Rev Chem Eng 2017; 33(3): 217–235

Open Access

Zdzisław Jaworski*, Barbara Zakrzewska and Paulina Pianko-Oprych On thermodynamic equilibrium of deposition from gaseous C-H-O mixtures: updating for nanotubes

DOI 10.1515/revce-2016-0022 Received April 29, 2016; accepted July 29, 2016; previously ­published 1 Introduction online August 26, 2016 The world energy infrastructure currently uses mainly Abstract: Extensive literature information on experimental fossil fuels such as and various types of thermodynamic data and theoretical analysis for deposit- coal with steadily growing contribution from renewable ing carbon in various crystallographic forms is examined, energy sources as the energy economy based on and a new three-phase diagram for carbon is proposed. as energy carrier is still in its infancy. One of the key prob- The published methods of quantitative description of lems associated with carbonaceous fuels is unfavorable gas-solid carbon equilibrium conditions are critically deposition of solid carbon from gaseous carbon-hydro- evaluated for filamentous carbon. The standard chemi- gen-oxygen (C-H-O) mixtures met in a range of industrial cal potential values are accepted only for purified single- processes (Rostrup-Nielsen 1997). The main sources of walled and multi-walled carbon nanotubes (CNT). Series depositing carbon were described in the literature as (i) of C-H-O ternary diagrams are constructed with plots of molecules of elemental carbon created in thermal crack- boundary lines for carbon deposition either as or ing reactions in gas phase (Jankhah et al. 2008) and (ii) nanotubes. The lines are computed for nine temperature C-H-O compounds of various proportions of the elements, levels from 200°C to 1000°C and for the total pressure of decomposed on catalyst surfaces (Chen et al. 2011, Korup 1 bar and 10 bar. The diagram for graphite and 1 bar fully et al. 2012). Carbon deposition in (i) consists in direct- conforms to that in (Sasaki K, Teraoka Y. Equilibria­ in fuel phase transformation of the element molecules from cell gases II. The C-H-O ternary diagrams. J Electrochem gaseous state into the solid form. Soc 2003b, 150: A885–A888). Allowing for CNTs in carbon Decomposition of several hydrocarbons was often deposition leads to significant lowering of the critical car- used to produce the so-called pyrolytic carbon (pyrocar- bon content in the reformates in temperatures from 500°C bon), which found significant applications initially in the upward with maximum shifting up the deposition bound- space and aircraft industries. Nowadays, carbon nano- ary O/C values by about 17% and 28%, respectively, at 1 materials are being manufactured mainly in the form of and 10 bar. single- or multi-walled nanotubes (Dasgupta et al. 2011, Prasek et al. 2011). In contrast, carbon deposition process Keywords: carbon deposition; C-H-O reformates; CNT (coking, fouling) is highly undesirable in petrochemistry effects; thermodynamic equilibrium. (Benzinger et al. 1996) at and dehydrogenation processes and also in the solid oxide fuel cell technology. Likewise, combustion of carbon containing fuels is fre- quently accompanied by soot formation due to incom- plete oxidation (Wijayanta et al. 2012). However, this study is focused on conditions of carbon *Corresponding author: Zdzisław Jaworski, Department of Chemical deposition from reformed fuels that is detrimental mainly Technology and Engineering, West Pomeranian University of to catalyst surfaces, depending on the morphology of the Technology, Szczecin, 71065 Szczecin, Poland, surface carbon (Pakhare and Spivey 2014). Therefore, the e-mail: [email protected] phenomenon of solid carbon formation both in syngas pro- Barbara Zakrzewska and Paulina Pianko-Oprych: Department of Chemical Technology and Engineering, West Pomeranian University duction and in preprocessing of fuels for solid oxide fuel of Technology, Szczecin, 71065 Szczecin, Poland cells (SOFCs) is of profound importance. The presence of

©2016, Zdzisław Jaworski et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. 218 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

C1 to C4 hydrocarbons and CO in reformate gases was found decomposition at catalyst surfaces, and associated mech- to be a major precursor of carbon formation in SOFCs (Bae anisms of filamentous deposit growth were proposed (de et al. 2010). On the other hand, the nucleation of graphite Bokx et al. 1985, Snoeck et al. 1997a, Wagg et al. 2005). over a catalyst is extremely sensitive to its nanostructure A range of carbonaceous deposit types, both amor- (Bengaard et al. 2002). The deposition usually occurs on phous and crystalline, was found in broad studies of carbon solid surfaces, but nuclei of solid carbon may also form in deposition. The deposits widely differ in morphology and the fluid phase (Guo et al. 2013, Lemaire et al. 2013). reactivity (Bartholomew 2001, Wagg et al. 2005, Diaz Alva- This review starts from a general description of litera- rado and Gracia 2012). Carbon deposition can result in che­ ture data on deposition of various forms of solid carbon mical reactions over a catalyst surface, where several forms from gaseous reformate mixtures. Based on the literature including atomic carbon can appear (Kee et al. 2005), or in experimental data, an original three-phase carbon diagram gas phase due to free-radical reactions ultimately forming is proposed for a wide P-T range followed by validated math- polyaromatic compounds (Sheng and Dean 2004). McCarty ematical expressions for equilibrium carbon vapor pressure and Wise (1997) observed four main types of carbon on a over carbon solid forms. In the following chapter, quantita- catalyst. Other early classifications (Rostrup-Nielsen tive description of thermodynamic equilibrium is included 1979, 1984) proposed three types of solid carbon formed at for a range of allotropic forms of solid carbon, including two reforming of fuels: (i) encapsulating film, (ii) whisker-like filamentous forms. Then the published models of deposi- (filamentous), and (iii) pyrolytic carbon. Those carbon tion equilibrium are briefly presented. Based on minimiza- forms were also observed by Sehested (2006). The encapsu- tion of the Gibbs energy of the considered C-H-O systems, lating tar-like carbon film (i), according to Rostrup-Nielsen it was possible to compute equilibrium phase concentra- (1979, 1984), is formed by slow polymerization of higher tions and detect the depositing carbon form. Series of such radicals at temperatures below 773 K. Accord- simulations for varied temperature and pressure allowed to ing to Sehested (2006), the encapsulating carbon (gum) construct ternary C-H-O plots showing boundaries of both deposits consist of a thin film of hydrocarbon or a few layers graphitic and filamentous carbon deposition zones. of graphite. Formation of the filamentous, graphitic type in the form of tubular filaments (whiskers, fibers ii) prevails in the temperature range from 720 K up to 870 K (Rostrup- Nielsen, 1979, 1984), whereas at the latter temperature, the 2 Carbon deposits formation of pyrolytic carbon (soot, iii) begins to predomi- nate as result of thermal cracking of hydrocarbons. The Three major types of industrial reforming of hydrocar- mechanism of pyrolytic carbon deposition in the range of bon/alcohol fuels can be distinguished. Those are steam 1073–1273 K was studied by Zheng et al. (2013). Alstrup et al. reforming (SR), catalytic partial oxidation (CPOX), and (1998) found that carbon filaments are formed on nickel dry reforming (DR). While SR and DR are endothermic catalysts when hydrogen is present in the gas phase while and CPOX is exothermic, a combination of SR and CPOX is encapsulating carbon dominated in pure CO reactions. named oxidative SR and its specific energy-neutral version Filamentous carbon deposits were detected more is called autothermal reforming (Diaz Alvarado and Gracia than 120 years ago by Hughes and Chambers (1889) during 2012). Depending on the process conditions, all those their search for carbon filaments for electric lighting. The reforming processes can result in formation of carbonic finding was confirmed by Davis et al. (1953) by means of solid. Thermal decomposition of hydrocarbons and alco- electron micrography. Sehested (2006) underlines the hols proceeds along complex paths, and the mechanism detrimental role of whisker carbon for catalysts and links details are still searched for (Alberton et al. 2007, Dufour development of pyrolytic carbon with the appearance of et al. 2009, Wang et al. 2009). Most of the studies of carbon higher hydrocarbons at elevated temperature. Generally deposition indicate formation of elemental carbon in the similar results were reported by Alberton et al. (2007) and reforming reactions as the main source of carbon deposi- He and Hill (2007) indicating the importance of catalyst tion, however, without supplying a validated mechanism. type and the highly destructive role of carbon dissolved Two models were considered for pyrolytic carbon (Zheng within the catalyst structure above 873 K. During cata- et al. 2013): a deposition droplet model proposed by Shi lytic and thermal cracking of ethanol in the temperature et al. (1997) and the combined mechanism of nucleation range from 523 K to 1123 K, Jankhah et al. (2008) found on graphene and of carbon growth at the edge of gra- that carbon deposits can be formed as filaments, both phene (Hu and Hüttinger 2002). Several carbon contain- rectilinear and helicoidal. Essentially, carbon nanotubes ing intermediate species were detected during (CNTs) are layers of coaxially assembled graphene planes, Z. Jaworski et al.: Carbon deposition: updating for nanotubes 219 and their continuous catalytic production was reviewed It can be summarized that carbon deposition rate by Ying et al. (2011). A variety of CNTs can exist ranging strongly depends on temperature, gas phase composition, from single-walled to multi-walled tubes with Young’s presence of catalysts, and the type of applied catalyst (Ros- modulus over 1 TPa and tensile strength about 150 GPa trup-Nielsen 1972, de Bokx et al. 1985, Kee et al. 2005, Mallon (Paradise and Goswami 2007). According to a thermody- and Kendall 2005, Ke et al. 2006, Kim et al. 2006, Chen et al. namic analysis carried out by Gozzi et al. (2007), the trans- 2011, Yurkiv et al. 2013). Several authors (­Rostrup-Nielsen formation of solid carbon from graphite to multi-walled 1972, 1984, Jankhah et al. 2008, Cimenti and Hill 2009, carbon nanotubes (MWCNTs) becomes spontaneous at Essmann et al. 2014) highlighted that both the thermody- the temperature, T, of 704 ± 13 K. The authors also found namic equilibrium conditions and the kinetic rate of all that thermal decomposition of methane to form MWCNTs reactions and phase transitions should be considered in is thermodynamically favored at T > 809 K. In a follow- predictions of carbon deposits. However, Rostrup-Nielsen ing paper (Gozzi et al. 2008), they concluded that carbon and Christiansen (2011) showed that the equilibrium con- nucleation from gas phase usually results in a mixture of stants for methane decomposition decisively depend on the various nanotubes and also amorphous or/and graphitic metal catalyst type and stated that “[t]he important ques- forms. Proportions of those carbon forms depend mainly tion is whether or not carbon is formed and not the rate at on temperature and the catalyst type and its granularity. which it may be formed.” Therefore, the following chapters Similar conclusions about coexistence of different forms are focused on the analysis of current literature informa- of solid carbon were drawn by Snoeck and Froment (2002) tion for temperature-pressure conditions for stable phases, and Makama et al. (2014). Thermodynamic data for single- which were first presented in the form of a gas-liquid-solid walled CNTs in bundles were also obtained using an indi- diagram for pure carbon and then in ternary diagrams for rect solid galvanic cell method (Gozzi et al. 2009). C-H-O reformates in thermodynamic equilibrium. A specific two-dimensional form of solid carbon, called graphene, can also be formed on metal surfaces, e.g. Ni (Arkatova 2010) and Cu. The properties of graphene were extensively described by Soldano et al. (2010). Three 3 Carbon phase diagram methods of graphene preparation were employed: (i) seg- regation of carbon from the bulk of the metal, (ii) chemi- Carbon is the lightest element of Group IV and can form cal vapor deposition of hydrocarbons, and (iii) carbon allotropes of three different covalent bond formations in vapor deposition (Xu et al. 2013). Despite intensive inves- condensed phases: sp3 hybridization (diamond, liquid), tigations, many fundamental aspects of the graphene sp2 (graphite, nanotubes, graphene, fullerenes, liquid), nucleation are still not fully understood (Mehdipour and and metastable sp (carbynes) (Ghiringhelli et al. 2008).

