Carbon deposition and hydrocarbon formation on group VIII metal catalysts

Article abstract of DOI:10.1021/jp980996o

Carbon formed from CO in CO₂ at around 500°C deposited as nanotubes and encapsulating carbons on a supported Ni catalyst without H₂ or as filaments if H₂ was present. A thermodynamic model explains how hydrogen in low concentrations controls filament morphology and why equilibrium is shifted from that for graphite during carbon deposition. Carbon deposition reaction rates at low carbon activity in the absence of hydrogen are reported. A new concept of the rate limiting step for metal-catalyzed carbon formation is proposed, where conditions inside the bulk metal are at least as important as the surface chemistry. A mechanism with an unusual type of active site can qualitatively explain carbon formation rates through a broad range of reaction conditions. When hydrogen is present, a series of hydrocarbons are believed to form, as in fuel synthesis (Fischer-Tropsch) chemistry. Surface vinyl species that have been recently shown to be intermediates in Fischer-Tropsch chemistry also may polymerize to form graphene. The formation of vinyls from CO and H via surface alkyls occurs at a greater rate than methane formation when the supply of hydrogen is limited. Hydrogen from the bulk catalyst metal (not surface adsorbed) hydrogenates the surface alkyls, indicating that hydrogen solubility may control the metal-catalyzed formation of various hydrocarbons and eventually solid graphitic carbon.

Full text of DOI:10.1021/jp980996o

J. Phys. Chem. B 1998, 102, 4165-4175
4165
Carbon Deposition and Hydrocarbon Formation on Group VIII Metal Catalysts
†
‡
,§
Peter E. Nolan, David C. Lynch, and Andrew Hall Cutler*
Carbomite Company, Apache Junction, Arizona 85219, Department of Materials Science and Engineering,
UniVersity of Arizona, Tucson, Arizona 85721, MinerVa Laboratories, 10 Thunder Run #28C,
IrVine, California 92614
ReceiVed: February 3, 1998; In Final Form: April 2, 1998
Carbon formed from CO in CO
supported Ni catalyst without H
2
at around 500 °C deposited as nanotubes and encapsulating carbons on a
or as filaments if H was present. A thermodynamic model explains how
2
2
hydrogen in low concentrations controls filament morphology and why equilibrium is shifted from that for
graphite during carbon deposition. Carbon deposition reaction rates at low carbon activity in the absence of
hydrogen are reported. A new concept of the rate limiting step for metal-catalyzed carbon formation is
proposed, where conditions inside the bulk metal are at least as important as the surface chemistry. A
mechanism with an unusual type of active site can qualitatively explain carbon formation rates through a
broad range of reaction conditions. When hydrogen is present, a series of hydrocarbons are believed to
form, as in fuel synthesis (Fischer-Tropsch) chemistry. Surface vinyl species that have been recently shown
to be intermediates in Fischer-Tropsch chemistry also may polymerize to form graphene. The formation of
vinyls from CO and H via surface alkyls occurs at a greater rate than methane formation when the supply of
hydrogen is limited. Hydrogen from the bulk catalyst metal (not surface adsorbed) hydrogenates the surface
alkyls, indicating that hydrogen solubility may control the metal-catalyzed formation of various hydrocarbons
and eventually solid graphitic carbon.
Introduction
as promoting reaction. The view generally held in the literature
is that the carbon is formed by a solution-diffusion-precipita-
Carbon deposition from gas precursors is important to a
variety of industrial processes. Typically, carbon deposition is
undesired since it deactivates catalysts. Carbon atoms on or in
the catalyst significantly impact processes such as steam
reforming, hydrogenation, methanation, water-gas shift, and
Fischer-Tropsch fuel synthesis. Indeed, the details of carbon
and hydrogen atoms’ behavior lead to the mechanisms that form
desirable products and undesirable byproducts or cause phe-
nomena like metal dusting.
tion process that generates graphitic (crystalline) carbon at
relatively low temperatures. The graphitic deposit has been
observed in various morphologies, as follows.
Filaments consist of stacked cone-segment (frustum) shaped
graphite basal plane sheets and grow with a catalyst particle at
2
,5
their tip. They are illustrated using schematic cross sections
in Figure 1 a,b. Hydrogen is believed to satisfy the valences at
cone edges in typical filaments; and with increasing hydrogen
concentration, the orientation angle between the graphite basal
Carbon nanotubes and filaments are cylindrical or tubular
carbon formations with radii on the nanometer scale and lengths
up to several micrometers. The primary difference between a
nanotube and a filament is the orientation of graphite basal
planes with respect to the axis. Since the properties of graphite
are anisotropic, its orientation will dictate resulting material
properties such as electrical and thermal conductivity, mechan-
ical strength, and modulus of elasticity (stiffness). Carbon
encapsulation of catalyst nanoparticles can protect ferromagnetic
metals from oxidation, making a promising magnetic medium.
Increased understanding of the mechanisms involved in metal-
catalyzed carbon formation can be used to optimize all the above
processes and products. Having had the fortune of doing those
few experiments necessary to see the extensive prior work of
others in a unified context, we are able to write a primarily
theoretical paper, in which we interpret the experimental results
of others as well as include a small amount of our own data.
Catalytic production of carbon results from the decomposition
6
planes and the tube axis (θ) increases. Under certain conditions
this morphological series may extend to where the basal planes
7
are perpendicular to the cylinder axis (θ ) 90°). Filaments
with large orientation angles are often not hollow, so are more
accurately described as solid cylinders.
Nanotubes are the low hydrogen end member of this series
of cylindrical carbon deposits. The direction of their graphite
basal planes is parallel to the tube axis (θ ) 0°), as shown in
Figure 1c. Nanotubes can be produced by catalytic carbon
8
,9
deposition with a catalyst particle at their tip and in a carbon
10,11
arc without a catalyst.
A nanotube is essentially a filament
with no graphite edges, requiring no valence-satisfying species
such as hydrogen. When H2 is present in a carbon arc reactor,
open-ended nanotubes can be produced with stabilized basal
12
plane edges only at the two ends of a tube.
Another graphitic nanomaterial produced by carbon deposi-
13,14
tion is encapsulated metal nanoparticles.
These are roughly
1-4
of a carbon-containing gas on certain transition metals.
The
spherical formations, originally called shells, consisting of
catalyst particles surrounded by graphitic carbon. They are
typically found to be limited to about 30 or 40 layers of graphite
basal plane (graphene) sheets, irrespective of their formation
conditions or size.
catalyst influences the structure of the carbon formed as well
†
Carbomite Co.
University of Arizona.
Minerva Laboratories.
‡
§
S1089-5647(98)00996-1 CCC: $15.00 © 1998 American Chemical Society
Published on Web 05/05/1998

4166 J. Phys. Chem. B, Vol. 102, No. 21, 1998
Nolan et al.
studied metal-catalyzed hydrocarbon decomposition and did not
observe a strong dependence of carbon deposition rates or
product morphologies on the gas composition. They showed
that the activation energy for carbon deposition in filament form
can match the activation energy of carbon diffusion through
the catalyst for a variety of metals and asserted the conclusion
that carbon diffusion through the catalyst particle is the rate-
2
1
limiting step.
