Carbon 43 (2005) 1445–1452

www.elsevier.com/locate/carbon

Desorption activation energy distribution function of nitricoxide chemisorbed on carbonaceous materials at 373 K

Pilar Garcıa, Alejandro Molina 1, Fanor Mondragon *

Institute of Chemistry, University of Antioquia, A.A. 1226, Medellın, Colombia

Received 11 September 2004; accepted 18 January 2005

Available online 25 February 2005

Abstract

The distribution function for the activation energy of NO desorption from carbonaceous materials treated with mixtures of NO,

NO/O2 and NO/H2O/O2 at 373 K, was determined. The algorithm employed in the calculation was a variation of the stochastic

method commonly used for the evaluation of the activation energies from TPD data. The calculated distribution function is a com-

bination of two normal distribution functions, centered at energies around 150 and 190 kJ/mol which corresponds to the desorption

of NO from organic structures as was previously determined by XPS analysis. The higher activation energy complex is promoted by

the catalytic activity of the mineral matter in the char. Molecular oxygen enhances the NO reversible chemisorption while water

partly inhibits this effect.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Char, coal; Temperature programmed desorption; Activation energy

1. Introduction

Since the pioneering work by Laine et al. [1] the study

of the complexes formed on the surface of carbonaceous

materials by Temperature Programmed Desorption

(TPD) experiments is a common practice. In addition

to the qualitative analysis of the TPD profiles, several

authors [2–4] developed a stochastic model that de-

scribes a TPD experiment as desorption of a series of

surface complexes with different desorption energies.Even though the model was originally developed for

the study of carbon–oxygen complexes, and the exten-

sion to carbon–nitrogen complexes is straightforward,

the numerical characterization of the TPD profiles of

nitrogen complexes is to our knowledge still missing.

0008-6223/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.carbon.2005.01.015

* Corresponding author. Tel.: +57 4 210 5659; fax: +57 4 263 8282.

E-mail address: fmondra@catios.udea.edu.co (F. Mondragon).1 Present address: Combustion Research Facility, Sandia National

Laboratories, 7011 East. Av., Livermore, CA 94550, USA.

The study of nitrogen–carbon complexes on the char

surface, has gained importance since Tomita andcoworkers [5,6] showed the significance of such com-

plexes in the reduction of nitric oxide by carbonaceous

materials. In the last 10 years, several studies [7–10] have

proposed different structures for carbon–nitrogen com-

plexes involved in NO formation [11] and reduction

[7–10]. Recently, a study by XPS [12] showed that –

NO2 complexes were responsible for reversible chemi-

sorption. These complexes are formed by NO adsorp-tion on active sites located between two semiquinone

groups [12,13]. Further characterization of the carbon–

nitrogen complexes is desired, particularly at atmo-

spheres that resemble those of combustion flue gas (i.e.

in the presence of O2 and H2O), in which the carbona-

ceous materials for NO reduction may be employed.

This paper gives insight into the nature of the nitro-

gen complexes formed on carbonaceous materials afterreaction with NO in the presence of O2 and H2O at

373 K. To do this, we perform TPD analyses of coal

1446 P. Garcıa et al. / Carbon 43 (2005) 1445–1452

chars, demineralized chars and phenilformaldehide res-

ins and analyze the results by a stochastic method for

the evaluation of the energy distribution function of

the desorption processes that allows further character-

ization of the surface complexes. Although, the distribu-

tion function of desorption activation energies can beused in the calculation of kinetic parameters [14,15]

our goal is not to derive precise kinetic parameters based

on the distribution function, but to use it as a parameter

that describes the nature of the surface complexes and

how they change with gas composition and in the pres-

ence of mineral matter.

2. Mathematical model

The first part of this section describes the mathemat-

ical derivation of the stochastic model for analysis of

TPD profiles based on previous work by Du et al. [2]

and Calo and May [3]. The second part describes some

modifications of the model derived by the authors to ac-

count for bimodal activation energies and to avert someof the assumptions in the original model.

