# Diffusion Enhanced Upconversion in Organic Systems

Authors: A. Monguzzi; R. Tubino; F. Meinardi
Journal: International Journal of Photoenergy
 (2008)

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## Abstract

The upconverted fluorescence generation in a solution of multicomponent organic systems has been
studied as a function of the temperature to investigate the role of resonant energy transfer processes and of the molecular diffusion on the overall emission yield. The strong blue emission observed exciting the samples at 532 nm derives from a bimolecular triplet-triplet annihilation between 9,10 diphenylanthracene molecules, which produces singlet excited states from which the higher energy emission takes place. Diphenylanthracene excited triplet states are populated by energy transfer from a phosphorescent donor (Pt(II)octaethylporphyrin) which acts as excitation light harvesting.
At low temperature, the experimental data on the efficiency of the transfer have been interpreted in the frame of a Dexter energy transfer in the Perrin approximation. At room temperature, the fast
diffusion of the molecules has been found to be the main factor which affects the energy transfer rates and the overall photon upconversion efficiency.


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## Body

## 1. Introduction

The well-known upconversion processes such as
second-harmonic generation or two-photon absorption usually require very high
excitation power densities [1], typically of the order of MW/cm2, being effective only by using laser sources. Recently,
a novel approach has been proposed based on the
exciton triplet-triplet annihilation (TTA) between organic molecules, which
gives rise to an upconverted fluorescence
indirectly excited via energy transfer (ET) from a second molecular species
acting as a light harvesting [2–7]. In such a way, the requested power density
to have upconverted photons is reduced to the level of the solar emission (as
low as ≈0.1W/cm2) [5].
Obviously, this makes these processes suitable for applications in the field of
organic photovoltaics [8],
which requires for methods for the conversion of the low energy tail of the
solar spectrum.In these multicomponent systems, the upconverted light
is the result of several intermediate photophysical processes: (i) absorption
of the excitation light by a phosphorescent donor(D) molecule producing triplet excited states;
(ii) energy transfer processes towards metastable triplet state of an acceptor
molecule (A); (iii) triplet-triplet annihilation giving
rise to high-energy singlet excited states of the second species, from which
the upconverted fluorescence takes place. The donor must exhibit large
absorption cross-section, while the acceptor must have as long as possible long
lived triplet states suitable to collect the excitation from the donor
[9] by ET and to generate singlet excited state via TTA. Hybrid
materials like organometallic compounds [3, 10]
are usually employed as donors, since the presence of heavy atoms strongly
enhances their ISC rate [11], thus giving a high
population of excited triplet states. Conjugated molecules like polyacenes are
reported to work well [12–14] as
acceptors, due to the extremely low oscillator strength of their T*‐S0 electronic transitions. The key passages which
can limit the overall process efficiency are the steps involving the ET and the
TTA, which can be sketched as (1)D3*+A→D+A3*,A3*+A3*→A+A1*, where the subscripts identify the singlet (1) and
triplet (3) states.The results presented in this paper focused our
attention on the ET step, in order to understand its role in the
upconversion-induced delayed fluorescence of a model multicomponent systems. To
this goal, we prepared solutions at a different acceptor concentration, which
has been considered as a simple quencher of the red emission of the donor.
Measurements of the ET efficiency on solutions at different temperatures
allowed us to evaluate quantitatively the contribution of the molecular
diffusion on the overall efficiency of the process.


## 2. Experimental

CW photoluminescence (PL) measurements have been carried out by exciting the
samples using a Coherent Verdi Nd:YAG laser at the wavelength of 532 nm with a
power density of0.3W/cm2. The emission from the solutions has been detected by a nitrogen
cooled CCD (Spex 2000) coupled to a monochromator (Triax 190 from J-Horiba)
with a bandpass of 0.5 nm. All the measurements have been recorded with the
sample inside a bath cryostat in helium atmosphere at room temperature (RT) and
77 K.PtOEP (Pt(II)octaethylporphyrin) and DPA (9,10
diphenylanthracene), both purchased from Aldrich and used as-is, have been
selected as the donor and acceptor moieties, respectively. Their molecular
structures are reported in Figure1. Mixed solutions have been prepared in
1,1,1-Trichloroethane with a fixed concentration of PtOEP (1.4×10−4M) while the concentration of DPA has been
varied from 10−5 to 4×10−2M. Solutions have been carefully deoxygenated
before the measurements by bubbling dry helium for 1 hour [15, 16]. After the deoxygenation, the measured
lifetime of the PtEOP emission in absence of the DPA is 27 microseconds which
corresponds to a decay rate (K0) of 3.7×104Hz.Molecular structures of (a) Pt(II)octaethylporphyrin
and (b) 9,10 diphenylanthracene.
(a)(b)Time resolved PL measurements, carried out to control
the effects of the deoxygenation, have been performed with the same
monochromator but using a pulsed laser at 355 nm for the excitation
(Laser-Export Co. LCS-DTL-374QT), and, for the detection, a photomultiplier
connected to a board for time correlated photon counting measurement (ORTEC
9353 100-ps Time Digitizer/MCS). The overall time resolution was better than
100 nanoseconds.


