Study of Carrier Generation in Phthalocyanines by Time-Resolved

We have studied the influence of electric field on fluorescence in particles of photoconductive TiOPc (I), TiOPc (IV), HOGaPc, and x-H2Pc dispersed in...
0 downloads 0 Views 110KB Size
Download PDF
J. Phys. Chem. B 2002, 106, 8625-8631

8625

Study of Carrier Generation in Phthalocyanines by Time-Resolved Fluorescence Zoran D. Popovic,*,† M. Iltaf Khan,‡ Ah-Mee Hor,† Joshua L. Goodman,‡ and John F. Graham† Xerox Research Centre of Canada, 2660 Speakman DriVe, Mississauga, Ontario L5K 2L1, Canada, and NSF Center for Photoinduced Charge Transfer, UniVersity of Rochester, Rochester, New York ReceiVed: March 13, 2002; In Final Form: May 16, 2002

We have studied the influence of electric field on fluorescence in particles of photoconductive TiOPc (I), TiOPc (IV), HOGaPc, and x-H2Pc dispersed in a polymer matrix. Electric field induced quenching of both the integrated and time-resolved fluorescence were measured. Time-resolved fluorescence decays were analyzed by fitting the data to a sum of two exponentials, representing the fast and slow fluorescence components. For HOGaPc, TiOPc(I), and TiOPc (IV), the fast fluorescence component exhibits both amplitude and lifetime quenching. These results indicate that carrier generation in HOGaPc, TiOPc(I), and TiOPc (IV) originates from both relaxed and nonrelaxed intrinsic excited singlet states, while the trapped excitons do not lead to significant carrier production. In contrast, for x-H2Pc, significant amplitude quenching of the fast component is observed only at high field, and the trapped excitons are an important source of photogenerated carriers. This indicates that x-H2Pc possesses at least some bulk-sensitized photocarrier generation. All of the phthalocyanines studied exhibited a quadratic dependence of integrated fluorescence quenching on electric field, indicating the existence of a neutral carrier precursor state.

1. Introduction Phthalocyanines represent an important class of organic photoconductors, both as model systems and as materials extensively used in organic xerographic photoreceptors. Despite numerous studies, a detailed picture of the carrier generation process in this class of materials has yet to emerge. In this paper we will present a detailed description of the photocarrier generation mechanism in TiOPc(I),1 TiOPc(IV),1,2 HOGaPc,3 and x-H2Pc.4,5 These photogenerators are of particular interest as they are commonly utilized in xerographic copiers and printers. It is also interesting to compare the photogeneration mechanism of two polymorphs such as TiOPc(I) and TiOPc(IV). It is known from xerographic measurements that TiOPc(IV), often referred to as TiOPc-Y, is considerably more sensitive than TiOPc(I), despite possessing the same molecular structure.1,2 Important information on the mechanism of photoconductivity in organic materials has been obtained by electric field modulated spectroscopies. Electric field induced fluorescence quenching was studied in solution,6 doped polymer systems,7,8 and crystalline organic pigments.9-12 These measurements, combined with photoconductivity measurements, enable investigation of electronic states participating in the carrier generation process. They supply additional information not available on the basis of photoconductivity measurements alone. Most electric field induced fluorescence quenching studies have been applied to total sample fluorescence. These studies demonstrated a correlation between fluorescence quenching and photocarrier generation efficiency and thus indicated that the first excited singlet state leading to fluorescence and carrier generation are linked. However, they could not distinguish between intrinsic and impurity controlled processes or resolve if the first excited † ‡

Xerox Research Centre of Canada. University of Rochester.

