Combustion and Flame 162 (2015) 2422–2430

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Combustion and Flame

journal homepage: www.elsevier .com/locate /combustflame

The effect of oxidation pressure on the equilibrium nanostructure of sootparticles

http://dx.doi.org/10.1016/j.combustflame.2015.02.0090010-2180/� 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

⇑ Corresponding author at: Department of Combustion Technology and ThermalEnergy, University of Miskolc, H3515 Miskolc-Egyetemvaros, Hungary.

E-mail address: toth.pal@uni-miskolc.hu (P. Toth).

Pal Toth a,b,⇑, Arpad B. Palotas b, Terry A. Ring a, Eric G. Eddings a, Randy Vander Wal c, JoAnn S. Lighty a

a Department of Chemical Engineering, University of Utah, 50 S. Central Campus Drive, Salt Lake City, UT 84112-9203, United Statesb Department of Combustion Technology and Thermal Energy, University of Miskolc, H3515 Miskolc-Egyetemvaros, Hungaryc John and Willie Leone Family Dept. of Energy and Mineral Engineering, & The EMS Energy Institute, Pennsylvania State University, University Park, PA 16802, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 16 October 2014Received in revised form 15 February 2015Accepted 15 February 2015Available online 9 March 2015

Keywords:SootOxidationHigh-pressureHRTEMImage analysis

The notion of equilibrium soot nanostructure was introduced by Hurt et al., who argued that the peculiarturbostratic carbon structure is an equilibrium arrangement of lamellar, graphene-like molecules. It wasproposed that the typical, onion-like internal structure of primary soot particles can be satisfactorilydescribed by thermodynamic principles. There are two main objectives of this paper. First, the effectsof oxidation pressures above atmospheric pressure on soot nanostructure are investigated experimental-ly. The analyzed soot was generated in premixed flames of liquid fuels: n-dodecane, m-xylene andn-butanol and further oxidized in a thermogravimetric analyzer under atmospheric, 10 atm and40 atm pressures. Nanostructure is described by utilizing high-resolution transmission electron micro-scopy and recently developed image analysis techniques. Second, empirical observations are comparedagainst behavior that is semi-quantitatively predicted by the thermodynamic model. The utilization ofthe novel analysis technique made direct comparison between observed and computed propertiespossible. Reasonable consistency was found between experimental and computational results. Theresults suggest that the known thermodynamic model can be used to predict equilibrium structure evenwhen soot is oxidized under pressurized conditions. Since diesel and jet engines operate at elevatedpressures, the conclusions drawn in this paper may find their use in predicting soot nanostructure inthe limiting case of equilibrium conditions.

� 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction

Soot is a product of the pyrolysis of carbonaceous materials andis generally considered as amorphous carbon [1]. Despite beingamorphous, in most cases soot nanostructure shows some degreeof crystalline order typically in the form of graphite microcrystals(mesophasic crystalline units or clusters exhibiting short-rangeorder in the form of parallel graphene layers, also called ‘stacks’),partial fullerenic (graphene layers in a concentrically symmetric,‘onion-like’ structure) or partial graphitic (longer range parallelityof layers) order [2–5]. Soot particles are composed of amorphousand crystalline fractions. For the balance of this paper, the amor-phous fraction is referred to as the ‘isotropic phase’ and the crys-talline fraction is called ‘nematic phase’. Soot nanostructure isaffected by the chemical and thermal environment [3,6,7] and also

by the combusted fuel type – different fuels may produce differentnanostructures [5,8–11].

The importance of soot nanostructure can be summarized asfollows. Current soot models account for nucleation, growth,coagulation and oxidation processes [12–14], among which, allexcept the first are affected by the molecular structure of soot –either through the density and distribution of active surface sitesdetermining the rate of chemical processes [15,16] or via affectingvan der Waals forces and therefore physical interactions [17,18].Experiments demonstrated [19], that the rate of surface growth isnot exclusively determined by surface area, which further supportsthe importance of the arrangement of surface sites. Similarly, dis-crepancies exist between observed oxidation rates [2] and the ratespredicted by the Nagle–Strickland-Constable equation [20], whichis applicable to describe the high-temperature oxidation of carbonblacks – these discrepancies are possibly caused by peculiarities ofsoot structure. The dependence of soot oxidation kinetics uponnanostructure was shown [21,22].

Hurt et al. showed, that soot nanostructure can be qualitativelymodeled by thermodynamic principles [23]. Their model described

P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430 2423

the typical core–shell nanostructure [5] as an equilibrium arrange-ment between the competing isotropic-nematic transformationand the free energy contribution of the splay deformation ofgraphene layers. They argued that the core–shell structure is a con-figuration that is simultaneously optimal for layer growth andaromatization and the Van der Waals forces acting between layers.According to their model, the equilibrium diameter of the isotropiccore is affected by the splay deformation constant, the free energychange of the isotropic-nematic transformation and properties ofthe nematic phase – molecular weight and density.