There are, however, indications that carbon diffusion is not
the rate-limiting step in carbon deposition under many circum-
stances. The activation energy of carbon diffusion through Ni
2
2
might abruptly change below 700 °C, while the reported
carbon deposition activation energy remains about the same.23
An adsorption-diffusion isotherm for filament growth from
methane on iron particles indicated that carbon diffusion through
the particle was rapid compared to the preceding step of carbon
Figure 1. Schematic illustrations of (a, b) filaments and (c) a nanotube.
Encapsulated nanoparticles typically take a range of sizes,
with radii from about 5 to over 100 nm. Nanotubes are more
restricted in radii, typically observed with 1-3 nm inner radius
24
formation at the top surface of the particle. There is evidence
that certain surface chemical reactions are responsible for the
and 5-20 nm outer radius. Single-wall nanotubes are found
to have less than 1 to approximately 2.5 nm radii.15 Filaments
2
5,26
rate-limiting step,
as is common in the established surface
may take any inner radius and range up to about 100 nm outer
8
science of heterogeneous catalysis. The inability of any one
proposed mechanism to explain the same phenomena over a
wide range of conditions indicates that the fundamental rate-
controlling mechanism is not yet understood. The purpose of
the present work is to gain insight into the complex catalytic
processes related to carbon deposition. Our carbon deposition
results, including product morphology information, are com-
bined with the prior work in an attempt to identify the
mechanistic elements important under a wide range of condi-
tions.
radius but are commonly of similar size to nanotubes. Tibbetts
explains how the radii of the cylindrical structures may be
controlled by equilibrium thermodynamics. We show that to
be the case for the inner radius. The outer radius is often
considered to be determined by the catalyst particle (for
catalytically produced structures), since they usually have the
same size in micrographs.4 That presumed causality is not
supported by other evidence. Nanotubes produced by carbon
arc with no catalyst particle have outer radii similar to those
produced catalytically. In supported catalysts with initially small
catalyst metal clusters, agglomeration takes place before typical
particle sizes are reached and carbon deposition begins. When
starting with a foil or large particles of catalyst metal,
fragmentation occurs (and fragments are smaller than the metal’s
grain size). These very different processes for catalyst particle
sizing produce similar filament radii, indicating a common
controlling mechanism. In the present work, nanotubes tightly
distributed around a 9 nm average outer radius coexisted with
encapsulated particles ranging to over 40 nm radius. Thus, even
when larger catalyst particles are present and undergoing carbon
deposition, the nanotubes restrict themselves to the smaller radii.
All of the above morphologies were produced in the present
work under similar conditions by CO disproportionation,
Recent results on the detailed molecular mechanism of
27
Fischer-Tropsch catalysis illuminate the mechanism by which
filaments grow with the graphene sheets generally parallel to
the catalyst particle surface and provide a dynamic mechanism
for the filament structure to attain equilibrium. Certain mecha-
nistic necessities of catalytic carbon formation may also clarify
the Fischer-Tropsch mechanism.
Experimental Section
Carbon deposition rates were measured by observing weight
gain during the nickel-catalyzed formation of carbon from CO.
The catalyst was 70 wt % Ni on 30 wt % of a SiO2-Al2O3
support (obtained from Johnson Matthey, #31276). It was
exposed to CO/CO2/N2 mixtures with concentrations of H2
between 0.00% and 3% and a temperature range of 745 K to
2CO ) C + CO2
(1)
7
85 K. The CO/CO2 mixture was set to give low aC and avoid
where C is carbon in the form of variously arranged graphene
sheets. Later it will be shown that these carbon deposits are
thermodynamically different from graphite. The driving force
for carbon deposition by CO disproportionation is the gas-phase
carbon activity (aC), defined as
the conditions that would allow Ni3C formation. Thermo-
gravimetry was used to measure weight gain by standard
28
methods. Mass transport calculations and preliminary experi-
ments were used to ensure that intrinsic chemical rates were
measured and that temperature measurements were accurate.
About 5 mg of catalyst in a Pt crucible was suspended in a
Cahn R-100 microbalance reactor. The CO/CO2/N2 concentra-
tions exiting the reactor were measured using a Shimadzu GC-
2
PCO
aC ) K
(2)
eqP
CO2
8
A gas chromatograph with a Alltech CTR II column to
PCO and PCO are the partial pressures of CO and CO2, and Keq
determine the reaction gas aC using eq 2. For each run, the
2
is the equilibrium constant for reaction 1 when the product is
graphite. There are apparently two kinetic regimes as carbon
activity is varied. At low carbon activity, carbon deposition
rates are linearly dependent on carbon activity.13 At sufficiently
high values of carbon activity, carbon deposition rates have little
dependence on it.1
The most elegant measurements of carbon deposition rates
were done by Baker and co-workers using controlled atmosphere
electron microscopy to observe filament growth.2,19,20 They
catalyst was held at 773 K for 3 h under flowing N2 to remove
-
5
moisture, then reduced in 10% H2, 90% N2 at 4 × 10 mol/s
for 30 min. After flushing the reactor with N2, the temperature
for the isothermal experiment was set and reaction gas flow
-
5
initiated at 6 × 10 mol/s.
6-18
Specimens of the material removed after a reaction experi-
ment were examined in a Hitachi H-8100 transmission electron
microscope (TEM) operating at 200 kV, to determine the
morphology of deposited carbon. The graphite orientation angle

Carbon Deposition and Hydrocarbon Formation
J. Phys. Chem. B, Vol. 102, No. 21, 1998 4167
Figure 2. Measured filament orientation angle (θ) versus H
2
concen-
Figure 4. Maximum rates of carbon deposition on Ni/SiO
2 2 3
/Al O as
tration during CO disproportionation: (9) 745 K experimental, (s)
a function of gas-phase H concentration at 745 K, a ) 18-19.
2
c
745 K theoretical, (b) 785 K experimental, and (---) 785 K theoretical.
TABLE 1: Minimum Gas-Phase Carbon Activity (a ) and
C
g
Gibbs Energy (∆g ) for Inception of Carbon Deposition
T (K)
a
C
∆g
g
(kJ/mol)
7
7
7
45
65
85
18
12
8
18
16
14
mass versus time) for a series of experiments are useful for
kinetics analysis. Figure 3 is a plot of the maximum carbon
deposition rates measured when no H2 or N2 was present in the
CO-CO2 gas mixture. The partial pressures of CO and CO2
are as determined from eq 2, with a total pressure of 1 atm.
Rates are plotted with respect to aC, showing a generally linear
response. The response of rates to the partial pressure of CO
(or CO2) at constant aC (e.g., by use of diluents or a different
Figure 3. Maximum rates of carbon deposition on Ni/SiO
2
/Al
O
2 3
as
total pressure) was not studied.
a function of gas-phase carbon activity (a
K, ([) 765 K, and (b) 785 K.
c
) and temperature: (9) 745
Below certain values of aC, inception could not be achieved,
and thus rates were zero. Those values of limiting aC and the
Gibbs energy (∆g ) RT ln aC) are given in Table 1.
