J . Phys. Chem. 1990,94, 1105-1 110 cusing and self-defocusing elements of the total nonlinear susceptibility. The noise is partially an artifact of the method of subtraction of the solvent’s conjugate signal. For example, if we subtract, point by point, our data from a hypothetical y = Ax2 representing the conjugate signal of the solvent in a region where the solvent signal is 1/2 of the total signal, our apparent signal-to-noise ratio decreases by a factor of 2. This effect is even more pronounced in the case where the particle signal is assumed in phase with the solvent signal (see Figure 3b). For this reason, it is difficult to say with certainty whether the saturation of the reflectivity in the 1-mJ pump energy region is total or partial. However, it should be noted that there was a significant variation in the conjugate signal’s far-field transverse spot size and structure, as observed pulse by pulse, which could result in a variation in the amount of light collected by the detectors. If the x(’) of the gold particles is due to more than one physical mechanism or if there is a nonlinear interaction between the particles and the solvent, then the phase may be intensity dependent. A mechanism dominant at low intensities may saturate at higher intensities resulting in the dominance of another mechanism and a possible change in phase. A complete determination of this functional dependence would clarify the dynamics of the nonlinear properties of gold spheres. It is already evident that the nonlinear susceptibility is huge for these particles. The
-
1105
phase conjugate reflectivity for pumping Au colloidal suspensions with less than 100 pJ is comparable with that of CS2,currently the standard of high-speed highly nonlinear materials. Given that the volume fraction is -4 X lod, this indicates a nonlinear susceptibility for gold particles which is -4 orders of magnitude higher than that for CS2.
Conclusions We have determined experimentally the intensity dependence of the picosecond phase conjugate reflectivity in gold colloids for pump intensities on the order of 1 GW/cm2, investigated the intensity dependence of sample damage, and determined the phase of the nonlinear susceptibility of gold colloids via interferometric methods using a C W mode-locked Nd:YAG laser and have also recognized the significance of the phase relationship of the nonlinear susceptibilities in a multicomponent system. This is significant in an applications environment since the functional intensity dependence could have its shape “tailor-made” by adjusting the stoichiometry of the constituents. Acknowledgment. This research has been supported by the Air Force Office of Scientific Research Grant F29601-87-KO057 and by Rockwell International Corp. Grant B8X197858. Registry No. Au, 7440-57-5.
Ultraviolet and Visible Charge-Transfer Absorption and Emission Spectra of Some Polar Dyes In Aqueous Solution under High Pressure’ Lorrie Comeford and Ernest Grunwald* Chemistry Department, Brandeis University, Waltham, Massachusetts 02254 (Received: June 1 , 1989; In Final Form: October 6, 1989)
The ultraviolet and visible absorption and emission spectra of aqueous solutions of four dyes, 4-amino-4’-cyanobiphenyl,carbostyril 124, coumarin 1, and coumarin 102, and the absorption spectrum of 4-nitroaniline were measured at pressures up to 6 kbar. The compressions produced red shifts or, in one case, virtually no shifts. The variations of vmx with pressure were reproduced by linear equations. The largest red shift was for the absorption of 4-nitroaniline, where the slope was -107 cm-’/kbar. The slopes for the two coumarin dyes were remarkably different, considering the similarity of their structures. Established theory of dielectric solvation effects on Franck-Condon transition energies was modified to apply to solvents of high dielectric constant and predicted pressure effects whose magnitude is small compared to observation. A quasi-thermodynamicapproach was more encouraging. Because the charge-transfer excited states are zwitterions, the hypothetical excitation process at equilibrium is attended by a large decrease in volume due to electrostriction of the solvent. Thus there is marked volume strain in the Franck-Condon final state. The decrease in volume was estimated for three of the substrates and accounts for a major part of the pressure shifts.
Medium effects on electronic transition energies have long been used as probes for solvation Especially useful have been the intramolecular charge-transfer transitions D-R-A D+-R-A- and their reverse, where the symbols D and A denote an electron donor and acceptor group, and R denotes an intermediate structure which provides a resonance p a t h ~ a y . ~Such ,~ transitions produce large changes in polar character as the polar substrate D-R-A changes to a zwitterion D+-R-A- whose electric dipole consists of two discrete monopoles. Moreover, London dispersion interactions with solvent are also relatively large, especially when the resonance pathway is long’ (as in merocyanine
-
(1) Dedicated to Professor Harry Drickamer on the occasion of his 70th birthday and retirement. (2) Scheibe, G.; Bruck, D. Z . Elekzrochem. 1950, 54, 403. (3) Kosower, E. M. J. Am. Chem. SOC.1958, 80, 3253, 3261, 3267. (4) Kamlet, M. J.; Abboud, J. L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1981, 13, 485. ( 5 ) (a) Dimroth, K.;Reichardt, C.; Siepmann, T.; Bohlmann, F. Liebigs Ann. Chem. 1963, 66/,1. (b) Reichardt, C.; Harbusch-Goernert, E. Ibid. 1983, 5, 721. (c) Tamura, K.; Imoto, T.Bull. Chem. SOC. Jpn. 1975, 48, 369. (6) Buncel, E.; Rajagopal, S. J. Grg. Chem. 1989, 54, 798.
