Dependence of size and size distribution on reactivity of aluminum nanoparticles in reactions with oxygen and MoO3

Article abstract of DOI:10.1016/j.tca.2006.03.001

The oxidation reaction of aluminum nanoparticles with oxygen gas and the thermal behavior of a metastable intermolecular composite (MIC) composed of the aluminum nanoparticles and molybdenum trioxide are studied with differential scanning calorimetry (DSC) as a function of the size and size distribution of the aluminum particles. Both broad and narrow size distributions have been investigated with aluminum particle sizes ranging from 30 to 160 nm; comparisons are also made to the behavior of micrometer-size particles. Several parameters have been used to characterize the reactivity of aluminum nanoparticles, including the fraction of aluminum that reacts prior to aluminum melting, heat of reaction, onset and peak temperatures, and maximum reaction rates. The results indicate that the reactivity of aluminum nanoparticles is significantly higher than that of the micrometer-size samples, but depending on the measure of reactivity, it may also depend strongly on the size distribution. The isoconversional method was used to calculate the apparent activation energy, and the values obtained for both the Al/O₂ and Al/MoO₃ reaction are in the range of 200-300 kJ/mol.

Full text of DOI:10.1016/j.tca.2006.03.001

Thermochimica Acta 444 (2006) 117–127
Dependence of size and size distribution on reactivity of aluminum
nanoparticles in reactions with oxygen and MoO3
Juan Suna, Michelle L. Pantoyab, Sindee L. Simona,∗
a Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, United States
b Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, United States
Received 28 August 2005; received in revised form 28 February 2006; accepted 2 March 2006
Available online 18 April 2006
Abstract
The oxidation reaction of aluminum nanoparticles with oxygen gas and the thermal behavior of a metastable intermolecular composite (MIC)
composed of the aluminum nanoparticles and molybdenum trioxide are studied with differential scanning calorimetry (DSC) as a function of
the size and size distribution of the aluminum particles. Both broad and narrow size distributions have been investigated with aluminum particle
sizes ranging from 30 to 160 nm; comparisons are also made to the behavior of micrometer-size particles. Several parameters have been used to
characterize the reactivity of aluminum nanoparticles, including the fraction of aluminum that reacts prior to aluminum melting, heat of reaction,
onset and peak temperatures, and maximum reaction rates. The results indicate that the reactivity of aluminum nanoparticles is significantly higher
than that of the micrometer-size samples, but depending on the measure of reactivity, it may also depend strongly on the size distribution. The
isoconversional method was used to calculate the apparent activation energy, and the values obtained for both the Al/O2 and Al/MoO3 reaction are
in the range of 200–300 kJ/mol.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Aluminum nanoparticles; MIC thermite reaction; Oxidation; MoO3; DSC
1. Introduction
calorimetry (DSC) is lower for aluminum nanoparticles in both
air, oxygen, and nitrogen environments compared with those for
micrometer-sized particles [4]. In addition, the onset tempera-
ture for oxidation of aluminum nanoparticles in air, as measured
by thermogravimetric analysis (TGA), decreases with decreas-
ing particle size [5,6] and is found to also depend on the type
and thickness of the passivation layer [5]. Agglomeration of
aluminum nanoparticles, on the other hand, decreases their reac-
tivity in air [7], and although high-melting point passivation
layers are said to reduce agglomeration [8], agglomeration has
been found to occur in spite of the presence of a passivating layer
[9]. In addition to reactivity in various gaseous environments,
the activation energy for the oxidation of aluminum nanoparti-
cles has been reported. Jones et al. used various thermal analysis
techniques to obtain the activation energy for oxidation of Alex
aluminum powder in air and reported values that ranged from
206 to 225 kJ/mol [10], whereas for a smaller diameter alu-
minum powder, Aumann found Ea to be 48 kJ/mol below 375 ◦C
and 164 kJ/mol above that temperature [11], the latter of which
was reported to be the same as that for oxidation of flat aluminum
samples. Tompa et al. compared the oxidation of 100 and 900 nm
The thermal behavior of nanoparticles is known to differ
from that in the bulk state due to their increased surface-area-
to-volume ratio [1]. For example, small particles have lower
melting points than bulk material because of the increased pro-
portionof loosely bound surfaceatoms [1]. Althoughthemelting
point depression can be as great as 500 K for gold particles of
1 nm radius [2], the depression is relatively small for aluminum
nanoparticles;forexample, adepressionofonly13 Kisobserved
for a particle having a 10 nm radius aluminum core with a pas-
sivation layer of approximately 10 nm [3].
In terms of reactivity, aluminum nanoparticles are more reac-
tive than their micrometer-sized counterparts and their reactivity
is found to depend on particle size, as well as on the type
and thickness of the passivation layer [4–7]. For example, the
reaction onset temperature measured in differential scanning
∗
Corresponding author.
E-mail address: sindee.simon@ttu.edu (S.L. Simon).
0040-6031/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2006.03.001

118
J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
aluminum nanoparticles in air using DSC and TGA and found
activation energies of 243 and 264 kJ/mol for the smaller par-
ticles and values of 394 and 364 kJ/mol for the larger particles
[12]. In addition to higher reactivity in air and nitrogen compared
to their micrometer-sized counterparts, aluminum nanoparticles
are also very sensitive to humidity, with complete oxidation of
particles less than 90 nm diameter occurring in 74 days at 90%
humidity [13].