Figure 4 shows how the carbon deposition rate increased
when small concentrations of H2 were added to the reaction
gas mixture at constant temperature. For those experiments,
aC as calculated from eq 2 was held approximately constant at
with respect to the axis (θ) and the number of graphite basal
plane edges per nanometer of tube length (E) were measured
from micrographs. The parameters θ and E are geometrically
related, so that
1
8-19.
sin θ ) 0.34E
(3)
since the spacing between graphite planes is constant (nominally
Discussion
0
.34 nm for bulk, flat graphite). Greater detail on experimental
1
. Morphological Thermodynamics of Carbon Deposits.
methods and the results (summarized below) are published
A thermodynamic understanding of the difference between a
nanotube and a filament can be obtained by theoretical analysis.
Tibbetts estimated the internal energy of a nanotube by
separately.29
8
Results
calculating the surface energy and strain energy (of bending
graphite planes) required to produce a nanotube from graphite.
Other contributions can be included, such as the misalignment
strain between graphite sheet layers in a nanotube30 since the
typical stacking sequence in flat graphite would not be
maintained in the nanotube configuration. We have extended
that analysis to estimate the Gibbs energy difference of a
filament from graphite. The resulting model explains hydro-
gen’s control of filament morphology, as well as literature
observations that carbon deposits are in equilibrium with a
substantially different gas composition than graphite is.
The following thermodynamic model uses standard literature
values for various properties or to make estimates thereof. The
small difference in Gibbs energy remaining after taking the
difference of these large and unrelated numbers bears a
qualitative relationship to our observations. This demonstrates
a more fundamental understanding of carbon product formation
than is possible through curve fitting to theoretical expressions
As discussed in the Introduction, different graphite morphol-
ogies were observed for the deposits formed in these experi-
ments. Nanotubes and encapsulating shells are formed without
hydrogen, and filaments are formed when hydrogen is present.
There is some poorly characterized material deposited in all
cases. Filament cone angle (θ) versus reaction gas H2 concen-
tration is shown in Figure 2 and is compared to the results of
a thermodynamic model developed below.
The reaction rate data from several experiments are shown
in Figures 3 and 4. Reaction rates are normalized to the mass
of nickel metal in the catalyst. For individual experiments,
carbon deposition weight gain curves exhibited characteristic
initiation (or inception), maximum rate, and deactivation stages.
These characteristic stages are common in carbon deposition
studies and were directly observed by Baker and co-workers
2
for the lengthening of individual filaments. The relative
maximum reaction rates (from the inflection point on plots of

4168 J. Phys. Chem. B, Vol. 102, No. 21, 1998
Nolan et al.
TABLE 2: Enthalpy and Entropy Terms (Compared to
Graphite) for Cylindrical Carbon Structures
term
∆h
T∆s
1
2
3
4
. The formation of basal plane ∆hbps cos θ T∆sbps cos θ
free surfaces (bps)
. The energy of bending
graphite basal planes
. Interlayer graphite stacking
misalignment
. Formation of graphite edges
with hydrogen-capped bonds
∆h
∆h
∆h
B
L
E
cos θ
cos θ
sin θ
T∆s
L
cos θ
+ ∆s
Figure 5. Illustration of reaction 9, a model for the replacement of
C-C bonds with C-H bonds at graphite edges.
T(∆s
E
M
) sin θ
bending strain energy in a filament of graphene sheets per mole
of carbon is
where the shape of the curve is substantially controlled by fitted
free parameters. While some of the less well constrained
parameters were fitted, they were bounded by theoretical
analysis, and the fitted values were found to fall inside those
bounds. As all of the numbers used here have fundamental
physical meanings, they could in principle be accurately derived,
each by a different method, and then combined to predict our
experimental results.
2
2
Ya ln(r /r )
Ya
ro dr
o i
∆hB )
∫
)
cos θ (8)
2
2
2
ri
2
o
12ν(r - r ) r sec θ 12ν(r - r )
o
i
i
where Y is Young’s modulus and a is the interlayer spacing for
12
-3
graphite (1 × 10 J m and 0.34 nm, respectively).
Consider the hypothetical reaction
For the inner radius to be controlled by thermodynamic
equilibrium, it should take the value where the strain energy of
bending another inner layer exceeds the surface energy recov-
ered by covering up the free basal plane surface of the innermost
layer. Equating the enthalpy (T ) 0) from eqs 7 and 8 for an
additional layer (ri ) ro - 0.34 nm) in a nanotube predicts ri to
be 2.7 nm. That value is in good agreement with average inner
radius observed in the present work of around 2.5 nm.
The value used for graphite stacking misalignment enthalpy
graphite + hydrogen gas ) nanotube/filament
(4)
to be at equilibrium, for which the Gibbs energy of reaction
must be zero (∆g ) 0). Then
∆
h ) T∆s
(5)
where values are molar specific to carbon (J/mol for ∆h and J
-
1
-1
mol
K
for ∆s). Table 2 gives the terms that must be
(∆hL, term 3) is estimated based on a lower limit of 1000 J/mol
included in the enthalpy and entropy to solve eq 5. The relations
and numeric values are derived assuming perfect (flaw free)
graphitic structures.
For the formation of basal plane free surface (term 1), the
factor of cos θ accounts for the amount of basal plane surface
exposed at the filament surface (illustrated in the Supporting
Information). As θ increases, a smaller area of basal plane is
exposed at the filament surface. When θ is zero, the structure
is a nanotube, and the entire inside and outside surfaces are
basal plane area.
(
the variation in half the heats of sublimation per carbon atom
31
of polycyclic aromatics ) and an upper limit of 5300 J/mol (the
enthalpy of turbostratic graphite ). The misalignment entropy
(
30
-1
-1
∆sL) is estimated as around 3 J mol
K
based on half the
average entropy of melting per carbon atom of various small
solid aromatic molecules (approximating a 50-50 split between
H and C). The cos θ factor accounts for the fact that these
terms are at a maximum when θ is zero, and are zero for
graphite, where θ is 90°. The values used for these term 3
constants are adjusted somewhat to give a good fit to the data.
To quantify the formation of graphite edges with hydrogen-
capped bonds (term 4), we used an analogous reaction:
To solve eq 5, it is rearranged to place the cos θ terms on
one side of the equality and sin θ terms on the other. For the
basal plane surface, ∆gbps ) ∆hbps - T∆sbps. Thus, when these
enthalpy and entropy terms are put together in eq 5, they become
C H + 3H ) 3C H
6
(9)
1
8
12
2
6
∆
gbps cos θ. By definition ∆gbps is the surface energy of a
-
2
graphite basal plane, γbps (given as 0.1 J m in the literature),
solid triphenylene and hydrogen producing solid benzene. It
is a model for the replacement of graphene C-C bonds by edge
C-H bonds, illustrated in Figure 5. For reaction 9, ∆hR )
multiplied by the surface area per mole for a graphite tube,
2
π(r + r )
o
i
2
-
1
-1
)
2
(6)
-5600 J/mol and ∆sR ) -45 J mol
K
(from thermody-
2
o
ν(r - r )
32
νπ(r - r )
o
i
i
namic tables ) on a per mol H basis, with less than 1% variation
per 100 °C. These enthalpy and entropy estimates should be
corrected for the effects of the different vibrational levels of
the bonds, and of the restricted size of the filaments and
nanotubes on the heat content of the material. Using spectro-
scopic data for the vibrational frequencies of the bonds and
standard tables of the thermodynamic properties of the quantum
simple harmonic oscillator, the correction to the enthalpy is
where ro is the tube outer radius, ri is the tube wall inner radius,
5
-3
and ν is the moles per volume of graphite (1.8 × 10 mol m ).
