J. Phys. Chem. 1991, 95, 5502-5509
5502
following expression for the concentration within the pores of the solid where the K,+ are dimensionless parameters which describe the experimentally observed decay. Generally KI*is much smaller than the other parameters in the series, and a short distance downstream of the flow-reactor entrance the solution may be taken as the first term in eq A1 16 v 8 Omitting the subscript 1, we have C(R,Z) = Ag(R) exp(-K*Z) (A121 For an experimentally observed exponential decay, P in eq A12 may be equated to ks(obs)ro/v. Substituting (A12) into (A6) leads to the following solution for the concentration in the gas-phase core of the reactor g(R) = ?B,Jt’” C ( R 2 ) = CS(Z)(gB,P”/ n=O kBn) n=O
(A14)
where C,(Z) is the concentration at the solid surface, i.e. C,(Z) = C( 1,Z)and the coefficients, B,, are functions of P and D l . The solution to (A7) can be written
+ bz exp(-4Ri)
(A151
(A161
By substituting into boundary condition (A9), we can obtain an expression for K,: m
m
-Di( E2nBn/XBB,)= K,/2 ne0
n=0
+ D l 4 tanh (4)
(A17)
By evaluating the parameters D l , K,, and 0,’ in terms of dimensional quantities and by noting that k,’ = r&,/2, ro - h = r,,, and D&/h = hpGgk,’/4, we arrive at the following expression 0)
-(2Dg/roz)(
m
E 2nBn/ n=O E Bn) = n=O kJ(1 - @J + h P 8 g tanh w / 4 1 (A181
(A13)
n-0
Cp(Ri,Z) = bi W 4 R i )
Cp(Ri,Z) = Cs(Z) cash (4Ri)/mh (4)
The left-hand side of eq A18 is exactly the solution obtained by Brown6 for the interaction of laminar flow and external diffusion in the absence of reaction within a porous substrate. In the present study, this solution is labeled k, and given above as eq 3. The quantity tanh (4)/4 is the effectiveness factor, 7, which is the ratio of the actual reaction rate in the pores to the maximum rate with very rapid d i f f ~ s i o n . ~With ’ ~ these substitutions and noting that for HNOS-HzO ices (1 - O)u = 1, we obtain eq 11.
ks, = kS(1 + 7hP8g)
Using the boundary conditions (A8) and (AlO), we obtain the
(1 1)
Photochemical Ring-Opening Reaction of Indoiinospiropyrans Studied by Subpicosecond Transient Absorption Niko P. Emsting* and Thomas Arthen-Engeland Max- Planck-Institut ftlr biophysikalische Chemie, Abteilung Luserphysik, D-3400 Gdttingen, Posrfach 2841, Federal Republic of Germany (Received: October 31, 1990)
The photochemical ring-opening reaction of spiropyrans BIPS (1 ’,3’,3’-trimethylspiro[2H- l-benzopyran-2,2’-indoline]), its naphthopyran analogue naphtho-BIB, and 6-nitro-BIB in n-pentane to the corresponding merocyanines has been followed by transient absorption spectroscopy. A broad absorption ca. 1 ps after UV excitation, covering the entire measurement range 380-680 nm, is assigned to transitions from the excited spiro compound. In the case of BIPS and naphtho-BIB, the merocyanine absorption bands rise with time constants of 0.9 and 1.4 ps, respectively. The transient spectra are compared with spectra taken several microseconds after excitation and with the spectra obtained when the spiropyrans are irradiated at low temperature in an argon matrix. There is evidence that a distribution of isomers is already established 10 ps after UV excitation of the spiroform. The reaction paths leading from excited BIPS to ground-state merocyanine isomers are classified according to their steric requirements. The internal molecular temperature after fast internal conversion is estimated to be ca. 900 K. We suggest that, at this temperature, a primary merocyanine product in its electronic ground state may isomerize further on the picosecond time scale, resulting in the observed distribution of isomers.
1. Introduction
Spiropyrans consist of a 2H-pyran moiety and a second moiety that are held orthogonal by a common spiro carbon atom. The r-electron systems of both parts of the molecule do not interact significantly, so that the absorption spectrum of the spiropyran resembles the sum of the spectra for the two parts of the molecules.’ Hence the spiropyran is generally colorless. For example, Figure 1 shows (onthe left-hand side) the structure and absorption spectrum of 1’,3’,3’-trimethylspiro[2H-1-benzopyran-2,2’-indoline] (BIPS). This compound is the parent of a great number of derivatives. In 1952, Fischer and Hirschberg reported that UV excitation of BIPS (and of other spiropyrans) leads to a heterolytic cleavage of the bond between the spiro carbon atom and the oxygen atom.* ~~
~
(1) Tyer, N. W., Jr.; Becker, R. S. J . Am. Chcm. Soc. 1970, 92, 1289.
(2) Fischer, E.; Hirshberg, Y. J . Chcm. Soc. 1952, 4522.
OO22-3654/9 1/2095-5502$02.50/0
The molbcule can now unfold, the two parts of the molecule are allowed to rotate relative to each other, and thus an extended, more planar configuration is attained. Now the r-electrons conjugate across the entire structure (which may be classed among the merocyanine dyes) resulting in an intense absorption in the range 500-600 nm. The merocyanine form of BIPS and its visible absorption spectrum are also shown in Figure 1. In a subsequent thermal back reaction, the photochemically induced color usually fades on a time scale of seconds to minutes (at room temperature), as the merocyanine form reverts to the thermodynamically more stable spiroform of the molecule. The photochromism of spiropyrans has been studied intensely.’ (A comprehensive review4 covers the literature until 1969, so that (3) (a) Hciligman-Rim, R.; Hinhberg, Y.; Fircher, E. J . Phys. Clrcm. 1%2,60,2465,2470. (b) Bercovici, T.; Heiligman-Rim,R.; Fwher, E. Mol. Photochcm. 1969, I , 23.
Q 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5503
Ring-Opening Reaction of Indolino-Spiropyrans merocyanine isomers
N I
......
CTC
100
........... D wavelength /nm Figwe 1. Absorption spectrum of B I B in n-pentane at 22 O C (left) and of its merocyanine photoproducts 10 ps after UV irradiation at 308 nm (right; the ordinate scale in this case is only approximate).
we will cite mainly more recent contributions.) In this paper we are concerned with just two broad topics: the existence of several merocyanine isomers and their characterization, and the mechanism of the photochemical ring-opening reaction leading from electronically excited spiropyran to one (or several) of the merocyanine isomers in their electronic ground state. Existence of Several Merocyanine Isomers. The open, mere cyanine form of the molecule possesses a central chain of three carbon-carbon bonds, c2
