and Two-Photon-Pumped Fluorescence from Rhodamine B in Solid

School of Chemical Sciences, Department of Physics and The Frederick Seitz Materials Research Laboratory,. UniVersity of Illinois, S. Mathews AVe., Ur...
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J. Phys. Chem. B 1998, 102, 4380-4385

One- and Two-Photon-Pumped Fluorescence from Rhodamine B in Solid Poly(acrylic acid) under High Pressure Z. A. Dreger, G. Yang, J. O. White, Y. Li, and H. G. Drickamer* School of Chemical Sciences, Department of Physics and The Frederick Seitz Materials Research Laboratory, UniVersity of Illinois, S. Mathews AVe., Urbana, Illinois 61801-3792 ReceiVed: January 23, 1998; In Final Form: March 10, 1998

We investigate the effect of pressure on one- and two-photon-excited fluorescence of Rhodamine B dissolved in solid poly(acrylic acid). We present the pressure dependence of the fluorescence intensity as well as the energy and lifetime of the emitting state for one- and two-photon excitation for three different excitation energies. All these parameters decrease with increasing pressure regardless of the mode and energy of excitation. The similar change with pressure of the lifetime and emission energy for one- and two-photon excitation reveals that the fluorescence originates in the same state for both excitations. The decrease of fluorescence intensity with pressure is attributed (i) to an increase of the nonradiative rate from the emitting state and (ii) to a decrease of the absorption cross section. The first process is correlated with a pressureinduced shift of the emission energy that coincides with the energy gap law. The observed larger pressure change in the absorption cross section for two-photon than for one-photon excitation indicates an additional pressure dependence of the transitions involving the intermediate states.

1. Introduction Materials with large optical nonlinearities can be useful for frequency conversion and modulation of laser radiation, leading to a wide range of applications including optical data storage, communications, and optical computing systems. Over the past decade or so much interest has centered on organic materials because they may exhibit nonlinear optical (NLO) properties that surpass those of the inorganic materials. Moreover, organic materials usually offer easier processing, faster response time, and lower cost. Prominent in this regard are solid organics with large twophoton absorption (TPA) and efficient two-photon-excited fluorescence (TPEF). These materials have recently attracted a growing attention due to their potential applications in solidstate upconversion lasers, three-dimensional optical memories, optical power limiters, and optical fiber amplifiers.1-7 The search for materials with an efficient two-photon process takes place through either the synthesis of new molecules or modification of existing compounds by chemical and physical methods. In our approach we employ an external pressure to modify the NLO properties of an organic solid without changing its chemical content. In a number of organic materials, we have shown that high pressure can tune two-photon-excited fluorescence by changing its emission intensity and spectral range.8-10 Furthermore, by introducing the pressure parameter, we have revealed that the two-photon-excited state relaxes to the same state as the one-photon-excited state, from which the emission takes place. However, in the case of low-symmetry polar molecules, pressure tunes emission intensity differently for oneand two-photon excitation. Since these molecules are not centrosymmetric (for centrosymmetric molecules transitions for * To whom correspondence should be sent.

one- and two-photon excitation obey different rules and thus take place to states with different symmetry), the source of this difference is not obvious. For these molecules, despite their low symmetry, we have proposed that one- and two-photon excitation take place to different excited states. Thus, pressure may alter differently these two absorption transitions. Furthermore, in the case of molecules with significant charge redistribution upon excitation (a large Stokes shift), the relaxation pathways may be differently perturbed by pressure for two modes of excitation. Consequently, fluorescence quantum efficiency changes with pressure differently for one- and twophoton excitation. In this paper we study the effect of pressure on two-photonexcited fluorescence of a well-known dye, Rhodamine B (RhB), dissolved in solid poly(acrylic acid) (PAA). In the past, twophoton excitation studies of RhB have only been performed in liquid solutions.11-16 In these solutions RhB is very sensitive to the environment and can exist in a number of molecular forms (zwitterionic, cationic, and lactone) and conformations due to the rotational motion of the diethyl groups around the xantheneamine bond.17-22 However, in poly(acrylic acid) the RhB molecules exist essentially in the cationic form and exhibit high fluorescence efficiency, since in a solid polymer the rotational motion is significantly suppressed. We have selected RhB in the solid matrix for several reasons: (i) a fluorescing dye trapped in a solid matrix has many practical advantages over liquid systems,23-26 (ii) RhB in PAA shows promising features (e.g., good photostability) as a solid-state lasing medium,27 (iii) RhB exhibits a strong two-photon process, (iv) one- and two-photon excitation can be examined for three different states that are present in the visible range, and (v) absorption and emission involve the same locally excited state (a small Stokes shift). Under the last condition one expects that fluorescence quantum efficiency will change similarly for one- and two-photon excitation. Thus, the eventual difference in fluorescence