The quantities of interest in the model of Hurt et al. can be esti-mated by analyzing the high-resolution electron micrographs(HRTEM) of soot. In HRTEM images, individual graphene layersare made visible by phase-contrast imaging. Since typical HRTEMimages contain hundreds of imaged graphene layers, in most prac-tical cases, their representative and accurate characterization canonly be carried out by using automated digital image analysis.Many automatic [24–26] and semi-automatic [27] algorithms areknown that can extract structural information characterizing gra-phene lamellae and their arrangement. It was shown that – despitebeing a two-dimensional technique [28] – HRTEM analysis canprovide results that are consistent with X-ray diffractometry[29,30].

Although practical combustion systems for transportation oper-ate at elevated (higher than atmospheric) pressures, there is a gen-eral lack of models describing the effects of elevated pressure onsoot nanostructure [31]. This paper is a follow-up of a previousstudy regarding pressure-dependent soot structure and reactionkinetics [21]. Soot was generated in an atmospheric flat flameand then oxidized in a high-pressure thermogravimetric analyzer(HTGA). HRTEM data are processed by means of a sophisticatedimage processing framework [32,33]. The extracted informationincludes interlayer spacing measurements and higher-order sym-metry quantification. An attempt is made to explain the observedstructural changes in the nanostructure by directly coupling pro-cessed HRTEM data with the thermodynamic model of Hurt et al.[23]. If successful, a thermodynamic model that can predict equi-librium soot nanostructure under pressurized conditions may pro-vide useful practical information about the limiting case of fastreactions or long residence times.

2. Materials and methods

In this section the conditions and equipment used for sootgeneration, oxidation and characterization are discussed. For thereader’s convenience, a brief overview is given on the recentlydeveloped image analysis framework and the meaning and sig-nificance of the extracted structural parameters.

Table 1Experimental conditions for soot generation.

Fuel Equivalenceratio

C/Oratio

Velocity,cm/s

Flametemperature, K

n-dodecane 1.7 0.65 4.6 1705m-xylene 2.15 0.7 4.6 1725n-butanol 2.8 1.21 4.3 1723

2.1. Soot generation

A premixed burner was used to create the soot samples fromdifferent liquid fuels. The soot was generated in an atmospheric,premixed, flat flame, under heavily sooting conditions and cap-tured on a water-cooled stabilization plate which was located50 mm above the burner surface.

The burner system consisted of a stainless steel chamber (50mm inner diameter, Schedule 80, 127 mm long), where fuel andair were injected and mixed prior to entering the burner. The flamewas stabilized over a tube bundle (1.578 mm inner diameter, 31.75mm long) through which the mixture passed in laminar flow. Anitrogen shroud was utilized to shield the premixed flame fromatmospheric interference. Air and the liquid mixture were fed tothe burner using a commercial vaporizer (Mesoscopic DevicesInc.) coupled to a syringe pump and temperature control system.

The vaporizer allowed for effective fuel vaporization before beingmixed with the air.

The temperature in the vaporizer was controlled depending onthe fuel used and vaporized fuel were analyzed by using gaschromatography to verify the performance of the vaporizer. Thevaporized fuel was trapped into a cold dichloromethane trap.

Soot was generated from n-dodecane, m-xylene and n-butanol.Several studies reported that the fuel type affects the nanostruc-ture of the generated soot [5,8–11], thus different fuels were tested– this particular choice of fuels represented paraffinic, aromaticand oxygenated fuels, respectively. The soot generated was collect-ed on the stabilization plate and then crushed into a powder. Flametemperatures were measured using a type-B thermocouple (wirediameter 0.02032 mm) at 50 mm above the burner surface, whichcorresponded to the distance where the soot is collected. The tem-peratures were corrected by radiation effects. The radiation correc-tion for the temperature was similar to that of McEnally et al. [34].

The combustion conditions for generating the samples were setin an attempt to simultaneously satisfy requirements regardingflame stability, the amount of soot generated and comparable tem-perature histories of the soot. Table 1 summarizes the conditionsfor each flame studied.

2.2. Soot oxidation

A high-pressure thermogravimetric analyzer, type CahnTherMax 500, was used to oxidize soot under controlled pressur-ized conditions. All tests were performed isothermally. 10 mg sootwas placed in a quartz crucible (18 mm diameter and 20 mmheight). The crucible was suspended from a ceramic coil attachedto a microbalance. The furnace and balance were purged withnitrogen prior to each experiment. An inert material (silicon-carbide beads) was used in all of the runs to minimize thermaland mass transfer effects by decreasing the stagnant atmospherebetween the surface of the soot and the entrance of the container.Isothermal tests were performed at 575 �C. A heating rate of10 K/min was used to reach the oxidation temperature in nitrogen.Nitrogen flowed at 0.55 l/min through the microbalance to protectit. The oxidizer, a mixture of oxygen and nitrogen flowed at1 l/min. Mass data was recorded approximately every second andthe experiments were terminated when the mass loss surpassed50%. After termination, the samples were quenched in nitrogenat 20 K/min. Soot was oxidized under different pressures to studythe effect of pressure on the soot nanostructure. In order torepresent conditions from atmospheric pressure to environmentsin typical aircraft engines [31], 1 atm, 10 atm and 40 atm atmo-spheres were used.

