trunk/nanoglass/introduction.tex

 \section{Introduction}

Excitation of the plasmon resonance in metallic nanoparticles has
attracted enormous interest in the past several years.  This is partly
due to the location of the plasmon band in the near IR for particles
in a wide range of sizes and geometries.  (Living tissue is nearly
transparent in the near IR, and for this reason, there is an
unrealized potential for metallic nanoparticles to be used in both
diagnostic and therapeutic settings.)  One of the side effects of
absorption of laser radiation at these frequencies is the rapid
(sub-picosecond) heating of the electronic degrees of freedom in the
metal.  This hot electron gas quickly transfers heat to the phonon
modes of the lattice, resulting in a rapid heating of the metal
particles.

Since metallic nanoparticles have a large surface area to volume
ratio, many of the metal atoms are at surface locations and experience
relatively weak bonding.  This is observable in a lowering of the
melting temperatures and a substantial softening of the bulk modulus
of these particles when compared with bulk metallic samples.  One of
the side effects of the excitation of small metallic nanoparticles at
the plasmon resonance is the facile creation of liquid metal
droplets.  

Much of the experimental work on this subject has been carried out in
the Hartland and von~Plessen
groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003yf,HuM._jp020581+,plech:195423}
They have [BRIEF SURVEY OF THE EXPERIMENTAL WORK]


Since these experiments are often carried out in condensed phase
surroundings, the large surface area to volume ratio makes the heat
transfer to the surrounding solvent also a relatively rapid process.
In our recent simulation study of the laser excitation of gold
nanoparticles,\cite{} we observed that the cooling rate for these
particles (10$^11$-10$^12$ K/s) is in excess of the cooling rate
required for glass formation in bulk metallic alloys.  Given this
fact, it may be possible to use laser excitation to melt, alloy and
quench metallic nanoparticles in order to form metallic glass
nanobeads.  

To study whether or not glass nanobead formation is feasible, we have
chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a
model system because it is an experimentally known glass former and
has been used previously as a theoretical model for glassy
dynamics.\cite{Vardeman2001} 

XXX stuff from ORP

In the sections below, we describe our
modeling of the laser excitation and subsequent cooling of the
particles in silico to mimic real experimental conditions.


constructing and relaxing the eutectic composition (Ag$_6$Cu$_4$) on a
FCC lattice with a lattice constant of 4.09 \AA\ for 20, 30 and 40
\AA\ radius nanoparticles. The nanoparticles are melted at 900 K and
allowed to mix for 1 ns. Resulting structures are then quenched using
a implicit solvent model where Langevin dynamics is applied to the
outer 4 \AA\ radius of the nanoparticle and normal Newtonian dynamics
are applied to the rest of the atoms. By fitting to
experimentally-determined cooling rates, we find that collision
frequencies of 3.58 fs$^-1$ for Ag and 5.00 fs$^-1$ for Cu lead to
nearly exact agreement with the Temperature vs. time data. The cooling
rates are therefore 2.37 x 10$^13$ K/s, 1.37 x 10$^13$ K/s and 1.06 x
10$^13$ K/s for the 20, 30 and 40 \AA\ radius nanoparticles
respectively.

Structural Measures for Glass Formation

Characterization of glassy behavior by molecular dynamics simulations
is typically done using dynamic measurements such as the mean squared
displacement, <r2(t)>. Liquids exhibit a mean squared displacement
that is linear in time. Glassy materials deviate significantly from
this linear behavior at intermediate times, entering a sub-linear
regime with a return to linear behavior in the infinite time
limit. Diffusion in nanoparticles differs significantly from the bulk
in that atoms are confined to a roughly spherical volume and cannot
explore any region larger than the particle radius. In these confined
geometries, <r2(t)> in the radial direction approaches a limiting
value of 6R2/40.

