Chemical Engineering Journal 250 (2014) 66–75

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Chemical Engineering Journal

journal homepage: www.elsevier .com/locate /ce j

Detailed kinetic analysis of the effect of benzene–acetylene compositionon the configuration of carbon nanoparticles

http://dx.doi.org/10.1016/j.cej.2014.03.0911385-8947/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +81 22 795 7251; fax: +81 22 795 6165.E-mail address: kiminori@tranpo.che.tohoku.ac.jp (K. Ono).

Kiminori Ono a,⇑, Aki Watanabe a, Kazuki Dewa a, Yoshiya Matsukawa a, Yasuhiro Saito a,Yohsuke Matsushita a, Hideyuki Aoki a, Okiteru Fukuda b, Takayuki Aoki b, Togo Yamaguchi b

a Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6-6-07 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japanb ASAHI CARBON CO., LTD., 2 Kamomejima-cho, Higashi-ku, Niigata 950-0883, Japan

h i g h l i g h t s

� The nuclei mole fraction increases with additive concentration.� The nucleation behavior affects the complexity of the aggregate shape.� The excess addition of additives contributes to the simplification of the shapes.� The calculated nucleation behavior describes the shapes obtained experimentally.

a r t i c l e i n f o

Article history:Received 21 November 2013Received in revised form 12 February 2014Accepted 22 March 2014Available online 1 April 2014

Keywords:Carbon blackSootParticle size distributionDetailed chemical kinetic reactionNucleation

a b s t r a c t

The reasons why benzene–acetylene composition has an effect on the configuration of carbon black,which is a type of carbon nanoparticle, were investigated using a fixed sectional approach by applyingthe detailed chemical kinetic reaction for our previous experimental work: the pyrolysis of benzene–acetylene in an inert atmosphere. By comparing the calculated behavior of polycyclic aromatic hydrocar-bon formation, nucleation, and the particle size distribution with experimentally observed configurationsfor carbon black, the impact of the benzene–acetylene composition on the configuration of carbon blackis discussed. The nuclei mole fraction increases with additive concentration, which strongly affects thecomplexity of the aggregate shape. Specifically, when the amount of benzene added to 3.0 vol% acetyleneis increased to 5.0 vol% benzene, the particle number concentration of 30–80-nm-sized particles, whichare considered as primary particles or spherical aggregates, increases. The increase in the number con-centration of 30–80-nm-sized particles contributes to the simplification of the aggregate shapes. Whenacetylene is added to 1.0 vol% benzene, although the particle size distribution at 200 ms begins to shiftto a bimodal shape with the addition of 0.5 vol% acetylene, a log-normal shape clearly appears at200 ms with the addition of 5.0 vol% acetylene because the nuclei mole fraction reaches equilibrium at200 ms. Thus, if the reaction is quenched before small particles (<10 nm in size) collide with larger par-ticles with a log-normal shape, the complexity of the aggregate shape increases. The results for both ofthese cases indicate that the calculated nucleation behavior and the particle size distribution describethe aggregate shapes obtained experimentally.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Carbon black, a carbon nanoparticle, is a type of soot that isindustrially produced by the partial combustion or thermal decom-position of hydrocarbons and is in the form of near-spherical par-ticles of colloidal size that are coalesced into particle aggregatesand agglomerates [1]. Carbon black particles can be used in

numerous applications, such as in fillers for elastomers, plastics,and paints that modify the mechanical, electrical, and optical prop-erties of the materials. Today, applications from the tire and rubberproduct manufacturing industry account for 90% of the world’s car-bon black production. The primary characteristics of carbon blackthat influence the properties of elastomer composites are primaryparticle size, aggregate size, and morphology of the carbon blackaggregates and their microstructure. In particular, the aggregateshape is important for understanding the role of carbon black inreinforcement and its influence on properties such as the modulus,

K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75 67

viscosity, and die swell [2]. Carbon black is produced on a largescale, mainly via the furnace black process [1]. In this process, car-bon black is produced by continuous pyrolysis of hydrocarbonsthat are sprayed into a high-temperature field (1500–2000 K) inthe furnace. This process is complicated because of the fact thatthe chemical reactions rapidly occur with heat and mass transfer,and therefore, it is difficult to control the aggregate shape.Although this process is well established on an industrial scale,the techniques used to control the aggregate shape of carbon blackparticles are based on trial-and-error, and the fundamentals of thisprocess are not well understood [3]. Thus, to precisely control theaggregate shape, a theoretical solution is required.