## 3. Results and Discussion

Considering
that the ET occurs betweenD3* and A3* triplet states, whose transition to the ground
state is weakly allowed or forbidden at all,
therefore, we expect that only Dexter ET via exchange interaction can take
place [17–19].In such a case, the transfer rate(kET) between a donor-acceptor pair at a distance R can be written as [18] (2)kET(R)=2πℏZ2∫FD(E)GA(E)dE, where FD(E) and GA(E) are the normalized donor emission and acceptor
absorption spectra, respectively. The integral of the products of these two
functions is the mathematical expression of the resonance
involved levels as required by the energy
conservation principle. Z is the exchange integral which can be
expressed by his asymptotic form (3)Z2=K2exp(−2RL), where K is a constant with the dimension of an energy,
and L is the so-called effective Bohr radius
measuring the spatial extent of the donor and acceptor wavefunctions. In
particular, (3) shows the dependence of the ET rate on the distance between
donor and acceptor, as a consequence of the molecular-wavefunctions exponential
decay in the space.For processes controlled by exchange interactions,FD(E) and GA(E) spectra are only hardly detectable as they
involve forbidden transitions. Moreover, the shape of the molecular
wavefunctions should be known for an exact evaluation of the parameter Z.
For these reasons, many models have been developed to simplify the original
Dexter equations [20–22]. The Perrin model [22] follows from the
observation that (3) gives at short distances, when R≪L,
an extremely fast ET rate, while the ET rate
becomes negligible at R>L.
The Perrin model assumes for each isolated donor-acceptor pair the existence of
a sort of active sphere of radius R0:
if the donor acceptor distance is shorter than R0,
the energy is totally transferred from the donor to the acceptor, while there
is no transfer for larger distances. In this frame, the kET(R) assumes the simple form (4)kET(R)={0forR>R0,∞forR<R0. In (4), R0 is defined as the effective radius, in
the sense that at this distance the ET rate equals the rate of the spontaneous
decay of the donor in absence of acceptors.R0 can be obtained experimentally from
measurements of PL relative quantum yield (QY) of the donor, by defining the QY
as the ratio between the donor PL intensity ϵ in the presence of a defined acceptor
concentration (CA), and that without it (ϵ0). By using (4), this relative QY can be
written as [19] (5)ϵϵ0=exp(−CAC0).C0 is a constant related to the Dexter parameters
(L,K) called critical transfer concentration.
Using units of moles per liter for C0,
the value of R0 in Ångstrom is equal to 7.346C0−1/3.In Figure2, PL spectra of PtEOP/DPA mixed solution
are reported as a function of the DPA content. At low DPA concentration, the
typical red phosphorescence (PH) of the PtOEP at 635 nm [16, 23] is clearly detected (Figure 2(b)). As
the acceptor concentration increases, the intensity of the peak at 635 nm is
reduced and a strong enhancement of the DPA emission band at 435 nm (FL) is
observed, as in a typical donor-acceptor system (Figure 2(a)). The only
difference in this case is that the emission of the acceptor occurs at an
energy higher than that of the emission of the donor because of the
upconversion process.(a) DPA FL spectrum and (b) PtEOP PH intensity at different DPA concentration
in PtOEP(1.4×10−4M)/1,1,1-Trichloroethane solution. Spectra
have been collected at RT exciting the solution at 532 nm.
(a)(b)To verify whether the ET process can be fully
described as a Dexter mechanism and to check if the Perrin approximation can be
employed for these systems, we measured the relative PL efficiency of the PtEOP
used in (5) as a function of the DPA concentration. In Figure 3 (blue circles),
the measurements performed on frozen solution are reported, where the molecules
diffusion is completely prevented. These data can be perfectly fitted using (5)
and are therefore consistent with an exchange driven transfer with an effective
radius R0 of 26.5Å.
A second set of measurements is carried out at RT
(Figure 3, red circles). Indeed the full process (Dexter ET plus diffusion) can
be formally described as a donor quenching due to direct collision with the
acceptor moiety [24] using the Dexter radius as the contact
distance. In such a case, the ET rate in steady state condition
is (6)KET=4πDR0CA, where D is the overall diffusion
coefficient defined as the sum of the diffusion
coefficients of donors (D) and acceptors (A). Diffusion coefficients are evaluated from