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Rhodamine B in Solid Poly(acrylic acid)

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intensity change under pressure for one- and two-photon excitation should reflect differences in their absorption processes. We present the pressure effect on time-averaged and timeresolved fluorescence characteristics of RhB in PAA. We compare the pressure dependence of one- and two-photonexcited fluorescence for three excited states. Finally, we discuss similarities and differences between the pressure dependence of one- and two-photon processes. 2. Experiment Laser grade Rhodamine B was purchased from Acros Organics and used without further purification. PAA of 250 000 average molecular weight (AMW) from Aldrich is dissolved with RhB in methanol (spectranalyzed, Fisher). Films of RhB in PAA are prepared in a glass dish where the solvent is allowed to evaporate slowly at room temperature. The transparent films of 10-4 and 10-5 mol/mol (mole of RhB per mole of the monomeric unit of the polymer) concentration are then placed in a vacuum oven for a few days at 50 °C. The thickness of the films is approximately 30 µm. The first excited state of RhB in PAA is reached by either a 1053 nm line (two-photon absorption) of the Nd:YLF laser (250 W peak power and 50 ps pulse duration, at 76 MHz) or its second harmonic at 526.5 nm (one-photon absorption). The excitation of higher energy states is by means of a titaniumsapphire (Ti-Al2O3) laser (13 kW peak power and 100 fs pulse duration, at 76 MHz) or its second harmonic generated with a BBO crystal. The beam of the laser is focused on a 7 × 10-2 mm2 area of the sample. High pressure is generated through a light mineral oil in a gasketed triangular type diamond anvil cell (DAC). The front-side excited fluorescence is corrected for the spectral sensitivity of the detection system. All measurements are made at room temperature. The details of the experimental setup have been described elsewhere.9,10 3. Results RhB in PAA is optically transparent for energies up to ∼15.6 × 103 cm-1, for one-photon excitations (low fluxes). Above that energy RhB absorbs strongly, and its spectrum exhibits several maxima in the visible and near-visible range (see Figure 1, solid line). The main absorption peak at 17.9 × 103 cm-1 (559 nm) corresponds to the S0 f S1 transition in the RhB molecule. For a 10-5 concentration sample the product of the absorption coefficient and thickness of the sample at the peak maximum is estimated to be ∼6 × 10-2, at atmospheric pressure. The main absorption band reveals also some irregularities on the high-energy side which are enhanced with increasing concentration of RhB in PAA. Since the RhB molecules tend to aggregate, this additional absorption is commonly attributed to the absorption of various types of dimers.28-33 In contrast to the S0 f S1 transition, the high-energy absorption maxima located at 23.8 × 103 cm-1 (420 nm), 25.3 × 103 cm-1 (395 nm), and 28.7 × 103 cm-1 (348 nm) are much less intense. The first two maxima are examined, because they are in the range of the Ti-Al2O3 laser, and assigned formally to the S2 and S3 excited states of the RhB monomer. These two states are strongly overlapped but well disconnected from the main absorption band. Under pressure the one-photon absorption spectrum reveals (i) a shift to lower energies (a main peak shift of ∼1000 cm-1

Figure 1. Absorption spectrum and emission spectrum (excitation at 526.5 nm) of 10-5 RhB in PAA, at atmospheric pressure. Points are referred to the relative two-photon absorption cross sections calculated according to eq 6. Arrows indicate the excitation energies of the Nd: YLF and Ti-Al2O3 lasers and their second harmonics employed for the fluorescence excitations.