The mechanism of formation of carbon black is considered to bethe same as that of soot. Although many important details of poly-cyclic aromatic hydrocarbon (PAH), carbon black, and soot forma-tion remain poorly understood, there is considerable agreementregarding the general features of the processes involved, whichare summarized as follows. The molecular precursors of the sootparticles are thought to be heavy PAHs with molecular weightsof 500–1000 amu [4]. The hydrogen-abstraction—carbon-addition(HACA) mechanism captures the essence of the thermodynamicand kinetic requirements for the formation of PAHs [5]. Shuklaet al. [6] suggested that a phenyl addition/cyclization pathway isefficient for PAH formation and growth in benzene pyrolysis.Although it is difficult to capture the formation of nascent carbonblack particles, nearly all recent studies conclude that in both pyro-lytic and flame systems, PAHs are the precursors of carbon nuclei[7–10]. After the formation of nascent carbon black particles, theirmass is increased by the addition of gas phase species, such asacetylene and PAHs, including PAH radicals. During the massgrowth process, these particles collide to produce larger sphericalparticles, which then aggregate into final carbon black clusters.The particles are converted into amorphous carbon and a progres-sively more graphitic material in the furnace. With a long residencetime, it is believed that aggregate growth occurs as a result of thefusion of primary particles [11]. Shishido et al. [12] proposed a sin-tering model in which they suggested that the rate of sintering ofthe primary particles depends on the size, temperature, surfaceenergy, and viscosity of the particles.

To improve the operating conditions for carbon black formation,several researchers have proposed numerical models [13–17]. Ivieand Forney [13] developed a numerical model for the synthesis ofcarbon black via benzene pyrolysis. They considered all of the rel-evant intermediate steps, such as radical species production, nucle-ation, growth, coagulation, and oxidation in order to elucidate themechanism of carbon black formation. Lockwood and Niekerk [14]implemented a quite sophisticated particle model, computing thecarbon black mass fraction and particle number concentration withthe assumption of spherical carbon black particles. Hayashi et al.[15] developed a three-dimensional spray combustion simulationto predict the reaction behavior and yield of carbon black. Baltha-sar et al. [16] proposed a model based on a combination of adetailed reaction mechanism and the joint composition probabilitydensity function (PDF) of these scalar quantities. They simulatedthe number density and yield of carbon black produced in turbu-lent reacting flows in systems that can be described by a partiallystirred plug flow reactor model. Nadimpalli et al. [17] incorporatedthe population balance model into the commercial computationalfluid dynamics software CFX in order to simulate the effect of flamedynamics on particle synthesis. They investigated the effect of theequivalence ratio on the maximum temperature of the flame, thespecific surface area of the particles, and the flame structure.Although the furnace temperature, particle number concentration,and the yield of carbon black in the furnace process can be pre-dicted, little attention has been paid to controlling the aggregateshape of carbon black.

In contrast, with respect to soot formation, numerous experi-mental and modeling studies have been conducted over the lasttwo decades in an attempt to describe the mechanism of formationof soot precursors and nuclei [18]. To assess the formation path-ways leading to carbon structures of increasing size, many experi-mental studies using analytical techniques, such as gaschromatography and mass spectrometry [19–24] or probe sam-pling followed by chemical or optical analysis, have been per-formed [25]. In a modeling study of PAH formation, detailedchemical kinetic reactions describing fuel pyrolysis and oxidation,benzene formation, and PAH mass growth and oxidation were pro-posed by Wang and Frenklach [26], and this work was improvedupon by Appel et al. [27]. Experimentally, Zhao et al. [28–30] andAbid et al. [31–33] reported that the particle size distribution func-tions (PSDFs) probed by a scanning mobility particle sizer demon-strated a persistent bimodality for an atmospheric-pressureethylene–oxygen–argon flame. They concluded that the bimodalityis intrinsic to an aerosol process involving particle–particle coagu-lation and particle nucleation dominated by monomer dimeriza-tion. Similar observations were made in a well-stirred reactorfollowed by a plug flow reactor [34,35]. In other modeling studies,detailed PSDFs of soot formed in laminar premixed flames weresolved using the Galerkin method [36] and a stochastic approach[37]. These studies showed the evidence of bimodal soot PSDFsin some flames.