0022-3654/90/2094- 1 105$02.50/0
dye molecules, for example), and hydrogen-bonding solvation can be significant, especially when the groups D and A are exposed to solvent. In this paper we report the effect of pressure on charge-transfer transition energies for five substrates in aqeuous solution at 25 OC. The substrates are 4-amino-4’-cyanobiphenyl(I), carbostyril 124 (11), coumarin 1 (111), coumarin 102 (IV), and 4-nitroaniline (V); structural formulas are given in Scheme I. Pressures range up to 4-6 kbar, in which range there are substantial changes in water properties. At 25 OC, between 1 atm and 5 kbar, the liquid density increases by 15.2%,8 the dielectric constant by 18.8%: and the refractive index by 3.8%.1° Substrates I-IV were measured both in absorption and emission, while 4-nitroaniline could be measured only in absorption. The latter substrate pro(7) (a) Grunwald, E.; Price, E. J. Am. Chem. SOC.1964, 86, 4517. (b) Grunwald, E.; Fong, D.-W. J . Phys. Chem. 1969, 73, 3909. (8) Grindley, T.; Lind, J. E. J. Chem. Phys. 1971, 54, 3983. (9) (a) Lees, W. L. Ph. D. Thesis, Harvard University, 1949. (b) Sciafe, B. K. P. Proc. Phys. Soc. London 1955, B68,790. (c) Srinivasan, K.R.; Kay, R. L. J. Chem. Phys. 1974,60, 3645. (10) Vedam, K.; Limsuan, P. J. Phys. Chem. 1978, 69,4772.
0 1990 American Chemical Society
1106
Comeford and Grunwald
The Journal of Physical Chemistry, Vol. 94, NO. 3, 1990
SCHEME 11: Dipole Moments for I and V from Ref 17a and 35"
SCHEME I
CK
Q NH*
6 +
' -0
t
N
+'o -
pi-6.1
0
+I
vided a welcome comparison with a prior measurement by Hamann and Linton at 2 kbar." The pressure dependence of vmax for the measured absorption and emission peaks of these substrates was generally linear. The four compounds whose band maxima were studied in emission showed very similar pressure dependences of Y,, ranging from -40 to -60 cm-l/kbar. In absorption, on the other hand, the pressure effects on uSbswere quite diverse, ranging from -107 to +2 cm-'/kbar. Pressure effects on (vah - uem) accordingly were also diverse, and in fact ranged from -27 to +44 cm-'/kbar. In a polar solvent such as water, the polarization induced by a polar solute molecule is nearly all due to orientation of solvent permanent dipoles; distortion of electron clouds is relatively unimportant. In a Franck-Condon transition the orientation polarization remains unchanged, and the configuration of the final solvation shell is that of the initial state. In the statistical average, this is normally the equilibrium solvent configuration of the initial state, because the average lifetime before a transition tends to be long compared to the dielectric relaxation time of the solvent. In the present case, the excited states are zwitterions with large dipole moments-for example, 16 D for I and 15 D for V;I7 see Scheme 11. Thus at equilibrium, the orientation of solvent molecules around the excited states is likely to be dominated by electrostatic interactions. On the other hand, the ground states of these substrates are less polar, and one may assume that, at equilibrium, structure-specific nonelectrostatic van der Waals interactions with solvent, especially London dispersion forces, are relatively important. An important property of zwitterions is that the electric forces generated by the ionic poles are strong enough to compress the surrounding solvent.12 As a result, apparent molal volumes of zwitterions tend to be smaller than those of uncharged structural analogs. This electrostriction can be quite large. In water, the order of magnitude is -10 mL/mol.13 ( I I ) Hamann, S. D.; Linton, M. Aust. J . Chem. 1975, 28, 701. (12) Drude, P.: Nernst, W. Z. Phys. Chem. 1894, 15, 79.