Thus
2
γbps
∆
hbps - T∆sbps
)
(7)
ν(r - r )
o
i
-
1
negligible. The entropy should be corrected by 5 or 10 J mol
K
-
1
For the energy of bending graphite basal planes (term 2),
for different bond vibration frequencies. A further cor-
∆
hB is found by the method of Tibbetts.8 Internal energy (∆u)
rection to the entropy term arises from the fact that the filaments
and nanotubes are of a size comparable to the wavelength of
some of the phonons contributing to the heat capacity of
graphite. The entropy of carbon structures of the size considered
is determined by that method, which is approximately the same
as enthalpy since ∆h ) ∆u + ∆(PV) and for solid carbon ∆-
(PV) is negligible. The radius of curvature, R, of a tangent circle
-
1
-1
perpendicular to a cone or frustum at a point of distance r from
the center line of the cone or frustum is r sec θ. Thus, the
here can be estimated to be 20-30 J mol
K
greater than
that estimated using model compounds. While detailed calcula-

Carbon Deposition and Hydrocarbon Formation
J. Phys. Chem. B, Vol. 102, No. 21, 1998 4169
tions of these two effects are in principle possible, in themselves
they would be the subject of a paper and are unlikely to be
reliable enough to allow accurate results to be derived from
first principles. Thus ∆sR was considered to be bounded
-
1
-1
between -20 and -5 J mol
K
and fit as a free parameter
within this range. To give these values a per mole C basis as
with the other terms of Table 2, they must be multiplied by the
moles of H per mole of C. That factor is determined
geometrically, assuming that one hydrogen atom is taken up to
6
satisfy valences for every two graphite edge atoms:
-
10
mol H 2.1 × 10
)
sin θ
(10)
mol C
r - r
o i
which gives the sin θ factor shown in Table 2.
In term 4 ∆sm is the entropy of mixing of the gas-phase
hydrogen evaluated using the standard equation for an ideal gas
g
Figure 6. Gibbs energy differences (∆g ) required to form carbon
(∆sm ) - R ln(P2/P1)). At 1 atm total pressure and on a per
structures: (+) for CO disproportionation,26 (0) for CH decomposi-
4
tion,26 (]) from inception time for CO disproportionation (present
work), and (s) theoretical (eq 14, present work).
mole H basis,
R
2
∆
s ) - ln P
(11)
m
H2
Equation 14 may be used to estimate the enthalpy of
formation of a nanotube, by setting T to zero. The resulting
value can be compared to what Setton derived using a (6, 12)
where PH is the partial pressure of hydrogen in the gas mixture.
2
This result also must be multiplied by eq 10 to put it on a per
mole of C basis. Note that the enthalpy of mixing for an ideal
gas is zero.
33
Lennard-Jones formulation. Setton calculated enthalpy values
of 6.9-8.7 kJ/mol for a nanotube with ro ) 3.2 nm and ri )
1
.7 nm. The present method gives an enthalpy of 7.2 kJ/mol
Using the above terms, eq 5 becomes
with those radii (and the same values for constants as used
above). The equation also gives the temperature at which
nanotubes are preferred to graphite (∆gnt < 0); this is where
nanotubes are the equilibrium form of carbon. For the typical
radii measured in the present work, that temperature is about
800 K, appropriate for the reaction temperatures used. For the
radii given above from Setton, that temperature is 2000 K,
appropriate for conditions in the carbon arc.
2
γbps
+
∆h + ∆h - T∆s cos θ )
B
L
L
(
)
ν(r - r )
o
i
-10
2.1 × 10
(
-∆h + T∆s - 4.2T ln P ) sin θ (12)
R
R
H
2
r - r
o
i
which is solved for θ to give the dependence of orientation angle
on H2 concentration:
When the different geometry is accounted for, the Gibbs
energy difference from graphite for spherical encapsulates can
be estimated as well. The expression is
2
2
γbps
Ya ln(r /r )
o
i
+
+ ∆h - T∆s
L L
2
2
ν(r - r )
o
i
12ν(ro - r )
2
o
2
2
-
1
i
3(r + r )γ
πYa (r + r ) ln(r /r )
θ ) tan
(13)
i
bps
o
i
o i
-
10
∆gencap.
)
+
+
2
.1 × 10
r - r
3
o
3
3
3
{
(-∆h + T∆s - 4.2T ln P )
}
ν(r - r )
16ν(r - r )
o i
R
R
H
i
2
o
i
∆
h - T∆s (15)
L L
Typical inner and outer radii measured in the present work
are 2.5 and 9 nm, respectively. These values and eq 13 are
used to produce the lines shown in Figure 2. A good fit to the
experimental data was achieved when setting ∆hL ) 1800 J/mol,
Equations 14 and 15 imply that nanotubes have smaller radii
than the encapsulates they are in equilibrium with. TEM
observations show that encapsulates have larger radii than
nanotubes in any given experiment.
-1
-1
-1 -1
∆
sL ) 3.6 J mol K , and ∆sR ) -10 J mol K , all within
There have been several reports of measured Gibbs energy
differences from graphite required before carbon deposition can
reasonable bounds derived from literature values. A table
summarizing the values used is given in the Supporting
Information.
26
occur. The term ∆gg will be used to refer to the Gibbs energy
difference between a given carbon product and standard-state
graphite. The values in the literature were found by measuring
the gas mixture at equilibrium when shifting between carbon
deposition and carbon gasification and comparing this composi-
tion to the mixture that would be predicted using standard
graphite equilibrium data.
The orientation angle is temperature dependent. Lower
orientation angles are found at higher reaction temperatures (with
a fixed hydrogen concentration). It is thus possible for
nanotubes to be produced from a gas with a significant hydrogen
concentration or fugacity (e.g., a hydrocarbon) at sufficiently
9
high temperature, as has been reported.
Data for hydrogen-free CO-derived deposits can be compared
to results obtained by us using an entirely different approach.
We considered the inception time at different gas compositions.