For a decade, our group has attempted to control the aggregateshape of carbon black. Watanabe et al. [38] simulated aggregateformation in a furnace process using the cluster–cluster aggrega-tion model called the Aggregate Mean free Path (AMP) model,which was developed by Hayashi et al. [39]. Their work indicatedthat particle number density contributes to the aggregate shape.In a recent study [11], to investigate the relationship betweenthe formation mechanism and the configuration of carbon blackand to determine the factors controlling its configuration, carbonblack was produced via pyrolysis of benzene in an inert atmo-sphere. We concluded that the factors controlling the configura-tion of carbon black were nucleation, surface growth, and thesintering of primary particles. In addition, a mixture of benzeneand acetylene was pyrolyzed in an inert atmosphere to investi-gate the influence of the benzene–acetylene composition on theconfiguration of carbon black [40]. When the benzene concentra-tion was changed and the acetylene concentration was held con-stant, the complexity of the aggregate shapes increased with thebenzene concentration. On the other hand, when the benzeneconcentration was greater than the acetylene concentration, theaggregate shapes were simple. However, only qualitative discus-sions were presented, and no quantitative data was reportedbecause the chemical species and nuclei were not measured orsimulated. Thus, in order to investigate the effect of unsaturatedaliphatic hydrocarbons on PAH formation, we conducted numeri-cal analyses using detailed reaction mechanisms [41]. However,this investigation still did not involve the calculation of the parti-cle size distribution; only the chemical species and nuclei behav-ior were considered. In addition, the calculations were not basedon experimental results.

The objective of the present study was to quantitatively clarifythe reasons for the effect of the benzene–acetylene composition onthe configuration of carbon black. A fixed sectional approach[42,43] was used by applying a known detailed chemical kineticreaction [27] and was calculated for our previous experimentalwork [40]: the pyrolysis of a mixture of benzene and acetylene inan inert atmosphere. By comparing the numerical behavior deter-mined for PAH formation, nucleation, and particle size distributionto the experimentally obtained configurations of carbon black, theimpacts of the benzene–acetylene composition on the carbon blackconfiguration were evaluated.

68 K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75

2. Methods

2.1. Gas phase kinetics and nucleation

The modeling of the gas phase chemistry and the formation andoxidation of carbon black particles was taken from Appel et al. (ABFmodel) [27]. The gas phase mechanism describes the oxidation ofthe fuel and the formation of PAHs. The PAH chemistry is describedup to pyrene, and further growth of the aromatic molecules isexcluded from the present study. The ABF model consists of 99chemical species and 538 reactions. It includes the pyrolysis of C1

and C2 species, the formation of higher, linear hydrocarbons up toC6 species, the formation of benzene and further reactions leadingto pyrene, as well as the oxidation pathways of the aromatic spe-cies. The ABF chemical mechanism has been validated previouslyby comparing the experimental species profiles with the computedones for a number of laminar premixed aliphatic flames. Particleinception was modeled by a nucleation reaction. Carbon black par-ticles are formed by the nucleation reaction, which is modeled asthe dimerization of two pyrene molecules [10,37] in the presentstudy:

RðtÞ ¼ 12

bpyreneN2pyrene; ð1Þ

where bpyrene is the coagulation kernel of the pyrene molecules andNpyrene is the number concentration of pyrene.

2.2. Sectional model

The fixed sectional approach for soot particle dynamics pro-posed by Kumar and Ramkrishna [42] offers a combination of com-putational speed and accuracy, and was adopted to modelagglomeration. The corresponding population balance equation(PBE), called the Smoluchowski equation, was designed to simulta-neously conserve two moments. Kumar and Ramkrishna proposeda general discretization technique to preserve any two properties(e.g., mass and number density) of the particle size distribution.The proposed technique offers a general grid that can be effectivelyadapted to special situations, including the ones that require a uni-form grid in a certain size range and a nonuniform or geometrictype grid elsewhere. The discretization of PBE is given as

dni

dt¼

Xk6j6i

mi�16ðmjþmkÞ6miþ1

1� dj;k

2

� �gi;j;kbj;knjnk � ni

XNBin

k¼1

bi;knk; ð2Þ

where ni is the number concentration of size class i at time t, bj,k isthe collision kernel at which particles of size class j attach to parti-cles of size class k, and dj,k is the Kronecker delta. For the particlesize class i, the first and second terms on the right-hand side corre-spond to birth and death due to aggregation. The parameter gi,j,k isthe fraction of a newly created particle that the size class i willreceive when two particles of sizes j and k are combined. Hence, gi,j,k

effectively assigns the new particle to two adjacent bins and isgiven by

gi;j;k ¼miþ1�ðmjþmkÞ

miþ1�mi; mi 6 mj þmk 6 miþ1

mi�1�ðmjþmkÞmi�1�mi

; mi�1 6 mj þmk 6 mi

8<: : ð3Þ

We used the bins distributed geometrically as

miþ1 ¼ fsmi; ð4Þ

where fs is a geometric spacing factor that was set to 2.0 in the pres-ent study.

