Abstract

The problem of reabsorption in luminescent solar concentrators (LSC) is discussed. A mathematical development is presented which enables the LSC gain to be calculated based on the optical properties of the materials and a random walk formalism. Two- and three-dimensional analyses are used. A detailed set of calculations for a common dye (rhodamine 6G) is used to examine the practicality of employing a single dye. The effects of diameter, thickness, and quantum yield on the LSC output are presented. The spectrum of the LSC output as a function of concentration is calculated. It is suggested that LSCs can be made more efficient with a system which utilizes radiationless electronic excited state transport and trapping as intermediate steps between absorption and reemission. Trap emission substantially avoids the reabsorption problem.

© 1981 Optical Society of America

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References

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  1. W. H. Weber, John Lambe, Appl. Opt. 15, 2299 (1976); J. S. Batchelder, A. H. Zewail, T. Cole, Appl. Opt. 18, 3090 (1979).
    [CrossRef] [PubMed]
  2. B. A. Swartz, T. Cole, A. H. Zewail, Opt. Lett. 1, 73 (1977).
    [CrossRef] [PubMed]
  3. W. D. Johnston, Solar Voltaic Cells (Dekker, New York, 1980).
  4. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943); E. W. Montroll, Proc. Symp. App. Math. 16, 193 (1964); E. W. Montroll, G. H. Weiss, J. Math. Phys. 6, 167 (1965); E. W. Montroll, J. Math. Phys. 10, 753 (1969).
    [CrossRef]
  5. M. D. Ediger, R. S. Moog, M. D. Fayer, unpublished results.
  6. I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules (Academic, New York, 1971).
  7. J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, New York, 1970).
  8. K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
    [CrossRef]
  9. R. Kopelman in “Radiationless Processes in Molecules and Condensed Phases,” F. K. Fong, Ed. (Springer, Berlin, 1976), p.297; A. Blumen, R. Silbey, J. Chem. Phys. 70, 3707 (1979); D. D. Dlott, M. D. Fayer, R. D. Wieting, J. Chem. Phys. 69, 2752 (1978); R. D. Wieting, M. D. Fayer, D. D. Dlott, J. Chem. Phys. 69, 1996 (1978).
    [CrossRef]
  10. C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
    [CrossRef]
  11. D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
    [CrossRef]
  12. C. W. Frank, L. A. Harrah, J. Chem. Phys. 61, 1526 (1974); C. W. Frank, M. A. Oashgari, Trans. N. Y. Acad. Sci. to be published (1981).
    [CrossRef]

1981 (1)

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

1979 (2)

K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
[CrossRef]

C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
[CrossRef]

1977 (1)

1976 (1)

1974 (1)

C. W. Frank, L. A. Harrah, J. Chem. Phys. 61, 1526 (1974); C. W. Frank, M. A. Oashgari, Trans. N. Y. Acad. Sci. to be published (1981).
[CrossRef]

1943 (1)

S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943); E. W. Montroll, Proc. Symp. App. Math. 16, 193 (1964); E. W. Montroll, G. H. Weiss, J. Math. Phys. 6, 167 (1965); E. W. Montroll, J. Math. Phys. 10, 753 (1969).
[CrossRef]

Andersen, Hans C.

C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
[CrossRef]

Berlman, I. B.

I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules (Academic, New York, 1971).

Birks, J. B.

J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, New York, 1970).

Chandrasekhar, S.

S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943); E. W. Montroll, Proc. Symp. App. Math. 16, 193 (1964); E. W. Montroll, G. H. Weiss, J. Math. Phys. 6, 167 (1965); E. W. Montroll, J. Math. Phys. 10, 753 (1969).
[CrossRef]

Cole, T.

Dlott, D. D.

K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
[CrossRef]

Ediger, M. D.

M. D. Ediger, R. S. Moog, M. D. Fayer, unpublished results.

Fayer, M. D.

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
[CrossRef]

C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
[CrossRef]

M. D. Ediger, R. S. Moog, M. D. Fayer, unpublished results.

Frank, C. W.

C. W. Frank, L. A. Harrah, J. Chem. Phys. 61, 1526 (1974); C. W. Frank, M. A. Oashgari, Trans. N. Y. Acad. Sci. to be published (1981).
[CrossRef]

Gochanour, C. R.

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
[CrossRef]

Harrah, L. A.

C. W. Frank, L. A. Harrah, J. Chem. Phys. 61, 1526 (1974); C. W. Frank, M. A. Oashgari, Trans. N. Y. Acad. Sci. to be published (1981).
[CrossRef]

Johnston, W. D.

W. D. Johnston, Solar Voltaic Cells (Dekker, New York, 1980).

Kopelman, R.

R. Kopelman in “Radiationless Processes in Molecules and Condensed Phases,” F. K. Fong, Ed. (Springer, Berlin, 1976), p.297; A. Blumen, R. Silbey, J. Chem. Phys. 70, 3707 (1979); D. D. Dlott, M. D. Fayer, R. D. Wieting, J. Chem. Phys. 69, 2752 (1978); R. D. Wieting, M. D. Fayer, D. D. Dlott, J. Chem. Phys. 69, 1996 (1978).
[CrossRef]

Lambe, John

Lutz, D. R.

