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the PS substrate. Therefore, the saw-tooth pattern corres-

ponds to the detachment of the adsorbed segments in a single

chain from the substrate. Moreover, the force curves

obtained on a quartz substrate have single peak force signals,

which is similar to PNIPAM [16]. This result is reasonable

since short hydrophobic PS segments cannot adsorb onto the

hydrophilic quartz substrate. This finding further confirms

that the weak rupture force obtained on the PS substrate

corresponds to the desorption of short PS segments from

the PS substrate [50].

The most probable desorption force at a given stretching

velocity, which is obtained from the histogram of desorption

force, is about 41 pN, as shown in Fig. 30.10b. Such a

distribution varies with the stretching velocity. The linear

dependence of the most probable desorption force on the

logarithm of the stretching velocity experimentally reveals

that the adsorption and desorption of the PS segments on the

PS substrate is a dynamic process [50]. Since it is known

that each PS segment contains 20 monomer units on aver-

age, the desorption force for per PS monomer unit from the

PS substrate in water is estimated in the range 1.3–2.1 pN,

depending on the imposed stretching velocity.

Besides the physical adsorption, the stable covalent at-

tachment of a single or a small number of polymer mol-

ecules to AFM cantilever tip is a most important prerequisite

in order to employ individual polymer molecules as inter-

facial, analytical probes for the identification and measure-

ment of various types of polymer-surface interactions [54].

Recently, Haschke et al. have covalently attached polyacrya-

mide molecule to the AFM cantilever tip. By approaching

and retracting the tip with the molecule to the surface of

interest, they have obtained force curves with multipeaks

[72]. The covalent attachment of the chain to the tip ensures

that any detachment measured in the force spectroscopy

experiment is the force between the molecule and the sam-

ple surface. Therefore, the multipeaks of force curves cor-

respond to detachment of multiple loops that are formed by

the physisorption of polyacryamide at interface, as shown in

Fig. 30.11.

30.4.2 Long Plateau Versus Train-like Structure

Provided that the polymer forms a train-like conformation

at interface, the desorption force should be similar when

detaching each adsorption point during the polymer chain

elongation. As a result, the force curves should show a

characteristic plateau. Seitz and his coworkers have used

chemisorption to immobilize polyvinylamine polymer chain

and studied the elasticity of the single polymer chain as a

function of polymer’s charge density and electrolyte con-

centration [51]. Their results indicate that, in addition to

electrostatic interaction between polyvinylamine and nega-

tively charged silica substrate which depends linearly on the

Debye screening length and the polymer’s line charge dens-

ity, a constant nonelectrostatic interaction plays an import-

ant role in the desorption process [51].

PAMPS and its random copolymer containing 18-crown-6

(PAMPS-co-crown), are used to further study the nonelec-

trostatic contribution to desorption force [56]. The primary

structures of polymers are shown in Scheme 30.5. As shown

in Fig. 30.12, the typical force curves of PAMPS with a

plateau are obtained from amino-modified quartz in the

buffer of water. The long plateau suggests that the desorption

process of the PAMPS chain from the substrate is smooth

and that it adopts a train-like conformation at the interface

and the desorption force remains about 120 pN. The desorp-

tion–adsorption process is in equilibrium in the experimental

time scale, which is confirmed by the constant desorption

force when changing the stretching velocity. The desorption

force of PAMPS from the amino-modified quartz has been

[ CH

CH ]

PS substrate

100–130 nm

[ CH

CH ]

n ~ 500, m ~ 20

< 1.1

~ 5,000,000

SCHEME 30.4. (a) Schematic of a linear segment PNIPAM-

seg-PS prepared by micelle copolymerization, in which short

PS segments are relatively evenly distributed on the chain

backbone. (b) A possible adsorption conformation of a linear

PNIPAM-seg-PS chain on a hydrophobic PS substrate in

water. Reproduced from Macromolecules (2003) with permis-

sion from American Chemical Society [50].