The rate constants bi,j appearing in Eq. (1) take different formsdepending on the Knudsen number:

Kni ¼ 2k=di; ð5Þ

where k is the particle mean free path and di is the particle diame-ter. If we denote bi,j in the free-molecular (Kni > 10), continuum(Kni < 0.01), and transition (0.01 6 Kni 6 10) regimes [44] as bf

i;j,bc

i;j, and bti;j, respectively, then for spherical particles it follows that

bfi;j ¼ Ca

34p

� �1=6 6kBTqs

� �1=2 1v iþ 1

v j

� �1=2

v1=3i þ v1=3

j

� �2; ð6Þ

bci;j ¼

2kBT3lL

� �1=2 Ci

v1=3i

þ Cj

v1=3j

!v1=3

i þ v1=3j

� �; ð7Þ

and

bti;j ¼

bfi;jb

ci;j

bfi;j þ bc

i;j

; ð8Þ

where vi is the volume of a single particle in the ith section and di itsdiameter, qs (=1800 kg/m3) is the density of the soot, kB is Boltz-mann’s constant, T is the temperature, lL is the laminar dynamicviscosity of the fluid, and Ca is the van der Waals enhancement fac-tor [45]. In the present study, Ca was set to 1.0. The Cunningham slipcorrection factor is expressed as a function of the Knudsen number[44,46]:

Ci ¼ 1þ 1:257Kni: ð9Þ

Although Bhatt and Lindstedt [43] calculated a case in which anaggregate structure with a fractal dimension was considered, wecalculated it as a spherical value because they concluded that thesensitivity to variations in the fractal dimension was notsignificant.

2.3. Surface growth and oxidation

The surface growth sub-model described by the mass increasethrough the HACA mechanism and the mass consumption throughthe oxidation of OH and molecular O2 was used in the ABF model[27]. To apply the mass variations calculated by the kinetic modelto the fixed sectional model, the two-point method proposed byPark and Rogak [47] was used and is given by

dni

dt¼ Ii�1ni�1

mi �mi�1� Iini

miþ1 �miand ð10Þ

dni

dt¼ Iini

mi �mi�1� Ii�1ni�1

miþ1 �mi; ð11Þ

for surface growth and oxidation, respectively. In the above equa-tions, Ii = dmi/dt is the surface mass addition (or subtraction) rateof the ith section.

2.4. Experimental method

The sectional method was applied to our previous experimentalwork [40], and the experimental procedure is described in detailelsewhere [11,40]. Carbon black was produced by the thermalpyrolysis of 0–5.0 vol% benzene mixed with 0–5.0 vol% acetyleneentrained by a N2 carrier flow. The feedstock flow rate was 3.0 L/min. The reactor consisted of an alumina tube with an ID of16 mm and was heated by an electric furnace. The axial gas tem-perature in the reaction tube was measured using an R-type ther-mocouple in a preliminary experiment (Fig. 1). The temperaturedistribution was used as input data. The maximum temperaturewas set to 1573 or 1673 K.

The carbon black powders trapped by a glass fiber filter weredispersed onto a collodion substrate and examined using a trans-mission electron microscope (TEM, TecnaiG2 20 ST, FEI) operatedat 120 kV. The shape characteristics of more than 1000 aggregates

600

800

1000

1200

1400

1600

1800

0 200 400 600 800 1000

Tem

pera

ture

[K

]

Distance [mm]

1673 K

1573 K

Fig. 1. Variation in the temperature of the reaction gas in the reactor.

(a) Acetylene 3.0 vol%, Benzene 0.1 vol%

K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75 69

in the TEM images were evaluated using an image analyzer (LUZEXAP, NIRECO). To compare the particle size distribution obtainedwith the sectional model and the TEM analysis, the equivalent cir-cle diameter (Dp) of the aggregates was calculated using the pro-jected area (A) as

Dp ¼ffiffiffiffiffiffi4Ap

r: ð12Þ

The aggregate shape was evaluated using shape parameters andwas classified into four categories—spheroidal, ellipsoidal, linear,and branched—according to the classification category criterion[2,12,48]. Branched and linear shapes are more complicated thanspheroidal and ellipsoidal shapes.

(b) Acetylene 3.0 vol%, Benzene 3.0 vol%

(c) Acetylene 3.0 vol%, Benzene 5.0 vol%

Fig. 2. Comparison of experimental and calculated particle size distributions in areactor.