D
7
p,-5.6 D(est.)
(111)
'The ground-state dipole moment for 111 was estimated from data in
ref 36.
Pressure effects on absorption and emission spectra in polar solvents are often plotted vs [(e - 1)/(2t + 1) - (n2- 1)/(2n2 + l ) ] , or vs [(e - I ) / ( € 2) - (n2- l)/(n2 + 2)], where t denotes the dielectric constant and n the refractive index."J4J5 Such plots are suggested by more general theories of medium effects in Franck-Condon t r a n ~ i t i o n s ' ~ Jbut ~ * ' ~assume specifically that solvation energies in the initial and final states may be approximated by the interaction energies of the respective permanent dipoles with their reaction fields. This approximation is most likely to apply if the electronic transition produces a large change in dipole moment, so that other interactions, especially those arising from dispersion forces, are relatively small. In such cases, the approximation should be especially appropriate when applied to the difference (uah - v,,).I4 On introducing data for t and n, one then predicts that in water, (uabs - )u, should decrease consistently for all substrates, by -0.5 to -l.l%/kbar. Since in fact the pressure effects on (uah - vem) for our substrates were variable and of a different magnitude, ranging from -0.25 to +0.9%/kbar, we took a fresh look at the approximate theory and found an inconsistency. As summarized in the Appendix and derived in the supplementary material,I8 if one makes the same assumptions as given above,
+
(13) Edsall, J. T. In Proteins, Amino Acids ond Peptides; Cohn, E. J., Edsall, J. T., Eds.; Reinhold: New York, 1943; Chapter 7. (14) Lippert, E. 2.Nuturforsch. 1955, IOU, 541. Lippert, E. Z. Phys. Chem. ( N . 0 1956,6, 125. (15) Robertson, W. W.; King, A. D. J . Chem. Phys. 1961, 34, 1511. (16) McRae, E. G. J . Phys. Chem. 1957,61, 562. ( I 7) (a) Liptay, W. In Excited States; Lim, E., Ed.; Academic Press: New York, 1974; Vol. 1, pp 129-229. (b) Liptay, W. In Modern Quantum Chemistry Isionbul Lectures; Sinanoglu, O.,Ed.; Academic Press: New York, 1965; Part 11, pp 173, 190-196. (18) See Supplementary Material Available paragraph at the end of this article.
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1107
Spectra of Polar Dyes
TABLE I: Pressure Effects on Charge-Transfer Transitions in Water at 25 O C ; Fit of Eq 1‘
a
mabm
compound
cm-I / kbar
(1) 4-amino-4’-cyanobiphenyl (11) carbostyril 124 (111) coumarin 1 (IV) coumarin 102 (V) 4-nitroaniline
-87 f 16 -16 f 10 -37 f 15 2 f 17 -107 f 9
mem,
cm-l 32 460
cm-l/kbar -6Of 15
29 280 26 200 25 680b 26 370
-60 f 15 -43 f 16 -40 f 15
(V.b6)0,
(Y,,)o,
cm-’
21 680 24 180 21 390 20 520
- mem,
cm-l/kbar -27‘ 44c 6c 42‘
Within experimental error, f30 cm-I, the intercepts agree with corresponding values of vmar measured at 1 atm. bf40. c&22.
Coumarin 1 (Eastman Kodak) was recrystallized from ethanol/water. This yielded pale yellow hexagonal plates; mp 70-71 OC (lit. 73 0C).23 Coumarin 102 (Eastman Kodak) was recrystallized from ethanol/water giving yellow needles; mp 152.5-1 53 OC (lit. 151-1 52
om hro;rot;&J;
~
oq.24
0 Optical WT Cell
Lamp Monochrmtor
Figure 1. Schematic diagram of the spectroscopic setup. The unlabeled square to the left of the optical cell houses the beam splitter. (uab - uem) should vary according to eq A.2 and, in water at 25 OC, should increase by +O.l%/kbar. The solvent refractive index does not enter the final relationship. The fact that this prediction also fails to reproduce the details of our results suggests that interactions other than those of solute dipoles with their reaction fields are highly significant.