singlet state or its precursor was involved in carrier generation. It was also found that in some phthalocyanines, photoconductivity depends strongly on the presence of impurities, for example, oxygen,13,14 and electron donors and acceptors.15 The perturbative influence of external electric fields on molecular energy levels (Stark effect) is usually quite small.15 In this paper, we will concentrate only on processes which can produce large fluorescence changes. These processes generally involve an intermediate state in which an electron and hole are separated by a finite distance. The consequence of this charge separation is strong coupling of the intermediate state to the external electric field which leads to modulation of either (i) the initial number of excited molecules or (ii) the decay rate of the fluorescent excited state. These two different mechanisms of fluorescence quenching are a signature of underlying molecular processes. They cannot be distinguished on the basis of fluorescence intensity measurements alone. However, timeresolved measurements can potentially distinguish them. In the first case, amplitude quenching, we expect to observe a decrease in fluorescence amplitude, but unchanged fluorescence lifetime. This happens when the precursor to the fluorescent state is quenched by the electric field, i.e., photogenerated carriers and fluorescent first excited singlet state have a common precursor. In the second case, rate quenching or lifetime quenching, the initial fluorescence amplitude remains constant but the lifetime decreases. This is a signature of direct quenching of the fluorescent state by the electric field, i.e., photogenerated carriers and fluorescence both originate from the first excited singlet state. The schematic diagrams of these two mechanisms are shown in Figure 1. In principle both mechanisms can operate simultaneously resulting in both amplitude and rate (lifetime) quenching. Fluorescence measurements are also important in developing an understanding of the sensitized carrier generation observed in some organic systems. In these systems the presence of a small electron donor molecule

10.1021/jp020700l CCC: $22.00 © 2002 American Chemical Society Published on Web 08/06/2002

8626 J. Phys. Chem. B, Vol. 106, No. 34, 2002 on the surface of an organic dye leads to the fluorescence quenching and generation of electron-hole pairs.17,18 Time-resolved electric field induced fluorescence quenching studies have been previously reported for two materials belonging to perylene and phthalocyanine classes. Time-resolved fluorescence experiments on the organic photoconductor N,N′bis(methyl)perylene-3,4,9,10-tetracarboxyl diimide showed multiphasic character, but deconvolution of the data demonstrated that the intrinsic (host) fluorescence was strongly quenched by the electric field by the rate quenching mechanism.19 It therefore follows that the intrinsic carrier generation process originating from the first excited singlet state did exist in this material. It is reasonable to expect that organic systems other than those containing perylene might also exhibit photoconductivity originating from the first excited singlet state. In a previous publication the processes of carrier generation in TiOPc(IV) was studied by both integrated fluorescence quenching and time-resolved fluorescence quenching.20 In this paper, we will broaden the study to include other technologically relevant phthalocyanines such as hydroxy gallium phthalocyanine (HOGaPc), metal free phthalocyanine (x-H2Pc), and other polymorphs of TiOPc, such as TiOPc(I). These materials have been previously studied by various electric field modulation techniques.10,21 In this publication, field induced changes in the time-resolved fluorescence are used to present a consistent picture of the carrier generation process in the previously mentioned phthalocyanines, which show varying photosensitivity.

Popovic et al.

Figure 1. In the amplitude quenching mechanism (a), the precursor state is affected by the electric field while the fluorescent state itself is not, leading to a decrease of fluorescence amplitude, but not the lifetime. In the rate quenching mechanism (b), the fluorescent state itself is affected by the electric field while the precursor state is not, leading to a decrease in fluorescence lifetime, but not the amplitude. If is time dependent fluorescence intensity. kr, knr, and kE are rate constants for radiative decay, radiationless decay, and charge generation, respectively.

2. Experimental Section The pigments used in this work were synthesized in-house using procedures described in the literature.1,3,5 Standard elementary analysis was used to confirm that they were of high purity with assays >98%. Most importantly, they met electrical requirements for xerographic photoreceptors, i.e., showed high sensitivity, low dark decay, and excellent cycling stability. Their polymorphic forms were determined by X-ray diffraction analysis. The pigment dispersions were prepared by roll milling 1.5 g of pigment, 1.0 g of polymer, and 47.5 g of butyl acetate with 300 g of 1/8 in. stainless steel balls in a 120-mL bottle. Total milling time was 48 h. The pigment dispersion films were dip coated onto the NESA to about 0.2-0.4 µm thick, making sure the maximum optical density of absorption peak was greater than one. All of the samples were thin film sandwich cells prepared on NESA glass substrates. The NESA was first coated with a silicon monoxide blocking layer, followed by dip coating of the phthalocyanine dispersed in a polymeric binder to a thickness of about 0.2-0.4 µm. The TiOPc (I), TiOPc (IV), and x-H2Pc were all dispersed at 60 wt % in a poly(vinylbutyral) matrix. The HOGaPc was dispersed at 60 wt % in a poly(vinyl chloride)-vinyl acetate-maleic acid terpolymer matrix. These polymer matrixes were chosen as they provided good pigment dispersion in the coating solvent. All pigment films were then overcoated with a 2 µm thick polycarbonate (GE Lexan) from a toluene solution in order to minimize the risk of sample breakdown at high electric fields. We did not take any special precaution to prevent interfacial mixing. However, since the solvent in the overcoat layer evaporated rather quickly, we do not expect that the mixing was very significant. For time-resolved fluorescence measurements, light excitation was provided by a synchronously pumped, mode locked dye laser system equipped with a cavity dumper. Excitation wavelength was 590 nm, using 5 ps pulses and a repetition frequency

