J. Phys. Chem. 1983, 87,4815-4822
TABLE 11: Thermochemical Data for Ketenea
EA(HCCO),eV AH' acid( CH,CO ), kcalimol DH" 298( H-CHCO), kcalimol AHfl 298(CH,CO),bkcalimol AHfo298( HCCO), kcalimol AHf 198( HCCO -), kcalimol
2.350 * 0.020 365 ?: 2 105.9 * 2.1 -11.4 t 0.4 42.4 k 2.1 -13.3 t 2.1
a In these calculations, P ( H ) = 313.6 kcal/mol and This value A H * ' ~ ~ ~=( H 52.1 ) kcalimol have been used. has been reported in ref 24.
rection factors is uncertain but is probably not more than f0.010 eV; consequently the final electron affinities are EA(HCC0) = 2.350 f 0.020 eV and EA(DCC0) = 2.350 f 0.020 eV. Thermochemistry. The enthalpy change for the process HA A- + H+ is defined as the gas-phase acidity (moa&& From this definition, the thermodynamic cycle
-
mo,,id(HA) = DHo(HA)
+ IP(H) - EA(A)
(12)
can be derived, where the ionization potential of hydrogenZ3is 313.6 kcal/mol. If either DHO (the A-H bond strength) or moa,.id is known, the other can be derived if EA(A) is available. Because we have found m o a c i d (CHzCO) as 365 f 2 kcal/mol and an EA(HCC0) of 2.350 f 0.020 eV, we find DHoZg,(H-CHCO) = 105.9 f 2.1 kcal/mol. The heat of formation of ketene has recently been remeasured by Vogt et al.;24 they find AHfo29s(23) D. R. Stull and H. Prophet, 'JANAF Thermochemical Tables", NSRDS-NBS-37, 2nd ed, National Bureau of Standards, Washington, DC, 1971. (24) J. Vogt, A. D. Williamson, and J. L. Beauchamp, J. Am. Chern. SOC.,100, 3478 (1978).
4815
(CHZCO) = -11.4 f 0.4 kcal/mol. Consequently the bond dissociation energy of ketene can be used to find the heat of formation of the ketyl radical, HCCO. We find mf0298(HCCO) = 42.4 f 2.1 kcal/mol. Finally we wish to extract a value for A&ozgs(HCCO-). The heat of formation is obtainedz5from the EA as follows: A"f0zg8(HCCO) - AHfo2g&HCCO-)= EA(HCC0) + (5/2)RT (13) In (13) (5/2)RT is the integrated heat capacity of the electron, 1.481 kcal/mol.26 It follows from our EA(HCC0) of 2.350 f 0.020 eV that the heat of formation of the ion, A&'"f098(HCCO-),is -13.3 f 2.1 kcal/mol. These thermochemical values are summarized in Table 11. Acknowledgment. We thank Chris Moylan, John Jasinski, and John Brauman for communicating the results of their ketene ICR experiments to us. We have also enjoyed several conversations with Barrie Peel about the CCO radical. This work has been supported by the Department of Energy (Contract No. DE-AC02-80ER10722), the Petroleum Research Fund, administered by the American Chemical Society, and the Army Research Office (Contract No. DAAG29-81-K-0169 [to G.B.E.] and DAAG29-82-K-0025[to V.M.B.]). GBE thanks the Alfred P. Sloan Foundation for a fellowship. Registry No. CCO-, 87191-88-6;HCCO-, 64066-01-9;DCCO-, 87191-89-7;CCO radical, 87191-90-0; HCCO radical, 55349-28-5; ketene, 463-51-4. (25) S. G. Lias in "Kinetics of Ion-Molecule Reactions", P. Ausloos, Ed., Plenum, New York, 1979, pp 223-54. (26) We use AHfozss(H+)= 367.2 kcal/mol. (27) C. R. Moylan, J. M. Jasinski, and J. I. Brauman, private communication.