It is important to point out that the analyzed soot was notgenerated in a pressurized flame, but oxidized in a HTGA. Hurtet al. [23] suggested that the structure of real soot (i.e., soot notoxidized in a controlled environment) may be satisfactorily esti-mated by using thermodynamic principles. Even though the sootwas oxidized up to an arbitrary 50% mass loss, it is hypothesizedhere that the conditions in the HTGA (low temperature and longresidence time) approximate equilibrium, such that the structurecorresponding to a given mass loss is a quasi-steady state

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structure. The hypothesis is tested in Section 3.3 by comparing theobserved structure with the predictions. This particularexperimental design was chosen so that the equilibrium structurescan be observed, with minimal effects from finite rate reactions.Results regarding the structure and other properties of the as-gen-erated soot can be found in [21].

2.3. HRTEM imaging

After oxidation, soot was placed in vials with ethanol (200proof). This mixture was filtered in a BHS Sonthofen pressurizedfiltration system. The remaining soot was then suspended in theethanol and sonicated for 15 min. Upon completion one drop froma glass micropipette was placed on a coated lacey carbon grid (TedPella 200-mesh Formvar). The grids were allowed to dry complete-ly prior to being stored in the grid holder. HRTEM micrographswere produced using a JEOL 2010F microscope. The micrographsused for further quantification were produced at 500,000X magni-fication under slightly over-focused phase contrast conditions.Further details regarding the instrument and the sampling proce-dure to ensure representative image collection (sampling) maybe found as previously reported [21].

2.4. Image analysis

HRTEM images were processed by a novel image analysisframework specifically designed for analyzing HRTEM micrographsof soot. The details of the framework can be found in [32,33]. Inbrief, the framework is based on filtering theory – the micrographsare filtered with special two-dimensional filters in order to extractinterlayer spacing and symmetry parameters. Gabor filters [35]tuned to frequencies present in soot HRTEM micrographs wereused to extract interlayer spacing distributions. Nematic and polarorder parameters (S2N and S2P , respectively) were extracted by theorientation-filtering technique described in [33]. These parameterswere first used to describe soot nanostructure by Shim et al. [26]and are defined as follows:

S2N ¼ 2hcos2 aið Þi � 1 ð1ÞS2P ¼ 1� 2hcos2 aið Þi ð2Þ

where S2N is the nematic order parameter, S2P is the polar orderparameter, ai is the angle between the fringe orientation vectorand a so-called director vector and <> means mean value. Thedirector vector is approximately the local mean orientation insidean image region in the nematic case; in the polar case, it is a vectorpointing from polar symmetry poles (amorphous particle cores) tothe fringe centroids. It is easy to see that S2N is 1 for a perfectlyordered structure and 0 for a perfectly disordered structure, whileS2P is 1 for perfect concentric symmetry, 0 for disordered phasesand �1 for radial symmetry. For further details about S2N and S2P ,the reader is referred to [26]. These parameters are also definedand computed in regions of specific size – the size of these regionsis called the scale of the symmetry, r. The term ‘long-scale symme-try’ therefore refers to cases in which a high value of either symme-try parameter is retained over long distances.

For the extraction of fringe length and fringe tortuosity, anextended version of the algorithm of Palotas et al. [24] was used.The image binarization scheme of Palotas et al. was extended byintroducing locally varying thresholds values for fringe separation.After fringe detection, the extraction of geometric properties(length and tortuosity) was done as described in [27].

The HRTEM image analysis technique was convenient for ourpurposes in the sense that every structural parameter relevantfrom the point of the thermodynamic model [23] was obtainableby using HRTEM image analysis alone. Furthermore, as far as the

authors know, there are no readily available methods for theextraction of the quantity of interest of Section 3.3, the amorphouscore diameter.

3. Results and discussion

In this section, results from both qualitative and quantitativestructural analysis are presented. The quantitative discussion con-sists of four parts. First, results from conventional fringe analysisare shown, demonstrating the differences in fringe length and tor-tuosity statistics between samples. Interlayer spacing distributionsare presented next, followed by the quantification of overall struc-tural symmetry.

3.1. Qualitative analysis

Between 10 and 20 micrographs were acquired from eachsample in a representative manner. Examples of the micrographsare shown in Fig. 1.

Pressure under which the soot had been oxidized apparentlyaffected the nanostructure of soot from all three fuel sources. Themicrographs shown in Fig. 1 were selected subjectively for demon-stration purposes, based on how well they represented the qualita-tive trends found in the different structures – note that thequantitative trends presented in Section 3.2 are averaged over allmicrographs within the respective samples.

All samples developed structures typical to combustion-generated carbonaceous residues. Core–shell structures [5,36]were predominantly found in the samples. Hollowed-out particlespreviously observed in Diesel and biodiesel soot [36] and sootheated by pulsed lasers [37] were not found among the analyzedsamples, despite the long residence times in the HTGA.

Generally, the internal structure of the imaged particles showedmore order with increasing oxidation pressure. The core–shellstructural units grew in size and individual amorphous coresseemed to coalesce by uniting their outer shells. The atmosphericsamples displayed low crystalline order and a high area coverageof the isotropic phase. Small core–shell sub-structures appearedin the samples oxidized under 10 atm – these sub-structures wereconsiderably larger in the case of samples oxidized under 40 atm.