Those measurements were used to determine the value of aC
The Gibbs energy difference of nanotubes from graphite can
be estimated based on the above modeling using the surface,
bending, and misalignment energy terms while omitting the
hydrogen terms. This gives
(or ∆gg) at which inception no longer occurs in finite time. The
2
results (Table 1) are plotted, along with the literature results,
in Figure 6. There is reasonable agreement between the two
methods of determining the ∆gg for carbon deposited by CO
2
γbps
Ya ln(r /r )
o
i
∆
g )
+
+ ∆h - T∆s
L
(14)
nt
L
(
ν(r - r )
2
2
)
o
i
12ν(r - r )
o i

4170 J. Phys. Chem. B, Vol. 102, No. 21, 1998
Nolan et al.
disproportionation. These ∆gg values are larger than those
reported for methane decomposition (also shown in Figure 6),
since hydrogen available in the methane system satisfies point
defects and opens the orientation angle to give a lower enthalpy
product. Increasing ∆gg values for CO disproportionation at
lower temperatures would also be due to an expected increase
in defects at lower temperatures. See the Supporting Informa-
tion for a discussion of point defects.
but are the shape of a cross section of the particle. Thus
cylindrical nanotubes with a circular cross section are produced
by spherical particles with a circular cross section. The
consequence of this, and the thermodynamics control shown in
section 1 above, belies the commonly held belief that the catalyst
particle determines the product size. It is more likely the
opposite. The thermodynamics of the carbon deposition system
determines the size and structure of the carbons formed, and
thus the size and shape of the catalyst particle. Crystallographic
considerations such as preferred planes for reaction and
Figure 6 also shows the ∆gg for nanotubes calculated using
eq 14. We expect the theoretical curve for nanotubes (no point
defects) and the experimental values for methane decomposition
derived filaments (with satisfied point defects) to have similar
magnitudes of ∆gg. Uncertainty in the standard thermodynamic
5
precipitation play a role, but do not solely determine the particle
shape.
3. Carbon Deposition Mechanisms. Reaction rate data for
CO disproportionation on a supported catalyst in the complete
absence of hydrogen are reported here. In prior literature where
reaction rates were measured, hydrogen was typically present
2
6
data for graphite is believed to be 9 kJ/mol. The greatest
source of error in the theoretical curve is from that uncertainty
in the Gibbs energy of graphite. Thus, error bars were placed
on the theoretical curve shown in Figure 6, showing that the
theoretical and the methane decomposition curves are indistin-
guishable.
3
as an impurity. The H2 impurity was either known to exist or
23
not reported but apparent since filaments were produced.
Although often not found to be the case,
1,37
there can be
2
. The Role of Hydrogen in Carbon Deposition. Hydro-
significant carbon deposition rates without hydrogen present,
as shown in Figure 3. Without hydrogen, carbon can only be
formed from CO by disproportionation (reaction 1). When H2
is added to the reaction gas, carbon may also form by the overall
reaction of CO hydrogenation,
gen has several well-known roles in carbon deposition. It is
believed to contribute to catalyst particle fragmentation, prevent
carbide formation, and control properties of the catalyst by lattice
restructuring. The relevance of hydrogen to filament orientation
angle has only recently been recognized.6 In the more simplified
experiments of the present work, the impact of hydrogen on
graphite edge formation was isolated as much as possible from
the other effects of hydrogen.
CO + H ) C + H O
(16)
2
2
which can be considered responsible for the increasing carbon
The impact of hydrogen on filament morphology clarifies
some details of the diffusion-precipitation mechanism. Free
valences (or dangling bonds) are excessively energetic and
cannot actually exist, even for an instant, at the edge of growing
graphite planes under conditions less energetic than the carbon
arc. During precipitation, something must cap the free valences
at the edge of the graphite sheet to which new carbons will
1,38
deposition rate shown in Figure 4.
Based on the literature, the rate and mechanism involved
in carbon deposition appear to depend on the reaction con-
ditions. Reaction conditions include temperature, reactant
partial pressures, particularly carbon activity (e.g., low aC
from a CO/CO2 mixture high in CO2 or high carbon activity
from pure CO or a hydrocarbon), hydrogen concentration
2
add. Without hydrogen, this means that the sp -hybridized
(
or fugacity for the case of hydrocarbons), and the catalyst
carbon orbitals in graphite, and hence the basal planes, must
point at the catalyst surface (the graphene sheet must be
perpendicular to it). Hydrogen can cap valences and allow free
plane edges to be left behind. It can also bond to the edges to
itself (e.g., the support used or the catalyst metal alloyed
with another metal). In the following, an attempt is made to
generate a single model operative for most of the above
conditions.
3
form sp -hybridized carbons so that the “free” carbon valences
The general trend of reaction rate response to the above
conditions may be found by foregoing a common assumption
of heterogeneous catalysis. Instead of only one type of active
site on the surface of the catalyst, we assume that there are two
different types of active site: possibly a surface site and a
subsurface site. Then the reaction path for CO disproportion-
ation can be generalized as having the following steps:
needed for plane growth can be stabilized by the catalyst surface
while the graphite basal plane lies parallel to it. Plane formation
then occurs by interconversion of the various C-H moieties at
the plane edge as carbon atoms are added to it, a process that
would also be catalyzed by the metals that catalyze filament
growth.
Using this knowledge of how carbon precipitates from the
catalyst surface, we can explain the shapes of the catalyst
particles shown in the literature associated with tubular carbon
CO + * + # ) C# + O*
(17)
(18)
3
4
products. Two commonly seen catalyst particle shapes
that are clearly different from each other are pear-shaped
roughly conical) and spherical. The conical particles are found
CO + O* ) CO + *
2
(
35
36
at the tip of filaments, and nearly spherical particles are
observed at the tip of nanotubes. That fits the concept that
filament formation, with the aid of hydrogen, entails carbon
precipitation generally parallel to the catalyst surface. The
carbon takes the shape of stacked cones precipitating one at a
time from the particle, determining the shape of the bottom of
the particle.
C# ) C + #
(19)
where * and # designate the two types of sites, and C
represents carbon in solution in the catalyst metal. The # active
site might be where individual carbon atoms form and dissolve
into the bulk catalyst metal. Rate limitation and catalyst
deactivation may result from slow removal of carbon atoms from
these sites. Step 17 incorporates what are probably several
complicated steps, but which are considered to be near
equilibrium. Taking step 19 as the rate-limiting step (all other
steps being near equilibrium), the rate equation for this
Nanotubes must precipitate from the catalyst generally
perpendicular to its surface in order to satisfy plane edge
valences by bonding to the catalyst particle surface. Accord-
ingly, the basal planes do not form in the shape of the particle,

Carbon Deposition and Hydrocarbon Formation
J. Phys. Chem. B, Vol. 102, No. 21, 1998 4171
mechanism can be derived (shown in the Supporting Informa-
tion). The result is
The effect of hydrogen on the above proposed mechanism
may be examined by considering the following reaction
steps:
a #
C
T
rate ) kK3
(20)
CO + * + # ) C# + O*
(22)
(23)
1
+ K3aC
H + 2* ) 2H*
2
where k is the temperature-dependent rate constant, K3 is a
combination of rate constants, and #T is the total of occupied
and unoccupied sites of the second type.