Figure 2. Waveform of the bias applied to the sample together with timing of pulsed laser illumination for time-resolved fluorescence quenching measurements.

of 20 kHz. Fluorescence was detected by a SPEX 1681 monochromator equipped with a Hamamatsu 3809U microchannel plate photomultiplier tube. Photon counts from the PM tube were processed by an EG&G ORTEC TAC system and accumulated in a PC equipped with a multichannel analyzer board and Edinburgh Instruments software package to control the measurements. Data were taken with a resolution of 6.68 ps per channel at a wavelength corresponding to the maximum detected signal around 840 nm. The detection wavelength was close to the absorption maximum of TiOPc(I), TiOPc(IV), and HOGaPc. Therefore the pigment region close to the ITO electrode was dominating the measured fluorescence, except for x-H2Pc, which has maximum absorbance around 780 nm. The absorption spectra were in agreement with the results reported in the literature.1-5 All experiments were carried out under dry nitrogen. The time dependence of the sample bias and the timing of laser excitation pulses for time-resolved measurements are given in Figure 2. For every applied field, three different decay curves were collected, corresponding to positive, negative, and zero sample bias for all samples. Positive and negative bias curves

Study of Carrier Generation in Phthalocyanines

J. Phys. Chem. B, Vol. 106, No. 34, 2002 8627

Figure 4. Example of time-resolved fluorescence decay curves for HOGaPc recorded at an applied voltage of 0 and 112 V/µm.

Figure 3. (a) Field dependence of integrated fluorescence quenching, Φ, in various phthalocyanines. (b) Field dependence of Φ1/2 in various phthalocyanines.

were identical for all samples, except x-H2Pc, and therefore were averaged to a single curve before data analysis. In x-H2Pc, small differences were observed for different bias polarities, indicating accumulation of space charge in the sample. It appears that during the charge generation process, one carrier is free, while the other becomes trapped and leads to the accumulation of space charge. This accumulation of space charge may be an indication of sensitized carrier generation. The pulse generator supplying the bipolar square wave of up to 400 V was custom built. It used two high voltage FET switches in a differential configuration.19 3. Experimental Results and Data Analysis 3.1. Integrated Fluorescence Quenching. In a previous paper, a detailed description of the interpretation of integrated fluorescence quenching results was presented.20 In summary, if a neutral first excited singlet state dissociates into geminate pairs, one would expect that fluorescence quenching will exhibit a quadratic relationship at low fields. This is a direct consequence of symmetry. At zero field, the probability of an excitedstate dissociating into electron-hole pairs oriented in opposite directions will be the same. When an external field is applied, the dissociation rate of a neutral excited state should not depend on the direction of the electric field. Therefore, fluorescence quenching should be an even function of the electric field, hence quadratic in the lowest order. However, if a charge transfer state dissociates into geminate pairs, a linear electric field dependence of fluorescence quenching is expected.22 Figure 3 depicts the electric field dependence of integrated fluorescence quenching, Φ, in TiOPc(I), HOGaPc(V), x-H2Pc, and TiOPc(IV). In a previous publication it was reported that fluorescence quenching of TiOPc(IV) possesses a linear dependence on applied electric field at low field. However, further experiments at improved resolution yielded a quadratic relationship between fluorescence quenching and electric field. In fact, as can be observed from Figure 3, all of the phthalocyanines studied exhibit a quadratic dependence of fluorescence quenching at low fields. This similarity in field dependence for the

