Photochromic reaction in a molecular glass as a novel host matrix: The 4-dimethylaminoazobenzene-4,4′,4″-tris [3-methylphenyl(phenyl)amino]triphenylamine system

Article abstract of DOI:10.1039/a805735d

For the purposes of clarifying the properties of a molecular glass as a novel host matrix and gaining information on the microstructure of the molecular glass, the photochromic behavior of 4-dimethylaminoazobenzene (DAAB) in a novel molecular glass of 4,4′,4″-tris[3-methylphenyl(phenyl)amino]triphenylamine (m-MTDATA) was investigated, and compared with its behavior in a polystyrene glass matrix and a benzene solution. It was found that the fraction of the photoisomerized cis-isomer of DAAB at the photostationary state is smaller in the m-MTDATA glass matrix than in the polystyrene matrix and the benzene solution, and that the apparent initial rate constant for the backward cis→trans thermal isomerization of DAAB is much larger in the m-MTDATA glass than in the polystyrene matrix and the benzene solution. These results suggest that the average size of local free volume in the molecular glass of m-MTDATA is smaller than that in the polystyrene glass.

Full text of DOI:10.1039/a805735d

J O U R N A L O F
Photochromic reaction in a molecular glass as a novel host matrix:
the 4-dimethylaminoazobenzene–4,4∞,4◊-tris[3-
methylphenyl(phenyl)amino]triphenylamine system
Kazuyuki Moriwaki, Mitsushi Kusumoto, Keiichi Akamatsu, Hideyuki Nakano and
Yasuhiko Shirota*
C H E M I S T R Y
Department of Applied Chemistry, Faculty of Engineering, Osaka University, Yamadaoka, Suita,
Osaka 565–0871, Japan. E-mail: shirota@ap.chem.eng.osaka-u.ac.jp
Received 22nd July 1998, Accepted 16th September 1998
For the purposes of clarifying the properties of a molecular glass as a novel host matrix and gaining information on
the microstructure of the molecular glass, the photochromic behavior of 4-dimethylaminoazobenzene (DAAB) in a
novel molecular glass of 4,4∞,4◊-tris[3-methylphenyl(phenyl)amino]triphenylamine (m-MTDATA) was
investigated, and compared with its behavior in a polystyrene glass matrix and a benzene solution. It was found that
the fraction of the photoisomerized cis-isomer of DAAB at the photostationary state is smaller in the m-MTDATA
glass matrix than in the polystyrene matrix and the benzene solution, and that the apparent initial rate constant for
the backward cisAtrans thermal isomerization of DAAB is much larger in the m-MTDATA glass than in the
polystyrene matrix and the benzene solution. These results suggest that the average size of local free volume in the
molecular glass of m-MTDATA is smaller than that in the polystyrene glass.
Amorphous glasses serve as excellent host matrices because of
their excellent film formation, transparency, isotropic proper-
ties, and homogeneous properties owing to the absence of
grain boundaries. Inorganic sol-gel glasses have been widely
used as host matrices, embedding a variety of functional
materials. Organic polymers have also been widely used as
matrices for embedding functional materials. For example,
molecularly-doped polymer systems where photoconducting
materials are dispersed in an amorphous polymer such as
polycarbonate have been put to practical use as photoreceptors
in electrophotography. Photochromic reactions of low molecu-
lar-weight organic compounds dispersed in a polymer matrix
have also been studied extensively, and microenvironmental
effects on photochromic reactions have been discussed in terms
of their molecular motions associated with glass transition and
the free volume of host polymer matrices.1–11
In contrast to polymers, low molecular-weight organic
compounds tend to crystallize readily. We have been making
studies of the creation of low molecular-weight organic com-
pounds that readily form stable amorphous glasses above
room temperature, which we refer to as ‘amorphous molecular
materials’ or ‘molecular glasses’, considering the following
aspects. Amorphous molecular materials are expected to con-
stitute a novel family of organic functional materials that
exhibit glass-transition phenomena usually associated with
polymers. Creating such amorphous molecular materials is of
interest and significance not only for technological applications
but also from a scientific viewpoint, opening up a new field of
organic materials science that deals with ‘molecular glasses’.
We have created several novel families of molecular glasses
matrices in comparison with those of amorphous polymers.