within 80 kbar), (ii) a stronger overlap between bands assigned to the S2, S3, and S4 state, and (iii) no significant change in the shape of the main absorption band. The last feature indicates that there is no further dimerization under pressure. However, a red shift of the absorption spectrum with pressure decreases the absorption coefficient at 526.5 nm excitation (approximately a factor of 2 over 60 kbar). The effect of pressure on the highenergy absorption bands cannot be estimated since these bands overlap more strongly with increasing pressure. Figure 1 also includes the relative values of the absorption coefficients (cross sections) for two-photon absorption at the energies a factor of 2 lower than the corresponding one-photon transitions. These values are calculated according to the formula given in the section 4.2. As we can see, the two-photon absorption is stronger to those states where the one-photon absorption is weak. In other words, the one-photon transition is strongly allowed to the S1 state and the two-photon transition to the S2 and S3 state. RhB in PAA exhibits a very efficient red emission when exposed to visible or infrared light (see Figure 2). The emission spectra at various excitation energies reveal essentially the same shape: one peak located at 16.7 × 103 cm-1 (∼599 nm), at atmospheric pressure. However, it is very characteristic that the bandwidth (fwhm) of two-photonexcited fluorescence (TPEF) is always narrower than onephoton-excited fluorescence (OPEF), perhaps due to a stronger reabsorption effect in the former case. The pressure dependence of the emission intensity integrated over energy and peak energy is presented in Figures 3 and 4. With increasing pressure, two main features are observed: (i) a moderate decrease of the emission energy (∼1000 cm-1 within 80 kbar), the same for all excitations; (ii) a decrease of the emission intensity for both the one- and two-photon excitation but somewhat stronger in the latter case. The change of emission intensity is also different when the lowestsS1 (526.5 nm, 2 × 1053 nm)sor highersS2 (420 nm, 2 × 840 nm) and S3 (395 nm, 2 × 790 nm)sstates are excited. In the first case, the emission intensity decreases, within 70 kbar, ∼10 and ∼25 times respectively for one- and two-photon excitation, whereas for higher states, the decrease

4382 J. Phys. Chem. B, Vol. 102, No. 22, 1998

Figure 2. Emission spectra of RhB in PAA following one- (526.5 nm) and two-photon (1053 nm) excitations at different pressures.

in intensity (the same for both states) is ∼6 and ∼15 times respectively for one- and two-photon excitation. To characterize further the pressure effect on fluorescence intensity, we determine pressure dependence of lifetime of the emitting state for different excitations. The data collected in Figure 5 reveal that (i) at atmospheric pressure the lifetime is almost the same (∼6 ns) for different excitations (see footnote as ref 34), (ii) the lifetime decreases by a factor of 2, over a 70 kbar range, and (iii) the decrease of lifetime is essentially the same regardless of the mode and wavelength of excitation. The results presented in Figures 3 and 5 strongly indicate that, for all excitations employed, fluorescence of RhB in PAA takes place from the same excited state.

Dreger et al.

Figure 3. Pressure-induced fluorescence intensity change for RhB in PAA following one- and two-photon excitation: (A) Nd:YLF and (B) Ti-Al2O3 laser.

4. Discussion The results show that the fluorescence intensity, energy, and lifetime of RhB in PAA decrease with pressure for three excitation energies and two modes of excitation. Whereas the energy and lifetime of the emitting state change similarly for one- and two-photon excitation, the fluorescence intensity behavior is different. Because the fluorescence intensity is controlled by both emission and absorption, we discuss below the participation of these two processes in the case of RhB in PAA. The experiments were performed under the conditions of weak light absorption (the product of the relevant absorption

Figure 4. Pressure dependence of the energy of the emitting state of RhB in PAA following various one- and two-photon excitations.

coefficient and thickness of the sample is much smaller than one) and absence of saturation and photobleaching processes. In this case the time-averaged fluorescence intensity (photons/

Rhodamine B in Solid Poly(acrylic acid)

J. Phys. Chem. B, Vol. 102, No. 22, 1998 4383

Figure 5. Pressure dependence of the lifetime of the emitting state of RhB in PAA following various one- and two-photon excitations.

