Sensors and Materials, Vol. 8, No. 6 (1996) 357-372
MYU Tokyo
S &M0251

Heat Dissipation in Small Drops on Free-Standing
Membranes Studied Using Thin Film Thermopiles
Johann Michael Kohler, Gudrun Steinhage1 , Jbrg Krause2*
and Karl Cammann1
Institut flir Physikalische Hochtechnologie IPHT,
Helmholtzweg 4, D07743 Jena, Fed. Rep. Germany
1Westfalische Wilhelms-Universitiit Munster, Institut fi.ir Chemo- und Biosensorik,
Mendelstr. 11, D 48149 Munster, Fed. Rep. Germany
2Westfiilische Wilhelms-Universitiit Munster, Institut fur Chemo- und Biosensorik,
Mendelstr. 11, D 48149 Munster, Fed. Rep. Gennany(Received March 29, 1995; accepted January 5, 1996)
Key words: thermal chemosensor, thermopile, time constants, redox reaction, internal calibration,
calorimetry, reaction enthalpy

The thermal response to electrical and chemical heating of thermally isolated drops ofliquid with volumes between 5 and 35 µl was studied. A thermopile transducer made from76 bismuth/antimony thin film thermocouples was used to measure temperature differ­ences between the drop/sensor interfaces and the surroundings. The time constant of thesensor arrangement alone is about 0.35 s. By placing a drop onto the sensor surface, twotime constants are obtained corresponding to the heat exchange between the drop and themembrane and the heat flow from the sensor-drop complex to the surroundings. Thesetime constants depend on the drop volume. Different thermoelectric transients wereobserved during the heating and evaporation of pure and binary liquids. The decay of thethermoelectric potential of fast exothermic chemical reactions such as neutralization
corresponds well to the time constant of the sensor arrangement in contact with the drop.
Different thermoelectric potential time characteristics were found for chemical reactions
with more complex reaction mechanisms and lower overall rates, such as inorganic andenzymatic redox reactions. The investigations prove that the arrangement of small dropson thin film membranes is suitable for both microanalytical applications and micro­
calorimetry.

*New address: ZUilig AG, Rheinbeck, CH-9424, Switzerland

357

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1.

Sensors and Materials, Vol. 8, No. 6 (1996)

Introduction

The measurement of enthalpies of chemical processes is a universal method in thecharacterization of materials, because most chemical processes are accompanied by con­sumption or production of heat. The measurement of heat as an analytical method has avery broad applicability, because the method is independent of the electrical conductanceor the optical transparency of the sample. Microcalorimetric experiments for micro­
analytical tasks were first performed using "thermistors". The electrical resistivity of thesetransducers changes depending on temperature, which changes during an exothermic orendothermic chemical or biochemical process.< 1, lResistive sensing elements require electric current during the measurement process,which supplies electrical power, in addition to the chemical power to be detected. Current­
free microcalorimetric measurements are possible using the thermoelectric principle. The
application of a series of thin film thermocouples (a "thermopile") in the detection ofreaction enthalpies was tested in chemical and biochemical analytical experiments_<3- 5l
In most experiments, the analyte has a small-area contact with the bulk material. This
contact causes intense heat flow between the reacting area with the "hot" thermojunctions
and the reference zone with the "cold" junctions of the thermopile. Thus, the time
constants of the heat exchange between hot and cold junctions are small, much smaller than
the reaction rates of many analytical reactions. This kinetic mismatch results in compara­tively low thermoelectric potentials, typically in the range of 0.01-1 mV. The use of anarrangement with a thermally isolated drop of analyte, situated in the central region of afree-standing thin film membrane not in geometrical contact with the bulk material of thesensor frame, leads to significantly higher thermoelectric potentials (up to 50 mV),corresponding to higher temperatures of the drop during chemical reactions. <6l Here, wereport investigations on the thermal behavior of drops on free-standing membranes in casesof external heating, endothermic physicochemical effects and exothermic chemical andbiochemical reactions.
22.

