4588
J. Phys. Chem. B 2002, 106, 4588-4595
Efficient Functionalized Photorefractive Polymers with Infrared Sensitivity E. Hendrickx,† C. Engels,‡ M. Schaerlaekens,*,† D. Van Steenwinckel,† C. Samyn,‡ and A. Persoons† Laboratory of Chemical and Biological Dynamics, UniVersity of LeuVen, Celestijnenlaan 200D, B-3001 LeuVen, Belgium, and Laboratory of Macromolecular and Physical Organic Chemistry, UniVersity of LeuVen, Celestijnenlaan 200F, B-3001 LeuVen, Belgium ReceiVed: June 5, 2001; In Final Form: December 20, 2001
We have prepared new photorefractive methacrylate copolymers functionalized with a highly polar bifunctional chromophore. The photorefractive response was studied by ellipsometry, four-wave mixing, and two-beam coupling and is compared to that of polymers and polymer composites studied previously. The polymer could be sensitized with C60 for operation at the writing wavelength of 780 nm, which results in an improved grating build-up time. At this wavelength, we have observed overmodulation of the internal diffraction efficiency at an applied bias field of 43 V/µm. We have found evidence for the formation of aggregates and phase separation in the copolymers.
Introduction The photorefractive (PR) effect was discovered first in inorganic crystals and is described as a refractive index change induced through the Pockels effect and a photogenerated spacecharge field. Because the refractive index change is reversible, photorefractive crystals are suitable for dynamic holography, such as in optical phase conjugation.1 After the first observation of the photorefractive effect in a polymer, intense research has led to a dramatic progress in the photorefractive parameters, for example, the diffraction efficiency, two-beam coupling gain coefficients, and grating build-up times.2,3,4 The benefits of polymeric materials over inorganic crystals are obvious: polymers can be processed into a variety of forms, have high resolution, and can be tailored through organic synthesis. The components of an organic polymer film reflect the stepwise buildup of the photorefractive index grating. The polymer matrix often is fabricated with a photoconducting polymer, such as poly(N-vinylcarbazole) (PVK). The photoconductivity of the matrix is extended to wavelengths up to 633 or 830 nm by the addition of an electron-accepting molecule, such as (2,4,7-trinitro-9-fluorenylidene)malononitrile (TNFM).5 TNFM forms a charge-transfer complex with the electron-rich carbazole, and upon illumination and application of an electric field, a photoinduced electron transfer occurs from carbazole to TNFM. The positive charge on carbazole then migrates by hopping from carbazole to carbazole, until it is trapped. The trapped charges set up the space-charge field. The third component of the polymer mixture is a chromophore with a large dipole moment, polarizability anisotropy, and first hyperpolarizability. In the total electric field, that is, the superposition of the applied field and the space-charge field, the polar chromophores reorient and change the refractive index through birefringence and the Pockels effect. Various approaches have been used to prepare photorefractive polymer mixtures. A frequently used strategy is to dope a † ‡
Laboratory of Chemical and Biological Dynamics. Laboratory of Macromolecular and Physical Organic Chemistry.
