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Photochemical Upconversion: The Primacy of Kinetics Timothy W Schmidt, and Felix N. Castellano J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/jz501799m • Publication Date (Web): 30 Oct 2014 Downloaded from http://pubs.acs.org on November 8, 2014

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The Journal of Physical Chemistry Letters

Photochemical Upconversion: The Primacy of Kinetics Timothy W. Schmidt∗,† and Felix N. Castellano∗,‡ School of Chemistry, UNSW Sydney, NSW 2052, Australia, and Department of Chemistry, North Carolina State University, Raleigh, NC 27695, USA

E-mail: [email protected]; [email protected] Phone: +61 439 386 109; +1 (919) 515-3021. Fax: +1 (919) 515-8909

∗ † ‡

To whom correspondence should be addressed School of Chemistry, UNSW Sydney, NSW 2052, Australia Department of Chemistry, North Carolina State University, Raleigh, NC 27695, USA

1

ACS Paragon Plus Environment


Abstract Incoherent photochemical upconversion is a process by which low energy light can be converted into a higher energy form with promising applications in solar energy conversion and storage, biological imaging, and photochemical drug activation. Despite intensive research in recent years, there remains an under-appreciation of the chemical kinetics that controls the eciency of the upconversion process. Here we provide a brief overview of research into photochemical upconversion and provide a tutorial to guide the design of ecient upconversion compositions. We further provide our perspective on where this area of research is heading, and how very ecient systems will be developed.

TOC Graphic (in nal size). 100 90

d[ 3A* ] = kφ [ 1S ]− k1A [ 3A* ]− k2AA [ 3A* ]2 dt

80 70 60

time /µs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50 40 30 20 10

525

Keywords:

550

575

600

625

wavelength /nm

650

675

triplet-triplet annihilation, third generation photovoltaics, triplet states

2


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Photochemical upconversion (PUC), also termed sensitized triplet-triplet annihilation (TTA) or sensitized triplet fusion, represents a rational methodology for the capture of low energy photons and their subsequent conversion into higher energy light through a sequence of energy transfer steps.

It has the advantage over second harmonic generation in that

incoherent, low intensity light may be used, and the advantage over upconversion in rareearth materials due to the almost limitless spectral exibility oered by molecular materials. Although the phenomenon was rst illustrated in the early 1960s,

1,2

it was not until the

21st century when it became apparent that non-coherent wavelength shifting posed a viable strategy to improve the energy conversion eciency of solar cells.

36

This realization has

led to an explosion of research activity in this area and several reviews highlighting major progress in the eld have appeared over the past few years.

711

The coupling of late transi-

tion metal-containing sensitizers with aromatic hydrocarbon acceptor/annihilators with near unity uorescence quantum yields, originally described by the Baluschev lano

15,16

1214

groups, set the stage for many of the advances that soon followed.

and CastelSome of the

more notable contributions include:

•

the observation of photochemical upconversion using non-coherent photons in solution and in soft polymer matrices;

•

6,1720

demonstrations of linear incident power dependence for the upconversion process using both coherent and non-coherent light sources;

18,21,22

23

•

expansion of the acceptor/annihilator genre beyond aromatic hydrocarbons;

•

the development of near-IR-to-visible light conversion compositions;

•

illustrations of upconversion quantum eciencies greatly exceeding the putative TTA spin statistical limit of 11.1%;

•

2426

7,21,27

rigorous kinetic analysis of the associated delayed uorescence decay process enabling maximum eciencies for a given donor-acceptor/annihilator pair to be extracted;

3


27,28


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1 3 3 1

S*

S* S

1

A

3 1

1

A*

A* A

A*

1 3

S

S* 1

S*

Figure 1: Top: photograph of red to blue upconversion in a cuvette. Bottom: The various 1 energy transfer steps involved in PUC: Sensitizer molecules ( S ) absorb low energy photons, 1 ∗ to be excited to their rst excited singlet state ( S ), which is followed by rapid intersystem 3 ∗ crossing to the lowest triplet ( S ). Triplet energy transfer places the absorbed energy with 1 an annihilator molecule, which is thus excited from its ground state ( A) to its lowest triplet 3 ∗ ( A ). Triplet-triplet annihilation between annihilator triplets places one in its excited singlet 1 ∗ ( A ) which then uoresces at a shorter wavelength than the absorbed light.

