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Spectral hole-burning and stark effect: a centrosymmetric molecule in polymers of different dielectric constants
Volume 190, number 1,2
CHEMICAL PHYSICS LETTERS
Spectral hole-burning and Stark effect: a centrosymmetric in polymers of different dielectric constants
28 February 1992
molecule
Alfred J. Meixner ‘, Alois Renn and Urs P. Wild Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092 Zurich, Switzerland Received 26 June 199 1; in final form 25 October 199 1
The electric field effect of spectral holes, in the S, +So absorption band of octaethylporphyrin (OEP), is studied in matrices with different dielectric constants, t. The analysis of the hole-contours shows that the Stark effect is linear and provides an average matrix-induced dipole moment, A&,,, which results from the polarization of the OEP molecules by the surrounding host molecules. The values of A&, increase with t of the host. The matrix materials were poly(methylmetacrylate), poly(vinylbutyral), polystyrene and polyethylene.
1. Introduction The influence of externally applied electric fields on spectral holes has been investigated in a several publications [ 1- 10 1. Since spectral holes can be three to five orders of magnitude narrower than inhomogeneously broadened absorption bands, moderate electric field strengths are sufficient to affect the Lorentzian hole contours significantly. In amorphous hosts often a broadening and decrease of the hole contours is observed as the applied field strength is increased. With sensitive detection techniques [ 111 precise measurements of the electric-field-dependent deformations of spectral hole contours can be performed. The analysis of the electric field effect indicates that the hole shapes do not only depend on the applied field strength but in addition on the orientation of the electric field with respect polarization of the light [ 6,7,12]. Spectral holes, in the inhomogeneously broadened S, tSo absorption band of cresylviolet perchlorate in a poly (vinylbutyral) matrix split when the electric field is applied parallel and broaden when the field is applied perpendicular to the polarization of the light [ 8 1. A detailed analysis which includes the dichroism of spectral holes and the geometry of the experiment, revealed that ’ Present address: IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95 120-6099, USA.
the experimental data can be best described by assuming that the difference between the electric dipole moments in the ground and the excited state is composed of an intrinsic molecular part, A,u,,,,~= 2.1 D, and a randomly oriented, matrix-induced part, A&, =0.9 D [ 81. AP:,.,~is fairly large and results from the polarization of the guest molecules by the surrounding host molecules. Also for centrosymmetric molecules like perylene, octaethylporphyrin, Zn-tetrabenzoporphin, and phthalocyanine [ 4,6,7, 10,13- 15 ] a linear Stark effect has been observed. Within the range of applied field strengths, which reached tens of kV/cm, the hole broadening was fully reversible and the original hole widths were recovered when the initial field strength was restored. In all examples the center frequencies of the holes were not affected by the applied electric field indicating that a second-order Stark effect can be neglected at these field strengths. The magnitude of the matrix-induced dipole moments being on the order of intrinsic dipole moments suggest that the distortion of the guest molecules by the surrounding host molecules is rather large. This reflects that an amorphous solid is highly anisotropic on a molecular scale and that a set of dye molecules with identical transition frequencies is not uniform with respect to the strengths of interactions between the guest and the host molecules. The matrix-induced Stark effect was interpreted by Bogner
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
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et al. [ 41 as polarization of guest molecules by local electric fields built up by the surrounding host molecules [ 4,6,13,15 ] and by dispersion interactions [ 91. The same mechanisms play an important role in the discussion of inhomogeneous line broadening and solvent shifts [ 16,17 1. In a recent publication a variation of the matrix-induced dipole moment difference and the optical zero-phonon linewidth over the inhomogeneously broadened absorption band has been found for octaethylporphyrine in polystyrene [ 141. As a consequence one expects that the matrixinduced dipole moments depend on the strength of the local matrix fields and thus are linked to the dielectric properties of the host. To test this hypothesis, we investigate in this Letter the effect of external electric field on spectral holes of the centrosymmetric molecule octaethylporphyrin (OEP) in host materials with different dielectric constants, t. The experimental electric-field-dependent hole contours are analyzed in terms of analytical expressions, derived from a detailed theoretical model. We observe a significantly stronger hole broadening by an external field in the polar matrices PMMA and PVB than in the apolar matrix PE. Consequently we find decreasing values for the matrix induced dipole moments, A&, from the host with the largest t to the matrix with the smallest t. In addition, the minimum detectable hole widths which are determined by optical dephasing and spectral diffusion [ 18,191, follow the same trend, with the exception of the OEP-PS guest-host system. From the matrix-induced dipole moments and the polarizability tensor difference of OEP we can calculate values for the internal matrix fields. We compare these local field values to reaction fields determined from the monomer dipole moments on the basis of the Onsager model [ 201.
LETTERS
28 February
1992
oration of the solvent, giving clear, transparent films of about 0.2 mm thickness. The PE and PS films were prepared by melting the polymers in glass shells and dissolving the pure dye in the melt. The hot doped polymers were squeezed to give thin raw films which could easily be removed from the glass surfaces after cooling to room temperature. Samples of good optical quality with a uniform thickness of z 100 pm were fabricated by annealing the raw films between glass plates at about 120°C for several hours. The glass plates carried an electrically conducting, optically transparent coating on the inner sides in order to apply an electric field to the sample. The optical density of the samples was on the order of 0.8 at the maximum of the S, cS,, absorption band. 2.2. Experimental arrangement and measurement Spectral holes were burnt and detected using the holographic detection method which gives shot noise limited zero background signals [ 11,2 11. Coherent CR 699-2 1 or CR 599-2 1 dye lasers were used as coherent narrow band light sources. The burning intensity was on the order of 10 uW/cm’ and the spot diameter on the sample was 3 mm. Details conceming the apparatus and the holographic detection method are described elsewhere [ 6,11,21]. The samples were in contact with liquid helium at a temperature of 1.7 K. The spectral holes were 5W deep. The hole contours were determined by measuring the diffracted light intensity at 5 12 positions equally spaced over a frequency range of 30 GHz, centered at the burning frequency. The applied field strengths typically ranged from + 5, ? 10 up to ? 30 kV/cm. The holes were slightly broadened due to photochemical bleaching. The minimum hole widths were determined by extrapolation to zero burning fluence from sets of spectral holes which had been burnt with decreasing fluences.
2. Experimental 2. I. Sample preparation
3. Line shape analysis
The PMMA and PVB films were prepared by dissolving the polymers in dichloromethane. OEP was dissolved in the same solvent and added to the solution of the polymers. The mixtures were stored in open glass shells for several days to allow the evap-
In this section, we derive an analytical expression for the electric-field-dependent hole contours, for molecules with matrix-induced dipole moments. The fact that the spectral holes are burnt and probed with linear polarized laser light is taken into account.
