... lattice parameter in c ( ~ 10 Ä) is negligible as compared to k T in .... the product o /VD ..... druck. Sonderdruckanforderungen an Dr. W. ACKERMANN, II. Phy-.
On Charge Separation at the Phase Boundary Molecular Crystal/Aqueous Electrolyte M . E . MICHEL-BEYERLE
Institut für Physikalische Chemie der Technischen Universität Mündien and
R . HABERKORN
Physik-Department der Technischen Universität München (Z. Naturforsch. 27 a, 1496—1504 [1972] ; received 8 August 1972)
Analysis of the electrostatics of charge carrier injection into molecular crystals during nonequilibrium electron transfer reactions demonstrates the unique advantage of aqueous or similar electrodes in measuring limiting currents which yield the rate constant of the injection process. At the phase boundary molecular crystal/aqueous electrolyte image forces are negligible due to the slow orientation polarization of water molecules with respect to the hopping frequency of injected charge carriers. Coulomb forces arising from slowly mobile or localized counter charges are shown to be effectively screened by water as a consequence of its relatively higher static dielectric constant as compared to that of the crystal.
Introduction
tempted to account f o r an image potential barrier, impeding the escape of charge carriers into the bulk
Hole and electron conductivity in organic h o m o molecular crystals of the anthracene type m a y originate f r o m unipolar carrier generation
(injection)
of the crystal. In the present paper the electrostatics of charge carrier
injection
during
non-equilibrium
photo-
at the crystal surface. Since the electronic exchange
chemical
interactions between molecules in such crystals are
sidered with special emphasis on aqueous electro-
electron transfer reactions
will
be
con-
weak ( 2 0 0 c m - 1 or less) as is indicated by the low
lytes as electrodes to the organic crystal. Injection
drift mobility o f 1 c m 2 / V sec, the injection of elec-
processes will b e formulated as photochemical elec-
trons into the lowest conduction band or, alterna-
tron transfer reactions, the energy of the conducting
tively, of holes into the highest valence band can be
crystal states being roughly approximated by
understood as a localized electron transfer reaction
energy of the radical ions. Charge carrier injection
in the crystal surface. At l o w field strength the cur-
through
rent-voltage
states can thus b e understood as electron transfer
charges
(j-V)
dependence is limited b y space
whereas it reflects the kinetics of the in-
the deactivation
between e x c i t o n s 4 '
5
of
electronically
the
excited
(singlet or triplet excitons at
jection reaction at higher fields as long as these are
the surface,
insufficient f o r field emission. Electron transfer re-
or acceptor ( A ) molecules in the aqueous phase:
actions, occurring at the phase boundary
JM0*
or
3M0*)
and electron d o n o r
crystal/
aqueous electrolyte yield at field strengths between
1M0#,3M0#
+ D,A
J
^M
rents, which have been correlated to the absolute rate constant of the injection reaction 2 . In the limiting current range the applied voltage is high enough to reduce to zero the surface concentration of charge carriers, so that the current becomes saturated as long as the applied field does not affect the electron
Reprint requests to Dr. M . E. MICHEL-BEYERLE, Institut für Physikalische Chemie der Techn. Universität München, D-8000 München 2, Arcisstraße 21.
+
,A"
(1)
ceptors (e. g. organic dyes) in the electrolyte or in adsorbed state and the crystal: 1
'3DV'3A* + M - ^ M + + D
+
,A".
(2)
\E j
crystal/
detail except in an earlier p u b l i c a t i o n 3 which at-
+D
or electron transfer between excited donors or ac-
transfer reaction. The electrostatics of charge sepaaqueous electrolyte has not yet been discussed in
T
\E j
10 3 and 10 5 V / c m voltage independent limiting cur-
ration at the interface organic molecular
(D)
This denotation indicates the primarily excited states and reactions products and gives no information as to the molecular interaction. The rate constants kx and k2 depend o n electronic energy levels (work function, ionisation energy and electron affinity) of
Unauthenticated Download Date | 11/24/15 9:02 AM
the crystal and reactants and are not affected b y the electric field of 10 5 V / cm. W i t h this maximum field strength the voltage d r o p across a lattice parameter in c
( ~ 10 Ä ) is negligible as c o m p a r e d to k T in
these non-equilibrium injection reactions. With increasing field strength the charge carriers are dragged away f r o m the surface region until their concentration approaches zero on reaching the limiting current. T h e field strength at which the j — F-plot enters the limiting current is governed by the electrostatic interaction of injected charges and the electrode. The motivation f o r this w o r k
arises f r o m the
possibility to discriminate through an electrochemical technique at the phase b o u n d a r y molecular crystal/aqueous electrolyte quenching processes due to electron transfer f r o m other interactions (excitation energy transfer, enhancement of internal conversion o r intersystem c r o s s i n g ) . Simultaneous to the measurement of the limiting currents, conventional spectroscopic methods
are applicable f o r
quantitative
5-104
5-10
E [l'km]
Fig. 1. Injection of electrons into p-chloranil crystals. A and B: reaction (3) at different Fe2+-concentrations (10 : 1). /lim, A=/max=e x 10 L. C: triplet exciton decay at an evaporated gold electrode. / 0 in A, B and C: 2 • 1013 photons/sec cm2.
description of the different deactivation channels in heteromolecular excited systems. T h e phase boundary molecular crystal/aqueous electrolyte might b e even relevant f o r biological membranes, the interface of
which is as well characterized b y a dis-
continuity of the static dielectric constant.
