Molecular Orientations in Azopolymer Holographic Diffraction Gratings

5754

J. Phys. Chem. B 1998, 102, 5754-5765

Molecular Orientations in Azopolymer Holographic Diffraction Gratings as Studied by Raman Confocal Microspectroscopy F. Lagugne´ Labarthet, T. Buffeteau, and C. Sourisseau* Laboratoire de Physico-Chimie Mole´ culaire, LPCM, UMR 5803 CNRS, UniVersite´ Bordeaux I, 351 cours de la Libe´ ration, 33 405 Talence, France ReceiVed: January 23, 1998; In Final Form: April 27, 1998

Optically isotropic films of an amorphous copolymer containing azobenzene moieties (pDR1M-co-MMA) were irradiated by interfering two circularly contrarotating polarized laser beams and permanent holographic diffraction gratings were prepared. These involve the formation of both birefringence and surface relief gratings. Using the Raman confocal microspectrometry, we have recorded various resonance enhanced polarized Raman spectra from the surface profile in order to get new insight into the orientational and angular distributions of the chromophore species. Different theoretical equations of the Raman scattering intensities, including a treatment taking into account the effect of the high numerical aperture objective, were thus derived. Calculations and simulations of these equations allowed us to extract the second 〈P2〉 and fourth 〈P4〉 coefficients of the chomophore orientation function in various regions of the surface grating and to obtain the corresponding information entropy normalized distribution functions. From the various shapes of the distribution functions we discuss the photoinduced effects and suggest that mass-transport effects must be also effective. Finally, in agreement with the modulated relative Raman intensities and four distinct distribution functions observed along the surface grating, we conclude that the orientational orders are primarily generated by an angular dependent photoselection process, which acts as an initializing force in the establishment of the various molecular organized domains. Such molecular organizations could occur in the viscoelastic state of the polymer and be responsible for an amplification of the light induced anisotropic effects in some regions (at the bottoms) and for a significant perturbation of the orientations in other regions (at the tops of the surface profile). In agreement with previous studies about the mechanisms of grating formation, these results are consistent with a model involving the existence of large pressure gradients due to a viscoelastic flow of the polymer.

I. Introduction Over the past decade, azo-dye containing polymer systems have been the subject of intensive research because of their potential uses in various optical applications such as photonmode optical memories,1,2 transducing optical information,3 optical switching,4 and nonlinear optics.5 One of the main interests of these amorphous polymer systems (high Tg) is due to their dichroic and birefringent properties when they are illuminated by a linearly polarized light; the photoinduced orientation of the azobenzene groups is due to trans-cis-trans isomerization and one can thus produce refractive index gratings and birefringence gratings (orientation and phase gratings). Recently, several groups have already found that large surface relief gratings could be directly recorded on azobenzene containing polymer films using two interfering polarized Ar+ laser beams (polarization recording) and high diffraction efficiencies up to 70-90% could be obtained in the first order diffracted beams.6-24 In fact, the formation of a surface relief modulation was first attributed to the polymer chain migration and, then, has been clearly demonstrated by atomic force microscopy (AFM) which has revealed surface profile depths near that of the original film thickness.9-14,17 Also, from dynamical experimental studies and polarization analyses of the transmitted (1 order diffraction beams during recordings, we * To whom correspondence should be addressed. E-mail: csouri@ morgane.lsmc.u-bordeaux.fr.

have recently characterized the contributions of the two distinct processes (i.e., the formations of a birefringence grating (∆n) and of a surface relief (∆d)) and found quite interesting and different results on DR1 dye-doped and -covalently bonded (or functionalized) polymer systems.25 In this study a general Jones’matrix formalism for birefringent materials was used and it was assumed that the orientation effects on the photochromic species were primarily governed by an “angular-hole-burning” (AHB) mechanism.26-28 Furthermore, the mechanism of optically inscribed highefficiency diffraction gratings in azopolymer films has been addressed by Barrett et al.;13 they propose that the phenomenon must involve pressure gradients as a driving force, due to different photochemical responses at different regions in the interference pattern. This would lead to regions of high transcis-trans isomerization bordered by regions of low isomerization. The resulting viscoelastic flow of the material from highpressure areas to low-pressure ones could explain the formation of the regularly spaced sinusoidal surface relief grating as observed by several groups. Under these conditions, from free volume requirements of the induced geometric changes and bulk viscosity properties of the polymer matrix, one can expect quite different orientation effects of the azo-chromophores on the tops and bottoms of the grating but, as far as we know, such molecular anisotropic orientation properties have not yet been revealed by any optical method. Since we have already shown that the Raman technique is a

S1089-5647(98)00859-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 07/08/1998

Raman Confocal Microspectroscopy

J. Phys. Chem. B, Vol. 102, No. 30, 1998 5755

SCHEME 1

very sensitive method to follow orientational and angular redistributions induced by a linearly polarized visible illumination in DR1-doped polymer films,29,30 in the present study we have similarly used the Raman scattering technique in conjunction with a confocal microscope to record various resonance enhanced polarized Raman spectra from the surface profile of an holographic diffraction grating already inscribed on an azofunctionalized polymer thin film. From theoretical equations of the relative Raman intensities, the Raman images obtained in the various areas are thus nicely explained. Moreover, this approach allows us to derive the second (〈P2〉) and fourth (〈P4〉) coefficients of the chromophore orientation function in the various regions by using either a simple formalism or a more accurate treatment taking into account the effect of the high numerical aperture objective. It is thus demonstrated that valuable information on the photoinduced and molecular orientation effects in such a potential optoelectronic system can be afforded by resonance Raman experiments. The paper is organized as follows: After the introduction, in section II, the samples and the experimental setup for the Raman measurements are described. In section III, the different theoretical equations of the Raman scattering intensities are derived and in section IV the results of the polarized Raman measurements are presented and discussed. Fittings of the experimental data and calculations of the two even parity 〈P2〉 and 〈P4〉 coefficients of the orientation distribution function are then discussed in section V; also, here the relative possible contributions of the photo- and mass transport-induced effects in the formation mechanisms of these diffraction gratings will be discussed and some main suggestions are presented. Finally, in section VI a summary of the main results obtained is given. II. Experiments The measurements reported were performed on samples of poly[4′-(((2-(methacryloyloxy)ethyl)-ethyl)amino)-4-nitroazobenzene-co-(methylmethacrylate)], hereafter so-called p(DR1M-coMMA). The general formula, the azo content, the glass transition temperature and the molecular weight of the analyzed copolymer are given in Scheme 1. Thin films were prepared by spin coating a chloroform solution of the copolymer onto a clean microscope glass substrate. The films were annealed for 20 min at 80 °C in order to remove any residual solvent and thicknesses varying from 0.9 to 1.5 µm were checked by profilometry measurements. Diffracting gratings were recorded by using a classical holographic set-up similar to that first proposed by Rochon et al.,10 which consisted of a sample film placed at right angle to a front surface miror. The incident beam, a 514.5 nm laser

