4230
J. Phys. Chem. 1995, 99, 4230-4240
Dipole Moments of Hole-Transporting Materials and Their Influence on Hole Mobility in Molecularly Doped Polymers Ralph H. Young* OfSice Imaging Division, Eastman Kodak Company, Rochester, New York 14650-2129
John J. Fitzgeraldt Manufacturing Research and Engineering Division, Eastman Kodak Company, Rochester, New York 14650-2104 Received: October 6, 1994@
Dipole moments have been measured for a number of hole-transporting donor compounds. Where possible, the results are interpreted in terms of group dipole moments and molecular conformations. The mobility of holes in molecularly doped polymers containing some of these compounds generally (but not universally) correlates with the dipole moment of the donor, consistent with previous results. Compensating effects that apparently contribute to the Correlation are pointed out, as are difficulties in constructing an “equitable” comparison of disparate materials. The physical origin of the correlation is discussed. An appendix presents formulas for the distribution of possible hole energies for a donor molecule containing a dipolar substituent with a rotational degree of freedom.
1. Introduction A charge-transporting molecularly doped polymer typically consists of charge-transporting molecules (CTM), strong electron donors or acceptors, dissolved in a polymeric host A charge-transporting molecular glass typically consists of a similar donor or acceptor without a b i n d e ~ - . ~Such - ~ materials are usually good insulators by themselves, but some can transport injected charge carriers efficiently over distances of many micrometers. The mechanism of transport may be viewed as an iterated solid-state intermolecularcharge-transfer reaction, for example, between a cation radical of a donor molecule and a nearby neutral donor, or it may be viewed as a hopping of the corresponding “hole” between donor “sites”. The combined insulating and charge-transporting abilities make molecularly doped polymers useful as components of the photoconductors used in electrophotography1-3 and make molecular glasses potentially useful in electroluminescent An important measure of the charge-transporting ability, affecting the response time of photoconductors, is the mobility of the charge carriers. One factor affecting the mobility in a molecularly doped polymer is the presence of polar groups in any component. The mobility becomes smaller and more strongly dependent on electric field strength and temperature with a binder containing polar group^,^^-^^ with a polar CTM,10,22-27or with introduction of a polar third component.20,28-34The same factor affects the mobility of charge carriers in single-component g l a ~ s e s . ~ + ~ ~ In this paper we report a study of the dipole moments and charge-transport properties of various hole-transporting molecules. The original purpose was to determine whether the effect of polar groups in a CTM is determined by the net dipole moment of a CTM or merely the presence of such groups. Recent studies, some based on the dipole moments reported here, now indicate that the net dipole moment is indeed a major f a ~ t o r . ~ ~ In - ~particular, ~ , ~ ~ -the ~ mobility ~ in two series of CTM has been found to decrease exponentially with increasing dipole Present address: General Electric Company, 260 Hudson River Road, MD 12/11, Waterford, NY 12188. Abstract published in Advance ACS Abstracrs, February 15, 1995. @
moment of the CTM.24-27 Nevertheless, as will become apparent, the correlation of mobility with dipole moment is neither universal nor conceptually straightforward. Another purpose was to investigate the mechanism behind the correlation. There are now several and a considerable body of relevant data, but it is possible to cast some more light on the subject. An additional purpose, in some cases, was to control for dipole moment in studies of other factors. Section 2 of this paper describes the experimental methods. Section 3 reports the dipole moments measured for various CTM and, where possible, offers an interpretation of the measured values in terms of group dipole moments and molecular conformations. In section 4, we discuss the correlation of hole mobility with the dipole moment of the CTM. Points addressed include difficulties of formulating an “equitable” comparison among CTM of various chemical classes and the compensation that apparently occurs among factors other than the dipole moment. In addition, we present a comparison of several CTM belonging to a single chemical family (triarylamines). By keeping the electron-donor portion of the molecule essentially constant, we are able to isolate the effects of polar substituents from other chemical variations and to distinguish more convincingly between the effects of group and net moments. In section 5 we attempt to analyze the connection between dipole moment and hole mobility using a microscopic theory, the Gaussian disorder model of Btissler and c o - w ~ r k e r s $and ~ ~data ~ ~ mostly from detailed studies in the literature. In section 6 we comment on two other models, one involving an enhancement of the dielectric constant of the medium by the presence of polar component^^*-^^^^^^^* and the other based on the notion that a dipole near a CTM is capable of turning that CTM into a hole trap.u-26,40-43 Section 7 is a short summary. In the Appendix, we present formulas for the distribution of possible energies of a hole on CTM that contains a freely rotatable dipolar substituent.
2. Experimental Methods Materials. Structures are shown in Table 1. Compound 1.4 was supplied by D. A. Chen and D. S. Weiss, 1.8 by J. E.
0022-365419512099-4230$09.00/0 0 1995 American Chemical Society
Dipole Moments of Hole-Transporting Materials
J. Phys. Chem., Vol. 99, No. 12, 1995 4231
Kaeding, and 1.5 by J. A. Sinicropi, all of Eastman Kodak Co. of the tail. Linear, rather than log-log, plots were used. For TTB (3.1) was supplied by M. Lodolini of GLM Telesis. more details, see ref 34. p - p E F P (4.1) was supplied by D. Terrell of Agfa-Gevaert N. 3. Dipole Moments and Molecular Conformations V. DEASP (9) was supplied by L. B. Schein of IBM. Trisp-bromophenylamine (1.7) and 2,5-bis(4-diethylaminophenyl)Structures and measured dipole moments are shown in Table 1,3,4-oxadiazole (98%) (OXD, 10) were purchased from 1. Available literature values are also shown. There is Aldrich. Other CTM were supplied from Kodak stock. 