9
Comparison of short carbon fibre surface treatments on epoxy composites I. Enhancement of the mechanical properties Hui Zhang, Zhong Zhang * , Claudia Breidt Institute for Composite Materials, University of Kaiserslautern, Erwin Schrodinger Strasse 58, D-67663 Kaiserslautern, Germany Received 7 August 2003; accepted 22 February 2004 Available online 12 April 2004 Abstract Pitch-based short carbon fibres were treated by both a gaseous oxidation and a cryogenic treatment approach. It was found by scanning electron microscopy that the fibre surface roughness was increased by various oxidative conditions, whereas the fibre diameter was reduced by the cryogenic treatment. In both cases, appropriate treatments could effectively improve the mechanical properties in their epoxy composites due to the enhanced fibre–matrix interfacial bonding. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Short carbon fibres; Fibre treatment; Gaseous oxidation; Cryogenic treatment; Epoxy; Mechanical properties 1. Introduction It is well known that the fibre/matrix adhesion strength plays an important role on the mechanical properties of fibre reinforced polymer composites [1–8]. When load is applied to composites, it will be distributed and transferred through fibre/matrix interfaces. A strong bonding promotes a better involvement of more fibres, accordingly increases the strength of composites. However, carbon fibres usually perform a poor bonding behaviour to polymer matrix due to their nature of smoothness and chemical inertness. In order to improve the bonding properties of carbon fibres, various ap- proaches can be applied, which were classified into ox- idative and non-oxidative treatments by Park and Kim [9]. Oxidation treatments involve gas-phase, liquid- phase and anodic oxidations, whereas the non-oxidative ones include plasma treatment, deposition of more ac- tive forms of carbon, or grafting of the carbon fibre surface with polymers [10]. Oxidation treatment of car- bon fibres in hot air is one of the commonly used ap- proaches owing to several advantages, e.g. easy operation, low cost and lack of pollution [11]. On the other hand, cryogenic treatment of carbon fibres, which could increase the fibre strength by clearing the weak layer of amorphous carbon, seems to be an interesting and relatively novel method. Few about this approach were reported. Rashkovan and Korabelnikov [12] trea- ted high-tenacity long carbon fibres in liquid nitrogen for 30 s, in order to improve the mechanical properties in composites. However, the effect on short carbon fibres with an extended treatment time, and the performance on mechanical properties of their composites are not yet fully understood. In the present work, two different approaches, i.e. air oxidation and cryogenic treatment, were applied to treat pitch-based short carbon fibres at various conditions. The configurations of treated carbon fibres and the fractography were studied by using scanning electron microscopy (SEM). The improvement on the mechani- cal properties of treated carbon fibres reinforced epoxy is reported. Further improvement of the tribological properties will be presented in the subsequent part of this paper [13]. * Corresponding author. Tel.: +49-631-2017213; fax: +49-631- 2017196. E-mail address: [email protected] (Z. Zhang). 0266-3538/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.02.009 Composites Science and Technology 64 (2004) 2021–2029 COMPOSITES SCIENCE AND TECHNOLOGY www.elsevier.com/locate/compscitech

Comparison of short carbon fibre surface treatments on epoxy composites: I. Enhancement of the mechanical properties

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COMPOSITESSCIENCE AND

Composites Science and Technology 64 (2004) 2021–2029

TECHNOLOGY

www.elsevier.com/locate/compscitech

Comparison of short carbon fibre surface treatmentson epoxy composites

I. Enhancement of the mechanical properties

Hui Zhang, Zhong Zhang *, Claudia Breidt

Institute for Composite Materials, University of Kaiserslautern, Erwin Schr€odinger Strasse 58,

D-67663 Kaiserslautern, Germany

Received 7 August 2003; accepted 22 February 2004

Available online 12 April 2004

Abstract

Pitch-based short carbon fibres were treated by both a gaseous oxidation and a cryogenic treatment approach. It was found by

scanning electron microscopy that the fibre surface roughness was increased by various oxidative conditions, whereas the fibre

diameter was reduced by the cryogenic treatment. In both cases, appropriate treatments could effectively improve the mechanical

properties in their epoxy composites due to the enhanced fibre–matrix interfacial bonding.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Short carbon fibres; Fibre treatment; Gaseous oxidation; Cryogenic treatment; Epoxy; Mechanical properties

1. Introduction

It is well known that the fibre/matrix adhesion

strength plays an important role on the mechanical

properties of fibre reinforced polymer composites [1–8].