Experimental

2.1 Preparation of sensors
A modified layout of a standard infrared absolute radiometer developed by IPHT Jena
was used as the transducer.Ol It was prepared using anisotropic silicon wet etching in orderto obtain a free-standing thin film membrane of a Si3N4 / SiO / Si3N4 multilayer system. A
BiSb/Sb thermopile consisting of 76 thermocouples (approx. 10 mV/K) was used as thedetection transducer. Electrical heating was realized using a thin Ag resistor (70-120ohms). The electrical layers and the surface were electrically insulated by cured photoresist
layers.
2

2.2 Measurement arrangement

Liquid drops were applied on the center of a free-standing membrane carrying thethermoelectric, insulating, and heating films. Wetting of the outer parts of the free-359

Sensors and Materials, Vol. 8, No. 6 (1996)

SENSOR, CROSS SECTION(a)

Si-frameheating layer
insulating layer
thermopile layer
carrier membrane

MEASURE!VIBNT ARRANGEMENT
micropipettes(b)temperature
controlled
box

power
supplyFig. 1.

l=====I AID converter

Principle of measurement arrangement: cross section (a) and experimental setup (b).

standing sensor surface was restricted by hydrophobization of the outer parts of the surface(Fig. 1 (a)).
The sensor was fixed on a socket and electrically connected to a programmable power
supply (potentiostat PS 4 and variator PV3 Meinsberg) to provide the heating current andan analog/digital (A /D) converter (ASO 1600 Keithley) to register the thermoelectric
potential and heating current by means of a personal computer (PC). The sensor and socket
were placed in a temperature-controlled glass box with two movable micropipettes. The
use of this box improved the thermal stability of the measurement arrangement andconsiderably reduced the noise caused by air convection (Fig. 1 (b)).

360

Sensors and Materials, Vol. 8, No. 6 (1996)

2.3 Measurement procedure

In the case of physical and physicochemical experiments, drops were placed on thesensor surface and allowed to stand for thermal relaxation for at least 3 minutes before thepotential measurement was performed. In the case of chemical reactions, liquid drops weresuccessively placed on the sensor surface using micropipettes, after beginning the registra­tion of the thermoelectric potential.
The thermoelectric potential was recorded on a PC, and the range of AID conversion
was adjusted to the expected maximum voltages in order to obtain sufficient voltage
resolution. Integration times between 150 ms and 3.6 s were chosen depending on therecording time.

3.

Results

3.1 Theoretical estimation of thermoelectric response in presence of drops

The dynamics of the thermal system consisting of the free-standing thin film systemand the liquid drop are mainly controlled by the heat flow from the drop to the surroundings
Q,, by the heat flow inside the drop Qr' and the thermal capacitance of the thermal system
CP.
In the case of drops with volumes of 1 µl or greater, the heat capacitance of the liquid ismuch greater than the heat capacitance of the thin film system. Therefore, the heat
capacitance of the whole system is given approximately by the product of the liquidvolume V, the specific weight p, and the specific heat capacity C, of the liquid.
Cp = Vxpx C,(1)

The time constant r is given by the ratio of CP to the heat conductance G, of thesurroundings.
(2)

The heat conductance G, was calculated for the sensor without liquid using the geometricaland material parameters of the thin film stack, i.e., the thermoelectric potential U in heating
experiments, the number of thermocouples n, the Seebeck coefficient a and the applied
heating power P.
G, = n x ax P I U = n x a I S(S: responsivity)(3)

A Seebeck coefficient of 135 µV/K for the BiSb/Sb thermocouples used and an value of
76 gave a thermopower a,, (an = n x a) of 10.3 mV /K (c.f. ref. 7). A very simplified
geometrical model was used in the estimation of the heat transport through liquid drops. It
is assumed that the liquid forms a cylinder of a volume V, of which the radius r is equal tothe height h (Fig. 2).

Sensors and Materials, Vol. 8, No. 6 (1996)

T

361

A

h

heat flow

assumption: r = hp" "v AlhFig. 2. Simplified geometrical model for the estimation of heat transfer from the thin film system tothe surface of a liquid drop (assumption:.cylindric shape with height h, cross-sectional area A, radiusrand volume V).

The transported heat power P,_ is proportional to the ratio of cross-sectional area A andh, the temperature difference AT and the heat conductivity ;\, of the liquid.

