J. Phys. Chem. C 2007, 111, 5963-5970
5963
Non-Noble Electrocatalysts for O2 Reduction: How Does Heat Treatment Affect Their Activity and Structure? Part I. Model for Carbon Black Gasification by NH3: Parametric Calibration and Electrochemical Validation Fre´ de´ ric Jaouen* and Jean-Pol Dodelet INRS EÄ nergie, Mate´ riaux et Te´ le´ communications, 1650 BouleVard Lionel Boulet, Varennes (Que´ bec) Canada, J3X 1S2 ReceiVed: December 1, 2006; In Final Form: February 28, 2007
In part I of this paper, a model for the gasification of pristine carbon blacks by NH3 is developed. Here, it is applied to investigate non-noble catalysts for the O2 reduction reaction (ORR) in fuel cells. These catalysts are produced by pyrolyzing a furnace black, loaded with 0.2 wt % Fe, in NH3. The model predicts (i) the gasification rate of an initially pore-free particle of furnace black and (ii) the internal porous network thereby created. The model assumes two rate constants for the gasification of carbon black: one for the graphitic crystallites and one for the disordered matrix phase. The model is fitted to experimental time-evolutions of (i) weight loss of carbon black and (ii) specific surface area measured during the synthesis of non-noble catalysts for the ORR. The fittings yield a rate constant that is ten times larger for the gasification of the disordered phase than that for the graphitic phase. For a 42 nm diameter particle, the model predicts that (i) the gas-carbon reaction, and therefore the internal porous network, occurs in an outer shell of thickness e8 nm and (ii) the particle shrinks beyond 45% weight loss. Experimentally, the micropore area created during the heat treatment controls the activity for the ORR of such catalysts. The model is able to reproduce the experimental micropore area if the fraction of disordered carbon of the pristine carbon black particle is assumed larger in the core (35%) than in the periphery (20%). Thus, in agreement with experimentals the model tells that Fe/N/C sites for the ORR are created when the micropore area increases (0 to 30-35 wt % loss) and destroyed when it decreases (weight loss >40%).
1. Introduction Carbon blacks are produced from the pyrolysis of hydrocarbons. As-produced (Brunauer-Emmett-Teller (BET) area of 30-130 m2 g-1), they are described by their graphitic crystallite size (10-25 Å), particle size (20-50 nm), and agglomerate size and shape.1 Pristine carbon blacks can be modified in a postproduction stage by an etching gas, leading to BET areas up to 1000-1500 m2g-1. The porous network and specific area thereby generated are of prime importance in heterogeneous catalysis and in particular in catalysts for electrochemical devices such as low-temperature fuel cells. The impetus for the present work stems from our recent finding that the microporous area (5-22 Å, i.e., literally nanopores) controls the activity of nonnoble catalysts for O2 electroreduction in acidic solution.2 In that work, catalysts were prepared by pyrolyzing in NH3 a furnace black onto which 0.2 wt % Fe had been adsorbed as iron acetate. The activity for the O2 reduction reaction (ORR) was found to be proportional to the post-pyrolysis microporous area. This finding led us to conclude that the catalytic sites for the ORR are hosted in micropores and that the latter limit the utilizable metal loading (about 0.2 wt %). This low utilizable metal loading is a major impediment to the replacement of platinum in polymer electrolyte fuel cells.3 Thus, it is desirable to investigate theoretically and experimentally the mechanism of formation of micropores in furnace black particles. As far as carbon blacks are concerned and to the best of our knowledge, no physical model has been developed to predict * Corresponding author. E-mail:
[email protected]. Fax: +1 450 929 8102.