Experimental Section Measuring System. The spectrometer, Figure 1, consisted of two McPherson monochromators, a scan controller, Hamamatsu photomultipliers, a Canrad-Hanovia lamp, and a high-pressure optical cell. These components were mounted on an optical bench. The high-pressure optical cell, Model 545.0043-1, and the associated pressure generating system, Model 560.0024, were purchased from Nova Swiss in Effretikon, Switzerland. An attractive feature of this high-pressure apparatus is that the solution being studied also serves as the hydraulic fluid, thus eliminating the need for an interface between two different liquids. The pressure generating system, as received from the manufacturer, worked for a short time up to 6 kbar but then developed leaks. Guided by our experience, the manufacturer then modified the seals on the handpump, and eventually stable pressures up to 4 kbar could be obtained reliably with aqueous solutions. Another problem was that the fittings which held the sapphire windows in the optical cell were deformed by the force needed to seal the windows. We found it necessary to replace them every time the cell was cleaned (Le., when a new solution was introduced). A description of the system, of our experimental checks for accuracy, and of details of the cleaning, tilling and pressurizing of the optical cell are reported el~ewhere.’~ In typical experiments, wavelength was scanned over a 50-nm range. The photomultiplier signals of the reference and sample were stored on a Gould digital oscilloscope and processed by an IBM PC. Peak assignments could be made with a reproducibility of *50 cm-I. The two monochromators were calibrated for wavelength accuracy. Linearity of photomultiplier response and absence of absorbing impurities in the pressure system were checked regularly. The water used for preparing the solutions was spectroscopically pure. Materials. Carbostyril 124 (Eastman Kodak) was recrystallized from a minimum of ethanol. This yielded large white crystals; mp 287-288 OC (lit.: 270.4-272 OC; 281.5-282 oC).20v2’ The maximum of the fluorescence band for the aqueous solution occurs at 416 nm (lit. 415 nm).22 (19) Comeford, L. L. Ph. D. Thesis, Brandeis University, 1989. (20) Wheelock, C. E. J . Am. Chem. SOC.1959, 81, 1348. (21) Woods, L. L.; Fooladi, M. M. J . Chem. Eng. Data 1968, 23, 440.
4-Nitroaniline (Aldrich) was recrystallized from a minimum of ethanol yielding large yellow crystals; mp 150.5-1 52.5 “C (lit. 148-149 0C).25 4-Amino-4’-cyanobiphenyl, I, was synthesized in two steps following the method of Ruolene and co-workers.26 In the nitration step, 4-cyanobiphenyl (Trans World Chemicals; 10 g, 0.056 mol) was dissolved in 100 mL of acetic anhydride. The solution was cooled in an ice bath. Fuming nitric acid (20 mL, 0.5 mol) was added dropwise to the stirred solution. A pale yellow precipitate of 4-nitro-4’-cyanobiphenyl formed. The mixture was stirred further at room temperature for 20 min and was then added to water. The precipitate was then removed by filtration, dried, and recrystallized from a 1:1 mixture of acetone and 1-propanol to yield pale yellow crystals; mp 198-200 OC (lit. 200-201 oC).26 The yield was 30%. In the reduction step, SnCl2.2Hz0 (14.4 g, 0.64 mol) was dissolved in concentrated hydrochloric acid (1 3 mL, 0.16 mol), and this solution was added dropwise to that of 4-nitro-4’cyanobiphenyl(3.5 g, 0.016 mol) in 75 mL of hot 2-propanol. The resulting reaction mixture was heated at reflux for 10 min, cooled to room temperature, and made alkaline with 5.0 M aqueous KOH. A yellow precipitate formed. The precipitate was filtered out and the filtrate was extracted four times with 25 mL of benzene. The benzene solution was dried over magnesium sulfate, the benzene was removed with a rotary evaporator, and the residual solid was recrystallized from 2-propanol to give a 32% yield of pale orange crystals; mp 184-185.5 OC (lit. 186-188 0C).26 Preparation of Solutions. 4-Nitroaniline, carbostyril 124, and coumarin 1 are soluble enough in water to allow solutions to be prepared by standard methods. Solutions of coumarin 102 and 4-amino-4’-cyanobiphenyl in water were prepared by making a saturated solution of the compound, filtering the supernatant liquid from the crystals, diluting the saturated solution by 10-25%, and measuring the final concentration spectroscopically. We used the following molar extinction coefficients (t), which were measured in ethanol. For coumarin 102, t = 2.36 X IO4 L/(mol cm), and for 4-amino-4’-cyanobiphenyl, t = 1.88 X lo4 L/(mol cm).