In addition, studies of photochromic reactions in the molecular
glass are expected to provide information on the microstructure
of the molecular glass as the host matrix.
In the present study, we have investigated photochromic
reactions in a molecular glass of 4,4∞,4◊-tris[3-methylphe-
nyl(phenyl)amino]triphenylamine (m-MTDATA) in order to
elucidate the properties of the molecular glass as a novel host
matrix and to gain information on the microstructure of the
molecular glass. An azobenzene derivative was chosen as a
photochromic compound because azobenzenes have been most
extensively studied. Since the m-MTDATA film shows an
electronic absorption band in the near UV region, we selected
4-dimethylaminoazobenzene (DAAB) as
a photochromic
probe compound, which shows an absorption spectral change
due to trans<cis isomerization in the visible region. The
photoisomerization behavior and the kinetics for the backward
cisAtrans thermal isomerization of DAAB in the molecular
glass of m-MTDATA are investigated in the temperature
region below and above the T . The results are discussed in
g
comparison with those in a polystyrene matrix and a benzene
solution. Preliminary results have been reported as
a
communication.37
Experimental
Materials
m-MTDATA was prepared according to the method described
in our previous paper.12 trans-DAAB was obtained commer-
cially (Tokyo Chemical Industry, Co., Ltd.) and purified by
sublimation (at ca. 80 °C and at 0.15 mmHg). Polystyrene was
commercially available (Wako Pure Chem. Ind., Ltd.) and
purified by repeated reprecipitation from benzene into
methanol (M =1.9×105, M /M =1.7).
with relatively high glass-transition temperatures (T s), which
g
include 4,4∞,4◊-tris(diphenylamino)triphenylamine (TDATA)
and its derivatives,12–16 substituted 1,3,5-tris(diphenylamino)-
benzenes (TDABs),17–24 4,4∞,4◊-tris(diphenylamino)triphenyl-
benzene (TDAPB) and its derivatives,25 and others.26–31 They
readily form uniform amorphous films by vacuum deposition,
spin coating or solvent casting and have found successful
application as materials for organic electroluminescent
devices.14–16,32–36 Like polymers, molecular glasses are also
expected to function as novel host matrices for embedding
functional materials such as photochromic materials. It is of
interest to elucidate the properties of molecular glasses as host
w
w
n
Preparation of glass samples for DSC measurement
Glass samples for the determination of T by differential
g
scanning calorimetry (DSC) were prepared as follows.
Appropriate amounts of m-MTDATA and trans-DAAB with
molar ratios of m-MTDATA5DAAB=351, 551, 1051 and
J. Mater. Chem., 1998, 8, 2671–2676
2671

N
N
CH3
CH3
N
N
H3C
m-MTDATA
H3C
Fig. 1 DSC curve of a glass obtained by cooling the melt of a
mixture of m-MTDATA and DAAB with a molar ratio of m-
MTDATA5DAAB=351.
N
N
H3C
N
Results and discussion
trans-DAAB
Glass formation of DAAB—m-MTDATA mixtures
It was found that the mixtures of varying amounts of
m-MTDATA and DAAB form homogeneous, amorphous
glasses, as confirmed by DSC, X-ray diffraction, and polarizing
microscopy. Fig. 1 shows a DSC curve of a glass obtained by
cooling the melt of the mixture of a molar ratio of m-
MTDATA5trans-DAAB=351. When the sample was heated,
a glass-transition phenomenon was observed at 60 °C, which
∆
hν
H3C
H3C
N
N
N
was 15 °C lower than the T of m-MTDATA itself. The result
g
that only one glass-transition phenomenon was observed sug-
gests that the DAAB molecules are homogeneously dispersed
in the m-MTDATA glass matrix. On further heating, an
exothermic peak due to crystallization of both m-MTDATA
and DAAB was observed at ca. 129 °C, followed by a broad
endothermic peak due to melting at around 193 °C. The X-
ray diffraction ( XRD) pattern of a glass with a molar ratio
of m-MTDATA5trans-DAAB=351 is shown in Fig. 2. No
appreciable difference in the XRD pattern was observed among
the glasses with varying molar ratios of m-MTDATA and
cis-DAAB
10051, were placed in a glass sample tube, and then the tube
was sealed off. After the sample melted on heating in the
sample tube, it was allowed to cool to room temperature to
give a homogeneous glass of m-MTDATA containing DAAB.