Table 1

Algorithm used to calculate f(E)

Step Procedure

1. Assume k002. Compute f(E) from (E4) and TPD data

3. Calculate k000 from (E3) and TPD data

4. Repeat step 2 until converge

5. Compute fI(E), fII(E) and a from (E6)

2.1. Current model

The stochastic model to characterize the TPD profile

assumes that a series of parallel steps like (R1) are

responsible for the NO desorption:

ðC–NOÞEþDE !k

NO þ ðCÞ ðR1Þ

(C–NO)E+DE represents the complexes desorbing with

energy between E and E + DE and (C) an active siteformed on the carbon surface after desorption.

The rate of NO desorption for an expression as (R1)

is

dNO

dt

����t

EþDE

¼ k0 expð�E=RT Þ½ðC–NOÞ�tEþDE ðE1Þ

where k0 is the pre-exponential factor (s�1); ½C–NO�tEþDEis the concentration (mol) of surface complexes remain-

ing on the particle surface with energies between E and

E + DE at time t (s) and d NOdt jtEþDE the instantaneous rate

of NO desorption (mol s�1) from surface complexes

with energies between E and E + DE at time t.

To calculate the rate of NO desorption in the whole

range of energies, the concept of energy distribution

function, f(E), is introduced. The energy distribution

function is defined in such a way that the initial

complexes with energies between E and E + DE,½ðC–NOÞ�t¼0

EþDE, are normalized to the total amount of

surface complexes, [(C–NO)]TOT as described in (E2):

C–NOð Þ½ �t¼0

EþDE ¼ ðC–NOÞ½ �TOTf ðEÞDE ðE2Þ

where f(E)DE is the fraction of complexes that desorb

with energies between E and E + DE.

The rate of NO desorbed at time t can be calculated

from the integration over all activation energies of (E1),

and C–NOð Þ½ �tEiþDE from the rate of disappearance of

(C–NO) complexes [2]. (E3) presents the finalexpression:

dNO

dt

����t

¼Z 1

0

k0 expð�E=RT Þ½ðC–NOÞ�TOTf ðEÞ

� exp

Z t

0

�ko expð�E=RT Þdt� �

dE ðE3Þ

A direct evaluation of f(E) from (E3) is a prohibitive cal-

culation problem. However, when a step function re-places the time integral, a numerical solution (E4)

becomes possible [16]:

f ðEÞ � dNO=dt½ðC–NOÞ�TOTðdE =dtÞ ðE4Þ

Since k0 is usually very large (for carbonaceous materi-

als k0 > 109 s�1) [2,17,18] the double exponential in theintegral of the time in (E3) will increase from 0 to 1 in

a small DE. E* represents the activation energy that

determines the jump in the step function used to approx-

imate the time integral. The value of E* results from giv-

ing an arbitrary value to the integral of the time between

0 and 1 [2,3,17]. Its derivation, dE/dt, is calculated from

(E5):

dE

dt� R

dTdt

a� ln aþ ln aa

þ ln a2a2

ðln a� 2Þ� �

ðE5Þ

where a ¼ ln k0TdT=dt

h i, R is the gas constant and dT/dt is

the heating rate in K/s. Since dNO/dt, dT/dt and (C–

NO)TOT can be determine from a TPD experiment,

(E4) can be used to obtain the energy distribution func-

tion f(E).

2.2. Variations to the model

To obtain the energy distribution function (f(E)), the

procedure described above was modified to account for

discrepancies between the values obtained when the

approximation in (E4) was used and those when the

complete expression (E3) was applied. The algorithm

is described in Table 1: first, a value of k0 (named k00)

P. Garcıa et al. / Carbon 43 (2005) 1445–1452 1447

was selected from the range predicted by quantum

chemical calculations for desorption of nitrogen-con-

taining compounds from graphite-like structures [19].

k00 was used to compute f(E) according to (E4). With

f(E), a new k0 (named k000) was calculated from a non-lin-

ear least square optimization of dNO/dt calculated from(E3) and the experimental data. The system is iterated

until k0 converges. The values of k0 and f(E) obtained

after convergence were used to simulate the experimen-

tal data through (E3).

The final step was to obtain an analytical description

of the energy distribution function. To do this, f(E) was

arbitrarily represented by a normal distribution function

in the cases where it had an unimodal character and bytwo normal distributions when a bimodal character was

evident. In each case a non-linear least square optimiza-

tion yielded the different parameters for the normal

distributions.