Figure 1. Experimental set-up for the polarized micro-Raman measurements. (a) Measurements of the Z(YY)Z h and Z(YX)Z h spectra in the first experimental configuration. (b) Measurements of the Z(XX)Z h and Z(XY)Z h spectra in the second configuration.

pump (∼100 mW/cm2) from an Ar+ laser (ILT 5490), was expanded to a diameter of 10 mm and a quarter wave plate was used to set circular polarization, so that two contrarotating interfering beams were impinging the sample. The sample holder was set on a goniometer in order to control the incidence angle (θinc) which defines the pattern period (Λ) according to Bragg’s conditions: Λ ) λ/2 sin θinc. The incidence angle was set to 5°(15°) in order to write 3 µm (1 µm) grating spacings. The surface relief depth has been estimated by AFM measurements and, in both cases, it was roughly equal to 300 nm. The Raman spectra were recorded in the back-scattering geometry on a Labram I (Dilor-France) microspectrometer in conjunction with a confocal microscope (100X objective). The incident linear polarization was fixed due to the configuration set-up of the instrument which contains a Notch filter, eliminating the low-frequency elastic and inelastic contributions, instead of a classical beam splitter (Figure 1). Polarization analyses were performed on the Raman scattered radiation with a GlanThompson polarizing prism in the vertical (V) or horizontal (H) position and a depolarization scrambler (λ/4) in front of the entrance slit of the monochromator. In order to record different polarized Raman spectra, the sample was thus rotated by 90° in the XY plane (Figure 1). In addition, the already inscribed 3 µm (1 µm) period gratings were mounted on the XY-motorized table with 0.5 µm × 4 µm (0.2 µm × 2 µm) controlled displacements along the X and Y directions, respectively, and the Raman data were collected over 15 × 16 µm2 (7 × 8 µm2) surface areas. The acquisition time was fixed to 60 s per spectrum, i.e. a total run time of 7200 s (8400 s). Each Raman image for a selected vibrational mode is thus the result of intensity integrations over the 120 (140) recorded spectra. A minimum intensity power (∼10-30 µW) of the 632.8 nm incident beam from an He-Ne laser, even though the laser wavelength was outside of the absorption band contour of the chromophore, was used in order to avoid any thermal, photochemical or bleaching effect. Indeed, such a low laser intensity still corresponds to a very large irradiance of 1-3 kW/cm2 but fortunately, this polymer film (Abs ) 1.56 at λmax ) 471 nm, i.e., )7 × 104 L mol-1 cm-1) is practically not absorbing at 632.8 nm (Abs ) 6 × 10-3, i.e., )270 L mol-1 cm-1). Any bleaching effect could also be controlled by times to times on a monitor displaying the video white light image of the surface

5756 J. Phys. Chem. B, Vol. 102, No. 30, 1998

Lagugne´ Labarthet et al.

SCHEME 2

SCHEME 3

grating. Finally, a high sensitivity CCD air cooled detector was used for detection and the wavenumber measurements ((3 cm-1) were calibrated using plasma lines.

the main molecular symmetry axis and the in-plane X grating axis of the laboratory frame. Then, one can easily checked that for a linear polarization state of the incident beam either parallel (|) (see configuration a in Figure 1) or perpendicular (⊥) (see configuration b in Figure 1) to the grating grooves, the backscattered intensity expressions are given by

III. Theoretical Part According to recent theories of photoinduced anisotropy by a polarized beam, the reorientation of molecules is due to rotation and diffusion of chromophores during the photoisomerization cycles. Following Dumont and coworkers’ model26-28 these rotations may occur during the photoexcitation process (AHB), during the lifetime of the isomers (“angular redistribution”), and spontaneously inside the trans form (“angular relaxation”). Under these conditions it is obvious that the angular distribution of molecules will no longer be isotropic. Indeed, from previous real-time visible dichroism measurements29 and polarized Raman experiments30,31 we have previously followed the primary intramolecular orientational mechanisms leading to birefringence and we have shown that the AHB mechanism is dominant under moderate optical pumping. Then, theories of laser-induced dichroism as largely developed in studies of the orientational statistics in liquid crystals32-38 and in solutions39,40 can be extended to the present case of anisotropic thin films. 1. Raman Intensities in the AHB Model. First, because of the cylindrical symmetry of DR1 chromophores and of the effective resonance Raman scattering processes, the following diagonal molecular polarizability tensor is considered:

(

R1 0 0 5 ) 0 R1 0 R 0 0 R3

)

(1)

I0IJ ) CIpump〈R2IJnT〉

(2)

∫0

)

∫0

dψ

∫-1d(cosθ)nT(θ)[T(θ,φ,ψ)R5T (θ,φ,ψ)]

dφ

1

(4)

N 2 (R + R23 - 2R1R3) ) I|,0 YX 15 1

(5)

2 I⊥,0 XY ∝ 〈RXYnT〉 )

Now, one must consider that the birefringence gratings are formed by the two interfering circularly polarized pump beams. As indicated in Scheme 3, the path difference δ)2πX/Λ between the two pumps, where Λ is the period of the grating, gives rise to electric field components proportional to cos(θinc)cos(δ/2) and sin(δ/2) along the X and Y directions, respectively. Also, in the AHB process the population nT(θ) is governed by the following expression:26-28

nT(θ) )