the microstructure evolution during gasification. In contrast, for activated carbons (biomass or coal chars), many models have been developed in the past 30 years.4-14 Despite carbon blacks being different from activated carbons (concentric versus random orientation of crystallites, particle size of 20-50 nm versus grain size of 1-2 µm, no pores in particles of pristine carbon blacks), these materials share common features (graphitic crystallites, pore-structure evolution upon gasification) that makes the review of models developed for activated carbons relevant. For clarity, it is stressed here that the term particle in carbon blacks does not correspond to the term particle used in the literature for activated carbons but rather to the term grain. For activated carbons, the random pore model developed by Petersen15 described the initial porous structure by cylindrical pores of a unique diameter being randomly distributed. This model was extended to an initial pore radius distribution and the random overlap of pores upon their growth (carbon gasification) was computed.4-5 These random pore models developed for activated carbons have since been refined for bimodal pore size distribution, pore shape,7 kinetic and diffusion control11 or particle fragmentation.9,11 Miura and Hashimoto introduced the concept of a disordered carbon phase binding the crystallites together.6 Alternatively, the evolution of the porous network can be regarded as a result of the recession of the graphitic crystallites rather than as a result of pore growth.8,10,16-17 This concept has been applied to predict the gasification of either activated carbons8,10 or single graphitic crystallites.16,17 For instance, Kyotani et al. modeled the gasification of a single crystal with
10.1021/jp068273p CCC: $37.00 © 2007 American Chemical Society Published on Web 04/04/2007
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three reaction rate constants at edge sites, one each for the zigzag, the armchair, and the type-D site.16-17 On the other hand, gasification of carbon black has not yet been modeled with the same concept. To fill this gap, the present work introduces a model based on the assumption of edge recession of single graphitic crystallites when attacked by NH3. The crystallites are assumed to be bound together by a disordered carbon phase. The present model can thus be viewed as the application of the recent singlecrystal gasification studies of Kyotani et al.16-17 to the particle model of Miura and Hashimoto6 in which the concept of disordered carbon was first introduced. One drawback of the latter work however is that edge recession was not considered, and instead it was assumed that a whole graphene plane inside a crystal was randomly removed. In the present paper, the unknown parameters of the model are first assessed by fitting model predictions to experimental data of weight loss and total specific area of non-noble catalysts for the ORR. These catalysts are obtained after gasifying a carbon black + 0.2 wt % Fe at 950 °C for various times in NH3.2 With model parameters obtained by fittings, it is then shown that the model can explain the rise and fall of the specific micropore area of a furnace black with the time of heat treatment in NH3. Because the micropore area controls the activity of these non-noble catalysts for the ORR in fuel cells, the model sheds new light on the mechanism of formation of Fe/N/C sites active for the ORR. In part II of this paper, Raman spectroscopy, scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM), and time-of-flight secondary ion mass spectrometry (ToFSIMS) techniques are used to check other model predictions that are not directly linked to the electrochemical activity of such catalysts, with the aim of further testing the model. 2. Experimental Section More experimental details are found in ref 2. The furnace black has a BET area of 71 m2 g-1 prior to pyrolysis. Catalysts for the ORR were prepared by adsorbing 0.2 wt % Fe as iron acetate on that carbon and pyrolyzing the mixture at 950 °C in NH3 for various times. The micropore (pore size 22 Å) were determined from N2 adsorption isotherms with the original nonlocal density functional theory (Quantachrome Instruments Autosorb-1). 3. Model for the Reaction of a Furnace Black Particle with NH3 3.1. Assumptions. The premise of the model is that the particles of a pristine furnace black are composed of two solid phases: (i) an ordered phase similar to the graphitic crystalline structure and (ii) a disordered phase resulting from the fast and out-of-equilibrium production of carbon blacks from oil feedstock. The ordered phase, henceforth named graphitic phase, consists of crystallites measuring 10-30 Å in the plane and 10 Å in height.1 It will be seen that if the disordered phase is gasified faster than the graphitic phase, then a porous network is created in the particle. Other assumptions are the following: 1. A single particle (here of diameter 42 nm) is considered, and its properties are assumed to represent those of a furnace black powder. The model could be extended to a distribution of particle size. However, it will be seen that the model is as sensitive or even more sensitive to the particle structure than to the particle size (section 3.3.3). 2. The assumed initial microstructure of the particle is represented in Figure 1A. Before reaction with ammonia, the
Figure 1. (A) Initial particle structure partitioned into m shells. Disordered phase (greyed zone) and graphite crystallites (black rectangles, not drawn to scale). (B) Etching of carbon black by NH3 in the three first outer shells as a function of time. τCd is the time necessary for disordered carbon to be removed from a shell of thickness δ.