Extension

Force

100 pN

200 nm

FIGURE 30.9. Measured force curves of linear segment PNI-

PAM-seg-PS chains adsorbed on a hydrophobic polystyrene

substrate in water. Reproduced from Macromolecules (2003)

with permission from American Chemical Society [50].

532 / CHAPTER 30

studied using different concentration of electrolyte as buffer.

A series of experiments show that the external salt does not

influence the desorption force of PAMPS.

In experiments, when the sample is immersed in the salt

solution, the ion screening effect would influence largely on

the electrostatic interaction but little on the nonelectrostatic

interaction between the polyelectrolyte and the substrate

[4,51]. It is possible for both the hydrophobic backbone

and the charged groups of PAMPS to adsorb onto the sub-

strate, since the static contact angle of amino-modified

substrate is about 678. It is reported that there is a ‘‘zero

charge contribution’’ by about 38 pN in the ionic strength

sensitive desorption force for the polyelectrolyte without

spacer [51,54]. In the case of PAMPS, the introduced spacer

between the charged groups and the backbone effectively

enhances the nonelectrostatic contribution to the interfacial

interaction, making the interfacial interaction insensitive to

the ionic strength. These results together reveal the none-

lectrostatic origin for the adsorption of the polyelectrolytes

[56].

The force curves of PAMPS-co-crown obtained from

amino-modified substrate are resembled to the curves

shown in Fig. 30.12, which also show a long plateau with

a height of about 120 pN. The long plateau indicates that

PAMPS-co-crown chains also assume a train-like conform-

ation at the interface. Similar to PAMPS, the desorption

force of PAMPS-co-crown is independent of the concentra-

tion of electrolyte and the stretching velocity. The result

indicates that the 20% content of crown ether side groups

in the copolymer chain does not influence the desorption

force. In other words, the interaction between PAMPS-co-

crown chain and the substrate could be mainly dominated by

the hydrophobic interaction. Based on the above discussion,

SMFS allows to measure adhesive forces on the single

molecule level and to gain new insight into the fundamental

interactions in polymer adsorption.

Distance (nm) Desorption force (pN)

Counts

100 120 140 160

114 nm

40 60

MPO

= 41 pN

FIGURE 30.10. (a) Statistics of the distance between two adjacent peaks in the measured force curves. (b) Distribution of the

measured desorption force for linear PNIPAM-seg-PS chains adsorbed on hydrophobic polystyrene substrate, where the

stretching velocity is kept at 4,600 nm/s. Reproduced from Macromolecules (2003) with permission from American Chemical

Society [50].

−800

−400

−600

−200

200

Tip-sample distance (nm)

Force (pN)

400 600 800 1,000 1,200

Sulfur–gold bond

Polymer

FIGURE 30.11. Force curve with a polyacrylamide molecule

end-grafted to a gold-coated cantilever tip obtained on mica in

water. Reproduced from Macromolecules (2004) with permis-

sion from American Chemical Society [72].

−

PAMPS

PAMPS-co-Crown

m/n = 20/80

SCHEME 30.5. Primary structures of PAMPS and PAMPS-

co-crown.

FORCE SPECTROSCOPY OF POLYMERS:BEYOND SINGLE CHAIN MECHANICS / 533

30.5 OUTLOOK

AFM based SMFS is a powerful tool in studying the

intermolecular and intramolecular interaction in polymer

systems, leading to opening a new field of nanomechanics

of polymers. Although many elegant experiments have been

performed, it must be point out that SMFS is still in the

nascent stage. The technique itself can be improved and

introduce new functions. For example, introduction of

force clamp mode allow for following the dynamic process

of the folding or unfolding probability of proteins [73]. It

will be necessary to combine SMFS with other spectro-

scopic methods in order to link the force signal with struc-

ture change. In addition, theoreticians and experimenters

need collaborate to realize the full potential of SMFS.

After accumulating enough data in her information store-

room and in combination with other detection methods,

SMFS will provide us new insight into the basic problems

in polymer science and life science.