Holographic Relaxation Spectroscopy of a Benzospiropyran in Mixtures of Water and Dioxane Danny G. Miles, Jr., Patrick D. Lamb, Kee Woo Rhee, and Charles S. Johnson, Jr.' Department of Chemistry 045A, University of North Carolina, Chapel Hill, North Carolina 27514 (Received: May 5, 1983)
The photochromic spiropyran derivative l-(~-carboxyethyl)-3,3-dimethyl-6'-nitrospiro[indoline-2,2'-2~benzopyran] permits the establishment of laser-induced gratings in aqueous solutions and thus is a potential label for biomolecules. Holographic relaxation experiments have been performed on this spiropyran in water/dioxane mixtures using UV radiation (330 nm) for x(H,O)= 0-0.8 and visible light (514 nm) for 0.8-1.0. Also, the lifetimes of the photoexcited states were measured. The diffusion coefficients for the spiropyran were obtained by analysis of the time dependence of the laser-induced gratings. In phosphate buffer (pH 7.5, 20 "C)the diffusion coefficient is (4.19 f 0.02) X lo4 cmz/s. Diffusion measurements were possible down to spiropyran concentrations of 0.01 mM, the lower limit being determined by the low repetition rates which were required in signal averaging by the long lifetimes of the photoexcited states.
I. Introduction Diffraction of light by transient laser-induced gratings has been used in recent years for the study of transport phenomena under the name forced Rayleigh scattering (FRS).'t2 A similar experiment designed to investigate the (1) Eichler, H.; Enterlein, G.; Munschau, J.; Stahl,H. Z. Angew. Phys. 1970, 31, 1-4. (2) Pohl, D. W.; Schwarz, S. E.; Irniger, V. Phys. Reo. Lett. 1973,31, 32-5.
kinetics of photochemical reactions has been called holographic photo~hemistry.~The principles of these holographic experiments are easy to grasp. In a typical experiment two beams derived from the same "writing" laser are superimposed in an absorbing sample, thus forming an interference pattern with a fringe spacing which depends on the crossing angle of the beams. The absorption (3) Brauchle, Chr.; Burland, D. M.; Bjorklund, G. C. J.Phys. Chern. 1981,85, 123-7.
0022-3654/83/2087-4815$0 1.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
4016
Miles et ai.
o=c\ OH
o=c\ OH
n
.......... ..,:,:.: ::.:.:...... .................. ............... :.:.:: :::j:j:j.j:.:j:j:j:.:j:::,::::::::i .................
i l
Flgure 1. Diffraction of a “reading” laser beam from a volume hologram for which the scattering vector has the magnitude K = 2 n / A The shaded areas represent molecules in photoexcited states.
of light inevitably causes a change in the absorbance and the refractive index of the sample, and a grating (volume hologram) is created which can diffract light from a probe “reading” laser. The situation is illustrated in Figure 1. When the writing beams are switched off, the time dependence of the amplitude of the induced hologram is determined by transport and reaction processes in the sample. This rate information can be recorded by monitoring the time-dependent intensity of the first-order diffraction spot of the probe beam. A recent report shows that absorbance changes of less than OD can be detected: and with modulation and background cancellation techniques the sensitivity should be even higher. In the following we refer to the study of photochemically induced transient volume holograms as holographic relaxation spectroscopy (HRS). Chemical and biochemical applications of HRS have developed very slowly. The first measurements of mass diffusion by means of HRS were reported in 1978 for a nematic liquid crystal and for polystyrene in benzene using photochromic molecules as probes and labels, respe~tively.~,~ The only biological application of which we are aware was reported by Chan and Pershan in a study of water and thermal diffusivity in a lipid-water smectic phase where a temperature grating induced a concentration grating through the Soret e f f e ~ t . ~ HRS offers an attractive alternative to photon correlation spectroscopy (PCS) for the study of dynamics in biological systems because of its sensitivity and its ability to detect labeled molecules in mixtures and in heterogeneous systems. HRS also determines the tracer diffusion coefficient in contrast to PCS, which usually provides only the mutual diffusion coeffi~ient.~?~ However, this application of HRS requires that labels be found which are photochromic in aqueous buffers and which can be attached to biological molecules using mild conditions. Two large classes of photochromic molecules are found among the derivatives of azobenzene and derivatives of benzospiropyran.1° The dye methyl red and some of its de(4)Rondelez, F.; Hervet, H.; Urbach, w. Chem. Phys. Lett. 1978,53, 138-43. (5)Hervet, H.; Urbach, W.; Rondelez, F. J. Chem. Phys. 1978,68, 2725-9. (6)Hervet, H.;Leger, L.; Rondelez, F. Phys. Reo. 1979,42, 1681-4. (7)Chan, W. K.;Pershan, P. S. Biophys. J. 1978,23, 427-49. (8)Berne, B. J.; Pecora, R. “Dynamic Light Scattering”;Wiley: New York., 1976. (9)Johnson, C. S., Jr.; Gabriel, D. A. In ”Spectroscopy in Biochemistry”; Bell, J. E., Ed.; CRC Press: Boca Raton, FL, 1981. (IO) Brown, G. H., Ed. “Photochromism”;Wiley-Interscience: New York, 1971. ~~
~
i
o=c\ 0-
(I) Flgure 2. Reported structures for the spiropyran used in this work. Form I, which is colorless, Is the stable form in dioxane. Form I1 is colored and is the stable form in water. The direction of the photoinduced reaction depends on the mole fraction of water.