Figure 5. Schematic diagram of the carrier generation model. S0 represents the ground state, Si represents the first excited intrinsic state, S* represents a precursor to the first excited-state such as a vibrationally, nonrelaxed excited state, and St represents the trapped state. Broken lines represent radiationless transitions. kr and ksr are the rate constants for radiative decay for the intrinsic state and the trapped state, respectively. knr and ksnr are the rate constants for nonradiative decay for the intrinsic state and the trapped state, respectively. kE, kE*, and kEt are rate constants for carrier production. kd and kt are the rate constants for the energy transfer process between the first excited intrinsic state and the trapped state.

different phthalocyanines indicates a certain amount of commonality in the carrier generation processes of these materials. As discussed previously, the quadratic dependence of fluorescence quenching on electric field indicates that the excited state, which dissociates into geminate pairs, is neutral rather than a charge transfer state. 3.2. Time Resolved Fluorescence Quenching. The timeresolved fluorescence quenching experiments consistently showed both rate and amplitude quenching by the electric field. However, the degree of field dependence varied significantly between the phthalocyanines. Time-resolved fluorescence decay curves were recorded for different electric fields for all the phthalocyanines. An example of time-resolved fluorescence decay curves recorded at an applied field of zero field and 112 V/µm for HOGaPc is given in Figure 4. The experimental curves were fit to a sum of two exponentials,

If(t) ) B1 exp(-t/τ1) + B2 exp(-t/τ2)

(1)

Since the integrated fluorescence measurements for all the phthalocyanines studied exhibited a quadratic dependence at low fields, we will use the model of carrier generation given in Figure 5. This model was found to be consistent with all of our experimental results. A more detailed description of the model and its derivation is given in the Appendix. In the figure, Si represents the first excited intrinsic singlet state, S* represents a precursor to the first excited-state such as vibrationally, nonrelaxed excited state, and St represents the trapped state. The various rate constants are defined in the Appendix, and the figure caption. As can be observed from Figure 4, the timeresolved fluorescence curve is composed of a fast component and a slow component. The fast component corresponds to

8628 J. Phys. Chem. B, Vol. 106, No. 34, 2002

Popovic et al.

Figure 6. Electric field dependence of lifetimes for the fast component of fluorescence decay (a) and the slow component of fluorescence decay (b).

fluorescence from the intrinsic (host) state, while the slow component corresponds to fluorescence from the trapped (guest) state. Since, the trapped state is vacant at time zero and must be populated by the intrinsic state, with a rate constant kt, eq 1 should be rearranged and expressed as

If(t) ) (B1 + B2)e-k1t + B2(e-k2t - e-k1t),

(2)

where k1 ) 1/τ1 and k2 ) 1/τ2. According to eq 2, (B1 + B2) and B2 represent the amplitudes of the fast and slow components of the fluorescence decay, respectively, and τ1 and τ2 represent the lifetimes of the fast and slow components of the fluorescence decay, respectively. With reference to terminology, the terms fast, intrinsic, and host are equivalent, while the terms slow, trapped, and guest are equivalent. Time-resolved fluorescence spectra recorded at longer times are slightly red shifted with respect to spectra recorded at shorter times. This is consistent with the existence, as presented in the model, of a trapped state with lower energy than the intrinsic state. Referring to the model in Figure 5 and its derivation in the Appendix, the relationship between the amplitudes in terms of the experimental results and the model is given by

|

B2 ke - k2 + Rkt Amplslow ) f fast exp B1 + B 2 k 1 - k2 Ampl

(3)

where R represents the ratio of intrinsic/trapped fluorescence at the measured wavelength. Figure 6a,b depicts the field dependence of the lifetime of the fast component and the slow component of the fluorescence decay, respectively. The lifetime of the fast component of the fluorescence decay, Figure 6a, is clearly field dependent for all of the phthalocyanines studied; however, the degree of field dependence varies between the samples. HOGaPc and TiOPc(IV) exhibit strong field dependence even at low fields, while x-H2Pc is only significantly field dependent at higher fields. In