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

Moog, R. S.

M. D. Ediger, R. S. Moog, M. D. Fayer, unpublished results.

Nelson, K. A.

K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
[CrossRef]

Nelson, Keith A.

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

Swartz, B. A.

Weber, W. H.

Zewail, A. H.

Appl. Opt. (1)

Chem. Phys. (1)

D. R. Lutz, Keith A. Nelson, C. R. Gochanour, M. D. Fayer, Chem. Phys. 85, 1989 (1981).
[CrossRef]

Chem. Phys. Lett. (1)

K. A. Nelson, D. D. Dlott, M. D. Fayer, Chem. Phys. Lett. 64, 88 (1979).
[CrossRef]

J. Chem. Phys. (2)

C. W. Frank, L. A. Harrah, J. Chem. Phys. 61, 1526 (1974); C. W. Frank, M. A. Oashgari, Trans. N. Y. Acad. Sci. to be published (1981).
[CrossRef]

C. R. Gochanour, Hans C. Andersen, M. D. Fayer, J. Chem. Phys. 70, 4254 (1979); C. R. Gochanour, M. D. Fayer, J. Phys. Chem. 85, 1989 (1981).
[CrossRef]

Opt. Lett. (1)

Rev. Mod. Phys. (1)

S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943); E. W. Montroll, Proc. Symp. App. Math. 16, 193 (1964); E. W. Montroll, G. H. Weiss, J. Math. Phys. 6, 167 (1965); E. W. Montroll, J. Math. Phys. 10, 753 (1969).
[CrossRef]

Other (5)

M. D. Ediger, R. S. Moog, M. D. Fayer, unpublished results.

I. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules (Academic, New York, 1971).

J. B. Birks, Photophysics of Aromatic Molecules (Wiley-Interscience, New York, 1970).

W. D. Johnston, Solar Voltaic Cells (Dekker, New York, 1980).

R. Kopelman in “Radiationless Processes in Molecules and Condensed Phases,” F. K. Fong, Ed. (Springer, Berlin, 1976), p.297; A. Blumen, R. Silbey, J. Chem. Phys. 70, 3707 (1979); D. D. Dlott, M. D. Fayer, R. D. Wieting, J. Chem. Phys. 69, 2752 (1978); R. D. Wieting, M. D. Fayer, D. D. Dlott, J. Chem. Phys. 69, 1996 (1978).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Absorption and emission spectra of rhodamine 6G. Notice the large overlap between the two spectra. Absorption spectrum has a long tail into the blue for which ɛ ≈ 1000. (b) Absorption spectrum far to the red of the origin. Absorption is very weak but can be important for a large diameter or high concentration LSC.

Fig. 2
Fig. 2

Curve A: Fluorescence spectrum of R6G in ethanol. Curves B and C: calculated fluorescence spectrum observed at edge of a 50-cm diam, 1-cm thick LSC containing R6G: (B) 10−4 M, (C) 5 × 10−3 M. The 3-D simulation calculation was employed, and areas under each curve are proportional to the probability that a photon reaches the LSC edge once absorbed. Note the red-shifts resulting from strong reabsorption of shorter wavelength fluorescence. Only red photons have long step lengths needed to reach the LSC edge.

Fig. 3
Fig. 3

Schematic representation of the excimer approach to avoiding LSC reabsorption problem: (1) Absorption occurs into concentrated dye system. (2) Radiationless transport brings the excitation to the vicinity of the excimer chromophores. (3) The excitation is trapped on the excimer chromophores. (4) Excimer formation takes place, i.e., the pair of chromophores becomes bound. (5) Strongly red-shifted emission from the excimer avoids reabsorption. Dissociative ground state prevents reabsorption by the excimer chromophores. The lower part of the figure shows the sequence in terms of the energy levels.

Tables (5)

Tables Icon

Table I First Passage Results.

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Table II Two-Dimensional Simulation Results, Q = 0.9, R6G Spectral Data

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Table III Three-Dimensional Simulation Results: 0.1-cm Thick LSC, Q = 0.9, R6G Spectral Data

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Table IV Three-Dimensional Simulation Results: 1.0-cm Thick LSC, Q = 0.9, R6G Spectral Data

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Table V Pout for Various Quantum Yields Q. 1.0-cm Thick LSC, R6G Spectral Data, 3-D Simulation Results

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

P out = ( Q P TIR ) N ,
N = ~ 1 8 ( r l ) 2 .
N = a ( l / r ) ( r l ) 2 .
l = - log 0.5 ɛ C = 0.3 ɛ C ,
N = a ( l / r ) [ r ɛ C / 0.3 ] 2 = 11 a ( l / r ) [ r ɛ C ] 2 .
N ( λ ) = 11 a ( l / r ) [ r ɛ ( λ ) C ] 2 ,
P out ( λ ) = ( Q P TIR ) N ( λ ) = ( Q P TIR ) [ 11 a ( l / r ) r 2 C 2 ɛ ( λ ) 2 ] .

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