DAAB. Table 1 lists the T s of the glasses of the mixtures of
g
Photochromic reaction in amorphous films
Amorphous films of m-MTDATA containing trans-DAAB
were prepared on a transparent glass substrate by spin coating
from a benzene solution containing appropriate amounts of
m-MTDATA and DAAB. The film was dried overnight under
reduced pressure before use. The resulting film was confirmed
to be amorphous by X-ray diffraction and polarizing
microscopy. Polystyrene films containing DAAB were also
prepared by spin coating from a benzene solution.
Photoisomerization of DAAB in the amorphous films of
m-MTDATA and polystyrene was carried out by irradiation
with 400 nm light with a bandwidth of 10 nm from a 500 W
Xenon lamp (UXL-500D, USHIO) through an interference
filter (IF-S 400, Vacuum Optics Co.) and an optical fiber.
Photochromic reactions were analyzed from the change in the
electronic absorption spectra.
Fig. 2 X-Ray diffraction pattern of a glass obtained by cooling the
melt of a mixture of m-MTDATA and DAAB with a molar ratio of
m-MTDATA5DAAB=351.
Table 1 Glass-transition temperatures (T s) of the glasses of mixtures
g
of m-MTDATA and DAAB
Sample
T / °C
g
Apparatus
m-MTDATA
75
71
63
60
60
m-MTDATA5DAAB=10051a
m-MTDATA5DAAB=1051a
m-MTDATA5DAAB=551a
m-MTDATA5DAAB=351a
T values were determined by DSC with a Seiko DSC220C.
g
Electronic absorption spectral change were measured with a
Hitachi U-3200 spectrophotometer. The sample was kept at a
constant temperature by using a temperature controller
(TM-105, Toho Electronics Inc.) with a tungsten heater.
aMolar ratio.
2672
J. Mater. Chem., 1998, 8, 2671–2676

Table 2 The cis-fraction (Y ) of DAAB at the photostationary state
upon irradiation with 400 nm light at 30 °C in m-MTDATA films
Reaction system
Y
10051-m-MTDATA film
1051-m-MTDATA film
551-m-MTDATA film
351-m-MTDATA film
0.26
0.48
0.54
0.54
than those for the polystyrene film and the benzene solution
indicates that a number of trans-DAAB molecules remain
unchanged in the m-MTDATA amorphous film, probably
because the local free volume around the remaining trans-
DAAB molecules is not large enough to allow the isomerization
of DAAB from its trans-form to the cis-form in the m-
MTDATA glass matrix. It is suggested that the average size
of local free volume in the m-MTDATA glass is smaller than
that in the polystyrene glass. The increase in the Y value with
increasing concentration of DAAB in the m-MTDATA glass
matrix indicates that the addition of DAAB into the m-
MTDATA glass causes a change in the microstructure of the
glass, e.g. the size and distribution of the local free volume. It
is suggested that the fraction of the local free volume that
allows the photoisomerization of DAAB increases with
increasing concentration of DAAB.
Fig. 3 Electronic absorption spectral change of 351-m-MTDATA film:
(a) before irradiation; (b)–(e) irradiated with 400 nm light for (b) 2,
(c) 5, (d) 10 and (e) longer than 30 min (photostationary state).
Electronic absorption spectra of ( f) an amorphous film of
m-MTDATA alone and (g) DAAB in
(1.0×10−5 mol dm−3).
a benzene solution
Next, the backward cisAtrans thermal isomerization of
DAAB in the m-MTDATA glass was examined. The ratio of
the concentration of cis-DAAB at the initial state and at time
t was determined from the absorbance at 410 nm according to
eqn. (2),
m-MTDATA and DAAB. It was found that the T decreases
g
as the concentration of DAAB increases.
Photochromism of DAAB in the m-MTDATA glass matrix
[cis]
A −A
0
t
0
2
=
(2)
[cis]
A −A
The amorphous film with
a
molar ratio of m-
t
2
MTDATA5DAAB=n51 prepared on a transparent glass sub-
strate by spin coating from a benzene solution is hereafter
referred to as the n51-m-MTDATA film (n=3, 5, 10, 100).