•

photochemical upconversion to perform actual visible-light sensitized cycloaddition photochemistry;

•

numerous recent examples of upconversion-integrated semiconductor devices including photovoltaics, tions;

•

29

3034

photoelectrochemical cells,

19,35

and water detoxication composi-

36

and upconversion in biocompatible media such as micelles and microemulsions.

37,38

As research in this area continues to expand in scope, even into the realm of biological imaging,

39

it is important to emphasize those factors crucial to proper design and charac-

terization of established and newly conceived upconversion compositions. It is the intention

4


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of this Perspective to illustrate how reaction kinetics ultimately control most facets of photochemical upconversion overall performance.

40

and that annihilation spin statistics does not necessarily limit

7,21,27

In light-producing photochemical upconversion reactions, sensitizer molecules are excited by incoming photons (Eq. 1), and undergo rapid intersystem crossing to their lowest excited triplet state (Eq.

2).

Excited triplet sensitizers (

3

S ∗)

undergo bimolecular triplet-triplet

energy transfer with an energetically appropriate acceptor/annihilator ( producing the triplet excited state of the acceptor ( decay rate of

3

A∗ ,

3

A∗ ),

Eq.

3.

1

A)

chromophore,

As a result of the slow

many additional sensitization reactions occur during its lifetime, yielding

a situation where the probability becomes large for two

3

A∗

molecules to engage in their own

energy transfer reaction, namely TTA, Eq. 4. This latter interaction ultimately yields singlet uorescence characteristic of the acceptor/annihilator molecule, Eq. 5. These processes are illustrated in Fig. 1.

S + hν1 → 1 S ∗

(1)

S ∗ → 3S ∗

(2)

S ∗ + 1 A → 1 S + 3 A∗

(3)

A∗ + 3 A∗ → 1 A∗ + 1 A

(4)

A∗ → 1 A + hν2

(5)

1

absorption :

1

ISC : 3

TET : 3

TTA :

1

emission :

Additionally, a number of deleterious processes occur,

3

triplet quenching by O2 :

where

X ∗ → 1X

(6)

X ∗ + 3 O2 → 1 X + 1 O2 ,

(7)

3

natural triplet decay :

X = A, E .

5



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Page 6 of 37

It is the simplicity of the reaction sequence that makes this process so appealing, but there are numerous kinetic considerations that must be taken into account if one desires to extract the maximal quantum eciency from a given

S/A

composition.

In the following,

each step is scrutinized in turn and recommendations are made as to how to ensure that each step is designed to be ecient. Undesirable processes are also discussed, and ways to mitigate them are suggested.

Finally, we propose a kinetic mechanism for the synergistic

action of two annihilator species.

Photoexcitation The rate of excitation of the sensitizer species ultimately determines, along with other factors, the concentration of triplet annihilator, which, in turn, determines the eciency of PUC. As such, it should be as high as possible, but without introducing untimely photodegradation.

11

The rate is given by

Z kφ = where

F

is in units of (photons) cm

dλF (λ)σ(λ),

−2 −1 −1 s nm , and

(8)

σ

2 is the absorption cross section in cm .

kφ = Φ(λ)σ(λ),

(9)

For monochromatic excitation,

where

Φ is in (photons) cm−2 s−1 .

The cross section is related to the chemists' molar decadic

extinction coecient,

σ= As such, a molar extinction coecient of of about

4 × 10−16 cm2 ,

2 or 4 Å . If

are excited at a rate of 5 s

−1

1000 ln(10) . NA

105 M−1 cm−1

F (λ)

(10)

is equal to an absorption cross section

is the AM1.5G solar spectrum, typical sensitizers

the sensitizer shown in Fig. 2 is excited at a rate of 7 s

−1

. If a

2 1 mW laser pointer at 650 nm is shone on a sample with a spot size of 1 mm , the excitation rate is 130 s

−1

2 if the cross section is 4 Å .

6


Page 7 of 37

If the incident light is the unconcentrated solar spectrum, the excitation rate can be increased by local geometric concentration, using a back-reector exhibiting spherical indentations.