(

) (

)

N N 1 1 ) 2 4π 1 + (σ φ τ I 4π 1 + Jcos2θp T TC cis pump)cos θp (6)

and in the weak pumping limit (J , 1) the angular density of trans chromophores is approximated by the equation

N (1 - Jcos2θp) 4π

(7)

where (θp) is the angle between the pump polarization direction and the main long axis of the chromophore. This last expression [7] should be used in the spatial averaging already given in eq 3, so that the calculated polarized Raman intensities are now modulated by a term proportional not only to the pump intensity J, but also on cos2(δ/2). After spatial averaging one gets

N 2 R (21 + 28a1 + 56a21) - J(15 + 105 3 δ 20a1 + 8a21) + Jcos2 (12 + 4a1 - 16a21) (8) 2

|,1 I(YY) ) (I|,0 YY - JIYY ) ∝

[

]

()

where C is a constant and the average quantity

2π

N (8R2 + 3R23 + 4R1R3) ) I|,0 YY 15 1

nT(θ) ≈

For standard Raman experiments in an isotropic medium, the angular density of scattering centers, nTrans ) nT ) N/4π, is independent of the tensor orientation but the Raman intensity depends on the averaging over all orientations in space:

〈R2IJnT〉 2π

2 I⊥,0 XX ∝ 〈RXXnT〉 )

t

2

(3)

is calculated using the normal T and transposed Tt classical Euler angle matrices. As shown in Scheme 2, θ is the angle between

|,1 ⊥,0 ⊥,1 I(YX) ) (I|,0 YX - JIYX) ) I(XY) ) (IXY - JIXY ) ∝

N 2 R (7 105 3

[

δ 14a1 + 7a21) - J(3 - 6a1 + 3a21) + Jcos2 (1 - 2a1 + a21) 2 (9)

()

]



N 2 R (21 + 28a1 + 56a21) - J(3 + 105 3 δ 8a1 + 24a21) - Jcos2 (6 + 2a1 - 8a21) (10) 2

1 〈P0〉 ) 1, 〈P2〉 ) 〈3 cos2θ - 1〉 and 2 1 〈P4〉 ) 〈35 cos4θ - 30 cos2θ + 3〉 (13) 8

where a1 ) R1/R3 is the ratio of the molecular polarizability coefficients, known to be very weak (,1.0) in such cylindrical polar molecules and the R3 tensor element is also expected to be dominant under resonance Raman conditions.30 Consequently, the above equations [8-10] show us that in the first experimental configuration (Figure 1a) with the incident field parallel to the grating grooves both Raman intensities (IYY) and (IYX) will be maxima for δ ) 0, 2π (at the tops) and minima for δ ) π (at the bottoms of the surface relief) and their Raman images should be in-phase. It must be underlined that one can easily checked the top and bottom positions of the surface relief by using a white lamp video transmission image of the grating under study. In contrast, in the second experimental geometry (Figure 1b) with the incident field perpendicular to the grating lines, the (IXX) Raman intensities will maximized for δ ) π and minimized for δ ) 0 or 2π, so that both (IXX) and (IXY) Raman images should be expected out-of-phase. This is a very important result, nicely verified in the experiments (see below), which will allow us to properly combine and scale along the X direction all the Raman results in order to obtain the variations of the ratios of relative Raman intensities along the surface relief, namely,

Furthermore, to extract mean values of these order parameters (or of the related 〈cos2θ〉 and 〈cos4θ〉 terms) with respect to the effective directions of the incident electric field, an additional rotation (R) around the Z axis has to be considered over the polarizability tensor. Indeed, this (R) rotation is necessary to take into account the changes in the direction of the incident electric field at different points of the grating and allows thus the calculation of the chromophore orientation functions anywhere along the surface relief. The corresponding Raman intensity expressions now depend on the following average quantities:

[

⊥,1 I(XX) ) (I⊥,0 XX - JIXX ) ∝

]

()

R1(δ) )

I(YX)

R2(δ) )

and

I(YY)

I(XY) I(XX)

(11)

and to extract values of the orientation coefficients in the various regions of the grating. However, we cannot go further using this simple model in which it is implicitly assumed in the spatial averaging that all the chromophores undergo similar orientation effects. Actually, the localized mass transport effects of the polymer chains which probably participate in the formation of a regularly sinusoidal surface relief must probably strongly perturbed the dye molecular orientations. 2. First Estimation of the Second and Fourth Coefficients in the Chomophore Orientation Function (Model 1). One considers now that all the photo- and/or transport-induced effects lead to anisotropic samples with localized regions keeping an uniaxial symmetry around the in-plane X axis of the grating (Scheme 2). The angular distributions of the chromophores are thus expressed by developing the function f(θ) on basis of the first even parity terms in Legendre’s polynomials:

〈nT〉 )

N

∫0

4π2

∫0

2π

dψ

2π

∫-1 f(θ) d(cosθ) )

dφ

∫-1+1 ∑

N

+1

( )

l)0,2,4

2l+1 2

〈Pl〉Pl(cosθ) d(cosθ) (12)

∫-1+1[21〈P0〉P0(cosθ) + 25〈P2〉P2(cosθ) +

〈nT〉 ) N

9 〈P 〉P (cosθ) d(cosθ) 2 4 4

]

where the coefficients 〈Pl〉 are the order parameters and for full cylindrical symmetry they are given by

5Tt(θ,φ,ψ)]Rt(R)]2〉 〈RIJ2〉 ) 〈[R(R)[T(θ,φ,ψ)R

(14)

It is noteworthy that R rotations of 0°, 45°, and 90° correspond to δ values equal to 0 (tops), π/2 (mid-slopes), and π radian (bottoms) or to X values equal to 0, Λ/4, and Λ/2 period on the grating, respectively (Scheme 3). Under these conditions and after substitution of 2R for δ, one can easily calculate the following intensity ratios for the two experimental geometries:

R1(δ) ) I(YX)/I(YY) ) {(0.75sin2 δ) + (4 - 7.5sin2 δ)〈cos2θ〉 + (8.75sin2 δ - 4)〈cos4θ〉}/ {0.75(cosδ + 1)2 + 1.5(3 - 2cosδ - 5cos2 δ)〈cos2θ〉 0.25(13 + 10cosδ - 35cos2 δ)〈cos4θ〉} (15) R2(δ) ) I(XY)/I(XX) ) {(0.75sin2 δ) + (4 - 7.5sin2 δ)〈cos2θ〉 + (8.75sin2 δ - 4)〈cos4θ〉}/ {0.75(cosδ - 1)2 + 3(1.5 + cosδ - 2.5cos2 δ)〈cos2θ〉 0.25(13 - 10cosδ - 35cos2 δ)〈cos4θ〉} (16) These complex expressions can be simplified for the particular cases δ ) 0, π/2, and π and lead to the more tractable equations:

R1(0) ) R2(π) )

4〈cos2θ〉 - 4〈cos4θ〉 3 - 6〈cos2θ〉 + 3〈cos4θ〉

R2(0) ) R1(π) )

8〈cos4θ〉

0.75 - 3.5〈cos2 θ〉 + 4.75〈cos4θ〉 π π ) R2 ) 2 2 0.75 + 4.5〈cos2θ〉 - 3.25〈cos4θ〉

()

R1

4〈cos2θ〉 - 4〈cos4θ〉

()

(17)

(18)

(19)

It is noteworthy that only in the last case (at the exact midslopes of the surface relief) both order parameters cannot be simultaneously determined. In any way, we have used this simple approach to estimate, what we call latter, approximate values in the model 1 of the 〈cos2θ〉 and 〈cos4θ〉 terms and of the 〈P2〉 and 〈P4〉 order parameters. 3. More Accurate Treatment Taking into Account the Effect of the High Numerical Aperture-Objective (Model 2). In back-scattering Raman microspectrometry it is well known that analyses of polarization measurements must be established using the known optical properties of the wide aperture objective and the refractive index of the sample. According to Turrell and coworkers’ studies41-43 and using the 〈R2IJ〉 expressions as derived from eq 14 in the first experimental geometry (Figure



1a) one must consider the more general intensity equations:

I(YX) ) (〈R2YX〉A + 〈R2YZ〉B)(2C0 + C2) + (〈R2ZX〉A + 〈R2ZZ〉B)(4C1) + (〈R2XX〉A + 〈R2XZ〉B)(C2) (20) I(YY) ) (〈R2YY〉A + 〈R2YZ〉B)(2C0 + C2) + (〈R2ZY〉A + 〈R2ZZ〉B)(4C1) + (〈R2XY〉A + 〈R2XZ〉B)(C2) (21) Similarly, in the second experimental configuration (Figure 1b), one must consider:

I(XY) ) (〈R2XY〉A + 〈R2XZ〉B)(2C0 + C2) + (〈R2ZY〉A + 〈R2ZZ〉B)(4C1) + (〈R2YY〉A + 〈R2YZ〉B)(C2) (22) I(XX) ) (〈R2XX〉A + 〈R2XZ〉B)(2C0 + C2) + (〈R2ZX〉A + 〈R2ZZ〉B)(4C1) + (〈R2YX〉A + 〈R2YZ〉B)(C2) (23) where the quantities A and B are obtained by integration of the squares of the electric vector components over the scattering cone and the coefficients C0, C1, and C2 are related to the focalisation efficiency and are calculated via integration of the incident electric field vector components over the effective irradiated volume. All these parameters are dependent on the angular semi-aperture of the objective (θm ) 64°.158 for an 100X lens with 0.9 numerical aperture) and on the refractive index of the sample (n ≈ 1.50) and their corresponding values can be found in the literature.43 In addition, it must be pointed out that for uniaxial systems the birefringence may introduce an additional depolarization which is expected significant when a weakly absorbing sample is illuminated along an optical axis. Fortunately, this depolarization is probably negligible in the present resonance Raman study of a strongly absorbing material since the effective volume of the sample is near the surface. Therefore, in this approach, hereafter called model 2, one can expect to determine more precise values of the order parameters, particularly at the tops and the bottoms of the surface relief where the sample surface is almost perpendicular to the revolution axis of the excitation and scattering cones. Nevertheless, it is clear that these last conditions are not fulfilled in the slopes of the grating; in these cases different average values of the A and B parameters can be estimated from geometric considerations but such corrections were found to be not significant. IV. Experimental Results Irradiation of a polymer film using an incident angle equal to 15° produces an holographic grating with the desired 1 µm intensity profile period (Λ) and reaching maximum diffraction efficiency of about 30-35% in 8000 s, as shown in Figure 2a. The efficiency of the grating is the ratio of the intensity of the first order (+1) diffracted beam to the incident read beam (λ ) 632.8 nm) intensity.25 We have checked that the image obtained by electronic microscopy revealed the modulation of the surface of the film and the formation of a regularly spaced surface relief coincident with the light intensity interference pattern. Here, in order to demonstrate the sensitivity of the Raman confocal microscopic technique a typical Raman image of this grating obtained on a large surface area (10 × 9 µm2) is presented in Figure 2b. This image corresponds to the unpolarized Raman relative intensities for the νsNO2 vibrational mode after integration over the 1280-1350 cm-1 spectral range. Even though we are working at the diffraction limits of the instrument

Figure 2. (a) Diffraction efficiency (%) on the +1 order diffracted beam as a function of time obtained for the 1 µm spacing grating recorded on a p(DR1M-co-MMA) functionalized polymer film during 8000 s. irradiation with the 514.5 nm pump laser lines (irradiance of about 80 mW/cm2) and probed without analyses by a vertically polarized He-Ne laser; one can note in the inset the interfering phase behaviors at short time and the slight efficiency increase at long time when the pump lasers are switched off. (b) Raman image of the same grating obtained for a 10 × 9 µm2 surface.