3.2. Quantitative analysis

Since being a projected length measure, the arclength of a fringevisible in a HRTEM image is indicative of the size of the graphenelayer which produced the fringe in the image. Because soot struc-ture is primarily composed of carbon atoms and the bond length ofthese atoms is known in graphene, a statistical measure of fringelength is proportional to the average molecular weight of graphenelayers in the structure. Detecting individual fringes in micrographsand measuring their lengths therefore yields quantitative informa-tion regarding the molecular weight distribution of the graphenesheets that compose a soot particle [38].

Another descriptor of the shape of individual graphene layers,fringe tortuosity is the measure of the curvedness of graphene lay-er projections. Since being a projected measure, fringe tortuosityonly qualitatively describes the three-dimensional structure of gra-phene sheets. Graphene layers can become curved due to irregula-rities in their lattice structure and as a result of the splaydeformation described in [23]. The former case represents theeffect of 5- and 7-membered rings being present in graphene andtypically results in high curvature; the latter case can deform reg-ular graphene sheets consisting of 6-membered aromatic rings aswell, but the deformation results in lower curvature.

Fig. 1. Examples of the acquired micrographs. A: n-butanol sample, oxidized at 1 atm. B: n-butanol sample, oxidized at 10 atm. C: n-butanol sample, oxidized at 40 atm. D: n-dodecane sample, oxidized at 1 atm. E: n-dodecane sample, oxidized at 10 atm. F: n-dodecane sample, oxidized at 40 atm. G: m-xylene sample, oxidized at 1 atm. H: m-xylene sample, oxidized at 10 atm. I: m-xylene sample, oxidized at 40 atm. The soot samples were generated in an atmospheric, fuel-rich, flat flame and then oxidized in aHTGA until 50% mass loss.

P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430 2425

Fringe length and tortuosity data were extracted from everymicrograph acquired from each sample. The extracted informationwas averaged over the micrographs representing a particular sam-ple. Figure 2 shows the obtained histograms and fit probabilitydensity functions (PDFs). Since only very slight differences werefound between the distributions, in order to present a better visu-alization, the differences between the pressurized and atmosphericPDFs were computed and plotted in Fig. 2. The slight differencesobserved suggest that increased oxidation pressure increases thesize of graphene layers. The significance of the obtained resultswas tested by Monte-Carlo uncertainty propagation (see e.g.,[39]) – the final uncertainty included the variation from PDF fitting.A statistically significant increase in the frequency of long fringesand a significant decrease in the frequency of short fringes wasfound in the case of n-butanol and n-dodecane samples oxidizedunder 10 atm and 40 atm, compared to the atmospheric case. Them-xylene sample showed the same trend only in the case of thesample oxidized under 40 atm. There were no statistically sig-nificant differences between the fringe length distributions of theatmospheric and 10 atm case. As longer fringes generally indicatemore ordered structures, the fringe tortuosity distributions showa similar trend: less curved fringes were observed in the 40 atmn-butanol and 10 and 40 atm n-dodecane samples, relative to theatmospheric samples. No statistically significant differences were

found between the atmospheric, 10 atm and 40 atm m-xylenesamples. Fringe length data was used to estimate molecular weightdistributions in the nematic phase (see Section 3.3). The resultsreported here are in agreement with those of [21], albeit producedby using a different method and have less measurementuncertainty.

Figure 3 shows extracted interlayer spacing distributions.Interlayer spacing is the distance between neighboring graphenelayers. As a number of previous studies has shown [40,36], asthe maturation of soot proceeds, stacked layers of graphenebecome more similar to graphite crystals. This similarity isexpressed in terms of the length, linearity and spacing of the layerscomposing the microcrystals. As Fig. 3 demonstrates, the generaltrend is that increased oxidation pressure decreases the mode ofthe interlayer spacing distributions. The spacing of graphene layersin the atmospheric samples was found to be the highest andincreasing pressure generally shifted spacing distributions towardlower values. It is worth noting at this point, that the slight com-paction of the nematic phase caused by elevated pressures is mostlikely an indirect effect; that is to say, the uniaxial force of externalcompression is orders of magnitude weaker than the short-rangeforces acting between graphene layers. Thus, the compaction ismore likely caused by changes in the chemical structure inducedby increased pressure – these changes may include the removal

Fig. 2. Extracted fringe length and fringe tortuosity histograms. The top row shows fringe length histograms with fit PDFs. The PDFs are maximum likelihood estimates oflognormal distributions. Histogram data are rescaled to improve comparability. The second row shows the differences between the fit PDFs relative to the 1 atm cases. Anegative difference means that there were less occurrences in a given length bin relative to the 1 atm case. The two bottom rows display the tortuosity data by the sameprinciples. Note that the scales of the horizontal axes of the top row are different than those of the middle and bottom rows. Statistically significant differences at a ¼ 0:95 inthe probability density difference plots are highlighted with gray.

Fig. 3. Extracted interlayer spacing histograms. The top row shows interlayer spacing histograms with fit normal PDFs. Histogram data are rescaled to improve comparability.The bottom row shows the differences between the fit PDFs relative to the 1 atm cases. A negative difference means that there were less occurrences in a given bin relative tothe 1 atm case. Statistically significant differences at a ¼ 0:95 are highlighted in gray.