furnace black particle is spherical and has no pores. The gray area represents disordered carbon, and black rectangles represent graphitic crystallites. Initially, all crystallites have a single size. 3. No assumption on the arrangement of crystallites is needed to calculate the weight of carbon gasified or the total surface area made by the pore walls. However, to calculate pore sizes, such an assumption is needed. On the basis of previous experimental works on carbon blacks,18-22 the crystallites are assumed concentrically arranged (Figure 1A). HRTEM images (part II of this paper) show that this holds true for the present furnace black. Though not fully representing the complex reality, this assumption is a suitable first-approach for carbon blacks. 4. No concentration gradient of gaseous reactants or products occurs in the particle or in the bed of carbon black (assumption supported by calculations involving diffusion coefficients, diffusion lengths, and reaction rate). The model computes, as a function of the reaction time in ammonia, how much mass of the graphitic and disordered carbon phases is found at every location inside the particle. From
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J. Phys. Chem. C, Vol. 111, No. 16, 2007 5965
these two quantities, other important quantities (surface at any location in the particle, crystallite, and pore size) are backcalculated. 3.2. Equations. 3.2.1. Initial Conditions. The space volume initially filled by the carbon black particle is virtually sliced in concentric shells of thickness δ, indexed from 1 to m (Figure 1A)
d(t ) 0) ) d0;
xd(t ) 0) ) xd,0 )
Vd(i,t ) 0) ; V(i) L1(t ) 0) ) L1,0 (1)
where d is the particle diameter, t is the time, xd is the volumetric fraction of disordered phase in shell i, and L1 is the in-plane size of the crystallites. In the base-case, the variables xd and L1 are assumed uniform in the particle at time zero (subscript 0). Vd(i,t) is the volume of disordered carbon in shell i at time t. V(i) is the volume of the ith shell. The radial axis delimiting the m spherical shells is defined by
r(2) ) r(1) - δ;...; r(1) ) d0/2; r(i) ) d0/2 - (i - 1)δ;...; r(m + 1) ) rkern (2) 3.2.2. Time-Dependence of the Structure of Any Spherical Shell. Reaction of the particle with ammonia initially occurs on the outer surface, shell 1 (Figure 1B). That surface consists of (i) basal planes of graphitic crystallites and (ii) disordered carbon. Basal graphitic planes are assumed to be nonreactive.16 Thus, at time zero NH3 reacts only with the disordered fraction of the outer surface (top of Figure 1B, arrows). It will take a certain time for NH3 to remove disordered carbon from the first shell. This time is noted τCd. At time t ) τCd, the situation has changed (Figure 1B, middle). There are now three types of surfaces: the basal-plane surface, which is assumed nonreactive, the disordered surface at the bottom of the newly created pore, and a new surface defined by the edges of the crystallites of the first shell. At time t ) 2τCd (Figure 1B, bottom), disordered carbon has been removed from the first and second shells while graphitic crystallites of the first shell have reacted with NH3 on their edges since t ) τCd. Consequently, the in-plane crystallite size L1 in shell 1 is now smaller than its initial value (Figure 1B, bottom). At a critical time noted τCg, the graphitic crystallites in the first shell have vanished. Now, this reasoning on the first shell can be applied to any shell. However, the onset of the reaction with NH3 of the disordered carbon found in shell i depends on the shell location; the onset is equal to (i - 1)τCd. Consequently, solving the equations for the volume of the graphitic and disordered carbon phases for one shell is also valid for all other shells, except that the onset reaction time must be properly written in the program. Below, the time equations governing the gasification of carbon in shell 1 are derived. Reaction of disordered carbon with NH3: 0 < t < τCd. The rate constant kd of reaction between disordered carbon and ammonia is defined as
dVd -kdsd , ) dt Fd
kd > 0
(3)
where Vd is the volume of disordered carbon, sd is its surface in contact with NH3, and Fd is the density of the disordered phase. For a given shell, the surface sd is assumed to be constant with time (as long as some disordered carbon remains). Equation 3 is integrated into
kdsd(i ) 1) t, Fd valid for 0 < t < τCd,
Vd(i ) 1,t) ) Vd(i ) 1,0) -
shell 1 (4)
Vd(i ) 1,0) is equal to xd,0V(i ) 1) (eq 1). Next, the surface sd of shell 1, sd(i ) 1), is equal to xd,0V(i ) 1)/δ in which V(i ) 1) is the volume of shell 1 and δ the shell thickness. After these rearrangements, eq 4 is transformed into