P,_ = ATx }.,xAI h(4)Using this approximation and AT= 1 K, a P,_ of 2.2 mW is obtained for 5 µl drops of water,
and a P,_ of0.66 mW for 5 µl drops of ethanol. These values are related to their specific heat
conductances of0.6 W /(Km) and 0.18 W /(Km).<8) The electrical power Pis dissipated byheat flow through the membrane, IR radiation and convective cooling of the back of themembrane (summed as the physical dissipation power Pp) and by heat flow through thedrop P;. and its successive dissipation by heat exchange at the drop surface. Two possible
cases of the control of heat dissipation from the drop surface are distinguished.
(A) The rate of heat dissipation from the drop surface is controlled by heat exchange atthe drop surface and the temperature gradient in the drop is low. In this case, the smface
temperature of the liquid should be equal to the temperature of the sensor. The dissipationof energy from the liquid surface should be mainly dependent on the rate of evaporation,
which is a physicochemical process controlled by an activation energy 11He following an
Arrhenius relation:(5)(R: universal gas constant)

with

(6)

Sensors and Materials, Vol. 8, No. 6 (1996)

362

PO and Afle can be estimated from a logarithmic plot of the difference between the electricalheating power P and the physical dissipation power PP against the inverse absolutetemperature under the assumptions that the surface temperature is equal to the transducer
temperature and \ to the value of the empty transducer:ln(P- \x t:,,T) = ln(P0)-Afle /RTwitht:,,T= Ulan
and
T= T,+t:,,T(T,: absolute temperature of the surroundings).

(7)

(8)
(9)

(B) The intensity of heat dissipation from the drop surface is controlled by heattransport through the drop, and the temperature gradient in the drop is high.
(10)Then the temperature difference t:,,T should be nearly linearly dependent on the electricalheating power P.
t:,,T= Pl(\+ }.,xA/ h),(11)

and for the cylindric shape model with r = h,t:,,T=Pl(\+}.,x nx 3�(V/n)).

(12)

The distinction between cases A and B is apparent in experiments due to the functional
dependence of U on P. The time taken for complete evaporation of drops depending on P
provides additional information about the heat transport.

3.2 Heat dissipation of sensor without liquid
A thermoelectric potential can be observed if the transducer is heated by the thin film
resistor, as is recognized in the unmodified absolute radiometer.<7l The responsivities S
were found to be 2.6 V /W ... 3.4 V /W in sensors constructed as described above. The
empty sensors used in dissipation experiments had S of 3.16 V /W. The time constant ofheat dissipation after switch-off varies slightly between individual transducers and wasfound to be in the range between 0.3 s and 0.42 s. The two sensors used in experiments withdrops had S values of 2.6 and 2.9 V /W.
The heat conductances G, can be estimated from Sand a,, using eq. (3).
G, (exp.)= an ! S = 10.3 mV /K x 0.316 mW /mV = 3.25 mW /K
The heat capacitance can be calculated from G, and the time constant -i: using eq. (2).

(13)

Sensors and Materials, Vol. 8, No. 6 (1996)

363

CP = G, x r= 0.98 mJ/K (r= 0.3 s)= 1.37 mJ/K (r= 0.42 s)(14)

Heating powers of up to 0.25 W were applied in heating experiments with sensors
without liquid. The stability of the thin film components and the supporting membrane ishigh enough to realize many heating cycles up to this power without any change in thethermoelectric response. The maximum temperatures on the surface of the thin film stacka.re expected to be about 100° C (11T= 77 K; room temperature 23° C) as predicted from eq.
(13). The maximum them10electric potential was found to be 0.71 V in this experiment,
which is slightly less than the expected maximum thermoelectric potential of 0.79 V.

3.3 Heat dissipation in the presence of drops

In the presence of drops, the thermal relaxation of the thermally insulated system ismore complex. The time constant is generally considerably higher due to the high heat
capacity of the drop in comparison with the heat capacities of the thin film stack. This
results in a slow saturation of thermoelectric potential after both switch-on and switch-offof the heating power (Fig. 3).
The response time of the transducer (S = 2.6V/W) in the presence of a 20 µl drop ofwater was found to be about 33 s. This corresponds roughly to the time constant given byeq. (2) using the specific heat of water (4.2 J/gK):
r= CP I G, = 84 mJ/K/3.96 mW/K = 21.2 s.

(15)

J.00

potential
[MU]
60

20

-20

5 µl water

-

I\
I
I

......._
(\

(\

(\

I

-60

--

I

on

off

-J.00
0

50

l.00

J.50

200

250

300
t

[sl

Fig. 3. Thermoelectric response of the thermopile in the presence of a 5 µl drop of water during
electric heating with a heating power of 10 mW.