The reversible transAcis and cisAtrans photoisomerizations
and thermal isomerizations of DAAB took place in the n51-
m-MTDATA amorphous film. Fig. 3 shows the electronic
absorption spectral change for the 351-m-MTDATA film
together with the electronic absorption spectra of an amorph-
ous film of m-MTDATA alone, prepared on a glass substrate
by spin coating from a benzene solution, and trans-DAAB in
a benzene solution. Upon irradiation with 400 nm light, the
absorbance of the film at around 410 nm decreased due to the
photoisomerization of trans-DAAB to the cis-form. When
irradiation was stopped after the reaction system had reached
a photostationary state, the absorption spectrum of the film
gradually began to recover to give the original one due to the
backward thermal isomerization of cis-DAAB to the trans-
form. The m-MTDATA film was stable to 400 nm light
irradiation under the same conditions.
where [cis] and [cis] represent the concentration of cis-DAAB
0
t
at the initial state and at time t, respectively, and A , A , and
0
2
A are the absorbances of the film at 410 nm at the initial and
t
infinite time, and at a time t, respectively. If the reaction
follows first-order kinetics, the plots of ln([cis] /[cis] ) vs. time
0
t
will be linear and the slope of the straight line represents the
rate constant for the reaction. Fig. 4 shows the first-order
plots for the cisAtrans thermal isomerization of the 351- and
10051-m-MTDATA films at 30 °C after the reaction sys-
tem has reached the photostationary state by irradiation
with 400 nm light. The results for
a benzene solution
The cis-fraction (Y) of DAAB in the n51-m-MTDATA film
at the photostationary state can be determined from eqn. (1),
e +ne
A
−A
int pss
t
h
Y=
(1)
A BA B
e −e
A
t
c
int
where e , e and e are the molar extinction coefficients of
t
c
h
trans-DAAB (e =2.9×104 −1 cm−1 at 405 nm),38 cis-DAAB
t
(e =2.0×103 −1 cm−1 at 405 nm),38 and the m-MTDATA
c
host matrix (e =6.2 ×102 −1 cm−1 at 405 nm), and A and
h
int
A
are the absorbances of the film at the initial and photo-
pss
stationary states, respectively. Table 2 shows the Y values for
the n51-m-MTDATA films at 30 °C. It was found that the cis-
fraction Y of DAAB in the m-MTDATA glass is smaller than
those (ca. 0.85) for a polystyrene glass and a benzene solution
and that the Y value increases when the concentration of
DAAB increases in the DAAB—m-MTDATA system. The
result that the Y value for the m-MTDATA glass is smaller
Fig. 4 First-order plots for the cisAtrans thermal isomerization of
DAAB in (a) 351-m-MTDATA film, (b) 10051-m-MTDATA film and
(c) 351-m-MTDATA film prepared under irradiation of 400 nm light,
(d) polystyrene film and (e) benzene solution. Solid lines are fitting
curves based on eqn. (3) for (a) and eqn. (4) for (b), (d) and (e).
J. Mater. Chem., 1998, 8, 2671–2676
2673

Table 3 Kinetic parameters based on eqn. (4) for the thermal
cisAtrans isomerization of DAAB at 30 °C
(3.3×10−4 mol dm−3) and a polystyrene glass matrix contain-
ing the same DAAB concentration as that in the 10051-m-
MTDATA film (0.28 wt%) are also shown in Fig. 4. It was
found that the cisAtrans thermal isomerization of DAAB in
the m-MTDATA and polystyrene films did not follow first-
order kinetics and that the apparent rate constant for the
cisAtrans thermal isomerization in the m-MTDATA glass is
initially much larger than those in the polystyrene matrix and
the benzene solution, gradually approaching the same value
as that in the solution. This result suggests that there exist cis-
isomers trapped in strained conformations in the host matrix,
which go back faster to the trans-isomers than the structurally
relaxed cis-isomers. In order to verify this idea, the 351-m-
MTDATA film was prepared by spin coating under 400 nm
light irradiation and the backward cisAtrans thermal isomeriz-
ation was examined. As a result, the first-order plot for the
351-m-MTDATA film prepared under irradiation showed less
deviation from the linear plot [Fig. 4(c)] than the film prepared
in the dark [Fig. 4(a)]. This result indicates that the amount
of the strained cis-DAAB in the film prepared under irradiation
is smaller than that prepared in the dark. Similar phenomena
have also been reported for polymer film systems.3,8
k /min−1
f
k /min−1
f
1
1
2
2
10051-m-MTDATA film
Polystyrene matrix
Benzene solutiona
0.083
0.062
—
0.54
0.12
—
0.003
0.003
0.003
0.46
0.88
1.00
aSingle component.