2426 P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430

of 5- and 7-membered rings and intercalations. While experimen-tal evidence suggests the partial removal of odd-numbered rings, itcan also be argued that strained structures are less stable thermo-dynamically, thus this hypothesis regarding the cause of the appar-ent compaction seems plausible. Interlayer spacing statistics were

used to compute the density of the nematic phase, which is used inSection 3.3.

Besides fringe statistics and interlayer spacing distributions,symmetries in graphene layer arrangement can be measured andused to describe soot nanostructure. The term ‘symmetry’ refers

P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430 2427

to regularities in the relative position and orientation of fringes inHRTEM micrographs. Symmetry can be characterized by orderparameters – the two used here is the polar ðS2PÞ and nematic orderparameter ðS2PÞ introduced by Shim et al. (see Section 2.4 or [26]).Maps of the symmetry parameters were computed by the algo-rithm described in [33]. The extracted maps of S2N and S2P wereintegrated over the analyzed areas to obtain an aggregate measureof symmetry strength in the samples. The results are shown inFig. 4. Figure 4 visualizes the overall symmetry present at par-ticular scales – certain scales are characteristic to certain structuralprimitives, e.g., strong polar symmetry at short scales representssmall fullerenic groups. The symmetry-scale distributions shownin Fig. 4 can therefore be interpreted as indicators that show therelative frequency of occurrences of particular structural primi-tives in the nanostructure.

The first peak in polar symmetry distributions corresponds tosmall-scale fullerenic structures, but is significantly affected bynoise. The second peaks are more expressive and were found atvarying scales above 6 nm – this peak represents the largeronion-like fullerenes or core–shell structures. Peak locations at thisscale roughly correspond to the average size of the onion fullerenesaround amorphous cores. Large-scale polar symmetry generallywere more dominant in samples prepared at higher oxidation pres-sures – long-scale symmetry was the most dominant in each sam-ple oxidized under 40 atm. The secondary peaks of the polarsymmetry distributions were shifted towards longer scales in thecase of samples prepared under elevated pressures. This indicatesthe growth of the concentric structural units, potentially alongwith the amorphous cores. Nematic symmetry distributions areindicative to the distribution of stacked graphene layers, namely,the number of graphene sheets in each identified microcrystal.Consistent with the results of [25], nematic symmetry distribu-tions that decreased with symmetry scale were observed. Thesmallest scale for the extraction of nematic symmetry was chosento be approximately 0.4 nm, which is the scale of 2-membered gra-phene stacks. Monotonically decreasing profiles indicate that therelative frequency of the occurrence of stacked layers is inverselyproportional to the number of graphene layers in them. All samplesdeveloped similar monotonically decreasing nematic symmetrydistributions. In the case of the n-dodecane and m-xylene samples,the effect of oxidation pressure was tractable by observing theincreased nematic symmetry over all spatial scales compared tothe atmospheric sample. Polar symmetry was used to estimatethe diameters of isotropic cores (see Section 3.4.2 in [33]) and

Fig. 4. Overall polar and nematic symmetry of the analyzed structures. The top row shnematic symmetry strength versus scale. The error bars indicate the standard errors of

nematic symmetry was used to locate fringes in the nematicphase – this was how the quantitative results of multi-scalesymmetry analysis fed into the model used in Section 3.3.

Figure 5 shows material properties derived from HRTEM struc-tural data. The results shown in Fig. 5 refer to the nematic phaseonly. The nematic phase was located by setting a threshold on thenematic order parameter and identifying image regions that fellover the threshold. The threshold limit was the theoretical limitset by the Maier–Saupe theory, S2N ¼ 0:43 [41,42]. This thresholdwas varied over a �10% range and along with the standard devia-tion of the structural parameters, the uncertainty resulting fromthe threshold variation was included in the error bars in Fig. 5.The molecular weight of the nematic phase was estimated byassuming a circular catenation mechanism of carbon atoms asdescribed in [38]. Assuming circular catenation, fringe length isdirectly proportional to the diameter of circular graphene layers,which, with some uncertainty, can be converted to molecularweight. The density of the nematic phase was estimated by assum-ing the geometry of a graphite lattice with slightly variable interlay-er spacing. The density is then given by q ¼ 4mC= 2a2d002 sin 120�

� �,

where mC is the mass of a carbon atom, a ¼ 0:142 nm and d002 is theinterlayer spacing in nm. The apparent crystallinity was defined asthe volume fraction of the nematic phase in the soot structure. Thethree-dimensional volume fraction was approximated by the two-dimensional area fraction [28].

Overall, the trends in the derived properties show the increasedcrystalline order with higher oxidation pressures. The molecularweight results were in agreement with previous studies reportinglaser microprobe mass spectrometry results of early soot [43]. Thedensity of the nematic phase was assumed to be determined byinterlayer spacing, therefore higher density signifies more compactstructures. The trends in the measured values of apparentcrystallinity was only statistically significant in the case of them-xylene sample, where the sample oxidized under 40 atmshowed higher crystallinity than the other two samples. Meanvalues and uncertainty ranges of the derived properties are shownin Fig. 5, since they were used in model predictions (with theexception of apparent crystallinity), as described in Section 3.3.