fact, the lifetime of the fast component of the fluorescence decay for x-H2Pc does not significantly change until ∼100 V/µm. TiOPc (I) possesses intermediate field dependence. The rate or lifetime quenching of the fast component of fluorescence decay observed for HOGaPc, TiOPc(I), and TiOPc(IV) indicates the first excited state, Si in Figure 5, is quenched by the electric field and therefore contributes to photogenerated charge carriers. While in the case of x-H2Pc, the first excited state is only significantly quenched at high electric fields and therefore only significantly contributes to photogenerated charge carriers at higher fields. In x-H2Pc carrier generation still occurs at lower electric fields, however, at a much lower efficiency when compared to the other phthalocyanines. Figure 6b shows the field dependence of the lifetime of the slow component of fluorescence decay. From the figure it is clear that the lifetime of the slow component of fluorescence decay for HOGaPc and TiOPc(I) changes little with electric field (i.e., minimal rate quenching). This suggests the state leading to the slow fluorescence component, the trapped state St, is not significantly quenched and therefore does not contribute significantly to photogenerated charge carriers. However, x-H2Pc does exhibit field dependence, thereby indicating that the trapped state does contribute to photogenerated carriers. Figure 6b also indicates that the lifetime of the slow component of the fluorescence decay for TiOPc(IV) is quenched by the electric field. Therefore in the case of TiOPc(IV), the trapped state also leads to photogenerated carriers, however, at a lower efficiency than the first excited intrinsic singlet state. For TiOPc(IV) the lifetime of the fast fluorescence component is quenched to ∼50% its original value at 75 V/µm, while the lifetime of the slow fluorescence component is quenched to only ∼80% of its original value at 75 V/µm. However, the contribution to photogenerated carriers from both trapped and intrinsic states may be a reason TiOPc(IV) is the most sensitive organic photogenerator known. Figure 7 provides information concerning amplitude quenching of the phthalocyanines. Figure 7a depicts the field dependence of the amplitude of the slow component of fluorescence decay corresponding to the fluorescence from the trapped exciton. As can be observed TiOPc(I), TiOPc(IV), and HOGaPc all exhibit significant amplitude quenching at all applied electric fields. This suggests the precursor to the trapped state is quenched by the electric field. Referring to the model in Figure 5, the trapped state is fed by the first excited intrinsic singlet state at a rate constant of kt. This is consistent with Figure 6a, which clearly demonstrates that the first excited singlet state, Si, is quenched by the electric field and hence contributes significantly to photogenerated charge carriers. In contrast, x-H2Pc does not exhibit amplitude quenching of the slow component until much higher fields than the other phthalocyanines, therefore indicating its precursor, the first excited intrinsic singlet state, is not significantly quenched at low fields. This is once again consistent with Figure 6a. Figure 7b is a plot of the normalized sum of amplitudes, which as previously mentioned is equivalent to the amplitude of the fast fluorescence component (eq 2). Amplitude quenching is clearly visible for TiOPc(I), HOGaPc, and TiOPc(IV). This indicates the presence of a precursor state, such as a vibrationally, nonrelaxed neutral excited state, S*, which is quenched by the electric field. However, in contrast, no significant amplitude quenching is observed for x-H2Pc even at high electric fields, such as 150 V/µm. Therefore, the precursor state to the first excited state does not significantly contribute to carrier generation in x-H2Pc.

Study of Carrier Generation in Phthalocyanines

J. Phys. Chem. B, Vol. 106, No. 34, 2002 8629

Figure 8. Plot of Rkt vs electric field.

Figure 7. Electric field dependence of amplitudes for the slow component of fluorescence decay (a), the fast component of fluorescence decay (b), and the ratio of the two amplitudes (c).