Due to their high mass caloricity, high reactivity, and the
non-toxic nature of the reaction products, aluminum nanoparti-
cles have been used to add energy and increase temperatures in
conventional explosives and propellants. Jones et al. have found
that adding aluminum nanoparticles to conventional explosives,
such as TNT and RDX, generally lowers the reaction onset tem-
perature and increases reaction rates [5,10]. Similar results were
reported by Brousseau and Anderson for TNT [14] although
reductions in detonation velocity were found in other systems
after adding aluminum nanoparticles [14,15]. Dokhan et al. also
found an increase in the burn rate for ammonium perchlorate
(AP) solid rocket propellant when adding aluminum having a
bimodal aluminum particle size distribution and containing 20%
nanometer Al [16].
Nanoparticles may also be components of a class of ener-
getic thermite materials known as metastable intermolecular
composites (MIC) which consist of a fuel, such as aluminum,
and an oxidizer, generally a metallic oxide. Since nanoparti-
cles approach molecular dimensions, intermixing of fuel and
oxidizer nanocomponents enhances homogeneity over that of
traditional micrometer-sized energetic materials. In addition, the
increase of surface area of nanoparticles allows more fuel to be
in contact with oxidizer, thereby reducing heat and mass dif-
fusion effects [17]. Consequently, compared with conventional
energetic materials, MIC materials have significantly higher
energy density [18–20]. Work from Pantoya’s group has recently
shown that ignition times are two orders of magnitude lower
for nanocomposites of aluminum and molybdenum trioxide
than for analogous composites composed of micrometer-size
aluminum, and that the nanocomposites show a correspond-
ing decrease in ignition temperatures [20]. Similar results were
found for Ni/Al thermite systems as a function of particle size
[21].
Although studies have shown that particle size and produc-
tion method do affect reactivity, the effect of particle size and
size distribution for particles manufactured in the same way and
for particles less than 100 nm has not been well documented.
Furthermore, the mechanism and reaction kinetics controlling
oxidation of MIC materials and the effect of particle size and
size distribution on the MIC reaction need further investiga-
tion. These are important both for modeling oxidation behavior
and for tailoring a composite for a specific application. The
objectives of this study are, thus, to determine the effect of alu-
minum nanoparticle size and size distribution on the reactivity
and kinetics of aluminum oxidation using differential scanning
calorimetry. Although the reaction conditions in the DSC dif-
fer from those used in thermite applications where temperatures
are significantly higher and reaction rates are orders of mag-
nitude faster, the insights gained in this study are relevant for
a complete understanding of the effects of particle size and
size distribution on reactivity. The systems studied include alu-
minum nanoparticles under an oxygen atmosphere (25% oxygen
in argon) and aluminum/molybdenum trioxide (Al/MoO3) MIC
mixtures under an argon atmosphere.
2. Experimental
2.1. Materials
Nanoscale aluminum particles were obtained from Technan-
ogy (Irvine, CA), and 3 ␮m size aluminum particles (3–4.5 ␮m,
97.5% purity) were purchased from Alfa Aesar (Milwaukee,
WI). The physical properties of the Al nanoparticles are listed in
Table 1. Two size distributions were studied: a broad and narrow
distribution. The average particle diameter and standard devia-
tion were obtained from SEM images; a typical size distribution
curve has been published [22]. Other characteristics, such as sur-
face area and size distribution, of the nanopowders have been
Table 1
Properties of aluminum nanoparticles
Particle
diameter (nm)
Standard
deviation (nm)
Weight-average
particle diameter (nm)
Al content (%)
Supplier
Oxide layer thickness (nm)
ꢀHm,T (J/gAl)
Our measurement
Suppliera
Our measurementa
Broad size distribution samples
17
25
52
76
101
12b
21
42
56b
56
31
51
105
142
160
38
54
74
80
82
33
47
59
–
2.2
2.2
2.5
2.9
3.5
2.5
2.7
4.1
–
292
300
320
340
360
–
–
Narrow size distribution samples
43
63
81
92
2
3
3
3
43
63
81
92
74
82
84
83
57
69
71
72
2.1
2.2
2.6
3.1
3.5
3.7
4.4
4.8
325
332
340
350
a
Both supplier and our estimates of the oxide layer thickness are based on Eq. (1) assuming that the oxide layer is amorphous. The calculated thickness is on
average 18% thinner if one assumes that the layer is crystalline.
b
Estimated based on the average ratio of standard deviation to particle size of the other three broad size distribution samples.

J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
119
reported [23]; similar data are available for the micrometer-size
particles [24].
anes and mixed using ultrasonic waves; no evidence of sintering
is observed using our mixing method based on SEM measure-
ments [29]. The solution was poured into a glass container and
after the solvent was completely evaporated the mixture was
carefully collected and put in a vial for further use. The equiv-
alence ratio (φ) of aluminum to molybdenum trioxide is 1.2,
where φ is defined as [30]:
The average particle size obtained from SEM experiments
reflects the number size distribution, whereas the heat flow
response in DSC experiments corresponds to the weight distri-
bution of the sample. Consequently, the number-average particle
size is converted to weight-average size assuming that the par-
ticles have Gaussian distribution; the weight-average sizes are
shown in Table 1. We note that although the log normal distri-
bution has been used to describe the particle size distribution for
particles generated using the same technique [9,11], the Gaus-
sian distribution has been shown to describe the particle size
distribution well for vapor-deposited indium nanoparticles [25],
and the calculated active aluminum content of our particles is
closer to the experimental values when we assume a Gaussian
distribution than when we assume a log normal distribution [3].