3.3. The interpretation of the results

Although the detailed modeling of soot nanostructure is not yetpossible, we asked the question whether the structural changes we

ows overall polar symmetry strength versus scale. The bottom row shows overallthe means.

Fig. 5. Derived properties from structural parameters extracted by HRTEM image analysis. Molecular weight was estimated by assuming a circular catenation mechanism forcarbon atoms. Density was estimated by assuming graphite lattice structure. The apparent crystalline fraction is the fraction of the nematic phase in the nanostructure. Allmaterial properties pertain to the nematic phase. Circles denote mean values. The confidence bounds around the means are indicated by the black error bars, while gray errorbars indicate standard deviations or the 32nd percentiles around the mean. The standard deviations and percentiles are given to illustrate the distributions of the data. Theconfidence bounds for density are not shown, due to the negligible measurement uncertainty of the interlayer spacing (several hundred thousands of datapoints wereextracted for each sample) and unknown uncertainty introduced by the assumption of graphite lattices – it is highly likely that all trends shown regarding density arestatistically significant at a ¼ 0:95.

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observed were consistent with the thermodynamic model of Hurtet al. [23]. In this model, the equilibrium diameter of the isotropic(amorphous) particle cores is computed as

dcore ¼ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2K11

q=MWð ÞDGN!I

s; ð3Þ

where K11 is the splay elastic constant, q is the density and MW isthe molecular weight of the nematic phase and DGN!I is the Gibbsfree energy change of the nematic-isotropic phase transition [23]:

DGN!I=T ¼ �Z T

Tc

DU þ pDV

T2 dT; ð4Þ

where DU is the internal energy change of the transition, p is pres-sure, T is temperature, Tc is the clearing temperature and DV is themolar volume change during the transition. DU is estimated by theMaier–Saupe mean field theory [41,42] by averaging the orienta-tional potential energy function of single molecules over an orienta-tion distribution obtained by solving a self-consistent equation forthe mean nematic order parameter [44]. The constants of the modelare K11; q; MW; Tc; DV and p, among which Tc; DV and K11 cannotbe directly measured by HRTEM techniques. However, dcore showsasymptotic behavior as a function of the reduced temperatureT=Tc , thus the asymptotic values can be considered as reference.DV depends on the molar mass and the density of the nematicphase, from which the molar mass is assumed to stay constant dur-ing the transition and density change is limited by the densities ofgraphite ð2:1 g=cm3Þ and amorphous carbon ð1:8 g=cm3Þ. The high-est value of DV can be estimated as 3 � 10�3 m3 mol�1 in the idealtransition from isotropic carbon to graphite – an intermediate valueof 1�10�4 m3 mol�1 was used here. Hurt et al. identified a meaning-ful value for K11 to be on the order of 10�12 N.

It has to be noted that since Tc was not measured directly, themodel remained qualitative in terms of predicting absolute corediamaters. However, it was found that when predicting the differ-ence between core diameters corresponding to atmospheric andelevated pressure, the predicted differences were not a strongfunction of Tc . Thus, here we focus more on modeling the relativedifferences in core diameters, not on the absolute prediction ofthem.

The experimental measurement of the isotropic core diameteris possible by recording S2P as a function of the symmetry scale rat distinct symmetry poles. This was done automatically asdescribed in Section 3.4.2 of [33]. In brief, S2P as a function ofsymmetry scale was measured at symmetry director poles andaveraged over the identified poles. Core diameters were defined

as the peak locations in these mean profiles. In some cases the pro-files of S2P showed bimodal trends, which indicate multiple pre-ferred core diameters. In these cases the uncertainty of themeasurement was determined as the range between the peaks,along with their standard deviation; in unimodal cases the uncer-tainty was estimated simply by the standard deviation of theGaussian distribution fit to the identified peak in S2PðrÞ. Figure 6summarizes the experimental measurement of core diametersand modeling results.

Under the nematic transition point, model predictions indicateda general growth of the amorphous cores with pressure. A relativedifference between the core diameters of equilibrium structurescorresponding to 1 and 40 atm of 102 ± 15% was obtained. This dif-ference included the experimentally observed changes in molecu-lar weight, as well as the density change of the nematic phase (seeFig. 5). Simple sensitivity analysis [45] revealed that the variationin molecular weight accounted for 19 ± 9% diameter variation,while pressure difference contributed 71 ± 1%. The effect of densityvariation on core diameter was negligible, around �1%.

The experimentally measured difference in core diameters was91 ± 25%. This value is a result of all the structural peculiaritiescaused by the oxidation process (including layer growth andcompaction), therefore it is difficult to separate the effect of highpressure. However, the very good agreement between theexperimental and model results suggests that the process is welldescribed by the thermodynamic model [23].

The experimentally observed core diameters were 3.4 ± 0.3 nmat 1 atm and 6.6 ± 1 nm at 40 atm. These results were wellapproximated with computed diameters of 3.4 ± 0.4 nm at 1 atmand 6.1 ± 0.4 nm at 40 atm – numbers corresponding to a clearingtemperature of 600 K. There was not much variation between thesamples in terms of measured core diameters, which suggests thatthese results may generalize well to other types of fuels. It may beworth noting though that the m-xylene sample exhibited the lar-gest experimentally measured core sizes, with a value of 3.8 at1 atm and 7.6 nm at 40 nm.

