opposed flow flame synthesis of molybdenum oxide ... · the nanorods growth model involves monomer...

Paper # 070HE-0344 Topic: Homogeneous combustion, sprays & droplets

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8th

U. S. National Combustion Meeting

Organized by the Western States Section of the Combustion Institute

and hosted by the University of Utah May19-22, 2013

Opposed Flow Flame Synthesis of Molybdenum Oxide

Nanostructures

S. Srivastava1, W. Merchan-Merchan

2, A.V. Saveliev

1, M. Desai

2

1Department of Mechanical and Aerospace Engineering

North Carolina State University 2School of Aerospace and Mechanical Engineering

University of Oklahoma

An opposed laminar flow flame formed with methane/acetylene and oxygen enriched-air was employed to produce molybdenum

oxide nanostructures directly in the gas phase. The composition of the fuel and oxidizer to form the flame was

96%CH4+4%C2H2 and 50%O2/50%N2, respectively. Raw material was introduced into oxidizer side of the flame in the form of

solid molybdenum wires with 99% purity. The high temperature and the oxygen rich chemical environment of the flame resulted

in fast surface oxidation of the probes and material etching from their surfaces. Upon their interaction with the flame, the probes

generated molybdenum trioxide vapors. The vapors were transported in the direction of the stagnation plane of the flame and

reduced to molybdenum dioxide as they entered the low temperature fuel rich zone. The velocity gradient and thermophoretic

forces in the flame affected the transport of the molybdenum dioxide precursors. These precursors in the gas phase formed

nanostructures that were thermophoretically collected from the flame volume. Essential morphological variations of generated

nanomaterials were observed depending on flame and probe parameters. The distance of the collection plane from the

molybdenum probe also played an important role in the morphology of generated nanoforms. The molybdenum probes with

diameters of 0.75 mm and 1 mm were used to achieve two distinct synthesis conditions. The variation of probe diameter affected

probe temperature and resulted in different supersaturation levels of molybdenum dioxide vapors. Experiments with 1.0 mm

diameter corresponded to lower supersaturation levels and resulted in the synthesis of well-defined convex polyhedron

nanocrystals and nanorods. Higher material etching rates and, hence, supersaturation levels were obtained with 0.75 mm

diameter probes. These conditions resulted in synthesis of mainly spherical molybdenum oxide nanomaterials agglomerated in

soot-like fractal aggregates. The effect of flame parameters and material concentration on shape and structure of generated

nanomaterial is also studied numerically. The underlying mechanisms governing the morphological variation of molybdenum

oxide nanocrystals are analyzed using the following steps: monomers formation, nucleation, and growth. The nucleation model

is based on the classical nucleation theory, and the growth model considers agglomeration and diffusion in the varying thermal

environment using thermophoretic analysis. The model predictions are in good qualitative agreement with the experimental data.

1.Introduction

Gas phase combustion synthesis is a process especially suited for the scalable and energy-efficient production of

nanoparticles. It provides great control on the size and shape of the particles due to the ability to adjust various

flame parameters including the fuel type, amount of oxygen in the oxidizer stream and strain rate. This method also

ensures self-purity of the products. Two conventional methods of combustion nanoparticle synthesis are the aerosol

and the spray pyrolysis method. These methods differ in the manner in which the raw material is introduced into the

flame volume. The aerosol method involves the delivery of precursors in the gaseous state (Jensen et al., 2000;

Stark et al., 2000) whereas in spray pyrolysis the precursor is introduced in the liquid form as a fine spray (Tani et

al., 2002; Qin et al., 2007). Transition metal oxide nanoparticles have some favorable distinct qualities like catalytic

activity (Beck and Siegel, 1992), electronic properties and superparamagnetic behavior (Zacharia et al., 1995).


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Hence they have potential applications in chemical industries and recording media (Dhas and Gedanken, 1997;

Anpo et al., 1988; Liu et al., 1996; Zhou et al., 2003).