However, glassy materials exhibit strong icosahedral ordering among nearest-neghbors in contrast to crystalline or liquid structures. Steinhart, et al., defined an orientational bond order parameter that is sensitive to the nearest-neighbor environment by using invariant combinations of spherical harmonics Yl,m(?,?).[10] Spherical harmonics involving the Y6,m(?,?) are particularly sensitive to icosohedral order among nearest neighbors as can be seen in the cartoon to the left. The second and third-order invariants, Q6 and W6 are used to determine the level of icosahedral order present in a quenched nanoparticle. Perfect icosahedral structures have a maximal value of 0.663 for Q6 and -0.170 for W6. A plot of the distributions of Q6 and W6 with cooling temperature indicates increasing icosahedral order with decreasing temperature. This is a clear indication that glassy structures are forming as the nanoparticles are quenched.
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2	gezelter	3217
3			Excitation of the plasmon resonance in metallic nanoparticles has
4			attracted enormous interest in the past several years. This is partly
5			due to the location of the plasmon band in the near IR for particles
6			in a wide range of sizes and geometries. (Living tissue is nearly
7			transparent in the near IR, and for this reason, there is an
8			unrealized potential for metallic nanoparticles to be used in both
9			diagnostic and therapeutic settings.) One of the side effects of
10			absorption of laser radiation at these frequencies is the rapid
11			(sub-picosecond) heating of the electronic degrees of freedom in the
12			metal. This hot electron gas quickly transfers heat to the phonon
13			modes of the lattice, resulting in a rapid heating of the metal
14			particles.
15
16			Since metallic nanoparticles have a large surface area to volume
17			ratio, many of the metal atoms are at surface locations and experience
18			relatively weak bonding. This is observable in a lowering of the
19			melting temperatures and a substantial softening of the bulk modulus
20			of these particles when compared with bulk metallic samples. One of
21			the side effects of the excitation of small metallic nanoparticles at
22			the plasmon resonance is the facile creation of liquid metal
23			droplets.
24
25			Much of the experimental work on this subject has been carried out in
26			the Hartland and von~Plessen
27			groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003yf,HuM._jp020581+,plech:195423}
28			They have [BRIEF SURVEY OF THE EXPERIMENTAL WORK]
29
30
31			Since these experiments are often carried out in condensed phase
32			surroundings, the large surface area to volume ratio makes the heat
33			transfer to the surrounding solvent also a relatively rapid process.
34			In our recent simulation study of the laser excitation of gold
35			nanoparticles,\cite{} we observed that the cooling rate for these
36			particles (10$^11$-10$^12$ K/s) is in excess of the cooling rate
37			required for glass formation in bulk metallic alloys. Given this
38			fact, it may be possible to use laser excitation to melt, alloy and
39			quench metallic nanoparticles in order to form metallic glass
40			nanobeads.
41
42			To study whether or not glass nanobead formation is feasible, we have
43			chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a
44			model system because it is an experimentally known glass former and
45			has been used previously as a theoretical model for glassy
46			dynamics.\cite{Vardeman2001}
47
48			XXX stuff from ORP
49
50			In the sections below, we describe our
51			modeling of the laser excitation and subsequent cooling of the
52			particles in silico to mimic real experimental conditions.
53
54
55			constructing and relaxing the eutectic composition (Ag$_6$Cu$_4$) on a
56			FCC lattice with a lattice constant of 4.09 \AA\ for 20, 30 and 40
57			\AA\ radius nanoparticles. The nanoparticles are melted at 900 K and
58			allowed to mix for 1 ns. Resulting structures are then quenched using
59			a implicit solvent model where Langevin dynamics is applied to the
60			outer 4 \AA\ radius of the nanoparticle and normal Newtonian dynamics
61			are applied to the rest of the atoms. By fitting to
62			experimentally-determined cooling rates, we find that collision
63			frequencies of 3.58 fs$^-1$ for Ag and 5.00 fs$^-1$ for Cu lead to
64			nearly exact agreement with the Temperature vs. time data. The cooling
65			rates are therefore 2.37 x 10$^13$ K/s, 1.37 x 10$^13$ K/s and 1.06 x
66			10$^13$ K/s for the 20, 30 and 40 \AA\ radius nanoparticles
67			respectively.
68
69			Structural Measures for Glass Formation
70
71			Characterization of glassy behavior by molecular dynamics simulations
72			is typically done using dynamic measurements such as the mean squared
73			displacement, <r2(t)>. Liquids exhibit a mean squared displacement
74			that is linear in time. Glassy materials deviate significantly from
75			this linear behavior at intermediate times, entering a sub-linear
76			regime with a return to linear behavior in the infinite time
77			limit. Diffusion in nanoparticles differs significantly from the bulk
78			in that atoms are confined to a roughly spherical volume and cannot
79			explore any region larger than the particle radius. In these confined
80			geometries, <r2(t)> in the radial direction approaches a limiting
81			value of 6R2/40.
82
83			However, glassy materials exhibit strong icosahedral ordering among nearest-neghbors in contrast to crystalline or liquid structures. Steinhart, et al., defined an orientational bond order parameter that is sensitive to the nearest-neighbor environment by using invariant combinations of spherical harmonics Yl,m(?,?).[10] Spherical harmonics involving the Y6,m(?,?) are particularly sensitive to icosohedral order among nearest neighbors as can be seen in the cartoon to the left. The second and third-order invariants, Q6 and W6 are used to determine the level of icosahedral order present in a quenched nanoparticle. Perfect icosahedral structures have a maximal value of 0.663 for Q6 and -0.170 for W6. A plot of the distributions of Q6 and W6 with cooling temperature indicates increasing icosahedral order with decreasing temperature. This is a clear indication that glassy structures are forming as the nanoparticles are quenched.