Results The absorption and emission spectra were recorded by using aqueous solutions in the concentration range (1-10) X M. Sample absorption spectra of a solution of 4-nitroaniline at 0.5 and 6.0 kbar are shown in Figures 2 and 3. A sample spectrum of the emission of coumarin 1 is shown in Figure 4. The assignments of the maxima were made graphically. (22) Hammond, P. R.; Fletcher, A. N.; Henry, R. A,; Atkins, R. L. Appl. Phys. 1975, 8, 3 11. ( 2 3 ) Kodak Laboratory Chemicals Catalog; Eastman Kodak: Rochester, NY, 1985; p 130. (24) Reynolds, G. A. US. Patent 3 932 415; Chem. Absrr. 1976, 84, 1234098. (25) CRC Handbook of Chemistry and Physics, 66th ed.; Weast, R. C., Ed.; CRC: Boca Raton, FL, 1985; p C-73. (26) Ruolene, Y . I.; Adomenas, P. V.;Adomenene, 0. K.; Denis, G. I. Zh. Org. Khim. 1984, 20, 1310.
1108 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
Comeford and Grunwald 26400$
26300
36B
388 398 Uauelenrth (m1
378
h
418
488
Figure 2. Absorption spectrum of 1.3 X lo4 M 4-nitroaniline in water at 0.5 kbar.
I 1
2
3
4 p‘l:)c,r)
5
6
Figure 5. Plot of vmar vs p for 4-nitroaniline. 0 p t i
1.w
C
1
11.988
I
t c I
8.W
S
i
t Y
1.71 I
I
I 3en
~
I
I
I I
t 1.188 e I I
i t 8.988 U
8.788
1.5881
158
’
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I
I
’
178
1
$88 Ylb,ciclcth In)
Figure 4. Emission spectrum of 4.8 X kbar.
I
1
I 191
I
1 5 1
M coumarin 1 in water at 2.0
When the frequency of the maximum of the band (umax) is plotted as a function of pressure, the resulting relationship is linear to within experimental error as in eq 1, where m denotes the fitted slope. The results for the absorption of 4-nitroaniline, shown in umax
= MP +
(vmax)o
(1)
Figure 5, are typical. The line drawn in the figure was computed by a least-squares alg~rithm.~’Results of the linear fits for our substrates are summarized in Table I. In each case the error (27) Wentworth, W. E. J . Chem. Educ. 1965, 42, 96.
of fit is within the experimental error of the data, and the intercept ( u , , , ~ , )is ~ consistent with the experimental value of umax at 1 atm. The standard deviations of the parameters listed in Table I are based on the experimental errors. It can be seen from the slopes given in Table I that, with one possible exception, the maxima of the bands shift toward lower frequency with increasing pressure. The possible exception is the absorption maximum of coumarin 102, but within one standard deviation that slope, too, could be negative. The largest negative slope is for the absorption of 4-nitroaniline. The result reported here is in satisfactory agreement with previous work in aqueous so1ution.l’ It is interesting to compare that slope with a similar result for ma&obtained in heptane solution.28 The initial slope for the heptane solution is 3 times the slope in aqueous solution, in agreement with prior observation that pressure shifts in aqueous solutions can be smaller than those in other solutions.29 No emission data are reported for 4-nitroaniline because it does not fluoresce in aqueous solution at room temperature. The results for the two coumarin dyes are striking in light of the dyes’ similar structures. In absorption, their slopes are very different, -37 cm-I kbar-I for coumarin 1 and 2 cm-’ kbar-I for coumarin 102. In emission, on the other hand, the slopes are nearly equal. For comparison, the solvent shifts (Av,,,) from water to cyclohexane are similar for the two compounds, although the shifts in emission are more than 30% greater than in a b ~ o r p t i o n . In ~~ the system ethanol/water, on the other hand, the solvent shifts are more complicated and show different dependences on percent water in absorption and emission.30a The last column in Table I gives the difference of the slopes for absorption and emission. It should be noted that these values are quite variable, both in magnitude and sign. The absorption maxima for carbostyril 124 are somewhat less accurate than those for the other substrates. This is because the absorption “band” of carbostyril 124 really is the convolution of two bands. The more intense of these is represented by the data in Table I; at 1 atm, its A, is 342 nm. The second band has ,A, near 327 nm. The corresponding emission consists of a single band. Carbostyril 124 exists predominantly in the keto form in its ground state.30b Discussion The pattern of the results in Table I is complicated and, as stated in the Introduction, interactions other than those of solute (28) Sawamura, S.; Taniguchi, Y.; Suzuki, K. Bull. Chem. Soc. Jpn. 1980, 53, 1898. (29) Zipp, A.; Kauzmann, W. J . Chem. Phys. 1973, 59, 4215. (30) (a) Jones 11, G.; Jackson, W. R.; Choi, C.; Bergmark, W. R.J . Phys. Chem. 1985,89,294. (b) Albert, A.; Phillips, J. N. J . Chem. Soc. 1956,1294. Mason, S . F. J . Chem. SOC.1957, 4874, 5010.