ACKNOWLEDGMENTS

This research was supported by the Major State Basic

Research Development Program (G2000078102), National

Natural Science Foundation of China (20474035), and Min-

istry of Education.

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2,000

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3,000

50 100 150 200 250 300 350

Extension (nm)

Extension/nm

Force / pN

Force (pN)

100

200

300

400

500

50 100 150 200 250 300

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FORCE SPECTROSCOPY OF POLYMERS:BEYOND SINGLE CHAIN MECHANICS / 535

CHAPTER 31

Carbon Black

Manfred Klu

ppel*, Andreas Schro

der

, and Gert Heinrich

*Deutsches Institut fu

r Kautschuktechnologie eV, Eupener Str. 33, D-30519 Hannover, Germany

Rheinchemie Rheinan GmbH, Du

sseldorfer str. 23–27, D-68219 Mannheim, Germany

Leibniz Institut fu

r Polymerforschung Dresden eV, Hohe Str. 6, D-01069 Dresden, Germany

31.1 Introduction . ............................................................. 539

31.2 Surface Roughness from Static Gas Adsorption .............................. 541

31.3 Surface Growth during Carbon Black Formation ............................. 544

31.4 Surface Energy Distribution from Static Gas Adsorption ...................... 547

31.5 Summary and Conclusions . ................................................ 549

Acknowledgments ........................................................ 549

References . . ............................................................. 549

31.1 INTRODUCTION

Carbon black (c.b.) plays an important role in the improve-

ment of the mechanical and/or electrical properties of high

performance rubber materials. The reinforcing potential is

mainly attributed to two effects: (i) the formation of a phys-

ically bonded flexible filler network and (ii) strong polymer

filler couplings. Both of these effects refer to a high surface

activity and specific surface of the filler particles [1–3].

So far, the formation and structure of the c.b. network and

the mechanical response is not fully understood. Consider-

able progress has been obtained in the past in relating the

pronounced drop of the elasticity modulus with increasing

dynamical strain (Payne effect) to a cyclic breakdown and

reagglomeration of filler–filler bonds [3–6]. Thereby, differ-

ent geometrical arrangements of particles in a particular

filler network structures, resulting e.g., from percolation [6]

or kinetic cluster–cluster aggregation [7–9], have been con-

sidered. Nevertheless, a full micromechanical description of

energy storage and -dissipation in reinforced rubbers is still

outstanding. Reviews of the different attempts are given in

[10,11] (see also Chapter ‘‘Reinforcement Theories’’ of this

book).

Useful hints concerning the structure and properties of

conducting c.b. networks in elastomers can be obtained from

examinations of the electrical percolation threshold and the

dielectric properties in a broad frequency range [8,11–13].

In particular, the percolation threshold decreases with in-

creasing specific surface and/or structure of the c.b. particles

and decreasing compatibility between polymer and filler.

This emphasizes the role of the mean particle distance or

gap size between particles or particle clusters. It refers to a

thermally activated hopping of charge carriers across the

gaps that governs the conductivity of c.b. filled polymers

above the percolation threshold [11–13].

The dielectric properties are closely related to the hopping

conductivity mechanism, as well. At low frequencies a

delayed charge carrier motion across the gaps that may also

be combined with a polarization of dead ends of the c.b.

network leads to extraordinary high values of the relative

dielectric constant (permittivity) «

ﬃ 10

---10

. With in-

creasing frequencies a polarization transition takes place

and the permittivity falls off drastically [14]. At high fre-

quencies the permittivity approaches a low plateau value and

the conductivity s

increases according to a power law. The

conductivity exponent in the high frequency regime can be

related to the anomalous diffusion exponent on fractal c.b.

clusters [11–13].