To be correct, aC in eq 20 should be replaced by a different
activity, aC′. This new term aC′ is the gas-phase carbon activity
relative to the type of carbon being formed, rather than to
graphite. The difference between aC′ and aC results from the
difference in Gibbs energy (Figure 6) between the actual carbon
products formed and graphite, such that (for CO disproportion-
ation)
2
H* + O* ) H O + 3*
(24)
(25)
2
C# ) C + #
The rate equation for this mechanism (with reaction 25 as
the rate-limiting step) is similar to eq 20, except that the carbon
activity (aC′ equivalent) is calculated from reaction 16 instead
of reaction 1. Unfortunately, to ascertain the carbon activity
associated with reaction 16, it would be necessary to measure
PH O on the catalyst surface, which is extremely difficult. In
2
principle, some combination of the two rates would account
for the increasing total reaction rate (for low H2 concentrations).
At high concentrations of H2, adsorbed hydrogen competes with
and “crowds out” the adsorption of CO, at which point the
above assumptions would no longer apply. The literature
findings that a surface chemistry step is rate limiting under some
conditions argue against the assumption that step 19 (or step
∆
gg/RΤ
a ′ ) a e
(21)
C
C
2
5
The trends that eq 20 predict are consistent with the literature.
It gives a rate that is linear in aC′ for small values of aC′ and
approximately constant (at a given #T) for large values of aC′.
As the thermodynamic properties of the carbon formed are not
generally known, aC is generally calculated instead of aC′.
Under reasonable conditions aC will be proportional to aC′ for
a given set of experiments, with a proportionality constant
typically between 2 and 25. To most closely model the data,
the relation of aC′ to aC must be accurately known for each
particular experiment. That information is not generally reported
in or derivable from the literature.
Control of reaction rate by the second type of active site
can account for other literature findings. Similarity of the
apparent activation energy of filament growth to that of carbon
diffusion in the catalyst metal could be due to the mobility of
carbon from subsurface sites, a mechanism potentially similar
to diffusion. The finding that significant rate increases result
from alloying a catalyst with a noncatalytic metal could be
explained by the ability of surface clusters to increase #T and
thus rate. Also, carbon on the second type of sites might be
compared to the surface carbide as discussed by Alstrup that
controls the carbon activity gradient through the catalyst particle.
The inception/deactivation property common to carbon deposi-
tion could be attributed to #T variation during the experiment.
That variation could be caused first by low carbon presence
creating sites, then by high carbon coverage blocking sites.
Determination of #T would probably not be as easy as measure-
ment of surface adsorption sites (i.e., *T). There is no reason
to expect that the response of # sites to gas adsorption compares
to that of typical surface active sites.
The general form of eq 20 can describe the known trends in
carbon deposition from CO at low aC, and can be applied to
hydrocarbon decomposition with very high carbon activity. In
other than CO disproportionation, aC as defined by eq 2 is
replaced by an appropriate determination of carbon activity for
the particular system. The simplicity of eq 20 disguises the
underlying broad complexity of this system. For instance, the
2
5) is limiting. The additional complexities introduced by the
presence of hydrogen call for a more detailed analysis. Other
steps involving hydrocarbon intermediates, of the form
C# + nH* ) CH * + #
(26)
n
where n is 1 through 3, are considered in section 4 below.
The overall rate law for CO consumption during carbon
deposition from CO and H2 might then take a form such as
2
k1*PCO + k2*PCO*PH . By analogy to the prior literature and
2
the above, the first term is likely a complex expression that
reduces to a dependence on PCO at very low pressure (such
2
that CO2 presence is negligible) and to carbon activity at higher
pressures. The second term in this rate law is important when
there is a high hydrogen concentration. A large fraction of the
surface carbon would be present as methyl (-CH3), and the
rate-limiting step becomes obtaining carbon from CO.
2
5
4
. Application to Fischer-Tropsch Catalysis. Fischer-
Tropsch (FT) catalysis is the reaction of CO and H2 at low
temperatures (e.g., 300 °C) to form hydrocarbons such as liquid
motor fuel. When considered in light of the present results,
27
the work of Maitlis and co-workers on FT catalysis leads to
a mechanistic understanding of the entire spectrum of catalysis
39
by transition metals. In addition, the work of Vannice and of
40
Johnson and co-workers can be used to clarify and confirm
certain important mechanistic details.
Methyl (-CH3) adsorbed on Ni has been shown to not react
4
0
with surface-bound hydrogen. It only reacts with hydrogen
dissolved in the Ni bulk phase. An illustration of methyl and
other surface species discussed here is given in the Supporting
Information.
Carbon as well as hydrogen dissolves in the typical FT
catalyst metals. Thus it is possible that the source of the
observed C2 product (C2Hn) is reaction of surface methyl with
dissolved carbon analogous to the reaction of surface methyl
with dissolved hydrogen. Methyl, methylene, and methyne are
all known to adsorb at the same surface site, nestled in the
#
T term is probably strongly dependent on a number of
parameters. The above rate law is the simplest hypothesis
consistent with the literature. Given the lack of information
needed to determine ∆gg, it is difficult to test this hypothesis
in greater detail. The principal weakness of the above formula-
tion is its inability to predict the effect of the partial pressure
of CO (at constant aC) that has been observed.26
4
1
hollow between three adjacent metal atoms. It is reasonable
to assume that higher alkyl species will bind in the same manner
to the same site (which is known to be true for ethylidyne).
Thus the addition of bulk dissolved carbon to produce ethylidyne

4172 J. Phys. Chem. B, Vol. 102, No. 21, 1998
Nolan et al.
Tavares and co-workers46 show that the addition of Cu to Ni
catalysts greatly reduces the rate of carbon deposition from CO-
H2 mixtures without significantly changing the rate of metha-
nation. That is as expected, since hydrogen solubility in Cu-
Ni alloys is not dependent on composition for Ni-rich alloys.47
Also, the methanation rates given for constant CO partial
1
/2
pressures fit well to PH2 . Carbon is far less soluble in Cu
than Ni, and solubility varies smoothly with composition. The
observation that carbon deposition rates fell as Cu was added
is consistent with the need for carbon to dissolve in the catalyst
before depositing. That Cu is not effective as an FT catalyst,
unlike metals such as Ni, Co, and Fe, in which carbon is much
more soluble, implies a role for bulk-dissolved carbon in forming
polymerization active surface species that lead to FT products
rather than methane.
Figure 7. The molar methane yield from Vannice,39 for H
of 1.6, versus metal-dissolved hydrogen availability estimated as ln(H
solubility × NCO ).
/CO ratio
2
Maitlis and co-workers27 show in model compounds that
-
3/2
carbon is preferentially incorporated into hydrocarbons from
methylene, not methyl. The metal must have reasonable
amounts of methylene in equilibrium with methyl on the surface
in order to be active as a FT or carbonization catalyst. In
(methyl methyne) occurs with the initial methyl bound to its
equilibrium adsorption site and produces ethylidyne already
bound to its equilibrium surface adsorption site. This could
also be the source of the vinyl that initiates further FT synthesis.
