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Chemical Physics 389 (2011) 75–80
Contents lists available at SciVerse ScienceDirect
Chemical Physics
journal homepage: www.elsevier.com/locate/chemphys
Dipolar disorder formalism revisited
Andrey Tyutnev ⇑, Vladimir Saenko, Evgenii Pozhidaev
Moscow State Institute of Electronics and Mathematics, Bol. Trechsvyatitel. per., 3, Moscow, Russia
a r t i c l e
i n f o
Article history:
Received 31 May 2011
In final form 3 August 2011
Available online 23 August 2011
Keywords:
Charge carrier transport
Molecularly doped polymers
van der Waals disorder
a b s t r a c t
The dipolar disorder formalism (DDF) of Borsenberger and Bässler has been further developed based on a
unified approach treating the van der Waals and the dipolar disorder energies as being proportional to
mean intersite distance in a certain power. Tested against real molecularly doped polymers with the concentration of the dopant changing in a wide range, this approach gives values of the exponent lying in the
interval from 1.5 to 2.5. The total disorder is represented by an algebraic combination of four material
parameters relating to the dopant and the polymer matrix weighted by their relative weight concentrations. What is important, we seem to get able to explain the near constancy of the total disorder when the
concentration of the polar dopant changes. Until recently, this unusual behavior of the total disorder
defied any reasonable explanation.
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
The dipolar disorder formalism (DDF) has been proposed by
Borsenberger and Bässler in 1991 [1] to explain a strong polarity
dependence of the charge mobility in molecularly doped polymers
(MDPs) [2]. It was based on the Gaussian disorder model (GDM) [3]
and in particular, considered the main parameter of the model r
(the total disorder energy) as consisting of two independent contributions: the dipolar rd and the van der Waals rvdW constituents:
The dipolar disorder rd relates to the polar molecules of the
dopant and the polymer matrix (repeat units in the last case). Their
dipole moments are treated as point, randomly oriented dipoles
occupying sites of a simple cubic lattice with probability f „ c,
which is equal to the relative weight concentration of the dopant
[5]. Under such conditions the corresponding rd relating to the
dopant (rdd) or the polymer (rdp) may be estimated using the following expressions [5,6] (r in eV, p in D, a and b in nm):
rdd ¼
r2 ¼ r2v dW þ r2d :
ð1Þ
The first term on the right hand side of this equation is the old r
in the original GDM accounting for the static fluctuations of the
polarization energy P of a unit charge placed on a hopping center.
It has long been established that this polarization energy is of universal nature, constitutes about 1–1.5 eV in organics (both ordered
and disordered) and accounts for the lowering of the ionization potential of a molecule in a condensed phase compared with the gas
phase by approximately 2P [4]. The second term accounts for the
static fluctuations of the electrostatic energy arising from the presence of various dipolar molecules.
One extracts r from experiment while rd comes from the theoretical estimations. The total disorder r appears in the temperature
2
dependence of the zero-field mobility lð0; TÞ ¼ l0 exp 49 kr2 T 2
found by extrapolating the mobility field dependence
ln l vs F1/2 to F = 0 at each temperature. At present, r is known
for almost every MDP [2].
⇑ Corresponding author.
E-mail address: [email protected] (A. Tyutnev).
0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2011.08.003
0:0707p 0:5
c
ea2
ð2Þ
or
rdp ¼
0:0707p
eb2
ð1 cÞ0:5 :
ð3Þ
Here e is the dielectric constant of the MDP in question, p is the
respective dipole moment of the dopant or the repeating unit of
the polymer; a is the lattice constant computed in the lattice gas
model for the dopant (c ? 1.0 in Eq. (2)) while b is the same for
the polymer matrix (c ? 0 in Eq. (3)).
The problem with the DDF is that so far there is no way to find
rvdW independently (see Section 4). Instead, Eq. (1) has been used
for this purpose. Generally, the DDF proved to be highly successful
in explaining polarity effects in the charge carrier mobility. But,
one aspect is glaringly defying a reasonable explanation. We mean
r staying almost constant (to within some percent) for concentration c of a polar dopant changing from 0.1 to 0.7. Clearly, Eq. (2)
predicts that rdd should rise by more than 2.5 times and this,
according to Eq. (1), should not go unnoticed by r. The standard
explanation is to assume that rvdW behaves in such a way as to exactly compensate the expected variation of rdd [7]. This line of reasoning was criticized in [8] and various compensating mechanisms
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A. Tyutnev et al. / Chemical Physics 389 (2011) 75–80
were discussed in the follow-on article [9], but still without success. The aim of the present work is to rationalize the DDF and resolve the above mentioned controversy.