and some focusing problems are evidenced on the left side of the figure (at the begining of each recorded line), this exemple demonstrates that one can reproduce nicely the surface relief profile and obtain new relevant information about the orientations at the molecular level. Valuable orientational parameters can thus be obtained from polarization analyses of the various resonance Raman spectra. In fact, the main troubles encountered in this case to get a good definition of the Raman images are to control not only the weak displacements (0.2 or 0.5 µm) of the X-Y table but also a perfect focus of the exciting radiation using a minimum intensity power (10-30 µW/µm2). It is also necessary to fix the acquisition time per spectrum, long enough to obtain a good signal/noise ratio but not too long to avoid any thermal or photochemical effect. Consequently, the main experimental results latter on discussed in this paper were obtained on Λ ) 3 µm period gratings (θinc ) 5°) and we have checked that similar conclusions could be drawn whatever are the displacements and resolutions along X (0.2 or 0.5 µm). 1. Polarization Analyses and Corresponding Raman Images. Typical polarized Raman spectra in the 950-1700 cm-1 region recorded using both experimental geometries (i.e.,



Figure 3. Polarized Raman spectra recorded in the tops and the bottoms of a 3 µm period grating in (a) Z(YY)Z h , (b) Z(YX)Z h , (c) Z(XX)Z h , (d) Z(XY)Z h , polarization configurations.

Z(YY)Z h , Z(YX)Z h in the first case and Z(XX)Z h , Z(XY)Z h in the second according to Porto’s notation) and corresponding to the tops and bottoms of the surface relief are shown in Figure 3. Even though we are dealing with a low dye content in the p(DR1M-co-MMA) film (11.7% azo molecule), it is noteworthy that the spectra are enhanced by resonance Raman effects and only the vibrational bands of the chromophore are detected with quite good signal/noise ratios.30 After integrations over the 1280-1352 cm-1 spectral range and over the whole investigated surface area of the intensities due to the νsNO2 mode at 1334 cm-1, one gets the corresponding four Raman images presented in Figure 4. These images nicely reproduce the Λ ) 3 µm period grating and, as expected, their intensity profiles along the X (δ) direction are in-phase in the two first spectra, Z(YY)Z h and Z(YX)Z h , and are nearly out-of-phase in the two other ones, Z(XX)Z h and Z(XY)Z h . We thus conclude that the main orientational effects on the dye molecules are governed by the AHB mechanism. To corroborate this conclusion we have checked that intensity integrations of the bands maximazing at 1585 cm-1 (ν8a or ωCdC), 1130 cm-1 (ν9a or δC-H), and 1100 cm-1 (νφ-N or ν18a) lead to similar results.

2. Experimental Intensity Ratios and Curve Fittings. The above integrated intensity variations of the νsNO2 mode along the surface grating can be more precisely analyzed and their variations in the four polarized spectra are shown in Figure 5. Even though there are some dispersed and scattered points, these experimental data can be fitted in all cases by using a simple function, m1 + m2cos(δ). It must be pointed out that the Z(XX)Z h data are more properly fitted by using the function m1 + m2cos(δ+π) ) m1 - m2cos(δ), because of the observed dephasing; the m1 and m2 intensity parameters correspond to the mean values and half-amplitudes, respectively. The obtained best fit h data, values are equal to m1)558, m2)168 for the Z(YY)Z m1)218, m2)64 or 80 for the Z(YX)Z h or Z(XY)Z h data, and m1)543, m2)200 for the Z(XX)Z h data. Obviously, all these parameters are subjected to ∼10% experimental errors and it must be emphasized that such low variations are not totally realistic since they neglect the mass transport effects and the possible dephasing (Φ0) between the birefringence and surface modulation grating mechanisms.25 In fact, the results of these model dependent curve fittings can also be sensitive to the number of experimental points or to the used lateral resolution



Figure 4. Polarized Raman images in the configurations (a) Z(YY)Z h , (b) Z(YX)Z h , (c) Z(XX)Z h , (d) Z(XY)Z h . The relative Raman intensities were calculated from the integration of the νsNO2 vibrational mode over 1280-1350 cm-1 spectral range.

along the X direction but it is clear that the fits for 0.2 µm controlled displacements (reported on Figure 6) are again not totally satisfactory. Actually, it must be pointed out that, according to the more general eqs 15 and 16, which are not model dependent, all the intensity data should be better fitted using more complex type functions (m1 ( m2cos(δ) + m3cos2(δ), for instance) but we have checked that the quality of the fits were not greatly improved. This demonstrates that the orientational order coefficients 〈cos2θ〉, 〈cos4θ〉 must vary significantly along the grating surface profile. Under these conditions, in the following a first estimate of the experimental intensity ratios of interest, R1(δ) ) I(YX)/I(YY)

and R2(δ) ) I(XY)/I(XX), has thus been made using the ratios of the above fitted curves (solid lines in Figure 7) and a second estimate was obtained directly from the mean experimental ratios observed for various corresponding surface points over several grating periods (circles in Figure 7). The results of such approximations can be compared in Figure 7. In the first experimental configuration, both approaches lead to almost similar results since the R1(δ) ratios are varying over a very narrow range of values, 0.400-0.387, in the different regions of the grating. In contrast, in the second experimental geometry, some discrepancies are evidenced and the R2(δ) values are now spread over a broader range of values, namely either in the 0.875-0.186 domain or in the 0.779-0.193 range.


Figure 5. Variations of the Raman intensities of the νsNO2 vibrational mode along the X axis (over four periods) for 0.5 µm controlled displacements of the motorized table. (a) Relative Raman intensities and corresponding curve fits for Z(YY)Z h and Z(YX)Z h spectra. (b) Relative Raman intensities and curve fits for Z(XX)Z h and Z(XY)Z h spectra.


Figure 6. Variations of the Raman intensities of the νsNO2 vibrational mode along the X axis (over two periods) for 0.2 µm controlled displacements of the motorized table. (a) Relative Raman intensities and curve fits for Z(YY)Z h and Z(YX)Z h spectra. (b) Relative Raman intensities and curve fits for Z(XX)Z h and Z(XY)Z h spectra.