Spectra of Polar Dyes
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1109
I
0: vs
sign on the left in (4b). On expressingp in kilobar, Vin mL/mol, and v in wavenumbers, and introducing the appropriate conversion factor, one obtains eq 5 at constant T. Subtraction of (5b) from (dvab/dp) = 8.36(Vh - Vg) + 4+18(Vg- Vh)’(dkh/dp) 2.79( V, - Vh)3(dlh/dp) (Sa)
*:
0:Vh
+
(dvem/dp) = 8.36(Vh - V,)
- 4.18(Vh
- VK)’(dkK/dp) 2.79( vh- VK)3(dlK/dp)(5b)
(sa) then yields (6). Note that, in (6), the pressure dependence Figure 6. Free energy state diagram in the quasi-thermodynamic approach. States A and B are at equilibrium, A‘ and B’ are final states for Franck-Condon (FC) transitions. (1) represents AGOph, the standard free-energy change at equilibrium; (2) represents AG,,; (3) represents AG,; and (4) and (5) represent the volume-strain energies Gstrain,hand Gstnin,gin the respective Franck-Condon final states.
dipoles with their reaction fields appear to be significant. In particular, for charge-transfer transitions, mechanical volume strains are important in the final states. This is because processes of the type D-R-A D+-R-A- at equilibrium are attended by substantial decreases in apparent molal volume, owing to electrostriction of the solvent by the zwitterionic charges of D+-RA-.I3 Thus the solvent around newly formed D+-R-A- in a Franck-Condon absorption is strained by being expanded, since it still has the molecular density in equilibrium with D-R-A. Similarly, the solvent around newly formed D-R-A in a Franck-Condon emission is strained by being too dense. Because electrostrictive volume changes can often be predicted, we shall interpret the measured pressure effects using a quasithermodynamic approach. While one may not claim that this approach can simplify inherently complex problems, it may clarify their scientific interpretation by looking at them from a different point of view. In the following, the subscript g will denote the ground state, h (for “high”) the excited state, and eq the existence of equilibrium. Vg and Vh denote the partial molar volumes of the respective species at equilibrium. VStrain denotes the volume strain: Vstrain -- V,, - Vq,in a nonequilibrium state. Other notation is defined in the caption to the free-energy state diagram of Figure 6. Using these definitions one obtains eq 2. Although eq 2 makes no
-
AGabs = =
AGog-h -AGog-h
+ Gstrain.h
(2a)
+ Gstrain,g
(2b)
assumptions about the interaction mechanisms contributing to GStrain, we shall proceed on the assumption that the dominant contribution comes from volume strain and see where that will take us. We shall therefore represent Gs,rainas a function of the single variable VStrain. The simplest approximation is a harmonic function: Gstrain= I/&( Vstmin)’.However, because in the present problem V,,i, is relatively large, we shall add an anharmonic term. On expressing V,,,, as a function of Vh and VKaccording to Figure 6, we obtain eq 3. Gstrain,h = l/Zkh(Vg - Vh)’ Gstrain.g
=
?2kg(Vh
- Vg)’
+ (1/3)lh(V g - Vh)3
(3a)
+ (1/3)1g(Vh - Vg’8)3
(3b)
Equations for the pressure dependence are readily derived from (2) and (3). For the standard free-energy change the thermodynamic expression is (dAGo,,h/dp)T = (Vh - VK).In the range of interest, (Vh - V K )may be treated as independent of pressure since our results are represented by linear equations of the form ( I).31a Hence we obtain (4) at constant T . Note the negative NOhc(dvabs/ap) = (dAGabs/dp) = (Vh - Vg) + f / z ( V g - Vh)Z(akh/ap) + (I/3)(Vg - Vh)’(dih/dp) (4a)
= -(Vh - V,) + l/Z(Vh - Vg)’(akg/ap) + (1/3)(Vh - Vg)’(alg/m (4b)