For the cases where f(E) presented a bimodal charac-

ter, f(E) was represented as the linear combination of

two normal distribution functions, fI(E) and fII(E) as de-

scribed by (E6):

F ðEÞ ¼ af1ðEÞ þ ð1 � aÞfIIðEÞ ðE6Þ

where a represents the relative concentration of com-

plexes with distribution fI(E) compared to that with en-

ergy distribution fII(E). Note that (E6) assumes that at

t = 0, two surface complexes, I and II, exist on the sur-

face of the particle (E7):

½ðC–NOÞ�t¼0

TOT ¼ a½ðC–NOÞ�t¼0

I þ ð1 � aÞ½ðC–NOÞ�t¼0

II

ðE7Þ

0

10

20

30

40

50

60

70

400 500 600 700 800 900

dNO/dt expko=4.7e12ko=4.8e13ko=5.2e14ko=5.5e15ko=5.4e16

dNO

/dt (

umol

/s)

T (K)

Fig. 1. TPD of coal char (sample CC), after reaction with NO/H2O/O2

at 373 K. Dotted: experimental data; lines: data calculated from (E3).

k0 (or k000, see text) evaluated from a non-linear least square optimi-

zation of dNO/dt calculated from (E3) and the experimental data.

3. Experimental

The char samples, were prepared from a subbitumi-

nous coal (sample CC), from its demineralized form

(sample CD), and from phenol-formaldehyde resin

(sample CR). To prepare the char, the coal samples were

pyrolyzed at 973 K for 2 h under N2 atmosphere. The

resin sample was pyrolyzed at 1273 K in N2 atmosphere

for 2 h, then the resin char was activated in nitric acid at333 K and finally gasified at 973 K with a concentrated

solution of NH3 to introduce nitrogen complexes similar

to those found in coal char [20,21]. The NO-char reac-

tion was carried out at 373 K in a tubular quartz reactor

using 0.4 g of sample. The reaction mixture was: NO,

NO/H2O, NO/O2 or NO/H2O/O2 at the following con-

centrations: NO, 2000 lmol/mol; O2, 5%; balance N2.

For the reactions with H2O, the gas mixture was passedthrough a water bubbler held at 333 K (PVH2O

= 2 · 104

Pa). Before each experiment, the sample was held at 973

K during 30 min under N2 flow. After reaction, the sys-

tem was purged in N2 flow for 30 min followed by

temperature programmed desorption (TPD) at 10 K/

min up to 1173 K. Although Du et al. [2] suggested that

different heating rates should be used to guarantee the

uniqueness of the desorption activation energy function,

we used 10 K min�1 to better resolve the TPD profile.

Clearly, this limits the distribution function derived tothis specific heating rate. However, we consider, based

on the results by Du et al., that the effect of the heating

rate on the model results is minor, as long as the TPD

profile is well-resolved. The NO evolved during TPD

was analyzed with a gas detector, Fisher-Rosemount

NDIR/UV gas analyzers, BINOS-1004 for NO and

NO2.

4. Results and discussion

4.1. Temperature programmed desorption of NO

Fig. 1 presents the TPD profile of NO from sample

CC after reaction in NO/H2O/O2 at 373 K (dashed line).

The calculated profile (continuous line) was obtainedafter the iterative process developed in this work. The

different values of k0 obtained after the iteration process,

are between 1012 s�1 and 1016 s�1 which are in the range

of desorption process of first order [22]. Values of k0

outside of this range did not produce an acceptable fit

or the iterative process did not converge.

Table 2 shows the maximum deviation of dNO/dt

calculated for different values of k0. The smallest devia-tion was obtained for k0 � 1014. A similar trend was ob-

served for data with other gas mixtures and with other

samples.