PVK matrix with up to 40 wt % of a polar chromophore and 10 wt % of plasticizer. These mixtures have produced very good results thus far but can show phase separation.6 Alternatively, a polar chromophore with charge-transporting properties can be used. The bifunctional chromophores often have an amino donor group and can be doped into an inert polymer matrix or can be directly attached to a polymer backbone.7,8 Additionally, both charge transporter and polar chromophore can be attached to the polymer backbone.9 Internal plasticizers or spacers with variable lengths can then be used to further reduce the polymer glass-transition temperature to room temperature and provide the necessary free volume for chromophore reorientation. We have studied PVK matrixes doped with various amounts of the polar chromophore Lemke-E.10 In these composites, the refractive index modulation amplitude increased with the chromophore number density up to chromophore number densities of 5.4 × 1020 cm-3. Here, we report on the synthesis and characterization (four-wave mixing (FWM), two-beam coupling, and ellipsometry) of two copolymers functionalized with a similar chromophore and an inert internal plasticizer. In both copolymers, larger chromophore number densities are attained and charge transport takes place through the bifunctional chromophore. Because the bifunctional chromophore has a low ionization potential, sensitization at 780 nm could be provided by C60. We have found that at the high chromophore number densities of 7.0 × 1020 and 8.1 × 1020 cm-3, a texture is formed in the pure copolymers. In one of the copolymers, the texture formation was eliminated by the addition of a plasticizer. In the latter, we have observed an improved dynamic range compared to the previously developed PVK-based composites. Replacing TNFM as sensitizer of the bifunctional polymer matrix by C60 led to an improved dynamic range and faster response times but also smaller photorefractive phase shifts. Section I discusses the polymer synthesis, while Section II reports on the spectroscopic properties of the polymers and their phase behavior. In Section III, we present the ellipsometric and
10.1021/jp012147y CCC: $22.00 © 2002 American Chemical Society Published on Web 04/17/2002
Photorefractive Polymers with Infrared Sensitivity
J. Phys. Chem. B, Vol. 106, No. 18, 2002 4589
TABLE 1: Polymerization Feed, Solvent, Yield, and Polymer Composition Determined by 1H NMR, Number-Average Molar Mass from GPC in THF, Polydispersity, and Glass-Transition Temperature by DSC for the Various Polymerization Reactions in DMF and THFa polymer P1 P2 P3 P4 P5 P6 P7 P8A P8B
feed
solvent
1 Chr 0.80 Chr 0.20 MMA 0.80 Chr 0.20 C12 0.50 Chr 0.50 C12 0.50 Chr 0.50 C12 0.50 Chr 0.50 LC 0.30 Chr 0.70 LC 0.40 Chr 0.20 C12 0.40 Cz 0.40 Chr 0.20 C12 0.40 Cz
DMF DMF
yield, %
comp
M h n, g mol-1
D
Tg, °C
polymers. Ellipsometric experiments were done by placing the sample, rotated 45° about both a horizontal axis and a vertical axis, between crossed polarizers, as in ref 11. If an electric field is applied over the sample, a change in the optical intensity transmitted through the sample (Iell) is induced that relates to the refractive index difference as observed in ellipsometry, ∆nell, according to
Iell Im ell
DMF DMF
36
THF
69
THF
59
THF
63
DMF
77
DMF
81.5
0.44 Chr 0.56 C12 0.43 Chr 0.57 C12 0.47 Chr 0.53 LC 0.31 Chr 0.69 LC 0.37 Chr 0.18 C12 0.45 Cz 0.38 Chr 0.20 C12 0.42 Cz
23 800
1.6 40
9 200
1.9 40
12 000
2.1 79
10 600
2.1
8 000
2.5 52
10 300
2.1 67
a
Polymer P8A corresponds to polymer 3 from ref 7; MMA is methyl methacrylate; C12 is dodecyl methacrylate; Cz is 6-(9-carbazoyl)-hexyl methacrylate.