2. Formulation of the problem
To start with, we split r for a two component MDP into four
independent parts, and namely, the dipolar disorder of the dopant
(rdd) and the polymer (rdp) as well as the van der Waals disorders
relating to each of these (rvdW,d and rvdW,p, respectively). Next, we
introduce four material constants relating to a pure dopant
(c ? 1.0) and a pure polymer (c ? 0) to be designated as corre_
sponding symbols with hats (for example, rdp ). As c-dependence
for the dipolar disorder is known [5] it is easy to find the composite
expression for the total dipolar disorder rd in the MDP under consideration (see [10])
_
_
r2d ¼ cr2dd þ ð1 cÞr2dp :
ð4Þ
Van der Waals interactions are also of the electrostatic nature
but unfortunately their c-dependence is not known (see Section 4).
Assuming that rvdW / cm/3 (in the case of a dipolar disorder
m = 1.5) we arrive at the general formula for r for a two-component MDP
_
_
_
_
r2 ¼ cr2dd þ ð1 cÞr2dp þ c2m=3 rv2 dW;d þ ð1 cÞ2m=3 rv2 dW;p :
Fig. 1. Experimental (1) and calculated (2–5) dependence of r on the dopant
concentration c for TAPC:PC. Parameter m is equal to 1.25 (2), 1.5 (3), 2.0 (4) and 3.0
(5).
ð5Þ
One should keep in mind that Eq. (5) has been derived under
condition that neither the dielectric constant, nor the density of
the MDP under question undergoing a c-changing experiment do
change. Unfortunately, this aspect of the problem was totally neglected in literature. As we show in Section 4 these assumptions
are a good approximation and we intend to use them as well. Below the dielectric permittivities for polystyrene (PS) and polycarbonate (PC) are taken to be 2.6 and 3.0 while their respective
densities are 1.05 and 1.2 g/cm3. These values will be used initially
in calculations of r in the analyzed MDPs.
Now we are going to apply Eq. (5) to experimental data starting
with those featuring r(c) dependence to extract material parame_
ters ri and m for the most common polymer binders and dopants.
In fact, the problem is the standard trial and error procedure of fitting the existing MDP data with Eq. (5). Of paramount importance
are the tables of the digitized r(c) values with the claimed accuracy
of about 1–3%. This data is indispensible for finding m.
3. Data analysis
Let us first consider TAPC:PC system investigated in [11] for c
changing in extremely broad range from 10% to 80% including
TAPC glass itself (c = 100%) with r falling from 0.136 to 0.067 eV
(Fig. 1).
_
_
Fitting procedure shows that rv dW;p ¼ 0:137 eV (rdp is equal to
_
0.047 eV as in [10]). As for TAPC we find rv dW;d ¼ 0:056 eV and
_
rdd ¼ 0:036 eV (p = 1.4 D). It is gratifying that the experimentally
found r in TAPC glass is 0.067 eV [12] and coincides with its value
for TAPC:PC in the limit c ? 1.0. As we see later, this result is unique and in other systems it holds only approximately.
Fig. 1 shows that the best value of parameter m is 1.5 (good
agreement gives 1.25 as well). Larger values (2.0 or 3.0) should
be rejected, especially the last one. It is important to note that in
this case we deal with a MDP, in which dipole moments of dopant
molecules and polymer repeating units (1.0 D) are close.
In TTA:PC system studied in [13] the experimental data for m is
_
bracketed by 1.25 and 1.5 (Fig. 2). For m = 1.5 parameter ðrv dW;d
_
equals 0.057 eV (rdd ¼ 0:041 eV, see [10]). Here, we kept disorder
parameters for PC the same as in a previous example.
Fig. 2. Experimental (1) and calculated (2–4) dependence of r on the dopant
concentration c for TTA:PC. Parameter m is equal to 1.25 (2), 1.5 (3) and 2.0 (4).
Most investigations refer to doped PS, in which p = 0.4 D,
_
b 0.55 nm, so that rdp 0:037 eV (see [10]). In TTA:PS [13], we
_
have r = 0.106 eV at c = 0.1 to give rv dW;p ¼ 0:110 eV. With
m = 2.5 (the best fit on Fig. 3) we arrive at the experimental r
_
_
(0.077 eV) at c = 0.5 for rv dW;d ¼ 0:057 eV (rdd ¼ 0:041 eV as in
[10]). From now on, we use the above-cited values for PC and PS
in analyzing the published data relating to various MDPs.