There are a number of studies on the application of flames for synthesis of one-dimensional carbon nanostructures

such as carbon nanotubes and nanofibers. However volumetric synthesis of one-dimensional transition metal oxide

(TMO) nanostructures is scarce [Height et al., 2006]. In this paper we report the volumetric synthesis of

molybdenum oxide nanomaterials using the flame-gradient synthesis method. A molybdenum probe flame

interaction is employed for generation of metal oxide precursors in the oxygen-rich part of the flame resulting in the

volumetric formation of elongated and spherical Mo oxide nanocrystals in the lower part of the flame where the

temperature is reduced. The synthesis is performed in a counter-flow oxy-flame with a rapid variation of

temperature and chemical composition that synergistically produces an ideal environment for synthesis of high-

purity nanomaterials with controlled structure, morphology, and composition.

Many efforts have been made to model the process of nanostructure growth as it is so susceptible to temperature,

residence time, and precursor concentration. Most of the modeling work has been focused on agglomeration and

sintering describing spherical particle size evolution and morphology (Kruuis et al., 1993; Tsantilis and Pratsinis,

2000). Although many numerical studies have been done in the area of whisker growth (Gretz, 1967; Sears, 1955),

they are particularly focused on the growth of nanorods on the surface of a substrate by a vapor-liquid-solid

mechanism. The numerical study presented here aims to comprehend the underlying mechanism of volumetric

growth of molybdenum oxide nanorods in the gas phase and has been validated by the experimental work done, in a

qualitative manner.

2. Methodology for the experimental studies

2.1 Experimental Setup

The details of the experimental setup have been elucidated in the earlier works (Yuan et al., 2001; Yuan and Hu,

2001; Vander Wall, 2000; Merchan-Merchan et al., 2002; Merchan-Merchan et al., 2006; Saveliev et al., 2003). A

counter-flow oxy-methane diffusion flame is employed for the synthesis of spherical and elongated inorganic

nanocrystals. The counter-flow flame is formed by two opposite gas streams. The fuel (96%CH4 + 4%C2H2) is

supplied from the top nozzle and the oxidizer (50%O2 + 50%N2) is introduced from the bottom nozzle. The nozzles

are separated by a distance of 25.4 mm. The fuel and oxidizer flows impinge against each other at a strain rate equal

to 20 s-1

to form a stable stagnation plane, with a diffusion flame established from the oxidized side. Technical

purity methane (98%, AGA Gas Inc.) seeded with atomic absorption purity acetylene (99.8%, AGA Gas Inc.) was

used as a fuel. The oxygen content in the oxidizer stream is controlled by adding oxygen to laboratory dry air

through a mass flow controller. The flows were metered with electronic mass flow controllers providing accuracy

within 1.5%.

A Mo wire (99.95% purity, Signa Aldrich Inc.) was used as a material source for the synthesis of the Mo oxide

nanostructures. Molybdenum probes were inserted into the flame zone parallel to the flame front at various

distances Z from the edge of the fuel nozzle. Molybdenum wires with diameters of d = 1 mm and 0.75 mm were

used as the probes. Thermophoretic sampling technique was employed for collecting the synthesized material

directly from inside the flame volume above the Mo wire.

The electron microscope grids used to capture particles were copper grids with a thin film of pure carbon deposited

on one side of the grid. Collected samples were characterized using transmission electron microscopy (TEM).

Detailed information on the burner, thermophoretic sampling technique, and electron microscopy analysis is

provided elsewhere (Merchan-Merchan et al., 2003; Merchan-Merchan et al., 2004; Beltrame et al., 2001).


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3. Methodology for Numerical studies

A numerical study has been undertaken to discern the mechanism of growth of transition metal oxide nanostructures

and to evaluate the dependence of the entire process on variables such as temperature and chemical gradients, strain

rate and the residence time of the nano-material in the flame. To achieve this purpose the numerical model has been

broken down into two sub-divisions: flame model and growth model.

In the flame model the flame has been modeled using the one-dimensional opposed flow diffusion flame code

Cantera (Goodwin, 2009). The fuel used is 96%CH4+4%C2H2 while the oxidizer is 50%O2/50%N2. A strain rate of

20 s-1

with a distance of 25.4 mm between the two nozzles is used. The calculation of the properties of the counter-

flow flames involves the solution of the coupled mass, momentum, energy and species conservation equations. The

temperature, chemical and velocity profiles given out by this model are subsequently used as input for the growth

model. The nanoparticle growth is subjected to the change in the flame environment and hence affecting its growth.