Fig. 2 shows the total and deconvoluted energy distri-

bution functions used in the calculation of the rate of

NO evolution represented by the continuous lines in

Table 2

Values of k000, maximum deviation of dNO/dt calculated from (E3) and

Ea deconvoluted described in (E6)

k0 % error Ea1 (kJ/mol) Ea2 (kJ/mol)

4.7 · 1012 10.0 143 165

4.8 · 1013 8.6 154 183

5.2 · 1014 7.5 165 195

5.5 · 1015 9.0 175 207

5.6 · 1016 9.5 188 221

0

5

10

15

20

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

f(E

)[(m

ol/k

J]x1

03

Ea (kJ/mol)

Fig. 2. Energy function distributions obtained from the desorption

profile shown in Fig. 1. Dashed line: f(E) from (E4), line with bold

circles: fI(E), line with blank circles: fII(E), bold line: F(E) from (E6),

fI(E) = afI(E), fII(E) = (1 � a)fII(E), k0 = 5.2 · 1014.

0

10

20

30

40

50

60

400 500 600 700 800 900

dNO/dt expdNO/dt model

dNO

/dt (

umol

/s)

T (K)

Fig. 3. TPD of coal char (sample CC), after reaction with NO/O2 at

373 K. Dashed line: experimental data; bold line: data calculated from

(E3). k0 = 3.2 · 1014 evaluated from a non-linear least square optimi-

zation of dNO/dt calculated from (E3) and the experimental data.

0

5

10

15

20

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

f(E

)[(m

ol/k

J]x1

03

Ea (kJ/mol)

Fig. 4. Energy function distributions of NO desorption after reaction

of the coal char with a mixture of NO/O2. Dashed line: f(E) from (E4),

line with bold circles: fI(E), line with blank circles: fII(E), bold line:

F(E) from (E6); fI(E) = afI(E), fII(E) = (1 � a)fII(E), k0 = 5.2 · 1014.

1448 P. Garcıa et al. / Carbon 43 (2005) 1445–1452

Fig. 1 with k0 = 5.2 · 1014. The dashed line corresponds

to the energy distribution (f(E)) obtained from (E4). The

lines with bold and blank circles are fI(E) and fII(E)respectively, which combined according to (E6), pro-

duce the f(E) profile. There is good agreement between

f(E) and F(E) in the regions where NO evolution reaches

maximum values, one centered on 165 kJ/mol and the

other on 195 kJ/mol.

Figs. 3 and 4 present the NO desorption profiles for

the exposure of sample CC to a mixture of NO/O2 and

the calculated distribution function respectively. The en-ergy distribution function can be described by two nor-

mal distribution functions. It was observed that f(E)

correctly describes the NO desorption profiles indepen-

dently of the oxidizing mixture used. This gives an indi-

cation that the reactivity of the active surface sites

towards NO is not drastically affected by the presence

of molecular oxygen.

Table 3 shows the mean activation energy and stan-dard deviations for the normal distribution functions

fI(E) and fII(E) that characterize the TPD profiles of

the complexes formed in mixtures of NO with O2 and

H2O. There is a variation of the ratio between complexes

(a in (E6)) and only minor differences in the standard

deviation of the normal distribution functions fI(E)

and fII(E).

Contrary to the TPD profiles of NO in mixtures with

O2, the NO desorption profiles of the samples that were

reacted with NO (Fig. 5) and NO/H2O (Fig. 6), are uni-

modal with a tailing to the left of the profile, which sug-gests a small contribution of NO that is not completely

resolved by the TPD experiment. The NO temperature

desorption range is the same as the one observed in

the case of bimodal NO desorptions. This finding shows

that the composition of the gas mixture does not change

the nature of the N-complexes formed on the surface.

However, it has an influence on the relative quantities

of the complexes that desorb NO by heating.Figs. 7 and 8 present the deconvolution of the energy

distribution functions obtained by (E4) for the mixtures

NO and NO/H2O respectively. Although the results

shown in both figures and in Table 3 indicate that the

Table 3

Parameters of the energy distribution function

Muestra/Mezcla k0 (s�1) Ea1 (kJ/mol) r (kJ/mol) Ea2 (kJ/mol) r (kJ/mol) a

CC (420 m2/g)* NO 3.0 · 1014 149 27 184 20 0.24

NO/H2O 3.0 · 1014 144 46 182 23 0.14

NO/O2 3.2 · 1014 161 15 190 14 0.39

NO/H2O/O2 5.2 · 1014 165 12 195 14 0.43

CR (716 m2/g) NO 4.6 · 1014 164 10 n.a. n.a. 1

NO/H2O 5.0 · 1014 165 11 n.a. n.a. 1

NO/O2 4.2 · 1014 164 12 n.a. n.a. 1

NO/H2O/O2 5.2 · 1014 162 10 n.a. n.a. 1

CD (471 m2/g) NO/O2 4.2 · 1014 150 8 n.a. n.a. 1

n.a.: not applicable.

r: standard deviation.

a: fraction of complexes with distribution f1(E).* Surface area of CO2 adsorption at 273 K.