Other researchers have also assumed a Gaussian distribution in
their work to mathematically demonstrate the influence of size
distribution on the oxidation wave speed [26]. For two of the
particle sizes studied having broad distributions, the standard
deviations are not available; to obtain the weight-average parti-
cle size we assumed that the ratio of the standard deviation to
particle diameter for these samples was the same as for the other
three broad size distributions for which the standard deviation
is reported.
Pure aluminum is pyrophoric, and thus, each aluminum
nanoparticle is passivated with a 2–4 nm Al2O3 layer to pro-
tect the particles from premature reaction. As the particle size
decreases, the total percentage of Al2O3 increases and can
become a considerable amount of the total powder. In Table 1,
the aluminum content (Al content) refers to the amount of active
aluminum present, i.e., that aluminum which is not in the form
of Al2O3. The aluminum content was obtained from mass gain
measurements using a TGA by the supplier and also by our
measurements as described in a subsequent section. Based on
the aluminum content and the particle size, the thickness of the
oxide layer (toxide) can be calculated through a mass balance:
(F/Ox)ACT
φ =
(2)
(F/Ox)ST
where F represents mass of fuel (Al), Ox the mass of oxidizer
(MoO3), and the subscripts ACT and ST indicate the actual and
stoichiometric ratios. The stoichiometric F/Ox mass ratio for the
reaction is 0.375 based on the following global reaction:
2Al + MoO3 → Al2O3 + Mo
(3)
The aluminum content as obtained from the supplier was used
in determining φ. The equivalence ratio of 1.2 was found to
be optimum for this reaction based on burn rate and ignition
sensitivity studies [20]. The actual equivalence ratio based on
the aluminum content obtained from our TGA measurements
(which are described below) is shown in Table 2. Interestingly
the actual equivalence ratio based on our measurements of the
aluminum content ranges from 0.92 to 1.06 for the MIC samples
studied with an average of 1.0, leading us to speculate that the
optimum value of 1.2 found in earlier burn rate and ignition
sensitivity studies [20] based on supplier values of aluminum
content may in actuality be closer to 1.0 as might be expected
from stoichiometric considerations. Also shown in Table 2 is the
weight fraction of aluminum in the MIC samples (not including
aluminum in the form of Al2O3).
2.2. Differential scanning calorimetry
Differential scanning calorimetry was performed using a
Perkin-Elmer DSC-7 instrument with an ethylene glycol/water
cooling system maintained at 10 ◦C. For the reaction of alu-
minum particles with oxygen, the runs were made under 25/75
ꢀ
ꢃ
ꢁ
ꢂ
1/3
ρAl O3 c
2
toxide = Ro 1 −
(1)
ρAl + c(ρAl O − ρAl)
2
3
Table 2
Properties of MIC samples
where Ro is the total particle size (including the oxide layer),
c is the fractional aluminum content, and ρAl O (3.05 g/cm3)
Al particle
diameter (nm)
Weight-average
particle diameter
(nm)
Weight fraction
aluminum in
MIC samples
Actual φ
2
3
[27] and ρAl (2.7 g/cm3) [28] are the densities of amorphous
aluminum oxide and aluminum at room temperature, respec-
tively. The oxide layer is assumed to be amorphous based on the
results of other researchers [24]; if the layer is assumed to be
crystalline, its thickness is on average 43% thinner than reported
in Table 1. Although our measurements show a lower aluminum
content compared to those of the supplier, the aluminum content
changes less than 3% during storage in our laboratory based on
the results of TGA experiments conducted two months apart.
Molybdenum trioxide was obtained from Climax Molybde-
num (Sahuarita, AZ) and is composed of rectangular sheet like
particles approximately 1 ␮m in length and 20 nm thick. To
make the MIC samples, an appropriate amount of aluminum
and molybdenum trioxide were immersed in a solvent of hex-
MICs with broad size distribution Al powders
17
25
52
76
31
51
105
142
160
0.180
0.216
0.224
0.289
0.290
1.05
1.06
0.96
–
101
–
MICs with narrow size distribution Al powders
43
63
81
92
43
63
81
92
0.214
0.243
0.255
0.254
0.92
1.00
1.02
1.05
MIC with bulk Al
3000
0.308
1.20

120
J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
oxygen/argon atmosphere; for the MIC reaction of aluminum
particles with molybdenum trioxide, the runs were made under
argon atmosphere. Alumina pans were used and sample sizes
varied from 3 to 10 mg. Temperature scans were made as fol-
lows: the sample was held at 200 ◦C for 20 min for the Al/O2
reaction and for 60 min for the MIC reaction to purge the sample,
followed by a temperature scan from 200 to 725 ◦C at a specified
heating rate. We note that longer purge times have no effect on
the reaction or the results reported. Heating rates of 3, 5, 10, and
20 K/min were used. For the reaction of aluminum particles with
oxygen, the mass of each sample was measured both before and
after each run using an analytical balance in order to calculate
the fraction of aluminum that reacted based on sample weight
gain (as described later).