For a deeper understanding of the mechanical and elec-

trical properties of c.b. filled rubbers it is necessary to

consider the morphology of the c.b. particles (primary ag-

gregates) more closely. Due to the disordered nature of c.b.

formation during processing in a furnace reactor, the morph-

ology of furnace blacks is well described by referring to a

fractal analysis. Recent investigations of the surface rough-

ness of c.b. by static gas adsorption point out that all furnace

539

blacks exhibit a pronounced surface roughness with an

almost unique surface fractal dimension D

 2:6 on atomic

length scales below 6 nm [15]. This universality can be

related to a particular random deposition mechanism of

carbon nuclei on the particles that governs the surface

growth of the particles during processing [16]. It will be

considered more closely in the following two sections.

According to the universal surface roughness of furnace

blacks independent of grade number one can expect that

the reinforcing potential and electrical effects owing to the

surface roughness of c.b. are similar.

Specific effects of the different grades of furnace blacks

on the mechanical and electrical properties result mainly

from differences in the specific surface and/or structure of

the primary aggregates. The specific surface depends

strongly on the size of the primary particles and differs

from about 10 m

=g up to almost 200 m

=g . The structure

of the primary aggregates describes the amount of void

volume and is measured e.g., by oil (DBP) absorption. It

typically varies between 0:3cm

=g and 1:7cm

=g for fur-

nace blacks [1]. The typical shape of c.b. aggregates is

illustrated in Fig. 31.1, where transmission electron micro-

graphs (TEM) of three different grades of furnace blacks

(N220, N330, N550) are shown. The various sizes of the

primary particles, increasing from top to bottom, become

apparent. It implies a decline of the specific surface from

113 m

=g for N220, 83 m

=g for N330 up to 39 m

=g for

N550. The structure or amount of specific voids of the three

grades is almost the same and differs between 1 cm

=g and

1:2cm

=g, only [8]. Since the specific weight of c.b. is

almost twice of that for DBP, this corresponds to a factor

two for the void volume as compared to the solid volume of

the aggregates. It means that about 2/3 of the aggregate

volume is empty space, i.e., the solid fraction f

A,1

of the

primary aggregates is relative small (f

A,1

 0:33). It is

shown in [8,11] that f

A,1

fulfills a scaling relation which

involves the size and mass fractal dimension of the primary

aggregates. Due to the significant deviation of the solid

fraction f

A,1

from one, the filler volume fraction f has to

be treated as an effective one in most applications, i.e.,

eff

¼ f=f

A,1

The fractal nature of the primary c.b. aggregates and

flocculated clusters can be quantified by TEM-techniques

[1] or dielectric measurements [8,11]. A further technique

that gives information about the morphological arrangement

of filler particles in elastomers is small angle X-ray scatter-

ing (SAXS). Figure 31.2 shows results of scattering inves-

tigations obtained for natural rubber (NR) samples filled

with different c.b. grades of varying specific surface. The

concentration of c.b. is kept constant (46 phr). The double

logarithmic plot in Fig. 31.2 demonstrates that in all cases

two scaling regimes are obtained. For small values of the

scattering vector q the slope is larger than 3, indicating

that the scattering is initiated by mass fractals. The mass

fractal dimension D

equals the negative value of the slope

b (D

¼b). It is found to vary between D

 2:1---2:4. This

is in fair agreement with TEM-estimates for the primary

aggregates [1,8]. The lower cut off length L

is obtained from

the cross-over points of Fig. 31.2 and increases some what

with decreasing specific surface (50 nm < L

< 80 nm). Its

value is of the order of the primary particle diameters, which

appears reasonable since the primary particles represent the

smallest units of the primary aggregates.

For large values of q the slope ß in Fig. 31.2 is almost

constant and smaller than 3. This refers to a surface

scattering by the filler particles. Accordingly, the surface

fractal dimension D

¼ 6 þ ß is found to be almost indepen-

dent of specific surface (D

 2:5). This is evaluated in the

length scale regime between 60 nm and 20 nm, roughly.

FIGURE 31.1. Transmission electron micrographs (TEM) of

three different grades of furnace blacks (N220, N330, N550).