33

It is calculated that such a device could deliver nine times the upconverted light as

compared to one without a back-reector at all. It is also possible that plasmonic near-eld eects could be harnessed to bring about an increase in and is a topic of current research.

kφ .

This is certainly a challenge,

4143

There has been no rigorous report of photodegradation in PUC systems, though it is widely acknowledged as an issue, and measures have been taken to mitigate against the deleterious eects of oxygen.

44,45

The Schmidt group have performed preliminary experiments

which demonstrate that photodegradation in the absence of oxygen occurs in proportion to the square of the triplet concentration, with a rate constant which additionally depends on the level of illumination.

11

3

σ (10−16 cm2)

4 2

2

1

0 550

600

650

700

750

wavelength (nm)

800

Figure 2:

Absorption cross section of the PdPQ 4 NA porphyrin −1 spectrum. Integrating the product yields kφ = 7 s .

7


F (ph. 1014 cm−2 s−1 nm−1)

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0 850 30

and the AM1.5G solar


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Page 8 of 37

Intersystem Crossing By incorporation of heavy atoms into the structure of the sensitizer, its triplet yield can be driven to near unity.

The palladium tetrakisquinoxalino porphyrin sensitizer (PQ 4 Pd)

favoured by the Schmidt group, for instance, has a singlet-state lifetime of 12 ps.

21,27

When

compared to the corresponding zinc porphyrin, which uoresces with a ns lifetime, one can estimate a triplet yield near unity. Many such compounds exist, and have been incorporated into PUC systems. This step is not considered to be troublesome. A good sensitizer should not lose too much energy at this step. A triplet state which lies

just under the excited singlet is ideal, since then the instersystem crossing will be enhanced due to favorable Franck-Condon factors. Further, while energy losses are necessary to drive upconversion, each loss reduces the nal achievable upconversion margin by double. Ideally, E-type delayed uorescence should be prevented. of 10 ns for the sensitizer 100 µs.

S1

state, an energy drop to

As such, we recommend

porphyrin exhibits

∆EST > 0.2 eV

∆EST ∼ 0.4 eV,

T1

47

46

For a typical radiative lifetime

of 9.2 kB T would increase this to

for ecient upconversion.

The PQ 4 Pd

which is perhaps excessive.

The Oxygen Problem The triplets, once formed, need to be transferred eectively into the acceptor manifold. Essentially, this means ensuring that the quenching rate far exceeds the decay rate of the sensitizer triplets by other means. Oxygen must be absent. Ground state dioxygen reacts with molecular triplet states with energy greater than 0.98 eV by a Dexter energy transfer process whereby the molecular triplet is quenched and the oxygen molecule is raised from the

3

Σ− g

to its

1

∆g

state.

intersystem crossing from the triplet back to the ground state.

48

4951

Oxygen can also enhance This is deleterious for two

reasons: A triplet state is lost, and therefore upconversion potential is also lost; and singlet oxygen is extremely reactive.

It is known to form endoperoxides with typical emitters

8


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employed in PUC such as rubrene and bisphenylethynylanthracene, the extended

52

and will also react with

π -conjugated naphthalo- and anthra- moieties of deep red absorbing sensitizers.

The quenching of triplet states by molecular oxygen proceeds at a rate usually exceeding

109 M−1 s−1

in a range of solvents.

ppm levels.

48

As such, its concentration should be reduced to below

Nevertheless, PUC systems have been demonstrated in air,

53

and have even

utilized singlet oxygen as an energy transmitter for emitters with triplet energies below 0.98 eV.

26

emerging.

Several strategies for long-term protection against the eects of oxygen are also

20 45

Triplet Energy Transfer If we assume that the decay of triplets only follows rst order kinetics (but see below), then the dynamic triplet energy transfer eciency systematically varies with the concentration of the acceptor/annihilator quencher and the associated Stern-Volmer plot contains the desired information. Inserting the appropriate data points from the Stern-Volmer plot into Eq. 11 yields the energy transfer quenching eciency ( ΦT ET ) at the specic concentration of

A

selected.