Sensors and Materials, Vol. 8, No. 6 (1996)

364

The time constant of thermal relaxation of drops depends strongly on drop size. Figure
4 shows that a small drop (5 µl) cools much faster than a large drop (35 µl). In the case ofboth small and large drops, a fast decay of thermoelectric potential is observed immedi­
ately after switching off the heating voltage. This decay has a time constant of about 0.1 s,
which is considerably faster than the time constant of the empty sensor (Fig. 5). The time
constant of this fast decay shows no significant dependence on the drop size. In contrast,
the decay reflects a higher temperature difference in the case of small drops. This decay isinterpreted in terms of the heat exchange between the thin film stack and the interior of thedrop.
The thermoelectric response was studied over a large range of electrical heating power
in order to obtain information about heat flux control in the thermal system in the presenceof liquids. Using 5 µl drops of water, we observed no significant change in the ratio ofthermoelectric potential to heating power over a range of 2.5 orders of magnitude ofheating power (Fig. 6). At the highest heating power investigated, the evaporation of waterfrom the drops can no longer be neglected, because the temperature of the transducer is justbelow the boiling point of the liquid. The observed behavior implies that the heat flux isdominated by the heat conductance in the interior of the drop. Case B (see section 3.1)
seems to be consistently valid for drop sizes of 5 µl and larger studied in the experiments
reported here. This finding is supported by the observed period for complete evaporationof drops, which depends not only on the activation energy of evaporation but also on theheat flux through the drop.

30

potential
[MU]
20

off

I
I

V
I

10

V

0

5 µl
-10

-20
240

I

280

I

320

360

400

440

480

t Cs]

Fig. 4. Decay of thermoelectric potential after switching off the heating current for two different
drop sizes (5 µl: fast decay; 35 µl: slow decay).

365

Sensors and Materials, Vol. 8, No. 6 (1996)
20
potential
[MV]

15

1-.
10

6

\

35 µI

5 µI
-4

I

266

268

I

270

272

I

274

276

278
t Cs)

Fig. 5. Decay of thermoelectric voltage in the first seconds after switching off the heating current for
two different drop sizes (5 µl: fast decay; 35 µl: slow decay; enlargement of part of the curves in Fig. 4).
1000

100

10

10

P [mW]

100

1000

Fig. 6. Dependence of the thermoelectric potential U,h during the heating of 5 µl of water on theheating power P (double logarithmic plot).

366

Sensors and Materials, Vol. 8, No. 6 (1996)

3.4 Thermoelectric transients in the case of drop evaporation

The applicable electric power (up to 0.77 W) for the thin film heater is sufficient toevaporate drops of water with volumes between 5 µI and 25 µI completely within a few
minutes. In all cases, a thermoelectric potential in the range between 0.7 and I.I V wasobserved, reflecting temperatures close to the boiling point of water.
The heat dissipation characteristics clearly indicate the existence of thermal transientstates in the cases of binary liquid mixtures. We used a mixture of water with ethanol in 5
µl drops as test samples (Fig. 7). The thermal voltages in the transient states are dependent
on the ethanol concentration. The lowest transient thermoelectric potential was obtainedwith the highest alcohol fraction (Fig. 8). The duration of the transient state increases withdecreasing ethanol concentration. It is assumed that the changes in surface and interface
tensions, which depend on the concentration, affected the time behavior due to modified
drop shape and wetting, in addition to the lower heat capacity, the lower boiling point andthe lower evaporation enthalpy of ethanol in comparison with water.

3.5 Calorimetric experiments

Microcalorimetric experiments were carried out without electric heating during themeasurement process. Only the heat-producing or heat-consuming chemical and physico­chemical processes contributed to thermoelectric power in these investigations. The
expected temperatures and the resulting thermoelectric potentials were much lower thanthose in most dissipation experiments which use electrical heating. In calorimetricexperiments , electric heating was used only for calibration procedures.
800r-----------------------------�
eotent ial
0-,Ul

600

10 %

400

20 %

40 %

200

60 %
ethanol in water0-200 �-----'------'------L-0

25

50

75

___L_ _____JL___

_ __J

1.00

1.25

1.50
t

tsl

Fig. 7. Transient thermoelectric potentials during the evaporation of 5 µl drops of water-ethanol
mixtures with a heating power of 0.36 W.