[
Vd(i ) 1,t) ) xd,0V(i ) 1) 1 -
]
F dδ , kd shell 1 (5)
t , τCd
with τCd )
Thus, τCd is now defined and the evolution with time of the volume of disordered carbon in shell 1 is described by eq 5. For any other shell of index i, eq 5 is valid replacing V(1) by V(i), and time t by t - (i - 1)τCd. The interval of validity is then τCd < t < iτCd. Reaction of graphitic carbon with NH3: τCd < t < τCg. At t>τCd, no disordered carbon is left in shell 1 (Figure 1B, center) and only the edge surfaces of the crystallites react with NH3. The rate constant for that the reaction, kg, is defined as
dVg -kgsg ) , dt Fg
kg > 0
(6)
where Vg is the volume of graphitic carbon and sg is its edge surface in contact with NH3. sg will not be constant with time due to crystallite shrinking. This edge-recession approach is similar to the model proposed by Kyotani et al.16 These authors showed that a difference in reactivity for the armchair or zigzag edge site could be accounted for by a mean rate constant, kg, because eventually the proportion of the different edge sites converges to a unique pattern. Thus, eq 6 has two timedependent variables, Vg and sg. As explained below, sg can be expressed against Vg. At any time and in any shell, the ratio sg/Vg is equal to the ratio of edge-surface to the volume of any single crystallite in that shell. The crystallites are considered to be parallelepipeds of volume L12L2 and the crystallite height, L2, is constant with time. Thus sg/Vg ) 4/L1 with L1 being the time-dependent size of crystallites in a given shell. Inserted into eq 6, this yields
dVg -4kgVg ) dt Fg L1
(7)
Now, one must express L1 against Vg. Considering a single crystal at any time and given that the crystallite height is constant, one can write
Vg(i,t) Vg(i,t ) 0)
)
(
L1(i,t)
L1(t ) 0)
)
2
(8)
Vg at time zero is equal to (1 - xd,0)V(i) for any shell i, where xd,0 is the initial fraction of disordered carbon, and V(i) is the volume of shell i. For shell 1, inserting the above into eq 8 yields the expression of L1 in shell 1 as a function of Vg
L1(i ) 1,t) ) L1,0 xVg(i ) 1,t)/x(1 - xd,0)V(i ) 1) , shell 1 (9)
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Replacing L1 by this expression into eq 7 leads to
(Vg)-1/2dVg )
-4kg x(1 - xd,0)V(1) dt, FgL1,0
shell 1
(10)
This differential equation on Vg is easily integrated and yields the expression of Vg1/2 as a function of time for shell 1. To determine the constant of integration for shell 1, one knows that at t ) τCd the volume of graphitic carbon is the same as at time zero and is thus equal to (1 - xd,0)V(i ) 1). Finally, the expression of Vg is
[
]
2 2kg (t - τCd) , FgL1,0 valid for τCd < t < τCg, shell 1 (11)
Vg(i ) 1,t) ) (1 - xd,0)V(i ) 1) 1 -
Now, τCg, the time at which no graphitic carbon is left in shell 1, is deduced from eq 11
τCg ) τCd +
FgL1,0 2kg
(12)
Equation 11 can be applied to any shell of index i, replacing t by t - (i - 1)τCd. Then eq 11 is valid for iτCd < t < (i - 1)τCd + τCg. 3.3. Modeling Results. 3.3.1. Model Parameters and Their Estimation from Experimental Data. The initial structural parameters of the carbon black that are required by the model must be determined. With pristine carbon blacks (free of internal pores), the initial particle diameter, d0, can be obtained from the initial BET area, SBET,0, through d0 ) 6/(SBET,0·F) (SI units, from (1)) in which F is the density of carbon in carbon blacks (2.0 g cm-3). For the present carbon black, d0 ) 42 nm. Next, the initial in-plane size of graphitic crystallites, L1,0 ) 15 Å was obtained from Raman spectroscopy.23-25 Three unknown parameters remain: kd and kg and the initial fraction of disordered carbon, xd,0. To find reliable values for these, the model is fitted to (i) the mass vs the time of reaction and (ii) the specific surface area vs the time of reaction. The search for an acceptable triplet [kd, kg, xd,0] is simplified by a short-time analysis of the model: at short times, the mass loss pertains only to disordered carbon because the graphitic surface area remains small. If M is the total mass of a particle, then at short times (order of a few τCd) one can write
M0 - M ) kdxd,0SBET,0, M0t
Figure 2. Gasification kinetics in pure NH3 at 950 °C of the carbon black under study. (A) Weight loss percentage of carbon versus time of heat treatment; experiment (b) and fitting of the model to experiment (line). (B) Time derivative of the weight loss percentage versus time. τCg is the time at which the crystallites in the first shell (periphery) are totally gasified, and (m - 1)τCd is the time at which all disordered carbon phase in the particle is gasified.