The obtained heat flow responses were corrected using base-
line subtraction, where the baseline was obtained by running the
empty reference and sample pans. The temperature of the instru-
ment was calibrated using zinc and potassium chromate under
argon atmosphere. Heat flow was calibrated using potassium
chromate.
are calculated to be less than 1 K for the Al/O2 reaction and less
than 0.1 K for the MIC reactions for all scan rates used in this
work. This calculation is corroborated by the observation that
our calculated apparent activation energies do not depend on
conversion; this result and its implication are discussed in more
detail later. Due to the small thermal gradients expected in these
samples, no correction for heat transfer effects are made.
2.3. Thermogravimetric analyzer
Although the aluminum nanoparticles were stored under an
argon atmosphere after delivery, they may have reacted with
adventitious oxygen between the time that the supplier made the
measurements of active aluminum content and our DSC experi-
ments. Therefore, the active aluminum content was determined
from mass uptake of oxygen using a Perkin-Elmer TGA-7. The
mass of the TGA samples varied from 1 to 3 mg and a 25/75 mix-
ture of O2/Ar was used as the analysis gas. Experiments were
performed for 960 min at 830 ◦C. The mass gain in the TGA
is attributed to oxidation of active aluminum, as shown by the
following reaction:
Heat transfer effects are known to smear transitions in DSC
scans, leading to broader transitions and a shift along the temper-
ature scale [31]. Although the heat of reaction is obtained from
the integrated heat flow and is not be affected by any smearing
of the transition, peak temperatures and reaction rates can be
affected. The temperature gradient in the sample can be esti-
mated following the arguments of Chang [32] by
4Al + 3O2 → 2Al2O3
(7)
The active aluminum content (c) can be calculated using the
following equation:
108
c (%) =
ꢀm (%)
(8)
96
L
ꢀT (K) ≈ 0.5
Q
(4)
Aλ
where ꢀm (%) is the percent mass gain in the TGA experiment.
The calculated aluminum content based on our TGA measure-
ments, as well as that reported by the supplier, is shown in
Table 1. We reiterate that only minor changes in aluminum con-
tent (<3%) were observed over the course of our experiments
due to storage in our laboratory.
where L is the sample thickness (assumed to be 1 mm), A the
sample area (0.126 cm2), λ the thermal conductivity, and Q is
the maximum heat flow. The thermal conductivity of our oxide-
coated aluminum nanoparticle samples can be estimated by first
calculating the average thermal conductivity for an individual
particle based on particle geometry and the thermal conductivi-
ties of aluminum (λAl = 2.36 W cm−1 K−1) and aluminum oxide
(λAl O = 0.3 W cm−1 K−1) [33]:
2.4. Data analysis
2
3
For the reaction of the aluminum particles with oxygen, the
fraction of aluminum that reacts to form Al2O3 during DSC
experiments was determined from the fractional mass gain of
the DSC sample (ꢀm), in an analogy to Eq. (8):
Ro
λparticle
=
(5)
(rAl/λAl) + (toxide/λAl O
)
3
2
where Ro is the total particle radius, rAl the radius of the alu-
minum core, and toxide is the oxide coating thickness. The
effective thermal conductivity, λeff, of the powder can then be
estimated by accounting for the void fraction using the Maxwell
theory [34]:
108
Fraction Al reacted =
ꢀm
(9)
96
The fraction of aluminum that reacts prior to melting can
also be independently determined from the area of the melting
endotherm (ꢀHm):
λeff
3
2
≈ 1 −
φ
(6)
λparticle
ꢀHm
Fraction Al reacted = 1 −
(10)
where φ is the void fraction in the sample. The thermal
conductivities of the individual particles range from 0.78 to
1.4 W cm−1 K−1, increasing with increasing particle diameter.
Assuming a void fraction of 50%, the thermal conductivity of the
samples ranges from 0.20 to 0.35 W cm−1 K−1, again increasing
with increasing diameter. Hence, Eq. (4) becomes ꢀT ≈ 0.002Q
to 0.001Q, for Q in milliwatts, with the prefactor decreasing with
increasing particle size. Thermal gradients in the DSC samples
ꢀHm,T(r)
where ꢀHm,T(r) is the total heat of melting expected if none of
the active aluminum reacts prior to melting; the heat of melting is
a function of particle radius (r). Although the bulk heat of fusion
of aluminum is 396 J/g [33], the heat of fusion of aluminum
nanoparticles decreases as the particle size decreases [3,35]; for
example, ꢀHm,T = 320 J/g for 40 nm radius passivated particles

J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
121
[3]. Therefore, the heat of fusion for each particle was deter-
mined experimentally in this work, and the values are shown in
Table 1; errors in ꢀHm,T are estimated to be 5% [3]. We note
that the difference in the fraction of aluminum reacted using
ꢀHm,T(r) rather than the bulk heat of fusion, ꢀHm,T(∞), in Eq.
(10) is small, ranging from 1 to 8%. As an aside, we note that
the heat of fusion is predicted to decrease with particle size due
to a relative increase in the surface energy as particles decrease
[36]:
2σsl
ρsr
ꢀHm,T(r) = ꢀHm,T(∞) −
(11)
where σsl is solid–liquid interfacial energy and ρs is the solid
phase density. However, experimental results in the literature
for metallic nanoparticles [3,35,37] and for organic materials
confined to the nanoscale [38] show a much larger depression
in the heat of fusion than is predicted by Eq. (11); the reason
for this discrepancy is not clear although explanations have been
put forth [3].