Taking into account the uncertainty and qualitative nature ofthe thermodynamic model used here [23], the qualitative agree-ment between model predictions and experimental data is a sig-nificant preliminary result. The observed structural changes werein accordance with model predictions in the sense that both indi-cated core growth (and implicitly, the prevalence of long-scalepolar symmetry, see Section 3.2). This suggests that the complicat-ed process consisting of molecule growth, compaction, the effect ofshort-scale and long-range forces and chemistry can be fairly wellreproduced by simple equilibrium models given that the time–temperature history of the soot approximates equilibrium

Fig. 6. Results regarding amorphous core diameters. The top two figures illustratethe measurement of core diameters based on multi-scale symmetry data.Symmetry director poles are detected as local maxima in maps of S2P. The coloroverlays indicate symmetry strength – green stands for nematic symmetry and bluemeans polar symmetry. The diameters are obtained by finding the peak locations inprofiles of S2P versus symmetry scale. For details, see [33]. The two identified poleshere correspond to core sizes of 6 and 8 nm, respectively. The bottom figure showsthe comparison of measured and computed core diameters. The red hashed area inthe bars indicate the contribution from pressure difference to the growth of theamorphous cores. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430 2429

conditions. It has to be pointed out that model predictions onlyhold under the nematic transition point, i.e., under a criticalmolecule weight above which the structure spontaneously preferslong-range order.

4. Conclusion

In this study we investigated the effects of oxidation pressuresabove atmoshperic pressure on equilibrium soot nanostructure.Soot from the flames of three surrogate liquid fuels, n-butanol,

n-dodecane and m-xylene were oxidized in controlled, high-pres-sure environments. Due to the time–temperature histories of thesamples (low temperature and high residence time), it washypothesized that the structures obtained at 50% mass loss werequasi-steady state (equilibrium) structures. HRTEM images wereacquired of the obtained soot samples. The lattice structure of sootwas investigated by utilizing state-of-the-art automated imageanalysis. Elevated oxidation pressure had an effect on the fringelength distribution and thus molecular weight of the analyzedsoot – higher pressures were found to produce structuresconsisting of larger graphene layers. Increasing oxidation pressurealso reduced the spacing between graphene sheets. Pressuresignificantly affected the symmetry of soot nanostructure. Resultsfrom symmetry measurements were interpreted by using thethermodynamic model of Hurt et al. It was shown that increasedpressure generally increases the radii of isotropic particle cores,consistently with model predictions. Modeling results suggestedthat the effect of elevated pressure was the most significantcontributor to the growth of amorphous cores. Fuel type did notseem to be a significant factor affecting equilibrium core sizes,suggesting that the behavior shown here might generalize to otherfuel types as well. These results may be useful in predicting alimiting case of soot nanostructure – that corresponding to fastreactions or long residence times.

Acknowlegments

This research was carried out in the framework of the Center ofExcellence of Sustainable Resource Management at the Universityof Miskolc. The authors thank Cristina Jaramillo and JosephLevinthal at the University of Utah for providing soot samples.This material is based upon work while Dr. Lighty served at theNational Science Foundation. Any opinions, findings, and conclu-sions expressed in this publication are those of the authors anddo not necessarily reflect the views of the National ScienceFoundation.

References

[1] P. Delhaes, Graphite and Precursors, first ed., Gordon and Breach SciencePublishers, Amsterdam, 2001.

[2] R.L. Vander Wal, A.J. Tomasek, Combust. Flame 134 (1–2) (2003) 1–9.[3] R.L. Vander Wal, A.J. Tomasek, Combust. Flame 136 (1–2) (2004) 129–140.[4] J. Yang, S. Cheng, X. Wang, Z. Zhang, X. Liu, G. Tang, Trans. Nonferr. Met. Soc.

China 16 (2006) 796–803.[5] T. Ishiguro, Y. Takatori, K. Akihama, Combust. Flame 108 (1-2) (1997) 231–234.[6] Z. Li, C. Song, J. Song, G. Lv, S. Dong, Z. Zhao, Combust. Flame 158 (2011) 1624–

1630.[7] D. Zhang, Y. Ma, M. Zhu, Proc. Combust. Inst. 34 (2013) 1869–1876.[8] R.L. Vander Wal, Soot Nanostructure: Definition, Quantification and

Implications, Tech. Rep. 2005-01-0964, SAE, 2005.[9] A. Santamaria, N. Yang, E. Eddings, F. Mondragon, Combust. Flame 157 (2010)

33–42.[10] K. Yehliu, R.L.V. Wal, O. Armas, A.L. Boehman, Combust. Flame 159 (2012)

3597–3606.[11] M. Lapuerta, F. Oliva, J.R. Agudelo, A.L. Boehman, Combust. Flame 159 (2012)

844–853.[12] P.R. Lindstedt, in: H. Bockhorn (Ed.), Soot Formation in Combustion

Mechanisms and Models, Springer, 1994, pp. 417–441.[13] C.W. Lautenberger, J.L. de Ris, N.A. Dembsey, J.R. Barnett, H.R. Baum, Fire Safety

J. 40 (2005) 141–176.[14] I.M. Kennedy, Progr. Energy Combust. Sci. 23 (1997) 95–132.[15] M. Frenklach, H. Wang, in: Symposium (International) on Combustion, vol.