ΦT ET Here,

Iq

and

τq

τq Iq = 1− = 1− I0 τ0

(11)

represent the photoluminescence intensity and phosphorescence lifetime of

the sensitizer at the specic concentration of recorded in the absence of

A.

Ideally,

ΦT ET

A

chosen while

I0

and

τ0

are the same values

will approach 1.0 under strong quenching con-

ditions, ensuring complete conversion of the light absorbing population into

3

A∗

molecules,

thereby best positioning the composition for TTA (see Fig. 3). Sensitizers with long triplet lifetimes,

τ0 ,

are thus most convenient.

Quenching of sensitizer triplet states in solution is due to a bimolecular reaction, where energy transfer takes place by the Dexter mechanism,

54

the mechanistic details of which

have been explained in the PUC context by Monguzzi and co-workers.

9


55

The second order


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Page 10 of 37

rate constant is absolutely limited by the rate of collisions, the so-called diusion limit,

kd .

The diusion limit may be estimated by

kd =

where

R

is the gas constant and

η

8RT 3η

(12)

is the solvent viscosity.

In the above equation, one should be careful to match the units of the rate in the usual M

−1 −1 s . For a viscosity of 1 mPa s,

R and η to bring about

kd = 7×109 M−1 s−1 .

rates are more than an order of magnitude less than this. Where

Often quenching

kq = 1 × 109 M−1 s−1 ,

quencher concentration of 0.1 mM will compete evenly with a sensitizer lifetime of 10

µs.

a

But,

eective transfer will require out-competing the triplet decay by two orders of magnitude, and thus 10 mM would be required for ecient TET in this example. Sensitizers with lifetimes of a

µs

sensitizers with tens to hundreds of

or less will be very hard to couple to acceptors, while

µs lifetimes may be used with ease.

in Fig. 3 has a phosphorescence lifetime of

> 600 µs.

The sensitizer shown

Typical acceptor concentrations reach

10 mM in most applications, but the above analysis clearly does not hold for solid state acceptor blends, or conjugated polymer acceptors.

Triplet-Triplet Annihilation Subsequent to the conversion of the excited sensitizer population to acceptor/annihilator triplets, the underlying kinetics determines the fate of their excited-state decay. The sensitized triplets decay with parallel rst and second-order kinetics, Eq. 13, where the rstorder term also includes the important contribution from

pseudo -rst-order quenching (by

dioxygen and other species) in addition to the usual rst-order triplet state decay, and the second-order term represents the TTA process, a proportion of which generates the desired upconverted uorescence. In the absence of hetero-TTA events between triplet sensitizers

10


Page 11 of 37

60

1.0

50

0.8

40

I0/Iq

0.6 30 0.4

20

0.2

10 0

0.0

0.1

0.2

0.3

0.4

0.5

ΦTET = 1–Iq/I0

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0.0

[DPA]/mM Figure 3: Stern Volmer plot and triplet energy transfer eciency for quenching of PdTPP by DPA in tetralin. In this case, 0.5 mM suces to bring about ecient TET. The Stern 5 −1 Volmer constant is 1.116(5) × 10 M , and the unquenched lifetime is 662 µs, giving kT ET = 1.69 × 108 M−1 s−1 .

and emitters,

d[3 A∗ ] = kφ [1 S] − k1A [3 A∗ ] − k2AA [3 A∗ ]2 . dt The combination of two triplet states projects onto tions (3

× 3).

(13)

nine possible product spin eigenfunc-

These are ve quintet states, three triplet states, and one singlet. It is this

latter state which is the desirable outcome, since it can cross over into the state whereby one acceptor is placed into the emissive excited singlet, while the other is quenched to the ground state. But, triplet or quintet character in the product state will potentially quench acceptor triplets. Happily, the molecular quintet states are normally too high to be accessed with the energy of two triplets, but the

T2

state of many hydrocarbons lurks in the vicinity of

can be problematic. In Eq. 14, we break the each spin channel.

The prefactor

nS,T,Q

k2

S1 , and

rate constant down into contributions from

denotes how many triplets are quenched through

that channel. For the singlet channel, this is 2, but for the triplet and quintet channels (if open), this is expected to be only 1, as one of the molecules will eventually return to the

11


T1


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Page 12 of 37

state.

k2 = nS kT T A−S + nT kT T A−T + nQ kT T A−Q The contributions to

(14)

k2 require a discussion of the details of molecular triplet states.