valid at short times (13)
Thus, measuring the left-hand-term and the initial BET surface area enables us to estimate the product kdxd,0. Then, the whole curve (M0 - M)/M0 against time is fitted by varying only the third parameter, kg. Then, to estimate separately xd,0 and kd, the model is fitted to the experimental curve of BET area versus time. To show the model’s ability to reproduce experimental data, an example is now given. Figure 2A shows the weight loss percentage, W ) 100(M0 - M)/M0, where M is the particle mass (model, line) or the furnace black mass (experiment, b) versus time of heat treatment. The gasification rate reaches a maximum at W ) 20% (Figure 2B). Such a maximum is often observed for activated carbons or chars and is predicted by other models if the initial microporosity is small enough.4-6,8-10,12,26-27 Figure 3 shows the total specific area (in m2 per gram of residual carbon) against the weight loss percentage, predicted
Figure 3. Total specific area (m2 per gram of residual carbon) versus time of heat treatment for the carbon black; from experiments (b) and from model fitting (line).
by the model (line) and experimentally measured (b). If one wants to compare Figure 3 to other works, one must ensure that the surface area is defined identically. The specific area is sometimes expressed in m2 per initial mass of material. This is a different definition that leads to completely different curves for the same raw data (ref 28, Figure 5.11). The values for the parameters xd,0, kd, and kg that best fit the model to the experimental data are 0.3, 75 × 10-7 g s-1 m-2, and 7 × 10-7 g s-1 m-2, respectively (Table 1). 3.3.2. Maximum Thickness of the Porous Layer. As long as graphitic crystallites are still present in shell 1 (outer shell), the particle region where both pores and crystallites coexist will increase with time. In the end, the thickness of that region is bounded, as explained as follows: the ratio of the time necessary to remove graphitic carbon from a shell once cleared of disordered carbon to the time necessary to remove disordered carbon in a subsequent shell is
τCg - τCd L1,0 kd Fg ) τCd 2δ kg Fd
(14)
With the base-case values (Table 1), assuming as a first approximation Fg ) Fd ) 2 g cm-3 and taking δ ) 3 Å for the computations (the distance between two graphitic layers is 3.35 Å in graphite and 3.5-3.9 Å in carbon blacks) one obtains (τCg - τCd)/τCd ∼ 27. This means that before all carbon is removed from shell 1, NH3 will have cleared all disordered carbon from
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TABLE 1: Base-Case Parameters of the Model structure
kinetics
carbon density F (g cm-3)
initial particle diameter d0 (nm)
initial in-plane crystallite size L1,0 (nm)
initial fraction of disordered carbon xd,0
reaction rate of NH3 with disordered carbon kd (g s-1 m-2)
2a
41.8b
1.5b
0.3c
75 × 10-7 c
reaction rate of NH3 with graphitic-edge carbon kg (g s-1 m-2) 7 × 10-7 c
a From literature. bFrom measurement of BET area for d and Raman spectroscopy for L . cFrom model fitting to experimental curves of BET 0 1,0 area and weight loss vs time of heat treatment at 950 °C in NH3. The above parameters yield τCd ) 80 s and τCg ) 2223 s. The model particle comprises m ) 63 shells of thickness δ ) 3 Å.