An interesting information has been provided by the studies of
the hole transport in TPM doped PS at fixed dopant concentrations
(35% and 45%) and in the respective TPM glasses [14–16]. Dipole
moments of the TPM molecules vary from 1.33 to 3.2 D. Let us consider extracted data for 3 TPM molecules. In TPM-A glass (p = 1.33
_
_
D) r = 0.093 eV and rdd ¼ 0:043 eV, so that rv dW;d ¼ 0:082 eV. In
two other glasses TPM-D (p = 2.1 D) and TPM-E (p = 3.2 D) the corresponding numbers are 0.106, 0.062, 0.087 eV, and 0.123, 0.093,
0.081 eV. Van der Waals disorders are rather close while dipolar
disorder rises with increasing p. Based on m = 1.5 we calculate r
for 3 respective 35% TPM:PS in the same order (in brackets, experimental values): 0.106 (0.106), 0.108 (0.110) and 0.113 (0.115) eV.
The agreement between experimental and calculated values is
satisfactory.
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A. Tyutnev et al. / Chemical Physics 389 (2011) 75–80
0.12
77
Fig. 4. Experimental (1) and calculated (2) dependence of r on the dopant
concentration c for ENA-D:PS. Parameter m is equal to 2.5 (2).
Br-substituted TTA (TPA-4) is given in [20]. Our calculations reproduce experimental data rather closely (Fig. 5). The flat r(c) dependence for TPA-4 is very reminiscent of the similar dependence
found in DEH, DEASP and DTNA doped PS and PC, which we are
now going to consider (see [8,9]).
First of all, there is a need for the reliable information to assess
the van der Waals disorder energy in typical polar dopants such as
DEH, DEASP and DTNA whose dipole moments rise in that order.
There is data published for the first two glasses [21,22] but it
_
arouses serious suspicions. In them rd exceeds r: 0.115 and
0.125 eV compared to 0.104 and 0.103 eV, respectively. Clearly,
there is no room left for the van der Waals disorder energy in this
case. This finding seems rather unphysical.
In [23] data has been presented for 45% HDZ:PS. Two hydrazones used (HDZ-C and HDZ-F (DEH) with dipole moments 2.27
and 3.16 D, respectively) are of special importance. Reported r values were 0.100 and 0.113 eV in that order. As data for PS is known
as well as dipole moments and molecular weights for both dopants
(468 and 343), we are able to make evaluation of their van der
Waals disorders (0.06 eV), which fits the above experimental data
exactly.
Let us try analogous assessment for moderately doped 50%
DEH:PS [24,25]. In both papers r equals 0.113 eV. Evaluated
_
r
v dW;d is 0.056 eV. In 50% DEASP:PS [25] r = 0.129 eV, so
_
rv dW;d ¼ 0:070 eV. Both numbers make sense and we use them in
calculations.
Let us now consider the c-changing experiment for DEH:PS described in [24]. The range of concentrations extends from 7 to
65 wt.% (Fig. 6). Also shown on the figure are all disorder components in this MDP and their change with the concentration of the
dopant. Fig. 7 presents analogous data for DEASP:PC. It is seen that
general agreement between experimental and calculated results is
satisfactory and a flat r(c) dependence is reproduced.
The above argumentation allows one to understand the reasons
for unusual behavior of r in c-changing experiments, in which it
stays nearly constant when polar dopant concentration varies in
a wide range (for DTNA:PS and DEASP doped PS and PC see Figs. 1
and 2 in [8]). Exactly these results forced authors of the review [8]
to conclude ‘‘that dipolar disorder does not contribute to the temperature dependence of the mobility’’. This conclusion has been
challenged in [9] on the ground that in reality dipolar disorder
could not escape contributing to the temperature dependence
In ENA-D:PS [17] the best choice of m is 2.5 (Fig. 4). In this sys_
tem rv dW;p ¼ 0:10 eV (slightly less than customary) and
_
rv dW;d ¼ 0:085 eV. The dipolar moment of the dopant (0.38 D) is
very close to that of the repeating unit in PS, so no changes of e
should be expected in a c-changing experiment. This way, we succeeded in accounting for a mild decrease of r from 0.100 to
0.078 eV for c rising from 0.07 to 0.65.
So far, we dealt with MDPs in which increasing c causes r to decrease. Now we take up MDPs with conspicuously flat r(c) dependence, starting with non-polar dopants in PS.