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When a static electric field is applied to the sample, the energy levels of a guest molecule is shifted due to the interaction of the electric dipole moments with the electric field. This results in a shift of the transition frequency Aw of a specific guest molecule which is, neglecting the second-order Stark effect, Am= f ]A,u] ]Es] cos/9.
(1)
Ap=p,, -p, is the difference of the electric dipole moments in the ground (S,) and the excited states (S,). Es is the change of the local electric field, Ei =EO +E,, due to the externally applied electric field, and j? is the angle between Ap and Es. Formally Ap can be interpreted as the product of the polarizability tensor difference, Au, between the ground and the excited states and the local electric field, Ei at the center of the guest molecule [ 61, Ap=AaEi.
(2)
The observation of a purely linear Stark effect suggests that 1EP I 3 IEs I. Hence the contribution of Es to Ei can be neglected in eq. (2 ). In order to calculate the electric-field-dependent hole shapes for molecules with a particular angle 8 between Ap and the transition moment, D, we introduced an orientation distribution function P(&B) sinBdS 161,
28 February 1992
field-dependent hole contour (eq. ( 11) of ref. [ 6 ] ) leads to 2(Aw,,, +m) r
Ao(w)=$V,SK +tan-’
(4)
No is the number-density of guest molecules before burning, S is the absorption cross section and K depends on the burning fluence and the quantum efficiency of the hole formation. jr is the hole width when no external field is applied and Ao,,,=~is the maximum frequency shift for a guest molecule which occurs when Apindand the external field are parallel (eq. (1) cos/3=1). In fig. la a(o) is plotted as a function of the frequency for field strengths corresponding to Ao, = 0, 2r, 4r, 6Tand gr As the field strength increases the hole broadens symmetrically with respect to the center frequency and the amplitude decreases, the area under the contour remains constant. At zero field strength Aa approximates a Lorentzian line
P(8,j?) sin 8 de = (A+Bcos2j?+Ccos4~)
sin8dfI.
(3)
P( 8, /3) sin fi d/3 is the relative number of molecules, absorbing the probing light, which have a frequency shift Ao= (A@Jfi) cos 8. The coefficients A, B and C depend on the angle 0 between Ar and D, and on the orientation of the applied electric field with respect to the polarization of the light, and are given in the Appendix. We suppose a random orientation of AFind in the plane of the OEP molecules, i.e. all angles 8 having the same probability. Averaging the orientation distribution function can be performed by integrating eq. (3) over 8 within the limits of 0 G 6% 2x. For both experimental geometries we find, A = $ while B= C= 0. This reflects that the hole contours become insensitive to the orientation of the applied field with respect to the polarization of the light. Introducing A = 2 into the expression for the electric-
-10
10
0 Frequency
[r]
Fig. I. Electric field dependent hole contours (a) and hologram signals (b) calculated from eq. (4) and eq. (A.2) for molecules with random orientation of matrix-induced dipole moments. The electric field dependent broadening, Aw= A&E,/fi is 0,2r, 4r, W, and 8I’. 77
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shape with a half-width of r. Since the spectral holes have been burnt and detected as laser-induced gratings (plane wave holograms) we present in addition (fig. 1b) the contours of the holographic signal. Details on the holographic detection technique are described elsewhere [ 6,2 11. The hologram efficiency depends on the amplitudes of both the spatially modulated absorption coefficient and the spatially modulated refractive index and is given in the Appendix (eq. (A.2) ). The area of the signal decreases proportional to Aw ;a,. The hole contours described by eq. (4) include the orientational averaging of matrix-induced dipole moments of one fixed size 1Apind 1. In addition the lengths Of AFind are not uniform. Here we assume an isotropic Gaussian distribution of local matrix fields (Bogner et al. [ 41). Due to the random structure of an amorphous host the vector sum of all matrix fields cancels. However, for a specific guest-host configurations the local fields may be large, leading to a considerable distortions of the guest molecules. For guest molecules with disk-like polarizability tensors the distribution function for the electric-field-dependent frequency shift, Awmax, is [ 6 ]
IF
OV/cm
lOkV/cm
1 ?lL
F
01
SOkV/cm
20kV/cm
/ww
-15
I
0
h1
I
il.5 Frequency
I
i
0
+15
[Gtiz]
Fig. 2. Influence of an applied electric field on a holographically detected spectral hole, burnt in the S,+S, absorption band of octaethylporphyrin (OEP) in a poly(vinylbutyra1) (PVB) matrix at 1.7 K.
2
xexpl(2)
J.
AWL,, = A&EJfi= AaEiE,/h is the root mean square value of the maximum frequency shift, Aa is the change of the polarizability tensor upon excitation and EI is the distribution parameter of the local matrix fields. The average of eq. (4) is then, Ao(A&,ax, m =
s 0
w)
G(Aw,,,)xAcY(w)~Aw,,,
.