0

5

10

15

20

25

400 500 600 700 800 900

dNO/dt expdNO/dt model

dNO

/dt (

umol

/s)

T (K)

Fig. 5. TPD of coal char (sample CC), after reaction with NO at 373

K. Dashed line: experimental data; bold line: data calculated from

(E3). k0 = 3.0 · 1014.

0

5

10

15

20

25

400 500 600 700 800 900

dNO/dt expdNO/dt model

dNO

/dt (

umol

/s)

T (K)

Fig. 6. TPD of coal char (sample CC), after reaction with NO/H2O at

373 K. Dashed line: experimental data; bold line: data calculated from

(E3). k0 = 3.0 · 1014.

0

5

10

15

20

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

f(E

)[(m

ol/k

J]x1

03

Ea (kJ/mol)

Fig. 7. Energy function distributions obtained from of NO desorption

after reaction of the coal char with NO at 373 K. Nomenclature similar

to Fig. 2. k0 = 3.0 · 1014.

0

5

10

15

20

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

f(E

)[(m

ol/k

J]x1

03

Ea (kJ/mol)

Fig. 8. Energy function distributions obtained from of NO desorption

after reaction of the coal char with a mixture of NO/H2O. Nomen-

clature similar to Fig. 2. k0 = 3.0 · 1014.

P. Garcıa et al. / Carbon 43 (2005) 1445–1452 1449

1450 P. Garcıa et al. / Carbon 43 (2005) 1445–1452

total energy distribution function can be represented by

two normal distribution functions centered at �147 and

�183 kJ/ mol, the energy distribution function at low

energies show a tendency to disappear. These results

show the applicability of the algorithm in cases of uni-

modal (Fig. 8) and bimodal distributions. An additionalobservation is that presence of water makes wider the

fI(E) and fII(E) distributions (larger r values for NO/

H2O, Table 2). This effect can be ascribed to the reduc-

tion of the population of complexes that desorb around

the central activation energy Ea1. One possible explana-

tion is that water competes with NO for the carbon ac-

tive sites through the formation of surface complexes

that inhibit the formation of the nitrogen complexes.Previously, Montoya et al. [23] showed that water can

dissociatively chemisorb on a carbon surface capping

up to three active sites, which become unavailable for

the NO reaction [12] and therefore causes a reduction

of the active sites where NO can react. Opposite to the

water effect, molecular oxygen enhances the NO chemi-

sorption on the carbon surface (Figs. 1 and 3). In this

case, the formation of N-surface complexes increaseswith the oxidation strength due to the formation of

NO2, and of HNO3 when water is present in the NO/

O2 mixture [12,24–26].

4.2. Mineral matter effect on the NO desorption profiles

The effect of the mineral matter on the NO-char reac-

tion was evaluated using samples CD and CR. Fig. 9aand b show the NO desorption profiles for samples

CD and CR respectively after the reaction with NO/

O2. The fact that the surface area of the CC (char)

and CD (demineralized char) is very similar (420 m2

g�1 vs. 471 m2 g�1 respectively, see Table 3) suggests

that demineralization had a minor effect in the sample

porosity distribution. Even though the char samples

are from different origin and have different surface area

0

20

40

60

80

100

120

140

400 500 600 700 800 900

dNO/dt expdNO/dt model

dNO

/dt (

umol

/s)

T (K)

(a)

Fig. 9. TPD of demineralized coal char (sample CD) (a) and of the resin ch

experimental data; bold line: data calculated from (E3).