When load is applied to composites, it will be distributed

and transferred through fibre/matrix interfaces. A

strong bonding promotes a better involvement of morefibres, accordingly increases the strength of composites.

However, carbon fibres usually perform a poor bonding

behaviour to polymer matrix due to their nature of

smoothness and chemical inertness. In order to improve

the bonding properties of carbon fibres, various ap-

proaches can be applied, which were classified into ox-

idative and non-oxidative treatments by Park and Kim

[9]. Oxidation treatments involve gas-phase, liquid-phase and anodic oxidations, whereas the non-oxidative

ones include plasma treatment, deposition of more ac-

tive forms of carbon, or grafting of the carbon fibre

surface with polymers [10]. Oxidation treatment of car-

* Corresponding author. Tel.: +49-631-2017213; fax: +49-631-

2017196.

E-mail address: [email protected] (Z. Zhang).

0266-3538/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compscitech.2004.02.009

bon fibres in hot air is one of the commonly used ap-

proaches owing to several advantages, e.g. easy

operation, low cost and lack of pollution [11]. On the

other hand, cryogenic treatment of carbon fibres, which

could increase the fibre strength by clearing the weak

layer of amorphous carbon, seems to be an interesting

and relatively novel method. Few about this approach

were reported. Rashkovan and Korabelnikov [12] trea-ted high-tenacity long carbon fibres in liquid nitrogen

for 30 s, in order to improve the mechanical properties

in composites. However, the effect on short carbon fibres

with an extended treatment time, and the performance

on mechanical properties of their composites are not yet

fully understood.

In the present work, two different approaches, i.e. air

oxidation and cryogenic treatment, were applied to treatpitch-based short carbon fibres at various conditions.

The configurations of treated carbon fibres and the

fractography were studied by using scanning electron

microscopy (SEM). The improvement on the mechani-

cal properties of treated carbon fibres reinforced epoxy

is reported. Further improvement of the tribological

properties will be presented in the subsequent part of

this paper [13].

2022 H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029

2. Experimental

2.1. Materials and compounding

Pitch-based short carbon fibres (M-2007S) weresupplied by Kureha Co. without treatment, which have

a density of 1.6 g/cm3, and average diameter and length

of 14.5 and 90 lm, respectively. They are graphite grade

short fibres with excellent mechanical properties, e.g.

tensile strength of 800 MPa, modulus of elasticity of 35

GPa, and elongation of 2.3%. For the oxidative treat-

ment, the carbon fibres were oxidized in a muffle furnace

at various temperatures for 1 h. The air vent was alwaysapplied to keep the air inside the furnace flowing during

processing. In the case of cryogenic treatment, short

carbon fibres containing in a ferrous vessel were im-

mersed into liquid nitrogen ()196 �C) for various min-

utes. All treatment details are summarized in Table 1.

The matrix used in this work was a bisphenol-A type

resin (DER331, Dow) hardened by an amine curing

agent (HY2954, Dow), with densities of 1.16 and 0.95 g/cm3, respectively. The composites were prepared in a

vacuum dissolver by mixing the epoxy resin with 15

vol.% untreated and treated short carbon fibres as de-

scribed in Table 1. The epoxy resin and the curing agent

were preheated at 70 �C in an oven for at least 4 h before

use. The mixing process was carried out at 70 �C with

stirring speed of 2000 rpm for 30 min under vacuum,

subsequently adding definite amount of curing agent,the mixture was stirred at 60 �C with stirring speed of

200 rpm for 15 min and then was poured into a rect-

angular aluminium mould for curing. The applied gel

temperature was 70 �C for 8 h, followed by a curing

stage at 122 �C for 16 h.

2.2. Mechanical properties

A Zwick universal testing machine was applied to in-

vestigate the flexural modulus and strength under a three-

point-bending approach according to DIN-ISO-178.

Specimens were cut at a dimension of 100� 10� 4 mm3.