3-Nisatisfactory agreement between our results and the literature. trobiphenyl (99%), used as a dipole moment standard, was We comment briefly on the interpretation of the dipole moments purchased from Aldrich. The polystyrene was Dylene 8X Beads in terms of group dipole moments and molecular conformations from Sinclair-Koppers. The bisphenol A polycarbonate was before addressing the correlation between dipole moment and Makrolon from Mobay Chemical. mobility in section 4. Dipole Moments. Dipole moments were evaluated from the Triarylamines. Triarylamines 1.1 ( P A ) and 1.2 (TTA) have dielectric constants and refractive indices of solutions of the been the subjects of several investigations.' Compounds 1.3 compounds of interest in nonpolar solvents. The concentrations and 1.4 were intended for studies of molecular conformation ranged from 0.001 to 0.1 m o a . The refractive indices were and packing, respectively. Triarylamines 1.5-1.8 were intended measured with an AbbB refractometer. The dielectric constants for studies of the effect of dipole moment on charge transport were measured via the capacitance of a cylindrical capacitor in chemically related compounds. Triarylamines 1.6 and 1.7 (Type DFL-1 sample holding cell, Kahl Scientific Instrument were intended for a study of which factor is more important, Co.) filled with the solution of interest. Water from a constant the number of polar substituents or the net dipole moment. temperature bath was circulated through a built-in jacket to The triarylamines 1.1-1.4 would have no net dipole moment maintain the temperature of the capacitor at 25.0 "C. The if their conformations in solution were that of a symmetric capacitance at 10 kHz was measured using a General Radio propeller (C3 symmetry with coplanar N-C bonds). Pyrami1689 Precision Digibridge. dalization of the nitrogen (as in dimeth~laniline~~) would result Before each series of measurements, the capacitance was in a dipole moment along the C3 axis. Unequal N-C bond measured with the cell filled with air and with toluene. The lengths and/or unequal tilts of the aryl rings around the N-C measured values were used to calibrate the capacitance of the bonds would result in a dipole moment in the plane of the three empty cell and evaluate that of the electrical leads. For each N-C bonds. All three features are evident in the single-crystal compound, typically five different concentrations were evaluated structures of TPA (1.1) and TTA (1.2).55,56 Thus, the direction in order of increasing concentration. At each concentration, of the net dipole moment is unknown and may vary if the the capacitance of the solution-filled cell was measured repeatconformation of the molecule varies in solution or in a edly, usually until the values obtained with at least three molecularly doped polymer. successive aliquots agreed within 0.03%. Not surprisingly, alkyl substituents in the para positions The solvent was usually toluene (Spectrograde, Eastman hardly affect the dipole moment (1.1, 1.2, 1.4), nor do the Kodak Co.). p-Xylene (99+%, Aldrich) was occasionally used sterically more significant ortho methyls in 1.3. It is possible, with solutes of small dipole moment in order to eliminate any of course, that the various kinds of asymmetry, mentioned above, effect of the nonzero moment of toluene (0.4 D, refs 49, 50). vary in such a way that the net dipole moment is fortuitously The data were analyzed by Guggenheim's a d a p t a t i ~ nof ~ ~ , ~ ~constant. Triarylamine 1.7, with three para-Br substituents, has a smaller dipole moment than 1.6, with one para-Br; evidently Debye's theory.53 Guggenheim's principal contribution was the the group dipole moments associated with individual bromoassumption that the atomic polarizabilities of the solute and the phenyl rings nearly cancel. solvent are in the same ratio as their partial molar volumes. The quantity (n2 2)-' - ( E 2)-l was plotted vs molar In any of these compounds, it is possible that various concentration of the solute. The slope of a least-squares fit was conformations with differing dipole moments coexist and that the measured dipole moment is a suitable average.57 When the identified as 4nNf12/(27kT), with Na as Avogadro's number. The reproducibility of the method was monitored by repeated molecule has two or more moieties that are linked so flexibly measurements on 3-nitrobiphenyl. Seven values obtained by that their orientations are independent, the measured dipole six different operators over a period of three years varied by moment p is related to moments of the independent moieties, only 7%; the average (3.96 D) agrees well with literature values pi, by (3.93 D, 4.12 D, ref 49). Hole Mobility. Hole mobility was measured by the standard p =( c p y time-of-flight experiment.' Each sample was a film, -10 p m i thick, coated from solution in dichloromethane. The polymer and the CTM were predried and then coated under dry nitrogen. just as if the moieties were present as independent molecules. The substrate was a poly(ethy1ene terephthalate) sheet coated In ESTER (lS),for example, it is likely that the triarylamine with a semitransparent Ni electrode layer and a -0.3 pm charge(0.85 D) and ethyl propionate (1.8 D, ref 49) groups are generation layer of amorphous selenium. A semitransparent Au independent in this sense. The value predicted using eq 1, 2.0 electrode was deposited onto the sample. The thickness of a D, agrees quantitatively with the measured value. (It would sample was evaluated from its capacitance. A relative dielectric also agree, however, for a geometry in which the two contribuconstant of 3.0 was used for consistency with previous studies. tions to the dipole moment are rigidly perpendicular.) On the other hand, in the less flexible compounds 1.6 and 1.8, the A potential was applied between the Ni and Au electrodes. orientation of the C-Br bond (1.6 D, ref 58) or the nitro group A flash of light generated holes in the selenium layer. The (4 D, ref 58) is probably correlated with that of the triarylamine applied potential drew the holes into and through the sample. moiety. Each measured dipole moment would then be the The current induced in an external circuit was monitored. A magnitude of a vector sum of the two components, appropriately typical current transient consisted of an early spike, a plateau, averaged over conformations and adjusted for the conjugated and a tail. The transit time of the holes was identified by the interaction of the nitrogen with the bromo or nitro group. The crossing of tangents drawn to the plateau and the steepest part
+
+
4232 J. Phys. Chem., Vol. 99, No. 12, 1995
Young and Fitzgerald
TABLE 1 dipole moment (P) experimentb (literature)
structure
Q
R-h
structure
dipole moment (P)
0.87 (0.26-0.72') (0.7od) (0.66cJ)
0.91 0.828 (0.859
0.588
0.738
1.98
2.609
1.3
0
II
1.5 (ESTER)
1.04
b
1.41
RmR
5.79
I
R
R
2.04
2.2
1.568
@
&R=*N R'
4.1 p-pEFTP
Q
1.918 1.978
1.52
7N
1.79
1 5.1 (TPM)
L
1.35 1.20
0.748
0.809
1.858
5.2 (MPMP)
7.1 (NIPC)
Dipole Moments of Hole-Transporting Materials
J. Phys. Chem., Vol. 99, No. 12, 1995 4233
TABLE 1 (Continued)
structure
dipole moment (D") experimentb (literature)
@Q 7.2
structure
dipole moment (Do)
3.32 (3.13h) 0 (DEH)
a 1 Debye = 3.34 x C m. Measured in toluene unless otherwise noted. Reference 49. Reference 78. Reference 54. f Values ranging from 0.13 to 1.95 D have been obtained by various methods; see references 79 and 80. g Measured in p-xylene. References 24 and 26.