Isolated

triplet-state molecules in solution, crystals, or solid matrices, can be considered to exist in three avors the eigenstates of the spin-spin Hamiltonian at zero eld, denoted

|zi. the

These are to the high-eld eigenstates what a chemist's p-orbitals ( px ,

l = 1 ml -eigenfunctions (if B

is held along the molecular

z

py

|xi, |yi and

and

pz )

are to

axis). When two such triplets

meet, there are thus nine pair states formed. These are not themselves spin eigenstates, but rather can be combined in various ways to bring about the one singlet, three triplet and ve quintet pair states. The singlet state is given by

|Si =

|xxi + |yyi + |zzi √ , 3

(15)

and is not a stationary state, as the components are of energies diering by some GHz (due to zero-eld splitting). reverse of TTA, the

|Si

When a singlet state undergoes ssion into two triplets, the

state is prepared impulsively, and the dephasing and rephasing

of the components is observed as quantum beats in the delayed uorescence.

56

However,

where triplets are prepared individually, the pair states will be a product of the individual eigenstates. For a pair of unaligned molecules in solution, there are two axis systems, and the pair states are of the form

|αβ 0 i,

where

α

and

β

span the

of the projection of the pair state onto the state

2

S = |hS|αβ 0 i| =

where

θαβ 0

|Si

x, y

and

z

molecular axes. The square

gives the state's singlet character,

1 cos2 θαβ 0 , 3

(16)

is the angle between the axes dening the spin states of the individual molecules.

The maximum singlet character of any collision is thus

S = 1/3.

12


Page 13 of 37

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kd .

Since

two triplets are removed for each successful PUC event, the inequality that holds is

k2
0.5.

This is obtained at the illumination intensity dened by Monguzzi and co-workers

as the threshold light intensity to achieve ecient PUC, and marks the transition regime between a quadratic and linear response of upconverted light to input light intensity.

18,60,61

To calculate the triplet concentration under steady-state conditions, without making the above assumptions in Eq. 26, one solves the quadratic equation

kφ [1 S] = k1A [3 A∗ ] + k2AA [3 A∗ ]2 ,

(31)

which gives

[3 A∗ ] =

−k1A

q 2 + k1A + 4k2AA kφ [S] 2k2AA

.

(32)

With the parameters:

k1A = 104 s−1 , k2AA = 109 M−1 s−1 , kφ = 10s−1 one arrives at

[3 A∗ ] = 10−7 M,

and,

[S] = 10−4

M,

which is far below the threshold value of

10−5 M

as outlined

above. From the form of Eq. 32, one sees that maximizing the concentration of sensitizer is desirable. In a suitable nanostructure, sensitizers may be concentrated to 0.1 M eective concentration. Sensitizers can be bound to nanoparticles with surface densities of

∼ 1 nm−2 .

The pore

volume fraction is 0.25952 for close-packed spheres, and since the surface area to volume ratio of a sphere is

3/r,

0.856/nm3 , or > 1 M. 62

the eective concentration of sensitizer on

r = 10 nm

particles is

This calculations shows that high concentrations of sensitizer can be

achieved in the pore-space of a nanostructured material. If this is realized, then exceed the desirable threshold. Concentration of light can also increase ecient PUC a viable outcome.

19


kφ ,

[3 A∗ ] should

making highly


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The term

ηc

Page 20 of 37

is a measure of the ecacy of the second order decay events. If it is assumed

that the singlet TTA channel always yields (potentially) emissive singlet states, then

ηc

may

be approximated

ηc =

2kT T A−S 2kT T A−S + kT T A−T

where we ignore the contribution from

kT T A−Q .