Fig. 1. DSC heat flow per gram of active aluminum as a function of temperature
for the Al/O2 reaction showing the effect of the size and size distribution of
the aluminum nanoparticles. Results are shown for a broad size distribution
sample having an average diameter of 52 nm (with a weight-average diameter
of 105 nm), a 42 nm narrow size distribution sample, and a 3 ␮m sample. The
DSC scans were performed at 3 K/min under 25/75 O2/Ar atmosphere.
For the reaction of aluminum with molybdenum trioxide,
there is no mass change upon the reaction. Hence, the fraction
of aluminum reacted during the DSC scan is obtained from the
heat of the DSC melting peak, as expressed by Eq. (10).
The kinetics of solid-state reactions is usually described by
the following equation:
size distribution sample (105 nm weight-average diameter), the
43 nm narrow size distribution sample, and the 3 ␮m Al particles
at a heating rate of 3 K/min under an a 25/75 O2/Ar atmosphere.
The heat flows are normalized by the aluminum content in the
samples in order to make a valid comparison. Fig. 1 shows that
there is a large exothermic reaction peak present for the nanopar-
ticles prior to the aluminum melting peak at 660 ◦C due to the
oxidation of aluminum by oxygen, whereas for the micrometer-
size material, only a small exotherm is present prior to melting.
The onset temperature for oxidation is also dramatically reduced
for the nanopowders. In addition, compared with micrometer-
size sample, the melting peaks for the nano-sized samples are
considerably smaller, suggesting that more aluminum in the
nanopowders reacted in the oxidation process prior to melting.
Hence, the reactivity of aluminum nanoparticles is considerably
higher than that of the micrometer-size sample. Qualitatively
similar results were reported by Mench et al. [4] in their com-
parison of Alex aluminum nanopowder and micrometer-size
aluminum particles by differential thermal analysis (DTA). The
effect of particle size distribution is also very striking in Fig. 1,
with the 52 nm broad size distribution sample showing higher
reactivity than the 43 nm narrow size distribution sample even
though the average particle size is larger for the broad size dis-
tribution sample; this finding will be discussed in more detail
subsequently.
For the data shown in Fig. 1, the fraction of aluminum that
reactspriortomeltingcanbecalculatedeitherfromthemassgain
of the DSC sample obtained by weighing the sample before and
after the DSC experiment or from the area of the melting peak,
using either Eq. (9) or (10), respectively. The results for all the
samples including nanoparticles with both narrow and broad size
distributions and micrometer-size particles are shown in Fig. 2
for DSC scans at 5 K/min as a function of reciprocal weight-
average particle diameter. The fraction of aluminum that reacts
prior to melting agrees between the two methods of calculation
and increases with decreasing particle size leveling off for sam-
ples smaller than approximately 100 nm. For the 3 ␮m sample,
ꢁ
ꢂ
dα
dt
E
= k(T)f(α) = A exp
f(α)
(12)
RT
where α is the degree of conversion, t the time, T the temper-
ature, k(T) the temperature-dependent rate constant, which is
usually described by the Arrhenius equation, A and E the pre-
exponential factor and apparent activation energy, respectively,
and f(α) is the reaction model for the certain reaction [39–42].
An isoconvensional method in which DSC scans are made at a
series of heating rates can be used to obtain kinetic parameters,
and the apparent activation can be obtained from the following
equation [42]:
Eα
ln(β) = c −
(13)
RTα
where c is a constant, β the heating rate, and Eα and Tα are the
apparent activation energy and temperature at a specific degree
of conversion α. The advantage of this isoconversional method
is that the activation energy can be obtained without specifying
a certain reaction model; therefore, this method is a model-free
method [42].
3. Results and discussion
3.1. Aluminum/oxygen reaction
The results of the DSC studies focusing on the reaction of the
aluminum nanoparticles with oxygen (Al/O2 reaction) are dis-
cussed first since they will provide insight into the more complex
oxidation reactions of the MIC materials. The effect of alu-
minum particle size on the reactivity of Al/O2 reaction is demon-
strated in Fig. 1, where DSC scans are shown for the 52 nm broad

122
J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
Fig. 2. Fraction of aluminum reacted prior to Al melting in the Al/O2 reaction as
a function of the reciprocal of the weight-average particle diameter for nanopar-
ticles with both narrow and broad size distributions and for a micrometer-size
sample. Results are based on DSC scans made at a heating rate of 5 K/min.
Circles represent the results calculated from the mass gain of the sample, and
squares represent the results calculated from the aluminum melting peak using
the size-dependent heat of fusion. The dashed line is only intended to show the
trend in the data.
Fig. 3. Heat of reaction for the Al/O2 as a function of weight-average particle
diameter. The values plotted and error bars are the average and standard devia-
tion, respectively, of the heat of reaction obtained at various heating rates. The
circles represent the results based on the fraction of aluminum calculated from
mass gain, and the squares represent the results based on the fraction of alu-
minum reacted calculated from the size of the aluminum melting peak using the
size-dependent heat of fusion. The solid line indicates the bulk heat of reaction
for Al/O2. The dashed line is only intended to show the trend in the data for
samples below 100 nm.
the fraction of aluminum that reacts prior to melting is less than
10%, whereas for particles of approximately 100 nm, the value
increases to 80% and does not appear to increase further for
smaller particles. Note that if the number-average particle size
instead of weight-average size were used for the samples hav-
ing broad distribution, the trend of the data would be obscured,
confirming the importance of using the weight-average size. In
this study, the effect of heating rate on the fraction of aluminum
reacted prior to melting was also investigated. The fraction of
aluminum that reacts prior to melting decreases by approxi-
mately 5% at 10 K/min and increases by approximately 5% at
3 K/min compared to the results shown for a 5 K/min heating
rate; this is as expected since at higher heating rates, the sam-
ples have less time to react, and vice versa at lower heating rates.