In TASB:PS with non-polar dopant (p = 0.54 D) the findings are
as follows [18]. The observed constancy of r (0.102 ± 0.002 eV)
_
was reproduced for rv dW;d ¼ 0:10 eV and the estimated
_
rdd ¼ 0:014 eV.
Even in the electron non-polar conductor DPQ:PS
r = 0.118 ± 0.001 in the range of c 0.2–0.6 [19].
Dipole moment
_
of DPQ molecule is 0.4 D. Here, by assuming rv dW;d of the dopant
_
to be equal to 0.120 eV (rdd ¼ 0:017 eV), we come to the constancy
of r (0.118 ± 0.001 eV) in the whole range of c tested (to achieve
_
this we assumed slightly smaller rv dW;p ¼ 0:10 eV for m = 1.5).
An interesting example of a strikingly different behavior of the
r(c) dependence for PS doped with TTA (TPA-1) and a more polar
Fig. 5. Experimental (1, 4) and calculated (2, 3, 5) dependence of r on the dopant
concentration c for TPA-4:PS (1–3) and TTA:PS (4, 5). Parameter m is equal to 1.75
(2, 3) and 2.5 (5). For curve 3 the dielectric permittivity at c = 0.5 was taken to be 2.8
(see Section 4).
1
TTA:PS
2
0.11
3
0.10
σ, eV
5
4
0.09
6
0.08
1
0.07
0
10
20
30
40
50
60
c, wt.%
Fig. 3. Experimental (1) and calculated (2–5) dependence of r on the dopant
concentration c for TTA:PS. Parameter m is equal to 1.25 (2), 1.5 (3), 2.0 (4), 2.5 (5)
and 3.0 (6).
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A. Tyutnev et al. / Chemical Physics 389 (2011) 75–80
It may be said that concentration dependence of r is generally
defined by the interplay of four material parameters:
_
_
_
_
rv dW;p ; rv dW;d ; rdp and rdd (their values are given in Table 1). Linear
combination of their squares (coefficients depend on the concentration c) defines r2 as has been demonstrated above. First two
and the last of them are crucial for polar dopants and here the
net result of r const is readily achieved. The compensation of rising rdd is effected mainly through decreasing rvdW,p (the role of the
second (rvdW,d) and the third (rdp) contributions are minor and, to
certain extent, they tend to compensate each other). Figs. 6 and 7
illustrate how each of these four disorder constituents changes
with the dopant concentration. Also shown are their partial combinations (dipolar rdt and van der Waals rvdW,t) as well as the resulting total disorder r.
4. Discussion
Fig. 6. Concentration dependence of the various computed components of the
disorder energy in DEH:PS including the experimental as well as the calculated r.
Fig. 7. Concentration dependence of the various computed components of the
disorder energy in DEASP:PC including the experimental as well as the calculated r.
Table 1
Materials disorder parameters used in this work (except when stated otherwise).
Material
p, D
PS
PC
DEH
DEASP
TTA
TAPC
TPD
TPM-A
TPM-D
TPM-E
DPQ
TASB
ENA-D
TPA-4
DTNA
0.4
1.0
3.16
4.34
0.9
1.4
1.52
1.33
2.1
3.2
0.4
0.54
0.38
2.6
5.78
_
rdd ; eV
0.115
0.125
0.041
0.036
0.046
0.043
0.062
0.093
0.017
0.014
0.016
0.104
0.19
_
rv dW;d eV
_
rdp eV
_
0.037
0.047
0.110
0.137
rv dW;p eV
0.056
0.070
0.057
0.056
0.06
0.082
0.087
0.081
0.12
0.10
0.085
0.06
0.07
(or r) but no plausible compensation mechanism to offset the
rising dipolar contribution of the dopant molecules (rdd in our
terminology) has been found.
The central idea of the DDF is that two kinds of disorder (the
dipolar and the van der Waals, both electrostatic in nature) add
up quadratically to give the square of the total disorder r. The most
important observation concerns the fact that total disorders in
polymer binders determined in the limit c ? 0 is strikingly large
(0.145 eV in PC and 0.116 eV even in non-polar PS) as Figs. 1–3
show. Since dipolar contributions in them do not exceed 0.05
and 0.04 eV in that order we conclude that the van der Waals parts
clearly dominate.