photorefractive results for the newly prepared polymers and directly compare these to a previously studied composite and copolymer. Methods Materials and Polymer Characterization. All reagents are commercially available and used as received. All synthesized products and polymers were characterized by a Bruker Avance 1H NMR (300 MHz). The molecular weights were determined by gel permeation chromatography (Waters HP/GPC), using THF as eluent and toluene as internal reference; polystyrene standards were used for calibration. The polymers were detected by a differential refractometer and by UV absorption. The glasstransition temperatures (Tg) of these systems were measured by differential scanning calorimetry (DSC), using a Perkin-Elmer DSC-7. The listed values were determined after a first heating cycle and at a scanning rate of 20 °C/min. Polymer Synthesis: General Procedure. The polymerizations were done under argon atmosphere at 65 °C in the presence of 1 wt % of AIBN for 24 h. The used solvent is listed in Table 1. The resulting polymer solution was diluted with solvent and poured into methanol to precipitate the polymer. The precipitated polymer was filtered, dissolved, and precipitated a second time, filtered, and finally dried under reduced pressure. Sample Preparation. Samples for photorefractive measurements were prepared by dissolving the polymer in dichloromethane and by adding the appropriate volume of 0.1 mg/mL C60 (MERCorp, sublimed grade) in toluene or 1 mg/mL TNFM (ACROS Organics, purified by crystallization from toluene) in dichloromethane. After passing this solution through a 0.2 µm PTFE membrane filter, the solvent was evaporated at elevated temperature and reduced pressure. The resulting mixture was then molten at 120 °C between two ITO-coated glass slides, and the thickness of the samples was controlled by glass spacers of 125 µm diameter. Optical Characterization. All of the optical experiments were performed at the glass-transition temperature of the
) 1 - A cos2
(
)
πL∆nell λ
(1)
where L is the length the beam propagates through the sample and λ is the optical wavelength. Im ell is the maximal intensity that is transmitted through the sample when it acts as a halfwave plate and A depends on the amplitude transmission coefficients for s and p polarization. The parameter ∆nell is related to the difference of the refractive indices of the principal semiaxes of the index ellipsoid, ne - no, of the poled polymer:9
n e - no )
∆nell
(2)
cos2 ψ
where ψ is the internal angle of propagation of the laser beam with the sample normal. Two-beam coupling experiments and four-wave mixing experiments were done with a setup similar to the one described in ref 12. All data were reproducible within 5% of the experimental values. The laser was a diode laser operating at a wavelength of 780 nm. The angle between the two writing beams outside the samples was 14° ( 1°, and the angle between the bisector and the surface normal was 50° ( 2°. For the twobeam coupling experiments, the two beams were p-polarized and had a power of 1.4 ( 0.1 W/cm2 each. The data were analyzed with the equation
(
Γd ) cos R1 ln
)
It1(I2*0) It1(I2)0)
(
- cos R2 ln
)
It2(I1*0) It2(I1)0)
(3)
It1 and It2 are the transmitted intensities of writing beams 1 and 2. Beam 1 is the beam closest to the surface normal, R1 and R2 are the angles between the writing beams and the surface normal in the sample, d is the sample thickness, and Γ is the gain coefficient. Four-wave mixing experiments were performed using spolarized writing beams and a p-polarized probe beam, counterpropagating to writing beam 1. The power of the writing beams was the same as in the two-beam coupling experiments, and the probe beam, collimated to 150 ( 10 µm, had a power of 1.0 ( 0.1 mW/cm2. The internal diffraction efficiencies were calculated using the formula
ηint )
Idiff It
(4)
where Idiff is the intensity of the light diffracted upon the photorefractive grating and It is the total amount of light transmitted through the sample, that is, the sum of the diffracted and transmitted intensities. Data points were taken with raising voltage applied over the 120 µm thick sample in steps of 0.5 kV. Between subsequent increments, we have waited 5 min to reach the steady-state diffraction efficiencies. Grating build-up times were measured at Tg after several minutes of uniform illumination with a 5 kV bias applied over the sample. The measurement starts when the second writing
4590 J. Phys. Chem. B, Vol. 106, No. 18, 2002
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SCHEME 1
SCHEME 2
beam is switched on. All transients could be fitted using a stretched exponential: β
[ (τt ) ]
η ) η0 - η0 exp -
(5)
where η0 is the steady-state diffraction efficiency, τ is the buildup time of the grating, and β is a parameter that indicates how fast the rate of increase slows with time and is physically related to the distribution of time constants that contribute to the buildup time of the grating. Section I: Synthesis The comonomer with the attached mesogenic group was prepared according to Portugall et al.,13 and the synthesis is summarized in Scheme 1. Because the attached group has mesogenic properties when pure, we refer to the comonomer as LC. Recently, mesogenic materials were shown to have a large photorefractive response at low values of the applied
electric field because of the cooperative alignment of the dipolar liquid crystals.14,15 In the copolymers reported here that contained LC, no liquid crystalline behavior was observed when examined by DSC or under a polarization microscope. Nevertheless, it is interesting to verify the effect of the LC side group on the polymer morphology and photorefractive performance. The synthesis of the chromophore monomer is depicted in Scheme 2.7 First, polymerizations were carried out in DMF with poor yields. Switching to THF greatly increased yields, as is shown in Table 1. For all further polymerizations, THF was used. Attempts were also made to prepare copolymers P1-P3 with chromophore concentrations exceeding 50 mol %. In polymers P1, P2, and P3, the chromophore number densities amounted to 1.4 × 1021, 1.3 × 1021, and 1.2 × 1021 molecules cm-3, respectively. Unfortunately, these polymers could not be characterized because of their insolubility in common organic solvents. We believe this may be caused by dipolar interactions. P4 and P5 had approximately the same composition, and alone
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J. Phys. Chem. B, Vol. 106, No. 18, 2002 4591
Figure 1. Molecular structure of polymers P5, P6, and P8.