Sensors and Materials, Vol. 8, No. 6 (1996)

367

800,--------�------,
>
E

L--J
+-'
+-'
::=)

600
400

D
D
D

200
20

40
60
ethanol [%]

80

100

Fig. 8. Transient thermoelectric potentials Un during the evaporation of 5 µI drops of water-ethanol
mixtures with a heating power of 0.36 W relative to ethanol concentration.

First, the influence of a drop of water on the thermoelectric potential was tested. When
drops were applied, a negative thermoelectric potential was observed. The potentials
increased with increasing drop size and increasing convection in the surrounding atmosphere.
The potentials could be reduced by creating a more humid atmosphere using a chamber
which contained a small puddle of additional water. Therefore, the negative thermoelectric
potential in the presence of water drops on the sensor surface can be well understood by the
influence of evaporation cooling. A typical case is shown in the upper curve in Fig. 9. A
decrease in the potentials after a water drop was placed on the transducer surface wasrecorded.
We observed a modified potential if a dissolution process took place after the water
drop was introduced. The lower curve in Fig. 9 was recorded after dropping 20 µl of water
onto the transducer surface, where about 3 mg of solid KCl had been placed previously. In
this case, a significantly lower thermoelectric potential is found after the application ofwater. This higher level of heat consumption can be explained by the dissolution of thesalt. This dissolution process consumes energy because the lattice energy of the solid KCl
is higher than the energy of dissociated ions. The increase in thermoelectric potential after
5-10 s indicates a decrease in the rate of dissolution corresponding to a reduction in the salt
crystal surface area and an increase in salt concentration. After about 3 minutes, the salt isdissolved completely, and the thermoelectric potential is similar to that obtained inexperiments without salt.
Exothermic chemical reactions can be monitored by the evolution of a positive thermo-

Sensors and Materials, Vol. 8, No. 6 (1996)

368

10,--------------------------------,

potential[MIJ]

no salt
-10

-20

-30

3 mg KCI-40�----�----�----�----�---�----�
0

50

100

150

200

250

300

t [sl

Fig. 9. Thermoelectric voltage after applying a drop of water (20 µ1) to an empty transducer surface(upper curve) and that in the presence of solid KCI (lower curve) without any electric heating.

electric potential during the reaction and dissipation of heat (Figs. 10 and 11). Ten µl of 2.5
M sulfuric acid were neutralized by NaOH solutions of different concentrations. A steep
increase in thermoelectric potential was observed immediately after mixing the twocompounds at the transducer surface. The potential depends strongly on the hydroxide
concentration. The observed decay of the thermoelectric potential does not depend on theconcentration, but corresponds to the purely physical relaxation of the thermal system.
This is to be expected in the case of chemical reactions in which the decay ofthe reaction
rate is faster than the thermal relaxation. The time-integrated potential is directly related to
the reaction enthalpy. The experimentally estimated reaction enthalpies for this standard
reaction agree with the values in the literature (67 kJ I mole <9l).
The overall kinetics of chemical reactions can be recorded in the case of slower
chemical reactions. We studied the redox reaction between malonic acid and bromate inhighly acidic media in the presence of Ce(IV) as a redox catalyst (c.f. ref. 6). The speed ofthis complex reaction is dependent on the cataly'st concentration (Fig. 11). The higher thecatalyst concentration the steeper the increase in thermoelectric potential after the start of
the reaction, the higher the exothermic peak Umax and the faster the postpeak decay. In thiscase, the thermoelectric decay is not dependent on the (physical) thermal relaxation, but on
the rate of the chemical reactions.
The transducer is also suitable for detecting biochemical reactions. Exothermic peaks
can be found using the drop method for the free-standing thin film transducer in the
enzymatic oxidation of glucose with glucose oxidase and in the decomposition of theSensors and: Materials, Vol. 8, No. 6 (1996)

369

30�-----------------------------

POtential[MU]

2.5 M NaOH

20

0.05 M NaOH

0.5 M NaOH
-20'------"-----L-----'------'---------'L--------'
0

30

60

90

120

150

180

t Csl

Fig. 10. Evolution of thermoelectric potential after the reaction of 10 µI 2.5 Msulfuric acid with 10µl of 50 mM, 0.5 Mand 2.5 MNaOH (no electric heating).
16r-----------------------------�

potential[MU]

40 mM Ce(IV)

12

8

4

0

-4'-------'------'------'-----.J.._----l-...---__J
0

300

600

900

1200

1500

1800
t Cs]

Fig. 11. Evolution of thermoelectric potential during a complex redox reaction of 10 µI of solution
A (6 M sulfuric acid, 0.6 M NaBrO3, 0.4 M malonic acid) with 10 µI of 15 mM, 20 mM and 40 mM
solutions of Ce(NH4)i(NO3)6 (no electric heating).