The general hypothesis for the growth of one-dimensional nanostructures in this process is as follows. The raw

material is introduced into the flame in the form of highly pure molybdenum probes which upon exposure to both

the high temperature and oxidative environment of the flame evaporate (sublimate) in a form of MoO3 vapor. The

vapors are transported by the flame gases that are traveling in the direction of the stagnation plane located in the fuel

side. Reduction to molybdenum dioxide takes place as the vapors approach closer to the fuel end. There is

sufficiently low saturation pressure and the reduced vapors form molybdenum dioxide nuclei which are the initial

monomers for the crystallization of the nanoparticles.

The nanorods growth model involves monomer formation, nucleation and growth. The monomer formation is

through the oxidization and vaporization of the probe material. The nucleation has been modeled on the basis of the

classical nucleation theory (Gibbs, 1928; Volmer and Weber, 1926; Asimov, 2003; Lovette et al., 2008; Christian,

2002; Katz, 1970). As shown by experimental studies the formation of one-dimension nanorods is highly favored

by small supersaturation levels of monomers in the flame (Sunagawa, 2005). These small supersaturation levels

stimulate the growth of nanostructures in one particular direction. The numerical model regards the growth as being

promoted by Vapor-Solid (VS) mechanism.

Newly arriving molecules will continue to deposit on the formed nucleus while the surfaces that have lower energy

start to form, such as the side surfaces. The growth on the rough tips is due to direct impingement of atoms

(Markov, 1941) and the diffusion of atoms from the smooth lateral surfaces (Venables, 1994; Blakely and Jackson,

1962; Dai et al., 2003) whereas lateral surfaces grow by layer growth due to 2D nucleation (Chernov, 1984; Gretz,

1967). At the high temperature of nanoparticle formation the precursor atoms have high mobility. The side surfaces

have low energies and in most cases are not able to prevent the desorption of the incident atoms to the environment.

Although some atoms arriving on the surface are able to diffuse on the surface and nucleate into surface layers thus

resulting in its expansion. The rough morphology present at the tip leads to a rapid accumulation of incoming

molecules. Rapid diffusion of atoms takes place from the low energy smooth surfaces to the rough ends where these

atoms attach themselves to the growth fronts and further facilitate in the one dimensional growth of the

nanostructure.

The model also considers the inclusion of thermophoretic and stokes forces that operate throughout the trajectory of

the particle and affect its residence time and hence its decrease in velocity near the stagnation plane (Reist, 1993).

The three processes i.e. a) direct impingement of atoms on the rough ends b) diffusion of atoms on the nanorod

surface c) 2 D layered nucleation have been schematically depicted in Fig. 1.


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Fig. 1. Schematic of a nanorod showing a) direct impingement of atoms on the rough ends b) diffusion of atoms on

the nanorod surface c) 2-D layered nucleation

3.1 Nucleation

The nucleation model is based on the classical nucleation theory. The nucleation rate is given as

1/ 21/ 2 4/ 32σ αNPv 9x γ 2/ 3

J = 1+ g x exp g x - xg x - xπm kT 2γ 3

where J is the number of nuclei formed per unit time per unit volume, P is the pressure, T is the temperature, m is

the mass per molecule and α is the mass accommodation coefficient. N is the total number of clusters of all sizes per

unit volume. x is the value of x at minimum n(x).

2/ 3n = Nexp xlnS - γxx

Here, S=P/Pe is the supersaturation and 1/ 3 σ2

γ = 36πvkT

with σ being the surface energy and v is the volume of

cluster with x atoms. The terms ( )g x , ( )g x and ( )g x are size-dependent correction factors which have been

introduced by various authors. These factors are zero for the classical nucleation theory. This relation gives us the

total number of nuclei formed as well as the critical size of each nucleus.

3.2 Growth model for the nanorod

3.2.1 Model for the rough growth of the tips

The increase in length of the nanorods proceeds through aggregation of atoms at the ends of the structure. The tips

of the nanorods are rough i.e. they have a lot of kink sites available and therefore they are the preferred locations of

attachment for the incoming atoms. The influx of atoms necessary for the growth of the structures is from two

sources: (i) direct impingement from the atmosphere and (ii) diffusion of atoms from the smooth low energy lateral

sides.

For direct impingement of atoms on the whisker tips the rate of growth is given by:

a

b

c


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P - PR = βdir v

P

2 3P aa ΔU

β = exp -vδ 2πmkT kT

where a is the dimension of kink site, is the spacing of the kink sites ( a / )2 is the geometrical probability of a

building unit arriving at the crystal surface to find a kink site. U is the kinetic barrier for the incorporation of the

building units.