TABLE 2: Sample Composition,a Chromophore Number Density, and Glass-Transition Temperatureb
sample 1 2 3A 3B 4
sample composition (wt %)
chromophore number density (cm-3)
glasstransition temperature (°C)
PVK/ECZ/Lemke-E/TNFM 42/28.2/28.5/1.3 P6/DOP/C60 83/16/1 P8A/TNFM 99/1 P8B/TNFM 99/1 P5/C60 99/1
5.4 × 1020
21
5.8 × 1020 6.6 × 1020 6.9 × 1020 8.1 × 1020
23 52 67 40
a PVK ) poly(N-vinylcarbazole); ECZ ) N-ethylcarbazole; TNFM ) (2,4,7-trinitro-9-fluorenylidene)malononitrile; DOP ) bis(2-ethylhexyl)phthalate ) dioctylphthalate. For polymer compositions, see Table 1 and Schemes 1 and 2. b Measured by DSC at a heating rate of 20 ˚C min-1.
P5 was studied. For P7, DSC experiments did not show a clear glass-transition temperature. The polymers used in photorefractive experiments are shown in Figure 1. Section II: Material Properties The composition of the samples studied is listed in Table 2. A PVK-matrix doped with a large concentration of polar chromophores is susceptible to phase separation because the polar chromophore crystallizes in the polymer matrix. Sample 1 is a polymer composite with a good thermal stability (shelf lifetimes exceeding 18 months), but a further increase of the chromophore number density beyond 5.4 × 1020 molecules cm-3 in PVK-based composites leads to accelerated crystallization of the chromophore. To prevent chromophore crystallization and obtain higher chromophore number densities of the Lemke-E chromophore, polymers P1-P8 (Table 1) were prepared. In these polymers, the chromophore is covalently attached to the polymer backbone and copolymerized with an internal plasticizer to reduce the glass-transition temperature and to improve the polymer solubility in organic solvents. Interestingly, microscopic images revealed a texture in the pure polymers P5 and P6. Microscopic images of P6 and sample 2 are shown in Figure 2. It is possible that this texture is caused by a phase separation in the copolymers due to the mutual incompatibility of the two monomers and the large chromophore number density. For P6, the texture disappeared after plasticizing the polymer with DOP (dioctylphthalate), as in the preparation of sample 2, which had a shelf life of over 8 months. For P5, the addition of a similar amount of DOP did not remove the texture. By adding DOP to
Figure 2. Microscopic images of (a) P6 and (b) sample 2. Both sample thicknesses were 120 µm. The length of the bar in both pictures is 120 µm.
P6, the chromophore is diluted and the polymer Tg is reduced. Note that the LC comonomer in P6 has a higher polarity (µ ) 3.3 D as measured by capacitance measurements of dilute solutions of the monomer in 1,4-dioxane) than the dodecyl chain in comonomer C12 of polymer P5, which will also provide a better compatibility with the polar chromophore and may contribute to the uniformity observed in sample 2.