Sensors and Materials, Vol. 8, No. 6 (1996)

370

intermediately formed hydrogen peroxide with catalase (Fig. 12). Only a short duration,
small potential was observed when buffer solution alone was added to the enzyme solution.
Significantly higher and broader peaks representing the biochemical reaction were observed
when glucose was present in the buffer solution. Thus, the maximum potential is affected
mainly by the concentration of the biocatalysts. In contrast, the amount of substrate(glucose) affects the duration of the reaction, and thus the shape of the reaction peak. Thisobserved behavior agrees well with the known mechanisms of enzymatic processes.
Different concentrations of glucose (substrate) can be well distinguished; therefore themethod is, in principle, applicable to biosensors.

4.

Conclusions

The system which involves adding of a drop on thermally isolated membranes withthermal thin film sensors has two time constants. The time constant for the thermal
relaxation of the whole system (thin film stack plus drop) is much higher than the time
constant for the sensor alone, which can be explained by the dramatically increased heat
capacity of the system due to the presence of the drop. In addition, a fast heat exchange
process is observed, which is interpreted as heat flow from the thin film stack to the interiorof the drop.

potential[mV]

0.0 ,------,------,------,------,------,-----�

-0.2
100mM

-0.4

-0.6
50mM

-0.8
buffer

-1.0-1.2 ,___.....___.______.______.______1..--____,..______J
500

1000

1500

2000
t[s]

Fig. 12. Evolution of thermoelectric potential during a biochemical reaction of 10 µl of an enzyme(5 U/µl glucose oxidase and 5 U/µl catalase) with 10 µl of 100 mM and 50 mM glucose in phosphatebuffer solution and pure phosphate buffer solution.

Sensors and Materials, Vol. 8, No. 6 (1996)

371

Evaporation from the drop surface has a cooling effect on the sensor. Evaporation
cooling can be detected as a negative thermoelectric potential, which, as expected, depends
on the surface size of the drop.
Using thin film resistors, it is possible to apply high heat flux densities to the drops. At
high electrical heating power, a considerable temperature gradient evolves inside the drop.
The energy is consumed by fast evaporation of liquid in the case of water or ethanol, whichleads to the complete evaporation of drops with volumes of 10 µl within a few minutes oreven seconds. The disappearance of liquids from the surface by evaporation is marked bya marked change in the thermoelectric potential in the case of constant heating power.
The thermal isolation of drops means that the system is suitable for detecting small
amounts of chemical substances in inorganic, organic and biochemical reactions. The
thermal relaxation of a fast reaction such as neutralization is mainly dependent on the time
constant of the sensing system. However, it was shown that the kinetic behavior of slower
and more complex chemical reactions such as the catalytic oxidation of malonic acid bybromate in the presence of cerium can also be accurately represented by the thermoelectric
potential with respect to time. Quantitative measurements are also possible in the detectionof biochemical processes. The influence of concentration of biochemical substrates on thetime-integrated thermoelectric potential and the influence of the enzyme concentration on
the thermoelectric potential correspond well with the known basic mechanisms of enzy­matic reactions.
Further work is necessary in order to evaluate the influence of parasitic and perturba­
tion effects on the thermal flow between thermally isolated drops and their surroundings. If
the physical limit of Nyquist noise (approx. 25 nV) can be determined by controlling the
disturbance of heat flow in the measurement apparatus, it might be possible to realize
microcalorimetry, microthermokinetic measurements and microscanning calorimetry withanalyte concentrations in the picomole range, which would be very important in environ­mental analysis, biotechnology and medical analysis.

Acknowledgments
We are indebted to I. Menzel, W. Schubert and P. Ratz (Jena) for technical assistance.
The investigations were supported by the Deutsche Forschungsgemeinschaft (Ko 1403/3-1).

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