The bar indicates a size of 100 nm. Reprinted from [11] with

kind permission of Springer Science þBusiness Media.

N115

N121

N339

0.05

0.1

q[1/nm]

Intensity [a.u.]

0.3

FIGURE 31.2. SAXS-data for the carbon black grades N115,

N121, and N339.

540 / CHAPTER 31

It compares to scattering results investigated in [17]. Note

however, that for smaller length scales at about 6 nm one

observes again a cross-over of the scattering intensity.

Hence, the surface fractal dimension D

 2:5 is related to

the surface roughness on a mesoscopic length scale regime

and doesn’t reflect the surface roughness on atomic length

scales, as obtained, e.g., by gas adsorption technique [15].

31.2 SURFACE ROUGHNESS FROM STATIC GAS

ADSORPTION

In this section we will demonstrate in some detail, how

the surface roughness of c.b. aggregates can be estimated by

gas adsorption techniques in the mono- and multilayer re-

gime. For this purpose, a classical volumetric adsorption

apparatus equipped with absolute capacitance pressure

transducers has been used for the estimation of adsorption

isotherms in the pressure range 10

3

mbar < p < 10

mbar.

Before adsorption measurements the c.b. samples were

extracted with toluene and water/methanol (1:1) and after

drying degassed at 3008C at a pressure below 10

4

mbar

overnight. The time allowed for equilibrium of each point of

the isotherm was between five and ninety minutes depend-

ing on the sample and the adsorbed amount.

For the morphological surface characterization in the

monolayer regime we refer to a variation of the estimated

BET-surface area with the size of adsorbed probe molecules

(yardstick method). On smooth flat surfaces the BET-area is

independent of the adsorbed probe size or applied yardstick,

while on rough surfaces it decreases with increasing probe

(yardstick) size due to the inability of the large molecules to

explore smaller cavities. This behavior is shown schematic-

ally in Fig. 31.3. A closer analysis shows that in the case of

c.b. a power law behavior of the BET-surface area with

varying yardstick size is observed, indicating a self-similar

structure of the c.b. surface. Double logarithmic ‘‘yardstick-

plots’’ of the BET-monolayer amount N

vs. cross-section s

of the probe molecules are shown in Fig. 31.4 for the original

furnace black N220 and a graphitized (T ¼2,500 8C) sample

N220g. It demonstrates that the roughness exponent or sur-

face fractal dimension D

differs for the two c.b. samples. By

using the relation introduced by Mandelbrot [18]:

 s



(31:1)

one obtains from the slopes of the two regression lines of

Fig. 31.4 a surface fractal dimension D

 2:56 for the

N220-sample and D

 2:32 for the graphitized N220g

sample. An extrapolation of both regression lines yields an

intersection at an ultimate cross-section that corresponds to

a yardstick length of about 1 nm, indicating that graphitiza-

tion reduces the roughness of c.b. on small length scales

below 1 nm, only. Figure 31.4 also demonstrates that the

reduction of BET-surface area due to graphitization is

length scale (yardstick) dependent, proving that it is related

to a change of surface morphology and not e.g., a result of

reduced energetic surface activity.

An important point in the above evaluation of c.b. surface

morphology is the correct estimation of the cross-section s

of the applied probe molecules. This is done by referring to

the mass density r of the probe molecules in the bulk liquid

state that are considered as spheres in a hexagonal close

packing:

s ¼ 1:091



2=3

: (31:2)

Here, M is the molar mass of the probe molecules and N

the Avogadro number. Note that any other close packing of

FIGURE 31.3. Schematic presentation of a fractal surface

covered with monolayers of (a) small and (b) large gas mol-

ecules, demonstrating the impact of the yardstick on the

estimated surface area. Reprinted from [11] with kind permis-

sion of Springer Science þBusiness Media.