Ostrikov 2012, Zhang et al. 2012, Kim et al. 2013). Thermal functions for gaseous carbon species C1 to C7 were A purely chemical kinetic analysis of pyrocarbon published (Lee and Sanborn 1973) over 40 years ago. deposition was performed by the team led by Hüttinger The overall graphical form of equilibrium phases is (Becker and Hüttinger 1998a,b,c,d, Hu and Hüttinger usually presented as a pressure vs. temperature, P-T, phase 2002). Kazakov et al. (1995) proposed a model for soot diagram indicating areas of existence of thermodynami- formation in laminar flames, and Appel et al. (2000) pre- cally stable forms. Two main points are characteristic for sented a new kinetic model of soot formation in flames. such diagrams: the triple phase point for the coexistence The kinetics of nucleation and growth of soot particles in of solid, liquid, and gas phases and the critical liquid-gas turbulent combustion flames was also numerically ana- point. The two points for carbon appear at high tempera- lyzed (Zucca et al. 2006, Chernov et al. 2012). A kinetic tures, above 4000 K. Therefore, experimental investi- expression for the formation rate on a nickel cata- gations of the carbon equilibrium conditions required lyst was derived by Ginsburg et al. (2005) and Asai et al. applications of special techniques. The published papers (2008), and evidence of a prior formation of unstable refer to either gas-solid (graphite) equilibrium (Marshall was presented by Kock et al. (1985). Based on an and Norton 1950, Clarke and Fox 1969, Lee and Sanborn elementary kinetic description presented by Bessler et al. 1973, Leider et al. 1973, Baker 1982, Lee and Choi 1998, (2007) for SOFCs, a modeling study for predicting carbon Havstad and Ferencz 2002, Joseph et al. 2002, Miller et al. deposition from reformates was also carried out (Yurkiv 2008) or equilibrium for liquid-graphite-diamond (Fried et al. 2013). A review and a thorough discussion of the and Howard 2000, Ghiringhelli et al. 2005, Savvatimskiy present knowledge of the factors controlling coke forma- 2005, Wang et al. 2005, Ghiringhelli et al. 2008, Yang and tion in SOFCs were presented by Wang et al. (2013). Li 2008, Umantsev and Akkerman 2010). The liquid-gas 220 Z. Jaworski et al.: Carbon deposition: updating for nanotubes phase boundary was given little attention with the excep- tion of Bundy et al. (1996). However, research papers on carbon equilibria were mostly devoted to theoretical studies rather than to the experimental ones.

3.1 Carbon solid – liquid and liquid – gas equilibria van Thiel and Ree (1989) proposed a phase diagram of graphite-diamond-liquid for bulk carbon. The P-T diagram was enhanced for bulk carbon by Bundy et al. (1996) up to T = 6000 K and extended for diamond melting by Wang et al. (2005) above 8000 K and also refined to account for carbon crystal size by ­Savvatimskiy (2005), who presented experimental thermodynamic Figure 1: Phase diagram for carbon. D, diamond; G, graphite; CNT, data for the graphite melting points. The diagram was carbon nanotubes; L, carbon liquid; V, carbon vapors; TGLV, solid- further adjusted for carbon nanocrystals of graphite and liquid-gas triple point; TGDL, graphite-diamond-liquid triple point; diamond by Yang and Li (2008). However, the entire CR, critical point. phase diagram should cover the regions of thermody- namically stable three phases: (i) solid phases of graphite data described in the next section. In order to better show (G), diamond (D), and CNTs; (ii) gas phase (vapors, V); details of the carbon diagram, the axis of equilibrium and (iii) a single liquid carbon (L) zone since Ghiringhelli carbon pressure, P∗, in Figure 1 is presented in the loga- et al. (2008) rejected existence of two phases of liquid C rithmic scale. carbon, as suggested elsewhere. The border line between An important issue results from the considerations in the G and V areas ends at the triple point G-L-V, which was section 3.1 that no stable liquid carbon phase is expected assumed according to Leider et al. (1973) for T = 4100 K GLV within the temperature range of T < 3000 K. It follows and P = 1.12 bar. It should also be mentioned that the GLV from the graph that the lines between G-D and D-L and NIST-JANAF tables (Chase 1998) suggest that T = 4765 K GLV L-V areas are of little importance to the deposition equilib- and P = 26.95 bar, and the same temperature value is GLV rium and only the (de)sublimation lines between carbon suggested for 1 bar by the CRC Handbook (Lide 2005). vapors V and either solid graphite G or nanotubes CNT Ghiringhelli et al. (2005) established the location of the play significant role. second triple point for graphite-diamond-liquid carbon at

TGDL = 4250 K and PGDL = 164,000 bar. It was also found that the P-T coordinates of the triple point, TGDL, shift to lower P and T with decreasing carbon nanocrystal size (Yang 3.2 Carbon solid – gas equilibria and Li 2008). According to Togaya (1997), the line between the The graphite-vapor equilibrium was empirically studied two triple points, GLV-GDL, has a maximum at the tem- by measuring evaporation rates at temperatures above perature of 4790 K and P = 5.6 GPa. The coordinates of 2000 K (Marshall and Norton 1950, Lee and Sanborn the critical point, CR, where differences between the 1973, Joseph et al. 2002). Carbon vapors were assumed to carbon liquid and gas phases vanish was adopted based contain several polyatomic species (Clarke and Fox 1969, on Leider et al.’s (1973) approximation at TCR = 6810 K and Leider et al. 1973) ranging from C1 to C7; however, C6 was

PCR = 2300 bar. The line dividing the gas (V) and liquid (L) later ruled out by Joseph et al. (2002). Careful selection, carbon phases was assumed linear between CR and GLV, tuning, and generalization of available experimental data and the line between the diamond (D) and liquid (L) areas for carbon led to establishing approved thermochemical was based on Savvatimskiy (2005) and Wang et al. (2005) tables, such as NIST-JANAF data (Chase 1998). Therefore, phase diagrams. The complete carbon phase diagram the equilibrium line for carbon sublimation that divides shown in Figure 1 was based on Bundy et al.’s (1996) pro- the area of carbonic vapors (V) and graphitic solid (G) in posal; however, it was widened to include important gas Figure 1 was based on the NIST-JANAF data presented in range and upgraded using a wide collection of literature details in the next section. Z. Jaworski et al.: Carbon deposition: updating for nanotubes 221

Typical temperature of reformate gases ranges from considered phase. As accepted by convention (e.g. Atkins ambient up to 1500 K; therefore, this range is adopted in 1998), the standard activity of any pure element in its the thermodynamic analysis for carbon solid depositions condensed state is equal to the unit for its stable form in of this present study. Thus the following thermodynamic the standard conditions (pure species under P0 = 0.1 MPa) analysis for reformates refers to relevant gas-solid equi- using various definitions and units of the activity. In a libria in that range, first for graphite and then for other similar way, the actual activity can be expressed by means carbon deposits. of various measures of species concentration, such as

pressure, molar ratio, etc. The species activity, aj, for gas

phases is usually termed “fugacity”, fj, and is defined as

3.2.1 Carbon vapors over graphite a product of the non-dimensional fugacity coefficient, φj,

and a species pressure, Pj: Required conditions for carbon deposition usually refer af==φ P (5) to the state of thermodynamic equilibrium of the species jj jj 0 containing carbon in the solid and gas phases. It is there- In that case, the standard activity of a species, aj , is also fore essential to apply proper tools of modeling of the related to the standard pressure, P0. On the other hand, equilibrium for C-H-O species and use current data of for gas species under pressures greatly lower than its thermodynamic properties of different forms of elemental critical pressure and for temperature very much higher carbon both in the gas and solid phases. than the species critical temperature, both the species The standard thermodynamic approach that assumes compressibility factor and fugacity coefficient are close equilibrium of a closed system is generally (e.g. Smith to 1 (Atkins 1998). Therefore, for the saturated carbon ∗ −19 et al. 2005) characterized by two conditions: a minimum vapor pressures, PC , below 10 bar and the analyzed of the total Gibbs energy at constant temperature and temperatures up to 1500 K (cf. Figure 1), one can safely 0 0 pressure, G, of the considered system, which consists of a assume a [Ci(g)] = P and also a[Ci(g)] = P[Ci(g)]. In addi- set of nj moles of species “j”: tion, the solid-state activities of graphite as the stable 0 form of solid carbon, both the standard, a [Cg(s)], and GT(,Pn,{ jj}) ==minimum or dG(,TP,{n }) 0 (1) actual, a[Cg(s)], ones are also very close to 1 at total pres- 0 and also by equality of the partial molar Gibbs energy, μj, sure close to P . i.e. chemical potential of each species in all phases (Smith However, one should distinguish between various et al. 2005), either gas (g), liquid (l), or solid (s). allotropic forms of carbon, appearing both in the gaseous,

Ci(g), and solid, Ck(s), states. Most published gaseous µjj(s)(==µµl) j(g) (2) forms of carbon arising from reformates are Ci(g) for i = 1