48
support of this, Alstrup and Tavares argue that during
deposition of carbon from methane on Fe and Ni, the conversion
of surface methyl to surface methylene is rate limiting. The
role of promoters and alloying additions may be to control the
Considering the above, we believe that the branching of
products to methane (CH4) or higher hydrocarbons (or the chain
termination probability for the higher hydrocarbons) is controlled
by the amount of hydrogen dissolved in the metal. The more
hydrogen available in solution, the more rapidly it adds to
surface methyl to form methane. Initially formed surface-bound
methyl will be hydrogenated before it can start down the FT
chemistry path. When dissolved hydrogen available to surface
species is limited, higher hydrocarbons have an opportunity to
form. Figure 7 gives the response of methane yield (as
4
9
relative ratios of methylene and methyl. Zaera discusses the
chemistry of surface bound C H ’s (1 e n e 3) and shows that
1
n
they are all close in energy and interconvert readily.
Orbital symmetry requirements (the Woodward-Hoffmann
rules) have been analyzed for the reaction of two metal-carbon
50
σ bonds to form a C-C bond. This “2+2” reaction is not
allowed for carbon or hydrogen atoms bonded to different metal
atoms. However, the reaction is allowed, and often observed,
for carbon or hydrogen atoms when both are bonded to the same
metal atom (in which case it is a reductive elimination).
39
determined by Vannice for the group VIII metals) to the
estimated availability of bulk-dissolved hydrogen at active sites.
Methane production is shown to increase with dissolved
hydrogen availability. The availability to an active site of
hydrogen dissolved in the catalyst metal is estimated as the
natural log of hydrogen solubility in the metal (atoms per
volume) times the diffusion volume. Hydrogen solubility values
used for Fe, Pt, Pd42 and Co, Ni are those for the temperature
at which the Vannice catalytic reaction data were taken.
Diffusion volume is the cube of diffusion distance, which is
proportional to the square root of the residence time. Residence
Presumably, on a metal surface, forward and reverse reductive
elimination (a 2+2 reaction) is symmetry allowed as long as
the surface-bound species are able to come close enough that
they are both bound to one common metal atom. The 2+2
reactions are symmetry forbidden if the two surface-bound
species cannot come close enough to share a common metal
atom. See the Supporting Material for further details.
Methyl and hydrogen can be bonded to the same metal atom
if a dissolved hydrogen atom occupies the interstitial site directly
below the 3-fold surface site occupied by the methyl. Adsorp-
tion or desorption of methane thus requires enough activation
energy to move the hydrogen atom from the interstitial site to
the surface, as well as to cause reaction (i.e., enthalpy terms
43
39
time is the inverse of turnover number, NCO, given by Vannice.
Thus we take the estimated dissolved hydrogen availability to
-
3/2
an active site as ln(H solubility × NCO ).
Palladium has an exceptionally high hydrogen solubility (2.2
-
4
-8
at. % compared to 5 × 10 to 10 % for the other group VIII
metals at 300 °C), and methane is the only product observed
from Pd under FT conditions.39 As seen in Figure 7, the
hydrogen availability in Pd is well above the level predicted to
lead to 100% methanation. Also, Ru (normally a FT catalyst
from dissolution, diffusion, and CH interconversion). Carbon
n
also dissolves interstitially in metals and could thus bond to
the same metal atom as a surface CH . Reductive elimination
n
would then form a C H surface moiety that could rearrange to
2
n
vinyl and take part in FT chemistry.
+
with a good yield of C2 ) becomes selective for methane as
The product stereochemistry and competitive branching ratios
CO is reduced to trace levels, where dissolved carbon falls as
27
reported by Maitlis and co-workers are consistent with orbital
1
/2
PCO, but dissolved hydrogen falls more slowly, as PH2 . This
gives a theoretical explanation for the industrial practice of
symmetry control of reaction between carbon species bonded
to two different metal atoms. The addition of a saturated alkyl
group to methylene and the insertion of methyl into the sp2
carbon to metal σ bond of a surface-bound vinyl group are both
forbidden on orbital symmetry grounds.
The addition of vinyl to methylene to form a tridentate allyl
product is an allowed reaction. This is illustrated for a metal
surface in the Supporting Information. A 1,3 hydrogen shift to
regenerate surface-bound vinyl is also symmetry allowed. Mass
spectral data kindly provided by Maitlis do not appear consistent
+
running FT plants at high total pressure, since C2 yield
1
/2 44
increases as PCO and methane yield increases only as PH2
.
Khassin and co-workers45 observe that, under constant
reaction conditions, the chain termination probability depends
on particle size for Co catalysts in the same way that hydrogen
solubility depends on Co particle size. This again implies that
methane formation and chain termination occur when a dis-
solved hydrogen atom reacts with an adsorbed surface species.

Carbon Deposition and Hydrocarbon Formation
J. Phys. Chem. B, Vol. 102, No. 21, 1998 4173
with a tridentate allylic intermediate. Some transition state in
which methylene addition to vinyl and a 1,3 hydrogen shift occur
at the same time is necessary, since the chain termination
probability in FT synthesis stays roughly constant over two
broad ranges of carbon number. If the metal surface is a catalyst
for isomerization of a metal-2-ene intermediate to metal-1-ene,
which could then add another methylene, then the 3-ene, 4-ene,
etc., species should also form. These could not add methylene.
A longer chain would have more positions for the double bond,
which would spend proportionately less time at position 1, bound
to the metal surface. It is only this surface-bound 1-alkene that
can add a further methylene group and extend the carbon chain.
Thus, if the double bond could be isomerized, it is reasonable
to expect that chains would grow more slowly as they become
longer, and the chain growth probability would decrease as
carbon number increased (since there is no reason to expect
the rate of chain termination to depend on length). However,
the chain growth probability is observed to maintain a constant
value over a wide range of carbon numbers, so we do not believe
that a monodentate allylic intermediate forms and later isomer-
izes.
stabilized against decomposition or reaction to form certain
54
intermediates. Typical surface science conditions are equiva-
9
lent to about 1 part in 10 H2 at atmospheric pressure.
Dehydrogenation is strongly favored, and carbon is the expected
product. Under FT conditions the equilibrium is reversed as
there is much more hydrogen. Thus ethylidyne should be the
precursor to vinyl under FT conditions instead of the product
of vinyl decomposition as it is under vacuum. For the typical
FT yield minimum at C2, we assume that ethylidyne or some
intermediate on its route to vinyl can react with some surface
CHn and form a C3 product that is a FT polymerization
intermediate. This unknown reaction must involve both carbons
of the ethylidyne, or methyne would also undergo it and there
would be no dip at C2.
The mechanism hypothesized above explains why FT prod-
ucts are formed at high relative values of hydrogen fugacity to
aC (e.g., 275 °C, H2/CO ) 2) while carbon filaments or
nanotubes with equilibrium controlled morphology are formed
over similar catalysts at low relative ratio of hydrogen fugacity
to aC (e.g., our experimental conditions, or 90% H2, 10% CH4
at 1050 °C). All of the surface-bound C1Hn (1 e n e 3) species
4
9
The orbital symmetry constraint does not directly require that
are in equilibrium on the surface. If products heavier than
methane are to form, hydrogen availability must be restricted
so that reasonable concentrations of methyne and methylene
exist to react with vinyl (discussed in the Supporting Informa-
tion).
2
3
an sp carbon rather than an sp carbon add to methylene. It
simply requires that the carbon adding also be part of a C-C
π bond that participates in the reaction in a concerted manner,
3
and an sp carbon cannot also be part of a π-bonded system.