The test speed was kept constant at 1 mm/min. Five

specimens of each composition were measured and an

Table 1

Details of specimens and treatment conditions

Treatment approach Sample No.

– CF_0

Oxidation (in air) CF_450

CF_500

CF_550

CF_600

Cryogenic treatment (in liquid nitrogen) CF_1

CF_5

CF_10

CF_20

average valuewas reported, with an error scattering of the

maximum absolute error.

2.3. SEM observation

The configuration of as-received, treated carbon fi-

bres as well as fracture surfaces of epoxy composites

were examined using a JEOL-5400 SEM. The diameters

of carbon fibres before and after liquid nitrogen treat-

ment were also determined by SEM. In the latter case,

the sample holder of SEM was adjusted to zero degree

and all samples were coated with gold films previously.

An average value of diameters was calculated from atleast 200 individual carbon fibres.

3. Results and discussion

3.1. SEM observation

The SEM configurations of as received, oxygen treatedand cryogenic treated short carbon fibres are given in

Fig. 1. Remarkable differences in micrographs can be

observed on untreated and treated carbon fibres. The

surface of as-received fibre (Fig. 1(a)) seems to be rela-

tively smooth and there are some small impurities ab-

sorbed on the fibre surface, which were introduced during

the fibre manufacturing process. Under a treatment

temperature of 450 �C the surface does not look appre-ciably different when compared to untreated ones, which

suggests that the treatment was mild and did not cause

essential morphological changes on the fibre surface [14].

However, by using the gas physical adsorption technique,

Wan et al. [11] reported that after treatment under a

similar condition mentioned above, the total carbon fibre

surface areawas doubled. Their result indicated that some

changes did take place on carbon fibre surface at 450 �C,although it was difficult to be recognized by SEM. Once

the treatment temperature was further increased, the

changes on the surface could be easily observed. At a

treatment temperature of 500 �C for 1 h (Fig. 1(b)), the

fibre surface became relatively rough and more pieces of

tiny fragments stuck to the fibre surface, which suggested

CF volume content Treatment details

15% As-received

15% 450 �C/1 h

15% 500 �C/1 h

15% 550 �C/1 h

15% 600 �C/1 h

15% 1 min

15% 5 min

15% 10 min

15% 20 min

Fig. 1. SEM configurations of carbon fibres treated under different conditions: (a) as-received; air-oxidized at (b) 500 �C/1 h, and (c) 600 �C/1 h;

cryogenic treated in liquid nitrogen for (d) 1 min, and (e) 10 min.

H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029 2023

that the absorbability of treated carbon fibres might be

enhanced to some extent. A great number of micro-pits

could be found on the fibre surface on account of a violent

oxygen etching at the highest oxidative temperature of

600 �C in our case (Fig. 1(c)). Those pits with the size in a

range of several hundred nanometres had irregular shapes

and distributed uniformly over the fibre surface. In some

places they were linked together and formed a ditch-like

Fig. 2. Diagram of the mechanism of the cryogenic treatment on

carbon fibres.

Table 2

Fibre diameter distribution before and after cryogenic treatment

Short

carbon fibre

Average

diameter (lm)

Peak

centre (lm)

Peak

width (lm)

Peak

height (%)

As-received 14.6 14.48 6.67 10.72

5 min 14.2 14.47 5.66 13.38

20 min 13.9 14.12 4.83 15.21

2024 H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029

structure. Obviously, this kind of treatment destroys the

original structure of carbon fibres, therefore, leading to a

loss of mechanical properties of the carbon fibres some-

how, as a consequence to that of the composites as well.

252015100

252015100

0

2

4

6

8

10

12 as-received

av=14.6µm

Fra

ctio

n [

%]

Diameter [µm]

0

2

4

6

8

10

12

14

16

18 20min

av=13.9µm

Fra

ctio

n [

%]

Diameter [µm](b)

(a)

Fig. 3. Typical diameter distribution of carbon fibres before and after

cryogenic treatment.