(6)
4. Results and discussion Fig. 2 illustrates the influence of an applied electric field on a spectral hole burnt into the Si cSo absorption band of OEP. The host material was PVB and the sample was kept at a temperature of 1.7 K 78
in liquid helium. The hole was burnt as a laser-induced plane wave grating and the diffracted light was detected during the frequency scan. It is clearly seen that the hole contour significantly broadens symmetrically with respect to the center frequency and decreases as higher electric field strengths are applied. The line center is hot shifted, ruling out a quadratic Stark effect within our field strength limits. The analysis of an experimental data set for a guest-host system was performed in two steps: First, the electric-field-dependent broadening, Aw ‘,,, , of a spectral hole was determined for every field strength separately by fitting eq. (A.2) to the hole contour, using the electric-field-dependent absorption coefficient (eq. (4) ) and refractive index (eq. (A.3) ) averaged with the distribution (eq. (5) ) for the electric-field-dependent molecular frequency shift Aw,,,. The fitting parameter in this procedure was the root mean square value, Aw A,, , of the distribution function (eq. ( 5 ) ). The value for the hole width at zero electric field strength was inserted as a fixed parameter and kept constant in the fitting of the fleld-de-
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CHEMICAL PHYSICS LETTERS
Volume 190, number 1,2
pendent curves. In the second step the matrix-induced dipole moment difference, A,&,, was obtained by a linear regression of A&.,,,, versus the applied field strength, Es, using the expression, The uncertainties for Am,,, A&,,, = A&E& from the curve fitting and for A,&, from the linear regression are on the order of 1%. In order to calculate the average local Stark field, Es, resulting from the applied voltage, we used the Lorentzian field correction [20],E,=f(e+2)(U/d),where Uistheapplied voltage, d is the distance between the electrodes and c is the dielectric constant of the host material. The Lorentzian field correction takes into account a contribution to the local field which results from the polarization of the matrix when the external field is applied. Dielectric constants at 1.7 K are not readily available. Thus we calculated the A&, values, using in the Lorentzian field correction either the dielectric constants or the squares of the refractive indexes, both for room temperature. When the square of the refractive index is smaller than the respective dielectric constant, as for PMMA and PS, a larger value results for the dipole moment difference. Hence, the values obtained with the refractive index represent an upper limit, whereas those obtained with the room temperature dielectric constant represent the lower limit. In table 1 Ap& is listed for the different polymers which are PMMA, PVB, PS and PE, together with the room temperature dielectric constants [ 221, the squares of the refractive indexes [23,24] and the minimum hole widths. An uncertainty of 8% has to be attributed to the results: 6% of which result from the thickness measurement of the sample, lob results from the determination of the applied voltage and 1Wfrom the fitted data. Our
values for the matrix-induced dipole moments OEP in the PS host are somewhat smaller than the results recently found by Kador et al. [ 141 in the same guest-host system. The excellent agreement between the experimental data and the theoretical model supports the concept that the linear, electric-field-dependent hole broadening can be explained as a linear Stark effect, based on the interaction of matrix-induced dipole moments and the externally applied electric field. In this model the matrix-induced dipole moments result from the polarization of the guest molecules by local matrix fields, created by the surrounding host molecules. Here we assumed homogeneous matrix fields and a disk-like point polarizability tensor, creating point dipoles at the centers of the guest molecules. A more elaborate model would be based on the specific interactions of a guest molecule and its immediate neighbours in the host material. In addition the interactions between the host molecules surrounding the guest molecule need to be included. The resulting energy level shifts with respect to an isolated guest molecule and the induced electric moments then have to be averaged over all possible guest-host configurations. We see clearly a correlation between the size of the matrix-induced dipole moments and the room temperature dielectric constant, E, of the host material, fig. 3. A&, increases by more than a factor of two from PE which has the smallest dielectric constant to PMMA with the largest dielectric constant. Another centrosymmetric molecule that has widely been used to investigate matrix-induced dipole moments in different hosts is perylene. The values for the dipole moments are on the same order of magnitude
Table 1 Matrix
e
nz
A/&
PMMA PVB PS PE
3.45 3.02 2.56 2.26
2.22 2.21 2.53 2.22
0.12 0.102 0.064 0.050
(D) ‘) 0.155 0.122 0.068 0.050
Ei (lO”Vcm-‘)
1.8 2.32 1.53 1.82 0.96 1.02 0.75 0.75
b,
Z- (MHz) 428 240 680 70
‘) The values for the dipole moment differences in the left column have been calculated by inserting the room temperature dielectric constant into the Lorentzian field correction and the values on the right side have been obtained by using instead the square of the refractive index. b, The values for the local field in the left column have been calculated from the dipole moments in the left column and the local field values on the right side have been calculated from the dipole moments in the right column.
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CHEMICAL PHYSICS LETTERS
PMMA PVB
t
t
PE +
01 1.0
b
8
’
8
’ 2.0
3
9”
1
’
8
’ 8 3.0
8. E
Fig. 3. Plot of the matrix-induced dipole moments, A&, of OEP against the dielectric constants e of the matrix materials. The matrices were poly( methylmetacrylate) PMMA, poly(vinylbutyral) PVB, polystyrene PS and polyethylene PE.
as for OEP and show a similar dependence on the polarity of the matrix: in PE as a host the dipole moment difference is 0.06 D [ 91 whereas in the polar host PVB a more than four times larger value of 0.28 D has been found [ 15 1. Gu and Hanson [ 25 ] recently found for perylene in polar host PVB that the electric-field-induced decrease of the hole depth is much more significant than the associated hole broadening. Gu and Hanson conclude that the effect of the applied electric field on the spectral hole cannot be explained by matrix-induced dipole moments. Instead, they propose a reversible hole tilling mechanism caused by an electric-field-induced change of the equilibrium distribution of intrinsic two level systems. They assume that this mechanism mainly affects the hole depth rather than the hole width. This behavior is not in accord with the data of fig. 2. Based on the concept of matrix-induced point dipoles we can derive the strengths of the local matrix fields for the different matrices using eq. (2), Apind = AaEi. For the polarization tensor difference we insert Aa/4nt0 = 20 A3 [ 141. We obtain local field strength values of 0.7510x lo6 to 2.23~ lo6 V/ cm from PE to PMMA, see table 1. To estimate the strength of local fields on the basis of dielectric properties we use the concept of reaction fields, developed by Onsager [ 261 and extensively described by Bijttcher and P. Bordewijk [ 201. In this approach we consider a monomer unit in a polymer chain as having a permanent dipole moment and polarizability. The neighbouring monomer units tend to be oriented and polarized by the dipole 80
28 February 1992
field of the center unit. Thus the dipoles of the surrounding units give rise to a reaction field which in turn polarizes the center unit. In Onsagers model the center unit is described by a point dipole and a point polarizability in a spherical cavity of radius r. The surrounding matrix molecules are approximated by a macroscopic dielectric with dielectric constant t and refractive index n. In this model the reaction field, R, at the center of the cavity is R=
1 2(t-l)(n2+2) 47rt0 3(n2+2e)
1 ;TsPI
(7)
where p is the permanent dipole moment of the monomer unit in vacuum. As an approximation for the dipole moments of the monomer units we use for PMMA the dipole moment of methylmethacrylate (p= 1.88 D), for PVB we insert the dipole moment of 2-ethyl-1,3-dioxane (p= 1.93 D), and for PS we use toluene (p = 0.36 D). The volumes per monomer unit, I’,, can be estimated from the density, 4 of the polymer, the molecular weight, MW, and the molecular weight per monomer unit. The molecular data and the resulting reaction fields are listed in table 2. Comparing the strengths of the reaction fields and the local fields obtained from the matrix-induced dipole moments we see an astonishingly good agreement. This provides further evidence that the matrix-induced dipole moments of OEP in these matrices can be explained by local fields created by the dipole moments of the host molecules. The values for Ei obtained form A& are somewhat smaller than those for the reaction field. Part of this systematic deviation can be referred to uncertainties of the values for Aa, r and ,u which we have used to calculate Eiand R.This could arise from the fact that the OEP molecules do not really replace a monomer but rather experience the reaction fields caused by neighbouring host molecules. Even though there is no dipolar monomer unit for PE, we obtain from A&, a substantial local field strength of 0.75x lo6 V/cm which is not much smaller than the local field value found for PS. Even though we can formally attribute a matrix-induced dipole moment difference for OEP in PE, the mechanism responsible for the linear, reversible electric field induced broadening of the spectral holes in this system cannot be derived from our measurements. Three mechanism could play a role in the experi-
CHEMICAL PHYSICS LETTERS
Volume 190, number 1,2
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Table 2 Polymer
MW
d
Vu( 10mz3cm’)
Monomer
p(D)
R (106Vcm-‘)
PMMA PVB PS
12000 36000 45000
1.18 1.08 1.06
14.1 21.7 16.3
methylmethacrylate S-ethyl-l ,3-dioxane toluene
1.88 a’ 1.93 b’ 0.36 c’
12.7 7.7 1.7
a) Ref. [27].
b)Ref. [28].