fact that the net dipole moment of 1.8 (5.8 D) is much larger than that of TTA (1.2) plus that of a nitro group presumably results from such an interaction. Oligomeric Triarylamines. In TAPC (2.1, 1.4D), TTB (3.1, 1.6D), and TPD (3.2, l.SD), if the two triarylamine groups were independent, the measured dipole moments should each be 2/2 times as large as that for TTA (1.2), namely, -1.2 D. Similarly, for p-pEFTP (4.1) the values are 1.9 D measured vs 1.5 D predicted; for the tetrameric compound 2.2 they are 2.0 D measured vs 1.7 D predicted. The somewhat larger experimental values may stem from incomplete independence of the orientations of the triarylamine group dipole moments. (For TTB and TPD, conjugation between the triarylamine groups may also contribute.) Given that the direction of the dipole moment of a single triarylamine group is unknown, this rationalization is somewhat speculative. Whatever the orientation of the dipole moment of a single triarylamine group, for compound 2.2 it is highly likely that the two pairs of triarylamine groups on opposite ends of the pentane chain are independent and that the two groups in a pair are correlated in the same way as in TAPC (2.1). If so, the dipole moment of 2.2 (2.04 D) should be 2/2 times that of TAPC (1.41 D). The predicted value, 2.0 D, is identical to the observed. Dialkylarylamines. The dipole moments of the dialkylarylamine compounds are more properly interpreted as vector sums of (more or less) rigidly oriented (dialky1amino)phenyl group dipole moments than in terms of orientationally independent group moments. If the group moments in the oligomeric triarylamines are indeed independent, the reason for the difference from the dialkylarylamines is presumably that the orientations of the group dipole moments relative to the saturated molecular skeleton (or the central benzene ring, in the case of p-pEFTP) are different in the two cases. The dipole moment of a 2-methyl-4-(diethylamino)phenyl group is -1.6 D, roughly parallel to the Ph-N bond.59 The reported dipole moment of tri~henylmethane~~ is -0.4 D and presumably parallel to the C-H bond (Phs--H6+).60 The dipole moment of TPM (5.1) should be the vector sum of the dipole moment of the parent triphenylmethane (0.4 D) and two additional 1.6 D contributions directed along the two Ph-N directions. The predicted magnitude, 1.65 D, is in reasonable agreement with the measured value, 1.8 D. (If we had assumed that the dipole moments are independent, eq 1 would have given too large a value, 2.3 D.) Nevertheless, the dipole moment of the 2-methyl-4-(diethylamino)phenyl group probably has a
significant component perpendicular to the phenyl ring,59 and the orientation of that component is probably subject to some fluctuation. In MPMP (5.2), the third phenyl ring has a methyl substituent with a group dipole moment of 0.4 D.58 The resultant of two 1.6 D and two 0.4 D moments (one representing the triphenylmethane skeleton), all at tetrahedral angles, is 1.40 D. This predicted value agrees well with the measured value, 1.3 D. A priori, the dipole moment of 6.1 (0.74 D) ought to be the same as that of N,N-diethylaniline (1.8 D, ref 49). It is puzzling that the actual moment is less than half as large. Given the distal location of the diethylamino group, it seems unlikely that steric factors can account for the discrepancy. Nevertheless, the value for 6.2 can be rationalized as the resultant of two group moments, each equal to that of 6.1 and each directed along a Ph-N bond. The magnitude of the resultant, 0.85 D, compares well with the measured value, 0.80 D. Other. The difference in the dipole moment between N-isopropylcarbazole (7.1, 1.8 D) and N-phenylcarbazole (7.2, 1.4 D) is comparable to the difference between trimethylamine (0.9 D, ref 49) and N,N-dimethylaniline (1.6 D, refs 49, 61). This comparison is necessarily rough because the geometry around the nitrogen, including the degree of planarity, varies. The dipole moment of OXD (10) can be rationalized, at least roughly, in terms of those of N,N-diethylaniline (1.8 D, ref 49) and dimethyloxadiazole (3.3 D, ref 49). We neglect the degree of nonplanarity of the diethylaniline and assume, concerning the oxadiazole, that (a) the dipole moment has the orientation N"-.*@+, (b) the contribution of the methyl groups is negligible, and (c) the ring is a regular pentagon. The predicted dipole moment is 4.4 D; the measured value is 5.2 D. Although we make no attempt to analyze the dipole moments of DEH (8) and DEASP (9), we note that they contain two or more polar groups apiece.
4. Correlation of Hole Mobility with Dipole Moment Sugiuchi et al.,24-26and later Kanemitsu and S~gimoto,~' have found a remarkable correlation of the magnitude of the hole mobility in a molecularly doped polymer with the dipole moment of the CTM. In Figure 1 we display a similar correlation for some of the CTM listed in Table 1. As in the first studies, the binder is bisphenol A polycarbonate, but for reasons of limited solubility, the proportion of CTM is 30 wt % rather than the previous 50%. The two most polar materials, DEASP and DEH, appeared in the previous studies. The data represent the mobility in the limit of zero-field strength; a plot
Young and Fitzgerald
4234 J. Phys. Chem., Vol. 99, No. 12, 1995 1o
- ~
I
I
TTA
1 o-6
I
I
1
I
I
I
TAPC
(ESTER)
n
0
m
>
>
’
0 IO-’ E
DEH
TPM ‘ESTER
v
3 1 o-&
6.2’
DEASP
’
6.1’ 1o
- ~
I
1
I
I
I
I
I
I
0 . 0 0 . 5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4 . 5
P (D) Figure 1. Semilogarithmic plot of the hole mobility at room temperature and zero field, p , vs the dipole moment of the charge-transport molecules (CTM).Solid circles represent 30 wt % of each CTM in a polycarbonate binder. Open circle represents ESTER at the same molar concentration as that of TTA. Structures are identified in Table 1.
at 20 V/pm is very similar. With the exception of the two tetraarylmethanes (6.1 and 6.2), a reasonable correlation again exists between the zero-field mobility and the dipole moment of the CTM. Similar data at 30 and 50 wt % in both the polycarbonate and polystyrene and at 100% as neat molecular glasses are collected from the literature in Table 2. Similar overall correlations of mobility and dipole moment exist in each case. The data in Figure 1 and Table 2 suggest that the hole mobility in various CTM, at a given weight fraction, is usually determined largely by the net dipole moment of the CTM. This suggestion, if correct, is surprising in light of the other ways in which the various CTM differ. Without impugning the correlation displayed in Figure 1 and Table 2, as well as in the data sets of Sugiuchi et al.24-26and Kanemitsu and S~gimoto,~’ we now discuss the difficulties involved in constructing an “equitable” comparison of such disparate materials. (1) The mobility in a given CTM is generally a strong function of its concentration,’ presumably because electrontransfer matrix elements depend strongly on intermolecular distance. For CTM with the same active moiety, therefore, it makes more sense to compare at equal molar concentrations than at equal weight fractions. For instance, the triarylamines TTA (1.2) and ESTER (1.5) should presumably be compared at, say, 39% ESTER and 30% TTA. In fact, increasing the molar concentration of ESTER to equal that of TTA (open circle, Figure 1) improves the correlation. The correlation at equal weight fractions (Figure l), in this case, is not too bad, in part because the electrically inert portion in ESTER is not too massive and in part because the 6 x effect of unmatched molar concentrations is much smaller than the overall range (> 100fold) of zero-field mobilities. Additional examples of electrically inert matter for which the concentrations presumably ought to be compensated are the unsubstituted and methyl-substituted phenyl rings in 6.1, 6.2, TPM (5.1), and MPMP (5.2), the cyclohexyl ring in TAPC (2.1), and other alkyl substituents. The molecular weights of the CTM represented in Figure 1 range over a factor of -2 (287 for TTA, 415 for TPM, 467 for DEASP, 627 for TAPC); therefore, so do the molar concentrations. Some of the heavier molecules display the lower