large as that of the slower component. The rate constant of
the slower component for the 10051-m-MTDATA and poly-
styrene films was found to be the same as for solution. It is
suggested that the faster and the slower components are
attributed to the reactions of the strained cis-isomer and the
structurally relaxed one, respectively. It is noteworthy that the
fraction of the faster component ( f ) is considerably larger
1
for the 10051-m-MTDATA film ( f =0.54) than for the poly-
1
styrene matrix film ( f =0.12). This leads to a larger apparent
1
rate constant at the initial stage for the 10051-m-MTDATA
film than for the polystyrene film. These results indicate that
the ratio of the number of the strained cis-isomers to the
relaxed cis-isomers at the photostationary state is much larger
for the 10051-m-MTDATA film than for the polystyrene film.
The reason why the cisAtrans thermal isomerization of DAAB
both in the 10051-m-MTDATA film and in the polystyrene
film can be analyzed in terms of the first-order kinetics for a
two component system rather than the Gaussian model is that
both the 10051-m-MTDATA film and the polystyrene film
involve the reaction of the relaxed cis-isomer to the extent of
46% and 88%, respectively.
Kinetic analysis of the cisAtrans thermal isomerization of
DAAB in m-MTDATA films
Since the cisAtrans thermal isomerization did not follow
simple first-order kinetics, the Kohlrausch–Williams–Watts
(KWW) function ([cis] /[cis] =exp[−(t/t)b]),39 the Gaussian
t
0
Model,40 and first-order kinetics for a two component system
were applied. As a result, the cisAtrans thermal isomerization
of DAAB in the 351-m-MTDATA film was successfully ana-
lyzed by the Gaussian Model, which assumes a Gaussian
distribution of the free energy of activation. In terms of this
model, the ratio of the concentration of the cis-isomer at a
time t to that at the initial time, [cis] /[cis] , is given by
The larger apparent rate constant for the cisAtrans thermal
isomerization in the m-MTDATA film relative to the poly-
styrene film also suggests that the average size of the local free
volume in the m-MTDATA glass is smaller than that in the
polystyrene glass.
t
0
eqn. (3),
The results of a larger cis-fraction at the photostationary
state and a larger ratio of the strained cis-isomer to the relaxed
one for the 351-m-MTDATA film relative to the 10051-m-
MTDATA film are ascribed to the difference in the size and
distribution of the local free volume between the 351-m-
MTDATA and 10051-m-MTDATA films. It is thought that
trans-DAAB can be isomerized to cis-DAAB when the local
+2
[cis]
1
t
=
exp(−x2)exp[−k t exp(cx)]dx (3)
AV
p1/2 P−2
[cis]
0
where x is the stochastic variable of a Gaussian distribution,
is the mean rate constant, and c is the spread of the
Gaussian distribution of the free energy of activation. The free
k
AV
energy of activation is represented as DG‡=DG‡ −cxRT,
AV
where DG‡ is the mean free energy of activation.
AV
free volume around the molecule is larger than V ; however,
0
photogenerated cis-DAAB is trapped in a strained confor-
The cisAtrans thermal isomerization of the 351-m-
mation in the host matrix when the local free volume is smaller
MTDATA film was found to fit eqn. (3) with the parameters
than V . The comparison of the cis-isomer fraction (Y ) at the
of k =0.034 min−1 and c=1.8. The value of k is much
1
AV
AV
photostationary state and the ratio of the strained cis-isomer
larger than the first-order rate constant (0.003 min−1) of the
cisAtrans thermal isomerization of DAAB in benzene solution.
These results suggest that most cis-isomers photochemically
generated in the 351-m-MTDATA film take strained confor-
mations and their free energies are subject to the Gaussian
distribution.
to the relaxed one between the 351- and 10051-m-MTDATA
films suggests that the fraction of the free volume larger than
V is larger for the 351-m-MTDATA film than for the 10051-m-
0
MTDATA film, but that the size of the local free volume is
smaller than V for the 351-m-MTDATA film, whereas a
1
local free volume larger than V is available for the 10051-
In the case of the 10051-m-MTDATA film, the cisAtrans
thermal isomerization of DAAB could not be analyzed by the
Gaussian Model but instead could be analyzed by first-order
kinetics for a two component system [eqn. (4)],
1
m-MTDATA film.
