We have investigated the effect of small amounts of a highly polar additive, t‐amylphthalonitrile (TAP), on the mobility of holes in polystyrene doped with tri‐p‐tolylamine. The mobility decreases rapidly and becomes more steeply dependent on electric field strength and temperature as the concentration of TAP is increased. The experimental results are compared with two current models. A ‘‘dipolar trap’’ model fails to reproduce the observed dependence of the mobility on TAP concentration. The Gaussian disorder model of Bässler and co‐workers [Phys. Status Solidi 175, 15 (1993)] can fit the dependencies on field strength and temperature at each concentration, but the concentration dependencies of the fitting parameters are problematic.
REFERENCES
1.
P. M. Borsenberger and D. S. Weiss, Organic Photoreceptors for Xerography (Marcel Dekker, New York, 1993).
2.
3.
4.
L. B. Schein, Electrophotography and Development Physics, 2nd ed. (Springer, New York, 1992).
5.
6.
7.
8.
9.
10.
11.
P. M.
Borsenberger
, E. H.
Magin
, and J. J.
Fitzgerald
, J. Phys. Chem.
97
, 8250
(1993
).12.
P. M.
Borsenberger
, J. J.
Fitzgerald
, and E. H.
Magin
, J. Phys. Chem.
97
, 11
314
(1993
).13.
14.
A.
Hirao
, N.
Nishizawa
, and M.
Suguichi
, J. Appl. Phys.
74
, 1083
(1993
).15.
H.-J. Yuh,D. M. Pai, and J. F. Yanus, U.S. Patent No. 5 028 502 (1991);
J. A. Pavlisko, L. J. Sorriero, and R. H. Young, U.S. Patent No. 5 232 800 (1993).
16.
P. M. Borsenberger, W. T. Gruenbaum, E. H. Magin, and L. J. Sorriero, Chem. Phys. (in press).
17.
M. Sugiuchi, H. Nishizawa, and T. Uehara, in Proceedings of the Sixth International Congress on Non-Impact Printing Technologies, edited by R. J. Nash (Society for Imaging Science and Technology, Springfield, VA, 1991), p. 298.
18.
(a) H. Nishizawa, M. Sugiuchi, and T. Uehara, in Macromolecular Host Guest Complexes: Optical, Optoelectric, and Photorefractive Properties and Applications, edited by S. A. Jenekhe, Mater. Res. Soc. Symp. Proc. 277 (Materials Research Society, Pittsburg, PA, 1992), p. 33;
19.
20.
(a)
R. H.
Young
and J. J.
Fitzgerald
, J. Phys. Chem.
99
, 4230
(1995
);(b)R. H. Young, J. A. Sinicropi, and J. J. Fitzgerald, ibid (to be published).
21.
P. M.
Borsenberger
and J. J.
Fitzgerald
, J. Phys. Chem.
97
, 4815
(1993
).22.
A. G.
Tyurin
, A. Yu.
Kryukov
, T. C.
Zhuravleva
, and A. V.
Vannikov
, Vyskomol. Soedin. Ser. B
30
, 739
(1988
);A. V.
Vannikov
, A. G.
Tyurin
, A. Yu.
Kryukov
, and T. S.
Zhuravleva
, Mater. Sci. Forum
42
, 29
(1989
).23.
A. V.
Vannikov
, A. Yu.
Kryukov
, A. G.
Tyurin
, and T. S.
Zhuravleva
, Phys. Status Solidi A
115
, K47
(1989
).24.
[
A. V.
Vannikov
and A. D.
Grishina
, Russ. Chem. Rev.
58
, 1169
(1989
)].25.
P. M.
Borsenberger
and H.
Bässler
, Phys. Status Solidi B
170
, 291
(1992
).26.
(a)
R. H.
Young
and J. J.
Fitzgerald
, J. Chem. Phys.
102
, 6290
(1995
);(b)
R. H.
Young
and J. J.
Fitzgerald
, 102
, 2209
(1995
)., J. Chem. Phys.
27.
M.
Abkowitz
, J. S.
Facci
, and M.
Stolka
, Appl. Phys. Lett.
65
, 1127
(1994
).28.
29.
(b)
S. V.
Novikov
and A. V.
Vannikov
, Chem. Phys. Lett.
182
, 598
(1991
);(d)
S. V.
Novikov
and A. V.
Vannikov
, J. Phys. Condensed Matter
6
, 10
519
(1994
).30.
R. H. Young (in preparation). Some data on have been reported by Yuh and Pai in Ref. 8.
31.
1 Debye
32.
P. Hedvig, Dielectric Spectroscopy of Polymers (Adam Hilger, Bristol, 1972), p. 24.
33.
34.
Y.
Kanemitsu
, H.
Funada
, and Y.
Masumoto
, J. Appl. Phys.
71
, 300
(1992
).35.
36.
L. B.
Schein
, A.
Rosenberg
, and S. L.
Rice
, J. Appl. Phys.