Therefore, these results show that the orientational coefficients and the order parameters derived from these ratios will be mainly dependent on the used Ri values; consequently, in the following calculations, we have considered two possible sets of R1(δ) and R2(δ) values at each grating point in order to obtain some insight into the dispersion of the results. V. Calculations of the Coefficients of the Orientation Distribution Functions and Discussion These calculations were performed by using the theoretical intensity expressions already derived in both models 1 and 2 (see section III) and two sets of R1, R2 ratios at each grating point, as previously mentioned. The corresponding calculated values at δ ) 0, 2π (on the tops), δ ) (π/3, (2π/3 (on the slopes) and at δ ) π, 3π (on the bottoms) of the 〈cos2θ〉, 〈cos4θ〉 coefficients and of the 〈P2〉 and 〈P4〉 order-parameters are reported in Table 1. First, whatever the investigated grating region, it is noteworthy that 〈P2〉 values are always negative and vary in the -0.094, -0.198 range in model 1 and in the -0.124, -0.233 range in model 2. This demonstrates that the principal long axis of the azobenzene side chain molecules has been reorientating, as expected, perpendicularly to the electric field vector of the actinic light. However, these 〈P2〉 values are far from the -0.5 limit expected for a complete ordering of all the chromophores and their orientations are spread over a wide range. In fact, more information about the distributions of molecular orientations are precisely delivered by looking at the available

Figure 7. Variations of the relative Raman intensity ratios, R1(δ) and R2(δ) over one and half grating periods; the solid lines correspond to the ratios extracted from fitted curves of the experimental data and the (full and empty) circles come from experimental values averaged over several periods.

〈P4〉 values which are alternately negative (δ ) 0 or 2π/3) and positive (δ ) π/3 or π) along the surface grating profile. These 〈P4〉 values are quite significant and markedly dispersed, but there is nothing unphysical about this apparent anomaly. Indeed, following Schwartz’s inequality,32,33 one expects the quantity

〈σ2〉 ) (〈cos4θ〉 - 〈cos2θ〉2)/〈cos2θ〉2

(24)



TABLE 1: Final Values of the Order Parameters, 〈P2〉, 〈P4〉, and of the Lagrange Multipliers, λ2λ4, According to the Information Entropy Theory in the Various Parts of Gratinga delta/rad 0 π/3 2π/3 π

R1

R2

0.3875 0.390 0.389 0.387 0.393 0.400 0.396 0.390

0.875 0.779 0.585 0.573 0.277 0.280 0.186 0.193

〈cos2θ〉 0.261 0.271 0.201 0.206 0.238 0.236 0.217 0.224

〈cos4θ〉

〈P2〉

(a) Without Objective Correction (Model 1)a 0.095 -0.108 0.106 -0.094 0.147 -0.198 0.149 -0.191 0.114 -0.142 0.114 -0.146 0.121 -0.175 0.126 -0.164

〈P4〉

λ2

λ4

-0.189 -0.177 +0.263 +0.255 -0.018 -0.008 +0.091 +0.085

-2.817 -1.908 -1.126 -1.068 -0.937 -0.931 -0.886 -0.826

-4.085 -3.153 +2.887 +2.736 -0.426 -0.315 +0.792 +0.745

(b) With Objective Corrections (Model 2)a A ) 3.579 and B ) 0.737 C0 ) 6.25, C1 ) 0.175, C2 ) 0.006 25 delta/rad 0 π/3 2π/3 π

R1

R2

〈cos2θ〉

〈cos4θ〉

〈P2〉

〈P4〉

λ2

λ4

0.3875 0.390 0.389 0.387 0.393 0.400 0.396 0.390

0.875 0.779 0.585 0.573 0.277 0.280 0.186 0.193

0.239 0.250 0.199 0.204 0.245 0.241 0.178 0.187

0.089 0.102 0.116 0.117 0.076 0.076 0.111 0.117

-0.141 -0.124 -0.201 -0.194 -0.133 -0.138 -0.233 -0.220

-0.131 -0.119 +0.134 +0.124 -0.206 -0.195 +0.195 +0.187

-2.291 -1.565 -1.001 -0.967 -6.078 -5.558 -1.181 -1.105

-2.786 -2.054 +1.255 +1.145 -7.079 -6.434 +2.004 +1.893

a

(a) Calculations without objective correction; the first raw data are derived from curve fit values of R1 and R2, while the second line data are average experimental values of R1 and R2. (b) Calculations taking into account the optimal parameters A, B, C0, C1, and C2, due to the high numerical aperture objective and to the refractive index of the polymer film; same legend as in (a) for the two line raw data at each grating point.

to be greater than or equal to zero, so that the following conditions must be always satisfied:

〈cos2θ〉2 e 〈cos4θ〉 e 〈cos2θ〉

(25)

In other words this means that 〈P2〉 and 〈P4〉 are not completely independent and, according to Jen et al.,32 they have to verify the following inequalities:

1 1 (35〈P2〉2 - 10〈P2〉 - 7) e 〈P4〉 e (5〈P2〉 + 7) (26) 18 12 All these conditions are normally fulfilled in the present study and a comparison of the results shows that in the more accurate model 2 the 〈P2〉 mean values are slightly more negative whereas the 〈P4〉 values are varying firstly over about the (0.130 range at the δ ) 0, π/3 points and, secondly, over about the (0.200 wider domain at the δ ) 2π/3, π points. We come thus to the important and surprising conclusion that the photoinduced mechanisms in conjunction with the polymer mass transport effects lead to the formation of alternated surface regions of weaker and stronger orientation phenomena. These results were confirmed by calculating the order parameters at various points along the surface grating and by using the data obtained with the 0.2 µm lateral resolution: in all cases, four distinct domains were always characterized over the (0-π) δ range (i.e., over a half-period grating). Such a result was quite unexpected from consideration of only the electric field amplitudes proportional to |E20|(cos2(δinc)cos2(δ/2)+sin2(δ/2)), responsible for the primary formation of the birefringence grating; these amplitudes are slightly varying along the grating period. As first suggested by Rochon et al. in such holographic gratings9-13 and by Stumpe et al. in photochromic liquid-crystalline polymer films,44,45 it is thus clear that the orientational order generated by angular dependent photoselection and photoorientation acts as an initializing force in the establishement of organized domains. In addition, according to Rochon et al.’s model involving the existence of large pressure gradients due to a viscoelastic flow of the polymer, one can suggest that the light induced optical anisotropy effects are amplified in the more organized molecular

regions. This suggestion is corroborated by the observation of more negative 〈P2〉 mean values and a final induced dichroism stronger than in films irradiated by only one linearly polarized light.25-31,44-46 Consequently, the orientational distribution functions in the various grating regions must differ significantly since, according to the above model, the effects of the viscoelastic flow of the polymer chains may be different in particular at the tops and the bottoms of the surface relief. Indeed, from the two first even parity order parameters above determined we have estimated the most probable orientational distribution functions f(θ) by utilizing the information entropy47-49 which leads to