(Table 3), being the CR sample more microporous, the

profiles are similar. This behavior suggests that the sur-

face complexes are of similar nature. Comparison of

these profiles with those presented in Figs. 3 and 4 re-

veals that the NO desorption signal at high temperature

disappears. It is clear that the generation of the surfacecomplexes that give rise to that signal is catalyzed by the

minerals in the char. Du [16] found a similar effect in

the carbon oxides desorption from oxidized chars, i.e.

the transformation of an unimodal to a bimodal desorp-

tion by adding calcium to his samples. The analysis by

fluorescence of the mineral matter revealed the presence

of Na, K, Ca and Fe, which catalyze the oxidation of car-

bon surface [9,27] and with this the formation of –NO2

complexes. It is important to mention that XPS charac-

terization of the N-surface complexes did not show any

inorganic nitrogen complexes [12], therefore, this signal

does not correspond to NO adsorbed on the mineral

matter. Similar effects have been published by Du [16]

and Illan-Gomez et al. [28], when metallic species were

added to carbon to enhance its reactivity towards NO.

The corresponding energy distribution functions arepresented in Fig. 10a and b. The activation energies

are centered at 150 and 164 kJ/mol respectively. Even

though Fig. 10 suggests the presence of a second peak

in the energy distribution function centered on 190 kJ/

mol, the intensity of this peak is too low to be resolved

by current analysis. This leads to unrealistic spread of

the deviation in the function distribution as the one ob-

served in Fig. 10b. Fig. 10a and b suggest that the chem-ical nature of the N-surface complexes for mineral-free

samples is similar to that of the low activation energy

peak observed for the CC sample (see Fig. 3) while the

complexes with activation energies centered at 190 kJ/

mol are practically disappeared. The fact that the peak

for the low activation energy complexes are more de-

fined in Fig. 10a and b than in Fig. 3 and the lower val-

ues of r for CR and CD samples in Table 3 suggest more

(b)

0

10

20

30

40

50

400 500 600 700 800 900

dNO/dt expdNO/dt model

dNO

/dt (

umol

/s)

T (K)

ar (sample CR) (b), after reaction with NO/O2 at 373 K. Dashed line:

0

10

20

30

40

50

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

f(E

)[(m

ol/k

J]x1

03

Ea (kJ/mol)

(a) (b)

0

5

10

15

20

25

100 150 200 250 300

f(E)fI(E)fII(E)F(E)

Ea (kJ/mol)

Fig. 10. Energy function distributions obtained from NO desorption after reaction of demineralized coal char (sample CD) (a) and of resin char

(sample CR) (b), with a mixture of NO/H2O. Nomenclature similar to Fig. 2. k0 = 4.2 · 1014 to both cases.

P. Garcıa et al. / Carbon 43 (2005) 1445–1452 1451

homogeneity of active sites for the resin and mineral-free

samples. This can be due to the turbostratic arrange-

ment of the graphene structures in the char preparedfrom coal as well as to the presence of minerals such

as Na, K and Ca which can modify the interaction of

NO with the carbon surface [9,27].

5. Conclusions

Reversible NO chemisorption on carbon surfaces at373 K and analysis by a probabilistic model shows that

there are two kinds of carbon surface complexes that

desorb NO after reaction with NO/H2O/O2 mixtures.

The lower activation energy complexes have desorp-

tion activation energies centered at �160 kJ/mol and

are present in carbonaceous materials with and with-

out mineral matter. The complexes that desorb NO

at higher temperatures are only present in materialswith mineral matter and have desorption activation

energies centered at �185 kJ/mol. The low-activation

energy complexes are of more homogeneous nature for

the mineral-free samples than for the char samples.

The presence of water reduces the reversible chemisorp-

tion of NO while molecular oxygen favors this reaction.

The algorithm used in the present research allows the

determination of kinetic parameters that reproduce theexperimental desorption profiles obtained by TPD and

that can be used to predict the rate of NO reaction with

char at low temperatures and in the presence of H2O

and O2.

Acknowledgments

The authors would like to acknowledge the financial

support from Colciencias and the University of Antio-

quia, project 1115-05-11504, the University of Antio-

quia, project IN-5216CE. The assistance of Prof.

Ruben D. Osorio in the development of the algorithm

is gratefully acknowledged. P. Garcıa wishes to thankColciencias and the University of Antioquia for the

financial support during her PhD studies. A. Molina

thanks the University of Antioquia for the financial

assistance as a visiting scientist during the second semes-

ter of 2002.

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