rivatives are not satisfactory for our purposes because these molecules are only photochromic in nonaqueous solvents and in aqueous solutions a t high pHs which destabilize proteins. Also, most derivatives of benzospiropyran are either insoluble or sparingly soluble in water. The aim of this phase of our work has been to identify photochromic molecules for use as labels and probes in aqueous environments in HRS experiments and to characterize the hydrodynamic and optical properties of these molecules. In preliminary work we have found that the spiropyran derivative l-(P-carboxyethyl)-3,3-dimethyl-6’nitrospiro[indoline-2,2’-2H-benzopyran] is a satisfactory label for some proteins and is useful as a probe for the study of transport in aqueous gels.” This compound, which we will call spiropyran in the following, is soluble in mixtures of water and dioxane and is slightly soluble in aqueous buffers. Furthermore, its absorption spectrum depends on the polarity of the solvent and thus may provide information about its local environment. In aqueous buffers spiropyran is colored and exhibits reverse photochromism; Le., irradiation with green light causes bleaching. Water/dioxane solutions a t mole fractions of water less than 0.8 are transparent and normal photochromism is found; Le., color can be generated by UV irradiation.12 The molecular changes associated with these reactions are illustrated in Figure 2,whieh serves to define spiropyran I and spiropyran 11. In the following sections we describe HRS experiments using UV and visible lasers as excitation sources for the study of aqueous solutions of spiropyran. In section I1 we review diffraction theory for absorption gratings and discuss the effects of mass diffusion and molecular relaxation on the decay of grating amplitudes. In section I11 we describe instrumentation and procedures for creating and recording transient holograms and for analyzing their time dependences. Experimental data are presented and discussed in section IV. To anticipate the results, we have been able to generate volume holograms consisting of periodic spatial concentration patterns of the polar (colored) form of spiropyran in waterldioxane solutions over the complete range of mole fractions. The decay rates of the (11)(a) Rhee, K. W.; Gabriel, D. A.; Johnson, C. S., Jr., manuscript in preparation. (b) Lamb, P. D.; Gabriel, D. A.; Johnson, C. S., Jr., manuscript in preparation. (12)(a) Namba, K.;Suzuki, S. Bull. Chem. SOC.Jpn. 1975,48,1323-4. (b) Namba, K.; Suzuki, S. Chem. Lett. 1975,947-50.
HRS of a Benzospiropyran
holograms were used to determine the tracer diffusion coefficient of spiropyran at concentrations which are inaccessible to PCS. Also, the lifetimes of the photoexcited states were determined by monitoring absorption changes after photoexcitation. A t high mole fractions of water the photobleaching reaction was found to be irreversible. The diffusion coefficients were corrected to 20 " C by using viscosities of the mixtures and estimates were made of the concentration limits of the HRS method. The present experimental design permits diffusion coefficients to be determined for spiropyran I1 in phosphate buffers a t pH 7.5 at concentrations down to 0.01 mM. Higher sensitivities are expected in cases where excited-state lifetimes are shorter and signal averaging can be used more effectively. 11. Theory
A. Diffraction Efficiency. Two coherent laser beams crossing at the angle 0 produce an interference pattern which has a fringe spacing A = X/(2 sin (0/2)) as illustrated in Figure 1. If an absorbing sample is placed in the crossing region, a periodic variation in the complex index of refraction n ik will be induced which can be described by n = ( n ) nl cos (2nx/A) (1)
+
+ k = ( k ) + kl COS ( ~ T x / A )