In the case of cryogenic treatment, an appreciable

characteristic is that only a very short treatment time (1

min, Fig. 1(d)) could make a difference in the mor-

phology of carbon fibres. The surface roughness of the

carbon fibre might, after a cooling treatment for 1 min,

nearly attain such a level that was reached by the air

oxidative treatment at much longer time (1 h at a

treatment temperature of 550 �C). When extending thetreatment time up to 10 min, the carbon fibre surface

became very rough, and lots of tiny fragments and some

striations along the fibre axis could be observed

(Fig. 1(e)). At the same time it led to a reduction of the

fibre diameter on account of the removing of the

amorphous carbon layer, which will be further discussed

later. So far as the enhancement of the surface rough-

ness and the treatment time are concerned, the cryogenictreatment seems to be more efficient than the air oxi-

dative one.

Fig. 2 illustrates a diagram of the cryogenic treatment

for carbon fibres. As pointed out by Rashkovan and

Korabelnikov [12], a carbon fibre is usually composed of

two parts, i.e. the proper carbon fibre, and a layer of

amorphous carbon deposited on it, so-called disordered

structure (cf. [15]). At low temperatures, due to thedifference of the coefficients of linear thermal expansion

(CTE) between these two parts, the carbon fibre is ex-

posed to a contraction of the amorphous carbon and an

0 5 10 15 2013.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

Dia

met

er [

µm]

Treatment Time [min]

Fig. 4. Dependence of the fibre average diameter on the cryogenic

treatment time.

H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029 2025

axial expansion of the proper fibre, while the proper fi-

bre has a negative CTE. Shear stresses arise on the in-

terface of the two parts and finally exceed the shear

strength between the proper fibre and the amorphous

carbon layer. Therefore the latter would easily shell offfrom the fibre surface. Due to its heterogeneity, the

amorphous carbon layer shells off along the fibre to

various extents resulting in an increase of the fibre sur-

face roughness, as confirmed by SEM micrographs.

3.2. Fibre diameter distribution

As mentioned above, the amorphous carbon layercan partly shell off from the fibre after the cryogenic

treatment. Accordingly, the diameter of the carbon fibre

is reduced to some degree. Fig. 3 shows the typical

3.5

3.4

3.5

3.5

3.9

3.0

3.5

4.0

4.5

CF_0 CF_450 CF_500 CF_550 CF_600

Fle

xura

l Mo

du

lus

[GP

a]

90.5

109.7107.7

98.1

88.9

80

90

100

110

120

CF_0 CF_450 CF_500 CF_550 CF_600

Fle

xura

l Str

eng

th [

MP

a]

3.473.23.323.333.36

0

1

2

3

4

5

CF_0 CF_450 CF_500 CF_550 CF_600

Elo

ng

atio

n a

t B

reak

[%

]

(a) (d

(e

(f

(b)

(c)

Fig. 5. Flexural properties of CF/epoxy composites: for air oxidation, (a) flex

cryogenic treatment, (d) flexural modulus, (e) flexural strength, and (f) elong

curves of the diameter distribution for as-received and

treated carbon fibres, which were fitted by Gaussian

distributions, and the parameters were summarized in

Table 2. It can be found that the fitting results of

cryogenic treated fibres shifted slightly to lower valuesand the width of the curve also became narrow. This

implicates that the amount of fibres with large diameters

decreased, possibly due to the fact that they possess

thicker amorphous carbon layers, which are easily to be

shelled off after cryogenic treatment. When the treat-

ment time reached up to 20 min, the average diameter

decreased about 4.8%. Fig. 4 demonstrates that at the

beginning of the treatment, the rate of ‘‘shelling off’’ ofthe amorphous carbon layer was higher. With an in-

creasing treatment time, the rate ran slowly down. Even

with only three points measured in Fig. 4, the average

4.0

4.44.5

4.0

3.5

3.0

3.5

4.0

4.5

5.0

CF_0 CF_1 CF_5 CF_10 CF_20

Fle

xura

l Mo

du

lus

[GP

a]

105.0

112.2

90.5

97.399.9

80

90

100

110

120

CF_0 CF_1 CF_5 CF_10 CF_20

Fle

xura

l Str

eng

th [

MP

a]

3.36 3.15 3.25 3.12 2.98

0

1

2

3

4

5

CF_0 CF_1 CF_5 CF_10 CF_20

Elo

ng

atio

n a

t B

reak

[%

]

)

)

)

ural modulus, (b) flexural strength, and (c) elongation at break; and for

ation at break.