“Ref. [29].
mentally observed effect: ( 1) Any low symmetry charge distribution surrounding a guest molecule reduces its symmetry and hence induces an electric moment. Since it is very unlikely that the PE chains are symmetrically aligned around the embedded OEP molecules, one expects inhomogeneous local fields, caused by the PE charge distribution near the OEP molecules. It should be noted that the eight peripheral ethyl groups of the OEP molecules are most likely not symmetrically stretched in an amorphous environment leading to small dipole moments. (2) Dispersive interactions between the guest and the host molecules (i.e. mutual guest-host polarization) lead to matrix-induced dipole moments and a general redshift of up to several hundred wave numbers [ 161. This red-shift is present in all solution spectra. Recent Stark effect measurements of van der Waals complexes in the gas phase have shown that dispersion interactions can result in significant electric dipole moments. The benzene-&-argon complex, where one argon atom is sitting above the benzene plane, has a static electric dipole moment of 0.12 D in the electric ground state of benzene [ 301. Gerblinger et al. [9] explain the electric-tield-induced hole broadening observed for perylene in PE as being caused by electric field induced variations of the dispersive guest-host interactions. (3) The local guest-host configuration may be modelled by an ensemble of two-energy-level systems [ 3 11. A reversible electric field associated tunneling process as suggested by Gu and Hanson [ 25 ] may happen. In contrast to Gu’s model, however, a distribution of two-level systems which give different frequency shifts for the guest molecules is required, to explain the experimentally observed linear electric field induced hole broadening. Finally, we want to note that the minimum hole widths decrease from PMMA, PVB, to PE as e decreases. This indicates that the coupling mechanisms responsible for dephasing in these matrices are of
similar nature as the static guest-host interactions. In PS however, we found by far the largest minimum hole width, though the dielectric constant is considerably smaller for PS than for PMMA or PVB. Recent comparisons between spectral hole widths and widths obtained from direct measurements of dephasing times, using photon echoes, have shown that the minimum hole widths in organic glasses are affected by dephasing and spectral diffusion [ 18,19 1. In PS spectral diffusion may be considerably larger than in the other matrices [ 321. A possible mechanism would be the tipping of phenyl rings in PS, in the vicinity of the probe molecules.
Appendix If the polarization of the probing light and the applied electric field are parallel [ 6 1, A=Q(3-6cos2B+3cos48), B=Q(-6+36cos28-30cos4t9), c= g (3 - 30 cos2e+ 35 cos4B) )
(A.la)
if the polarization of the light and the applied electric field are perpendicular [ 61,
A=&(9+6C03e+9C0S48), B= & (6 + 36 Cos28- 90 COS40) , c=g
(9-
90~02.28+io5C0S4e).
(A.lb)
In holographic detection it is convenient to separate grating effects and the average absorption. The normalized diffraction efficiency of a laser-induced grating can be defined as the ratio between the intensities of the diffracted and the transmitted beam, For gratings with low normalized difV=zdifT/ztra*s* fraction efficiency [ 2 1 ] 81
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CHEMICAL PHYSICS LETTERS
9=(&)2+(&g.
(AZ)
c~, is the amplitude of the spatially modulated absorption coefficient and /I, = (2x/&)n, is related to the amplitude of the spatially modulated refractive index, n,. d is the thickness of the grating and 8’ is the angle between the transmitted and the diffracted beam. For a shallow spectral hole the absorption and refractive index gratings are harmonic, and the grating amplitudes, (11,and n,, are the same as the hole depth, ACY,and the corresponding refractive index change, An. An can be calculated in the same way as Acr. Introducing A = 2, andB=C=Ointoeq. (12) of ref. [ 6 1, gives An(w)= $yK tin (r/2J2+
X
(r/2)2+
(Ammax +wJ2
(AU,,, -0)’
(A.3)
The statistical average of eq. (A.2) over the distribution of Apind is in analogy to eq. (6), An(A&,,,, 0) 03 =
s
G(A&&
xn(w)
dAw .
(A.4)
0
[ 11 A.P. Marchetti, M. Scozzafava and R.H. Young, Chem. Phys. Letters 5 1 ( 1977) 424. [ 21 V.D. Samoilenko, N.V. Razumova and R.I. Personov, Opt. Spectry. 52 (1982) 346. [3] F.A. Burkhalter, G.W. Suter, U.P. Wild, V.D. Samoilenko, N.V. Rasumova and R.I. Personov, Chem. Phys. Letters 94 (1983) 483. [4] U. Bogner, P. Schlitz, R. See1 and M. Maier, Chem. Phys. Letters 102 (1983) 267.