(2) where the x direction lies in the plane defined by the writing beams. According to Kogelnik's coupled wave theory, the diffraction efficiency q for a volume hologram of this type which has the thickness T is given by13 q = exp(-4r(k)L/X)[sin2 (mlL/X) + sinh2 (*k,L/X)I (3) where L = T/cos (012). The diffraction efficiency can be estimated by using the Lorentz-Drude model for electronic susceptibility with the Lorentz-Lorenz correction for local fields in condensed phases. We define the grating contrast as 6N/N where N is the average number density of molecules responsible for the diffraction and N + 6N is the density at a maximum in the grating. Also, we assume that a single electronic transition centered a t wo and having the line width y is dominant and that n, and k , are sufficiently small to permit only linear terms to be retained in the expansions of sine and hyperbolic sine terms in eq 3. Under these conditions the diffraction efficiency is given by14J5 q = exp[-R~~F(w)](R~/16)F(w)(6N/N)~ (4) where (5) Fi(0) = yi2/[4(wi - w)2 + yi21 Here R = (4rLkO/A)@ and ko = (Nfe2)/(2(n)~mwoy) where f is the oscillator strength and the other constants have their usual meanings. The Lorentz-Lorenz correction is contained in the factor a, which is equal to ((n)2+ 2)2/9, is the total path length of the probe beam in the and CUL sample which may exceed the thickness L of the grating. The maximum absorbance A, occurs at w = wo and is related to R through the equation A, = &/2.303. When CUR < 1, eq 4 predicts that maximum efficiency occurs at w = wo. However, when aR > 1, maxima occur in the efficiency curve at w = wo f (y/2)(aR - l)llz and it is advantageous to tune the probe away from the absorption maxima.
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983 4817
B. Time Dependence. Laser-induced gratings in solutions may include periodic spatial distributions of temperature, density, and concentration. Here we focus attention on the time interval from 1 ms to 1 s after the writing laser pulse during which time only the concentration grating is important in diffracting light. The time dependence of the amplitude of the concentration grating, i.e., the grating contrast, may result from mass diffusion, from the lifetimes of electronic states, and/or possibly from slow chemical reactions. Consider a solution containing photochromic molecules which can exist in either state A or state B. Furthermore, suppose that state A has an electronic absorption close to the frequency of the probe laser and that it contributes to diffraction of the beam while state B does not contribute significantly to the diffracted power. Two cases are of interest: (a) at equilibrium the photochromic molecules are in state B, and irradiation with the writing beams excites a grating of type A molecules; and (b) at equilibrium the molecules are in state A and irradiation bleaches the sample to produce a grating of type B molecules. In either case diffraction results from the distribution of type A molecules, but the time dependence of the grating amplitude may be different in the two cases. In the following we assume that the laser-induced reactions are reversible so that the s u m of the concentrations of type A and B molecules is constant in time. Also, we assume that the grating amplitudes decay only by mass diffusion and internal molecular changes. Case a. The writing laser pulse generates type A molecules with the local number density A(r,t). It is assumed that these molecules diffuse according to Fick's law and eventually relax back to the lower energy state B. Thus, the subsequent time dependence is described by dA(r,t)/dt = (DAV2- l/rA)A(r,t) (6) where DA and 7 A are the diffusion coefficient and the mean lifetime of state A, respectively. The amplitude of the laser-induced concentration grating having the wavenumber K = 2x/h is denoted by A(K,t), and Fourier transformation of eq 6 shows that A(K,t) = 6.4 exp[-(DAp + 1 / 7 ~ ) t ] (7) where 6A is the amplitude immediately after the writing pulse is switched off. Equation 7 is valid for any fist-order decay process which determines 7 A even if state B is not regenerated. Case b. The writing laser pulse generates type B molecules with the local number density B(r,t). These molecules diffuse according to Fick's law and eventually relax back to the lower energy state A. We require the following coupled set of equations in order to determine the time dependence of A(K,t): dA(r,t)/dt = DAVzA(r,n+ B ( r , t ) / ~ ~ (8) dB(r,t)/dt = (DBV2- 1 / ~ ~ ) B ( r , t )
(9) where DB and are the diffusion coefficient and the mean lifetime for state B, respectively. The Fourier amplitudes A(K,t) can be obtained by Fourier transforming eq 8 and 9 and applying the initial conditions A(K,O) = -6A and B(K,t) = 6A. The result is A(K,t) = -6A(C1 eXp(-DApt) + c2 eXp[-(DBp + l / T g ) t ] ] (10) where
(13) Kogelnik, H.Bell Syst. Tech. J. 1969, 48, 2909-47. (14)Johnson, C. S.,Jr., J. Opt. SOC.Am. 1983, 73, 1263-7. (15)Nelson, K.A.; Casalegno, R.; Miller, R. J. D.; Fayer, M. D. J . Chem. Phys. 1982, 77, 1144-52.