Experimental Results In Figs. 1 and 2 typical j — F-plots f o r carrier injection a c c o r d i n g to reactions
(1)
and
(2)
are
depicted. All measurements refer to electron injection at the ab-plane of p-chloranil
(tetrachloro-p-
b e n z o q u i n o n e ) crystals, which p r o v i d e clear experiments, prototypic f o r other molecular crystals (e. g. aromatic h y d r o c a r b o n s ) . D u e to the high intersystem crossing rate in pchloranil the diffusing and reacting exciton in Fig. 1 is essentially the triplet exciton, even when singlet excitons are the primarily excited species 6 . N o
fluo-
rescence or appreciable l o n g range energy transfer to the electrode have to b e considered. The high energy of the triplet exciton in chloranil allows application of
dye molecules as electron donors
in
Eq. ( 2 ) which on energetic g r o u n d s
5-70
5-10* E [v/cm]
Fig. 2. Injection of electrons into p-chloranil crystals via excitation of the cyanine dye S 27 in monomolecular layer. / 0 = 2 - 1 0 1 2 photons/sec cm2. with the electron transfer reaction
(2)
and charge
carrier generation in a subsequent reaction ( 1 ) be-
z1£(S0^S1)d 1 (d = crystal thickness), the limiting current can be described by the relationship /lim —
e
8:
field, surface products
according
arise. As a consequence, a slight slope (in Fig. 1,
)
to
(4)
gradually
if one does not
apply the limiting field strength p r i o r to excitation of the crystal. The slope disappears u p o n
rinsing
the crystal with suitable solvents. The gold filter in curves A and B has been used to allow comparison of the quantum yield of the reaction
(3)
with that of the analogous decay of
triplet excitons at an evaporated g o l d contact. In the context of this paper g o l d seems to b e especially suitable because of its high work function (Fig. 3 ) . Gold does not inject electrons in the dark and is not
[3CA0]
involved in any kind of chemical reaction with chlor-
[Fe2+] = e * /
0
L ( l +
L
^
F e 2 + ]
)
anil in its electronic ground state which might de-
1
teriorate the crystal surface.
with e = elementary charge, 7 0 = light intensity, D = diffusion coefficient in the direction of the applied field
electric develops
triplet excitons. F o r homogeneously intersystem crossing d x < l
cannot compete with the removal of electrons f r o m has been shown 2 ' 1 0 that without a sufficiently high
\E i with
(4)
the surface in presence of a high electric field. It
Charge injection in Fig. 1 occurs according to 3CA0
CAH •
(_L ab-plane)
^ 1 0 - 4 c m 2 / s e c 6 . The expres-
sion f o r the limiting current is simplified, since a
Figure 2 represents sensitized charge carrier injection 1 D2 d
+ CA
D+ +
CA~.
(5)
\E j
quenching reaction not leading to charge carriers does not occur in this case. At high concentrations of Fe 2 + -ions
(which d o not inject electrons in the
dark to a measurable extent), the current becomes diffusion controlled with regard to the triplet excitons and the quantum yield of reaction
(3)
for
At l o w conversion rates current is given b y
(/V D = const)
the limiting
7
j\\m = eI0oNB-
k5f (k5 + k')
diffusion
where a denotes the absorption cross section and
T o illustrate
/VD the number of adsorbed dye molecules, while k'
the highly effective quenching process ( 3 ) , the cor-
unifies the sum of deactivation steps not leading to
triplet
excitons
generated
within
their
length approaches the order of unity
8a.
responding energy levels of the crystal and the re-
charge carriers. At insufficient electric fields recom-
dox reaetant are sketched schematically in Figure 3.
bination according to ( 4 ) or
Exciton
decay
conditions
reactions
yielding,
under
with equally high quantum
suitable
D+ + C A " ^ D + CA
efficiency,
electron injection into chloranil as well as hole in-
(6)
will compete. In the case of Fig. 2, a cyanine dye
jection into anthracene crystals 8 , d o not support the
has been applied to the crystal surface in a mono-
suggestion 9 , that hole ejection is less effective than
molecular layer after the technique of KUHN
electron ejection.
the product o /VD
Because of the chemical instability of in presence of
hydroxylic
ions,
injection
chloranil experi-
11.
From
( c o r r e s p o n d i n g to 2 % light ab-
sorption at 5 6 5 nm, which has been measured spectroscopically by an effect modulation technique
12).
ments are preferably carried out under high proton
the intensity / 0 and the limiting current / l i m a quan-
concentration ( [ H + ] = 1 M ) .
tum yield in der order of
Unauthenticated Download Date | 11/24/15 9:02 AM
unity f o l l o w s f o r
the
/
/rff //r
/ 7/
q-d dq
Fig. 5.