mobilities. Hence, some of the trend displayed in Figure 1 might be ascribed to a dependence on concentration rather than dipole moment. (The correlations in refs 24-27 do not appear to be confounded by this factor.) The issue of molar concentration is complicated, however, by the following consideration. (2) Depending on how many equivalent, nonconjugated donor moieties they contain, some CTM can be regarded as “monomeric” (TTA (1.2), ESTER (lS),and compound 6.1), and others as “dimeric” (TAPC (2.1), TPM (5.1), MPMP (5.2), and compound 6.2). DEH (8) and DEASP (9), with two or three different donor groups, fit neither category; likewise, TTB (3.1) and TPD (3.2), each with two conjugated donor groups. For closely related monomeric and dimeric CTM, it is more reasonable to compare mobilities at equal monomer concentrations than at equal weight fractions. In the case of TTA and TAPC, there is little difference: equal concentrations of triarylamine “monomers” correspond to roughly equal weight fractions of the CTM in the molecularly doped polymer. Although the molecular concentrations of TTA, DEH, and DEASP decrease in that order, the “monomer” concentrations for DEASP and perhaps DEH (depending on whether both donor groups contribute to charge transport) are higher than those of TTA. Hence, it is not particularly likely that the correlation in Figure 1 actually represents a trend in concentrations. (3) It is not obvious how the mobility in CTM with different n electronic structures should compare, especially with n systems of very different extents (7 atoms in each “monomer” in TPM (5.1), 19 in TTA (1.2) or ESTER (1.5)). In fact, the mobilities in TPM and ESTER are comparable, even though the molar concentration of diethylaniline groups corresponding to TPM in Figure 1 is 1.8 times the concentration of triarylamine groups corresponding to ESTER, and the molecules have comparable dipole moments. At equal monomer concentrations (17% TPM, 30% ESTER), the mobility in TPM would be much In this case, it appears that a comparison at equal weight fractions entails a compensation between the smaller extent of the n systems in TPM and the higher concentration of those systems. (A quantitative assessment of the compensation should incorporate a correction for the “dead weight” of the unsubstituted phenyl ring in TPM and the alkyl groups in both CTM.) So far, we have addressed questions of molecular and monomer concentration for the charge-transporting donor moieties. There are analogous issues connected with the concentration of dipolar species. (4) In molecularly doped polymers containing small amounts of a highly polar third component, the greater the concentration of the third component, the more the mobility of holes is d e p r e s ~ e d . ~ ~ Presumably, * ~ * - ~ ~ the effect of the dipole moment of a CTM is a similar function of concentration. (This dependence has been verified in a comparison of TTA (1.2) and ESTER (1.5) at various concentration^.^^) Thus, the comparison of various CTM is affected by differences in molecular weight. For the CTM in Figure 1, in fact, the most polar molecule (DEASP) is also one of the heavier and, therefore, less concentrated. Hence, the comparison in Figure 1 tends to underestimate the effect of CTM dipole moment. ( 5 ) It is not obvious a priori that the mobility should correlate with net dipole moment, rather than group dipole moments, especially when the groups are as large as a diethylaniline or a triarylamine. To carry the argument to an extreme, imagine a molecule with two donor groups connected by a long, rigid, saturated hydrocarbon bridge. Certainly, the important factor would be the dipole moments of the individual groups, not their resultant. In this context, it is worth recalling from section 3
Dipole Moments of Hole-Transporting Materials
J. Phys. Chem., VoE. 99, No. 12, 1995 4235
TABLE 2: Dipole Moments (p), Room-Temperature Mobilities in the Limit of Zero Electric Field @), Parameters of the Gaussian Disorder Model (a and PO),and the Temperature-DependenceFactors of the Model, exp(-(2a/3kT)*), for Various Charge-Transport Molecules (CTM) ref
P (D)
TAPC DEH
74 16 15
0.9 1.4 3.3
MPMP DEASP
10 71
1.3 4.3
TTA MPMP
34 10
0.9 1.3
ESTER DEH DEASP
63 15 71
2.0 3.3 4.3
lTA
74 16 16 10 15 71
0.9 1.4 1.4 1.3 3.3 4.3
MPMP
75 75 10
1.4 0.9 1.3
DEH DEASP
15 71
3.3 4.3
TAPC P-PEFTP
76 64 38 39 37 77
1.4 1.9 1.6 1.3 3.3 4.3
CTM ‘ITA
TAPC (TAPC, 55%) MPMP DEH DEASP (TAPC, 55%) ‘ITA
TTB
MPMP DEH DEASP
u (m eV) exp(-(2~/3kT)~) 30% CTM in Polvcarbonate 115 1.1 x 10-4 119 5.8 x 10-5 124 2.5 10-5 126 1.8 x 10-5 134 4.2 x 138 2.0 x 10-6 30% CTM in Polystyrene 85 6.9 10-3 114 1.3 x 10-4 122 3.5 x 10-5 103 6.7 x 10-4 129 1.1 x 10-5 140 1.4 x 50% CTM in Polycarbonate 108 3.2 x 10-4 118 6.8 x 115 1.1 x 10-4 130 8.8 x 10-6 129 1.1 x 10-5 132 6.1 x 50% CTM in Polystyrene 76 1.9 x 78 1.5 x 129 1.1 x 10-5 134 4.2 x 132 6.1 x 133 5.1 x 100%CTM (Binderless) 73 2.5 x lo-* 2.1 x 10-2 75 76 1.9 x 108 3.2 x 10-4 100 5.8 x 10-4 117 8.0 x 10-5
that highly flexible molecules with multiple polar groups (e.g. compound 2.1) can have larger dipole moments than their “monomeric” analogs (e.g. TTA, 1.2) simply as a consequence of averaging over random configurations rather than any systematic alignment of group dipole moments (such as was invoked above for TPM and OXD). (6) The comparison between TPM (5.2) and compound 6.2 illustrates that other factors can matter. The mobility in 6.2 is about 12 times lower than that in TPM at equal weight fractions. Each compound contains two (diethy1amino)phenyl groups connected by a saturated carbon. The dipole moment of 6.2 (0.8 D) is considerably smaller than that of TPM (1.8 D). Compound 6.2 contains more electrically inert matter, and its molecular weight is higher, but bringing the two to equal molar concentrations (33.5 wt % 6.2,30 wt % TPM) would not change the ratio of mobilities significantly. The additional facts that (a) the dipole moment of 6.2 is much smaller than that of TPM, despite their very similar structures, and (b) the mobility in 6.2 is not much greater than that in 6.1 at comparable concentrations suggest that these molecules are affected by some rather unusual factor, perhaps steric. (7) The binder contains carbonate groups, which are moderately polar. An advantage of comparing at equal weight fractions of CTM is that the concentration of these groups is constant. A comparison at equal molar or moiety concentrations would generally be complicated by variations in the concentration of such groups. A relatively nonpolar binder, such as polystyrene, would be preferable for such a comparison. An alternative comparison that sheds some light on these issues is shown in Figure 2, in which the zero-field mobilities
PO (cm2/(VSI) 5.5 x 10-2 1.9 x 5.5 10-3
P ( c m W s))
6.6 x 2.1 x 10-2 7.7 x 10-3
3.4 x 1.2 x 1.4 1.2 x 9.1 x 1.6 x
1.5 x 8.5 x 9.2 x 3.3 x 10-3 8.1 x 10-2 1.6 x
1.1 x 10-4 1.3 10-5 3.8 x 2.4 x 8.6 x 2.4 x
1.5 x 10-1 6.0 x 7.0 x 1.4 x lo-’ 2.5 x 1.2 x 10-2
4.7 x 4.8 x 7.7 x 1.2 x 2.7 7.4 x
10-5
5.6 x 5.9 x 9.2 x 7.5 x 3.7 x 1.5 x
1.1 x 9.2 x 1.2 x 3.9 x 2.3 x 8.3 x
10-3 10-4 10-5 10-6 10-7
5.4 x 1.0 x 5.6 x 3.6 x 1.3 x 3.8 x
10-3 10-3 10-4 10-4
1.9 x 7.6 x 2.5 x 4.9 x 1.4 x 5.7 x
10-2
10-l 10-1 10-2 10-1 10-1 10-3 10-3
10-6 10-6 10-7 10-7 10-8
10-6 10-6 10-7 10-8
10-7
in five triarylamine derivatives are plotted vs their dipole moments. For this comparison, polystyrene is used as the binder so that the principal polar component is the triarylamine compound, and the molar concentration of triarylamine groups is the same in each case. The mobility in the “monomeric” triarylamines with polar substituents and larger dipole moments (ethyl propionate in ESTER (lS),bromine in 1.6) is again considerably lower than that in TTA (1.2). (The fact that it is no lower in 1.6 than in ESTER deserves further study.) However, the mobility in the oligomeric triarylamines TTA (1.2), TAPC (2.1), and 2.2 does not decrease with increasing dipole moment or decreasing molar concentration of (oligomeric) molecules, even though 2.2 has approximately the same dipole moment as ESTER. The fact that the mobility actually increases somewhat can be ascribed to a slight decrease in disorder with increasing degree of clustering, as will be described elsewhere. In this comparison, the mobility is determined by the concentration and dipole moment of the donor (triarylamine) groups rather than the concentration and net dipole moment of the whole molecule. Such information may be obscured in plots like Figure 1 that encompass several chemical classes. The present comparison of TTA, TAPC, and compound 2.2 is extreme in one way: The weight fraction of CTM is roughly constant, but the concentration of dipolar molecules decreases 4-fold across the series. One could argue that this decrease counteracts the increase in molecular dipole moment. (The molecular concentrations represented in Figure 1 vary by much less.) Another special feature of the series TTA, TAPC, and 2.2 may be that the dipole moments increase across the series TTA, TAPC, and 2.2 largely as a consequence of tying