23(1), 1991, pp. 1559–1566.[16] J.B. Howard, in: Symposium (International) on Combustion, vol. 23(1), 1991,

pp. 1107–1127.[17] S.J. Harris, I.M. Kennedy, Combust. Sci. Technol. 59 (1988) 443–454.[18] I.M. Kennedy, S.J. Harris, J. Colloid Interface Sci. 130 (2) (1989) 489–497.[19] U. Wieschnowsky, H. Bockhorn, F. Fetting, in: Symposium (International) on

Combustion, vol. 22(1), 1989, pp. 343–352.[20] J. Nagle, R.F. Strickland-Constable, in: Proceedings of the Fifth Conference on

Carbon, Pergamon, 1962, pp. 154–164.[21] I.C. Jaramillo, C.K. Gaddam, R.L.V. Wal, C.-H. Huang, J.D. Levinthal, J.S. Lighty,

Combust. Flame 161 (11) (2014) 2951–2965.

2430 P. Toth et al. / Combustion and Flame 162 (2015) 2422–2430

[22] A. Liati, P.D. Eggenschwiler, D. Schreiber, V. Zelenay, M. Ammann, Combust.Flame 160 (2013) 671–681.

[23] R.H. Hurt, G.P. Crawford, H.S. Shim, Proc. Combust. Inst. 28 (2000) 2539–2546.[24] A.B. Palotas, L.C. Rainey, C.J. Feldermann, A.F. Sarofim, J.B.V. Sande, Microsc.

Res. Tech. 33 (3) (1996) 266–278.[25] A. Sharma, T. Kyotani, A. Tomita, Fuel 78 (1999) 1203–1212.[26] H.S. Shim, R.H. Hurt, N.Y.C. Yang, Carbon 38 (2000) 29–45.[27] K. Yehliu, L.R. Vander Wal, A.L. Boehman, Combust. Flame 158 (2011) 1837–

1851.[28] S.A. Saltykov, Stereometric Metallography, second ed., Moscow, 1958. (in

Russian).[29] A. Sharma, T. Kyotani, A. Tomita, Carbon 38 (2000) 1977–1984.[30] H. Aso, K. Matsuoka, A. Sharma, A. Tomita, Carbon 42 (2004) 2963–2973.[31] A.E. Karatas, O.L. Gulder, Soot formation in high pressure laminar diffusion

flames, Progr. Energy Combust. Sci. 38 (2012) 818–845.[32] P. Toth, A.B. Palotas, E.G. Eddings, R.T. Whitaker, J.S. Lighty, A novel framework

for the quantitative analysis of high resolution transmission electronmicrographs of soot I. – improved measurement of interlayer spacing(Combustion and Flame, accepted manuscript).

[33] P. Toth, A.B. Palotas, E.G. Eddings, R.T. Whitaker, J.S. Lighty, A novel frameworkfor the quantitative analysis of high resolution transmission electron

micrographs of soot II. – robust multiscale nanostructure quantification(Combustion and Flame, accepted manuscript).

[34] C.S. McEnally, U.O. Koylu, L.D. Pfefferle, D.E. Rosner, Combust. Flame 109 (4)(1997) 701–720.

[35] D. Gabor, J. Inst. Electr. Eng. III: Radio Commun. Eng. 93 (26) (1946) 429–441.[36] J. Song, M. Alam, A.L. Boehman, U. Kim, Combust. Flame 146 (2006) 589–604.[37] R.L.V. Wal, M.Y. Choi, Carbon 37 (2) (1999) 231–239.[38] V. Fernandez-Alos, J.K. Watson, R.L. vander Wal, J.P. Mathews, Combust. Flame

158 (2011) 1807–1813.[39] C.E. Papadopoulos, H. Yeung, Flow Measur. Instrum. 12 (4) (2001) 291–298.[40] C.R. Shaddix, A.B. Palotas, C.M. Megaridis, M.Y. Choi, N.Y.C. Yang, Int. J. Heat

Mass Transfer 48 (2005) 3604–3614.[41] W. Maier, A. Saupe, Z. Naturforsch. A 14 (1959) 882.[42] W. Maier, A. Saupe, Z. Naturforsch. A 15 (1960) 287.[43] R.A. Dobbins, R.A. Fletcher, H. Chang, Combust. Flame 115 (3) (1998) 285–298.[44] P.J. Wojtowicz, in: E.B. Priestley, P.J. Wojtowicz, P. Sheng (Eds.), Introduction

to Liquid Crystals, Plenum Press, New York, 1974.[45] J.E. Campbell, G.R. Carmichael, T. Chai, M. Mean-Carrasco, Y. Tang, D.R. Blake,

N.J. Blake, S.A. Vay, G.J. Collatz, I. Baker, J.A. Berry, S.A. Montzka, C. Sweeney, J.L.Schnoor, C.O. Stanier, Science 322 (2004) 1085–1088.