Fig. 3. Energy level diagram, a) Crystal data of chloranil are taken from Ref. 6. Electron affinity, EAC = 4.1±0.2EV, the work function estimate as well stems from injection experiments, b) For simplicity triplet exciton energy is indicated in the one particle energy spectrum, c) Conversion of standardredox potentials vs. (NHE) into the absolute energy scale after F. L O H M A N N , Z . Naturforsch. 22 a, 8 4 3 [ 1 9 6 7 ] . d) Photoemission threshold of crystalline S 27. J. KINDER, personal communication, e) Work function of spectroscopic pure gold, 7 C =5.2EV after J. C. RIVIERE, Work Function Measurements and Results, Metallurgy Div. Atom. Energy Res. Etabl., Harwell 1 9 5 7 . f) H. P . TROMMSDORFF, P. S A H Y , and J . K A H A N E - P A I L L O U S , Spectrochim. Acta 26 A, 1135 [1970]. Lowest excited singlet state in chloranil crystals: n — j r * A u . g) Ref. 12. h) Extrapolation of SX — Tj-splitting in dyes after R. W. CHAMBERS and D. R. KEARNS, Photochem. Photobiol. 10, 1 2 1 5 [ 1 9 6 9 ] . i) Ref. 13. k) J. B. BIRKS, Photophysics of Aromatic Molecules, Wiley-Intersci., New York 1970. sensitized
electron
injection.
This
high
quantum
Fig. 6. Fig. 5. Potential energy of electrons vs. distance inside crystal from electrode. Fig. 6. Location of charge q and image charge q'.
W e will s h o w that f r o m the characteristic deviation
yield seems possible on the basis of the energy dia-
of the limiting current behaviour mechanistic infor-
gram
mation as to the injection reaction might be derived.
(Fig. 3 ) , which indicates that the minimum
energy condition / C ( D ) — EAC{€.\)
2 eV
as well as the spectral features of A , which follow
as compared to chloranil) reveal. The geometry of
the isotropic absorption spectrum of the crystalline
the ab-plane of m o n o c l i n i c crystals as well as the
complex, indicate that the dominant injection me-
epitaxial adsorption of dye molecules h e r e o n 8 analyzed with polarized light)
(as
chanisms in A is indeed connected to the excited
certainly does not
charge transfer species. It should be stated that the
favour the principle of maximum overlap of inter-
complex d o e s not inject electrons in the dark, al-
acting orbitals in TI — ;r*-charge transfer complexes
though the proximity of m o r e than one molecules
13.
In Fig. 4 a j — F-dependence different f r o m that
of the complementary species can cause the ground
in Fig. 2 is depicted f o r another kind of sensitized
state of the complex in the solid phase to have con-
electron injection. In this figure, however, the d o n o r
siderably m o r e ionic character than the ground state
species is an excited n — n * charge transfer complex.
of an isolated donor-acceptor-pair in inert environ-
Unauthenticated Download Date | 11/24/15 9:02 AM
Discussion By the non-equilibrium reactions
(3)
and
(6)
charge carriers are generated at the distance £ = 0 f r o m the surface. These may migrate into the bulk of the crystal by diffusion and drift in an electric field or recombine according to ( 4 ) or ( 6 ) at the surface, thus being removed f r o m current carrying. W e assume a potential barrier (Fig. 5 ) at the crystal surface, which inhibits the transport of charge carriers into the interior of the crystal. The potential barrier is thought to exhibit its maximum value Vm in a distance
109
f r o m the surface and may arise
f r o m residual space charges or f r o m forces between the charge carriers and their image charges or real counter
charges
on
the other side of
the phase
boundary. This model has been considered in a more general
way
by
KALLMANN
and
POPE
3,
using
the
Fig. 4. Injection of electrons into p-chloranil crystals via excitation of the (HMB . . . CA) -complex (A) and the reaction of homogeneously excited triplet excitons with Fe2+-ions (B) at the illuminated crystal face with the direction of the electric field reversed.
where 1 represents the primary injection rate of
ment. For weak charge transfer interactions of the
face. By simple arguments it is possible to deduce
Mulliken type the contribution of the charge-trans-
an equation f o r the j — F-plot which is identical
boundary condition
(9)
j = I-vn0
carriers, v, a finite surface recombination velocity, , the concentration of charge carriers at the sur-
fer structure in the ground state is small and charge-
with the general equation in Ref. 3 , if suitable para-
transfer absorption is mainly due to transition f r o m
meters are chosen. At a distance
the non-bonding ip0 (HMB . . . C A ) structure to the
surface the current may be given solely in terms
f r o m the
ionic structure \pt (HMB 6 + . . . C A 5 - ) . Whether in-
of charge carrier drift (density n m , drift mobility
jection upon excitation of the complex occurs via
/