(s cm2)) for one- and two-photon excitation can be expressed as follows:

I1 ) Kg1Φ1σN0LPav1

(1)

I2 ) Kg2(Φ2/2)δN0(L/A)Pav22

(2)

In the above equations subscripts “1” and “2” correspond to one- and two photon excitation; K is the efficiency of the emission collecting system (per unit area of the detector (cm-2)), and it does not change with mode of excitation; g1 represents the duty cycle of the laser excitation, and it is inversely proportional to the product of pulse repetition rate (f) and pulse width (∆t); g2 is a measure of the second-order coherence of the laser beam35 (a ratio of the shape of the laser pulse and the duty cycle); Φ1 and Φ2 are the fluorescence quantum yields (note that Φ2 is divided by two because two photons participate in each event of excitation); σ (cm2) and δ (cm4 s/photon) are the one- and two-photon absorption cross sections; N0 is the number of molecules per unit volume (cm-3); L is the absorption path length in centimeters (equal to the sample thickness in the weak focusing case); Pav1 and Pav2 are the average laser powers (photon/s); and A is the area of the laser beam at the sample (cm2). For a focused Gaussian beam the term L/A in eq 2 may be replaced be π/2λ.36,37 To analyze the pressure effect on fluorescence intensity, it is convenient to introduce the expressions (I1′, I2′) for relative intensities defined as fluorescence intensities at any pressure (p) normalized to the value at atmospheric pressure (0). Thus, eqs 1 and 2 can be reduced to the following forms:

I1′ )

I2′ )

I1(p)

)

k1r(p) τ1(p) σ(p)

I1(0)

k1r(0) τ1(0) σ(0)

I2(p)

k2r(p) τ2(p) δ(p)

I2(0)

)

k2r(0) τ2(0) δ(0)

and relevant lifetime (τ) of the emitting state. Furthermore, one should note that although both the concentration (N0) and thickness (L) change with pressure, the product of N0L does not; i.e., the number of molecules in the light path is constant (the size of the beam is 4/3 of the size of sample, and up to 80 kbar there is no measurable deformation of the gasket). Expressions 3a and 3b indicate that pressure dependence of the fluorescence intensity is determined by pressure changes in the emission (fluorescence quantum yield, i.e., radiative rate and lifetime of the emitting state) and absorption of the light (absorption cross section). 4.1. Nonradiative Rate. At atmospheric pressure, RhB in PAA exhibits a small Stokes shift (∼1300 cm-1) and a high fluorescence quantum yield (∼0.9).27 As pressure increases, a red shift of the emission peak appears which may cause an increase of the nonradiative transitions between different electronic states and consequently a decrease of the fluorescence quantum yield. In the case of RhB in PAA, two nonradiative processes can be considered: an internal conversion of the energy between the excited and ground state and/or intersystem crossing between the excited singlet and triplet state. At present, there are several reasons to believe that internal conversion is the main nonradiative relaxation path of the excited state. For example, for RhB in PAA (i) there is no experimental proof for the existence of a triplet state near the singlet state, (ii) there is no information on the rate constant for the intersystem crossing, and (iii) it is not obvious that increasing pressure would increase the intersystem crossing rate. However, the most important evidence comes from the analyses presented below. As we will see, these analyses show a good correlation between the nonradiative rate and the energy difference existing between the excited singlet state and its ground state. Taking into account that, in polymeric matrixes, the radiative rate (kr) changes usually much less with pressure than the nonradiative rate (knr),38 the pressure dependence of the latter can be calculated from the following relation:

knr(p) )

Φ(0) 1 τ(p) τ(0)

(4)