4592 J. Phys. Chem. B, Vol. 106, No. 18, 2002
Figure 3. Absorption spectra of a 120 µm thick sample of P5 without sensitizer and a 120 µm thick sample of P5 with 1 wt % C60 (sample 4). C60 itself does not have visible absorption beyond 700 nm at these concentrations, which leads to the conclusion that the charge-transfer complex between C60 and the chromophore of P5 is responsible for the increased absorptivity at higher wavelengths. The background is due to light scattering from the polymer matrix and the reflectivity of the electrodes.
A general approach to extend the sensitivity of a photoconducting polymer matrix into the red and infrared exists in adding a small amount of an electron-deficient molecule that forms a charge-transfer complex with the charge transporter. To extend the sensitivity of polymer matrix to 830 nm, mostly TNFM has been used as sensitizer for carbazole matrixes.3 Another well-known sensitizer is C60, which strongly increases the photoconductivity of PVK and reduces the photorefractive grating build-up times.16 This can be attributed to the improved photogeneration efficiency of the charge-transfer complexes formed between C60 and aromatic amines.17,18 The useful absorption of the carbazole-C60 charge-transfer complex, however, strongly decreases at wavelengths higher than 700 nm, which prevents C60 from being used as a sensitizer at infrared wavelengths in photorefractive samples with a carbazole holetransporting matrix.19 Thus, the carbazole-containing samples 1, 3A, and 3B were sensitized with TNFM. In samples 2 and 4, however, because of the absence of carbazole, the chromophore will form a charge-transfer complex with the sensitizer. Because the chromophore used in these polymers has an ionization potential that is smaller than that of carbazole,20 the absorption of the charge-transfer complex is red-shifted compared to that formed between carbazole and the sensitizer. The carbazole-C60 complex did not show absorption at our experimental wavelength of 780 nm, but the complex between C60 and the chromophore did have useful absorption, and samples 2 and 4 could be sensitized with C60. The absorption spectra of P5 with and without C60 are shown in Figure 3. Section III: Ellipsometry and Photorefractive Characterization The holographic response was studied by a combination of ellipsometry, four-wave mixing, and two-beam coupling experiments. Photorefractive experiments measure a refractive index change that is induced by the externally applied field and the space-charge field, whereas ellipsometry only involves a refractive index difference induced by the externally applied field. In the ellipsometric experiments, the experimental refractive index change can be compared to a calculated refractive index change to study dipolar correlation effects without making assumptions on the value of the photorefractive space-charge field. Then, it can be studied how the refractive index change
Hendrickx et al.
Figure 4. Refractive index change as observed in ellipsometry for 120 µm thick samples 1′-4′ at 780 nm and measured at the glasstransition temperature. The sample compositions correspond to those listed in Table 2 but without sensitizer.
TABLE 3: Experimental and Theoretically Calculated Refractive Index Difference as Observed in Ellipsometry at an Applied Bias Field of 50 V/µm, Ratio between the Experimental and Theoretical Refractive Index Differences at 50 V/µm, and General Curve Fit to the Experimentally Observed Refractive Index Differencea
sample
∆nell (exptl, 50 V/µm)
∆nell (calcd, 50 V/µm)
∆nell(exptl)/ ∆nell(calcd)
∆nell (exptl fit)
1′ 2′ 3A′ 3B′ 4′
0.0031 0.0033 0.0017 0.0026 0.0039
0.0040 0.0044 0.0035 0.0036 0.0056
0.77 0.75 0.48 0.72 0.69
1.3 × 10-6 × E2.0 1.6 × 10-6 × E2.0 1.9 × 10-6 × E1.7 5.9 × 10-7 × E2.1 1.7 × 10-6 × E2.0
a
E is in V/µm.