4236 J. Phy Chem., Vol. 99, No. 12, 1995
Young and Fitzgerald
1 0-2
1o
- ~
n
1 D) group dipoles as molecules. This fact is certainly more important for rationalizing the “anomalously” high value of B than the difference between the group moments and the net moment that has been invoked b e f ~ r e . In ~ ~fact, , ~ ~that difference is quite small (-1.6 D vs -1.3 D). The value of u for MPMP is also found to be “anomalously” large in the molecularly doped polymers. In particular, at 30% in polystyrene, ESTER has a much smaller value of u (0.103 eV) than does MPMP (-0.118 eV), even though the dipole moment of ESTER exceeds both the group and the net dipole moments of MPMP. Again, it appears that the group dipole moments (and their relatively high concentration) are important factors. Regardless of whether group or net dipole moments are important to determining the value of u, it is problematic that this parameter is sensibly independent of binder (i.e.,the same in polystyrene and in the polycarbonate) for DEH and DEASP at both 30 and 50 wt % and for MPMP at 50%, whereas it depends strongly on the binder for TTA and for TAPC. The latter difference is most easily rationalized as an effect of the dipole moments of the carbonate groups.10-12,37If the CTM and the binder contribute independent random amounts to the site energies, with root mean square widths u m and Obbinder, the overall width u should satisfyl1-l4
‘
= ‘CTM
-k
‘binder
(5)
If u m is the same in both binders, uz should be larger in the more polar binder by an amount equal to the difference in
u2bbder. The order of magnitude of the difference in u2bbder is established by that for TTA: 0.006 (eV)2at 30 wt % and 0.0055 (eV)? at 50 wt %. If the same value applied to DEH, DEASP, and MPMP (at 50 wt %), u2 would be larger in the polycarbonate than in polystyrene by -0.020 eV in each case. Now, Ubmder probably varies from one CTM to another, and u m may change if the packing of CTM is different in the two binders. Even so, it seems most likely that the DOS is always considerably wider in polycarbonate than in polystyrene. Yet, the width parameter u, inferred via the GDM from the temperature dependence of the mobility, is independent of binder in these cases. This fact is most eadily interpreted as a failure of the GDM, perhaps because the DOS is not adequately Gaussian. Borsenberger and Schein have proposed that part of the energetic disorder in DEASP-doped polymers arises from random intramolecular charge-dipole interaction^.^^ Such interactions are likely to give a DOS that is very far from Gaussian, as illustrated in the Appendix. It is also likely that the different donor moieties in DEASP would have somewhat different ionization potentials even if they did not interact.71If so, the GDM representation by a single Gaussian DOS is questionable. Both arguments might apply also to DEH, and the first argument to MPMP (depending on the degree to which the group dipoles do not have rigidly fixed directions). Hence, it would not be surprising if the DOS for DEASP and DEH (and perhaps MPMP) deviated markedly from Gaussian. Contrary to the notions in ref 71, however, the argument surrounding eq 4 indicates that the DOS should nevertheless be wider in the polycarbonate than in polystyrene, regardless of whether it is Gaussian. It is puzzling, therefore, that the “observed” u’s, i.e. the strengths of the temperature dependences, are completely independent of binder in these cases.
6. Other Models Two other mechanisms might explain the correlation between dipole moment and mobility. First, the dielectric constant of the molecularly doped polymer may be increased by the presence of highly polar CTM, and the result may be an enhanced polaron-type contribution to the activation energy for hopping. Such a mechanism has been proposed for the effect of varying binders by Duke and MeyeP7 and Kanemitsu and Einami?8 and it was invoked by Vannikov et al.28-32 to explain the effect of highly polar additives on hole mobility in triphenylamine-doped polystyrene. In a system similar to the latter, we have found that the proposed effects were much too small to explain the observed decreases in mobility and increases in activation energy or Yamaguchi et al. have drawn a similar conclusion for the effect of a polar binder.44 Thus, this mechanism seems unlikely to explain the analogous effects of polar CTM. A second mechanism is the dipolar trap model of Sugiuchi et al.24-26and Novikov and V a n n i k o ~ . ~In- ~essence, ~ it asserts that an occasional CTM site can become a trap because the charge-dipole interaction with a neighboring CTM reduces the site energy. This model may be viewed as an alternative limiting case of energetic disorder in which the site energy is dominated by interaction with one neighbor rather than the net influence of several neighbors. In our study of polar additives, we found that the dependence on the concentration of the additive was inconsistent with the predictions of this It is dubious, therefore, that this dipolar trap model applies to the effect of dipole moments associated with the CTM. Novikov and Vannikov have recently proposed a more elaborate version of the dipolar trap model in which the chargedipole part of the site energy ( E , our notation) is determined by
Young and Fitzgerald
4238 J. Phys. Chem., Vol. 99, No. 12, 1995 interaction of a charge with all of the dipoles They used the dipolar lattice model of Dieckmann et to evaluate the probability distribution for E, and they gave an approximate analytical expression for the distribution. Under conditions appropriate to a polar CTM in a moderately polar binder, the distribution is Gaussian. They proposed that the relatively few sites with large E (of the proper sign) are traps, but that for most sites E is small enough to be neglected. This model gives a distribution of trap depths, but they used a single effective trap depth that is a constant multiple (-3) of the root mean square width of the trap distribution. If the dipole moment of the CTM (p) is large enough to dominate that of the polymer, the trap depth (A, our notation) would be proportional top, say A = ap. All other things being equal, in the presence of dipolar traps, the mobility then has the form P(T) = Mom exp(-“
= Mo(T)exp(-q/kT)
j z ‘exp(-E/kT)ciPi(c)
de, i =for t
Pf
1 + (cJc,)F(T)
F(T) = lPt(E)e-dkTdc/jPf(E)e-”kT de
-NkT
-112
exp(-e2/2a,2)
(14)
A simple calculation yields7*
(16)
(7)
Thus, the effective trap depth is temperature dependent and proportional to the square of at, rather than being a constant multiple of ut, as assumed by Novikov and Vannikov. For ct = cf, this model is very similar to how Novikov and Vannikov model their distribution of traps. (The distribution in eq 14 adds “trap” states near E = 0, but these states have no obvious effect if at is large enough that their occupation probability is low.) Since their calculation shows that ut is proportional to the dipole moment of the CTM (p), it appears that the dipolar trap model predicts a quadratic dependence of the In ,P on p. rather similar to that in eq 4.73 A third problem with the dipolar trap models in general concerns whether sites can ever properly be separated into “freecarrier sites” whose energies are unaffected by charge-dipole interactions and “trap sites”. Most likely, this issue can be resolved only be detailed calculations on specific models.