However, the trend for the fraction of aluminum that reacts prior
to melting as a function of particle size is the same for all heating
rates investigated.
The heat of reaction for the Al/O2 reaction (ꢀHR) can be
determinedfromtheareaoftheexothermicreactionpeak(shown
in Fig. 1) coupled with knowledge of the amount of aluminum
that reacted (Fig. 2). The results are shown in Fig. 3 as a function
of the weight-average particle diameter for aluminum nanopar-
ticles with both broad and narrow size distributions. At particle
sizes less than approximately 100 nm, the heat of reaction is
23 kJ/gAl, 75% of the theoretical value (31 kJ/gAl) [43]. For par-
ticle sizes larger than 100 nm, the heat released per gram of
aluminum reacting unexpectedly decreases with increasing par-
ticle size. We emphasize that the value reported is per gram of
aluminum reacted. Our results for the smallest particles are con-
sistent with work by Jones and co-workers [13] in which a value
of approximately 22 kJ/gAl was obtained for Alex aluminum
nanoparticles by TG/DTA. We note that the heating rate has no
effect on the heat of reaction values, and the data shown in Fig. 3
are the average and standard deviation of all the values obtained
at different heating rates; i.e., although the fraction of aluminum
reacted depends on heating rate, the heat of reaction per gram of
aluminum reacted does not. In addition, the length of the purge
prior to the DSC scan did not affect our results indicating that
the lowered heats are not due, for example, to adventitious air or
nitrogen in the samples. Although it may seem surprising that
the heat of reaction for the nanoparticles is smaller than that for
bulk aluminum, perhaps such a result is not so unexpected given
the lack of understanding of material behavior at the nanoscale,
including, for example, the large reductions in the heat of fusion
observed at the nanoscale [3,35,37,38].
The size distribution of the nanopowders impacts their reac-
tivity, as was shown in Fig. 1, where the exothermic reaction
peak for the broad size distribution sample is shifted to lower
temperatures by about 50 ◦C relative to that of the narrow size
distribution sample, even though the broad size distribution sam-
ple has a larger average particle size. In an attempt to quantify the
differences in reactivity, the onset and peak temperatures for all
ofthesamplesareshowninFig. 4asafunctionofweight-average
particle diameter for DSC scans at 5 K/min. [We note that the
onset temperature is defined as the temperature at which the
extrapolated descending peak slope intersects with the baseline;
this value depends on heating rate and is a measure of reactiv-
ity, not a direct measure of the temperature at which reaction
begins.] As shown in Fig. 4, the onset and peak temperatures
are lower for the broad size distribution samples than for the
narrow size distribution samples, but in neither case do they
depend strongly on particle size. The onset temperatures for
samples with broad size distributions is approximately 505 ◦C,
about 50 ◦C lower than those samples with narrow size distribu-
tions. For the micrometer-size sample, the onset temperature is
close to that of the samples with narrow size distributions. The

J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
123
Fig. 6. Natural logarithm of the heating rate vs. the reciprocal temperature for
various conversions, α, for the Al/O2 reaction of the 25 nm sample having a
broad size distribution. The lines show the best linear fits from which Eα is
obtained. The dependence of Eα on conversion is shown in the inset with error
bars indicating the standard error from the fit. The horizontal line in the inset
indicates the average value of Eα for all conversions.
Fig. 4. Onset and peak temperatures as a function of weight-average particle
diameter for the reaction of Al/O2 for DSC scans at 5 K/min. Circles represent
the onset temperature, and squares represent the peak temperature. The dashed
and solid lines are only intended to show the trends in the data.
trend is the same for peak temperature, i.e., samples with broad
size distributions have a lower peak temperature than those with
broad size distributions. Both the onset temperature and peak
temperatures are affected by the heating rates as expected, with
the values being an average of 10 K lower for 3 K/min scan-
ning rates and an average of 10 K higher for 10 K/min scanning
rates. The results indicate that broad size distribution samples
are more reactive than the narrow size distribution samples. This
may be attributable to the presence of more small nanoparticles
in a broad size distribution sample, which then may enhance the
reactivity of the entire mixture.