Figure 7c illustrates the ratio between the amplitudes of the fast and slow fluorescence components as described by eq 3. One of the interesting features of this plot is the contrast between the behavior of x-H2Pc and the other phthalocyanines studied. For TiOPc(I), TiOPc(IV), and HOGaPc, the amplitude of the fast fluorescence component is dominant, whereas for x-H2Pc the slow or trapped component plays a major role. 4. Discussion It is worthwhile at this point to summarize the time-resolved fluorescence measurements for each of the phthalocyanines studied. HOGaPc, TiOPc(I), and TiOPc(IV) exhibited similar photocarrier generation properties, while x-H2Pc clearly possesses the most unique mechanism of the four. For HOGaPc, TiOPc(I), and TiOPc(IV) the fast fluorescence component exhibits both amplitude and lifetime quenching. The amplitude quenching indicates that a precursor state, which is quenched by the applied electric field, does exist and hence contributes to carrier generation. The lifetime quenching indicates that the intrinsic excitons are also quenched by the electric field and therefore also produce photogenerated carriers. The precursor to free excitons, which is quenched by electric field, is most likely a vibrationally nonrelaxed neutral excited state. The other possible candidate is a charge transfer state which has been detected in TiOPc near the absorption edge by electroabsorption measurements.2 However, the first possibility is supported by the quadratic dependence of integrated fluorescence on applied field. As previously mentioned, this indicates both the precursor

state and the fluorescing state itself are neutral. One distinguishing feature of TiOPc(IV) as compared to TiOPc(I) and HOGaPc is the contribution to photocarrier generation from the trapped state. This additional contribution may explain the improved sensitivity of TiOPc(IV) as compared to the other pigments. Of all the pigments studied in this paper, x-H2Pc possesses the most unique photocarrier generation mechanism. In x-H2Pc the fast fluorescence component exhibits minimal amplitude quenching and significant lifetime quenching only at high fields. Therefore, the intrinsic excitons only significantly contribute to photogenerated carriers at higher fields. However, the lifetime of the slow fluorescent component exhibits quenching at all applied electric fields, thereby indicating trapped excitons are contributing to photocarrier generation. In x-H2Pc, the trapped state significantly contributes to the number of photogenerated carriers, particularly when compared to the other phthalocyanines studied. As mentioned above, this is an indication that x-H2Pc possesses at least some bulk-sensitized photocarrier generation. In a previous publication it was stated that the ratio of the trapped, It, and intrinsic, Ii, fluorescence intensities was proportional to the intrinsic exciton lifetime.20 However, this assumption is only valid in the case of no radiationless decay, which is not the case for the phthalocyanines studied. In this paper we have presented a more consistent model (Appendix), which accounts for radiationless decay. With reference to eq A.8 in the Appendix, it can be stated that ke ≈ k2, assuming that kd is small. Therefore, eq A.23 may be rewritten as,

(

)

B2(k1 - k2) ≈ Rkt B 1 + B2

(4)

In Figure 8, the recorded data for Rkt is plotted against applied field. As can be observed from the figure, Rkt is field dependent. This decrease in Rkt with applied electric field is consistent with the fact that the exciton diffusion length must decrease as the applied electric field increases and the exciton lifetime decreases. As the exciton diffusion length decreases, the probability of energy transfer between the intrinsic and the trapped state decreases. One should also keep in mind that the description of energy transfer by a single rate constant, kt, is approximate. The energy transfer process is much more complex and involves both exciton diffusion and energy transfer once the exciton is close enough to the energy acceptor molecule. An important fundamental question is what excited-state properties govern high carrier generation efficiency in some phthalocyanines. The hypothesis of Yamasaki et al.23 that it is the proximity in energy and the coupling of the lowest lying charge transfer and neutral excited states is very appealing. The quadratic dependence of fluorescence quenching in many phthalocyanines would indicate that the lowest excited singlet

8630 J. Phys. Chem. B, Vol. 106, No. 34, 2002

Popovic et al.

state is neutral and that the charge transfer state is higher in energy. In that case, the field dissociation of the first excited singlet state leads to carrier production possibly through an intermediate charge transfer state.11 In a previous publication it was speculated that the precursor state to both fluorescence and photogenerated carrier for TiOPc(IV) was a charge transfer state itself.20 This conclusion was drawn from the observed linear dependence of fluorescence quenching on the applied electric field. However, the fluorescence quenching data collected for this paper clearly exhibit a quadratic relationship with electric field for all of the phthalocyanines studied. Therefore, in all cases the carrier generation mechanism involves a neutral precursor, which leads to carrier production possible through an intermediate charge transfer state.

) 0. Equations A.3 and A.4 can be combined and rearranged to yield the following expressions for Ni(s) and Nt(s), with No substituted for Ni(0).