The difficulty of decomposing phenyl model compounds
similar to that for methyl compounds) is presumably because
2
7
At low hydrogen fugacity, multidentate hydrocarbons will
add carbon from the metal phase, forming additional growth
centers, and react with themselves to form polycyclic structures.
These surface hydrocarbon islands can reach equilibrium through
repeated addition and loss of hydrogen and carbon atoms
dissolved in the metal catalyst. This dynamic process allows
the frusta in filamentssfor example, C30,000H400 moleculessto
achieve the exact shape that allows them to stack into the
filament structure and have an angle θ determined by the
equilibrium availability of hydrogen.
(
the double bond of the vinyl moiety is involved in the
reactionsas required by orbital symmetry considerationssand
thus the aromatic character of the benzene ring is temporarily
lost in the activated complex. Thus, much more activation
energy would be required to cause methylene addition at a
reasonable rate or, alternatively, to activate energetic multistep
processes that lead to “forbidden” products.
The presumption of orbital symmetry control also leads to
the correct conclusion that group Ib and IIb elements should
be catalytically inactive for FT synthesis. Symmetry require-
ments for all of the candidate reactions require that two different
d orbitals on a single metal atom participate in the reaction,
Nanotube growth in the absence of hydrogen occurs by the
addition of carbon atoms diffusing through the catalyst metal
to the growing edges of aromatic graphene sheets. With
hydrogen present, the edge carbons in the growing graphene
9
10
3
something not possible with d or d metals.
sheet can be hydrogenated to a tetrahedral sp state so that the
Thus we hypothesize that chain growth starts with the
formation of ethylidyne by addition of dissolved carbon to
surface methyl. This ethylidyne then isomerizes to vinyl. Chain
growth continues by concerted addition of surface-bound
methylene to surface-bound alk-1-enen to form surface-bound
alk-1-enen+1. Growth is terminated by addition of metal bulk
dissolved hydrogen to the metal-carbon σ bond.
free valences can point down and bind to the metal surface while
the graphene sheet lies parallel to it. Details of aromatization
are discussed in the Supporting Information.
5. Kinetics of Heterogeneous C-H Reactions. Without
hydrogen, nanotubes grow edge-on to the catalyst metal surface
and clearly must grow by solution and diffusion of carbon atoms
through the bulk metal. There are no methylenes to add onto
the carbon since no hydrogen is present. Kinetics derived from
this model is discussed in section 3 above. With hydrogen, in
the limiting case of methanation, carbon is a surface species
This mechanism does not explain the relative lack of C2
versus C3 product normally found in FT synthesis. Addition
of various sources of vinyl was found to dramatically increase
51
+
C2 yield to well above C3 yield. Yet at higher carbon numbers
and C2 products cannot form from CHn-CHn surface reactions.
+
(
C5 ), there was still an Anderson-Schultz-Flory product
In Fischer-Tropsch catalysis, carbon is present in surface
species, and chain growth occurs by carbon moieties finding
each other through surface diffusion. We believe that the C2
initiator for chain growth is formed by reaction of surface methyl
with a bulk-dissolved carbon atom. If this is so, then the rate
of forming surface C2, and hence the branching between
methanation and FT products, is also directly related to solution
of carbon atoms into the bulk metal.
distribution consistent with constant chain propagation (or
termination) probability. To explain the lack of C2 product in
typical FT synthesis would require methylene to react with some
rearrangement product of ethylidyne before it can isomerize to
vinyl.
In the surface science literature ethylidyne is observed to form
52
under vacuum conditions from vinyl iodide on various metals.
Under these conditions, ethylidyne is believed to form through
a vinyl intermediate regardless of the precursor.53 For ethyli-
dyne layers with coadsorbed H and CO in equilibrium with gas-
phase H2 and CO at elevated pressures, the ethylidyne was
As hydrogen becomes less available than in FT chemistry,
the chain growth probability becomes unity, and the hydrocar-
bons will lose hydrogen back to the metal until they become
graphene. Diffusion of hydrogen through metals is much faster

4174 J. Phys. Chem. B, Vol. 102, No. 21, 1998
Nolan et al.
than that of carbon (the ratio of their diffusion constants in Ni
at 500 °C is about 3 × 10 ). Hydrogen concentration or activity
for their assistance, and Ib Alstrup for helpful observations.
Support was provided by Minerva Laboratories, Carbomite
Company, and in part by the NASA/UA Space Engineering
Research Center.
6
gradients are unlikely in a catalyst particle. Adequate hydrogen
should be available at the carbon to metal particle interface to
form whatever hydrocarbon moieties are sterically or mecha-
nistically required at this interface. Under various conditions
hydrocarbon surface species are abundant and have much higher
mobility than carbon does through the bulk metal. Thus in
filaments there may be regimes where carbon is delivered to
the growing edge by diffusion of surface species, and the
filament is filled in by bulk carbon diffusion through the catalyst.
Meanwhile the uniform hydrogen concentration in the catalyst
particle facilitates restructuring and annealing of the growing
carbon layers.
References and Notes
(
1) Walker, P. L.; Rakszawski, J. F.; Imperial, G. R. J. Phys. Chem.
1
959, 63, 133-149.
(2) Baker, R. T. K.; Harris, P. S. The Formation of Filamentous Carbon.
In Chemistry and Physics of Carbon; Walker, P. L., Thrower, P. A., Eds.;
Marcel Dekker: New York, 1978; Vol. 14, pp 83-165.
(
3) Jablonski, G. A.; Geurts, F. W.; Sacco, A.; Biederman, R. R. Carbon
1
992, 30, 87-98.
(4) Rodriguez, N. M. J. Mater. Res. 1993, 8, 3233-3250.
(5) Yang, R. T.; Chen, L. P. J. Catal. 1989, 115, 52-64.
(6) Nolan, P. E.; Schabel, M. J.; Lynch, D. C.; Cutler, A. H. Carbon
1
995, 33, 79-85.
Conclusion
(
(
(
7) Murayama, H.; Maeda, T. Nature 1990, 345, 791-793.
8) Tibbetts, G. G. J. Cryst. Growth 1984, 66, 632.
9) Ivanov, V.; Nagy, J. B.; Lambin, P.; Lucas, A.; Zhang, X. B.; Zhang,
Theoretically derived approximate thermodynamic expres-
sions for the relationship between filament cone angle and
hydrogen partial pressure, for the Gibbs energy of carbon
formations, and for the inner radius of nanotubes match
experimental results reasonably well. They show that the
morphologies of carbon deposits are largely equilibrium con-
trolled. This increased understanding allows control of deposit
morphology and, hence, properties. Materials properties might
be tailored by controlling the hydrogen concentration when
making filaments and nanotubes catalytically, so as to control
the orientation of graphite basal planes.
X. F.; Bernaerts, D.; Van Tendeloo, G.; Amelinckx, S.; Van Landuyt, J.
Chem. Phys. Lett. 1994, 223, 329-335.
(10) Bacon, R. J. Appl. Phys. 1960, 31, 283-290.
(
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