For a physical phase transfer or a chemical reaction up to 8. Solid carbon, Ck(s), can be limited here to four between species Aj linked by the stoichiometric equation­ basic classes: graphitic, k = g, two filamentous k = f, and ν A = 0 and in the state of their thermodynamic amorphous k = a. When necessary, two filamentous forms ∑ j jj will be distinguished, the multi-wall, k = MW, and single- ­equilibrium, denoted by “*”, the species system undergo- wall, k = SW. ing phase transfer or/and reaction obeys Equation (3). Applying Equations (3–5) and the conventions for ∗ ν µ = 0. (3) carbon in the gas (j = Ci(g)) or solid (j = Ck(s)) phases in the ∑ jj j state of thermodynamic equilibrium (*), we get:

The chemical potential of a pure species in any phase is ∗ 00aC[(i g)] usually presented as a sum of its standard-state value, µ [(Cgik)]+=RT ln 0 µ [(Cs)], (6) 0 aC[]i ()g µj ()T , and the contribution resulting from a ratio of the species activities in a current state, aj, and in the reference 0 and as in the considered cases of carbon deposition below state, normally the standard state, aj . 1500 K, φCi ≅ 1, one can express the equilibrium (satura-

0 aj tion) pressure over the graphitic carbon solid phase, µjj=+µ RT ln 0 (4) a shown by the “/Cg(s)” index as j 00 ∗ µ [(Cgig)] − µ [(Cs)] P [(Cg)(/xCs)] =−PC0[(g)]e p. Equation (4) is valid both for pure species and for species ig i RT   in a single-phase mixture. The aj activity depends on the actual temperature, T; pressure, P; and composition of the (7) 222 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

That form is convenient for analyzing the relationship at varied temperature, T, was also computed from two * P [Ci(g)] using the standard values of the chemical poten- other literature sources: correlation of Miller et al. (2008), tial for various gaseous carbon molecules, Ci(g), available which is compatible with table data of Chase (1998). either directly or indirectly in the subject literature (Yaws The Miller et al. (2008) correlation for such equilib- 1995, 2012, Chase 1998, Scientific Group 1999, Lide 2005) rium pressures, P* in Pa, against temperature, T in K, and also in the open source Cantera (Goodwin 2009) or recalculated in SI units can be presented as the commercial software HSC (HSC Chemistry 2014). The ∗ 85900 chemical potential of formation of gas carbon molecules P [(Cg)(/1Cs)] =−.47·1013 exp. (9) totg T 0 0 from graphite is equal to the numerator, μ [Ci(g)] – μ [Cg(s)] of Equation (7). Due to the convention used in physical The dependence is graphically shown for comparison in chemistry, it is often assumed μ0[C (s)] = 0 for the basic g Figure 2 as the thin solid line. The relationship of Equa- solid form of atomic species such as graphite in the refer- tion (9) is especially useful for a quick comparison with ence standard conditions. However, this must be coherent the equilibrium pressure of gaseous carbon resulting with parallel assumptions for the standard partial molar from selected reactions of C-H-O reformates. It was also enthalpy, H 0 , and partial molar entropy, S0 , to comply j j concluded that the three sources (Chase 1998, Miller with the general relationship G0 = H0 – TS0. One should et al. 2008, HSC Chemistry 2014) deliver very similar also remember that a direct deposition process of carbon parameters of equilibrium conditions for carbon gases vapors is only possible when the local pressure of carbon over solid graphite. In addition, a similarly good agree- vapors, P[C (g)], exceeds the corresponding equilibrium i ment in the individual equilibrium pressures for C up to (saturation) counterpart, P*[C (g)], resulting from Equa- 1 i C over graphite was found when data from Chase (1998) tion (7). 5 and (HSC Chemistry 2014) were compared (not shown The temperature influence on the equilibrium pres- here). sure of gaseous carbon allotropes, C to C , over solid 1 8 Two additional P vs. T lines for CNTs, SWCNT, and graphite is depicted in Figure 2, as computed with the HSC MWCNT are also shown in the figure, and their experimen- software (HSC Chemistry 2014). It shows that the first mol- tal origin is presented in the next section. The equilibrium ecule, C , exhibits principal contribution to the total equi- 1 carbon vapor pressures over the nanotubes are not largely librium pressure of gaseous carbon and the contribution different from the total pressure over graphite within of C to C molecules can be safely neglected. 4 8 the investigated temperature ranges, as can be seen in The total pressure of carbon vapors over graphite Figure 2. (/C (s)), g In summary, it may be stated that gaseous carbonic 8 P∗∗[(Cg)(/]Cs)] = PC[(gC)/ ()s species accompany any solid carbon, although at very low tot gi∑ i1= g (8) partial pressures. In addition, surpassing the carbon equi- librium pressures described in Equation (7) creates condi- tions of supersaturation of carbon vapors and tendency to solid carbon depositions.

3.2.2 Equilibrium conditions for non-graphitic deposits

As early as 1905, Schenck and Heller (1905a,b) found that the equilibrium of the Boudouard reaction was influenced by the catalysts used and the obtained reactant composi- tions differed from those without presence of a catalyst. A similar conclusion was drawn by Pring and Fairlie (1912) in respect to the equilibrium of methane pyrolysis. The discrepancies were later ascribed to formation of solid

filamentous carbon (Cf(s)), which has the standard chemi- μ0 Figure 2: Equilibrium partial pressures of gaseous carbon mole- cal potential, [Cf(s)] different from that of graphite. The 0 cules over graphite and nanotubes; MWCNT (Equation 16) and values of μ [Cf(s)] were first estimated by Rostrup-Nielsen SWCNT (Equation 17). (1972) and de Bokx et al. (1985) resulting in their equality Z. Jaworski et al.: Carbon deposition: updating for nanotubes 223

∗ 0 0 to that for graphite, μ [C (s)] = μ [C (s)], roughly at 950 K pH O f g K = 2 (14) for the selected size of catalyst grains. p,25 pp∗∗ HC2 O Three methods of estimation of the standard chemical potential were published for solid carbon deposits, (Ck(s)), A number of experimental data for such Kp,i quotients are other than graphite (Cg(s)). The most accurate type was available in the subject literature (Bromley and Strick- based on measuring the standard electromotive force, E0, land-Constable 1960, Rostrup-Nielsen 1972, Bernardo of high temperature, solid-state galvanic cells (Jacob and et al. 1985, de Bokx et al. 1985, Tavares et al. 1994, Ros- Seetharaman 1995, Gozzi et al. 2007, 2009) with single- trup-Nielsen et al. 1997, Snoeck et al. 1997a,b, Snoeck and crystal CaF2 as a solid electrolyte. The virtual, resultant Froment 2002). Formally, each of the partial pressures in cell reactions between graphite and purified solid forms of Equations (12) to (14) should be divided by the reference 0 filamentous or amorphous carbon were Cg(s) = Ck(s). Then pressure, P = 1 bar. Therefore, those published quotient the standard chemical potential change of the “i” reaction values depend on the pressure units used, and this must 0 between solid carbon species, Δi μ [C(s)] was calculated as be accounted for when calculating the chemical potential a temperature function from the measured standard elec- deviation by means of Equation (15) or more general Equa- 0 tromotive force, Ei ()T , using Equation (10): tion (19). The “i” subscript denotes a considered trans- formation reaction between different allotropic forms of 00 ∆µii[]Cs()()Tn=− FE ()T , (10) solid carbon, Cg(s) and Ck(s). where n is the number of electrons transferred per carbon KCpi, [(g s)] RTCln = ∆ µ0[(s)] (15) atom in the cells and F denotes the Faraday constant. The ik KCpi, [(k s)] investigated chemical potential of the non-graphitic solid 0 carbon, μ [Ck(s)], can be then derived from That energy difference can be used to determine the standard chemical potential for deposited non-graphitic 00 0 µ [(Cs)]()TC=+µ∆[(sT)]() µ [(Cs).]()T (11) 0 kgik carbon, μ [Ck(s)], from Equation (11), applying literature 0 thermodynamic data for graphite, μ [Cg(s)]. Such method 0 However, the reference value of μ [Cg(s)] in Equation (11) was already used in 1960 by Bromley and Strickland- was dependent on the convention used. Constable (1960) and also by the Rostrup-Nielsen group Another method of determination of the chemical (­Rostrup-Nielsen 1984, Bernardo et al. 1985). In principle, 0 potential value for single-walled CNTs, μ [Cf(s)], is based it should be possible to derive temperature dependences 0 on precise oxidation calorimetry (Levchenko et al. 2011) of μ [Cf(s)](T) for filamentous deposits (Ck = Cf) based on with entropy changes calculated using heat capacities of the equations for threshold constants cited by Snoeck and graphite and single-walled CNT. co-authors (Snoeck et al. 1997a,b, Snoeck and Froment 0 Yet most published estimates of μ [Ck(s)] relied on 2002) for methane cracking and wet reforming of methane. measuring gas reactant partial pressures at equilibrium However, those constants resulted in different standard ∗ conditions, pj , and they were determined either at the enthalpy and entropy values for varied methane partial beginning of coking (Bernardo et al. 1985) or more typi- pressures (Snoeck et al. 1997a) and also the computed 0 cally at the coking threshold obtained for both growing μ [Cf(s)] values significantly differed from those pub- and decreasing pressures. Carbon depositions accompa- lished earlier. In addition, one has to conclude that major- 0 nying the Boudouard reaction (21) and methane pyrolysis ity of the papers quoting quantitative data for Δi μ [Ck(s)] 0 (23) were investigated and reported in a wide temperature did not clarify how the μ [Cg(s)] values for graphite were range, in most cases, with dispersed nickel as a catalyst. calculated for determining Kp,i[Cg(s)]. Nevertheless, it is Usually, the relevant equilibrium quotients (constants), informative to compare the published temperature func- 0 Kp,i, used in the subject literature, like those cited in Equa- tions of the chemical potential deviation, Δi μ [Ck(s)]=f(T), tions (22), (24), and (26), respectively, for reactions (21), and a collection of such plots of black (for CNT) and grey (23), and (25), were originally calculated as follows: solid lines is graphically presented in Figure 3 along with ∗ information on data sources. The dotted reference line of pCO K = 2 (12) Δ μ0[C (s)]=0, for graphite is also shown in Figure 3. p,21 p∗2 i g CO Preferred depositing conditions for filamentous 0 carbon rather than graphite are those where Δi μ [Ck(s)] < 0, p∗2 H2 and most of the lines in Figure 3 go below the chemical K = (13) p,23 p∗ potential level for graphite (dotted line) at the temperature CH4 224 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

cannot be regarded as a sufficient proof of the deposit purity. Consequently, it was accepted in this study that thermodynamic data only for pure forms of filamentous carbon or graphite should be used in predicting equilib- rium conditions of their deposition. Therefore, reliable experimental data for the purified multi-wall (Gozzi et al. 2007) and bundled single-walled (Gozzi et al. 2009) CNTs, shown in Figure 3 as black solid lines, are applied with thermodynamic fundamentals in the following sections to derive conditions of carbon deposition for various reformate compositions. Relevant relationships reported for purified CNTs were published by Gozzi et al. (2007)

for Ck(s) = MWCNT in temperature ranging from 820 K to 920 K:

0 Figure 3: Plots of literature Gibbs energy differences between ∆i µ []MWCNTT() =±(8250 90)−±(11.72 0.9)T [J/mol] graphite and other solid carbon forms. [1] Snoeck and Froment for T[K] (16) (2002); [2] Gozzi et al. (2007); [3] Jacob and Seetharaman (1994); [4] Rostrup-Nielsen (1972); [5] Gozzi et al. (2009); [6] Bromley and Strickland-Constable (1960); [7] Bernardo et al. (1985); [8] Lee et al. and by Gozzi et al. (2009) for bundled SWCNT in the tem- (2013). perature range from 750 K to 1015 K in a polynomial form:

9 ∆µ0[]SWCNTT()=−3FaTTn [J/mol] for [K] in∑n=0 (17) ranging from 430°C to 680°C. It can also be concluded where F denotes the Faraday constant. from Figure 3 that a relatively wide scatter exists between Latini et al. (2014) reported in 2014 that there were no the direct or calculated data for ∆ µ0 , which were pub- iC()s articles other than the two by Gozzi et al. (2007, 2009) that lished by different authors, and it may be useful to identify dealt with thermodynamic measurements at high tem- possible sources of such discrepancies. For instance, even perature on carbon nanostructures. In the study of Wagg from data in a single paper (Snoeck and Froment 2002), et al. (2005), an upper bound of the chemical potential of five different Δ μ0[C (s)] values can be derived (1a to 1e in i k SWCNT growth threshold was estimated for T > 700°C as Figure 3). In the authors’ opinions, two key reasons for the presented scatter can be indicated: (i) lack of crystallo- ∆µ∗ =− max8{}i []SWCNTT() 0960 116T [J/mol] graphic purity of the investigated carbon deposits and (ii) for T[]°C, (18) use of different values for the standard chemical poten- tial of graphite, which led to differences in the Kp,i[Cg(s)] which indeed results in significantly higher values than equilibrium quotients. The latter may have stemmed from those calculated from Equation (17). different selections of the standard and reference states The necessity and importance of purifying the inves- used in the published papers. For instance, the standard tigated samples of solid carbon deposits were clearly entropy value for graphite at 298.15 K is assumed either explained by Gozzi et al. (2009). Moreover, the authors in a about 5.7 J mol−1 K−1, e.g. in Rostrup-Nielsen and Bak further study obtained significant differences in the stand- Hansen (1993), Lide (2005), and HSC Chemistry (2014), or ard enthalpy and entropy even for separated and single- 0.0 J mol−1 K−1, e.g. in Chase (1998) and Yaws (1995, 2012). wall-in-bundle carbon nanofibers. A similar rationale can 0 0 Moreover, some authors apparently assumed μ [Cg(s)]=0, possibly explain substantial differences in Δiμ [Ck(s)]=f(T) independent of temperature for the graphitic solid carbon, for amorphous carbon samples (Jacob and Seetharaman which is in clear disagreement with the dependence of 1994, Terry and Yu 1995). It should also be mentioned that both standard enthalpy and entropy on temperature for in another study (Lee et al. 2013), the standard partial every species. molar enthalpy and entropy of the CNT formation were 0 −1 0 −1 −1 Based on the evidence delivered by Gozzi et al. (2007), estimated as ΔfH = 54.46 kJ mol and ΔfS = 68.9 J mol K one may expect that usually more than one crystallo- based on literature data of de Bokx et al. (1985) and the graphic form of solid carbon appears in carbon deposits. NASA data (McBride et al. 2002) for graphite. The values The photographic SEM evidence of presence of filamen- were then used to derive C-H-O concentration boundaries tous carbon, which was often shown in relevant papers, for depositing CNT at varied temperature and resulted in Z. Jaworski et al.: Carbon deposition: updating for nanotubes 225

the deposition boundary lines in a ternary diagram largely the shift equilibria.” In that case, Kp,observed > Kp,equilibrium and different (Lee et al. 2013) from the corresponding one Δμ[Ck(s)] < 0, and it is true except for noble metals as cata- shown in Figure 4B. lysts (Rostrup-Nielsen and Christiansen 2011). The steady-

Perhaps Diaz Alvarado and Gracia (2012) were the only state activity of solid carbon, a[Ck(s)], was also defined authors who concurrently considered published equilib- based on a kinetic analysis (Rostrup-Nielsen 1984). The ria of various solid carbon forms: graphite, MWCNT, amor- principle of actual gas was presented by Rostrup-Nielsen phous, and polymeric for glycerol reforming systems. The and Christiansen (2011) and has been often used to assess authors used data for multi-walled nanotubes based on the risk of carbon formation in a non-equilibrium, steady-

Gozzi et al. (2007) and found existence of two regions: state process. In that case, the quotient, Kp,observed, should the most favorable carbonaceous solid type was graphite be calculated for actual, non-equilibrium concentrations. below 450°C, whereas CNTs were preferred to form above In an early study, de Bokx et al. (1985) concluded that threshold temperature. However, the deposition that the deposited filamentous carbon in the presence of threshold temperatures determined in this study, shown catalysts is a metastable intermediate of a higher by the vertical broken lines in Figure 3, were 431°C for the chemical potential than that of graphite but is not decom- graphite-to-MWCNT change (as in Gozzi et al. 2007) and posed to graphite due to a high activation barrier for the about 590°C for the MWCNT-to-SWCNT transformation. In homogeneous nucleation of graphite, which causes a very conclusion, it should be stressed that carbon vapors are low rate of the nucleation. It also implies that almost fil- always expected in equilibrium over solid graphite or CNT, ament-free operation is possible for more carbon bearing however, with a very small partial pressure. gases than it results from graphite equilibria. A thermodynamic analysis of carbon deposition accompanying methane SR (Xu and Froment 1989) was carried out using a ratio, V , of the pressure quotient of the 4 Published models of deposition i actual partial pressures of species “j”, pj, to the quotient equilibrium for equilibrium conditions of the “i” reaction, the latter

being the equilibrium constant, Kp,i, for that reaction. Several proposals for quantitative description of equi- ν librium conditions for carbon deposition from gaseous p j ∏ j j = ( )i (20) reformates have already been published, and an early Vi K pi, communication in 1972 was delivered by Rostrup-Nielsen (1972). In the paper, formation of whisker carbon was evi- That approach was also applied by Hou and Hughes (2001) denced, and the equilibrium constants for actual reac- for methane reforming. Magnitude of the ratio indicates tion with carbon deposition, Kp,observed, were compared whether a reaction goes to the right (Vi < 1) or to the left to the theoretical equilibrium constant computed for (Vi > 1) or remains at equilibrium (Vi = 1). A related pres- graphite, Kp,graphite. Higher CH4 or CO concentrations were entation of the conditions of carbon deposition was used detected (Rostrup-Nielsen 1979) before carbon formation in an analysis for catalyzed reforming of methane (Gins- on catalysts than for non-catalyzed graphite deposition, burg et al. 2005), in a SOFC fueled by sewage biogas (van which implies smaller constants, Kp,observed, than those for Herle et al. 2004), and also when the fuel cell was fed with graphite, Kp,graphite, at a given temperature (Rostrup-Nielsen methane (Klein et al. 2007).

1984). The excess chemical potential, Δμ[Ck(s)], of the One of the similar approaches (Tsiakaras and Demin deposited carbon compared to that based on graphite was 2001) was based on consideration of the Boudouard reac- estimated (Rostrup-Nielsen 1972) on the basis of the two tion of carbon , Equation (21). constants, Equation (19). 2COC=+OC2 (21) K 00 pg, raphite The relevant equilibrium constant of Equation (21), K , ∆µ[Cska( )]=−∆µ ctual ∆µgraphite = RT ln (19) p,21 K po, bserved for species pressures, pi, was used (Tsiakaras and Demin 2001) to define the carbon activity, a[C (s)], , which is a That approach was further developed by the intro- k 21 reciprocal of V . duction of the so-called principle of equilibrated gas i (­Rostrup-Nielsen 1984), which states “[c]arbon forma- Kp2 tion is to be expected if the gas shows affinity for carbon p,21CO aC[]k (s),21 = (22) after the establishment of the methane reforming and pCO 2 226 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

It was commonly assumed that the carbon activity 2013, Liu et al. 2013) using various software codes. Deter- equals 1 at the thermodynamic equilibrium, and solid mination of the carbon deposition boundary was based carbon formation is possible only when a[Ck(s)],21 > 1 on assumption of a very small but non-zero amount of (­Assabumrungrat et al. 2004, Tsiakaras and Demin 2001). solid carbon in equilibrium (Koh et al. 2002) or a fraction That analysis was also extended by considering carbon of 10−6 of the total carbon amount (Sasaki and Teraoka activities resulting from other reactions (Assabumrungrat 2003a). A similar criterion of the minimum carbon frac- et al. 2005, Sangtongkitcharoen et al. 2005, Assabumrun- tion, xC,min, for carbon deposition to occur was proposed −4 grat et al. 2006): methane pyrolysis (23) and reverse gasi- by Heddrich et al. (2013) as xC,min=10 , which resulted fication (25) from the thermodynamic equilibrium concentrations computed by minimizing the Gibbs energy of reacting CH =+2H C (23) 42 systems. In another study, Jankhah et al. (2008) performed a Kpp,23CH 4 thermodynamic analysis for DR of ethanol and also for aC[ k (s),] 23 = 2 (24) p H2 its thermal cracking based on a commercial software that uses the Gibbs energy criterion, Equation (1). Minimum

CO +=HH22OC+ (25) temperatures for thermodynamic exclusion of carbon formation at various oxidant/ethanol ratios were deter-