Among the atoms condensing on the whisker sides some of them gain sufficient energy and start to migrate

diffusing to the whisker ends and adding to the overall length of the nanorod. The formation of the diffusion model

is as follows. Let N be the number of atoms condensing on the whisker per cm2/second and let NA be the number of

adsorbed atoms per cm2 on the whisker sides. Thus the diffusion equation is:

2

2

N N N dxA A Adx D dx Ndx

t x

For the steady state assumption this equation becomes –

2A A

2

N NN+ - = 0

D Dτx

where N is the flux of atoms and is the residence time of the atoms on the nanoparticle given by

;2

1exp

P

mKT

EdesN

KT

and desE is the energy of desorption of the atom from the surface of the substrate and D is the diffusion coefficient.

These diffusing atoms migrate to the rough faces of the nanorod and attach themselves further contributing towards

the increase on length of the crystal. The rate of increase of length due to surface diffusion is given by

34a

R = Ndiff A 2πd

and 'AN is the number of atoms reaching the rough ends

N AN = D πdA

x


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3.2.2 Layer growth model for the lateral sides

The lateral sides of the crystal are smooth. The atoms arrive on the surface from the environment and migration of

the atoms starts. Most of the atoms are desorbed into the atmosphere but few that manage to stay on the surface

form clusters through surface nucleation thereby starting a formation of new layers and increasing the nanorod

diameter. Details of this process are given as

*E - E ΔG* des sd 2

J = 4l aNΓN exp expo okT kT

and

1/ 2*

ΔG2Γ =

*24πKTn

2χs* cl =

Δμ

24χ s* c

ΔG =2Δμ

oJ is the rate of two dimensional nucleation, cs is the area occupied by the surface atom, is the specific edge

energy, sdE is the energy of surface diffusion, *2G is the free energy of nuclei formation on the lateral surface and

oN is the density of sites. The lateral rate of the increase in the diameter of the nanorod is therefore given by

R J dLaodia

where a is being the size of incoming monomer, L is the length of nanorod and d is the nanorod diameter.

3.3 Thermophoretic force analysis

As a nanoparticle travels through the flame volume it experiences thermophoretic force ( ThF ) and Stokes force ( StF

) due to the variation in temperature gradients and viscosity which affect the motion of the particle.

2μ d T

F = -0.5πμThρ λ T

where is the dynamic viscosity of the fluid, is the density of the fluid, d is the projected diameter, is the mean

free path and T is the temperature gradient in the flame.

St

3πμvd κn nF =

Cc Where dn is the diameter of the sphere whose projected area is the same as the normal projected area of the

nanoparticle and v is the velocity of the particle,

dsκ = 0.357 + 0.684 + 0.00154ψ + 0.0104An

dn

24L

ψ = ; A = 12

πD


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sd is the diameter of a sphere whose effective surface equals that of the nanoparticle.ψ is the ratio of square of axis

parallel to direction of motion. A is the ratio of the longest axis in the projected area normal to the direction of

motion

21 exp

2

bdC A Qc

d

Q is an empirical constant.

F = -F + mg + Fpar St Th

4. Results and Discussion

A flame method can be characterized as a flame-gradient chemical deposition process representing a unique and

versatile technique for the synthesis of TMO nanostructures. A study of probe-flame interaction for material

synthesis was performed along the axial direction of the counter-flow flame using Mo probes of different diameters

as a material source. The opposed flow flame is characterized by an inner sooty yellow zone rich in carbon species

and an outer blue zone rich in oxygen and oxygen radicals. The flame possesses strong axial gradients of

temperature and chemical species that vary dramatically along the axial direction. The temperature gradients reach

~2000 K/cm and the chemical environment changes rapidly from a hydrocarbon-rich zone on the fuel side of the

flame to the oxygen-rich zone on the oxidizer side (Fig. 2). As a result, the probe position strongly affects the

synthesis process. The results are also affected by the diameter of the probe. The temperature of the probe is always

lower than the local flame temperature due to the radiant and conductive heat losses.

(a) (b)

Fig. 2. Schematic illustrating the volumetric flame synthesis method: (a) cut view of a flame section with

corresponding flow directions and wire inserted in the flame as the metal precursor source; (b) evolution of

molybdenum oxide from vapor phases to well-defined nanocrystals

The metal probe inserted in the flame is heated by convection and cooled by radiation and axial heat conduction.