Ni(s) ) Nt(s) )

N0(s + ke)

(A.5)

(s + ki)(s + ke) - kdkt N0kt

(A.6)

(s + ki)(s + ke) - kdkt

Solving for (s + ki)(s + ke) - kdkt ) 0 yields

s2 + s(ke + ki) + (kike - kdkt) ) 0

(A.7)

With k1 ) -s1 and k2 ) -s2, the solutions of (A.7) are given by

5. Conclusions Analysis of time-resolved electric field induced fluorescence quenching measurements clearly show that for HOGaPc, TiOPc(I), and TiOPc(IV) the fast fluorescence component exhibits both amplitude and lifetime quenching. The amplitude quenching indicates a precursor state exists and is quenched by the electric field. The lifetime quenching indicates that the intrinsic excitons are also quenched by the electric field and therefore also contribute to photogenerated carriers. One distinguishing characteristic of TiOPc(IV), when compared to HOGaPc and TiOPc(I), is the contribution to photocarrier generation from the trapped state. Of all the phthalocyanines studied x-H2Pc possesses the most unique generation mechanism in that the trapped state is an important source of photogenerated carriers. The recorded data indicate that x-H2Pc possesses some bulksensitized carrier generation. The quadratic dependence of fluorescence quenching on electric field for all of the phthalocyanines indicates both the precursor state to S1 and S1 itself are neutral.

1/2 1 1 k1,2 ) (ke + ki) ( (ke + ki)2 - (kike - kdkt) (A.8) 2 4

(

As (A.7) is quadratic, k1,2 must satisfy the following relationship

dNi ) -kiNi + kdNt dt

(A.1)

k1 + k2 ) ke + ki

(A.9)

k1k2 ) kike - kdkt

(A.10)

Referring back to eq A.5 and substituting in eqs A.9 and A.10 yields

s + ke Ni(s) ) N0 (s + k1)(s + k2)

(A.11)

which can be reduced to

( )

( )

ke - k2 1 Ni(s) k1 - ke 1 ) + N0 ∆ s + k1 ∆ s + k2

Appendix In this Appendix, the derivation of the model utilized throughout the paper for data interpretation is given. Referring to Figure 5 as the graphical representation of the model, we will first examine the rates at which the intrinsic state, Si, and the trapped state, St, are depopulated: Sum of all Si or intrinsic state rate constants: ki ) kr + knr + kE + kt. Sum of all St or trapped state rate constants: ke ) kd + ksr +ksnr + kEt. The rate at which the population of the intrinsic state changes is given by

)

(A.12)

where ∆ ) k1 - k2. The inverse Laplace transform of eq A.12 with slight rearrangement (the justification for rearranging the expression in this manner will be given later in the Appendix) yields

Ni(s) k1 - k2 -k1t ke - k2 -k2t ) + - e-k1t) (A.13) e (e N0 ∆ ∆ Equation A.13 provides the expression for the population of the intrinsic state as a function of all the rate constants for both the intrinsic and the trapped state. Following the same steps we obtain an expression for the time dependence of the population of the trapped state:

The rate at which the population of the trapped state changes is given by

Nt(s) kt -k2t ) (e - e-k1t) N0 ∆

dNt ) ktNi - keNt dt

Since the fluorescence intensity is proportional to the population of the intrinsic and trapped states, the time-dependent fluorescence intensity will be given by

(A.2)

By use of Laplace transforms, eqs A.1 and A.2 can be expressed as

sNi(s) - Ni(0) ) -kiNi(s) + kdNt(s)

(A.3)

sNt(s) - Nt(0) ) ktNi(s) - keNt(s)

(A.4)

Since, the trapped state is not populated at t ) 0, the term Nt(0)

Iflour(t) ∼ Ni(t) + RNt(t) Iflour(t) ∼

(A.14)

(A.15)

k1 - k2 -k1t ke - k2 + Rkt -k2t e (e + - e-k1t) (A.16) ∆ ∆

where R is the ratio of intrinsic and trapped fluorescence yields at the observed wavelengths. For time-resolved fluorescence