found in ellipsometry translates into a photorefractive index change through the space-charge field. The refractive index change, as observed by ellipsometry and calculated from eq 1, is shown in Figure 4. For these experiments, the samples were identical to those listed in Table 2 but without sensitizer to avoid effects associated with the creation of a space-charge field, such as beam fanning. We note these samples by 1′, 2′, 3′, and 4′. The curves are fits to the general equation ∆nell ) aEb, and the results from the fitting are listed in Table 3. At the molecular level, the refractive index difference observed in ellipsometry is caused by the chromophore reorientation and the electrooptic effect. We have used the theory as outlined in ref 21 to calculate the expected refractive index difference ne - no based on the dipole moment, polarizability anisotropy, and hyperpolarizability of the chromophore.8 From the calculated value of ne - no, ∆nell was calculated using eq 2. In ref 19, the dipole moment that appears in the equations is the effective dipole moment, µ*. The effective dipole moment takes into account the influence of the polymer matrix and can be calculated by considering the polarization of the dipole in its own reaction field. A general equation that links the effective dipole moment to the dipole moment as measured using Onsager theory in dilute solution (9.3 D in 1,4-dioxane) is given in eqs 4.99 and 4.100 of ref 22:
µ j* )
µ j 1 - faRa
(6)
where Ra is the linear polarizability in the direction of the dipole moment (56 × 10-24 esu as calculated with the INDO/SCI
Photorefractive Polymers with Infrared Sensitivity
J. Phys. Chem. B, Vol. 106, No. 18, 2002 4593
Figure 5. Refractive index change from ellipsometry as a function of applied electric field for samples 3A′ and 3B′. The inset shows the internal diffraction efficiency as a function of applied electric field for samples 3A and 3B. With these data, we would like to rectify the data reported in ref 7.
approach)7 and fa is given by
fa )
3 Aa(1 - Aa)( - 1) abc + (1 - )Aa
(7)
Here, the dipole is considered to be elliptical with axis lengths a, b, and c. Aa is an ellipsoid shape factor and is the polymer dielectric constant. According to these expressions, the effective dipole moment is a factor of 2.3 larger than the dipole moment measured in solution. Recently, Dalton and co-workers have developed a theory that considers the effects of the formation of dipolar aggregation on the poling-induced order in polymer films doped with large concentrations of highly polar molecules.23 Dipolar correlations result in a chromophore alignment by the orienting field that is smaller than predicted by the Langevin equations in the oriented gas model and have been shown to generate an optimum in the dependence of the electrooptic coefficient on the chromophore number density. By comparing the experimentally observed refractive index differences with the calculated index differences, it can be seen that the experimentally observed values are 2030% smaller than the theoretical values. In samples 1′, 2′, and 4′, the field dependence of ∆nell closely follows the expected quadratic dependence on the applied electric field. In agreement with its large chromophore number density, sample 4′ has the highest refractive index difference. In sample 3A′, the dependence was subquadratic, and in addition, a large dark current could be observed at bias fields larger than 20 V/µm. The large dark currents were not observed in the other polymers. This suggests that, in addition to dipolar aggregation, a contamination by ionic species reduced the attainable index difference in sample 3A′. Extra purification of P8A by precipitation did not improve its photorefractive performance. Thus, we reprepared the polymer. From the newly prepared polymer P8B, sample 3B′ was prepared. As can be seen in Figure 5 and in Table 3, sample 3B′ showed a stronger ellipsometric response than 3A′. In addition, the dependence of the index modulation amplitude is closer to quadratic and, as was the case in the other materials, constitutes approximately 70% of what can be achieved theoretically. Also note that as the concentration of polar chromophores increases upon going
Figure 6. Electric-field dependence of the dynamic range calculated from the experimental diffraction efficiency at 780 nm for samples 1 ()), 2 (3), 3B (2) and 4 (O). The experimental diffraction efficiencies of the same samples as a function of applied electric field are shown in the inset.