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[ 51 A.I.M. Dicker, L.W. Johnson, M. Noort and J.H. van der Waals, Chem. Phys. Letters 94 (1983) 14. [6] A.J. Meixner, A. Renn. S.E. Bucher and U.P. Wild, J. Phys. Chem. 90 (1986) 6777. [7] L. Kador, D. Haarer and RI. Personov, J. Chem. Phys. 86 (1987) 5300. [8] A. Renn, S.E. Bucher, A.J. Meixner, E.C. Meister and U.P. Wild, J. Luminescence 39 (1987) 181. [ 9 ] J. Gerblinger, U. Bogner and M. Maier, Chem. Phys. Letters 141 (1987) 31. [lo] Th. Sesselmann, L. Kador, W. Richter and D. Haarer, Europhys. Letters 5 ( 1988) 36 1. [ 111 A. Renn, A.J. Meixner, U.P. Wild and F.A. Burkhalter, Chem. Phys. 93 (1985) 157. [ 121 P. Schatz and M. Maier, J. Chem. Phys. 87 (1987) 809. [ 131 A.J. Meixner, Ph.D. Thesis, Dissertation ETH Nr. 8726 (1988). [ 141 L. Kador, S. Jahn, D. Haarer and R. Silbey, Phys. Rev. B 4 1 (1990) 12215. [ 151 Y. Kanaan, T. Attenberger, U. Bogner and M. Maier, Appl. Phys. B 51 (1990) 336. [ 161 E.G. McRae, J. Phys. Chem. 61 (1957) 562. [ 171 W.Z. Liptay, Z. Naturforsch. 20a (1965) 1441. [ 181 CA. Walsh, M. Berg, L.R. Narasimhan and M.D. Fayer, J. Chem. Phys. 86 (1987) 77. [ 191 M. Berg, C.A. Walsh, L.R. Narasimhan, K.A. Littau and M.D. Fayer, J. Chem. Phys. 88 (1988) 1564. [20] C.J.F. Bottcher and P. Bordewijk, Theory of electric polarization, Vol. 1 (Elsevier, Amsterdam, 1978). [ 211 A.J. Meixner, A. Renn and U.P. Wild, J. Chem. Phys. 91 (1989) 6728. [ 221 Reference Data for Radio Engineers, 5th Ed. (ITT, 1968) 4-28. [23] J. Brandrup and E.H. Immergut, eds., Polymer handbook, 3rd Ed. (Wiley, New York, 1989). [ 241 Aldrich catalog 1990 (Aldrich Chem. Co., Wisconsin, 1990). [25] W. GuandD.M. Hanson, J. Chem. Phys. 89 (1988) 2615. [26] L. Onsager, J. Am. Chem. Sot. 58 (1936) 1486. [27] R.K. Khanna and J. Sabhanadri, J. Phys. D 6 (1973) L63. [ 281 A.L. Mcclellan, Tables of experimental dipole moments, 3rd Ed. (Rahara Enter-prices, El Cerrito, 1989) p. 283. [ 291 A.L. Mcclellan, Tables of experimental dipole moments, 2nd Ed. (Rahara Enterprices, El Cerrito, 1974) p. 246. [ 301 Th. Brupbacher and A. Bauder, Chem. Phys. Letters 173 (1990) 435. [ 3 11 J.M. Hayes, R. Jankowiak and G.J. Small, in: Persistent spectra1 hole-burning: science and applications, ed. W.E. Moemer (Springer, Berlin, 1988). [ 321 P.J. Van der Zaag, J.P. Galaup and S. Viilker, Chem. Phys. Letters 166 (1990) 263.
CHEMICAL PHYSICS LETTERS
Spectral hole-burning and Stark effect: a centrosymmetric in polymers of different dielectric constants
28 February 1992
molecule
Alfred J. Meixner ‘, Alois Renn and Urs P. Wild Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092 Zurich, Switzerland Received 26 June 199 1; in final form 25 October 199 1
The electric field effect of spectral holes, in the S, +So absorption band of octaethylporphyrin (OEP), is studied in matrices with different dielectric constants, t. The analysis of the hole-contours shows that the Stark effect is linear and provides an average matrix-induced dipole moment, A&,,, which results from the polarization of the OEP molecules by the surrounding host molecules. The values of A&, increase with t of the host. The matrix materials were poly(methylmetacrylate), poly(vinylbutyral), polystyrene and polyethylene.
1. Introduction The influence of externally applied electric fields on spectral holes has been investigated in a several publications [ 1- 10 1. Since spectral holes can be three to five orders of magnitude narrower than inhomogeneously broadened absorption bands, moderate electric field strengths are sufficient to affect the Lorentzian hole contours significantly. In amorphous hosts often a broadening and decrease of the hole contours is observed as the applied field strength is increased. With sensitive detection techniques [ 111 precise measurements of the electric-field-dependent deformations of spectral hole contours can be performed. The analysis of the electric field effect indicates that the hole shapes do not only depend on the applied field strength but in addition on the orientation of the electric field with respect polarization of the light [ 6,7,12]. Spectral holes, in the inhomogeneously broadened S, tSo absorption band of cresylviolet perchlorate in a poly (vinylbutyral) matrix split when the electric field is applied parallel and broaden when the field is applied perpendicular to the polarization of the light [ 8 1. A detailed analysis which includes the dichroism of spectral holes and the geometry of the experiment, revealed that ’ Present address: IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95 120-6099, USA.
the experimental data can be best described by assuming that the difference between the electric dipole moments in the ground and the excited state is composed of an intrinsic molecular part, A,u,,,,~= 2.1 D, and a randomly oriented, matrix-induced part, A&, =0.9 D [ 81. AP:,.,~is fairly large and results from the polarization of the guest molecules by the surrounding host molecules. Also for centrosymmetric molecules like perylene, octaethylporphyrin, Zn-tetrabenzoporphin, and phthalocyanine [ 4,6,7, 10,13- 15 ] a linear Stark effect has been observed. Within the range of applied field strengths, which reached tens of kV/cm, the hole broadening was fully reversible and the original hole widths were recovered when the initial field strength was restored. In all examples the center frequencies of the holes were not affected by the applied electric field indicating that a second-order Stark effect can be neglected at these field strengths. The magnitude of the matrix-induced dipole moments being on the order of intrinsic dipole moments suggest that the distortion of the guest molecules by the surrounding host molecules is rather large. This reflects that an amorphous solid is highly anisotropic on a molecular scale and that a set of dye molecules with identical transition frequencies is not uniform with respect to the strengths of interactions between the guest and the host molecules. The matrix-induced Stark effect was interpreted by Bogner
0009-2614/92/S 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
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et al. [ 41 as polarization of guest molecules by local electric fields built up by the surrounding host molecules [ 4,6,13,15 ] and by dispersion interactions [ 91. The same mechanisms play an important role in the discussion of inhomogeneous line broadening and solvent shifts [ 16,17 1. In a recent publication a variation of the matrix-induced dipole moment difference and the optical zero-phonon linewidth over the inhomogeneously broadened absorption band has been found for octaethylporphyrine in polystyrene [ 141. As a consequence one expects that the matrixinduced dipole moments depend on the strength of the local matrix fields and thus are linked to the dielectric properties of the host. To test this hypothesis, we investigate in this Letter the effect of external electric field on spectral holes of the centrosymmetric molecule octaethylporphyrin (OEP) in host materials with different dielectric constants, t. The experimental electric-field-dependent hole contours are analyzed in terms of analytical expressions, derived from a detailed theoretical model. We observe a significantly stronger hole broadening by an external field in the polar matrices PMMA and PVB than in the apolar matrix PE. Consequently we find decreasing values for the matrix induced dipole moments, A&, from the host with the largest t to the matrix with the smallest t. In addition, the minimum detectable hole widths which are determined by optical dephasing and spectral diffusion [ 18,191, follow the same trend, with the exception of the OEP-PS guest-host system. From the matrix-induced dipole moments and the polarizability tensor difference of OEP we can calculate values for the internal matrix fields. We compare these local field values to reaction fields determined from the monomer dipole moments on the basis of the Onsager model [ 201.