The maximum oxidation rate per gram of aluminum reacted
(Qmax), which is determined by the heat flow rate at the exotherm
peak (with heat flow normalized by the total mass of aluminum
of the sample) is plotted against weight-average particle diame-
ter for all the samples studied in Fig. 5. With increasing particle
size, the maximum oxidation rate decreases from approximately
55 W/gAl for the particle of 60 nm diameter to 2 W/gAl for the
micrometer-size sample. Although Fig. 4 shows that the onset
and peak temperatures are affected by the size distribution and
not affected by the size of the particles, Fig. 6 indicates that the
maximum reaction rate is strongly dependent on the particle size
and not on the size distribution. Other parameters to character-
ize reactivity of aluminum nanoparticles besides onset and peak
temperatures include the specific heat release (J/g) and maxi-
mum oxidation rate (g/min) in TG-DTA experiments [5,6,13]
and the maximum self-heating rate (Rmax) in ARC experiments
[5,13]. Consistent with our data, other researchers have shown
that aluminum nanoparticles ranging from 130 to 280 nm have
considerably higher values of specific heat release [6] compared
with 80 ␮m aluminum particles, and that with decreasing par-
ticle size, the values increase [6]. On the other hand, the onset
temperatures for these aluminum nanoparticles from TG-DTA
experiments show no large differences within the range studied
[6], also in agreement with our DSC data. It is important to rec-
ognize that different measures of reactivity give different results,
e.g., some measures indicate that particle size is important and
that size distribution is unimportant, whereas others indicate the
opposite. It is clear that a full description of reactivity requires
multiple characterization methods.
The kinetics of the reaction of the aluminum nanoparticles
with oxygen was studied using the isoconvensional method to
calculate the apparent activation energy. Fig. 6 shows the natural
logarithm of the heating rate (β) as a function of the reciprocal
temperature at which a given conversion was obtained during the
DSC scan for the 25 nm particle; the conversion α ranges from
0.1 to 0.6 since the final conversion for a heating rate of 20 K/min
was less than 70%. From the slope of the ln β versus 1/T curves,
Eα is calculated using Eq. (13). The results are shown in the inset
of Fig. 6, where Eα is plotted as a function of conversion with
the error bars giving the standard error from the fits. The values
of Eα are not statistically different; this is consistent both with a
simple reaction mechanism and with the absence of significant
thermal gradients [44].
The average values for Eα and standard deviations are shown
in Fig. 7 as a function of weight-average particle diameter. For
all of the nanoparticles studied, the activation energies are in
the range of 200–300 kJ/mol. This is in reasonable agreement
Fig. 5. Maximum reaction rate as a function of weight-average particle size for
the reaction of Al/O2 for DSC scans at 5 K/min.

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J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
minum particles, respectively. For the MIC sample containing
52 nm aluminum particles, there is a large exothermic peak
followed by a small aluminum melting peak, whereas for the
sample containing micrometer-sized aluminum, there is only a
small exothermic peak followed by a large melting peak. Fig. 8
suggests that reducing aluminum particle size can significantly
increase the reactivity of the Al/MoO3 MIC, similar to the results
shown in prior figures for the reaction of aluminum with oxy-
gen. However, there are poignant differences between the MIC
reaction and Al/O2 reaction. First, the scale for heat flow for the
reaction with the argon/oxygen mixture is over 10 times greater
in Fig. 1 than for the MIC reaction shown in Fig. 8. In addition,
the MIC reaction appears to be somewhat more complex with
several peaks often observed in the temperature range from 250
to 600 ◦C. The apparent complexity may be due in part to the
scale of the heat flow in Fig. 8 relative to Fig. 1; heat evolved
due to reactions of the aluminum with adsorbed O2 or H2O
or due to the phase change of aluminum oxide (Al2O3) from
the amorphous to the crystalline state during temperature scan
[24,45,46] may not be noticeable in Fig. 1 due to the scale of
the heat flow. DSC experiments were performed separately for
aluminum nanoparticles and for MoO3 under argon atmosphere,
and the results suggest some heat evolution for the aluminum
nanoparticles either due to adsorbed O2 or to the phase change
of the Al2O3, whereas for MoO3, no obvious peaks exist during
the entire temperature scan.
Fig. 7. Apparent activation energy calculated using the isoconversional method
vs. particle size for the Al/O2 reaction. The values plotted and error bars are the
average and standard deviations, respectively, of the activation energies obtained
at different conversions. The lines are only intended to show the trends in the
data.
with literature values: a value of 164 kJ/mol was reported for
oxidation of aluminum nanoparticles synthesized by gas con-
densation using TGA [18]; an average value of 254 kJ/mol was
obtained by DSC and TGA experiments for oxidation of Alex
aluminum nanoparticle [12]; also for Alex particles, a value of
225 kJ/mol was reported using DTA experiments [10]. From
Fig. 7, we can also see that the apparent activation energies for
particles with narrow distributions are slightly higher than those
with broad distributions. For the aluminum nanoparticles with
broad size distributions, the apparent activation energies are in
the range of 220 20 kJ/mol, whereas for those with narrow size
distributions, the apparent activation energies are in the range of
270 20 kJ/mol.
The fraction of aluminum that reacts prior to melting is deter-
mined from the area of the melting endothermic peak, which
reflects the amount of aluminum left in the sample. Fig. 9 shows
the fraction of aluminum reacted prior to melting for DSC scan at
5 K/min asafunction of reciprocalof theweight-averageparticle
size calculated using the modified bulk heat of fusion. Compared
with the sample containing micrometer-sized aluminum parti-
cles, the samples containing nano-sized aluminum particles are
considerably more reactive; for example, 70% of the aluminum
reacts in the MIC reaction for the 30 nm particles, whereas only
3.2. Aluminum/molybdenum trioxide MIC reaction
The effect of aluminum nanoparticle size on the reactiv-
ity of the Al/MoO3 MIC reaction is also studied using DSC
experiments. Fig. 8 shows a comparison of DSC scans run at
5 K/min for the MIC samples containing 52 nm and 3 ␮m alu-
Fig. 9. Fraction of aluminum reacted prior to Al melting in the Al/MoO3 MIC
reaction as a function of the reciprocal of the weight-average aluminum particle
diameter for nanoparticles and micrometer-size particle from DSC scans made
at a heating rate of 5 K/min. The values are calculated from the size of aluminum
melting peak using the size-dependent heat of fusion. The dashed line is only
intended to show the trend in the data.