c1 = h D @ / ( h D p + 1 / 7 ~ ) cz = (1/7~)/(mp + 1/7~)
4818
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
Miles et al.
absorption band for some samples. As expected from eq 14 this procedure increased the diffraction efficiency but required special precautions to avoid bleaching the sample. $ i In practice a mechanical shutter was also used in the probe DIGI-PLOT beam to reduce the exposure to a few decay times. The writing laser beams were polarized normal to the scattering plane in all cases; however, the reading laser beam was used in both the normal and parallel orientations. All lasers and optical components rested on a Modern Optics vibration-isolation table system, and the sample cell was mounted on a Palmgren rotary table. The heart of the spectrometer system, namely, the 50150 beam splitter (BS), the mirrors M2 and M3, the prism (P), and the dichroic mirror DM, were bolted to a 0.75 in. thick cold Flgure 3. Schematic diagram of the HRS spectrometer. rolled steel plate to achieve the proper elevation while avoiding flexing problems which we encountered earlier and AD = DB- DA. Equation 10 is, of course, valid only with aluminum and thinner steel sheets. To prevent air when A is regenerated from B without loss. In the limit currents and the resulting changes in optical path lengths, that both 7 A and 7B become long, eq 7 and 10 are identical, the steel plate and associated optical components were and the time dependence is determined entirely by the enclosed in a Plexiglas box with a hinged lid. With the diffusion coefficient of state A. When irreversible phoexception of the Corion dichroic mirror, protected alutobleaching occurs, the second term on the right-hand side minum UV mirrors from Newport Research Corp. were of eq 8 is no longer present, and again the diffusion used throughout. The coated prism and the 50150 visible coefficient DA determines the decay rate. More complibeam splitter were obtained from Melles-Griot, and the cated photochemical reactions have been considered by UV dielectric beam splitter was supplied by Acton ReBurland and Brauchle.16 search Corp. 111. Experimental Methods The beam from the pump laser was guided by mirror A. Sample Preparations. The photochromic spiroM1 to be incident at a 45O angle to the 50150 beam splitter pyran, l-(~-carboxyethyl)-3,3-dimethyl-6’-nitrospiro[in- BS. Mirrors M2 and M3 were adjusted separately so that doline-2,2’-2H-benzopyran], was custom synthesized by both beams incident on the prism were perpendicular to Chroma Chemicals of Dayton, OH, following the procedure the optical axis defined by a line, on the steel plate, which of Aizawa et al.17 The elemental analysis was done by bisected the prism. The prism, the mirror M3, and the Galbraith Laboratories and compared with calculated dichroic mirror were mounted on one-dimensional transvalues. Anal. Calcd for CzlHmO5Nz:C, 66.30; H, 5.30; N, lational stages. Also, the mirror M2 was mounted on a 7.37; 0, 21.05. Found C, 66.20; H, 5.38; N, 7.35; 0, 21.00. piezoelectric translator (PZT-Burleigh Model PZSO). The Also, the visible-UV absorption spectrum agreed with that lens L1 was biconvex silicon with a focal length of 50 cm. reported in ref 12a. With this arrangement two coherent beams from the The spiropyran dioxanelwater solutions were prepared writing laser could be directed parallel to the optical axis by diluting 0.1 mL of a concentrated stock solution (about onto the focusing lens L1, and their separation could be M) of spiropyran in dioxane with 9.9 mL of solvent easily adjusted by translating the prism. The beams were with the appropriate mole fraction of water and dioxane. focused into a sample by L1 to produce an interference The solutions were allowed to stand in the dark overnight pattern. The probe beam was directed parallel to the before any measurements were made. Fresh stock soluoptical axis by the dichroic mirror at the proper separation from the optical axis to permit Bragg diffraction from the tions were prepared every 2 days. B. Instrumentation. The layout of the HRS speclaser-induced grating in the sample. trometer system is shown in Figure 3. The type of pump The collection optics as well as the photomultiplier tube or writing laser was determined by the wavelength of the for the detection of the diffracted light were monitored on radiation required. For excitation in the UV, a flashthe arm of the rotary table. This equipment consisted of lamp-pumped dye laser (Chromatix CMX-4) equipped a spatial fiiter including a 12 cm focal length achromat lens with frequency-doubling crystals was used. This system (L2), a 0.45-mm pinhole situated 12 cm behind