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1992
oration of the solvent, giving clear, transparent films of about 0.2 mm thickness. The PE and PS films were prepared by melting the polymers in glass shells and dissolving the pure dye in the melt. The hot doped polymers were squeezed to give thin raw films which could easily be removed from the glass surfaces after cooling to room temperature. Samples of good optical quality with a uniform thickness of z 100 pm were fabricated by annealing the raw films between glass plates at about 120°C for several hours. The glass plates carried an electrically conducting, optically transparent coating on the inner sides in order to apply an electric field to the sample. The optical density of the samples was on the order of 0.8 at the maximum of the S, cS,, absorption band. 2.2. Experimental arrangement and measurement Spectral holes were burnt and detected using the holographic detection method which gives shot noise limited zero background signals [ 11,2 11. Coherent CR 699-2 1 or CR 599-2 1 dye lasers were used as coherent narrow band light sources. The burning intensity was on the order of 10 uW/cm’ and the spot diameter on the sample was 3 mm. Details conceming the apparatus and the holographic detection method are described elsewhere [ 6,11,21]. The samples were in contact with liquid helium at a temperature of 1.7 K. The spectral holes were 5W deep. The hole contours were determined by measuring the diffracted light intensity at 5 12 positions equally spaced over a frequency range of 30 GHz, centered at the burning frequency. The applied field strengths typically ranged from + 5, ? 10 up to ? 30 kV/cm. The holes were slightly broadened due to photochemical bleaching. The minimum hole widths were determined by extrapolation to zero burning fluence from sets of spectral holes which had been burnt with decreasing fluences.
2. Experimental 2. I. Sample preparation
3. Line shape analysis
The PMMA and PVB films were prepared by dissolving the polymers in dichloromethane. OEP was dissolved in the same solvent and added to the solution of the polymers. The mixtures were stored in open glass shells for several days to allow the evap-
In this section, we derive an analytical expression for the electric-field-dependent hole contours, for molecules with matrix-induced dipole moments. The fact that the spectral holes are burnt and probed with linear polarized laser light is taken into account.
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When a static electric field is applied to the sample, the energy levels of a guest molecule is shifted due to the interaction of the electric dipole moments with the electric field. This results in a shift of the transition frequency Aw of a specific guest molecule which is, neglecting the second-order Stark effect, Am= f ]A,u] ]Es] cos/9.
(1)
Ap=p,, -p, is the difference of the electric dipole moments in the ground (S,) and the excited states (S,). Es is the change of the local electric field, Ei =EO +E,, due to the externally applied electric field, and j? is the angle between Ap and Es. Formally Ap can be interpreted as the product of the polarizability tensor difference, Au, between the ground and the excited states and the local electric field, Ei at the center of the guest molecule [ 61, Ap=AaEi.
(2)
The observation of a purely linear Stark effect suggests that 1EP I 3 IEs I. Hence the contribution of Es to Ei can be neglected in eq. (2 ). In order to calculate the electric-field-dependent hole shapes for molecules with a particular angle 8 between Ap and the transition moment, D, we introduced an orientation distribution function P(&B) sinBdS 161,
28 February 1992
field-dependent hole contour (eq. ( 11) of ref. [ 6 ] ) leads to 2(Aw,,, +m) r
Ao(w)=$V,SK +tan-’
(4)
No is the number-density of guest molecules before burning, S is the absorption cross section and K depends on the burning fluence and the quantum efficiency of the hole formation. jr is the hole width when no external field is applied and Ao,,,=~is the maximum frequency shift for a guest molecule which occurs when Apindand the external field are parallel (eq. (1) cos/3=1). In fig. la a(o) is plotted as a function of the frequency for field strengths corresponding to Ao, = 0, 2r, 4r, 6Tand gr As the field strength increases the hole broadens symmetrically with respect to the center frequency and the amplitude decreases, the area under the contour remains constant. At zero field strength Aa approximates a Lorentzian line
P(8,j?) sin 8 de = (A+Bcos2j?+Ccos4~)
sin8dfI.
(3)
P( 8, /3) sin fi d/3 is the relative number of molecules, absorbing the probing light, which have a frequency shift Ao= (A@Jfi) cos 8. The coefficients A, B and C depend on the angle 0 between Ar and D, and on the orientation of the applied electric field with respect to the polarization of the light, and are given in the Appendix. We suppose a random orientation of AFind in the plane of the OEP molecules, i.e. all angles 8 having the same probability. Averaging the orientation distribution function can be performed by integrating eq. (3) over 8 within the limits of 0 G 6% 2x. For both experimental geometries we find, A = $ while B= C= 0. This reflects that the hole contours become insensitive to the orientation of the applied field with respect to the polarization of the light. Introducing A = 2 into the expression for the electric-
-10
10
0 Frequency
[r]
Fig. I. Electric field dependent hole contours (a) and hologram signals (b) calculated from eq. (4) and eq. (A.2) for molecules with random orientation of matrix-induced dipole moments. The electric field dependent broadening, Aw= A&E,/fi is 0,2r, 4r, W, and 8I’. 77
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shape with a half-width of r. Since the spectral holes have been burnt and detected as laser-induced gratings (plane wave holograms) we present in addition (fig. 1b) the contours of the holographic signal. Details on the holographic detection technique are described elsewhere [ 6,2 11. The hologram efficiency depends on the amplitudes of both the spatially modulated absorption coefficient and the spatially modulated refractive index and is given in the Appendix (eq. (A.2) ). The area of the signal decreases proportional to Aw ;a,. The hole contours described by eq. (4) include the orientational averaging of matrix-induced dipole moments of one fixed size 1Apind 1. In addition the lengths Of AFind are not uniform. Here we assume an isotropic Gaussian distribution of local matrix fields (Bogner et al. [ 41). Due to the random structure of an amorphous host the vector sum of all matrix fields cancels. However, for a specific guest-host configurations the local fields may be large, leading to a considerable distortions of the guest molecules. For guest molecules with disk-like polarizability tensors the distribution function for the electric-field-dependent frequency shift, Awmax, is [ 6 ]
IF
OV/cm
lOkV/cm
1 ?lL
F
01
SOkV/cm
20kV/cm
/ww
-15
I
0
h1
I
il.5 Frequency
I
i
0
+15
[Gtiz]
Fig. 2. Influence of an applied electric field on a holographically detected spectral hole, burnt in the S,+S, absorption band of octaethylporphyrin (OEP) in a poly(vinylbutyra1) (PVB) matrix at 1.7 K.
2
xexpl(2)
J.
AWL,, = A&EJfi= AaEiE,/h is the root mean square value of the maximum frequency shift, Aa is the change of the polarizability tensor upon excitation and EI is the distribution parameter of the local matrix fields. The average of eq. (4) is then, Ao(A&,ax, m =
s 0
w)
G(Aw,,,)xAcY(w)~Aw,,,
.