∫-1+1f(θ) ln(f(θ))d(cosθ)

S(f(θ)) ) -

(27)

The distribution function is obtained by maximizing the information entropy on the conditions that

〈P2〉 )

∫-1+1P2(cosθ)f(θ) d(cosθ)

(28)

〈P4〉 )

∫-1+1P4(cosθ)f(θ) d(cosθ)

(29)

and the Lagrange’s method of undetermined multipliers gives the distribution functions:

f(θ) ) Z-1 exp[λ2P2(cosθ) + λ4P4(cosθ)]

(30)

where Z denotes a normalization constant,

Z)

∫-1+1exp[λ2P2(cosθ) + λ4P4(cosθ)] d(cosθ)

(31)

and λ2, λ4 are the Lagrange multipliers. Therefore, from the experimentally determined 〈P2〉 and 〈P4〉 values, one can estimate λ2 and λ4 by numerically integrating eqs 28 and 29 after substituting eqs 30 and 31 into the integrals of interest. It must be recalled that the functions f(θ) calculated by this way do never take negative values, which have no physical meaning,



Figure 8. Normalized f(θ) distribution functions in four distinct regions of the grating surface (δ)0, π/3, 2π/3, and π, respectively) calculated from 〈P2〉 and 〈P4〉 values extracted in model 2; the full circle curves come from the fits of R1(δ) and R2(δ) variations whereas the empty circle curves are obtained from average values of R1(δ) and R2(δ).

differently from f(θ) estimated by the truncated (not converging) Legendre’ expansion with the same values of 〈P2〉 and 〈P4〉. The corresponding normalized information entropy distribution functions f(θ) were thus calculated using values of the order parameters extracted from the model 2 at the δ ) 0, π/3, 2π/3 and π (rad) points and they are shown in Figure 8. They give rise also to the corresponding representations in polar coordinates reported in Figure 9. Similar calculations were also attempted from parameters extracted from the model 1 but they generally lead to significantly broader functions. As emphasized by Pottel et al.,48 the f(θ) solutions of the integral equations at δ ) 0 and 2π/3 lead to broad and single peaked distribution functions over the 0-π/2 (θ) range and they show that the socalled “cone model” could be a possible distribution. Actually, these functions are peaking at an angle of ∼58° instead of 90° and their orientation maxima are inclined to (32° with respect to the perpendicular direction; moreover, the distributions are markedly broader at the tops of the surface relief (with fullwidth at half-maximum, ∆θ, equal to 0.67 rad at δ ) 0), where the mass transport effects (if any) are probably more effective, than in the slopes (with FWHM, ∆θ, equal to 0.37 rad at δ ) 2π/3). In contrast, the solutions at δ ) π/3 and π lead to double peak f(θ) functions with a weak maximum for θ ) 0° and a stronger one for θ ) 90°, as expected; here, for the more intense contributions at θ ) 90°, the distributions are relatively broad in the slopes (∆θ ) 0.75 rad at δ ) π/3) as well as in the bottoms (∆θ ) 0.60 rad at δ ) π). In fact, these two last distributions are largely governed by the high 〈P4〉 positive values and they are also related to the variance in 〈P2〉 defined as48

〈∆P22〉 ) 〈P22〉 - 〈P2〉2 )

18 2 1 〈P 〉 + 〈P2〉 + - 〈P2〉2 (32) 35 4 7 5

This variance is a measure of the fluctuations of 〈P2〉 and, according to eq 26, 〈∆P22〉 must also satisfy the relation,

1 0 e 〈∆P22〉 e (1 - 〈P2〉)(1 + 2〈P2〉) 2

(33)

In the present cases, similar 〈∆P22〉 values equal to 0.17 (δ ) π/3) or 0.18 (δ ) π) are estimated and, even though the distribution functions are maximizing at θ ) 90°, there is a concomitant increase in the fluctuations of 〈P2〉. These fluctuations come from the fact that experimentally one measures a weighted mean for 〈P2〉; the major fraction of probe molecules are actually oriented perpendicularly to the actinic light while the remaining fraction are still oriented parallel to the local electric field. Finally, the information entropy theory results confirm the important photoinduced orientations in the nearly perpendicular direction of the incoming light and allow us to conclude to the existence of relatively broad distribution functions even in the bottom regions (δ ) π) of the grating surface relief. In these regions of greater polymer removal, it is clear that the mass transport phenomena have perturbed to some extent the primary photoinduced orientations. Therefore, as emphasized by Rochon et al.,9,13 during the grating formation a molecular organization could take place in the viscoelastic state of the polymer and this process could involve localized mass transport of the polymer chains to a high degree, as confirmed by atomic force microscopy which reveales



Figure 9. Polar representations of the normalized f(θ) distribution functions in four distinct regions of the grating surface (δ)0, π/3, 2π/3, and π, respectively) calculated from 〈P2〉 and 〈P4〉 values extracted in model 2; same legend as in Figure 8 for the full and empty circle curves.