CF_0 CF_450 CF_500 CF_550 CF_6000.8

0.9

1.0

1.1

1.2

1.3

1.4

Rel

ativ

e Im

pro

vem

ent

Air Oxidation

flexural modulusflexural strengthelongation

CF_0 CF_1 CF_5 CF_10 CF_200.8

0.9

1.0

1.1

1.2

1.3

1.4

Rel

ativ

e Im

pro

vem

ent

Cryogenic Treatment

flexural modulusflexural strengthelongation

(a)

(b)

Fig. 6. Relative improvements on the mechanical properties of

(a) air-oxidation, and (b) cryogenic treatment.

2026 H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029

thickness of the amorphous carbon layer can be roughly

estimated as approximately 0.7 lm.

3.3. Mechanical properties

The effects of the air oxidative treatment on the

flexural strength, the modulus and the elongation of CF/

EP composites are given in Fig. 5. The flexural moduli

of treated samples increase slightly in the range of

treatment temperature between 450 and 550 �C. The

modulus decrease at a treatment temperature of 600 �C,which may due to the loss of the distinct fibre strength

(Fig. 5(a)). A maximum modulus value can be found ata temperature of 550 �C, i.e. 3.9 GPa, about 10% im-

provement compared with that of untreated one. On the

other hand, the flexural strength of treated samples en-

hances monotonically with an increased oxidation level

(Fig. 5(b)). A maximum strength value can be observed

at the treatment temperature of 600 �C, i.e. 109.7 MPa,

about 21% improvement compared with that of un-

treated one. Although under these conditions the propercarbon fibres were damaged, the strong interfacial

bonding may contribute these improvements on both

strength and modulus. To summarize the above results,

the flexural strength of the composite is more sensitive

to the change of fibre–matrix interface than the modu-

lus. The latter is largely dominated by the stiffness of the

fibres.

In term of the cryogenic treatment, the flexuralmoduli and the strength of treated samples also in-

creased effectively comparing to untreated ones

(Fig. 5(d) and (e)). The flexural modulus and strength

reach their maximum value at a treatment time of 10

min, i.e. 4.5 GPa and 112.2 MPa, respectively, which

were about 29% and 24% improvement comparing with

that of untreated one. However, these effects tend to

decrease with an increased treatment time. It is consid-ered that there is an optimum treatment condition for

the carbon fibres and their composites. After too long

treatment time, too much amorphous carbon shelled off

from the fibre, corresponding to a decrease in the

amounts of interlocking sites. For both treatments, the

elongations of the samples appeared to no obvious

changes compared to that of the untreated ones

(Fig. 5(c) and (f)), indicating that the elongation is adominate of the matrix.

Fig. 6 demonstrates the relative improvements on

mechanical properties of epoxy composites for both

treatment approaches. The main difference consists in

the changes of flexural moduli of CF/EP composites.

For the air oxidative treatment (Fig. 6(a)) the flexural

moduli of their epoxy composites increased slightly,

since the mechanical properties of the carbon fibres didnot change at mild treatment conditions or rather de-

creased to some degree due to the excessive oxygen

etching. In term of the cryogenic treatment in Fig. 6(b),

it is opposing. It is worth to mention that the maximum

values for both modulus and strength of the cryogenic

treated samples are higher than those of air-treated

results.

3.4. SEM fractography

The improvement on flexural properties of CE/EP

composites could be attributed to the enhancement of

the interfacial adhesion strength of the fibre and matrix

after fibre surface treatments. There are several mech-

anisms for the fibre–matrix bonding, which involve

mechanical interlocking, adsorption interaction, elec-trostatic interaction, and diffusion of polymer chain

segments [16]. As far as air-treated samples are con-

cerned, the mechanical interlocking could be the most

important factor. As shown in SEM micrographs

(Fig. 1), with increased treatment temperatures the fi-

bre surfaces become rougher, i.e. the fibres possessed a

larger surface area, which could contact with matrix

and thus formed more mechanical interlocking sites. In

H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029 2027

addition, the enhancement of the surface roughness

reduces the contact angle between fibre and matrix and

hence increases the wettability [17] as well. SEM frac-

tographies of three-point-bending tests are given in

Fig. 7. It is easily recognized in Fig. 7(a) that untreated

Fig. 7. SEM fractographies of CF/epoxy composites: (a) as-received; oxidized

(d) 10 min, and (e) 20 min.