Fig. 8. DSC heat flow per gram of active aluminum as a function of temperature
for the Al and MoO3 MIC reaction showing the effect of aluminum particle size.
The DSC scans were performed at 5 K/min under argon atmosphere.

J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
125
20% reacts for the 3 ␮m aluminum particles. For the aluminum
nanoparticles with broad size distributions, the fraction of alu-
minum reacted appears to increase with decreasing particle size.
For the narrow size distribution aluminum nanoparticles, which
are all less than 100 nm, no significant differences exist for all
four samples; this is consistent with the results for Al/O2 reac-
tion in which the fraction of aluminum that reacts before melting
was independent of size for particles less than 100 nm. Note that
since the actual equivalence ratio (φ) is lower than 1.2, as shown
in Table 2, the fraction of aluminum reacted prior to melting may
exceed 83%, the expected maximum for an equivalence ratio of
1.2. The effect of heating rate is significant for this reaction with
the fraction of aluminum that reacts prior to melting decreasing
with increasing heating rate; it is less than 35% for a heating rate
of 10 K/min.
The heat of reaction for the Al/MoO3 MIC reactions obtained
from the integrated heat of the exothermic peak, is shown in
Fig. 10, where the average heat of reaction is plotted against
weight-average particle diameter. The heats of reaction obtained
are considerably lower than the theoretical value (17 kJ/gAl)
[43], consistent with the results for the Al/O2 reaction shown
in Fig. 3 and the results of others [13]. For all the aluminum
nanoparticles studied, the heats of reaction for MIC mixture are
in the range of 6 4 kJ/gAl, approximately 35% of the theoreti-
cal value. The percentage of heat evolved per gram of aluminum
reacting is much lower than that for the Al/O2 reaction, and the
results also show more scatter. Again, we emphasize that it is
perhaps not surprising that the heat of reaction is lower than the
bulk value given that a similar and, as yet, unexplained reduction
is observed for the heat of fusion at the nanoscale.
Fig. 11. Onset and peak temperatures as a function of weight-average aluminum
particle diameter for the Al/MoO3 MIC reaction for DSC scans at 5 K/min.
Circles represent onset temperatures, and squares represent peak temperatures.
The dashed and solid lines are only intended to show the trends in the data.
aluminum particle is 518 ◦C, slightly higher than any samples
having aluminum nanoparticles. The aluminum particle size
appears to have no significant effect on the onset temperature
for either narrow or broad size distributions for the Al/MoO3
reaction, consistent with the results for the Al/O2 reaction. The
peak temperatures show a similar trend but with larger variations
compared with the onset temperatures. The values of onset and
peak temperatures increase with increasing heating rate and are
approximately 10 K higher for a heating rate of 10 K/min.
The maximum reaction rate per gram of aluminum prior to
aluminum melting for the Al/MoO3 MIC reaction is shown in
Fig. 12. With increasing aluminum particle size, the maximum
oxidation rate appears to decrease with the trend being more
obviousforthesamples containing aluminumnanoparticles with
broad size distributions. For the sample having micrometer-size
aluminum, the maximum reaction rate is 0.6 W/gAl, whereas for
the sample having the smallest particles the value is approxi-
mately 10 times higher. The trend is similar to that for the Al/O2
reaction although the rates are considerably lower.
The onset and peak temperatures for the Al/MoO3 MIC
reaction are shown in Fig. 11 for DSC scans at 5 K/min. The
onset temperatures of the MIC samples containing aluminum
nanoparticles with broad size distributions remain constant at
approximately 460 ◦C, whereas those with narrow size distri-
butions show onset temperatures at approximately 500 ◦C. The
onset temperature for the sample containing micrometer-size
Fig. 10. Heat of reaction for the Al/MoO3 MIC reaction as a function of weight-
average aluminum particle diameter. The values plotted and error bars are the
average and standard deviations, respectively, of the heat of reaction obtained at
various heating rates. The solid line indicates the bulk heat of reaction, and the
dashed line is only intended to show the trend in the data.
Fig. 12. Maximum reaction rate prior to melting as a function of weight-average
aluminum particle size for the Al/MoO3 MIC reaction for DSC scans at 5 K/min.

126
J. Sun et al. / Thermochimica Acta 444 (2006) 117–127
isoconversional method was used to calculate activation ener-
gies; for both the Al/O2 Al/MoO3 reactions, Ea ranges from 200
to 300 kJ/mol, suggesting the same rate-limiting step in these
two reactions.
Acknowledgements
Theauthorsgratefullyacknowledgethefinancialsupportpro-
vided from the National Science Foundation DMR-0304640
(SLS) and the Army Research Office DAAD19-02-1-0214
(MLP).
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Fig. 13. Apparent activation energy calculated using the isoconversional method
vs. weight-average aluminum particle diameter for the Al/MoO3 MIC reaction.
The values and error bars represent the average and standard deviation of the
activation energy obtained at different conversions, respectively. The dashed line
is only intended to show the trend in the data.
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