Kpp,25COHp mined. Later on, Wang and Cao (2010) assumed, in their aC[]()s , = 2 (26) k 25 p analysis of the conditions for solid carbon formation, HO2 that the partial molar Gibbs energies both of gas carbon In seven further studies (Sangtongkitcharoen et al. 2005, and solid carbon, μ[C(g,s)], have zero value independ- Klein et al. 2007, Nikooyeh et al. 2008, da Silva et al. 2009, ent of temperature. This assumption may have caused Vakouftsi et al. 2011, Nematollahi et al. 2012, Trabold significant impact on the authors’ assessment of critical et al. 2012), the same or slightly transformed definitions, temperatures above which coke is not formed. A two-case as those in Equations (22), (24), and (26), were applied limit model for the driving force of graphene deposition to determine values of the solid carbon activity, a[Ck(s)]. from hydrocarbons was proposed by Lewis et al. (2013) for The calculations were based on minimization of the Gibbs a hot wall reactor. Case 1 corresponded to thermodynamic energy using either commercial software or thermody- equilibrium of chemical reactions of hydrocarbons in the namic data from literature. gas phase, and a separate Case 2 considered the solid-gas Other types of carbon deposition analyses were phase equilibrium composition over a growing graphene based on the C-H-O diagrams, and they were relatively film. often quoted in the subject literature. Bartholomew Thermodynamic properties of metallurgical coke (1982) was perhaps the first to publish equilibrium iso- formation were also investigated and discussed (Terry therms at 450°C and 1.4 atm both for graphite and amor- and Yu 1991, Jacob and Seetharaman 1994, Jacob and phous carbon plotted in a C-H-O ternary diagram. The Seetharaman 1995, Terry and Yu 1995). A decrease of isotherm lines were based on literature experimental solid carbon amount resulting from application of data and clearly showed the deposition region for amor- the amorphous carbon properties instead of those for phous carbon was smaller than that for graphite, i.e. its graphite was verified by Cimenti and Hill (2009) in their boundary was shifted towards higher C content of C-H-O thermodynamic calculations. They also found that due mixtures. Eguchi et al. (2002) possibly pioneered sys- to a higher energy of the amorphous form than that for tematic application of that approach supported by com- graphite, a joint use of properties of the two carbon mercial software for computing the equilibrium phase forms results in the same equilibrium composition as contents with assumed temperature, pressure, and input that for graphite. moles. The boundaries were also presented in a ternary It follows from the literature presented in this section C-H-O diagram. A comprehensive study by Sasaki and that the thermodynamic equilibrium is one of the key Teraoka (2003b) led to detail boundaries of graphitic factors controlling the formation of carbon deposits carbon deposition for equilibrium temperature ranging during reforming of C-H-O mixtures. The thermodynamic from 100°C to 1000°C. Essentially the same approach analyses carried out for a range of oxidized fuels indicated was reported in several other papers (Koh et al. 2001, the predominant role of the mixture composition and tem- 2002, Sasaki and Teraoka 2003a, Sasaki et al. 2004, Kee perature in solid carbon formation. The boundaries of no- et al. 2008, Aravind et al. 2009, Chen et al. 2011, Lee et al. deposition operational regimes were determined using Z. Jaworski et al.: Carbon deposition: updating for nanotubes 227 different thermodynamic criteria and properties. In the decided that only the galvanic cell data (Gozzi et al. 2007, majority of the published thermodynamic approaches, 2009) for filamentous carbon can be regarded as trustwor- different authors considered solid carbon and typically thy and useful in the thermodynamic analysis. By analogy neglected existence of carbon vapors in their thermo- to approaches applied by other authors (Diaz Alvarado dynamic calculations. However, the carbon element is and Gracia, 2012), the chemical potential dependence known of having different allotropic forms both in the on temperature by Gozzi et al. (2007) was assumed valid gas and solid phases and their thermodynamic equilibria down to 600 K (inclined dotted line in Figure 3). In addi- may be critical in understanding the conditions of carbon tion to graphite data as a reference, table data for diamond deposition. Those aspects are considered in the following and experimental data for the chemical potential of for- chapter. mation of amorphous carbon (Jacob and Seetharaman 1994) were also added and applied in the HSC software (HSC 2014). However, the amorphous data along with that for diamond did not turn out significant within the ranges 5 Thermodynamic equilibrium for considered in this study, i.e. temperature between 200°C C-H-O mixtures and 1000°C and pressure of 1 and 10 bar.

5.1 Temperature dependence of carbon 5.2 Numerical predictions of C-H-O equilibria deposition equilibrium A wide series of computations of equilibrium phase con- Carbonaceous depositions can occur as a result of side centrations of C-H-O reformates were performed with reactions in reforming popular hydrocarbons such as finding of the depositing carbon form, for varied tem- methane from natural/bio gas, propane with butane from perature between 200°C and 1000°C with 100°C incre- LPG, or higher hydrocarbons from diesel fuel. The preced- ments and two pressure levels of 1 bar and 10 bar. Based ing section on gas-solid carbon equilibrium clearly quan- on those results, boundary lines between the deposition tified the equilibrium partial pressures of carbon vapors, and no deposition zones were drawn in ternary diagrams which exist over different crystallographic forms of solid and their selection is presented in Figures 4–7. In order to carbon. However, most authors who analyzed thermody- verify the simulation procedure, such boundary plots for namic conditions of carbon deposition neglected the pres- 1 bar and graphite only in the solid phase (Figure 4A) were ence of carbon vapors in Equations (22), (24), and (26), first compared with the original ternary plots published assuming perhaps that all atomic carbon was completely by Sasaki and Teraoka (2003b) (not shown here) and the transferred to the solid phase and therefore did not influ- two line sets turned out practically identical within the ence the reaction equilibrium. The importance of carbon temperature range from 200°C to 1000°C. 0 gas pressure was explicitly found in only two papers The effect of adding Δi μ [Cf(s)] data for filamen- (Bromley and Strickland-Constable 1960, da Silva et al. tous carbon, either MWCNT [Equation (16)] or SWCNT 2009); however, the solid carbon activity was used there [­Equation (17)], as a thermodynamic equilibrium alterna- in calculations of the reaction constants. Critical compo- tive to graphite is visually presented in Figure 4. In the sitions of C-H-O mixtures for carbon deposition to occur performed calculations, the most stable forms of solid were usually studied with the help of commercial software carbon were generally graphite for temperatures from based on principles expressed in Equations (1) to (7). 200°C to 431°C; MWCNT from 431°C up to about 577°C; and Several papers (Bartholomew 1982, Koh et al. 2001, above it, the SWCNT prevailed. Therefore, corresponding Eguchi et al. 2002, Koh et al. 2002, Sasaki and Teraoka boundary lines for a given temperature are identical up to 2003a,b, Sasaki et al. 2004, Kee et al. 2008, Aravind et al. 400°C, as only graphite was computed in the solid phase, 2009, Chen et al. 2011, Lee et al. 2013, Liu et al. 2013) and differ significantly for higher temperatures where fil- reported C-H-O equilibrium calculations and their com- amentous carbon was predicted. Based on the presented prehensive presentation in ternary diagrams. Most of the results, it may be stated that by the time new reliable published studies considered only the graphitic form of thermodynamic data for the chemical potential of fila- solid carbon. However, the thermodynamic data for CNTs mentous carbon are published, the boundary lines shown by Gozzi et al. (2007, 2009), respectively, for the multi- in Figure 4B should be used as reference in reforming wall and single-wall in bundles are also considered in this processes with nickel catalyst where filamentous carbon section. As already mentioned, the authors of this study deposits may be formed. 228 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

Figure 4: Ternary plots for solid phase of graphite only (A) and all carbon allotropes (B) at P = 1 bar.

Figure 5: Deposition boundaries for graphitic carbon ( ) and all solid forms ( ) at 1 bar.

For clearer viewing of the differences in the bound- 5.3 Pressure effect on carbon deposition ary lines, two diagrams for the total pressure of 1 bar are equilibrium shown in Figure 5. Each of them presents three pairs of corresponding temperature lines either for graphite only The course of deposition boundary lines was found (broken lines) or for all considered carbon solid forms dependent also on the total pressure, P, of the C-H-O (solid lines). Extension of the carbon deposition regions mixtures. A visual comparison of ternary plots with the towards lower C concentration, with reference to those equilibrium boundary lines computed for 10 bar, sepa- for graphite, is due to accounting also for the filamentous rately for graphite and for all considered solid carbon carbon forms and is illustrated in Figure 5 by grey shading. allotropes, is shown in Figures 6A and B, respectively. The One can conclude that the deposition boundary lines for equilibrium simulations were done for the same tempera- P = 1 bar differ mainly for the reformate temperature close ture range from 200°C to 1000°C as before for 1 bar. For to 800°C and the line differences decrease towards the that elevated pressure, the conditions of carbon depo- limits of the studied range from 500°C to 1000°C. sition also significantly depended on the solid carbon Z. Jaworski et al.: Carbon deposition: updating for nanotubes 229

Figure 6: Ternary plots for solid phase of graphite only (A) and all carbon allotropes (B) at P = 10 bar.

Figure 7: Deposition boundaries for graphitic carbon ( ) and all solid forms ( ) at P = 10 bar. allotropes considered. Identical to the threshold tempera- the reformate temperature of about 900°C, i.e. somewhat tures at 1 bar, graphite was in solid phase for temperatures higher than for the total pressure of 1 bar. from 200°C to 431°C, while MWCNT formed solid phase The character of temperature influence on the course from 431°C up to about 577°C, and above it, the SWCNT of the deposition boundary lines depends on the hydro- prevailed. gen concentration; for low H values, an increase in tem- A graphical presentation of the effect of considering perature lowers the critical C value, whereas for high either graphite only or filamentous carbon allotropes in hydrogen concentration (lower left part of diagrams), the the equilibrium simulations is shown in Figure 7 for the temperature effect is opposite. Those effects are qualita- total pressure of 10 bar, which is qualitatively similar to tively similar for the two considered pressure values of 1 that in Figure 5 for 1 bar. One can notice that both at the and 10 bar and either carbon deposit. total pressure of 1 bar and 10 bar of the C-H-O mixtures, The effect of total pressure on the studied equilibrium carbon deposition can occur when C > 0.5, independent conditions can also be assessed by comparing locations of of the H and O atomic ratios. When considering all solid the corresponding pairs of boundary lines in Figures 4A and carbon forms, the maximum shift of the equilibrium 6A for graphite only and those in Figures 4B and 6B for all boundary line relative to that for graphite was found for solid carbon forms. Two other ternary graphs were prepared 230 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