−0.9

−3.5

−3.4

−3.3

−3.2

−3.1

−3

−2.9

−2.8

−0.7−0.8 −0.6

log (σ[nm

])

log (N

[mol/g])

−0.5 −0.4

FIGURE 31.4. Yardstick-plot of N220 (~) and a graphitized

N220g (.) with adsorption cross section s determined from

the bulk liquid density r according to Equ. (31.2); Applied

gasses are: 1 argon, 2 methane, 3 ethane, 4 propane, 5

isobutane, 6 n-butane; The slopes yield for N220:

¼ 2:56  0:04, for N220g: D

¼ 2:32  0:03. Reprinted

from [11] with kind permission of Springer Science þBusiness

Business Media.

CARBON BLACK / 541

probe molecules can be used since it doesn’t alter the scaling

exponent 2/3 of Eqn. (31.2). The crucial point is the tem-

perature dependence of r that differ for the different probe

molecules, mainly due to variations in the characteristic

temperatures, e.g., the evaporation points.

It was found [15] that Eq. (31.2) can be applied without

further corrections and high correlation coefficients of the

‘‘yardstick-plots’’ in Figs. 31.4 and 31.5 are obtained, only if:

(i) the temperature during the adsorption experiments is

chosen according to the theory of corresponding states and

(ii) a series of chemically similar gases is used. Fig. 31.5

shows that for the same c.b. (N220g) a different scaling

factor is obtained for the ‘‘yardstick-plots’’, if the adsorption

temperatures are chosen with respect to different reference

pressures, i.e., the evaporation temperatures at p

¼ 10

mbar and p

¼ 10

mbar, respectively. A different scaling

factor is also observed in Fig. 31.5 for the two homological

series of gases, i.e., the alkanes and alkenes, respectively.

However, the scaling exponent and hence the surface fractal

dimension D

 2:3 is unaffected by the choice of the refer-

ence pressure or applied series of adsorption gases.

An alternative approach to the characterization of surface

morphology of c.b. is the consideration of film formation of

adsorbed molecules in the multilayer regime. In this case,

the surface roughness is evaluated with respect to a fractal

extension of the classical Frenkel-, Halsey-, Hill (FHH)-

theory, where beside the van der Waals surface potential

the vapor–liquid surface tension has to be taken into account

[19,20]. Then the Helmholtz free energy of the adsorbed

film is given as the sum of the van der Waals attraction

potential of all molecules in the film with all atoms in the

adsorbent, the vapor–liquid surface free energy and the free

energy of all molecules in the bulk liquid film. This leads to

the following relation between the adsorbed amount N and

the relative pressure p=p

[19,20]:

N  ln



q

with:

q ¼

3  D

FHH-regime (31:3a)

q ¼ 3  D

: CC-regime (31:3b)

The different exponents for the FHH- and capillary

condensation (CC)-regime consider the two cases where

adsorption is dominated by the van der Waals potential

and the vapor–liquid surface tension, respectively. Note

that in the CC-regime a flat vapor–liquid surface is obtained

due to a minimization of curvature by the surface tension. In

the FHH-regime the vapor–liquid surface is curved, since it

is located on equipotential lines of the van der Waals poten-

tial with constant distance to the adsorbent surface.

At low relative pressures p=p

or thin adsorbate films,

adsorption is expected to be dominated by the van der Waals

attraction of the adsorbed molecules due to the solid poten-

tial that falls off with the third power of the distance to the

surface (FHH-regime, Eq. (31.3a)). At higher relative pres-

sures p=p

or thick adsorbate films the adsorbed amount N is

expected to be determined by the surface tension g of the

adsorbate vapor interface (CC-regime, Eq. (31.3b)), because

the corresponding surface potential falls off less rapidly with

the first power of the distance to the surface, only. The

cross-over length z

crit:

between both regimes depends on

the number density n, the surface tension g, the van der

Waals interaction parameter a as well as on the surface

fractal dimension D

[19,20]:

crit:

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

 2)g

: (31:4)

Note, that the cross-over length z

crit:

decreases with

increasing surface fractal dimension D

, implying that the

FHH-regime may not be observed on very rough surfaces,

i.e., the film formation may be governed by the surface

tension g on all length scales z > a (compare Fig. 31.7).

