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.
Revision:	3217
Committed:	Thu Sep 6 15:02:07 2007 UTC (17 years, 8 months ago) by gezelter
Content type:	application/x-tex
File size:	5068 byte(s)
Log Message:	big changes underway
#	Content
1	\section{Introduction}
2
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.