(33)

The quintet state is not usually accessible

on energetic grounds, and the fate of the quintet state generated is unknown. The prefactor of 2 before

kT T A−S

is due to there being two triplets annihilated through the singlet channel,

while it is assumed that the triplet channel will annihilate only one. Notwithstanding spinstatistical arguments that suggest

kT T A−T = 3kT T A−S ,

which would imply

ηc = 0.4

if the

rate constants for the two spin-channels were equal, values comfortably exceeding this have been reported. The Schmidt group (then at Sydney) established that rubrene has which they rationalized in terms of the triplet channel, assumed to access the

T2

endothermic. This could be tested by determining the eect of temperature on the triplet channel can be shut down by choosing molecules with high-lying

ηc

T2

ηc ≈ 0.6,

state, being

ηc .

If indeed

states, then

may approach unity and there appears to be no fundamental limitation to prevent

ΦU C

approaching 0.5. Of course, achieving this under technologically relevant conditions is the Grand Challenge of PUC.

The State-of-the-Art Eciencies The literature contains many reports of upconversion eciencies. Gray et al.

63

have neatly

summarized many of these reports in their Perspective. Of these, the highest reported is from the Castellano group,

35

who reported

ΦU C = 0.18, on the scale of 0−0.5 for the PdOEP/DPA

couple. This was achieved in the strong annihilation limit, at an irradiance of 350 mW cm

2

at 514 nm. A similar couple, PdTTP/DPA, was recently investigated by the Schmidt group using a home-built biased action spectrometer. a maximum of

ΦU C = 0.22 (ηc ∼ 0.45),

64

Extrapolation to high irradiance predicted

in good agreement with the value actually achieved

20


Page 21 of 37

by Castellano for DPA. These measurements are also in agreement with Monguzzi et al., who found a limit of state.

ΦU C = 0.22

for PtOEP/DPA in solution, and

ΦU C = 0.17

Similar limits have been observed for rubrene in pulsed experiments

should approach 0.30 under intense cw excitation ( ηc in-principle, limit on

ηc

and as such it is likely that

∼ 0.6). ΦU C

19

in the solid

21,27

but

ΦU C

As stated above, there is no,

values approaching 0.5 will be

reported in the near future. There remains a paucity of reports for eciencies under one-sun equivalent excitation. For a PdPQ 4 NA/rubrene composition in toluene, has estimated

Φ U C = 0.005

64

the Schmidt group

and for a PdTPP/DPA composition in tetralin

The viscosity of tetralin, being some 3.4 times that of toluene, suggests

65 Φ U C = 0.035.

Φ U C = 0.1

should

be achievable for a DPA composition.

1

3 3

1 1

S

A

T

A*

T*

S*

1

3

3

1

S*

A*

T*

1

1

S

T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

S*

1

S*

Figure 6: Photochemical upconversion with an energy transmitter.

Synergistic Dual Annihilator System It is optimal to discover annihilators which display rapid sensitizer quenching, long triplet lifetimes, rapid and ecient (high

ηc ) annihilation and a high uorescence yield.

However, some

of these attributes are found in some annihilators, with the complementary attributes found in others. For instance, rubrene (RUB) has a long triplet lifetime, a high

ηc ,

a high uores-

cence yield, but very slow bimolecular kinetics, whereas 2-chlorobisphenylethynylanthracene

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(2CBPEA) is a rapid annihilator, with a questionable

ηc .

Page 22 of 37

These can be combined to bring

about a PUC system which is more ecent than either system on its own. Such synergistic systems have been reported previously.

66,67

In the work of Turshatov and co-workers,

66

a

phenyl-perylene annihilator was found to harvest triplets eectively, but was a poor annihilator, while a BODIPY dye was found to be a poor triplet acceptor, but had a

S1

state

of a more appropriate energy. A covalently linked annihilator exhibiting the best characteristics of both was found to be better, but a mixture still outperformed either alone.

Cao

et al. also reported a synergistic dual-annihilator system, but with no satisfactory explanation of the synergy.

67

It has been suggested that hetero-TTA events are not subject to the

same spin-statistical considerations as homo-TTA events. However, consider triplet-energy quenching by triplet oxygen to bring about excited singlet oxygen. This can be considered a hetero-TTA event.