from sample 1′ to 2′, 3B′, and 4′, the ratio of the experimentally observed and theoretically possible refractive index change decreases from 77% to 69%. The diffraction efficiencies were measured by four-wave mixing experiments at 780 nm. The refractive index changes were calculated from the internal diffraction efficiency using the theory by Kogelnik:24
ηint ) sin2(584∆nfwm)
(8)
where 584 is the numerical value of a combination of various constants that depend on the geometry of the FWM experiment.21 The inset in Figure 5 also shows the improved diffraction efficiency of sample 3B over that of sample 3A. The internal diffraction efficiencies and refractive index changes of samples 1, 2, 3B, and 4 are shown in Figure 6. Samples 2, 3B, and 4 show overmodulation of the diffraction efficiency at applied bias fields lower than that observed in the polymer composite sample 1 and thus rank with the best infrared-sensitive oligomeric PR systems25 and PR polymers reported.26 The highest diffraction efficiencies, with overmodulation at an applied bias field of 43 V/µm, are observed in samples 2 and 3B. Regardless of the larger refractive index difference observed in ellipsometry and the use of sensitizer C60 in both samples, sample 4 has a smaller dynamic range than sample 2. We believe that light scattering from the texture present in sample 4 may prevent the translation of the favorable ellipsometric refractive index change into a photorefractive hologram by reducing the contrast and resolution. The results from the fitting of ∆nfwm to the general equation aEb, along with data from two-beam coupling, are listed in Table 4. The electric-field dependence of the refractive index change as observed in four-wave mixing is the closest to quadratic for the two samples sensitized with C60 and for sample 3B, indicating that in these materials a larger photorefractive trap density accumulates.27 These three samples also have a small (7.9 × 1020 molecules cm-3 in 3B) or zero carbazole number density compared to the carbazole number density in sample 1 (2.4 × 1021 molecules cm-3). When sample 4 was sensitized with TNFM instead of C60, the value of b dropped from 1.7 to 1.4 and the dynamic range at 50 V/µm from 0.0027 to 0.0021. This clearly illustrates the improved space-charge field saturation and dynamic ranges obtained by using C60 as sensitizer. Note
4594 J. Phys. Chem. B, Vol. 106, No. 18, 2002
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TABLE 4: Fit Equation that Provided the Best Match to the Dynamic Range as Determined by Four-wave Mixing Experiments, Experimental Dynamic Range at an Applied Electric Field of 50 V/µm, Experimental Two-beam Coupling Gain, and Grating Phase
sample
∆nfwm (exptl fit)a
∆nfwm (exptl, 50 V/µm)
1 2 3A 3B 4
5.0 × 10-6 × E1.6 3.7 × 10-6 × E1.75 2.8 × 10-6 × E1.6 4.1 × 10-6 × E1.7 3.6 × 10-6 × E1.7
0.0025 0.0035 0.0013 0.0036 0.0027
Γ2BC (cm-1) (exptl, 50 V/µm)
phase (deg)b
142 100 45 112 96
21 10 12 11 12
a E is in V/µm. b Calculated from eq 9 and the data in columns 3 and 4.