The enthalpies of molybdenum oxidation and evaporation of molybdenum oxides also contribute to the thermal

balance. As a first approximation, we can neglect the axial conduction losses and contributions of surface chemical

reactions and evaporation. Then, assuming steady state conditions, the energy balance of the probe can be

represented as:

4p f p p phA T -T -σεA T =0


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4p

p f

σεTT = T -

h

where h is the heat transfer coefficient, Ap is the surface area of the probe, is the Stefan-Boltzmann constant, Tp

and Tf are the probe and flame temperature, respectively. The heat transfer coefficient depends on the fluid

properties, the diameter of the probe, and the velocity of the fluid:

nk k

h = Nu = c Red d

where Nu is the Nusselt number, Re is the Reynolds number, k is the thermal conductivity of the fluid. The values

of c = 0.8 and n = 0.28 can be used for a case of forced convection over a cylinder (Morgan et al., 1975).

These equations predict that temperature of the probe is always lower than the flame temperature approaching flame

temperature only in the limit of the infinitely small diameter. Conversely, the probe temperature drops with a

diameter increase. The rates of oxidation and evaporation are strong functions of the probe temperature. As such,

the application of smaller diameter probe will result in higher concentration of molybdenum oxide in the gas phase

affecting the synthesis conditions. The experiments with two probe diameters d = 0.75 mm, and d = 1 mm were

conducted to study the effect of Mo oxide concentrations in the gas phase on the shape and morphology of generated

nanomaterials. It should be noted that a reduction of the probe diameter from 1 mm to 0.75 mm resulted in the

probe temperature increase from 1100 to 1300 ˚C and a great increase in a green flame chemiluminescence induced

by the presence of molybdenum species.

The high temperature flame containing O and OH radicals provides rapid oxidation of the probe inserted in the

flame environment resulting in the formation of metal oxides in high oxidation states. These oxides are evaporated

or sublimated from the surface of the wire and transferred with the gas flow in the direction of the zero flow velocity

plane also referred to as the stagnation plane. As the oxides are transferred across the flame front they can be

chemically transformed, e.g. reduced to lower oxidation states that also typically have lower equilibrium vapor

pressures. In addition, the temperature of the flame is lower near the fuel side. The volumetric synthesis occurs

near the fuel side of the flame and samples of the generated nanomaterials are collected directly from the flame

volume using the thermophoretic sampling technique. The molybdenum probe inserted in the flame is oxidized

forming several characteristic oxide layers with an outermost layer of MoO3 (Merchan-Merchan et al., 2006).

Relatively volatile MoO3 is evaporated, transported by the gas flow across the flame front surface, reduced in the

fuel-rich zone, and condensed downstream in the form of MoO2.

This synergetic action of chemical and temperature gradient creates a synthesis media characterized by

supersaturation ratios as well as kinetic and thermodynamic conditions that are favorable for the synthesis of

structured nanomaterials. The level of the supersaturation can be controlled by the probe diameter while keeping all

other flame parameters unchanged. It is generally accepted that morphology of generated nanocrystals is affected by

the ratio Δμ/kT, where Δμ is the difference of chemical potential between solid and gas phase, k is the Boltzmann

constant, and T is the synthesis temperature [34]. The difference of chemical potential is a function of temperature

and vapor concentration N in the gas phase Δμ(N,T). Thus, the variation of probe diameter in the conducted

experiments directly affects the level of supersaturation in the synthesis zone. Probes with diameters of d = 1 mm

and d = 0.75 mm generate low and high supersaturation levels, respectively, greatly affecting the structure and

morphology of generated nanomaterials as discussed below.


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4.1 Synthesis at low supersaturation levels (d = 1 mm)

The TEM image shown in Fig. 3(a) represents the structures collected thermophoretically from the grid at a distance

of Z = 12 mm from the edge of the fuel nozzle. Material collected at the flame height of 12 mm from the edge of the

fuel nozzle and just 0.5 mm above the surface of the probe shows a high density of ultra-small particles on the

surface of the TEM grid. The ultra-small particles are surrounded by a few heavier nucleated spherical particles as

shown by the black arrows in Fig. 3(a). The spherical particles are less than 8 nm in size. Additional TEM studies

showed that these particles are formed by Mo oxide vapors condensed on the TEM grid during the thermophoretic

sampling procedure. Hence, this flame zone can be characterized as a “molybdenum oxide vapor” zone. The

appearance of molybdenum oxide vapors is due to the very high temperature (~ 2500 ˚C) of the flame in the blue

zone at a position of 12 mm confirming that probe–flame interaction forms molybdenum oxide vapors as almost

immediately as the probe is exposed to the flame environment.