(6)
4. Results and discussion Fig. 2 illustrates the influence of an applied electric field on a spectral hole burnt into the Si cSo absorption band of OEP. The host material was PVB and the sample was kept at a temperature of 1.7 K 78
in liquid helium. The hole was burnt as a laser-induced plane wave grating and the diffracted light was detected during the frequency scan. It is clearly seen that the hole contour significantly broadens symmetrically with respect to the center frequency and decreases as higher electric field strengths are applied. The line center is hot shifted, ruling out a quadratic Stark effect within our field strength limits. The analysis of an experimental data set for a guest-host system was performed in two steps: First, the electric-field-dependent broadening, Aw ‘,,, , of a spectral hole was determined for every field strength separately by fitting eq. (A.2) to the hole contour, using the electric-field-dependent absorption coefficient (eq. (4) ) and refractive index (eq. (A.3) ) averaged with the distribution (eq. (5) ) for the electric-field-dependent molecular frequency shift Aw,,,. The fitting parameter in this procedure was the root mean square value, Aw A,, , of the distribution function (eq. ( 5 ) ). The value for the hole width at zero electric field strength was inserted as a fixed parameter and kept constant in the fitting of the fleld-de-
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pendent curves. In the second step the matrix-induced dipole moment difference, A,&,, was obtained by a linear regression of A&.,,,, versus the applied field strength, Es, using the expression, The uncertainties for Am,,, A&,,, = A&E& from the curve fitting and for A,&, from the linear regression are on the order of 1%. In order to calculate the average local Stark field, Es, resulting from the applied voltage, we used the Lorentzian field correction [20],E,=f(e+2)(U/d),where Uistheapplied voltage, d is the distance between the electrodes and c is the dielectric constant of the host material. The Lorentzian field correction takes into account a contribution to the local field which results from the polarization of the matrix when the external field is applied. Dielectric constants at 1.7 K are not readily available. Thus we calculated the A&, values, using in the Lorentzian field correction either the dielectric constants or the squares of the refractive indexes, both for room temperature. When the square of the refractive index is smaller than the respective dielectric constant, as for PMMA and PS, a larger value results for the dipole moment difference. Hence, the values obtained with the refractive index represent an upper limit, whereas those obtained with the room temperature dielectric constant represent the lower limit. In table 1 Ap& is listed for the different polymers which are PMMA, PVB, PS and PE, together with the room temperature dielectric constants [ 221, the squares of the refractive indexes [23,24] and the minimum hole widths. An uncertainty of 8% has to be attributed to the results: 6% of which result from the thickness measurement of the sample, lob results from the determination of the applied voltage and 1Wfrom the fitted data. Our
values for the matrix-induced dipole moments OEP in the PS host are somewhat smaller than the results recently found by Kador et al. [ 141 in the same guest-host system. The excellent agreement between the experimental data and the theoretical model supports the concept that the linear, electric-field-dependent hole broadening can be explained as a linear Stark effect, based on the interaction of matrix-induced dipole moments and the externally applied electric field. In this model the matrix-induced dipole moments result from the polarization of the guest molecules by local matrix fields, created by the surrounding host molecules. Here we assumed homogeneous matrix fields and a disk-like point polarizability tensor, creating point dipoles at the centers of the guest molecules. A more elaborate model would be based on the specific interactions of a guest molecule and its immediate neighbours in the host material. In addition the interactions between the host molecules surrounding the guest molecule need to be included. The resulting energy level shifts with respect to an isolated guest molecule and the induced electric moments then have to be averaged over all possible guest-host configurations. We see clearly a correlation between the size of the matrix-induced dipole moments and the room temperature dielectric constant, E, of the host material, fig. 3. A&, increases by more than a factor of two from PE which has the smallest dielectric constant to PMMA with the largest dielectric constant. Another centrosymmetric molecule that has widely been used to investigate matrix-induced dipole moments in different hosts is perylene. The values for the dipole moments are on the same order of magnitude
Table 1 Matrix
e
nz
A/&
PMMA PVB PS PE
3.45 3.02 2.56 2.26
2.22 2.21 2.53 2.22
0.12 0.102 0.064 0.050
(D) ‘) 0.155 0.122 0.068 0.050
Ei (lO”Vcm-‘)
1.8 2.32 1.53 1.82 0.96 1.02 0.75 0.75
b,
Z- (MHz) 428 240 680 70
‘) The values for the dipole moment differences in the left column have been calculated by inserting the room temperature dielectric constant into the Lorentzian field correction and the values on the right side have been obtained by using instead the square of the refractive index. b, The values for the local field in the left column have been calculated from the dipole moments in the left column and the local field values on the right side have been calculated from the dipole moments in the right column.
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PMMA PVB
t
t
PE +
01 1.0
b
8
’
8
’ 2.0
3
9”
1
’
8
’ 8 3.0
8. E
Fig. 3. Plot of the matrix-induced dipole moments, A&, of OEP against the dielectric constants e of the matrix materials. The matrices were poly( methylmetacrylate) PMMA, poly(vinylbutyral) PVB, polystyrene PS and polyethylene PE.