that for sample 3A a quadratic dependence of the dynamic range on the applied field was not expected because the dependence of the refractive index difference as observed in ellipsometry was not quadratic. The smaller than expected dynamic range in this material corresponds to the smaller than expected index difference as found in ellipsometry and indicates that the reduction in the dynamic range can partly be attributed to incomplete chromophore reorientation. Finally, none of the samples has a dependence of the index modulation amplitude that is fully quadratic in the applied electric field, which demonstrates that in our experimental conditions the photorefractive space-charge field is not completely saturated. Thus far, none of the functional polymers that we have studied at 780 nm has shown a build-up time of the photorefractive grating as short as the subsecond build-up time (τ ) 0.72(s), β ) 0.70) of the polymer composite in sample 1.20 The dynamics of grating buildup in sample 2 is shown in Figure 7. Sample 4 showed dynamics that were almost identical. The grating buildup times in samples 2 and 4 (τ ) 6.3 s, β ) 0.77 and τ ) 4.13 s, β ) 0.68, respectively), however, show a clear improvement over the same materials sensitized with TNFM. Sensitizing sample 2 with 0.2 wt % TNFM instead of C60 led to response times that were several times larger at identical values of the applied electric field (τ ) 28 s, β ) 0.66). Also, the grating buildup of a polymethacrylate functionalized with a bifunctional azo dye previously measured was approximately 5 times slower at 780 nm under identical experimental conditions.28 The two-beam coupling gain coefficient at an applied bias field of 50 V/µm is also listed in Table 4. The gain coefficient Γ is related to the dynamic range by the equation
Γ)
4π (ej ‚ ej/)∆n sin θ λ 1 2
(9)
where ej1 and ej2 are the polarization vectors of the two writing beams. We have used the gain coefficient and the dynamic range calculated from the diffraction efficiency to obtain an estimate of the photorefractive phase shift with eq 9. These estimates are listed in Table 4. The largest phase shift is found in sample 1, which is also the sample with the largest carbazole number density. Sensitizing sample 4 with TNFM instead of C60 increased the gain coefficient at 50 V/µm from 96 to 147 cm-1, whereas the dynamic range decreased from 0.0027 to 0.0021. For the phase shift, this corresponds to an increase from 13° to 26°. Thus, within a similar matrix, replacing TNFM by C60 results in a larger dynamic range and smaller gain coefficient, which indicates a smaller photorefractive phase shift. Because the photorefractive phase shift decreases with increasing trap density, this implies that in the C60-sensitized samples a larger
Figure 7. Dynamics of the diffraction efficiency buildup in sample 2 at two different values of the applied field.
trap density is present, as was also concluded from the fourwave mixing experiments. Conclusion In conclusion, we have studied two new photorefractive polymethacrylates functionalized with a previously studied bifunctional chromophore. Larger chromophore number densities could be achieved than in our previously studied PVKbased composites doped with chromophore Lemke-E but resulted in the formation of a texture in the pure copolymers. Optically clear samples could be made after adding 16 wt % of DOP to the copolymer having the LC comonomer with the highest polarity. Ellipsometric experiments showed that only 70-80% of the theoretically possible refractive index difference was realized because of orientational correlations. The bifunctional polymers could be sensitized with C60 for operation at 780 nm. Overmodulation of the diffraction efficiency was observed at an applied electric field of 43 V/µm, a clear improvement over our previously studied polymer composites. The improvements in ∆n came at the cost of lower speed and lower 2BC gain. None of the polymers studied at 780 nm showed a full quadratic dependence of the index modulation amplitude on the applied electric field, which indicates that the space-charge fields are not completely saturated. The PVK-based polymer composite had the largest carbazole number density and the fastest grating build-up time but, according to the field dependence of the dynamic range and the large photorefractive phase shift, also the smallest trap density. Within a similar polymer matrix, sensitization with C60 led to improved photorefractive grating build-up times and diffraction efficiencies but reduced photorefractive phase shifts. Acknowledgment. E.H. is a research associate and D.V.S. a research assistant of the Fund for Scientific Research-Flanders (Belgium) (FWO). C.E. is a research assistant of the Flemish Institute for Promotion of the Scientific-Technological Research in Industry (IWT). This research was supported by research grants from the FWO (Grants G.0338.98 and S 2/5-AV. E 8), the University of Leuven (Grant GOA/ 2000/ 03), and the Belgian Government (Grant IUAP P4/11). The authors thank Prof. K. Binnemans for experimental assistance. References and Notes (1) Gu¨nter, P.; Huignard, J.-P. PhotorefractiVe materials and their applications; Springer-Verlag: Berlin, 1988, 1989; Vols. I and II. (2) Moerner, W. E.; Grunnet-Jepsen, A.; Thompson, C. L. Annu. ReV. Mater. Sci. 1997, 27, 585.
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