Temperature dependence of the kinetic parameters for the
10051-m-MTDATA film
[cis]
t
= f exp(−k t)+f exp(−k t)
(4)
The temperature dependence of the kinetic parameters for the
cisAtrans thermal isomerization were investigated with regard
to the 10051-m-MTDATA film, the reaction of which was
analyzed by first-order kinetics for a two component system
according to eqn. (4). Fig. 5 shows the first-order plots for the
cisAtrans thermal isomerization of the 10051-m-MTDATA
1
1
2
2
[cis]
0
where f and k are the fractions and the rate constants for the
i
i
faster (i=1) and the slower (i=2) components, respectively.
Likewise, the cisAtrans thermal isomerization of DAAB in
the polystyrene film was analyzed by first-order kinetics for a
two component system. Table 3 lists the kinetic parameters for
the reactions in the 10051-m-MTDATA film, the polystyrene
film, and the benzene solution at 30 °C. The rate constant of
the faster component for the 10051-m-MTDATA film and the
polystyrene film was found to be ca. 27 and ca. 21 times as
film at various temperatures below T . The apparent rate
g
constant of the reaction increased with rising temperature.
The kinetic parameters in eqn. (4) obtained for the 10051-m-
MTDATA film are summarized in Table 4. The results show
that the values of f and f are almost constant irrespective of
1
2
2674
J. Mater. Chem., 1998, 8, 2671–2676

isomerization of the 10051-m-MTDATA supercooled liquid
film in the temperature region above T , at 75 and 77 °C, was
g
found to follow simple first-order kinetics, as shown in Table 4
and Fig. 6.43 The rate constant is comparable to that predicted
from the Arrhenius plots for the slower reaction component
below T . This result suggests that the photogenerated cis-
g
isomer can take a relaxed conformation in the supercooled
liquid state, probably because molecular motion is not
restricted in the supercooled liquid state.
Summary
The photochromic behavior of DAAB dispersed in a molecular
glass of m-MTDATA was investigated in order to elucidate
the properties of the molecular glass as a novel host matrix
and to gain information on the microstructure of the molecular
glass. The m-MTDATA glass was found to function as a host
matrix, homogeneously embedding the photochromic molecule
DAAB. It was shown that the fraction of the photoisomerized
cis-isomer at the photostationary state in the m-MTDATA
matrix is smaller than that in the polystyrene matrix and that
the apparent rate constant at the initial stage for the backward
cisAtrans thermal isomerization of DAAB in the m-MTDATA
glass matrix is considerably larger than those in a polystyrene
matrix and in a benzene solution. These results indicate that
there is a large difference in the size and distribution of local
free volume between the molecular glass of m-MTDATA and
the polystyrene matrix. That is, the local free volume in the
molecular glass of m-MTDATA is suggested to be smaller
than that in the polystyrene glass. The present study presents
the first example of photochromic behavior in a molecular
glass as a novel host matrix and can be extended to other
photochromic compounds and other molecular glasses to gain
further information on the properties of molecular glasses as
a novel class of host matrix and on the microstructure of
molecular glasses.
Fig. 5 First-order plots for the cisAtrans thermal isomerization of
DAAB in 10051-m-MTDATA film at various temperatures: (a) 30,
(b) 40, (c) 50 and (d) 60 °C. Solid lines are fitting curves based
on eqn. (4).
Table 4 Kinetic parameters based on eqn. (4) for the cisAtrans
thermal isomerization of DAAB in 10051-m-MTDATA film at various
temperatures
T / °C
k /min−1
f
k /min−1
f
1
1
2
2
30
40
50
60
75a
77a
0.083
0.11
0.16
0.37
—
0.54
0.54
0.54
0.53
—
0.003
0.011
0.029
0.061
0.346
0.382
0.46
0.46
0.46
0.47
1.00
1.00
—
—
aSingle component.
the temperature, whereas the rate constants k and k increase
with rising temperature. Fig. 6 shows the Arrhenius plots for
1
2
References
both k and k . The activation energies for the reactions of
1
Photochromism, Molecules and Systems, ed. H. Durr and
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