The film thickness z is related to the surface relative

coverage N=N

and the mean thickness a  0.35 nm of

one layer of nitrogen molecules [21] according to the scaling

law [18]:



3D

(31:5)

The monolayer amount N

can be estimated from a classical

BET-plot and hence the film thickness z can be obtained

directly from the adsorbed amount N if the surface fractal

dimension D

is known.

So called FHH-plots of the nitrogen adsorption isotherms

at 77 K of two graphitized furnace blacks are shown in

Fig. 31.6. The graphitized furnace blacks have three linear

−0.7

−3.5

−3.45

−3.4

−3.35

−3.3

−3.25

−3.2

−3.15

−3.1

−0.65 −0.6 −0.55

log(s [nm

])

log (N

[mol/g])

−0.5 −0.45 −0.4

FIGURE 31.5. Yardstick-plots of the graphitized black N220g

obtained with alkenes (ethylene, propylene, isobutylene) (hol-

low symbols) and alkanes (ethane, propane, isobutane) (filled

symbols); Adsorption temperatures are chosen as evapor-

ation points at vapor pressures p

 1,000 mbar (lower

curves) and p

 1,000 mbar (upper curves) of the con-

densed gases, respectively. Reprinted from [11] with kind

permission of Springer Science þBusiness Media.

542 / CHAPTER 31

ranges. Starting from low pressures the first linear range is

fitted by Eq. (31.3a), because the film is not very thick and

the van der Waals attraction of the molecules by the solid

governs the adsorption process (FHH-regime). With rising

pressure, at a critical film thickness of about z

crit:

 0:5nm,

the vapor–liquid surface tension g becomes dominant and a

second linear range appears that is fitted according to Eq.

(31.3b). The fractal FHH-theory claims almost identical

fractal dimensions of D

 2:3 for both linear regimes up

to a length scale of z  1 nm. At this length scale a geomet-

rical cut-off appears and the surface becomes rougher. In the

final linear regime (z > 1 nm) the fractal dimension takes

the value D

 2:6 (CC-regime). This linear range has an

upper cut off length of approximately z  6 nm.

Figure 31.7 shows that, contrary to the graphitized blacks,

the untreated furnace blacks have only one linear range with

a fractal dimension of D

 2:6 (CC-regime, Eq. (31.3b)).

Obviously the van der Waals attraction can be neglected and

the surface tension g controls the adsorption process on all

length scales. This is due to the larger surface fractal dimen-

sion D

as compared to the graphitized furnace blacks that

shifts the cross-over length z

crit:

to smaller values (Eq.

(31.4)). Assuming that the number density n, the surface

tension g of the adsorbate and the van der Waals interaction

parameter a are approximately the same for a nitrogen

adsorbate film on graphitized and untreated furnace blacks,

a cross-over length of z

crit:

 0:35 nm can be estimated

from Eq. (31.4) with the experimental values of the fractal

−0.8

−3.3

−3.2

−3.1

−3

−2.9

−2.8

−2.7

−2.6

= 2.57

= 2.34

CC-Regime FHH-Regime

= 2.33

= 2.34

= 2.31

= 2.58

Graphitizised N134

Graphitizised N220

−2.5

−2.4

−2.3

−0.6 −0.4 −0.2 0

(in(p 0/p))

log(N [mol/g])

0.2 0.4 0.6 0.8 1

FIGURE 31.6. FHH-plot of nitrogen adsorption isotherms at 77 K for the two graphitized blacks N134g and N220g.