the viscosity of the solvent (η=1.2 cP at RT [25]) and from
the effective molecular radii (Rm) estimated accordingly to Bondi [26]. In such a way,
the Einstein relation (D=3kT/6πηRm) gives an overall diffusion coefficient
of 1.8×10−5cm2/s.Figure 3
Relative PL
quantum yields of the PtOEP PL as a function of the DPA concentration at 77 K
(blue circles) and 300 K (red circles). The dashed line has been calculated by
combining the contribution of the molecular diffusion and the ET process as a
contact interaction. The continuous line is the fit of the data collected at 77 K considering a pure Dexter ET (Dexter radius26.5Å).The relative PL quantum efficiency of PtEOP, taking in
to account the diffusion contribution, is then calculated as the ratio between
the PtEOP decay rates with and without the donor[ϵ/ϵ0=K0/(K0+KET)] and has been
shown in Figure 3 (dashed line). This curve matches well the corresponding
experimental data. It must be pointed out that in this comparison no adjustable
parameters (K0,D,R0) are involved. By considering that for DPA
concentration values higher than 1×10−2MKET≫K0,
from (6) we can deduce that in the absence of competitive de-excitation
channels, PtOEP PH intensity is inversely proportional to the concentration of
acceptor CA.
In Figure 4(a), the values of PH intensity varying CA of three orders of
magnitude are reported, and by using a
semilogarithmic scale to plot concentrations, we expect a linear decrease of PH
intensity. The data reported in Figure 4(a) are indeed strictly consistent with
the prevision of collision ET/diffusion model proposed by (6) (dashed line).
For TTA is a second-order process, the blue light
intensity should be proportional to the square of acceptor triplet excited
states population [27]. In such a way by considering that the
number of excited acceptors is proportional to CA (see (6)), then also upconverted light
intensity should be proportional to the square of acceptor concentration. In
Figure 4(b), the FL intensity versus the DPA concentration (by using
logarithmic scale) has been plotted at fixed concentration of donor. The
experimental data fit well with a linear function with an angular coefficient m=1.9 which is in very good agreement with the
considerations done on the TTA process (the quadratic dependency gives an exact
value of 2 for the slope m).(a) PtOEP PH
intensity at different acceptor concentration. Dashed line is the fit with a
linear function. (b) Corresponding DPA FL intensity. Dashed line is the fit
with a linear function withm=1.9.
(a)(b)Obtained results indicate that in the investigated
multicomponent system, ET is the main mechanism to populate DPA triplets, and
that there are not competitive alternative channels through which donor centers
can loss the absorbed energy. At RT it is clear
that the molecular diffusion plays a key role in enhancing the ET efficiency.
In fact, because of the involvement of long-living donor triplet states, the
diffusion lengths of excited molecules are the order of magnitudes larger than
the effective radiusR0 of the ET. In the case of PtOEP/DPA solutions,
the overall diffusion length goes up to 210 nm with a 10−3 DPA concentration. Only for really large acceptor concentrations (≫10−2M), the effect of migration can be considered
negligible and only the direct donor-acceptor ET is effective. This implies
that in order to enhance the efficiency of the ET of these
systems in solution, it is necessary to improve the
molecular mobility by using solvents with low viscosity and/or small molecular
species.


## 4. Conclusions

The effects of
the molecular diffusion on the triplet-triplet exciton ET between PtEOP and
DPA, an organic system model for upconversion-induced delayed fluorescence,
have been studied as a function of the temperature. At low T, the results can
be well described as a Dexter ET by using the Perrin approximation with an
effective radius of26.5Å.
On the contrary, at RT the molecular diffusion is the main phenomenon which
affects the ET efficiency, which is very high also for low acceptor
concentrations as a consequence of overall molecular diffusion lengths. As
shown, RT experimental data can be strictly interpreted by using an
ET/diffusion combined model. These findings clearly explain why high
upconversion efficiencies are usually reported for systems in solution
[3, 6], while the performance of the corresponding films, where
donors and and acceptors moieties are not able to move, is much lower [2, 7].



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*Source: 684196-2008-05-25.xml*