-Nohc(dvem/dp) = (dAG,,/dp)
- v e ~ n l / ~ p=) 4‘18(Vg - Vh)Z(a[kh + k g l / d p ) + 2.79(vg - vh)3(a[1h - lg]/ap) (6) of AGog-.h cancels out, and the right side of the equation depends solely on the pressure dependence of the strain energies. Moreover, the assumption that Gstminis dominated by the volume strain ( VK - Vh) is optional. On the other hand, if a similar analysis is made in terms of Gstrain,without specifying the nature of the strain, the resulting eq 7 are general. (dvahs/dp) = 8.36([Vh - Vg1 (dvem/dp)
= 8*36([Vh -
Vgl
+ [dGstrain,h/dpl) - [dG~train,g/dpl)
(7a) (7b)
(d[vabs - vemI/dP) = 8.36(a[Gstrain,h + Gstrain,gI/dP) (7C)
-
We shall now estimate (Vh - VK)for substrates 11, 111, and I v by methods of analogy. (V, - V.) for the process D-R-A D+-R-A- consists of two parts: an intrinsic volume change as the benzenoid ground state is converted to a quinonoid excited state, and a volume change due to the marked electrostriction of the solvent. While the intrinsic volume change probably is not zero, it is almost certainly small compared to the volume change caused by electrostriction, and we shall neglect it. The electrostriction is evaluated by comparing the measured apparent molal volume ( VOb)of the zwitterion with its intrinsic volume (V,,,,), the latter being determined by additivity rules or from molal volumes of uncharged isomers measured in the same s o l ~ e n t . ’ ~In~water, ~ ~ * ~the ~ electrostriction ( Vobs- V&) has thus been evaluated for a number of amino acid zwitterions and for their quaternary N+ analogues, the betaine^.^'^^^ For amino acid zwitterions, the electrostriction is typically -1 3 to -1 6 mL/m01.~’ For betaine itself it is -8 mL/mol, and for betaines with aromatic part structures it is -5 to -10 mL/moL3j The aromatic betaines strike us as suitable models for the excited states of I11 and IV because the plus charge in these structures resides on alkyl-substituted N’, and thus we estimate that (vh - VK)for I11 and IV is between -5 and -10 mL/mol; we shall use -8 mL/mol. Similarly, the amino acids serve as models for the excited state of I1 because the plus charge now resides on N+ with hydrogen substituents, and thus we estimate (Vh - V,) for 11 to be about -13 mL/mol. Using these estimates, the contribution of the g h equilibrium to (dv/dp)is about -70 cm-’/kbar for I11 and IV, and about -1 10 cm-’/kbar for 11. On comparing these values with the experimental results for emission (Table I), one finds31b from (7b) that the effect of is pressure on the strain energy in the ground state, dGstrain,K/ap, around -30 cm-’/kbar (-360 J/kbar) for 111 and IV, and around -50 cm-l/kbar (-600 J/kbar) for 11. On comparing the g h equilibrium values with the experimental results for absorption, one finds that the effect of pressure on the strain energy in the excited state, dGstrain,h/dp,is positive, amounting to +90, +30, and +70 cm-l/kbar for 11, 111, and IV, respectively. In summary, in the three cases in which model data for estimating (Vh - V,) are available, the quasi-thermodynamic treatment indicates that the pressure dependence of the strain energy is negative for the ground state and positive for the zwitterionic
-
-
would be a nonlinear (31) (a) If a( V, - V,)/ap were significant, AGO function of p , and so would the strain energy. (b) Ginstance, for 111, using eq 7b and the value for mcmin Table I, -43 = -70 - aGs,,in,/ap. (32) Cohn, E. J.; McMeekin, T. L.; Edsall, J. T.; Blanchard: M. H. J . Am. Chem. SOC.1934, 56, 784. (33) Edsall, J. T.; Wyman, J. J . Am. Chem. SOC.1935, 57, 1964.