Study of Carrier Generation in Phthalocyanines

J. Phys. Chem. B, Vol. 106, No. 34, 2002 8631

measurements the first term would correspond to the fast component of the fluorescence decay and the second term would correspond to the slow component of the fluorescence decay. Experimentally we fit the time-resolved fluorescence to the equation

Ifluorexp(t) ) B1e-k1t + B2e-k2t

(A.17)

Since the trapped state is vacant at time zero and must be populated by the intrinsic state, with a rate constant kt, eq A.17 should be rearranged and expressed as

Ifluorexp(t) ) (B1 + B2)e-k1t + B2(e-k2t - e-k1t)

(A.18)

Combining (A.16) and (A.18) we obtain

|

B2 ke - k2 + Rkt Amplslow ) f fast exp B1 + B 2 k 1 - k2 Ampl

(A.19)

B2(k1 - k2) ke - k2 + Rkt ) ≈ Rkt B1 + B 2 k1 - k2

(A.20)

or

which follows from (A.8), assuming that kd is small. References and Notes (1) Martin, T. I.; Mayo, J. D.; Jennings, C. A.; Gardner, S.; Hsiao, C. K. Proceedings of IS&T’s EleVenth International Congress on AdVances

in Non-Impact Printing Technology; The Society for Imaging Science and Technology: Springfield, VA, 1995; Vol.1, 30. (2) Fujimaki, Y.; Takakro, Y.; Oda, H.; Yoshioka, T.; Homma, T.; Moriguchi, H.; Watanabe, K.; Konishita, A.; Hirose, A.; Itami, A.; Ikeuchi, S. J. Imaging Sci., Technol. 1991, 17, 202. (3) Daimon, K.; Nukada, K.; Sakagushi, Y.; Igarashi, R. J. Imaging Sci., Technol. 1996, 40, 249. (4) Loutfy, R. O. Can J. Chem. 1981, 59, 549. (5) Sharp, J. H.; Lardon, M. J. Phys. Chem. 1968, 72, 3230. (6) Bullot, J.; Cordier P.; Gauthier M. J. Chem. Phys. 1998, 69, 1374. (7) Comizzoli, R. M. Photochem. Photobiol. 1972, 15, 399. (8) Yokoyama, M.; Endo, Y.; Mikawa H. J. Lumin. 1976, 12/13, 865. (9) Popovic, Z. D.; Menzel, E. R. J. Chem. Phys. 1979, 71, 5090. (10) Popovic, Z. D. J. Chem. Phys. 1983, 78, 1552. (11) Popovic, Z. D. Chem. Phys. 1984, 86, 311. (12) Popovic, Z. D.; Loutfy, R. O.; Hor, A. Can. J. Chem. 1985, 63, 134. (13) Yasunaga, H.; Kasai, K.; Takeya, K. J. Phys. Soc. Jpn. 1979, 46, 839. (14) Mizuguchi, J. Jpn. J. Appl. Phys. 1982, 21, 822. (15) Loutfy, R. O.; Menzel, E. R. J. Am. Chem. Soc. 1980, 102, 4967. (16) Liptay, W. Angew. Chem., Int. Ed. Engl. 1969, 8, 177. (17) Popovic, Z. D.; Hor, A.; Loutfy, R. O. Chem. Phys. 1988, 127, 451. (18) Umeda, M.; Shimada, T., Aruga, T.; Niimi, T.; Sasaki, M. J. Phys. Chem. 1993, 97, 8531. (19) Popovic, Z. D.; Loutfy, R. O.; Hor, A.; Jackson, W. B.; Street, R. A. Proc. SPIE 1987, 743, 29. (20) Popovic, Z. D.; Khan, M. I.; Atherton, S. J.; Hor, A. M.; Goodman, J. L. J. Phys. Chem. B 1998, 102, 657. (21) Popovic, Z. P.; Hor, A. M. Proceedings of IS&T’s Tenth International Congress on AdVances in Non-Impact Printing Technology; The Society for Imaging Science and Technology: Springfield, VA, 1994; Vol. 1, 236. (22) Esteghamatian, M.; Popovic, Z. D.; Xu, G. J. Phys. Chem. 1996, 100, 13 716. (23) Yamasaki, K.; Okada, O.; Oka, K.; Kotani, M.; Yamada, H. J. Phys. Chem. B 1997, 101, 13.