On the other hand, the nonradiative rate for the internal conversion can be formulated within the theory of radiationless transitions in large organic molecules, given by Englman, Jortner, and Freed.39,40 Their treatment is based on the assumptions that molecular vibrations are harmonic and that normal modes and their frequencies are the same in the initial and final states. In the case when the electronic energy is dissipated by a single vibrational mode and the relative horizontal displacement of the potential energy surfaces in the initial and final electronic state is small (Stokes shift is comparable with the mean vibrational energy), they derive an analytical expression in the weak coupling limit. In this case the rate constant of a radiationless transition between electronic states changes with the energy gap between these states and assumes the following form, known as an energy gap law:

(3a)

knr ) K0 exp(-γ∆E/pωM)

(5)

where

(3b)

Since, for RhB in PAA, the same electronic state that emits also absorbs, the fluorescence quantum yields in eqs 1 and 2 are replaced by the product of the relevant radiative rate (kr)

K0 ) C2(2π)1/2p-1(pωM∆E)-1/2 and γ ) ln(2∆E/dpωM∆M2) - 1 (5a) ∆E is the energy of the thermally equilibrated excited state above the ground state (energy gap), C2is the nuclear momentum

4384 J. Phys. Chem. B, Vol. 102, No. 22, 1998

Dreger et al. energy surfaces in the two electronic states, the pressure method may serve as an important tool in investigation of the electronic states in different local environments. The preexponential factor in eq 5 for RhB in PAA obtained from fitting is 1.3 × 1015 s-1. Thus, the matrix element for vibronic coupling (C2) is estimated to be ∼3 × 106 cm-2 (4.67 × 10-2 (eV)2) for pωM ) 3000 cm-1, typical for C-H stretches. The value of C2 for RhB is in the range of the coupling terms estimated for various aromatic molecules (105-107 cm-2).39 4.2. Two-Photon Absorption vs One-Photon Absorption. As presented in Figure 1, the absorption cross sections for twophoton excitation are larger for the S2 and S3 states than for the S1 state, in contrast to one-photon absorption. The relative twophoton absorption cross sections for different energies are determined by comparison of the fluorescence intensity produced by two-photon absorption at different wavelengths:

δ′(λ2) )

Figure 6. Plots of nonradiative rate (knr) versus emitting state energy: (A) one- and two-photon excitation respectively for 420 and 840 nm; (B) collected data for all excitation energies. Lines represent the leastsquares fits of the experimental results.

matrix element for promoting vibration which leads to the transition between states, and d and ∆M denote respectively the degeneracy and reduced displacement of the molecular vibration at maximum angular frequency (ωM). Because K and γ depend on much less than the exponential function, eq 5 gives essentially an exponential dependence of knr on ∆E. To test the applicability of the energy gap law in the case of RhB in PAA, we plot ln knr(p) (eq 4) at each pressure (every 5 kbar) versus the energy of the emitting state (energy gap, ∆E) taken from Figure 4. Figure 6 presents plots of ln knr vs ∆E for the 420 and 840 nm line (A) and for data obtained for all energies and modes of excitation (B). The lines shown are the least-squares fits to the data and have slopes of -1.98 × 103 cm (-16.0 (eV)-1) and -2.06 × 103 cm (-16.6 (eV)-1) respectively for cases A and B. As can be seen, the data follow the exponential relationship predicted by the energy gap law. Because knr is calculated according to eq 4 which assumes the pressure independence of kr, this would confirm the applicability of the latter assumption. We believe that any differences in the slope and intercept, among different excitation lines, have no physical meaning but are likely the errors of the experimental method. The average slope (-16.6 (eV)-1) for RhB in PAA is close to the value of -19.2 (eV)-1 obtained for fluorescein (xanthene dye) by the solvent method in deuterated alcohols.41,42 Since the slope parameter contains the pertinent structural information concerning the relative displacement of the potential

δ(λ2) δ(λ1)

)

I2(λ1) g2(λ1) λ2Pav22(λ1) I2(λ2) g2(λ2) λ1Pav22(λ2)

(6)