3. Results and discussion

The sectional model was developed considering the detailedchemical kinetic reaction, which was then applied to the dataobtained during our previous experimental investigation [40].We used our original code, which was verified by comparing theresults of the PFR reactor model in CHEMKIN-Pro [49] and theresults calculated by the house code.

The computed feedstock concentration was set to 0–5.0 vol%benzene-0–5.0 vol% acetylene–nitrogen as the initial condition.The measured temperature distribution, as shown in Fig. 1, wasused as the temperature profile, and the residence times in thereactor (whose length is 1000 mm) were 823 and 765 ms at 1573and 1673 K, respectively. The axial and radial temperature distri-butions were neglected because the flow rate was small. The tem-perature distributions were calculated using a computational fluiddynamics (CFD) code and confirmed that the radial temperatureprofile was slightly lower at 10 mm downstream from the inlet.In the current numerical study, 65 bins were assigned geometri-cally to cover particle sizes starting from 0.878 nm. In the sootresearch field, oxidation is very important to account for the chem-ical reaction and soot formation because the concentrations of O2

are around 12–32% in the combustion field [27]. It decreases themass of PAH and soot material through the formation of CO andCO2. In the present study, we focused on the morphology of carbonblack, so the oxidation process was excluded. The model was capa-ble of treating oxidation, but that it was not necessary in this case.In the present study, two conditions were calculated: (i) the ben-zene concentration was varied from 0 to 5.0 vol% while the acety-lene concentration was held constant at 3.0 vol% and the furnacetemperature was 1573 K and (ii) the acetylene concentration wasvaried from 0 to 5.0 vol% while the benzene concentration washeld constant at 1.0 vol% and the furnace temperature was

1673 K, because the variations in the configuration were found tobe large in the previous experimental investigation [40].

The starting point of the discussion is the validation of thenumerical model by comparing the particle size distributionobtained with the sectional model and image analysis of TEM pic-tures of the experimentally produced particles. In Fig. 2(a–c), thecomputed particle size distribution is compared with the experi-mental measurements. The numerical results denote the same ten-dency of the experimental data, while the numerical result atbenzene concentration of 3.0–5.0 vol% overestimate the measured

70 K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75

data. This difference would be caused by not considering deptheffects in the two-dimensional TEM image and by the fact thatthe numerical diameter was calculated using the particle volume.

20.5 25.0 27.2 28.4

22.1 23.2

32.0 25.9

51.9 47.8 35.5

37.3

5.49 3.93 5.39 8.31

0

20

40

60

80

100

0 0.10 3.0 5.0

Exi

sten

ce r

atio

[%

]

Benzene concentration [vol%]

Spheroidal

Ellipsoidal

Linear

Branched

Fig. 3. Existence ratio of aggregate shapes with benzene concentration at 1573 K[40].

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0 200 400 600 800 1000

Mol

e Fr

actio

n

Residence time [ms]

(a) Acetylene 3.0 vol%, Benzene 0 vol%

Benzene

H2

C2H2

Pyrene

Phenanthrene Nuclei

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0 200 400 600 800 1000

Mol

e Fr

actio

n

Residence time [ms]

(b) Acetylene 3.0 vol%, Benzene 0.1 vol%

Benzene

H2

C2H2

Pyrene

Phenanthrene

Nuclei

Mol

e Fr

actio

nM

ole

Frac

tion

Fig. 4. Typical mole fraction profiles of the main s

The effect would be large because the aggregate structure becamecomplex with the benzene concentration, as discussed later. Thedifference would be small using a scanning mobility particle sizer(SMPS) which is now routinely used to follow the evolution of sootparticle size distribution function [28–32]. Considering above dis-cussion, the numerical results of the present study can bediscussed.

To examine the effect of the addition of benzene to acetylene onthe morphology of carbon black, the previously obtained experi-mental results for the carbon black configurations [40] were firstconsidered. Fig. 3 shows existence ratio of aggregate shapes withbenzene concentration at 1573 K. Under the first set of conditions(the acetylene concentration was 3.0 vol% and the furnace temper-ature was 1573 K), when the benzene concentration was 0–3.0 vol%, the aggregate shapes became complex with an increasein the benzene concentration. However, when the benzene concen-tration reached 5.0 vol%, the aggregate shapes were simpler thanthose obtained when the benzene concentration was 3.0 vol%. Todiscuss the variation in aggregate shape, the mole fraction profilesof the major species and nuclei calculated for the alumina reactorare shown in Fig. 4(a–d). As can be seen in Fig. 4(a), in the case ofacetylene pyrolysis, the acetylene mole fraction began to decrease

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0 200 400 600 800 1000

Residence time [ms]

(c) Acetylene 3.0 vol%, Benzene 3.0 vol%

Benzene

H2

C2H2

Pyrene

PhenanthreneNuclei

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0 200 400 600 800 1000

Residence time [ms]

(d) Acetylene 3.0 vol%, Benzene 5.0 vol%

Benzene

H2

C2H2

Pyrene

Phenanthrene

Nuclei

pecies with addition of benzene to acetylene.