carbon fibres performed very poor interface bonding

with epoxy matrix. After oxidation treatment shown in

Fig. 7(b) and (c), strong interlocking of fibre–matrix

bonding can be observed as marked by arrows in

Fig. 7(c), which was termed as ‘‘mechanical anchor’’ by

at (b) 500 �C/1 h, (c) 600 �C/1 h; cryogenic treated in liquid nitrogen for

2028 H. Zhang et al. / Composites Science and Technology 64 (2004) 2021–2029

Kalantar and Drzal [16]. The mechanical interlocking

provides a strong interface bonding even though other

effects are weak [18]. Another possible reason for the

enhancement on interfacial adhesion is chemical inter-

action. Many researchers [19–22] have analysed theO1s/C1s ratio of carbon fibre surface by means of a X-

ray photoelectron spectroscopy (XPS), and reported

that gaseous oxidative treatment could increase the

oxygen concentration on carbon fibre surface, which

means that the amount of functional groups could be

increased, e.g. hydroxyl (–OH), carbonyl (–C@O) and

carboxyl (–COOH) groups. These functional groups

may improve the wettability by enhancing the surfaceenergy. Therefore chemical reactions can take place

with epoxy group forming covalent bonding at the

interface.

In the case of cryogenic treatment, similar mechanical

interlocking was also observed which plays an important

role to the improved interfacial adhesion, as shown in

Fig. 7(d) marked by arrows. It is interesting that even

some broken fibres can be found (Fig. 7(e)) which in-dicates the mechanical interlocking in some regions was

very strong. Since the average length of carbon fibres

applied in this study is much shorter compared to the

fibre broken critical length as reported in literatures of

several hundreds microns [23,24], fibre pull-out and

matrix fracture should be the main failure modes in our

case. An improved fibre–matrix bonding with fibre

broken involving will definitely improve the strength ofcomposites. Another reason for the enhancement of the

flexural properties is the strengthening effect of carbon

fibres of the cryogenic treatment [12]. After treatment

the average strength of the carbon fibres usually in-

creased due to the removal of the weak layer and at-

tached particles, which act as concentrators and

decrease the fibre strength to some extent. On the other

hand, it should be mention that not all the carbon fibreshad the similar obvious changes after cryogenic treat-

ment. Some carbon fibres still kept much smoother

surface with poor bonding to the matrix as shown in

Fig. 7(e) as well. The possible reasons of this phenom-

enon could be: (i) the heterogeneity of fibres, while some

carbon fibres, which may possess very thin amorphous

carbon layer, do not form a rough surface after treat-

ment; and (ii) the treatment process, while some fibreswere not effectively treated due to the thermal conduc-

tion. An optimum treatment process is still a task to

fully exert the potential of this approach on the en-

hancement of carbon fibre–matrix bonding of polymer

composites.

4. Conclusions

Based on this work devoted to studying the effect of

surface treatment on mechanical properties of short

carbon fibre reinforced epoxy composites, the following

conclusions can be drawn:

1. Both oxidative and cryogenic treatments could signif-

icantly increase the surface roughness of carbon

fibres, accordingly to improve the interfacial adhe-sion strength of fibre and epoxy bonding due to the

mechanical interlocking.

2. The cryogenic treatment has advantages of very short

treatment time and environment-friendly media, as

well as higher improvement on both modulus and

strength compared to the oxidative one.

3. The carbon fibres used in this study were relatively

short; therefore the improvement on mechanicalproperties was limited. Further enhancement of the

tribological properties will be concentrated on the

subsequent part of this paper [13].

Acknowledgements

Z. Zhang is grateful to the Alexander von Humboldt

Foundation for his Sofja Kovalevskaja Award, financed

by the German Federal Ministry of Education and Re-

search (BMBF) within the German Government’s‘‘ZIP’’ program for investment in the future. The au-

thors appreciate Prof. Dr.-Ing. Dr. h.c. K. Friedrich,

IVW, for his valuable discussions during the course of

this work and the preparation of this paper.

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