(not shown here) for all carbon solid forms with boundary presented in Sections 3 and 4. Verified table data for the line pairs for 1 and 10 bar and for three temperature levels chemical potential of other solid forms, such as graphite, in each diagram, similarly to those in Figures 5 and 7. From diamond, and amorphous carbon, were also used in the their analysis, it was concluded that the maximum diver- computations. gence in the lines, i.e. the strongest pressure effect, was in C-H-O atomic concentration diagrams with equilib- the temperature range from 700°C to 800°C when graphite rium ternary plots for deposition boundaries of the carbon was the only solid form allowed. However, the temperature form, characterized by a minimum of its Gibbs energy range of the maximum influence of pressure was shifted up (Equation (1)), were constructed for varied temperature by about 100°C when all solid carbon allotropes were con- and pressure. The obtained diagram for graphite as the sidered in equilibrium simulations for the total pressure of single solid carbon was practically identical with that 10 bar, compared to those for 1 bar. published by Sasaki and Teraoka (2003b). Within the ana- lyzed ranges of T-P, only either graphite and or one of the two nanotube types turned out as the depositing carbon 6 Concluding remarks form. The following threshold temperatures were esti- mated for carbon allotropes in solid phase: 431°C for the The Gibbs and activation energies of chemical reactions transition of graphite to multi-walled nanotubes, which and physical phase transformations are dependent on is similar to conclusions of Diaz Alvarado and Gracia temperature; therefore, both the equilibrium condi- (2012). A higher threshold at about 580°C was found for tions and kinetics of the relevant carbon phase changes SWCNT replacing MWCNT, independent of pressure at 1 are also temperature sensitive, which was confirmed by and 10 bar. The thresholds are shown by dotted lines in several researchers. Carbon can deposit in variety of crys- Figure 3. Consideration of the chemical potential data tallographic forms on different catalysts, including single- for filamentous carbon in addition to that for graphite walled and multi-walled nanotubes (Jankhah et al. 2008, resulted in shifting the deposition boundary lines towards Gozzi et al. 2008, Makama et al. 2014). Although thermo- lower carbon ratio in C-H-O reformates for temperatures dynamic criteria indicate either graphite or fibrous carbon above 431°C. This was valid independent of pressure, P, as stable solid forms at T < 1500 K, the kinetics of their at constant temperature and of temperature for constant mutual direct transformation can be extremely slow and pressure. The strongest effect of the presence of filamen- difficult to detect. tous carbon on lowering the critical carbon atomic ratio, Wide literature information on both theoretical and C, was found for reformates without hydrogen, i.e. for experimental studies on carbon deposition from C-H-O H = 0. The maximum shift in the boundary molar C ratio reformates was examined in this review. Based on the was estimated as ΔC1,G-CNT = −0.042 for nearly 800°C at 1 bar analysis of published models, it was concluded that the and as ΔC10,G-CNT = −0.052 for nearly 900°C at P = 10 bar. The thermodynamic conditions for deposition of various two shift values corresponded to an increase in the critical carbon allotropes require stringent specification. In the oxygen-to-carbon atomic ratio, O/C, by about 17% or 28% first step, the three-phase carbon diagram was updated for 1 bar and 10 bar, respectively. for only graphite and diamond in the solid phase. It was It is also envisaged that similar analyses focused on confirmed that within the temperature and pressure practical fuel reformates from different reforming methods ranges up to 1500 K and 10 bar, respectively, the carbon will be presented as a follow-up in a separate paper. equilibrium should be considered between only the gas and solid phases. Acknowledgments: The research program leading to these Physical chemistry fundamentals along with rel- results received funding from the European Union’s Sev- evant experimental data for filamentous carbon were enth Framework Programme (FP7/2007-2013) for the Fuel reviewed in Section 3. Significant differences were found Cells and Hydrogen Joint Undertaking (FCH JU) under in the standard chemical potentials estimated from the grant agreement no. [621213] with the STAGE-SOFC acro- literature equilibrium concentrations for carbon deposi- nym. Information contained in the paper reflects only tion reactions. The lack of crystallographic purity of the the view of the authors. The FCH JU and the Union are carbonaceous deposits was suggested as the major cause not liable for any use that may be made of the informa- of the discrepancy. Therefore, only the electrochemi- tion contained therein. The work was also financed from cal measurement data for purified both single-walled an the Polish research funds awarded for project no. 3126/7. multi-walled CNTs (Gozzi et al. 2007, 2009) were accepted PR/2014/2 of international cooperation within STAGE- for filamentous carbon in the thermodynamic analysis SOFC in the years 2014–2017. Z. Jaworski et al.: Carbon deposition: updating for nanotubes 231

Becker A, Hüttinger KJ. Chemistry and kinetics of chemical vapor References deposition of pyrocarbon – V. Influence of reactor volume/ deposition surface area ratio. Carbon 1998d; 36: 225–232. Alberton AL, Souza MMVM, Schmal M. Carbon formation and its Bengaard HS, Norskov JK, Sehested J, Clausen BS, Nielsen LP, influence on ethanol steam reforming over Ni/Al2O3 catalysts. Molenbroek AM, Rostrup-Nielsen JR. Steam reforming Catal Today 2007; 123: 257–264. and graphite formation on Ni catalysts. J Catal 2002; 209: Alstrup I, Tavares MT, Bernardo CA, Sùrensen O, Rostrup-Nielsen JR. 365–384. Carbon formation on nickel and nickel- catalysts. Benzinger W, Becker A, Hüttinger KJ. Chemistry and kinetics of Mater Corros 1998; 49: 367–372. chemical vapor deposition of pyrocarbon: I. Fundamentals of Appel J, Bochorn H, Frenklach M. Kinetic modeling of soot formation kinetics and chemical reaction engineering. Carbon 1996; 34: with detailed chemistry and physics: laminar premixed flames 957–966.

of C2 hydrocarbons. Combust Flame 2000; 121: 122–136. Bernardo CA, Alstrup I, Rostrup-Nielsen JR. Carbon deposition and Aravind PV, Woudstra T, Woudstra N, Spliethoff H. Thermodynamic methane steam reforming on silica-supported Ni-Cu catalysts. evaluation of small-scale systems with biomass gasifiers, solid J Catal 1985; 96: 517–534. oxide fuel cells with Ni/GDC anodes and gas turbines. J Power Bessler WG, Gewies S, Vogler M. A new framework for physically Sources 2009; 190: 461–475. based modeling of solid oxide fuel cells. Electrochim Acta Arkatova LA. The deposition of coke during carbon dioxide 2007; 53: 1782–1800. reforming of methane over intermetallides. Catal Today 2010; Bromley J, Strickland-Constable RF. Role of nucleation processes 157: 170–176. in the reactions between and nickel. Trans Asai K, Nagayasu Y, Takane K, Iwamoto S, Yagasaki E, Ishii K, Inoue Faraday Soc 1960; 56: 1492–1500. M. Mechanism of methane decomposition over Ni catalyst at Bundy FP, Bassett WA, Weathers MS, Hemley RJ, Mao HK. high temperatures. J Japan Petr Inst 2008; 51: 42–49. The pressure-temperature phase and transformation Assabumrungrat S, Pavarajarn V, Charojrochkul S, Laosiripojana N. diagram for carbon; updated through 1994. Carbon 1996; 34: Thermodynamic analysis for a solid oxide fuel cell with direct 141–153. internal reforming fueled by ethanol. Chem Eng Sci 2004; 59: Chase MW. NIST-JANAF thermochemical tables, 4th ed., Washington, 6015–6020. USA: American Chemical Society, 1998. Assabumrungrat S, Laosiripojana N, Pavarajarn V, Charojrochkul Chen T, Wang WG, Miao H, Li T, Xu C. Evaluation of carbon S, Sangtongkitcharoen W, Tangjitmatee A, Praserthdam P. deposition behavior on the nickel/yttrium-stabilized zirconia Thermodynamic analysis of carbon formation in a solid oxide anode-supported fuel cell fueled with simulated syngas. fuel cel with a direct internal reformer fuelled by . J Power Sources 2011; 196: 2461–2468. J Power Sources 2005; 139: 55–60. Chernov V, Zhang Q, Thomson MJ, Dworkin SB. Numerical Assabumrungrat S, Laosiripojana N, Piroonlerkgul P. Determination investigation of soot formation mechanisms in partially- of the boundary of carbon formation for dry reforming of premixed ethylene–air co-flow flames. Comb Flame 2012; 159: methane in a solid oxide fuel cell. J Power Sources 2006; 159: 2789–2798. 1274–1282. Cimenti M, Hill JM. Thermodynamic analysis of solid oxide fuel cells Atkins PW. Physical Chemistry, 6th ed., Oxford: Oxford University operated with methanol and ethanol under direct utilization, Press, 1998. steam reforming, dry reforming or partial oxidation conditions. Bae G, Bae J, Kim-Lohsoontorn P, Jeong J. Performance of SOFC J Power Sour 2009; 186: 377–384. coupled with n-C4H10 autothermal reformer: carbon deposition Clarke JT, Fox BR. Rate and heat of vaporization of graphite above and development of anode structure. Int J Hydrog Energy 2010; 3000 K. J Chem Phys 1969; 51: 3231–3240. 35: 12346–12358. da Silva AL, de Fraga Malfatti C, Műller IL. Thermodynamic analysis Baker RL. A multiple species non-equilibrium thermodynamics of ethanol steam reforming using Gibbs energy minimization model of carbon sublimation. J Non-Equilib Thermodyn 1982; method: a detailed study of the conditions of carbon 7: 309–322. deposition. Int J Hydrog Energy 2009; 34: 4321–2330. Bartholomew CH. Carbon deposition in steam reforming and Dasgupta K, Joshi JJ, Banarjee S. Fluidized bed synthesis methanation. Catal Rev-Sci Eng 1982; 24: 67–112. of carbon nanotubes – a review. Chem Eng J 2011; 171: Bartholomew CH. Mechanisms of catalyst deactivation. Appl Catal A 841–86. General 2001; 212: 17–60. Davis WR, Slawson RJ, Rigby GR. An unusual form of carbon. Nature Becker A, Hüttinger KJ. Chemistry and kinetics of chemical vapor 1953; 171: 756. deposition of pyrocarbon II. Pyrocarbon deposition from de Bokx PK, Kock AJHM, Boellaard E. The formation of filamentous ethylene, acethylene and 1,3-butadiene in the low temperature carbon on and nickel-catalysts. I Thermodynamics J Catal regime. Carbon 1998a; 36: 177–199. 1985; 96: 454–467. Becker A, Hüttinger KJ. Chemistry and kinetics of chemical vapor Diaz Alvarado F, Gracia F. Oxidative steam reforming of glycerol deposition of pyrocarbon – III. Pyrocarbon deposition from for hydrogen production: thermodynamic analysis including

propylene and benzene in the low temperature regime. Carbon different carbon deposits representation and CO2 adsorption. 1998b; 36: 201–211. Int J Hydrog Energ 2012; 37: 14820–14830. Becker A, Hüttinger KJ. Chemistry and kinetics of chemical vapor Dufour A, Valin S, Castelli P, Thiery S, Boissonnet G, Zoulalian A, deposition of pyrocarbon – IV. Pyrocarbon deposition from Glaude P-A. Mechanisms and kinetics of methane thermal methane in the low temperature regime. Carbon 1998c; 36: conversion in a syngas. Ind Eng Chem Res 2009; 48: 213–224. 6564–6572. 232 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