the 27 shells underneath (i.e., a thickness of 27δ ) 8.1 nm). This represents the maximum thickness of the shell region in which both pores and solid carbon coexist. This region is of course very important for heterogeneous and electrochemical catalysis. One might wonder how the graphitic crystallites in the outer shell still hold to the particle when they are no longer surrounded by disordered carbon. Van der Waals forces between the graphene planes as well as criss-crossing of the stacked crystallites (see HRTEM in part II, Figure 5) probably ensure the integrity of the particle after removal of the disordered carbon phase. 3.3.3. SensitiVity of the Model to Initial Values of Crystallite Size, Particle Size, and Fraction of Disordered Carbon. To test to which extent a distribution of particle sizes (encountered experimentally in carbon blacks) would change the results, the sensitivity of the model to a change in (i) particle diameter, d0, (ii) crystallite size, L1,0, and (iii) fraction of disordered carbon, xd,0, in the initial particle was studied. These parameters were changed one by one while all others were kept as in Table 1 (base-case parameters). The particle diameter d0 (base-case 41.8 nm) was set to low and high values of 30 and 50 nm, respectively (most of the particles in the studied carbon black have sizes comprised between 30 and 50 nm, part II, Figure 2A). The crystallite size L1,0 (base-case 1.5 nm) was set to a high value of 3 nm. No value lower than the base-case was chosen because it is improbable that any carbon black has initial crystal sizes much smaller than 1.5 nm. The disordered fraction xd,0 (base-case 0.3) was set to low and high values of 0.15 and 0.60, respectively. Figure 4A shows the curves of weight loss versus time predicted by the model. All other things being constant, a particle size larger than the base-case leads to a slower gasification rate (curve E). A crystallite size larger than the basecase also leads to a slower gasification rate (curve F). In contrast, a fraction of disorder phase larger than the base-case leads to a faster gasification rate, especially at short times (curve C) due to the reaction rate constant kd of that phase being higher than that of the crystallite edges, kg. In summary, in the range of weight loss 0-50% all three parameters d0, L1,0, and xd,0 equally influence the overall gasification rate of the particle. It can also easily be conceived that a same line of weight loss versus time can be computed for several triplets of the parameters d0, L1,0, and xd,0 by simultaneously changing two or three of these variables. Therefore, the model will not necessarily predict a faster gasification rate for a smaller particle if the two other structural parameters L1,0 and xd,0 also change. For carbon blacks, the average particle diameter of a powder (or BET area) is modified by changing the flow rates of oil, natural gas, or air in the production furnace. It is thus probable that not only the average particle size is then modified, but the two other parameters are as well. Figure 4B shows the curves of total specific area versus weight loss. All other things being constant, a particle size larger
Figure 4. Sensitivity of the model to the structural parameters: particle size, crystal size, and fraction of disordered carbon. (A) Weight loss percentage of carbon versus time of heat treatment. The thick line is the base-case line (parameters of Table 1). Other lines were obtained by changing one parameter at a time (see legend). (B) Total specific area versus weight loss. Same comments as for Figure 4A.
than the base-case leads to a decreased specific area (curve E) especially at weight loss >40 wt %. A crystallite size larger than the base-case leads to a smaller specific area in the range 0-60 wt % but to a higher specific area at weight loss >60% (curve F). A fraction of disorder phase larger than the basecase leads to a lower specific area (curve C). The reason for this is that more disordered carbon leads to a smaller number of crystallites per volume and thus to a smaller amount of edge surface. In summary, in the range of weight loss 0-40 wt % the structural parameter most determining for the specific area is the fraction of disorder carbon xd,0, second comes the crystallite size L1,0, and last the particle diameter d0. Finally, comparing Figure 4A,B, one realizes that a carbon black being
5968 J. Phys. Chem. C, Vol. 111, No. 16, 2007 gasified faster does not necessarily mean a larger specific area for the resulting material (e.g., curve C is above the base-case curve in Figure 4A but below the base-case curve in Figure 4B). In conclusion, slight experimental variation of particle diameters around an average value will not drastically change the model predictions. Reasonably accurate values for the model parameters (xd,0, kd, kg) can be resolved by fitting model results to experimental data. 3.3.4. EVolution of the Internal Structure of the Particle: Base-Case Parameters (Table 1). With the model parameters adjusted to the present furnace black, it is possible to look at the internal structure of the particle. Before reaction with NH3 (0 wt %) the particle radius is d0/2 ) r0 ) 20.9 nm. At 20 wt %, the reaction front has moved in to a radial position r ) 18.5 nm but the particle radius is still 20.9 nm. At 45 wt % loss, the reaction front is at r ) 15.9 nm. The calculated crystallite size in the most outer shell is then about 5 Å (i.e., about the width of two benzene rings). Physically, a crystallite cannot be smaller than that. Thus, for calculated crystallite size 45 wt %. Decrease of the particle diameter with weight loss is predicted as well by models developed for