Fig. 3. Result of thermophoretic sampling performed at various flame positions in experiments with 1 mm diameter

Mo probe positioned at Z = 13 mm: (a) metal oxide vapor clusters at Z= 12 mm; (b) nanorods with rectangular

cross-section formed at Z = 10 mm.

The metal oxide vapors travel through the flame as they are carried by the combustion gasses in the direction of the

stagnation plane where they start to form metal oxide nanocrystals. Particles captured using the thermophoretic

sampling technique at Z = 10 mm from the edge of fuel nozzle exhibit exciting and interesting transformation of the

Mo oxide materials in the area of the low temperature flame zone. Figure 3(b) shows a TEM image of the as-

synthesized molybdenum oxide structures collected approximately 2.5 mm from the edge of the 1 mm diameter Mo

probe. The temperature of the probe at this flame position is 1300 ˚C as compared to the flame temperature of 2500

˚C at a height of Z = 12 mm.

Samples collected thermophoretically from inside a flame volume at the flame position of 10 mm from edge of the

fuel nozzle appear to be composed of structures of unique shapes. The structures collected at this flame height are

well-defined convex polyhedron nanocrystals bounded with six faces resembling rectangular parallelepipeds. The


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positions and orientations of these nanoparticles collected at this height of Z = 10 mm are random and hence most of

them are not completely exhibiting their fully grown structures, i.e. they appear to be two dimensional structures of

square or rectangular shape.

A low supersaturation is required for the growth of one dimensional nanorods and well-defined nanocrystals. In

case of nanorods, the selective growth of elongated prismatic structures occurs through preferred material deposition

on the tips of the growing structures where the bonding energy is high. In case of nanocrystals, the planar growth

dominates, and well-defined low bonding energy faces, so called F-faces, are formed. The increase of

supersaturation leads to irregular growth with spherical powders obtained at high supersaturation degrees.

4.2 Synthesis results at high supersaturation level (d = 0.75 mm)

Experiments with a smaller diameter molybdenum probes of d = 0.75 mm were performed to achieve higher

supersaturation levels of molybdenum oxide vapors in the gas phase. Similarly to the 1 mm probe, the 0.75 mm

diameter Mo probe was positioned in the flame height at Z = 13 mm from the edge of the fuel nozzle. The particles

were collected thermophoretically from the flame volume at various flame heights from the edge of the fuel nozzle.

Figure 4 shows low and high resolution TEM images of the particles collected directly within the flame volume.

Compared to the particles collected in the experiments with 1 mm diameter probe, the number of particles

synthesised in this case is undoubtedly higher. The entire surface of the grid is covered with the generated

nanomaterials, as shown in Fig. 4(a).

As the diameter of the probe is reduced, the temperature of the probe increases. This contributes to a higher rate of

molybdenum oxide evaporation from the surface of the molybdenum probe. As a result, higher concentrations of

molybdenum oxides are formed near the probe and then carried away from the surface in the upward direction

towards the stagnation plane with the gas flow. The high concentration of the molybdenum oxides in the gas flow

results in larger amounts of material captured on the microscopic grids with the thermophoretic sampling technique.

Figure 4 shows various TEM images of the particles captured at Z = 10 mm. Fig. 4(a) is a low resolution TEM

image of the particles captured. With higher resolution of the same image at certain area, large amount of highly

agglomerated nanoparticles captured on the grid can be observed, as shown in Fig. 4(b). These particles are

spherical in shapes. The largest spherical crystal is ~80 nm in diameter and the smallest is ~5 nm in diameter.

Figure 4(c) shows high degree of particle agglomeration in other part of the grid sample. The average particle size

for these structures is 500 nm as can be seen from Fig. 4(c).