L2, a spike produced peak intensity a t approximately 330 nm when filter immediately behind the pinhole, and an EM1 Genrhodamine 640 was used as the laser dye. The pulse ducom 9785B PMT. In some experiments a prism polarizer ration was between 1and 2 ps, but a low-intensity tail was was placed in front of the pinhole to discriminate against detected for several microseconds. For excitation in the stray light from the writing laser. visible region an argon ion laser (Spectra-Physics 165) with Samples which absorbed visible light were contained in a mechanical shutter (Vincent Model 23 Uniblitz) was used 5 mm path length thermostated cells supplied by Hellma. at 514 nm. The minimum pulse duration with this arA closed-loop circulating system incorporating a Buchler rangement was 1ms. This laser was also equipped with peristaltic pump was arranged so that the solution was a polarization rotator. The probe or reading beam was automatically circulated for 5 s immediately after the probe usually supplied by a small He-Ne laser (Melles-Griot shutter was closed. For samples requiring UV pump 05-LHP-151). However, on occasion a CW dye laser pulses, a rectangular q& cell having a 5-mm path length (Spectra-Physics 375) with a noise reduction system (Cowas used. This cell was not thermostated and was not herent Associates 307) was used to obtain a tunable probe. attached to the circulating system. However, the scattering Also, part of the CW writing beam from the argon ion laser room was maintained at 20 f 1 OC and the temperature was split off to provide a probe close to the center of the was monitored during each experiment so that corrections could be made to the diffusion coefficients when necessary. (16) Burland, D.M.; Brauchle, Chr. J. Chem. Phys. 1982,76,4502-12. C. Alignment and Calibration. First, the dichroic (17) Aizawa, M.; Namba, K.; Swuki, S. Arch. Biochem. Biophys. 1977, mirror was adjusted so that the He-Ne probe beam was 180,4143. WRITING LASERS
READING LASER
n
a
HRS of a Benzospiropyran
collinear with the optical axis, and the rotary table was positioned so that the probe beam passed through a pinhole mounted on the rotation axis of the table. The translation stage holding the prism was positioned so that the writing beams were parallel to the optical axis and equidistant from it. The lens L1 was then put into place and fine adjustments were made to ensure that the writing beams passed through the pinhole as well. Finally, the dichroic mirror was translated to move the probe beam so that the proper Bragg angle was obtained at the sample. In order to monitor the contrast and stability of the fringe pattern, a microscope objective was substituted for the pinhole a t the position to be occupied by the sample. In this way an enlarged fringe pattern could be observed on a wall. It was possible to alternate the phase of the grating between 0 and 7 by applying appropriate voltages to the PZT, and this alternation could be observed on the wall (see section 1II.D). Alignment was much more difficult when using the CMX-4 pump laser because of the extremely short coherence length ( 0.8) the ionic form shown as structure I1 in Figure 2 is thought to be most stable. The effect of water on the wavelength of maximum absorbance for spiropyran in the visible region is illustrated in Table I with data from this work which are consistent with measurements at different mole fractions reported in ref 12a. The shift of the absorption maximum to shorter wavelengths with increasing mole fraction of water presumably results from the stabilization of spiropyran I1 by solvation with polar solvents.21 It has been reported that the change in optical density is +0.95 a t A,, when x(HzO) = 0, drops to approximately 0 at x(HzO) = 0.80, and is -0.25 a t x(H,O) = 0.88.12 This suggests that the energies of spiropyrans I and I1 are roughly equal a t x(H,O) = 0.8. A t high values of x(H,O) the solutions are pinkish and are easily bleached by irradiation with green light, while at low values of x(H,O) the solutions are colorless and require UV irradiation to produce color. The lifetimes of the photoexcited states were determined by monitoring the absorbance after UV irradiation for 0.1 mM solutions of spiropyran having various values of x(H,O)at 20 "C. First-order kinetics were found in the range of mole fractions from 0 to 0.6. Characteritic times 7,for the decay of coloration are listed in Table I. The time 7,increased until above mole fraction 0.8 the effect of irradiation was essentially irreversible photobleaching. (21) Sunamoto, J.;Iwamoto, K.; Akutagawa, M.; Nagase, M.; Kondo, H.J . Am. Chem. SOC.1982, 104, 4904-7.