surface profile depths near that of the original film thickness. These authors13 have also suggested the existence of regions of high trans-cis-trans isomerization bordered by regions of low isomerization, a mechanism which was justified from the phase addition of two linearly polarized laser beams (“p + p”, for instance) in the interference pattern. The same mechanism is no more justified in the present case of two circularly polarized pump beams since one expects quite similar trans-cis-trans degrees of isomerization in all regions. However, as the transfcis isomerization requires free volume in excess of that available in the starting isotropic film (∆V/V ∼ 15% for a complete process), it is clear that the photochemical reaction produces a laser-induced internal pressure above the yield point of the polymer. Indeed, from previous visible absorption dichroism results under similar laser irradiations29 we have found that the cis concentration in the photostationary state may be as large as 40-50% and, assuming the bulk modulus of the material B, equal to 3 × 109 Pa,50 we can estimate the pressure due to this volume change: P ) B(∆V/V)[cis]%. This leads to pressures ranging from 1.8 × 108 to 2.5 × 108 Pa, far above the yield point of the polymer of ∼ 2 × 107 Pa.50 Therefore, in complete agreement with Rochon et al.,9,13 one can imagine a resulting viscoelastic flow of the polymer and the existence in the various domains of large constraints and stresses which are acting as opposing or restoring forces against the imposed localized orientations. Such a mechanism is reinforced by the fact that we have above shown that the material is removed from the regions of higher perpendicular orientation (at the bottoms) and build up in the regions of weaker orientations (at the tops). Nevertheless, in the intermediate regions the final orientations are found alternately weaker and

higher and this could come from competing forces and/or from more or less efficient cooperative (or dye-intermolecular) orientation effects during the formation of the regularly spaced sinusoidal surface relief grating. VI. Conclusions In this study, by using a modern Raman confocal microspectrometer and by analyzing the resonance enhanced polarized Raman spectra recorded on optically inscribed high-efficiency diffraction gratings in azo polymer films, we have obtained for the first time new information about the second 〈P2〉 and fourth 〈P4〉 order parameters of the chromophore orientation function. We have found that the primary orientational orders generated by the angular dependent photoinduced effects act as an initializing force in the establishement of more or less organized four domains over a half-period grating. Indeed, because of the existence of large pressure gradients, these molecular organizations could occur in the viscoelastic state of the polymer and, finally, the light-induced optical anisotropy effects appear to be amplified. In addition, we have demonstrated that the corresponding information entropy distribution functions are different in the various regions of the grating, particularly in the tops and the bottoms of the surface relief. We thus conclude to the existence between the different domains of large constraints and stresses which probably act as opposing or restoring forces against the light imposed localized orientations. In order to confirm the above conclusions, additional Raman confocal microspectroscopic investigations are planned on similar polymer holographic gratings written using either (p +

Raman Confocal Microspectroscopy p) or (p + s) linearly polarized interfering pump beams. Also, additional accurate Raman intensity measurements over a grating cross section are planned in order to estimate the dye concentration gradients, N(δ), and to draw definitive conclusions about the mass translational diffusion or transport effects.51 Such studies are in progress and theirs results will be published in due course. Acknowledgment. The authors are indebted to the CNRS (Chemistry Department) and to Re´gion Aquitaine for financial supports in Raman equipments. They are thankful to A. Natansohn for providing the functionalized copolymer, to P. Rochon for fruitful discussions, to J. L. Bruneel for technical assistance in Raman measurements, and, finally, to P. Maraval for computer programm developments. References and Notes (1) Bach, H.; Anderle, K.; Fuhrmann, Th.; Wendorff, J. H. J. Phys. Chem. 1996, 100, 4135. (2) Maak, J.; Ahuja, R. C.; Tachibana, H. J. J. Phys. Chem. 1995, 99, 9219. (3) Tachibana, H.; Nakamura, T.; Matsumoto, M.; Komizu, H.; Mannda, E.; Niino, H.; Yabe, A. J. Am. Chem. Soc. 1989, 11, 3080. (4) Xie, S.; Natansohn, A.; Rochon, P. Chem. Mater. 1993, 5, 403. (5) Dumont, M.; Froc, G.; Hosotte, S. Nonlinear Opt. 1995, 9, 327. (6) Todorov, T.; Nikolova, L.; Tomova, N. Appl. Opt. 1984, 23, 4309 and 4588. (7) Todorov, T.; Nikolova, L.; Stoyanova, K.; Tomova, N. Appl. Opt. 1985, 24, 785. (8) Ivanov, M.; Todorov, T.; Nikolova, L.; Tomova, N.; Dragostinova, V. Appl. Phys. Lett. 1995, 66, 2174. (9) Rochon, P.; Mao, J.; Natansohn, A.; Batalla, E. Polym. Prepr. 1994, 35, 154. (10) Rochon, P.; Batalla, E.; Natansohn, A. Appl. Phys. Lett. 1995, 66, 136. (11) Paterson, J.; Natansohn, A.; Rochon, P.; Callender, C. L.; Robitaille, L. Appl. Phys. Lett. 1996, 69, 3318. (12) Ho, M. S.; Barrett, C.; Paterson, J.; Esteghamatian, M.; Natansohn, A.; Rochon, P. Macromolecules 1996, 29, 4613. (13) Barret, C. J.; Natansohn, A. L.; Rochon, P. L. J. Phys. Chem. 1996, 100, 8836. (14) Ramanujam, P. S.; Holme, N. C. R.; Hvilsted, S. Appl. Phys. Lett. 1996, 68, 1329. (15) Holme, N. C. R.; Nikolova, L.; Ramanujam, P. S.; Hvilsted, S. Appl. Phys. Lett. 1997, 70, 1518. (16) Jiang, X. L.; Li, L.; Kumar, J.; Kim, D. Y.; Shivshankar, V.; Tripathy, S. K. Appl. Phys. Lett. 1996, 68, 2618 and references therein. (17) Kim, D. Y.; Lian, Li.; Jiang, X. L.; Shivshankar, V.; Kumar, J.; Tripathy, S. K. Macromolecules 1995, 28, 8835. (18) Xu, J.; Zhang, G.; Wu, Q.; Liang, Y.; Liu, S.; Sun, Q.; Chen, X.; Shen, Y. Opt. Lett. 1995, 120, 504. (19) Wu, P.; Zhou, B.; Wu, X.; Xu, J.; Gong, X.; Zhang, G.; Tang, G.; Chen, W. Appl. Phys. Lett. 1997, 70, 1224.

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Molecular Orientations in Azopolymer Holographic Diffraction Gratings

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