At a higher resolution of a different area of the same grid, we see the presence of nanostructures with different

shapes and morphologies. In Fig. 4(d), spherical structures are present with many one dimensional nanostructures

surrounding them. Figure 4(e) shows one-dimensional nanorod, different sizes of spherical and cubical

nanocrystals. The strong temperature gradient and varying chemical species concentrations within the flame volume

at this position provide the ideal conditions for the rapid and direct formation of these unique nanostructures.

A high degree of aggregation is observed for the spherical MoO2 particles. In contrast, very low aggregation degree

is observed for well-defined nanocrystals generated in the experiments with d = 1 mm probe. The agglomeration of

spherical particles is enhanced by the following two factors: (i) a high particle concentration resulting in the high

collision rate, and (ii) a high probability of particle attachment due to the surface structure with available high

energy bonding sites.


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Fig. 4. Representative TEM images of structures synthesized using 0.75 mm diameter Mo probe as a material

source: (a) an overview of the as-grown nanostructures in the flame volume; (b,c) highly agglomerated spherically

shaped nanoparticles; (d, e) TEM images showing a presence one-dimensional nanorods and well defined

nanocrystals in certain grid areas.

4.3 Numerical results

Simulations have been carried out for three different cases of supersaturation ratios of molybdenum. The

concentration of molybdenum oxide vapors in the code has been represented by their partial pressure. The precursor

vapors are released into the flame environment where upon sufficient cooling they nucleate to form the building

blocks of the nanostructures. Since saturation pressure is a function of temperature, it starts to reduce as the

temperature lowers down and at suitable position in the flame the material starts to condense. The code tracks the

growth of the nanoparticle as it travels through the flame subjected to the flame velocity and thermophoretic forces.

Three cases have been carried out at partial pressures of the molybdenum oxide vapors including 100 Pa, 500 Pa and

1000 Pa.

The velocity and temperature profiles of the flame as given by Cantera [25] are shown in Figs. 5 and 6. As can be

seen the distance between the two nozzles is 25.4 mm. The fuel nozzle is located at 0 mm and the oxidizer nozzle is

located at 25.4 mm. Hence everywhere in the plots positive values show a direction towards the oxidizer nozzle

whereas negative values show a direction from oxidizer to the fuel side.

As can be seen from the above equations, a higher partial pressure dictates a higher influx of atoms onto the

substrate. This can be conveniently observed in Fig. 7 and Fig. 8 where higher partial pressures of the precursor has

resulted in greater increase in the length as well as diameter of the nanorod. When the monomer concentration is

lessened the nanoparticles grow in a one-dimensional fashion giving rise to nanorods with aspect ratio 73. Contrary

to this when we have a high monomer concentration due to a larger influx of atoms we obtain slightly spherical

shaped nanoparticles with aspect ratio 12. This numerical result is in perfect qualitative agreement with results

obtained from experiments.

Temperature on the other hand has an inverse relation to the atomic flux. Gaining enough kinetic energy at the high

temperature, majority of the atoms on the surface are desorbed into the gas phase. Some of these atoms remain on

the surface and begin to migrate thus diffusing over to the ends of the growing nanorods. This diffusion effect is


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extremely important for the growth of crystals as it tends to have a higher contribution than direct impingement of

atoms from the environment. The difference can be clearly seen in Fig. 9 and Fig. 10. Since the saturation pressure

is an exponential function of temperature therefore the direct impingement rate of atoms is initially low and

increases exponentially as the saturation pressure decreases rapidly. The rate of increase in length by diffusion of

atoms on the other hand is initially high because the length of the nanoparticle in the beginning is smaller than the

diffusion distance. This results in the approach frequency of atoms to the rough ends being high and the frequency

immediately goes down as the length increases beyond the atomic diffusion distance. This approach frequency is

also inversely proportional to the nanorod diameter. This is the cause of a gradual fall in the increase of length by

the diffusion phenomena as the diameter of the nanorod increases.

Fig 5. Velocity profile of the flame as given by Cantera

[25]

Fig 6. Temperature profile of the flame as given by

Cantera [25]

Fig. 7. Variation of length of a nanorod with time.at

three different monomer partial pressures of P = 100

Pa, 500 Pa and 1000 Pa

Fig. 8. Diameter of nanorods a function of time for

different monomer partial pressures of P = 100 Pa, 500

Pa and 1000 Pa.