60
, 4287
(1986
);L. B.
Schein
, A.
Peled
, and D.
Glatz
, J. Appl. Phys.
66
, 686
(1989
)., J. Appl. Phys.
37.
If the finite extents of the molecules are neglected, the probability that the shortest TAP–TTA distance does not exceed R is We define a “typical” distance by the condition
38.
We consider the site energy to be the total energy of the MDP with a hole on that site, relative to that of the uncharged MDP. Thus a trap is a low-energy site, whether the charge carrier is an electron or a hole.
39.
(b)
S. V.
Novikov
and A. V.
Vannikov
, Chem. Phys. Lett.
224
, 501
(1994
);40.
R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer, New York, 1991), Sec. 1.2.
41.
42.
43.
44.
P. M.
Borsenberger
, L.
Pautmeier
, and H.
Bässler
, J. Chem. Phys.
94
, 5447
(1991
).45.
46.
P. M.
Borsenberger
, L.
Pautmeier
, and H.
Bässler
, J. Chem. Phys.
95
, 1258
(1991
).47.
48.
P. M.
Borsenberger
and J. J.
Fitzgerald
, J. Phys. Chem.
97
, 4815
(1993
).49.
L.
Pautmeier
, R.
Richert
, and H.
Bässler
, Synth. Met.
37
, 271
(1990
).50.
(a) The simulations by Bässler et al. are actually done at constant temperature ( 295 K) for various σ[H. Bässler (private communication)]. Equations (A1) and (A2) in the Appendix result from a reasonable but not exactly correct assumption on how the simulated σ dependence maps into a T dependence at constant σ. Use of Eq. (15), Sec. IV E, results in Eqs. (4) and (5) instead. (b) The value of C found in the simulations should be multiplied by (c) The threshold fields found in Ref. 49, around 50 V/μm, are reduced by a factor of 6 Å/11.5 Å. See Refs. 2, 28, and 49 for details and further discussion.
51.
52.
53.
L.
Pautmeier
, R.
Richert
, and H.
Bässler
, Philos. Mag. B
63
, 587
(1991
).54.
(b)
L. B.
Schein
, J. C.
Scott
, L. Th.
Pautmeier
, and R. H.
Young
, Mol. Cryst. Liq. Cryst.
228
, 175
(1993
).55.
Figure 4 shows that, over the limited data range available, the values of and are accurately given by the GDM formulas, Eqs. (4) and (5), with the parameters given in Table I. Hence, plots of Eq. (7) using those formulas and parameters would have slopes that fit within the scatter of the data for the TAP-containing samples.
56.
57.
58.
(a) We take this opportunity to point out that the assumption in Eq. (14), that exothermic hops are not affected by the difference in site energies, is not inconsequential. It necessarily affects the ability of a very deep state to capture or recapture a charge carrier in competition with other, not-so-deep states.
59.
(a)
Yu. N.
Gartstein
and E. M.
Conwell
, Chem. Phys. Lett.
217
, 41
(1994
);(b)
Yu. N.
Gartstein
and E. M.
Conwell
, J. Chem. Phys.
100
, 9175
(1994
);(c)
B.
Hartenstein
, H.
Bässler
, S.
Heun
, P.
Borsenberger
, M.
Van der Auweraer
, and F. C.
De Schryver
, Chem. Phys.
191
, 321
(1995
).60.
61.
I. R.
Gould
, D.
Noukakis
, L.
GomezJahn
, R. H.
Young
, J. L.
Goodman
, and S.
Farid
, Chem. Phys.
176
, 439
(1993
).62.
63.
64.
A.
Dieckmann
, H.
Bässler
, and P. M.
Borsenberger
, J. Chem. Phys.
99
, 8136
(1993
).65.
66.
R. H. Young, Philos. Mag. (to be published).
67.
This estimate is based on formulas in Ref. 66, assuming that the nondipolar contribution to the DOS has a Gaussian distribution with the same width (88 meV) as the experimental value for TTA+PS alone.
68.
Let f be the fraction of lattice sites occupied by dipoles in the lattice model described in Sec. IV F (Refs. 64–66). Thisf is usually comparable to the weight fraction of dipolar species in the material (Ref. 66). Let A represent the energy of a single charge–dipole interaction when the charge and the dipole are nearest neighbors on the lattice and the dipole points toward the charge, and let be the variance of the model DOS (excluding any nondipolar contributions). Then (Ref. 66) and if For the thermal average of the total charge–dipole interaction energy is If and then is larger than A, and a charge–dipole energy equal to the thermal average must represent the contribution of more than one dipole.
69.
R. H. Young (unpublished).
70.
71.
P. M.
Borsenberger
, H.-C.
Kan
, E. H.
Magin
, and W. B.
Vreeland
, J. Imag. Sci. Technol.
39
, 6
(1995
).
This content is only available via PDF.
© 1995 American Institute of Physics.
1995
American Institute of Physics
You do not currently have access to this content.