Proceedings of CUChE Alumni Symposium 2022
On “Circular Economy on Sustainable Basis: The Role of Chemical Engineers”
CUChEAA ISBN: 978-81-954649-1-3
December 2022 P a g e | 59 Volume 2, Issue 1
Self-Assembly driven Ripening of Nanoparticles
Mona Vishwakarma, Debdip Bhandary
*
Department of Chemical Engineering & Technology, Indian Institute of Technology (BHU) Varanasi
Corresponding author: debdip.che@iitbhu.ac.in
Abstract
The formation and growth mechanism of gold nanoparticles on gold (111) surfaces under the influence of micelles are
being investigated through molecular dynamics simulation. The model system consists of cetyltrimethylammonium
bromide (CTAB) units adsorbed on a gold (111) surface. The CTAB forms cylindrical or spherical micelles in solutions
and adheres to the gold (111) surface. The micelles create a negatively charged zone at their interstitial position, and this
could pave the way to the crystallization of different metals on that particular surface; essentially, it could provide a path to
prepare high-entropy alloy or poly-elemental-nanoparticles in the We have used free energy calculations to find out the
energy barrier that needs to be overcome to achieve a poly-elemental nanoparticle in the solution phase. Strong Au-Br ion
interaction leads to a high energy barrier for the Au atom. The means of lowering the energy barrier is the need for the
hour.
Keywords: nanoparticles, poly-elemental, cetyltrimethylammonium bromide, crystallisation
1. Introduction
Nanoparticles and their assemblies can play a crucial
role in many applications, e.g., optics, electronics
1-6
,
chemical sensors
7-9
, drug delivery
10-12
, catalysis
13-15
,
medical imaging
16
, cancer treatment
9, 17-20
etc. They
possess unique and novel optical, electronic, and
catalytic properties, which are related to their size and
are different from bulk materials. Nucleation is the
process in which nuclei act as templates for crystal
growth. It can change the morphology and size of metal
nanoclusters, which further affects their electrical,
optical, structural, and magnetic properties
21-24
. For
many years, nucleation and growth of nanoparticles have
been described by LaMer-Brust nucleation
mechanisms
25
, Oswald ripening
26
, Finke-Watzky two-
step nucleation mechanism
27
, coalescence and
orientation attachment mechanism
28, 29
and so forth.
These classical theoretical models have been used to
understand the thermodynamic process of nucleation and
growth of nanoparticles. In all the above mechanisms,
the metal nanocrystals start nucleating slowly, followed
by autocatalytic growth. The growth of nanoparticles
depends on the diffusion of atoms from the solution to
the nanocrystal’s surface. Fick’s first law can describe
the flux of atoms. The concentration of the atoms at a
distance from the surface is a critical controlling
parameter. Often, different surfactants are used as a
stabilizer and growth-driving agents of metal
nanoparticles
30-33
. Surfactants are amphiphilic molecules,
form agglomerates and ordered structures in solutions.
Surfactants at lower concentrations form ordered packed
structures at the interfaces, e.g., the vapor-liquid
interface of water. Further increase in the concentration
of surfactant in a solution will lead to micellization. The
most common and successful method for the synthesis of
gold nanorods is the seed-mediated growth mechanism,
which is first developed by murphy et al.
34
to produce
Penta-twinned nanorods Further, it was modified by.
Nikoobakht et al
35
to produce single crystal nanorods.
Electron diffraction analysis and electron microscopy
have been used to determine the structure of gold
nanorods prepared by seed-mediated surfactant-directed
synthesis. Briefly, in this seed-mediated surfactant-
directed synthesis, the growth of nanoparticles is
mediated by the addition of metallic gold atom at the
surface of previously prepared small gold nanoparticles
(seeds) by a controlled reduction of Au(I) species at the
surface of the seeds that grow in an anisotropic way due
to presence of CTAB as growth -driving agent
32
.