HRS of a Benzospiropyran
The Journal of Physical Chemistty, Vol. 87, No. 24, 1983 4021
8000, 5800
1
-
5.0
1800 b400 4000 -
5200
0 0 5 M phosphate pH57 5
3800 -
_.i' /
n i.04
2800
2400
i
1
d
d
II
ib
ii
ib
ib
0
t (msec)
0 0
0.2
0.4
0.6
0.8
i.0
X (H20)
Flgure 4. Data points from a holographic relaxation experiment and the best-fit line obtained by using NONLIN.
Flgure 6. Diffusion coefficients for spiropyran in water/dioxane mixtures vs. the mole fraction of water x(H,O).
TABLE 11: Diffusion Coefficients of Spiropyran I1 in Water/Dioxane Mixtures and Viscosities of the Solvent Mixtures at 20 "C
0
100
200
2s 1
300
/
241
400 I a
x(H,O)
106D,cmZ/s
0.00 0.20 0.40 0.60 0.80 0.93 1.00
3.48 i 0.25 3.05 ?: 0.23 2.82 t 0.36 2.50 0.31 2.21 ?: 0.06 2.79 t 0.04 4.19 ?: 0.02
*
T
I00
200
300
400
500
A2(prnz)
Flgure 5. Typical lots of the relaxation time 7 vs. the square of the grating spacing A t Data in part a were obtained with an argon ion laser for green light excitation. Data in part b were obtained with a flash-lamp-pumped dye laser for UV excitation.
This effect is attributed to the stabilization of spiropyran I1 by more polar solvents. B. Holographic Relaxation and the Diffusion Coefficient of Spiropyran. Laser-induced gratings were established in solutions of spiropyran in water/dioxane mixtures using UV excitation in the mole fraction range x(H,O) = 0 to x(H,O) = 0.6, and visible light at 514.5 nm for mole fractions above 0.8. A typical decay curve, which resulted from averaging 10 transients, is shown in Figure 4 for spiropyran in 0.05 M phosphate buffer a t pH 7.5. For samples having x(H,O) 2 0.8, a closed-loop circulation system with a peristaltic pump was used to ensure complete mixing of the partially bleached sample between writing pulses. Characteristic times (7)obtained by analyzing such curves were plotted vs. the square of the grating spacing as shown in Figure 5. Figure 5b illustrates the much larger errors which were present when the CMX-4 was used. Since the photochromic lifetimes were much greater than the T = (I')-l values observed in the transient grating experiments, the decays were attributed entirely to mass
1.291 t 1.380 t 1.630 t 1.998 i 2.230 i: 1.604 t 1.002a
0.016 0.017 0.015 0.020 0.021 0.015
is related to the diffusion coefficient 7
b
cp
Value used for calibration.
diffusion. Thus, D by
'i
7j,
= A2/(47r2D)
(18)
Figure 5 and similar curves for other values of x(H20) confirmed this linear relationship and permitted the tracer diffusion coefficient for spiropyran I1 to be determined. In Figure 6 we plot the diffusion coefficients corrected to 20 OC vs. x(H,O), and the values are listed in Table 11. The correction was made by using the equation
Do = D l ( ~ l / v o ) ( ~ o / ~ l )
(19)
where Do is the corrected diffusion coefficient, D, is the measured value of D a t temperature T1,and qo and vl represent the viscosities of the solvent mixture at temperatures Toand Tl,respectively. The error bars indicate outer limits for slopes obtained from plots of 7 vs. A2. The errors in D were approximately f10% when using the flash-lamp-pumped dye laser (CMX-4) in the UV mode as the writing laser. However, with the argon ion laser (SP-165) the errors were less than i3% and for x(H,O) = 1.0 were approximately fl % . In these measurements a He-Ne laser a t 633 nm was used as the reading laser. The signal-to-noise ratio could have been improved by using a green probe, but the errors resulted primarily from poor beam quality and instability of the writing laser rather than low diffracted signal. The very low repetition rates required for some of the samples contributed to the stability problem. The energy delivered to the scattering volume was of concern since heating, thermal lensing, etc., can influence the apparent diffusion coefficient.22 To investigate this (22) Hall, R.S.; Oh,Y. S.; Johnson, C. S., Jr. J.Phys. Chem. 1980,84, 756-7.