(a) Acetylene (Feedstock)

(b) Benzene (Additive)

(c) Pyrene (Former of nuclei)

Fig. 5. Reaction rate of the major species with addition of benzene to acetylene.

K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75 71

and the benzene mole fraction began to increase around 100 ms, atwhich point the temperature was approximately 1400 K. The molefractions of phenanthrene, pyrene, and the nuclei graduallyincreased with the residence time. The addition of benzenedecreased the acetylene mole fraction with the consumption ofbenzene near 80 ms, at which point the temperature was approx-imately 1300 K. The mole fractions of phenanthrene, pyrene, andthe nuclei also increased with the benzene concentration. The reac-tion rate of major species, which are acetylene, benzene, and pyr-ene would support understanding the behavior, as shown inFig. 5(a–c). The reaction rate denotes the formation (plus value)and the consumption (minus value). The consumption rate of acet-ylene and benzene increases with the benzene concentration. Inparticular, the reaction rate of pyrene increases between 0 and3.0 vol%. These indicate the formation of PAH and nuclei wouldbe strongly affected by not only acetylene, which has been widelyconsidered to be the important role of the HACA mechanism, butalso the presence of benzene at 1573 K. As shown in Fig. 4(a–c),the effect of the addition of benzene on the increase in the nucleimole fraction was large—between 0 and 3.0 vol%. This behaviorstrongly supported the observation that the complexity of theaggregate shapes increased as the benzene concentration increasedbetween 0 and 3.0 vol% [40]. On the other hand, the variation in themole fractions of the major species and the nuclei were smallbetween 3.0 and 5.0 vol%. The mole fractions of the residual phen-anthrene and acetylene slightly increased, whereas the equilibriummole fraction of benzene barely changed. In this case, the aggre-gate shapes obtained during the pyrolysis experiment wereslightly simpler.

To further elaborate this point, the variations in the particle sizedistributions computed for the four benzene concentrations as afunction of residence time were plotted and are shown inFig. 6(a–d). Carbon black particles are formed by the nucleationreaction, which is modeled as the dimerization of two pyrene mol-ecules calculated by the detailed chemical kinetic reaction [10,37],and the particle is set to the first bin. The calculated particle diam-eter, Dp, is described as the equivalent volume diameter of anaggregate and is not, fundamentally, the primary particle diameter.In experimental studies on the particle size distribution[29,30,34,35], because the critical level of the particle number den-sity in the probe was approximately 105 cm�3, the focus of thisstudy was on the number density above 104 cm�3. The particle dis-tributions shifted from the power-law component to the bimodalshape with an increase in the residence time. Bimodal particle sizedistributions have been previously observed, both experimentallyand computationally [28–30,36]. Bimodal features are caused bythe underlying competition between nucleation and coagulation[50,51]. The power-law and log-normal components are causedby consecutive nucleation and the coagulation of particles, respec-tively. Thus, the log-normal component of the bimodal shape sug-gests that particles sufficiently collide, and it is possible that theaggregate shapes are complex in the log-normal component. At100 ms, the particle number concentration of the particles with asize less than 10 nm increased with the benzene concentrationon account of an increase in the nuclei mole fraction. The log-nor-mal shape appears clearly at 823 ms (i.e., the furnace outlet point)with the addition of benzene to acetylene. These points also sup-ported the observation that the complexity of the aggregate shapesincreased as the benzene concentration increased between 0 and3.0 vol% [40]. When the benzene concentration was 5.0 vol%, theparticle number concentration of particles with sizes ranging from30 to 80 nm increased without changing the width of the log-nor-mal component at 823 ms obtained when the benzene concentra-tion was 3.0 vol%. Considering that the experimental value of themean primary particle diameter was 54 nm in this case, it can beconcluded that the aggregates consisted of at most three primary

particles, which suggests that the aggregate shapes were simple.The increase in the particle number concentration of 30–80 nm-sized particles must be due to a slight increase in the nuclei mole

104

106

108

1010

1012

1014

1 10 100 1000

(a) Acetylene 3.0 vol%, Benzene 0 vol%

100 ms

200 ms

400 ms

600 ms

823 ms

dN/d

logD

p [1

/cm

3 ]