−0.8

−3.7

−3.5

−3.3

−3.1

−2.9

−2.7

−2.5

−2.3

−0.6 −0.4

N660 D

= 2,58

N550 D

= 2,58

N339 D

= 2,58

N220 D

= 2,60

N134 D

= 2,57

−0.2

CC-Regime

(In(p 0/p))

log(N [mol/g])

0.2 0.4 0.6 0.8 1

FIGURE 31.7. FHH-plot of nitrogen adsorption isotherms at 77 K for several furnace blacks. Reprinted from [11] with kind

permission of Springer Science þBusiness Media.

CARBON BLACK / 543

dimensions and the crossover length z

crit:

 0:5nm on a

graphitized c.b. The value z

crit:

 0:35 nm is already in the

range of the detection limit given by the layer thickness a 

0.35 nm. Hence, the nitrogen adsorption on furnace c.b.s is

dominated by the vapor–liquid surface tension on all length

scales and a cross over between the FHH- and the CC-

regime does not appear. More details of these investigations

are found in [15,22,23].

It must be noted that these results obtained by a rigorous

gas adsorption analysis are not contradictory to recent small

angle X-ray scattering results [17,24,25] that indicate a

nonuniversal surface roughness of furnace blacks with sig-

nificantly smaller values for D

. The scattering results were

obtained in a complementary length scale regime for scat-

tering vectors q < 1nm

1

. This corresponds to length scales

larger than about 6 nm. Below this length scale the scatter-

ing data show a cross-over to a different scaling behavior

indicative for sheet like structures consistent with graphitic

layers [24]. Obviously, on atomic length scales smaller than

6 nm the scattering from the surface is shielded by that of

the graphitic crystallite structures.

In the following we present a hypothetical mechanism of

c.b. formation that explains the universal value D

 2:6of

c.b. surface topography on atomic length scales. The model is

based on physical concepts of disordered surface growth,

which wererecently applied in many different fields in nature.

31.3 SURFACE GROWTH DURING CARBON

BLACK FORMATION

The morphology of c.b. is closely related to the conditions

of surface and primary aggregate growth during c.b. pro-

cessing, which is now discussed in some detail. Figure 31.8

shows a schematic representation of c.b. formation in a

furnace reactor, where a jet of gas and oil is combusted

and quenched, afterwards. Beside the aggregate growth,

resulting from the collision of neighboring aggregates, sur-

face growth due to the deposition of carbon nuclei on

the aggregates takes place during the formation of primary

c.b. aggregates. Due to the high temperature in the reactor,

aggregate as well as surface growth take place under ballis-

tic conditions, i.e., the mean free path length of both growth

mechanisms is large compared to the characteristic size of

the resulting structures [11,32]. Then the trajectories of

colliding aggregates (or nuclei) can be considered to be

linear. Numerical simulations of ballistic cluster-cluster ag-

gregation yield a mass fractal dimension D

 1:9---1:95

[37]. This prediction is somewhat smaller than the SAXS-

result shown in Fig.31.2. However, the assumption of bal-

listic cluster–cluster aggregation during c.b. processing

should hold only in the asymptotic limit of large aggregates

and for the relatively fine blacks. For the more coarse

blacks, with a typically small primary particle number, finite

size effects can lead to a more compact morphology that

differs from the scaling prediction of ballistic cluster aggre-

gation. A further deviation can result from electrostatic

repulsion effects due to the application of processing agents

(alkali metal ions) for designing the coarse blacks.

It is a challenging problem to model chemical and phys-

ical phenomena that take place in a few milliseconds of the

c.b. formation process. These processes go so quickly from a

hydrocarbon with a few carbon atoms to an aggregate made

of several millions of carbon atoms. This is a kind of

gaseous–solid phase transition where the solid phase ex-

hibits no unique chemical and physical structure. The c.b.

SG SG AG AG SG SG

Oil

Gas

FIGURE 31.8. Schematic view of c.b. processing in a furnace reactor. Primary aggregates are built by two simultaneous growth

processes: (i) surface growth (SG) and (ii) aggregate growth (AG). Reprinted from [11] with kind permission of Springer

Science þBusiness Media.

544 / CHAPTER 31