However, the aspect ratio of gold nanoparticles increases
with the chain length of the surfactants
36
. Further,
Murphy and co-workers
37
investigated the first model
explaining the origin of the anisotropic growth of gold
nanorods in the presence of aqueous CTAB. They
proposed that the surfactants bind as a bilayer to the
growing nanoparticle and assist in the nanoparticle
elongation via zipping mechanism. Inter-chain packing
Proceedings of CUChE Alumni Symposium 2022
On “Circular Economy on Sustainable Basis: The Role of Chemical Engineers”
CUChEAA ISBN: 987-81-954649-1-3
December 2022 P a g e | 60 Volume 2, Issue 1
of the surfactants assists in the formation of the
nanorods. Jana
38
proposed another model for the
anisotropic growth of gold nanorods, namely the soft
template model. In this model, a seed with a diameter of
1-3 nm can penetrate through the template generated by
elongated CTAB micelles in the growth solution. Then,
the shape of the micelle, that is, the soft template,
induces anisotropy. According to this model, the
temperature and CTAB concentration must be within a
certain range to generate elongated micelles that induce
the formation of gold nanorods. Pérez-Juste et al
39
proposed electrochemical mechanism for gold nanorod
formation. In this mechanism, AuCl
4
-
ions are bound to
cationic micelles, displacing bromide ions. Then, the
reduction of AuCl
4
-
to AuCl
2
-
by ascorbate takes place
on the micelle surface. AuCl
2
-
remains adsorbed to the
micelle. The bounded gold ions are transported to the
growing seed particles. This is controlled by the double-
layer interaction of the cationic micelles with the
micelle-coated gold seed. Perala et al.
39
have used the
two-phase Brust-Schiffrin method (BSM) to synthesize
highly stable gold nanoparticles. In this two-phase
synthesis, the metal precursor (HAuCl
4
for gold) is a
first transfer from an aqueous phase to an organic phase
using tetraoctylammonium bromide (TOAB) as a phase
transfer catalyst (PTC). The particle formation is
initiated by contacting the organic phase with an
aqueous phase of sodium borohydride, a reducing agent.
The nucleation of reduced metal precursors, the growth
of particles, and their capping by alkanethiols lead to the
synthesis of highly stable gold nanoparticles. In the
presence of gold surfaces, the CTAB headgroup tends to
adhere to the gold surface and forms a distorted
cylindrical micelle. Meena et al.
40
have found that the
channel between two micelles provides direct access for
ions to the surface. The authors have shown that the
growth of Au using AuCl
2
-
ions can freely diffuse from
the bulk solution to the gold surface. The aim of the
study is to understand the growth of nanocrystals on the
gold (111) surface with the presence of CTAB
surfactant.
2. Model and Methodology
2.1 Molecular Model
We have used a standard forcefield to model the
conformational energy of CTAB molecules from the
literature
Here,
represents the bonded interactions that
arise from bond stretching (
), bond bending
(
) and torsion (
)
where,
Here, is the bond distance between two atoms, and
is the equilibrium bond length. defines the angle
between three atoms and
is the equilibrium angle.
defines a dihedral of four atoms.
,
,
,
,
, and
are constants.
is the nonbonded interactions that we are
modelled in terms of Lennard-Jones 12-6 (LJ-12-6)
potential to calculate the nonbonded interactions
between the atoms. The LJ pair potential is defined by
where
,
, and
are the potential well depth,
atomic diameter, and the distance between two atoms
and , respectively. All the interaction parameters used
in this study are listed in Table 1 and are taken from the
literature. We use the Lorentz-Berthelot combination
rules for the cross-interaction parameters.
2.2 Simulation Details
The spherical system consists of 90 CTAB molecules
randomly located within a sphere so that the heads point
out and the tails point towards the center of the sphere in
a simulation box of 4 nm × 4nm × 4nm and solvated
with 12000 water molecules by using Packmol
software
41
. CTAB was modeled as a 16-alkyl carbon
chain with a headgroup of trimethylammonium. CH
3
and
CH
2
groups were considered united atoms. The charges
on the united atoms are taken according to the forcefield
data, GROMOS96 53a6.
42
An extended Simple Point
Charge (SPC/E) rigid water model was used to model
the solvent. All MD simulations were performed using
LAMMPS software
43
. Periodic boundaries were
considered in all three directions. The initial
configuration was subjected to energy minimization for
5000 steps of the steepest descent method. A constant
temperature of 300K and a constant pressure of 1 bar
were maintained by the Nosé-Hoover thermostat
(relaxation time is 0.5 picosecond) and the Parrinello-
Rahman barostat (relaxation time is 1.0 picosecond),
respectively. The system was equilibrated in an NPT
ensemble for 1 nano-second. Molecular dynamics
production runs were performed for 5 nano-seconds at
different temperatures. A timestep of 2 femtoseconds
was employed, and trajectory was stored at every 1 pico-
second. In addition, our spherical micelle system was
placed on a gold surface.