Dp

[nm]

104

106

108

1010

1012

1014

1 10 100 1000

(b) Acetylene 3.0 vol%, Benzene 0.1 vol%

100 ms

200 ms

400 ms

600 ms

823 ms

d N/d

logD

p [1

/cm

3 ]

Dp

[nm]

104

106

108

1010

1012

1014

1 10 100 1000

(c) Acetylene 3.0 vol%, Benzene 3.0 vol%

100 ms

200 ms

400 ms

600 ms

823 ms

dN/d

log D

p [1

/cm

3 ]

Dp

[nm]

104

106

108

1010

1012

1014

1 10 100 1000

(d) Acetylene 3.0 vol%, Benzene 5.0 vol%

100 ms

200 ms

400 ms

600 ms

823 ms

d N/d

logD

p [1

/cm

3 ]

Dp

[nm]

Fig. 6. Variation in the particle size distribution in the reactor as a function of the residence time for the addition of benzene to acetylene.

10.8

30.2 33.519.9

25.6 28.1

62.3

41.3 35.8

6.99 2.87 2.58

0

20

40

60

80

100

0 0.50 5.0

Exi

sten

ce r

atio

[%

]

Acetylene concentration [vol.%]

Spheroidal

Ellipsoidal

Linear

Branched

Fig. 7. Existence ratio of aggregate shapes with acetylene concentration at 1673 K[40].

72 K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75

fractions after 300 ms. Therefore, when the benzene concentrationwas 5.0 vol%, the shape of the aggregate became slightly simplercompared to those observed when the benzene concentrationwas 3.0 vol%.

Next, the previously obtained experimental results for carbonblack configurations [40] were evaluated in order to examine theeffect of the addition of acetylene to benzene on the morphologyof carbon black. Fig. 7 shows existence ratio of aggregate shapeswith acetylene concentration at 1673 K. Under these conditions(the benzene concentration was 1.0 vol% and the furnace tempera-ture was 1673 K), as the acetylene concentration was increasedfrom 0 to 5.0 vol%, the aggregate shapes became increasingly com-plex. However, the variation was small when the acetylene concen-tration was 5.0 vol%. To discuss the variation of the aggregateshapes, the mole fraction profiles of the major species and nucleicalculated for the alumina reactor were plotted and are shown inFig. 8(a–c). The nucleation rate and the nuclei mole fractionsincreased with the acetylene concentration. As can be seen inFig. 8(a), in the case of benzene pyrolysis, the acetylene mole frac-tion represented a rise-then-drop behavior followed by the pro-duction of pyrene and nuclei. The acetylene mole fraction sharplydecreased at the same time as that when the nuclei were produced(approximately 80 ms after the addition of the acetylene). Thisresult indicates that the addition of acetylene to benzene, whichis the primary starting point for PAH synthesis, works as a ‘‘pro-moter’’ of PAH synthesis. The reaction rate of major species, whichare acetylene, benzene, and pyrene would support understandingthe behavior, as shown in Fig. 9(a–c). The consumption rate of ben-zene and acetylene increases with the acetylene concentration. The

point of consumption of these species appeared at later stage withthe addition of 5.0 vol% of acetylene. This strongly affects the pointof the formation of pyrene as shown in Fig. 9(c). The reaction rateof pyrene which is the former of nuclei increases with the additionof acetylene. Therefore, the nucleation rate and the nuclei molefraction increase as a result of acetylene addition, and the increasein the complexity of the aggregate shapes observed experimentallymust be attributed to this behavior.

To examine the variation in the shape of the aggregates due toaddition of acetylene, the variation in the particle size distributions

10-6

10-5

10-4

10-3

10-2

10-1

0 100 200 300 400 500 600 700 800

Mol

e F

ract

ion

Residence time [ms]

(a) Benzene 1.0 vol%, Acetylene 0 vol%

Benzene H2

C2H2

Pyrene

Phenanthrene

Nuclei

10-6

10-5

10-4

10-3

10-2

10-1

0 100 200 300 400 500 600 700 800

Mol

e F

ract

ion

Residence time [ms]

(b) Benzene 1.0 vol%, Acetylene 0.5 vol%

Benzene H2

C2H2

Pyrene

Phenanthrene

Nuclei

10-6

10-5

10-4

10-3

10-2

10-1

0 100 200 300 400 500 600 700 800

Mol

e Fr

acti

on

Residence time [ms]

(c) Benzene 1.0 vol%, Acetylene 5.0 vol%

Benzene

H2

C2H2

Pyrene

Phenanthrene

Nuclei

Fig. 8. Typical mole fraction profiles for the main species with addition of acetyleneto benzene.