activated carbon or carbon char.9,11,14 However, in these models, particle shrinkage is the result of a diffusion control yielding a higher reaction rate at the periphery. In part II of this paper, the average experimental diameter is measured against weight loss by SEM and is compared to the curve predicted by this model. It must also be noted that 45 wt % is close to the point at which the activity for ORR of the catalysts reaches a maximum for that carbon.2 Finally, at 80 wt % loss the reaction front is at r ) 10.8 nm and the particle radius is 15.8 nm. Thus, the thickness of the shell in which both pores and crystallites coexist is about 5 nm. This is slightly smaller than the 8.1 nm calculated from the ratio of the critical times τCd and τCg in section 3.3.2 because in the algorithm, an “if” statement was added to force the model to discard crystallites smaller than 5 Å. If no such condition is imposed and the crystallites are allowed to shrink continuously down to 0 Å, then the value of 8.1 nm would still prevail as the maximum shell thickness. 4. Application of the Model to Non-Noble Catalysts for O2 Electroreduction Experimentally, for the furnace black investigated in this paper, it was shown that the electrocatalytic activity for O2 reduction observed after the heat treatment of the furnace black with 0.2 wt % Fe is governed by the specific area of micropores created during the heat treatment (Figure 6 in ref 2). The activity of the catalysts increased by nearly two decades when the micropore area rose from 20 to 400 m2 g-1. The present model allows us to go one step further by reproducing the experimental evolution of the micropore surface area as a function of the time of heat treatment. Pore areas predicted by the model are separated into two families: the micropore area (calculated pore size 10 Å). With base-case parameters (Table 1), the evolution of the total micropore and mesopore areas as a function of weight loss during heat treatment is shown in Figure 5A. These areas calculated by the model will now be compared to areas obtained from the fitting of adsorption isotherms by
Jaouen and Dodelet
Figure 5. Predicted and experimental micro- and mesopore areas versus weight loss percentage. Areas expressed in m2 per gram of residual carbon black. (A) Model predictions with base-case parameters (Table 1). Specific area provided by (a) all pores, (b) by micropores (size 10 Å). (B) Experimental results: BET (9), micropore (b, pore size 22 Å). (C) Model predictions from nonuniform initial fractions of graphitic and disordered carbon in particle. The assumed initial profiles are seen in quadrant D. Curves (a-c) correspond to different pore sizes as defined for quadrant A. (D) Initial profiles of graphitic and disorder carbon used for model predictions seen in C.
the original nonlocal density functional theory (NLDFT) with slit micropore geometry. However, a pore size calculated by the present model for carbon black gasification cannot be directly compared to the same pore size estimated by the original NLDFT model: the latter has generally recognized shortcomings to fit isotherms of disorganized carbon materials due to some assumptions being inadequate for such materials (infinite slit micropore, flat surface of the pore walls, no heterogeneity of adsorption energy). Recently, Ustinov and co-workers developed another density functional theory model adapted for disorganized carbon materials.29 Their model could exactly fit the isotherms of an activated carbon while the original NLDFT model could not (Figure 7 of ref 29). Due to the misfit, the latter model overestimated the pore size by 5-10 Å (compare Figure 8a,c of ref 29: the peak at 27 Å in Figure 8a is shifted to 17 Å in Figure 8c; and the peak at 15 Å in Figure 8a is shifted to 9 Å in Figure 8c). Thus, the experimental micropore area was chosen to be defined by pores of size 22 Å, as given by the original NLDFT model. The experimental as-defined total area (BET area) and micropore and mesopore areas are seen in Figure 5B. It is observed that the calculated micropore area (Figure 5A, curve b) reaches a plateau between 20 and 50% weight loss, but never decreases upon higher weight loss. This contrasts with the experimental observation (Figure 5B, b). One possible reason for this difference is as follows: from experimental measurements on a carbon black, Hjelm et al. concluded that the outer shell density is 20% higher than the core density, and that the outer shell is 2-10 nm thick.20 This suggests that the fraction of disordered carbon is larger in the core than in the periphery of the particle. On that basis, the initial fraction of disordered carbon (base-case: xd,0 ) 0.3 used for calculations shown in Figure 5A) was modified; the disordered phase fraction, xd, was given a lower value of 0.2 in the outer shells and a higher value
Non-Noble Electrocatalysts for O2 Reduction, Part I
J. Phys. Chem. C, Vol. 111, No. 16, 2007 5969 of a single electron. Because a particle contains a constant number of Fe atoms throughout the pyrolysis, the rise and fall of the activity per particle (Figure 6B) can only be explained in terms of construction and destruction of active sites. Comparing Figure 6A with Figure 6B, it is obvious that the number of active sites in a single particle is controlled by the available micropore area per particle. Upon long heat treatment, small micropores transform into larger micropores or mesopores, thereby annihilating many sites because the active sites are believed to be a molecular bridge between close edges of two crystallites.2 5. Conclusions
Figure 6. (A) Micropore area per particle vs weight loss. Experimental micropore area (b) (pore size