Now diluting these polymers with non-polar or slightly polar
dopants is expected to decrease r if their van der Waals disorders
are appreciably smaller than that of a polymer (TAPC, TTA, ENA-D,
TTB, TPD to name just a few) or almost not to change if these are
comparable (TASB, DPQ). For polar DEH and DEASP r stays almost
constant due to compensation of the falling rvdW,p with rising rdd
in c-changing experiments in both PC and PS.
Now let us discuss the problem of a gradual increase of e with
rising concentration of the polar dopant. It has been shown that
in 30% TTA:PS e = 2.652 compared to 2.54 in pure PS (4% rise)
[26]. Adding TAP (p = 6.6 D) to original MDP further raises e to
2.676 (2 wt.%), 2.805 (4 wt.%) and lastly to 3.011 at 8 wt.% (almost
20% increase compared with PS). Even more striking effect has
been found in 33 wt.% TPA:PS as adding of 6.2% of o-DNB increased
e from initial value of 2.9 to 3.3–3.6 [26] or even 4.9 [27]. But
6 wt.% data point is even smaller than the starting concentration
in a typical c-changing experiment. In this precarious situation,
we had to rely mostly on common sense in evaluating results of
such experiments.
In this situation, we made preliminary measurements of e in PS
and PC doped with polar dopants (Table 2). The samples have been
prepared at Kodak using Ni-coated PET substrates. Diameter of Al
electrodes (about 7 nm thick) were 32 or 23 mm. Thickness of
the samples varied between 16 and 35 lm and free surfaces were
Table 2
Dielectric constants of MDPs.
MDP
e (Error bars = 0.05)
50%
30%
70%
30%
70%
70%
50%
70%
3.0
2.65
2.85
2.95
3.3
3.0
3.1
3.15
DTNA:PS
DEH:PS
DEH:PS
TPA-4:PS
TPA-4:PS
DEASP:PS
DEH:PC
DEASP:PC
Pure polymers
PS
PC
2.6
3.0
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A. Tyutnev et al. / Chemical Physics 389 (2011) 75–80
either mirror-like or rather rough with point defects. TPA-4:PS
samples were not properly dried and stayed rather sticky exhibiting high dark conductivity. Processing was done with due care for
all these interfering factors. In pure PS and PC the dielectric permittivity was close to 2.6 and 3.0 as expected (measurements made at
103 Hz). Table 2 shows that e does not change in any significant
way (610%) except in TPA-4:PS (polymer in a rubber state) and
50% DTNA:PS or 70% DEASP: PS (15%).
The increase of e should appreciably reduce the dipolar disorder
as Eq. (2) requires (rd / 1/e). According to P. Parris [28] in a medium containing randomly distributed polarizeable spherical molecules (number density q3) we have
rv dW / q3=2 / c1=2 :
ð6Þ
On the other hand, the same problem formulated for a lattice
leads to rather different result. In this case, rvdW = 4PK [3] where
K is the relative average fluctuation of the intermolecular separations (in units of the lattice constant a). Now as P is proportional to
a4, we finally obtain that
rv dW / a4 / c4=3 :
ð7Þ
Dependences (6) and (7) are substantially different so the best way
in this situation is to use c-dependence with an adjustable parameter m (rvdW / cm/3) to fit the experiment. Exactly this approach has
been adopted in the present work (see Eq. (5)).
Much stronger dependence should occur for the van der Waals
disorder as now rvdW / 1/e2 [28]. To accommodate e variation we
used the modified Eq. (5)
_
_
_
_
r2 ¼ n2 cr2dd þ k2 ð1 cÞr2dp þ n4 c2m=3 rv2 dW;d þ k4 ð1 cÞ2m=3 r2v dW;p :
ð8Þ
Here the correction coefficients n and k are the ratios of the permittivities in the limit c ? 1.0 (n) and c ? 0 (k) to that in the MDP with
the given concentration c. The permittivity is assumed to change
linearly with concentration of the polar dopant from that of the
polymer (c ? 0) to that (em) at the highest dopant concentration
cm used in experiment
eðcÞ ¼ ep þ em ep c=cm :
ð9Þ
Curve 3 on Fig. 5 serves to confirm that the flat r(c) dependence
stays almost intact when e variation is taken into account.
Fig. 8 presents r(c) curves (both computed and experimental) in
DEH:PS (1), DEASP:PC (2) and DTNA:PS (3). Calculations use Eqs.
(8) and (9) and data presented in Tables 1 and 2. Note that material
disorder parameters were determined independently (see Table 1).
Contrasted with the first two MDPs, the third one exhibits strongly
rising r(c) dependence even in a limited range of 20–60 wt.% contrary to the experiment [7]. It is a challenge to the DDF.