21

But, Porter and co-workers showed that the rate of quenching was

limited to 1/9 the rate of encounters (with no limit on yield), suggesting that spin-statistics plays a role in hetero-TTA. Here we present a kinetic model which accounts for the observed behaviour in a 2CBPEA/RUB dual annihilator system. The energy transfer chain is shown in Fig. 6. In the synergistic system, there is a sensitizer, a

transmitter, and an annihilator. The

transmitter is the primary quencher of sensitizer triplets, and the primary of donor of triplet energy to the annihilator. It may also perform as a PUC annihilator on its own, with UC rate

WUTC

η T ΦT = c F k2T T 2

kφ [1 S] k1T

2 .

(34)

Likewise, the annihilator acting on its own will generate upconverted light at a rate

WUAC

η A ΦA = c F k2AA 2

Now, consider the conditions where by slow kinetics of

A,

kφ [1 S] k1A

2 .

(35)

kTSTET [T ] kTSA ET [A],

which may be brought about

and a lower concentration. The triplet energy of

22


A is lower than T ,

so

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the dominant decay of

3

T∗

is by quenching by

1

1

S∗

(36)

S∗ →

3

S∗

(37)

S ∗ + T → S + 3T ∗

(38)

T ∗ + A → S + 3 A∗

(39)

3 3 3

A∗ + 3 T ∗ →

1

A∗ + T

(40)

3

T ∗ + 3T ∗ →

1

T∗ + T

(41)

A∗ + 3 A∗ →

1

A∗ + A

(42)

1

A∗ → A + hν2

(43)

1

T ∗ → T + hν3

(44)

3

f2 ,

The following sequence may be imagined:

S + hν1 → 1

Assuming low

A.

we may now write

kφ [1 S] . A kTT ET [A] + k1T

(45)

A kTT ET [A][3 T ∗ ] kφ [1 S] T A = ΦT ET . k1A k1A

(46)

[3 T ∗ ] =

and

[3 A∗ ] =

The rate of upconversion of the mixed system is now

WUTCA

ηcA ΦA ηcT A ΦA ηcT ΦTF T T 3 ∗ 2 F AA 3 ∗ 2 F TA 3 ∗ 3 ∗ = k2 [ A ] + k2 [ A ][ T ] + k2 [ T ] . 2 2 2

(47)

Let us examine the model system given by the parameters in Table 1. The annihilator, is slowly diusing but annihilates with high yield. The transmitter,

A,

T , has a low annihilation

eciency to populate the singlet state, but faster kinetics. Either triplet acceptor on their own would generate upconverted photons at a rate of

A/T

WU C ∼ 5 × 10−7 M s−1 .

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 37

Table 1: Parameters for a model synergistic dual annihilator system. parameter k1A k2AA ηcA ΦA F kTSA ET

value 104 s−1 108 M−1 s−1

[A] ηT A k2T A

variable

1 1 8 10 M−1 s−1

parameter k1T k2T T ηcT ΦTF kTSTET

value 104 s−1 109 M−1 s−1

[T ] kφ [1 S] A kTT ET

0.01 M −1 0.001 M s 109 M−1 s−1

1 8 10 M−1 s−1

0.1

9

10

1 −1 −1 M s

Now, assuming that the hetero-TTA events are ecient, and that these populate the state, then

WUTCA

will depend on the concentration of

A.

Where

1

A

∗

[A] is very large (> 10−2 M),

the concentration of transmitter triplets is so small that the system essentially behaves as a sensitizer-annihilator system, and

WUTCA = WUAC .

Likewise, where

[A]

is very small, the

triplets do not eectively transfer to the annihilator population and the system behaves as though the transmitter is the sole annihilator,

WUTCA = WUTC .

There exists an optimum,

where

ΦTT A ET ∼ 0.5.

Here, hetero-TTA events dominate. The rate of hetero-TTA is maximized

where

[3 A] = [3 T ].

If this is ecient and rapid, it will dominate the proceedings, and in the

present model an enhancement of 3-fold is obtained over systems with either the annihilator or transmitter alone.

The behaviour of the model synergistic dual annihilator system is

shown in Fig. 7. Indeed, what this shows is that the nal emitter need not diuse at all, and can be axed to a support structure such as a gel or nanoparticle.

The Future of Ecient PUC systems The grand challenge of PUC is to create a system which eciently upconverts a broad band of spectrum under one-sun conditions. Mixing several sensitizers, providing higher energy bands do not interfer with the UC light, seems to be the way to go. Indeed, this has been shown to broaden the spectral acceptance of the upconversion system.