as for OEP and show a similar dependence on the polarity of the matrix: in PE as a host the dipole moment difference is 0.06 D [ 91 whereas in the polar host PVB a more than four times larger value of 0.28 D has been found [ 15 1. Gu and Hanson [ 25 ] recently found for perylene in polar host PVB that the electric-field-induced decrease of the hole depth is much more significant than the associated hole broadening. Gu and Hanson conclude that the effect of the applied electric field on the spectral hole cannot be explained by matrix-induced dipole moments. Instead, they propose a reversible hole tilling mechanism caused by an electric-field-induced change of the equilibrium distribution of intrinsic two level systems. They assume that this mechanism mainly affects the hole depth rather than the hole width. This behavior is not in accord with the data of fig. 2. Based on the concept of matrix-induced point dipoles we can derive the strengths of the local matrix fields for the different matrices using eq. (2), Apind = AaEi. For the polarization tensor difference we insert Aa/4nt0 = 20 A3 [ 141. We obtain local field strength values of 0.7510x lo6 to 2.23~ lo6 V/ cm from PE to PMMA, see table 1. To estimate the strength of local fields on the basis of dielectric properties we use the concept of reaction fields, developed by Onsager [ 261 and extensively described by Bijttcher and P. Bordewijk [ 201. In this approach we consider a monomer unit in a polymer chain as having a permanent dipole moment and polarizability. The neighbouring monomer units tend to be oriented and polarized by the dipole 80
28 February 1992
field of the center unit. Thus the dipoles of the surrounding units give rise to a reaction field which in turn polarizes the center unit. In Onsagers model the center unit is described by a point dipole and a point polarizability in a spherical cavity of radius r. The surrounding matrix molecules are approximated by a macroscopic dielectric with dielectric constant t and refractive index n. In this model the reaction field, R, at the center of the cavity is R=
1 2(t-l)(n2+2) 47rt0 3(n2+2e)
1 ;TsPI
(7)
where p is the permanent dipole moment of the monomer unit in vacuum. As an approximation for the dipole moments of the monomer units we use for PMMA the dipole moment of methylmethacrylate (p= 1.88 D), for PVB we insert the dipole moment of 2-ethyl-1,3-dioxane (p= 1.93 D), and for PS we use toluene (p = 0.36 D). The volumes per monomer unit, I’,, can be estimated from the density, 4 of the polymer, the molecular weight, MW, and the molecular weight per monomer unit. The molecular data and the resulting reaction fields are listed in table 2. Comparing the strengths of the reaction fields and the local fields obtained from the matrix-induced dipole moments we see an astonishingly good agreement. This provides further evidence that the matrix-induced dipole moments of OEP in these matrices can be explained by local fields created by the dipole moments of the host molecules. The values for Ei obtained form A& are somewhat smaller than those for the reaction field. Part of this systematic deviation can be referred to uncertainties of the values for Aa, r and ,u which we have used to calculate Eiand R.This could arise from the fact that the OEP molecules do not really replace a monomer but rather experience the reaction fields caused by neighbouring host molecules. Even though there is no dipolar monomer unit for PE, we obtain from A&, a substantial local field strength of 0.75x lo6 V/cm which is not much smaller than the local field value found for PS. Even though we can formally attribute a matrix-induced dipole moment difference for OEP in PE, the mechanism responsible for the linear, reversible electric field induced broadening of the spectral holes in this system cannot be derived from our measurements. Three mechanism could play a role in the experi-
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Table 2 Polymer
MW
d
Vu( 10mz3cm’)
Monomer
p(D)
R (106Vcm-‘)
PMMA PVB PS
12000 36000 45000
1.18 1.08 1.06
14.1 21.7 16.3
methylmethacrylate S-ethyl-l ,3-dioxane toluene
1.88 a’ 1.93 b’ 0.36 c’
12.7 7.7 1.7
a) Ref. [27].
b)Ref. [28].
“Ref. [29].
mentally observed effect: ( 1) Any low symmetry charge distribution surrounding a guest molecule reduces its symmetry and hence induces an electric moment. Since it is very unlikely that the PE chains are symmetrically aligned around the embedded OEP molecules, one expects inhomogeneous local fields, caused by the PE charge distribution near the OEP molecules. It should be noted that the eight peripheral ethyl groups of the OEP molecules are most likely not symmetrically stretched in an amorphous environment leading to small dipole moments. (2) Dispersive interactions between the guest and the host molecules (i.e. mutual guest-host polarization) lead to matrix-induced dipole moments and a general redshift of up to several hundred wave numbers [ 161. This red-shift is present in all solution spectra. Recent Stark effect measurements of van der Waals complexes in the gas phase have shown that dispersion interactions can result in significant electric dipole moments. The benzene-&-argon complex, where one argon atom is sitting above the benzene plane, has a static electric dipole moment of 0.12 D in the electric ground state of benzene [ 301. Gerblinger et al. [9] explain the electric-tield-induced hole broadening observed for perylene in PE as being caused by electric field induced variations of the dispersive guest-host interactions. (3) The local guest-host configuration may be modelled by an ensemble of two-energy-level systems [ 3 11. A reversible electric field associated tunneling process as suggested by Gu and Hanson [ 25 ] may happen. In contrast to Gu’s model, however, a distribution of two-level systems which give different frequency shifts for the guest molecules is required, to explain the experimentally observed linear electric field induced hole broadening. Finally, we want to note that the minimum hole widths decrease from PMMA, PVB, to PE as e decreases. This indicates that the coupling mechanisms responsible for dephasing in these matrices are of
similar nature as the static guest-host interactions. In PS however, we found by far the largest minimum hole width, though the dielectric constant is considerably smaller for PS than for PMMA or PVB. Recent comparisons between spectral hole widths and widths obtained from direct measurements of dephasing times, using photon echoes, have shown that the minimum hole widths in organic glasses are affected by dephasing and spectral diffusion [ 18,19 1. In PS spectral diffusion may be considerably larger than in the other matrices [ 321. A possible mechanism would be the tipping of phenyl rings in PS, in the vicinity of the probe molecules.
Appendix If the polarization of the probing light and the applied electric field are parallel [ 6 1, A=Q(3-6cos2B+3cos48), B=Q(-6+36cos28-30cos4t9), c= g (3 - 30 cos2e+ 35 cos4B) )
(A.la)
if the polarization of the light and the applied electric field are perpendicular [ 61,
A=&(9+6C03e+9C0S48), B= & (6 + 36 Cos28- 90 COS40) , c=g
(9-
90~02.28+io5C0S4e).
(A.lb)
In holographic detection it is convenient to separate grating effects and the average absorption. The normalized diffraction efficiency of a laser-induced grating can be defined as the ratio between the intensities of the diffracted and the transmitted beam, For gratings with low normalized difV=zdifT/ztra*s* fraction efficiency [ 2 1 ] 81
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9=(&)2+(&g.
(AZ)
c~, is the amplitude of the spatially modulated absorption coefficient and /I, = (2x/&)n, is related to the amplitude of the spatially modulated refractive index, n,. d is the thickness of the grating and 8’ is the angle between the transmitted and the diffracted beam. For a shallow spectral hole the absorption and refractive index gratings are harmonic, and the grating amplitudes, (11,and n,, are the same as the hole depth, ACY,and the corresponding refractive index change, An. An can be calculated in the same way as Acr. Introducing A = 2, andB=C=Ointoeq. (12) of ref. [ 6 1, gives An(w)= $yK tin (r/2J2+
X
(r/2)2+
(Ammax +wJ2
(AU,,, -0)’
(A.3)
The statistical average of eq. (A.2) over the distribution of Apind is in analogy to eq. (6), An(A&,,,, 0) 03 =
s
G(A&&
xn(w)
dAw .
(A.4)
0
[ 11 A.P. Marchetti, M. Scozzafava and R.H. Young, Chem. Phys. Letters 5 1 ( 1977) 424. [ 21 V.D. Samoilenko, N.V. Razumova and R.I. Personov, Opt. Spectry. 52 (1982) 346. [3] F.A. Burkhalter, G.W. Suter, U.P. Wild, V.D. Samoilenko, N.V. Rasumova and R.I. Personov, Chem. Phys. Letters 94 (1983) 483. [4] U. Bogner, P. Schlitz, R. See1 and M. Maier, Chem. Phys. Letters 102 (1983) 267.
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