Eguchi K, Kojo H, Takeguchi T, Kikuchi R, Sasaki K. Fuel flexibility nanofilaments’ production. Int J Hydrog Energ 2008; 33: in power generation by solid oxide fuel cells. Solid State Ion 4769–4779. 2002; 152–153: 411–416. Joseph M, Sivakumar N, Manoravi P. High temperature vapour Essmann C, Maier L, Li A, Tischer S, Deutschmann O. Natural gas pressure studies on graphite using laser pulse heating. Carbon steam reforming over rhodium/alumina catalysts: experimental 2002; 40: 2021–2040. and numerical study of the carbon deposition from ethylene and Kazakov A, Wang H, Frenklach M. Detailed modeling of soot carbon monoxide. Ind Eng Chem Res 2014; 53: 12270–12278. formation in laminar premixed ethylene flames at a presuure of Fried LE, Howard WM. Explicit Gibbs free energy equation of state 10 bar. Combust Flame 1995; 100: 111–120. applied to the carbon phase diagram. Phys Rev B 2000; 61: Ke K, Gunji A, Mori H, Tsuchida S, Takahashi H, Ukai K, Mizutani 8734–8743. Y, Sumi H, Yokoyama M, Waki K. Effect of oxide on carbon

Ghiringhelli LM, Los JH, Meijer EJ, Fasolino A, Frenkel D. Modeling deposition behavior of CH4 fuel on Ni/ScSZ cermet anode in the phase diagram of carbon. Phys Review Lett 2005; 94: No. high temperature SOFCs. Solid State Ion 2006; 177: 541–547. 145701, 4pp. Kee RJ, Zhu H, Goodwin DG. Solid-oxide fuel cells with hydrocarbon Ghiringhelli LM, Valeriani C, Los JH, Meijer EJ, Fasolino A, Frenkel D. fuels. Proc Combust Inst 2005; 30: 2379–2404. State-of-the-art models for the phase diagram of carbon and Kee RJ, Zhu H, Sukeshini AM, Jackson GS. Solid-oxide fuel cells: diamond nucleation. Molec Phys 2008; 106: 2011–2038. operating principles, current challenges, and the role of Ginsburg JM, Piňa J, El Solh T, de Lasa HI. Coke formation over syngas. Combust Sci Tech 2008; 180: 1207–1244. a nickel catalyst under methane dry reforming conditions: Kim HK, Saiz E, Chhowalla M, Mattevi C. Modeling of the self-limited Thermodynamic and kinetic models. Ind Eng Chem Res 2005; growth in catalytic chemical vapor deposition of graphene. 44: 4846–4854. New J Phys 2013; 053012, 15: 1–15. Goodwin D. Cantera: an object-oriented software toolkit for chemical Kim T, Liu G, Boaro M, Lee S-I, Vohs JM, Gorte RJ, Al-Madhi OH, kinetics, thermodynamics, and transport processes, Pasadena: Dabbousi BO. A study of carbon formation and prevention in Caltech, 2009, available at: https://code.google.com/p/ hydrocarbon-fueled SOFC. J Power Sour 2006; 155: 231–238. cantera. Klein J-M, Bultel Y, Georges S, Pons M. Modeling of a SOFC fuelled Gozzi D, Iervolino M, Latini A. The thermodynamics of the by methane: from direct internal reforming to gradual internal transformation of graphite to multiwalled carbon nanotubes. reforming. Chem Eng Sci 2007; 62: 1636–1649. J Am Chem Soc 2007; 129: 10269–10275. Kock AJHM, De Bokx PK, Boellaard E. The formation of filamentous Gozzi D, Latini A., Lazzarini L. Chemical differentiation of carbon carbon on iron and nickel-catalysts. II. Mechanism J Catal 1985; nanotubes in a carbonaceous matrix. Chem Mater 2008; 20: 96: 468–480. 4126–4134. Koh J-H, Kang B-S, Lim HCh, Yoo Y-S. Thermodynamic analysis of Gozzi D, Latini A, Lazzarini L. Experimental thermodynamics of high carbon deposition and electrochemical oxidation of methane for temperature transformations in single-walled SOFC anodes. Electrochem Solid-State Lett 2001; 4: A12–A15. bundles. J Am Chem Soc 2009; 131: 12474–12482. Koh J-H, Yoo Y-S, Park J-W, Lim HCh. Carbon deposition and cell Guo H, Gu Z, Thomson KA, Smallwood GJ, Baksh FF. Soot formation performance of Ni-YSZ anode support SOFC with methane fuel. in a laminar ethylene/air diffusion flame at pressures from 1 to Solid State Ion 2002; 149: 157–166. 8 atm. Proc Combust Inst 2013; 34: 1795–1802. Korup O, Schlogl R, Horn R. Carbon formation in catalytic partial Havstad MA, Ferencz RM. Comparison of surface chemical kinetics oxidation of methane on platinum: model studies on a models for ablative reentry of graphite. J Termophys Heat Transf polycrystalline Pt foil. Catal Today 2012; 181: 177–183. 2002; 6: 508–515. Latini A, Tomellini M, Lazzarini L, Bertoni G, Gazzoli D, Bossa L, He H, Hill JM. Carbon deposition on Ni/YSZ composites exposed to Gozzi D. High temperature stability of onion-like carbon vs humidified methane. Appl Catal A 2007; 317: 284–292. highly oriented pyrolytic graphite. PLoS ONE 2014; 9: e105788; Heddrich MP, Jahn M, Michaelis A, Näke R, Weder A. SOFC 1–16. system design using ideal efficiency modeling – model and Lee EL, Sanborn R-H. Extended and improved thermal functions for

experimental implementation. Fuel Cells 2013; 13: 612–622. the gaseous carbon species C1-C7 from 298 to 10,000 K. High Hou K, Hughes R. The kinetics of methane steam reforming over a Temp Sci 1973; 5: 438–453.

Ni/a-Al2O catalyst. Chem Eng J 2001; 82: 311–328. Lee KH, Choi BK. Solid-vapor phase boundary of carbon at low HSC Chemistry v.8 software, Outotec (Finland) Oy, Research Center temperature and low pressure. Solid State Commun 1998; 108: Pori, Finland, 2014. 133–137. Hu ZJ, Hüttinger KJ. Mechanisms of carbon deposition – a kinetic Lee WY, Hanna J, Ghoniem AF. On the predictions of carbon approach. Carbon 2002; 40: 617–636. deposition on the nickel anode of a SOFC and its impact Hughes TV, Chambers CR. Manufacture of carbon filaments. US Patent on open-circuit conditions. J Electrochem Soc 2013; 160: 405480, June 18, 1889, application filed August 30, 1886. F94–F105. Jacob KT, Seetharaman S. Thermodynamic stability of metallurgical Leider HR, Krikorian OH, Young DA. Thermodynamic properties of coke relative to graphite. Metall Mater Trans B 1994; 25B: carbon to the critical point. Carbon 1973; 11: 555–563. 149–151. Lemaire R, Bejaoui S, Therssen E. Study of soot formation during Jacob KT, Seetharaman S. Thermodynamic stability of metallurgical the combustion of Diesel, rapeseed methyl ester and their coke relative to graphite, Author’s reply. Metall Mater Trans B surrogates in turbulent spray flames. Fuel 2013; 107: 147–161. 1995; 26B: 656–658. Levchenko AA, Kolesnikov AI, Trofymluk O, Navrotsky A. Energetics Jankhah S, Abatzoglou N, Gitzhofer F. Thermal and catalytic dry of single-wall carbon nanotubes as revealed by calorimetry and reforming and cracking of ethanol for hydrogen and carbon neutron scattering. Carbon 2011; 49: 949–954. Z. Jaworski et al.: Carbon deposition: updating for nanotubes 233

Lewis AM, Derby B, Kinloch IA. Influence of gas phase equilibria on Rostrup-Nielsen JR, Bak Hansen JH, Aparicio LM. Reforming of the chemical vapor deposition of graphene. ACS Nano 2013; 7: hydrocarbons into synthetic gas on supported metal catalysts. 3104–3117. Sekiyu Gakkaishi 1997; 40: 366–377. Lide DR, editor. CRC Handbook of chemistry and physics. Internet Rostrup-Nielsen JR, Christiansen LJ. Concepts in Syngas Version 2005 available at: http://www.hbcpnetbase.com. CRC Manufacture. Catalytic Sci Series 2011, 10: 247, Imperial Press, Boca Raton, FL, 2005. College Press, London. Liu M, Lanzini A, Halliop W, Cobas VRM, Verkooijen AHM, Aravind PV. Sangtongkitcharoen W, Assabumrungrat S, Pavarajarn V, Anode recirculation behavior of a solid oxide fuel cell system: Laosiripojana N, Praserthdam P. Comparison of carbon a safety analysis and a performance optimization. Int J Hydrog formation boundary in different modes of solid oxide Energy 2013; 38: 2868–2883. fuel cells fueled by methane. J Power Sources 2005; 142: Makama AB, Salmiaton A, Abdullah N, Choong TSY, Saion EB. Recent 75–80. developments in purification of single wall carbon nanotubes. Sasaki K, Teraoka Y. Equilibria in fuel cell gases I. Equilibrium Separ Sci Technol 2014; 49: 2797–2812. compositions and reforming conditions. J Electrochem Soc Mallon C, Kendall K. Sensitivity of nickel cermet anodes to reduction 2003a; 150: A878–A884. conditions. J Power Sour 2005; 145: 154–160. Sasaki K, Teraoka Y. Equilibria in fuel cell gases II. The C-H-O ternary Marshall AL, Norton FJ. Carbon vapor pressure and heat of diagrams. J Electrochem Soc 2003b, 150: A885–A888. vaporization. J Am Chem Soc 1950; 72: 2166–2171. Sasaki K, Watanabe K, Shiosaki K, Susuki K, Tearoka Y. Multi-fuel McBride BJ, Zehe MJ, Gordon S. NASA Glenn coefficients for capability of Solid Oxide Fuel Cells. J Electroceram 2004; 13: calculating thermodynamic properties of individual species. 669–675. NASA/TP—2002-211556, Glenn Research Center, 2002; Savvatimskiy AI. Measurements of the melting point of graphite available at http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa. and the properties of liquid carbon (a review for 1963–2003). gov/20020085330_2002141071.pdf. Carbon 2005; 43: 1115–1142. McCarty JG, Wise H. Hydrogenation of surface carbon on alumina- Schenck R, Heller W. Experimentelle Studien über die Vorgänge bei supported nickel. J Catal 1997b; 169: 250–262. der Reduction des Eisens. Ber deut chem Gesell 1905a; 38: Mehdipour H, Ostrikov K. Kinetics of low-pressure, low-temperature 2132–2139. graphene growth: Toward gingle-layer, single-crystalline Schenck R, Heller W. Ueber die gegenseitigen Beziehungen der structure. ACS NANO 2012; 6: 10276–10286. verschiedenen Kohlenstoffmodificationen. Ber deut chem Miller SA, Jolivet CS, Stoner Jr. JO. New methods for testing cyclotron Gesell. 1905b; 38: 2139–2143. carbon stripper foils. Nucl Instr Methods Phys Res A 2008; 590: Scientific Group Thermodata Europe, Group IV, Vol. 19, 57–65. Thermodynamic properties of inorganic materials compiled by Nematollahi B, Rezaei M, Lay EN, Khajenoori M. Thermodynamic SGTE. Springer-Verlag Berlin, 1999. analysis of combined reforming process using Gibbs energy Sehested J. Four challenges for nickel steam-reforming catalysts. minimization method: in view of solid carbon formation. J Nat Catal Today 2006; 111: 103–110. Gas Chem 2012; 21: 694–702. Sheng ChY, Dean AM. Importance of gas-phase kinetics within the Nikooyeh K, Clemmer R, Alzate-Restrepo V, Hill JM. Effect of anode channel of a solid-oxide fuel cell. J Phys Chem A 2004; hydrogen on carbon formation on Ni/YSZ composites exposed 108: 3772–3783. to methane. Appl Catal A Gen 2008; 347: 106–111. Shi R, Li HJ, Yang Z, Kang MK. Deposition mechanism of pyrolytic