(8)
(9)
(10)
(11)
When both the free-carrier and the trap sites have energy distributions that are narrow compared to kT, we would have
P/Pf = (cdct)e
P ~ ( E > =( 2 n q2
A = ‘/2kT(aJkT)2
When the effect of traps is severe, the denominator in eq 9 is large, and a good approximation is
P/Pf = cdctF(T)
Finally, consider the case of a sharp free-carrier level at energy E = 0 and a Gaussian distribution of trap levels also centered at E = 0,
(6)
+
1
(13)
(15)
The trap-limited mobility @) is jointly proportional to the freecarrier mobility @f) and the fraction of charge carriers that are free at any time, n$(nf nt). A brief calculation yields
E=
A = kTln F(T)
F(T) = exP(1/2(04kT)2)
where Mo(T) is the same for all CTM. This form indicates a linear dependence of In p on the dipole moment of the CTM (at constant temperature), as is observed, rather than the quadratic dependence predicted by eq 4. This treatment has three interconnected problems. First, it is hard to distinguish this version of the dipolar trap model from the GDM, which gives eq 4 instead of eq 7. For example, if there is no energetic disorder except that created by the dipoles, then this model has a Gaussian distribution of site energies, exactly as in the GDM. Now, the GDM incorporates certain ancillary assumptions, and it is conceivable that other ancillary assumptions would alter eq 4 in the direction of eq 7. It is clear, in any case, that eq 7 is not correct in general. A second problem concerns the choice of “effective trap depth” to represent a broad distribution of trap levels. Consider a system containing “free-carrier” sites and trap sites. Let their concentrations be cf and ct, and their distributions in energy be P ~ Eand ) Pt(c), both normalized to unity. By the site energy, we mean the energy of a bulk sample of the material when a single charge carrier occupies that site. With this convention, traps are low-energy sites for either electrons or holes. We assume that the concentration of charge carriers is low, so that the probability of occupation of a site of energy E is Z-’ exp(-dkQ, where Z is a normalizing constant. The concentrations of free and trapped carriers, nf and nt, are given by
ni =
where A is the distance between these levels (Le., the trap depth). For wider distributions of site energies, the effective trap depth that makes eq 12 work is
(12)
7. Summary and Concluding Remarks We have measured the dipole moments of various holetransporting materials (see Table 1). Our data supplement those of Sugiuchi and co-workers and agree well with them for the three compounds in common. Dipole moments of electrontransporting materials will be discussed in future reports. For the triarylamines, the dialkylarylamines, and the oxadiazole derivative (OXD), the measured dipole moments could be rationalized in terms of group dipole moments and molecular conformations. The small dipole moments of the tetraphenylmethane derivatives 6.1 and 6.2 are a puzzle. We have investigated briefly a reported correlation between the hole mobility at room temperature and the dipole moment of the charge-transporting molecules (CTM). We find similar correlations (Figure 1 and Table 2). The correlations are at constant weight fraction of CTM in a common polymer binder. It is remarkable that such a correlation exists across several chemical classes, with CTM of different molecular weights, numbers of electron-donor moieties, degrees of conjugation between the moieties, extents of the z systems of the individual moieties, and compositions of the net dipole moment from group moments. The overall correlation with the dipole moment must entail a compensation among some of those factors. The correlation is not without exception, however. The tetraphenylmethane derivatives, 6.1 and 6.2, fall far below the trend line established by the other CTM. Temperature-dependence data on several CTM offer a closer look at the underlying physics. Analysis of these data using the Gaussian disorder model (GDM) of Bassler and cow o r k e r ~ suggests ~ . ~ ~ that, in most cases, much of the variation in the mobility is a consequence of variations in the degree of
Dipole Moments of Hole-Transporting Materials energetic disorder, which tends to increase with increasing dipole moment. Nevertheless, (a) the prefactor mobility (representing a hypothetical material with no energetic disorder) also varies considerably and rather nonsystematically, (b) there is reason to suspect that the group dipole moments of the individual donor moieties are at least as important as the net moment in determining the degree of energetic disorder, so that it becomes hard to connect trends in energetic disorder with the observed correlation of the room-temperature mobility with net dipole moment, and (c) intramolecular disorder and the presence of two or more chemically distinct donor species in some molecules are likely to lead to non-Gaussian distributions of site energies. Again, it appears that the overall correlation with net dipole moment involves several compensating andor complementary effects. Much of the difficulty in dissecting the connection between dipole moments and charge-carrier mobility stems from the chemical diversity of the CTM investigated to date. Differences in ,DO, for instance, may represent differences in n electronic structure or packing proclivities. Differences in u may represent differences in the sensitivity of a given n system to other sources of disorder, such as the charge-induced dipole interaction that has been proposed for nonpolar s y ~ t e m s . 4 ~(A* site ~ energy of a charge carrier that is delocalized over several moieties, as perhaps in TTB or TPD, is an average over the “site energies” that would characterize the individual moieties. The distribution of such an average should be narrower than the distribution of “site energies” of the individual moieties.) Moreover, some of the CTM have two donor groups, those groups potentially have different solid-state ionization potentials (DEH or DEASP), and the difference would confound the interpretation of temperaturedependence data in terms of a single Gaussian distribution of site energies. The effect of dipole moment could be investigated more easily with sets of CTM that contain only one kind of donor group and are as similar as possible except for differences in dipole moment. In a companion paper we report a detailed comparison of two such CTM, the monomeric triarylamines TTA and ESTER.63
Acknowledgment. We thank D. A. Chen, J. E. Kaeding, M. Lodolini, J. A. Sinicropi, and D. S. Weiss for chemical syntheses; L. B. Schein and D. Terrell for additional materials; T. D. Binga, J. Chambers, K. S. Kohl, M. C. Margevich, E. Roscoe, J. A. Sinicropi, and K. R. Wemer for dipole moment measurements; and N. L. B e h a p , D. K. Chow, W. E. Gefell, L. F. Jones, S. J. Lenander, E. Roscoe, L. M. Salatino, and K. R. Wemer for mobility measurements. Helpful conversations with H. Bassler, P. M. Borsenberger, J. I. Brauman, W. Kohler, and J. M. Pochan are gratefully acknowledged. Appendix. Intramolecular Dipolar Contribution to the Distribution of Site Energies Borsenberger and Schein7’ have pointed out the possibility of intramolecular dipolar contributions to the distribution of site energies (DOS). Here we evaluate the form of this contribution for two simple models of a molecule containing an occupied charge-transport site (modeled by a point charge q) flexibly linked to a polar group (modeled by a point dipole p at a fixed vector distance r from the charge). The shift in energy of the transport site (E) is given by
J. Phys. Chem., Vol. 99, No. 12, I995 4239 where P and fi are unit vectors parallel to r and p, K is a relative dielectric dielectric constant, and EO is the permittivity of free space. The use of a point charge, a point dipole, and a macroscopic dielectric constant for an intramolecular effect renders the calculation qualitative at best, but the qualitative conclusions are significant. The probability density for E is denoted P(E). In the f i s t model, the dipole has an equal probability of pointing in any direction (isotropic distribution). Let 6 be the angle between r and p, so that E = -A cos 6 . The probability that the angle be between 6 and 6 BO is ‘/2sin 6 66. The probability that the energy be in the corresponding interval between E and E BE is P(E) 6~ = ‘/2sinO BO. Hence P(E) ddd6 = It2 sin 6, and P(E)is given by
+
+
Thus, the distribution of intramolecular contributions to the site energy is constant over the allowed range of E. In the sec2nd model, the dipole makes a constant angle p with an axis b, while its component normal to b has a uniform distribution of directions. The dipole might represent a polar group having a fixed F g l e with a bond and free rotation around the bond direction (b). The angle between P and the bond direction is a. It is convenient to introduce a ?artesian coordinate system such that the z-axis is parallel to b, and f lies in the xz-plane. The projection of p onto the xy-plane has a magnitude p sin p and makes an angle q5 with the x-axis. All values of q5 between 0 and 2n are equally probable; the probability density is 1/2z A simple calculation gives.