In this equation g2(λ1) ) s/(f∆t)1 and g2(λ2) ) s/(f∆t)2. For pulses with a Gaussian temporal profile s ) 0.664,16 whereas (f∆t)1 ) 3.8 × 10-3 (for Nd:YLF laser) and (f∆t)2 ) 7.6 × 10-6 (for Ti-Al2O3 laser). The RhB molecule in the ground state has relatively low symmetry, belonging essentially to the C2V point group. Thus, the S0 ground state of the π-electrons has the totally symmetric representation A1, and the excited states are represented by either A1 or B2. The first excited singlet state is represented by B2. The higher states, S2 and S3, are considered to be of A1 symmetry.13 Both transitions to A1 and B2 are symmetryallowed for two-photon absorption. Since the S0 f S2 and S0 f S3 transitions take place between states of the same symmetry (A1 f A1), it is not unexpected that absorption cross sections for these transitions, which take full advantage of the π-electron delocalization, are substantially stronger than for the S0 f S1 transition (A1 f B2). Moreover, two-photon transitions to higher excited states (S2, S3) can be enhanced by the contribution of S1, participating as an additional intermediate state. The last effect has been theoretically predicted for Rhodamine 6G by the sum-over-states (SOS) calculations.13 As pressure increases, the fluorescence intensity decreases for both the one- and two-photon excitation. This effect is always stronger for two-photon excitation than for one-photon. Because for RhB in PAA the following relations are applicables (i) τ1(p) ) τ2(p) (from the experiment) and (ii) k1r(p) ) k2r(p) (since for one- and two-photon excitation emission originates from the same state)sthe ratio of the relative absorption cross sections for two- and one-photon excitation can be simply expressed from the intensity measurements:

δ′/σ′ = I2′/I1′

(7)

As can be seen in Figure 7 the ratio decreases gradually by a factor of 2 within 60 kbar. Moreover, the changes are approximately the same for three different excited states. At present it is difficult to account for the origin of such a result. However, we can propose the following possibilities. Pressure, by increasing the coupling between the dye molecule and polymer, may alter the symmetry of the molecule and thus change the distribution among the absorption transitions associated with one- and two-photon excitations. In addition, since two-photon absorption involves the transitions through the intermediate states, the pressure dependence of these

Rhodamine B in Solid Poly(acrylic acid)

J. Phys. Chem. B, Vol. 102, No. 22, 1998 4385 Materials Research Laboratory. The experiments were performed in the MRL Laser Facility. References and Notes

Figure 7. Pressure effect on ratio of the relative absorption cross section for two-photon excitation δ′ to relative absorption cross section for one-photon excitation σ′ for various excitations.

transitions may perturb the overall two-photon process further than the one-photon (direct absorption). The stronger pressure decrease of the two-photon absorption cross section compared to the one-photon absorption cross section has been observed for other low-symmetry dyes.10 It seems that this effect is characteristic in molecules for which the two-photon absorption peak is blue-shifted with respect to the one-photon absorption. 5. Conclusions We have reported experiments on the pressure effect on fluorescence of RhB in PAA induced by one- and two-photon transitions for different excitation energies. It appears that twophoton absorption is stronger to higher energetic states than the first excited state, i.e., the reverse situation of one-photon excitation. With increasing pressure we observe a decrease of energy, lifetime, and fluorescence intensity for both one- and two-photon excitation. These observations lead to the following conclusions: (i) the one- and two-photon absorbing states relax to the same electronic state, (ii) a decrease of lifetime (or increase of nonradiative rate), attributed to the emitting state, correlates with a decrease of the energy between the excited and ground state, (iii) both the one- and two-photon absorption cross sections decrease with pressure, and (iv) the two-photon absorption cross section is more strongly perturbed by pressure than the one-photon absorption cross section; this is likely due to the pressure dependence of the intermediate absorbing states. Although, in the present case, pressure decreases the efficiency of the two-photon-induced process, it is believed that in the future high-pressure studies could benefit the design of upconversion materials with wide spectral tunability and high efficiency. Acknowledgment. The authors would like to acknowledge continuing support by the U.S. Department of Energy, Division of Materials Science, Grant DEFG02-96R45439, through the University of Illinois at Urbana-Champaign, Frederick Seitz

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