68

Use of semiconductor

nanocrystals may seem an attractive option to funnel more energy into the PUC system, but

24


Page 25 of 37

TA

ΦTET = 0.5

10

[3X] (10-8 M)

8 6

T A

4 2 0

16 14 homo-A homo-T hetero-TA total

12

WUC (10-7 Ms-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10 8 6 4 2 0 -8

-7

-6

-5

-4

-3

-2

log10([A]/M) Figure 7: Behaviour of the model synergistic dual annihilator system as a function of [A]. TA The highest upconversion rate is found where ΦT ET ∼ 0.5 and the concentrations of triplets for the two annihilator species are equal. Parameters are given in Table 1.

25



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Page 26 of 37

since these do not exhibit band absorption, but rather step-function absorption, it would seem that they will unavoidably absorb upconverted light. A high concentration of sensitizers, and thus resulting triplets, is desired. To overcome solubility limits without aggregation, sensitizers should be attached to a support structure such as a nanoparticle.

If these can be embedded with plasmonic particles, then local

light concentration might be achieved.

Device-level engineering is also expected to play

a role: microstructured back-reectors can bring about local concentration and boost device upconversion yields.

33

It is generally unproblematic to quench the sensitizer triplet energy eciently in a solution-based system.

To achieve this in a solid or near-solid system requires proximity

of the annihilators to the sensitizers and/or residual diusion. It has been shown that rubbery polymers permit diusion,

10,17

but another way to ensure that the system is

locally a

liquid, while exhibiting bulk solid-like properties is to gelate a solvent. The Schmidt group will report on this in the near future.

65

Finally, providing as many photons are absorbed per unit volume as possible, and that these are harvested by annihilators, all that remains is for the actual TTA to proceed eciently. Several blue-emitting annihilators are known to exhibit fast diusion and high

ηc

values, with perylene and DPA being favorites. But, there are fewer green or red emitting systems that have high

k2AA rates while retaining other desirable characteristics.

As described

above, transmitter-annihilator couples may prove to be the nal piece in the PUC puzzle Current upconversion systems can achieve several % conversion eciency of absorbed photons into unconverted photons under one-sun illumination. With all of the the improvements suggested above, it would seem that highly ecient PUC systems are within reach.

26


Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Author Biographies Timothy W. Schmidt

Timothy W. Schmidt is a Professor of Chemistry at The University of New South Wales, in Sydney, Australia.

Previous appointments include The University of Sydney, CSIRO

Australia and Universität Basel.

His research group studies molecular spectroscopy, both

in the condensed and gas phase, with applications ranging from astrophysics to renewable energy. http://www.chemistry.unsw.edu.au/sta/timothy-schmidt

Felix N. Castellano

Felix N. Castellano is currently a Professor of Chemistry at North Carolina State University and was previously the Director of the Center for Photochemical Sciences at Bowling Green State University.

His research focuses on metal-organic chromophore photophysics

and energy transfer, photochemical upconversion phenomena, and solar fuels photocatalysis. http://www.ncsu.edu/chemistry/people/felix_castellano.html

Acknowledgement

This research was supported under Australian Research Councils Discovery Projects funding scheme (DP110103300) and the Air Force Oce of Scientic Research (FA9550-13-1-0106). TWS acknowledges the Australian Research Council for a Future Fellowship.

Quotes •

It is the intention of this Perspective to illustrate how reaction kinetics ultimately control most facets of photochemical upconversion and that annihilation spin statistics does not necessarily limit overall performance.

27



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•

...

Page 28 of 37

we propose a kinetic mechanism for the synergistic action of two annihilator

species.

•

Current upconversion systems can achieve several % conversion eciency of absorbed photons into unconverted photons under one-sun illumination.

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Graphical TOC Entry 100 90

d[ 3A* ] = kφ [ 1S ]− k1A [ 3A* ]− k2AA [ 3A* ]2 dt

80 70 60

time /µs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50 40 30 20 10

525

550

575

600

625

wavelength /nm

650

675

37


Photochemical Upconversion: The Primacy of Kinetics - The Journal of

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