= cos a c o s p
+ sin a s i n p cos 4
(19)
From eq 17a, the average E is Z = -A cos a cos p and the range of E extends from Z - A to Z A, where A = IA sin a sin PI. An argument like that for the f i s t model gives P(c)(dc/dq51 = 1/(2n). (The absolute value is required when E is a decreasing function of 4.) A straightforward calculation gives
+
P ( E )= (23t)-l[A2 - ( E -
for F - A I F I F
+A (20)
The distribution of intramolecular contributions to the site energy is U-shaped, with a minimum at E = Z and tending to infinity at the end points of the range of allowed values, E Z f A. In neither case does the distribution resemble a Gaussian distribution. To the degree that intramolecular dipolar contributions to the distribution of site energies (DOS) are important, the DOS will also deviate from Gaussian.
-
References and Notes (1) Borsenberger, P. M.; Weiss, D. S. Organic Photoreceptors for Electrophotography; Marcel Dekker: New York, 1993. ( 2 ) Schein, L. B. Electrophotography and Development Physics, 2nd ed.; Springer: New York, 1992. (3) Pai, D. M.; Springett, B. E. Rev. Mod. Phys. 1993, 65, 163. (4) Borsenberger, P. M.; Magin, E. H.; van der Auweraer, M.; de Schryver, F. C. Phys. Status Solidi A 1993, 140, 9. (5) Tang, C. W.; VanSlyke, S. A. Appl. Phys. Lett. 1987, 51, 913. (6) Tang, C. W.; VanSlyke, S. A.; Chen, C. H. J . Appl. Phys. 1989, 65, 3610. (7) Adachi, C.; Tsutsui, T.; Saito, S. Appl. Phys. Lett. 1989,55, 1489. ( 8 ) Adachi, C.; Tsutsui, T.; Saito, S . Appl. Phys. Lett. 1990, 57, 532. (9) Borsenberger, P. M.; Kan, H.-C.; Vreeland, W. B. Phys. Status Solidi A 1994, 142, 489. (10) Borsenberger, P. M. Phys. Srarus Solidi B 1992, 173, 671. (11) Borsenberger, P. M.; Rossi, L. J. J. Chem. Phys. 1992, 96, 2390. (12) Borsenberger, P. M.; Magin, E. H. J. Phys. Chem. 1993,97,9213.
4240 J. Phys. Chem., Vol. 99, No. 12, 1995 (13) Borsenberger, P. M.; Magin, E. H.; Fitzgerald, J. J. J . Phys. Chem. 1993. 97. 8250. (14) Borsenberger, P. M.; Fitzgerald, J. J.; Magin, E. H. J . Phys. Chem. 1993, 97, 11314. (15) Schein, L. B.; Borsenberger, P. M. Chem. Phys. 1993, 177, 773. (16) Borsenberger, P. M. J . Chem. Phys. 1992, 72, 5283. (17) Yuh, H.-J.; Pai, D. M. Mol. Cryst. Liq. Cryst. 1990, 183, 217. (18) Yuh, H.-J.; Pai, D. M. Philos. Mag. Lett. 1990, 62, 61. (19) Borsenberger, P. M.; BLsler, H. J. Chem. Phys. 1991, 95, 5327. (20) Yuh, H.-J.; Pai, D. M. J . Imaging Sci. Technol. 1992, 36, 477. (21) Pavlisko, J. A,; Somero, L. J.; Young, R. H. U.S. Patent 5,232,800, 1993. (22) Pai, D. M.; Yanus, J. F.; Stolka, M.; Renfer, D.; Limburg, W. W. Philos. Mag. 1993, 48, 505. (23) Bassler, H. Philos. Mag. B 1984, 50, 347. (24) Sugiuchi, M.; Nishizawa, H.; Uehara, T. In Proceedings of the Sixth International Congress on Non-Impact Printing Technologies; Nash, R. J., Ed.; Society for Imaging Science and Technology: Springfield, VA, 1991; p 298. (25) Nishizawa, H.; Sugiuchi, M.; Uehara, T. In Macromolecular HostGuest Complexes: Optical, Optoelectric, and Photorefractive Properties and Applications, Materials Research Society Symposium Proc.; Jenekhe, S . A., Ed.; Materials Research Society: Pittsburgh, PA, 1992; Vol. 277, p 33. (26) Sugiuchi, M.; Nishizawa, H. J . Imaging Sci. Technol. 1993, 37, 245. (27) Kanemitsu, Y.; Sugimoto, Y. Phys. Rev. B 1992, 46, 14182. (28) Tyurin, A. G.; Kryukov, A. Yu.; Zhuravleva, T. S.; Vannikov, A. V. Vyskomol. Soedin. B 1988, 30, 739. (29) Vannikov, A. V.; Tyurin, A. G.; Kryukov, A. Yu.; Zhuravleva, T. S . Mater. Sci. Forum 1989, 42, 29. (30) Vannikov, A. V.; Kryukov, A. Yu.; Tyurin, A. G.; Zhuravleva, T. S. Phys. Status Solidi A 1989, 115, K47. (31) Vannikov, A. V.; Grishina, A. D. Usp. Khim. 1989,582056 (Russ. Chem. Rev. 1989, 58, 1169). (32) Vannikov, A. V.; Kryukov, A. Yu. J. lnf. Rec. Mater. 1990, 18, 341. (33) Borsenberger, P. M.; Bassler, H. Phys. Status Solidi B 1992, 170, 291. (34) Young, R. H.; Fitzgerald, J. J. Submitted to J . Chem. Phys. (35) Dieckmann.. A,:, Bassler., H.:, Borsenbereer. P. M. J . Chem. Phvs. 1993,99, 8136. (36) Borsenbereer, P. M. Mol. Crvst. Lia. Crvst. 1993. 228. 167. (37j Borsenberger; P. M. Adv. Miter. Opt. Eiectron. 1992, ‘ I , 73. (38) Borsenberger, P. M.; Fitzgerald, J. J. J . Phvs. Chem. 1993,97,4815. (39) Borsenberger, P. M.; Pgutmeier, L.; BGsler, H. J . Chem. Phys. 1991, 95, 1258. (40) Novikov, S. V.; Vannikov, A. V. Khim. Fir. 1991, 10, 1692. (41) Novikov, S. V.; Vannikov, A. V. Chem. Phys. Lett. 1991, 182, 598. (42) Novikov, S. V.; Vannikov, A. V. Chem. Phys. 1993, 169, 21. Vannikov, A. V.; Grishina, A. D.; Novikov, S. V. Usp. Khim. 1994, 63, 107 (Russ. Chem. Rev. 1994, 63, 103). (43) Novikov, S. V.; Vannikov, A. V. J . Imaging Sci. Technol. 1994, 38, 355. (44) Yamaguchi, Y.; Fujiyama, T.; Tanaka, H.; Yokoyama, M. Solid State Commun. 1991, 80, 817. (45) Bassler, H. Phys. Status Solidi B 1993, 175, 15. (46) Bassler, H. Phys. Status Solidi B 1981, 107, 9. (47) Duke, C. B.; Meyer, R. J. Phys. Rev. B 1981, 23, 2111. (48) Kanemitsu, Y.; Einami, J. J. Appl. Phys. 1990, 57, 673. (49) McClellan, A. L. Tables of Experimental Dipole Moments; Freeman: San Francisco, 1963. (50) 1 Debye (D) = 3.34 x C m. (51) Guggenheim, E. A. Trans. Faraday SOC.1949, 45, 714. (52) Thompson, H. B. J. Chem. Ed. 1966, 43, 66. (53) Bottcher, C. J. F. Theory of Electric Polarization; Elsevier: New York, 1973; Chapters 5 and 14. (54) Klages, G.; Wieczorek, E. Z.Natuiforsch. 1982, 37a, 113. (55) Sobolev, S. N.; Belsky, V. K.; Romm, I. P.; Chemikova, N. Yu.; Guryanova, E. N. Acta Crystallogr. C 1985, 41, 967. (56) Reynolds, S. L.; Scaringe, R. P. Cryst. Struct. Commun. 1982, 11, 1129. (57) The description of the proper average is complicated by the fact that the partition among conformations may be perturbed by an electric field. (58) Minkin, V. I.; Osipov, 0. A.; Zhdanov, Y. A. Dipole Moments in Organic Chemistry; Plenum: New York, 1970; p 91. (59) The reported dipole moment of N,N-diethylaniline is -1.8 D (ref 49). As a rough approximation, we assume that it is directed along the “