In this context, it should be reminded that mobility measurements in [7] clearly refer to the non-equilibrium transport (see
Fig. 2 in the cited paper). To account for this fact thebasic formula
2
for retrieving r has been changed: lð0; TÞ ¼ l0 exp 14 kr2 T 2 . This
formula should be compared with a similar one given in the Introduction section. Obviously, experimental data for DTNA:PS should
be revisited.
Theoretical findings of the paper [29] regarding accuracy of Eq.
(2) are worth mentioning. It has been shown that e-dependence of
the dipolar disorder is practically absent for e changing in the range
from 2.0 to 4.0 while the magnitude of the rdd is approximately 1.6
times smaller than that given by Eq. (2) for e = 1.0. It is possible
that such implications are also expected for e-dependence of the
rvdW as well. Future theoretical work in this direction is highly
desired.
5. Summary
The central idea of the dipolar disorder formalism suggesting
that the van der Waals rvdW and dipolar disorder rd energies combine as independent components to form total disorder energy r
according to Eq. (1) seems quite reasonable. We have shown that
treating rvdW for a polymer and a dopant as being algebraically
proportional to their fractional mass densities enables one to rationalize data for PS and PC doped with weakly polar dopants such as
DAS-A, TASB, TTA, TTB, TPD, etc. (p = 0.3 to 2.2 D). The case of polar
dopants (TPA-4, DEH and DEASP) featuring unusually flat r(c)
dependence can also be explained (at present, DTNA defies this approach). Thus, the long-standing controversy about a flat r(c)
dependence in polar MDPs has been resolved in the framework
of the modified dipolar disorder formalism without making use
of any extraordinary assumptions unsuccessfully sought in literature [9]. Molecular glasses of polar dopants still present a challenge
to the above approach. Future theoretical work to account for the
permittivity dependence of both the dipolar and the van der Waals
disorder energies in the spirit of the paper [29] is necessary.
Acknowledgements
The authors would like to acknowledge fruitful discussions with
late Lawrence Schein and Paul Parris. The authors would also like
to thank D. Weiss for preparation of the samples of PS and PC
doped with polar dopants.
Appendix A
Definition of Initials used in this paper
DEASP
Fig. 8. Calculated total disorders r in DEH doped PS (1), DEASP doped PC (2) and
DTNA:PS (3), filled symbols. Experimental values of r are denoted by primed
numbers (empty symbols).
DEH
DTNA
DNB
DPQ
ENA-D
HDZ-C
HDZ-F
1-Phenyl-3((diethylamino)styryl)-5-(p(diethylamino)phenyl)pyrazoline
p-Diethylaminobenzaldehyde diphenylhydrazone
Di-p-tolyl-p-nitrophenylamine
Dinitrobenzene
3,30 -Dimethyl-5-50 -di-t-butyldiphenoquinone
N(2,2-Diphenylvinyl)-diphenylamine
4-Ditolylaminobenzaldehyde diphenylhydrazone
=DEH
(continued on next page)
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80
A. Tyutnev et al. / Chemical Physics 389 (2011) 75–80
Appendix A (continued)
PC
PS
TAP
TAPC
TASB
TPA
TPA-4
TPM-A
TPM-B
TPM-C
TPM-D
TPM-E
TPM-F
TPD
TTA
TTB
Bisphenol-A-polycarbonate
Polystyrene
t-Amylphthalonitrile
1,1-Bis(di-4-tolylaminophenyl)cyclohexane
Bis(ditolylaminostyryl)benzene
Tri-p-phenylamine
1-Br(Substituted) p-tritolylamine
Bis(4-N,N-diethylamino-2-methylphenyl)-4methylphenylmethane
Bis(4-N,N-diethylamino-2-methylphenyl)(4-propylphenyl) methane
Bis(4-N,N-diethylamino-2-methylphenyl)(4-phenylphenyl) methane
Bis(4-N,N-diethylamino-2-methylphenyl)(4-phenyl) methane
Bis(4-N,N-diethylamino-2-methylphenyl)(4-methoxyphenyl) methane
Bis(4-N,N-diethylamino-2-methylphenyl)(4-chlorophenyl) methane
N,N0 -diphenyl-N,N-bis(3-methylphenyl)-[1,10 biphenyl]-4,40 diamine
Tri-p-tolylamine
N,N0 ,N00 ,N000 -Tetrakis(4-methylphenyl)-(1,10 biphenyl)-4,40 -diamine
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