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The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
effect, D was measured as a function of the energy of the writing laser pulse for a 0.01 mM solution of spiropyran in 0.05 M phosphate buffer a t pH 7.5. The power a t the sample was adjusted to be 70 mW using the argon ion laser, and the pulse duration was varied from 2 to 8 ms. Here 514-nm light was used for the probe. The measured values of D were within 5% in all cases and the effect of pulse energy appeared to be negligible. The concentration dependence of D was also studied over a limited range of concentrations. The system chosen for this measurement had x(H,O) = 0.8 and the concentrations of spiropyran ranged from 0.02 to 0.1 mM. At 0.02 mM D was equal to 2.17 X lo4 cm2/s and a t 0.1 mM it was 2.21 X lo4 cm2/s, which within experimental error indicates no significant concentration dependence of D in the dilute region. The sensitivity of the HRS method using spiropyran in aqueous buffers is important because of the potential role of spiropyran as a label and probe molecule. According to eq 4, the maximum diffraction efficiency for solutions having absorbances less than unity is obtained by tuning the probe laser to the absorption maximum. For spiropyran in aqueous buffers the 514-nm line from the argon ion laser satisfies this condition quite well. By using this probe we were able to measure D to f5% without difficulty for spiropyran a t 0.01 mM. Typically we accumulated 10 decays with a delay between pulses from the writing laser of approximately 1min to permit replacement of bleached molecules by diffusion. When 633 nm was used for the probe, a concentration of 0.05 mM was required to obtain similar accuracy. C. Diffusion and Viscosity. Figure 6 shows that the diffusion coefficient drops by about one-third when the mole fraction of water is decreased from 1.0 to 0.8. This change is also reflected in the viscosity of the solvent mixture. In Table I1 we list viscosities measured at 20 OC. These values and those that we obtained above 20 OC agree with fluidity measurements in ref 23. The viscosity more than doubles in going from mole fraction 1.0 to 0.8. Thus, there is quantitative, but far from exact, agreement with the elementary diffusion theory that the diffusion coefficient is inversely proportional to the viscosity. The (23) Geddes, J. A. J. Am. Chem. SOC.1933,55, 4832.
Miles et al.
product of the diffusion coefficient and the viscosity is constant within experimental error for dioxane-rich mixtures, but for large mole fractions of water where errors in the measured diffusion coefficients are less than 3% this does not hold. The apparent activation energy for viscosity reaches a maximum value of about 21 kJ/mol at x(H,O) = 0.8 and then drops to less than 10 kJ/mol in pure dioxane. The extrema in the diffusion coefficient, the viscosity, and the activation energy for viscosity all occur in the vicinity of x(H,O) = 0.75.
V. Conclusion Concentration gratings of photoexcited spiropyran have been induced in waterldioxane solutions over the entire range of mole fractions. UV radiation was required for x(H,O) = 0-0.8, but green light (514 nm) was effective at mole fractions equal to or greater than 0.8. In all cases the transient decays were analyzed to determine tracer diffusion coefficients for spiropyran. Large errors (&lo%) were unavoidalbe when using a flash-lamp-pumped dye laser as a UV writing laser because the poor beam quality interfered with measurements of the grating spacing. Also, with this arrangement the phase of the grating could not be controlled. Errors less than f 3 % and often closer to f l % were found in the region where an argon ion laser could be used to establish the grating. In the experiments described here spiropyran has essentially been used as a probe molecule. This application is straightforward for aqueous solutions, mixtures, gels, etc. The lower concentration limit for accurate diffusion measurements appears to be about 0.01 mM. This value is determined primarily by the contrast of the grating and the lifetime of the photoexcited state. Spiropyran can also be used as a label for proteins, but at the level of one label per protein molecule the sensitivity is somewhat lower than for solutions for spiropyran alone because of the increased turbidity. We are currently using spiropyran as a label for a-amylase and bovine serum albumin and are investigating the properties of other photochromic labels. Acknowledgment. This work was supported in part under National Science Foundation Grant CHE 8022198. Registry No. H20,7732-18-5; dioxane, 123-91-1; I-@carboxyethyl)-3,3-dimethyl-6’-nitrospiro[ indoline-2,2’-W-benzopyran], 55779-26-5.