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Fig 9. Contribution of direct atom impingement towards

rate of increase of length with time at three different

monomer partial pressures

Fig 10. Contribution of atom diffusion towards rate of

increase of length with time at three different monomer

partial pressures

Fig 11. Thermophoretic force with time.

Fig 12. Plot representing velocities of particles at

different positions for three monomer partial pressures

As the nanocrystals travel through the flame volume they are acted upon by the thermophoretic and stokes forces.

The thermophoretic force results from the variation in temperature in the flame. Since the thermophoretic force

depends on the projected diameter of the body, which in this case is greater for higher partial pressures (as higher

partial pressures result in bigger particles) we see in Fig. 11 an increase in the force as the concentration of precursor

increases. This increase in force also results in higher deviations for the particle with larger dimensions i.e. higher

partial pressure. This can be clearly seen in Fig. 12 where the particle generated in a flame with 1000 Pa partial

pressure of monomers has a prominent movement to the fuel side owing to the thermophoretic forces. The small

nanostructure attains a zero velocity and comes to rest sooner than the larger nanostructures. This is due to the

greater mass of the larger nanoparticles. The nanoparticles generated at higher pressures P = 500 Pa and 1000 Pa,

however, have still not come to rest.

Figure 13 shows the variation of the aspect ratio of formed nanostructures at a fixed temperature of 1200 K. The

partial pressure of the monomers represents their concentration in the flame. With increasing the concentration both

the length as well as the diameter of the nanostructure increases. However, as the monomer concentration in the


14

flame increases the shape of the formed nanostructures changes from essentially one-dimensional to spherical.

These preliminary numerical results are in good qualitative agreement with the experimentally observed trends.

Fig. 13. Model predictions for aspect of MoO2 nanorods formed at different monomer concentrations as

represented by the partial pressure of molybdenum oxide vapor at T = 1200 K. The images in the figure are

obtained by experiments which confirm the numerical results i.e. decrease in aspect ratio of the structures with

increasing suparsaturation ratio, from nanorod to spherical nano particles

4. Conclusions

Molybdenum oxide nanomaterials have been synthesized directly in the gas-phase by introducing solid-fed supports

in the form of molybdenum probes in a counter-flow methane oxygen-enriched air flame. The strong temperature

gradient and varying concentrations of chemical species within the flame volume provide the ideal conditions for the

rapid and direct formation of unique nanostructures. The probes placed in the high temperature oxygen-rich zone of

the flame at Z= 13 mm served as a material source. Oxidation of Mo and evaporation of MoO3 occurring in the

lower part of the probe facing the oxygen-rich zone was followed by the reduction to MoO2 and the formation of

molybdenum oxide nanomaterials in the lower temperature, fuel rich zone of the flame. Nanomaterials were

collected thermophoretically from the flame heights of 12, 11 and 10 mm from the edge of the fuel nozzle.

The molybdenum probes with diameters of 0.75 mm and 1 mm were used to achieve two distinct synthesis

conditions. The variation of probe diameter affected probe temperature and resulted in different supersaturation

levels of evaporated molybdenum oxides. Experiments with 1.0 mm diameter probe resulted in synthesis of well-

defined convex polyhedron nanocrystals and nanorods. Higher material etching rates and supersaturation levels

were achieved with 0.75 mm diameter probes resulting in synthesis of mainly spherical molybdenum oxide

nanomaterials agglomerated in soot-like fractal structures. The obtained results suggest that homogeneous synthesis

of one-dimensional inorganic nanomaterials and well–defined nanocrystals in flames can be achieved at low

supersaturation degrees of transferred inorganic materials in the gas phase.

A numerical model has been developed for the growth of one-dimensional nanostructures of molybdenum oxide.

Simulations have been performed and comparisons have been made between three different monomer

concentrations. The numerical model is shown to successfully demonstrate the growth of nanocrystals in different

conditions and have excellent qualitative agreement with the experiments. The model is able to capture the variation


15

of aspect ratios of the nanoparticles and also take into account the thermophoretic and Stokes forces along with the

diffusion, direct impingement and layer growth phenomena.

Ongoing work includes a kinetic model for molybdenum evaporation, predicting the distribution of sizes of

nanorods and also understanding the fuel and strain rate effects on the morphology of the particles.

Acknowledgements

The support of this work by the National Science Foundation through the Collaborative Research Grants: CTS-

0854433 and CTS 0854006 is gratefully acknowledged.

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