Pakhare D, Spivey J. A review of dry (CO2) reforming of methane at temperature between 800-1200 degrees C. Carbon over noble metal catalysts. Chem Soc Rev 2014; 43: 1997; 35: 1789–1792. 7813–7837. Smith JM, Van Ness HC, Abbot MM. Introduction to chemical Paradise M, Goswami T. Carbon nanotubes – production and engineering thermodynamics, 7th ed., Boston, USA: industrial applications. Mater Design 2007; 28: 1477–1489. McGraw-Hill, 2005.

Prasek J, Drbohlavova J, Chomoucka J, Hubalek J, Jasek O, Adam V, Snoeck J-W, Froment GF. Steam/CO2 reforming of methane. Carbon Kizek R. Methods for carbon nanotubes synthesis – review. filament formation by the boudouard reaction and

J Mater Chem 2011; 21: 15872–15884. by CO2, by H2, and by steam: kinetic study. Ind Eng Chem Res Pring JN, Fairlie DM. The methane equilibrium. J Chem Soc Trans 2002; 41: 4252–4265. 1912; 101: 91–103. Snoeck JW, Froment GF, Fowles M. Filamentous carbon formation Rostrup-Nielsen JR. Equilibria of decomposition reactions of carbon- and gasification: Thermodynamics, driving force, nucleation, monoxide and methane over nickel catalysts. J Catal 1972; 27: and steady-state growth. J Catal 1997a; 169: 240–249. 343–356. Snoeck JW, Froment GF, Fowles M. Kinetic study of the carbon Rostrup-Nielsen JR. Symposium on the Science of and Its filament formation by methane cracking on a nickel catalyst. Application in Industry, FPDIL, Sindri, February 22-24, 1979, J Catal 1997b; 169: 250–262. Paper No. 29, cited after Bartholomew (1982). Soldano C, Mahmood A, Dujardin E. Production, properties and Rostrup-Nielsen JR. Catalytic steam reforming, Chapter 1. In: potential of grapheme. Carbon 2010; 48: 2127–2150. Anderson JR, Boudart M, editors. Catalysis – Science and Tavares MT, Alstrup I, Bernardo CA, Rostrup-Nielsen JR. CO Technology, vol. 5. Akademie Verlag, Berlin, 1984. disproportionation on silica-supported nickel-copper catalysts. Rostrup-Nielsen JR. Industrial relevance of coking. Catal Today 1997; J Catal 1994; 147: 525–534. 37: 225–232. Terry BS, Yu X. Determination of thermodynamic stability of

Rostrup-Nielsen JR, Bak Hansen JH. CO2 reforming of methane over metallurgical cokes, with respect to graphite. Ironmaking transition metals. J Catal 1993; 144: 38–49. Steelmaking 1991; 18: 27–32. 234 Z. Jaworski et al.: Carbon deposition: updating for nanotubes

Terry BS, Yu X. Discussion of “Thermodynamic stability of Yurkiv V, Latz A, Bessler WG. Modeling and simulation the metallurgical coke relative to graphite”. Metall Mater Trans B influence of solid carbon formation on SOFC performance and 1995; 26B: 655–656. degradation. ECS Trans 2013; 57: 2637–2647. Togaya M. Pressure dependences of the melting temperature of Zhang L, Pejaković DA, Marschall J, Dougherty M, Fletcher DG. graphite and the electrical resistivity of liquid carbon. Phys Laboratory investigation of the active nitridation of graphite by Review Lett 1997; 79: 2474–2477. atomic nitrogen. J Thermophys Heat Transf 2012; 26: 1–13. Trabold TA, Lylak JS, Walluk MR, Lin JF, Troiani DR. Measurement Zheng GB, Sano H, Uchiyama Y. A layer-by-layer deposition and analysis of carbon formation during diesel reforming mechanism for producing a pyrolytic carbon coating on carbon for solid oxide fuel cells. Int J Hydrog Energy 2012; 37: nanotubes. Carbon 2013; 57: 267–273. 5190–5201. Zucca A, Marchisio DL, Barresi AA, Fox RO. Implementation Tsiakaras P, Demin A. Thermodynamic analysis of a solid oxide fuel of the population balance equation in CFD codes for modeling cell system fuelled by ethanol. J Power Sources 2001; 102: soot formation in turbulent flames. Chem Eng Sci 2006; 61: 210–217. 87–95. Umantsev A, Akkerman Z. Continuum theory of carbon phases. Carbon 2010; 48: 8–24. Vakouftsi E, Marnellos GE, Athanasiou C, Coutelieris F. CFD modeling of a biogas fuelled SOFC. Solid State Ionics 2011; 192: Bionotes 458–463. van Herle J, Maréchal F, Leuenberger S, Membrez Y, Bucheli O, Zdzisław Jaworski Favrat D. Process flow model of solid oxide fuel cell system Department of Chemical Technology and supplied with sewage biogas. J Power Sources 2004; 131: Engineering, West Pomeranian University 127–141. of Technology, Szczecin, 71065 Szczecin, van Thiel M, Ree FH. Theoretical description of the graphite, Poland, diamond, and liquid phases of carbon. Intern J Thermophys [email protected] 1989; 10: 227–236. Wagg LM, Hornyak GL, Grigorian L, Dillon AC, Jones KM, Blackburn J, Parilla PA, Heben MJ. Experimental Gibbs free energy considerations in the nucleation and growth of single-walled Zdzisław Jaworski, DSc, PhD, has been employed as an academic carbon nanotubes. J Phys Chem B 2005; 109: 10435–10440. teacher since 1980 and, from 2004, has held a professor position Wang W, Cao Y. Hydrogen-rich gas production for solid oxide fuel of Chemical Engineering at the West Pomeranian University of Tech- cell (SOFC) via partial oxidation of butanol: thermodynamic nology, Szczecin. His research interest was focused on numerical analysis. Int J Hydrogen Energy 2010; 35: 13280–13289. modeling of transport processes, mixing and reaction technology, Wang X, Scandolo S, Car R. Carbon phase diagram from ab initio heat transfer, multiphase fluid flow, rheology, thermodynamics, molecular dynamics. Phys Rev Lett 2005; 95: 185701-1-4. multi-scale modeling, and fuel cell technology. He has led several Wang X, Li M, Wang M, Wang H, Li S, Wang S, Ma X. Thermodynamic research projects, both national and European, and published over analysis of glycerol dry reforming for hydrogen and synthesis 150 refereed papers. gas production. Fuel 2009; 88: 2148–2153. Wang W, Su C, Wu Y, Ran R, Shao Z. Progress in solid oxide fuel cells with nickel-based anodes operating on methane and related Barbara Zakrzewska fuels. Chem Rev 2013; 113: 8104–8151. Department of Chemical Technology and Wijayanta AT, Alam MS, Nakaso K, Fukai J. Numerical investigation Engineering, West Pomeranian University of Technology, Szczecin, 71065 Szczecin, on combustion of coal volatiles under various O2/CO2 mixtures using a detailed mechanism with soot formation. Fuel 2012; Poland 93: 670–676. Xu J, Froment GF. Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AICHE J 1989; 35: 88–96. Xu L, Jin Y, Wu Z, Yuan Q, Jiang Z, Ma Y, Huang W. Transformation of carbon monomers and dimers to graphene islands on Co(0001): thermodynamics and kinetics. J Phys Chem C 2013; Barbara Zakrzewska has been employed as an academic teacher 117: 2952–2958. since 1996 at the West Pomeranian University of Technology, Yang CC, Li S. Size-dependent temperature-pressure phase diagram ­Szczecin. She was awarded a PhD with distinction in 2003. Her of carbon. J Phys Chem C 2008; 112: 1423–1426. research interest was focused on CFD modeling of transport Yaws CL. Chemical properties handbook, New York: McGraw-Hill, processes in mixing technology and application of artificial neural 1995. network in reactor modeling, and currently, she is involved in Yaws CL. Yaws’ critical property data for chemical engineers and multi-scale modeling in chemical and process engineering and fuel chemists. 2012. Online version available at http://app.knovel. cell technology. She has participated in several national and three com/hotlink/toc/id:kpYCPDCECD/yaws-critical-property. European research projects. Ying LS, Salleh MAM, Yusoff HM, Rashid SBA, Razak JA. Continuous production of carbon nanotubes – a review. J Ind Eng Chem 2011; 17: 367–376. Z. Jaworski et al.: Carbon deposition: updating for nanotubes 235

Paulina Pianko-Oprych Department of Chemical Technology and Engineering, West Pomeranian University of Technology, Szczecin, 71065 Szczecin, Poland

Paulina Pianko-Oprych was awarded her PhD with distinction in 2005, and in 2016, she received the DSc degree. She has been a lecturer since 2008 at the West Pomeranian University of Technol- ogy, Szczecin. Her research results were published in 70 papers. With over 16 years of experience in CFD applications, she is involved in fuel cell modeling and the creation of BoP system models using process simulator tools. She is now a research-team leader and project manager in two EU projects.