J . Phys. Chem. 1990, 94, 11 10-1 113
1110
excited state. It also indicates that the value is more sensitive to substrate structure in the excited state than in the ground state but that result can be derived directly from the data in Table I and does not require any estimation of (vh- V,). The change in sign of the pressure dependence of the strain energy, on the other hand, does depend on the estimates of (V, - V,). We believe that the change in sign is real, and the preceding equations permit it. If we assume, as before, that the strain energy is dominated by volume strain according to eq 3, and that I, and Ih have the same sign (k, and kh are both positive), the pressure dependences of Gstrain,*and Gstrain,h would have opposite signs if the anharmonic term, Le., the term in (AU3,were dominant. Considering the size of AV, that is distinctly possible. Strains by other mechanisms may also have opposite signs in the FranckCondon ground and excited states. For instance, the deviation of the reaction field from equilibrium, for the present substrates, is positive in the Franck-Condon ground state and negative in the excited state. Acknowledgment. This work was supported by a grant from the National Science Foundation. Appendix In this section we shall summarize a derivation based on the model of polarizable point dipoles interacting with their reaction fields. The derivation shows that, for a Franck-Condon transition taking place in a medium of high dielectric constant, (vah - vem) is independent of the solvent refractive index. In addition, it predicts that, in our experiments, the contribution to the pressure effect on umax due to the interaction of dipoles with their reaction fields is quite small. The full derivation is presented as supplementary material.l8 Let subscript 1 denote the solvent, i the electronic ground state of the solute, and k the electronic excited state of interest. Let e l denote the dielectric constant of the solvent, aiand a k denote molecular polarizabilities, and ai and ak denote radii of the cavities containing the respective solute molecules at solvation equilibrium. Thus in a Franck-Condon absorption [i k], the cavity radius is ai; in a Franck-Condon emission [k i], it is ak. Furthermore, let = 2(c1 - 1)/(2tl + l), yi = ai/ai3and yk = ak/a2. We shall treat the dipole vectors pi and C(k as parallel. (The full derivationI8 does not make this assumption.) These vectors are precisely parallel for substrates I and V, and nearly
--
so for 11, 111, and IV; sample vector diagrams and predicted excited-state resonance structures are shown in Scheme 11. Upon treating fii and pk as parallel, the solvation energy difference derived in the supplementary material (eq S.15) reduces to eq A.l. r
To reduce the number of unknown parameters, two further assumptions are often made.I4-l6 (i) ai and ak are assigned a common value a which is treated as independent of the medium. (ii) yi and Y k are assigned a common value y. As a corollary of (i) and (ii), ai= a k . On introducing these assumptions, (A.1) simplifies to (A.2). For polar molecules in liquid dielectrics, y hC(vabs - vem) = 2(1.(k- Wi)''#'l/[a3(1 - '#'IT)]; ai = ak; ai = ak; pi and pk are parallel (A.2) is always C1 and typically between 0.25 and 0.5." For the present substrates, y = 0.4. On using that value and introducing values of e l for water as a function of pressureg at 25 OC, one finds that a In (vah - ve,)/dp is +O.OOl/kbar. Values of (va& - (v,& in Table I are about 10000 cm-I for I and 5000 cm-' for 11,111, and IV. Hence a(vah - vem)/apis predicted to be +10 cm-'/kbar for I and +5 cm-'/kbar for 11, 111, and IV. Registry No. I, 4854-84-6; 11, 19840-99-4; 111, 91-44-1; IV, 4126776-9; V, 100-01-6.
Supplementary Material Available: General derivation of eq A.l and vector diagram of dipole moments (8 pages). Ordering information is given on any current masthead page. (34) Bottcher, C. J. F. Theory of EIectric Polarization; Elsevier: New York, 1952; Chapter 3. (35) Baumann, W. J. Mol. Struct. 1978, 47, 237. (36) (a) Exner, 0. Dipole Moments in Organic Chemistry;Georg Thieme: Stuttgart, 1975. (b) Ananta Krishnan, S.V.; Jacob, P. J. Indian J . Chem. 1969, 7, 234. (c) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, 1963; p 349.
Shock Wave Compression of Mixtures of Powders with Liquefied Gases G . A. Adadurov and V. I. Goldanskii* N . N . Semenov Institute of Chemical Physics, USSR Academy of Sciences, Ulitsa Kosygina, 4, 1 1 7334, Moscow, USSR (Received: June 1 1989; In Final Form: October 13, 1989) ~
A new approach in physical chemistry at high pressures has been theoretically proposed and experimentally confirmed. The approach is based on shock compression of solid particles placed in liquefied gas with preservation of the products after compression. Shock compression of such heterogeneous systems has been shown to result in very high temperature states with subsequent rapid and deep cooling of the solid phase due to heat dissipation into the evaporating gas which expands after compression during the isentropic decrease of pressure. The cooling promotes preservationof the shock-formed metastable structures. As a result of specific combinations of high pressures and temperatures, usually inaccessible and insufficiently known regions of the P,T-state diagram can be achieved.
Introduction The physical chemistry of shock compression is based on proin which mechanisms and kinetics are determined by specific conditions appearing during the shock wave (sw)passage through the sample. In the experiments with preservation of substance in ampules, isentropic unloading waves rapidly lower the pressure
0022-3654/90/2094-11 l0$02.50/0
and temperature. The rate of cooling at this stage is estimated to be 10' K/s.' However, due to the irreversible nature of shock compression, samples remain heated even after the pressure relief. This often results in the annealing O f structural changes which (1) Adadurov, G. A. Russ. Chem. Rev. 1986, 55, 282.
0 1990 American Chemical Society