(a) Benzene

(b) Acetylene

(c) Pyrene (Former of nuclei)

Fig. 9. Reaction rate of the major species with addition of acetylene to benzene.

K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75 73

computed for the three acetylene concentrations were plotted as afunction of the residence time, and the results are shown inFig. 10(a–c). At 100 ms, the particle number concentration for

particles with sizes less than 10 nm increased with the acetyleneconcentration due to an increase in the nuclei mole fraction. Thevariation in the aggregate shapes between 0.5 and 5.0 vol% acety-lene can be considered on the basis of two key points. First is thatthe particle size distributions at the furnace outlet point (765 ms)were nearly unchanged. Although the log-normal componentshifted to a slightly larger particle size owing to the addition of

104

106

108

1010

1012

1014

1 10 100 1000

(a) Benzene 1.0 vol%, Acetylene 0 vol%

100 ms

200 ms

400 ms

600 ms

765 ms

d N/d

logD

p [1

/cm

3 ]

Dp

[nm]

104

106

108

1010

1012

1014

1 10 100 1000

(b) Benzene 1.0 vol%, Acetylene 0.5 vol%

100 ms

200 ms

400 ms

600 ms

765 ms

dN/d

logD

p [1

/cm

3 ]

Dp

[nm]

104

106

108

1010

1012

1014

1 10 100 1000

(c) Benzene 1.0 vol%, Acetylene 5.0 vol%

100 ms

200 ms

400 ms

600 ms

765 ms

dN/d

log D

p [1

/cm

3 ]

Dp

[nm]

Fig. 10. Variation of the particle size distribution in the reactor as a function of theresidence time for the addition of acetylene to benzene.

74 K. Ono et al. / Chemical Engineering Journal 250 (2014) 66–75

5.0 vol% acetylene, the peak point and number concentration at thepeak were nearly the same as those observed for other acetyleneconcentrations. Second is the variation in the particle size distribu-tion. Although the particle size distribution at 200 ms began toshift to a bimodal shape with the addition of 0.5 vol% acetylene,the log-normal shape clearly appeared at 200 ms with addition of5.0 vol% acetylene because the nuclei mole fraction reached equi-librium at 200 ms. In addition, the diameter of the particle size dis-tribution increased and the size of the small particles (<10 nm)decreased with an increase in the residence time. Small particles

with a size <10 nm can collide with larger particles, increasingthe primary particle diameter and filling voids in the aggregates,and thus leading to simplification of the aggregate shapes. There-fore, in the view of the decrease in the size of the particles of<10 nm, the aggregate shape would be expected to be complex ifthe reaction was quenched at 200–400 ms when 5.0 vol% acetylenewas added.

4. Conclusion

A fixed sectional approach was used by applying the pyrolysisof benzene–acetylene in an inert atmosphere, a detailed chemicalkinetic reaction for our previous experimental work: the pyrolysisof benzene–acetylene in an inert atmosphere. By comparing thenumerical behavior of PAH formation, nucleation, and the particlesize distribution with the experimentally observed configurationsfor carbon black, the impact of varying the benzene–acetylenecomposition on the configuration of carbon black was evaluated.

The nuclei mole fraction increased with the additive concentra-tion. This increase strongly affects the complexity of the aggregateshapes. When benzene was added to 3.0 vol% acetylene at a con-centration of 5.0 vol%, the particle number concentration of parti-cles with sizes ranging from 30 to 80 nm increased withoutchanging the width of the log-normal component at the furnaceoutlet point as compared to that observed when the benzene con-centration was 3.0 vol%. The increase in the number concentrationof particles with a size of 30–80 nm contributes to the simplifica-tion of the aggregate shapes. On the other hand, when acetylenewas added to 1.0 vol% benzene, although the particle size distribu-tion at 200 ms began to shift to a bimodal shape with the additionof 0.5 vol% acetylene, the log-normal shape clearly appeared at200 ms with the addition of 5.0 vol% acetylene because the nucleimole fraction reached equilibrium at 200 ms. If the reaction isquenched before the small particles (<10 nm) collide with largerparticles with a log-normal shape, the aggregate shapes will becomplex. The calculated results for both these cases indicate thatthe theoretical nucleation behavior and the particle size distribu-tion describe the aggregate shapes observed experimentally. Onthe basis of the observed variation in the aggregate shape and molefractions of the chemical species, it is probable that there is anoptimal concentration and composition of the feedstock that pro-vides complicated aggregate shapes.

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