3. Results and Discussion
Figure 1 shows the characterization of CTAB micelle in
an aqueous solution. Figure 1a indicates that the micelle
radius formed by 90 molecules is ~2.25 nm. All the alkyl
groups are within the micelle, and water molecules are
rare inside the micelle, as the density of water molecules
is 0 below 1.5 nm. Figure 1b shows the arrangement of
water molecules from the nitrogen atom in the head
group of the surfactant. Water molecules form a
Proceedings of CUChE Alumni Symposium 2022
On “Circular Economy on Sustainable Basis: The Role of Chemical Engineers”
CUChEAA ISBN: 987-81-954649-1-3
December 2022 P a g e | 61 Volume 2, Issue 1
solvation layer around the head group of every surfactant
molecule. Due to heterogeneity in the micelle, the RDF
did not saturate at unity. Figure 1(c) shows that the
radius of gyration of the cationic part of the micelle
decreases with an increase in temperature. Due to
increased kinetic energy, the anion mobility increases, so
the solvation shell becomes weaker. Therefore, the size
of micelles decreases.
Figure 1: (a) Mass density profiles of different segments
as a function of distance from the center of mass of a
CTAB micelle at 300 K (b) Radial distribution functions
(RDFs) of water at 300 K (c) Variation of Radius of
gyration with temperature.
Figure 2: (a) Mass density of N, CH
X
, and H
2
O as a
function of distance from Au(111) gold surface (b)
Charge density of (CH
3
)
3
N
+
-CH
2
-
, Br
-
as a function of
distance from Au(111) gold surface.
In the presence of a gold surface (111), the micelle's
behavior was monitored. The micelles were strongly
adsorbed on the surface. In the density profile, figure 2a,
two sharp peaks of water adjacent to the surface (near
zero), indicating a strong interaction between the surface
and water molecules. However, a peak in nitrogen
concentration (red line) indicates that the micelles
interacted strongly with the first solvation layer. The
micelles are ~4.5nm in diameter, indicating that it is
holding their spherical shape. Since the micelles have a
mobile anion and the micelles are strongly adhered to
the surface, it will be interesting to look into the charge
profile of such a system. In figure 2b, charge density
profiles are shown. The charge density profiles of anions
(blue triangle) and cations (purple square) look
symmetric. However, the overall charge density profile
is not charge-neutral everywhere. A negative charge
density, figure 2b, in the interstitial position of two
micelles is an important break-in. This net charge can
provide additional force to the atoms to get deposited on
the surface. A free energy landscape is being calculated
to justify the process.
Figure 3: Potential mean force with position
We have calculated the potential of the mean force to
understand the energy landscape for the atoms. Many
steered molecular dynamics simulations (~100) were
carried out to construct the PMF shown in figure 3.
Since the interaction between the gold atoms and the
bromide ions are strong, any gold atom will always be
accompanied by bromide ions and its solvation shell. In
the negatively charged zone between the two micelles,
the gold-bromide and its solvation shell will face much
electrostatic repulsion, and thus the force required to
move towards the surface becomes higher. However,
once it reaches near to the surface, the solvation of the
bromide would break, and the gold atoms can be
deposited, and it will release the energy of ~0.2557.
4. Conclusion
Our work has shed more light on micellar structure of
CTAB in solution and on adsorption of species on a
surface. A relatively small number of bromide ions on
the gold surface leads to the formation of adjacent
adsorbed micelles on it. The formation of adsorbed
cylindrical micelles with inter-micellar channel allows
the gold atom to reach on the gold surface and is
therefore proposed to be the driving force for the growth
of nanocrystals A molecular dynamic simulation-based
investigation is carried out to understand the growth of
nanocrystals in the presence of micelles. The work
provides the free energy landscape to understand the
growth mechanism of nanocrystals on the gold (111)
surface with the presence of CTAB surfactant.
Acknowledgment:
Param Shivay Supercomputing facility is used to carry
out the simulations. DB acknowledges the initial
research grant from IIT (BHU) Varanasi, and the Start-
up research Grant from SERB, Govt. of India. MV
thanks MHRD, Govt. of India, for the financial
assistantship.
Proceedings of CUChE Alumni Symposium 2022
On “Circular Economy on Sustainable Basis: The Role of Chemical Engineers”
CUChEAA ISBN: 987-81-954649-1-3
December 2022 P a g e | 62 Volume 2, Issue 1
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