressibility. p 1 implies that the solute-solvent perturbation potential goes as P.If so, it is clear that it cannot be the repulsive part, which dominates v(R). Since electronic excitation blows up the probe molecules to some extent, pressure and solvent shift would be exclusively to the blue.18 It is also clear that the long-range
-
dipoledpole or ion-dipole forces cannot play a role since their random nature averages their contribution to the line shift to zero. What remains is the dispersion and the higher order electrostatic interactions. Both fall off as R-6. Consequently, according to eq 6, the slope of the straight lines in Figure 4 is given by 2K. Note that the higher order electrostatic forces lead to a blue shift, if the dipole moment in the excited state changes its direction or its size. Hence, the interplay between dispersive and higher order electrostatic interactions can indeed account for what we observe experimentally: a uniform slope factor of the pressure shift vs bum frequency and the Occurrenceof pressure shifts to the red as well as to the blue. It seems that what we observe in our pressure experiments is well accounted for by the R-6 terms in the impurity-solvent interaction. What could be a possible reason that the repulsive term in the potential does not seem to play an important role? We have the followingargument: The repulsive force originates from an atomatom interaction. Its influence, on a ?r-electron of the probe scales with the square of the molecular orbital coefficient a t the contact position, i.e., roughly with ( l / d z ) 2 , with z being the number of atoms in the dye probe contributing to the r-electron. We can now use a rough scaling argument: if the probe increases in size, the number of solvent molecules in the first shell increases roughly in the same fashion so that the total contribution of the repulsive forces to the solute-solvent interaction remains constant. In other words, this term is of the same size no matter whether a large molecule or small impurity ion interacts with the solvent. The dispersion forces, on the other hand, increase with the extension of the ?r-electron system because the polarizability increases. Due to the longer range of these forces, many more solvent molecules are involved and, hence, these forces may dominate the solute-solvent interaction. A similar argument holds for the higher order electrostatic forces. Although the results (Figure 4) are understood in a straightforward way by assuming that the R6 term dominates the solute-solvent interaction, a problem remains. An interaction of this type does not lead to a broadening (eq 2), since p2 = 0. How can this discrepancy be resolved? First, we note that the pressure-induced broadening depends on p in a quadratic fashion. As a consequence, small deviations of p from 1 can already lead to a significant line broadening. Second, we argued above that line shift and line broadening may result from different interaction terms with totally different properties. For example, for all four probe molecules there is a dipolar coupling to the solvent molecules. Because of the randomness of the solvent dipoles, it is only the width that is influenced, not the shift. The conclusion is that p = 1 in the line shift behavior does not contradict the simultaneous Occurrence of pressure broadening, since different interactions may be responsible. Third, even if the dipolar interaction between solute and solvent is absent, pressure broadening can occur. The dispersion and the higher electrostatic interactions have angular degrees of freedom. For the pressure-induced shift, this seems to be of no concern, since we can always averageover these angular degrees of freedom. However, for the line width, they can definitely make a significant contribution. They lift the degeneracy of the microscopic configurations of solvent molecules around an impurity probe which would prevail if the interaction would depend on R,solely. From the line-broadeningdata in Figure 5 , we even get some hint of the type of interaction which dominates the pressure broadening. It is obvious that the broadening per unit pressure is rather different for the various dyes, quite in contrast to the uniform slope in the pressure shift. For the largest impurity, protoporphyrin IX, it is smallest, and for the smallest impurity molecules, dimethyl-s-tetrazine, it is largest. This behavior obviously reflects the fact that the number fluctuation of closeby solvent molecules is larger for small probes.19 Consequently,
6906 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993
ce .15
m
-600
-300 vb-u,,,
/
0
l
300
cm-1
Figure 5. Broadening per pressure unit as a function of burn frequency.
we have to assume that it is the dispersion and (or) higher order electrostatic interaction which determine, via their angular degrees of freedom, the broadening of burnt-in holes under pressure. For the long-rangedipolarinteraction, there will not be any significant number fluctuation, because these forces are of infinite range.
Summary We investigated spectral holes burnt into the red edge origin of the absorption spectrum of a series of rather different probe molecules as they shift and broaden under pressure. The host glass was in all cases the same, ethanol/methanol glass. We focused on the color effect in the pressure-induced shift of the holes. The corresponding slope was the same for all the probe molecules investigated,whereas the pressure-induced broadening showed significant variations. From these observations, we concluded that the slope in the color effect of the pressure shift is a property of the host glass solely and is given by twice the
Pschierer et al. isothermal compressibility. We showed that this is the case when the solute-solventinteraction is dominatedby dispersion or higher order electrostatic forces. In this case, the pressure shift of a frequency-selected ensemble of molecules is proportional to the associated solvent shift. Of practical interest is the result that pressure shift tuning of spectral holes is a reliable technique for measurement of compressibilities by purely optical means. This is an important outcome for the applicationsof this technique to globular proteins.
Acknowledgment. We thank D. Haarer and L. Kador for valuable discussions. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 213-B15) and by the Fonds der Chemischen Industrie. References and Notes (1) Drickamer, H. G.; Frank, C. W. Electronic TransirionsandtheHigh Pressure Chemistry and Physics of Solids; Chapman and Hall: London, 1973. (2) Reichard, C. Solvent Effecrs in Organic Chemistry; Verlag Chemie: Weinheim, 1988. (3) Bayliss, N. S.; McRae, E. G. J . Phys. Chem. 1954,58,1002,1006. (4) Liptay, W. 2.Naturforsch. 1965, 20a, 1441. (5) Laird, B. B.; Skinner, J. L. J . Chem. Phys. 1989,90, 3274. ( 6 ) Richter, W.; Schulte, G.; Haarer, D. Opt. Commun. 1984,51,412. (7) Sesselmann, Th.;Richter, W.; Haarer, D. J. Lumin. 1987,36,263. (8) Gradl, G.; Zollfrank, J.; Breinl, W.; Friedrich, J. J. Chem. Phys. 1991, 94, 7619. (9) Reul, S.; Richter, W.; Haarer, D. Chem. Phys. Lett. 1991, 180, 1. (10) Zollfrank, J.; Friedrich, J.; Fidy, J.; Vanderkooi, J. J. Chem. Phys. 1991, 94,8600. (11) Zollfrank, J.; Friedrich, J.; Parak, F. Biophys. J . 1992, 61, 716. (12) Fidy, J.; Vanderkooi, J.; Zollfrank, J.; Friedrich, J. Biophys. J. 1992, 61, 716. (13) Zollfrank, J.; Friedrich, J. J. Opt. SOC.Am. 1992, 89, 956. (14) Falk, H.; Schmitzberger,W. Mowtsh. Chem. 1992, 123, 731. (15) Zollfrank, J.; Friedrich, J. J. Phys. Chem. 1992, 96, 7889. (16) Gradl, G.; Feis, A.; Friedrich, J. J . Chem. Phys. 1992, 97, 5403. (17) Zollfrank, J.; Friedrich, J. J . Phys. Chem. 1992, 96, 7887. (18) Saxton, M. J.; Deutch, J. M.J. Chem. Phys. 1974,60, 2800. (19) Kador, L. J. Chem. Phys. 1991,95, 5574.