I
Young and Fitzgerald Ph-N bond. (In fact, it probably makes an angle of ca. 30” with the Ph-N bond, as is the case for N,N-dimethylaniline, ref 58.) An additional methyl group in the meta position (group dipole ca. 0.4 D, ref 58) should reduce the net moment to 1.6 D. Again, we neglect the small angle between this resultant and the Ph-N bond direction. (60) We regard toluene and triphenylmethane as substituted methanes and vectorially sum the “group moments” of the attached hydrogen and phenyl groups. Then the fact that the dipole in toluene is directed toward the methyl group (ref 58) implies that the dipole in triphenylmethane is directed toward the methyl hydrogen. (61) For a consistent comparison of trimethylamine with dimethylanilhe, we take the values for both in benzene. (62) Cf. ref 22 or the following: Pai, D. M.; Melnyk, A. R. SPIE 1986, 61 7, 82. (63) Young, R. H.; Sinicropi, J. A,; Fitzgerald, J. J. Submitted to J . Phys. Chem. (64) Van der Auweraer, M.; De Schryver, F. C.; Borsenberger, P. M.; Fitzgerald, J. J. J . Phys. Chem. 1993, 97, 8808. (65) Borsenberger, P. M.; Bassler, H. J . Imaging Sci. Technol. 1991, 35, 79. (66) Young, R. H. Philos. Mag. 1994,69,577. The correct expression for p should have an additional factor of TJT, where TI = 295 K. The corrections to the best-fit values of po and u are inconsequential for present purposes. For the field dependence of the mobility, not discussed here, the corresponding corrections are major. (67) For TTA in bisphenol A polycarbonate (ref 74), u is evaluated from the reported parameter TOas u = 3/2kTo. For studies in which “d’and “pO” were evaluated at nonzero field strengths E and the field-dependence parameters “C’ and “E” were evaluated using “d‘instead of u, the zerofield parameters u and po were evaluated as u = K“d’ and po = ‘‘pi’ exp(““‘X’2E’~2), where K = (1 9/4“C’E’”)’”. Although not used here, the corresponding expressions for the parameters C and I: are C = K-2“C’ and I:= K‘Z”. When C was not reported, we extract it from the slope, S, of a plot of ln(mobi1ity) vs at room temperature according to S = “C’[(“d’/kn2 - T“2].For the formulas on which this analysis is based, see ref 45. (68) Kanemitsu, Y.; Funada, H.; Masumoto, Y. J . Appl. Phys. 1992, 71, 300. (69) Dieckmann et al. (ref 35) attributed the curvature of this plot to a tendency of dipole-dipole interactions to favor antiparallel orientations of adjacent dipoles during film formation, but no supporting evidence was offered. (70) There are problems with the analysis. The slope of the (rough) linear correlation between l n p a n d p (0.16 D-l) agrees with that predicted by the lattice model of ref 35 for a lattice constant of a = 6 A, with 50% of the lattice points occupied by a dipole, and with a relative dielectric constant of 3.5;but the agreement is fortuitous. The CTM were each present at 50 wt %, and their average molecular weight was 385. The mass density corresponding to these parameters is much too high, 3.0 g ~ m - and ~, a more appropriate value of the lattice constant (-8.1 A, for a density of about 1.2 g ~ m - ~would ) decrease the predicted slope by a factor of 3. Moreover, the data of Sugiuchi and Nishizawa (ref 26) represent a field strength of 25 V/pm, whereas eq 3 is for the zero-field limit. At nonzero field, simulations (ref 45) indicate a linear relationship of the same form as eq 3 but with an even lower slope. All of the foregoing is superceded, however, by the fact that the formula for obtained by Dieckmann et al. from simulations (ref 35) disagrees considerably with the result of a simple analytical evaluation (ref 70a). When the correct formula is used, the predicted slope (-0.17 D-l) again agrees well with the observed value (0.16 D-l). (a) Young, R. H. Philos. Mag., in press. (71) Borsenberger, P. M.; Schein, L. B. J . Phys. Chem. 1994, 98, 233. (72) Cf.: Marshall, J. M. Philos. Mag. 1977, 36, 959. (73) (a) As pointed out by Nishizawa (ref 73b), the temperature dependence implied by eqs 11 and 14 is very similar to that of the GDM if pf has no temperature dependence of its own. The numerical factors l/2 ad (2/3)2 differ by only about 12%. (b) Nishizawa, H. Proc. Ann. Con$ Jpn. Hardcopy; SOC.Electrophotogr. Jpn.: Tokyo, 1991; p 137. (74) Borsenberger, P. M. J . Appl. Phys. 1990, 68, 6263. (75) Young, R. H. Manuscript in preparation. (76) Borsenberger, P. M.; Pautmeier, L.; Richert, R.; Bbsler, H. J. Chem. Phys. 1991, 94, 8276. (77) Bassler, H.; Borsenberger, P. M. Chem. Phys. 1993, 177, 763. (78) Cumper, C. W. N.; Thurston, A. P. J . Chem. SOC.B 1971, 422. (79) Vij, J. K.; Srivastava, K. K. Indian J . Pure Appl. Phys. 1969, 7, 391. (80) Vij, J. K.; Singh, B.; Rao, V. V. R. Indian J . Phys. 1973, 47, 533.
+
JF’942690X
