Subscriber access provided by CMU Libraries - http://library.cmich.edu
Article
Mechanism of Nanorod Formation by Wormlike Micelle Assisted Assembly of Nanospheres Advait Chhatre, Suvajeet Duttagupta, Rochish Thaokar, and Anurag Mehra Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02086 • Publication Date (Web): 08 Sep 2015 Downloaded from http://pubs.acs.org on September 12, 2015
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Mechanism of Nanorod Formation by Wormlike Micelle Assisted Assembly of Nanospheres Advait Chhatre,†,‡ Suvajeet Duttagupta,†,‡ Rochish Thaokar,† and Anurag Mehra∗,† Department of Chemical Engineering, Indian Institute of Techology – Bombay, Powai, Mumbai 400076, India E-mail:
[email protected] Phone: +91(0)22 25767217. Fax: +91 (0)22 25726895
Abstract Hierarchical self-assembly is an elegant and energy-efficient bottom-up method for the structuring of complex materials. We demonstrate the synthesis of maghemite nanorods via directed self-assembly, assisted by wormlike micelles, under controlled shear. The experimental data is analyzed by formulating a “slithering snake” mechanism and simulating it on a cubic lattice, using a coarse-grained Monte Carlo framework. The influence of shear rate, precursor concentration, and length of Kuhn segment on the morphology of the nanorods are examined. Experiments indicate that the shear is necessary for the formation of nanorods, although diameter and length of the nanorods are insensitive to the shear rate, within the range of shear rates investigated. The model adequately captures the features of directional aggregation of particles, and the computed length and diameter correspond to the typical dimensions ∗
To whom correspondence should be addressed Indian Institute of Technology – Bombay ‡ Contributed equally to this work †
1 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
of the nanorods obtained experimentally. The protocol has considerable potential for producing nanorods of several materials simply by changing the precursors.
1
Introduction
2
Studies on hierarchical nanostructures, formed by self-assembly or directed self-assembly of
3
nanoparticles, have experienced tremendous growth in the past decade. 1–8 In self-assembly,
4
the building blocks 4,5,9 get organized into ordered structures through either interparticle
5
interactions or externally modulated interactions. Often templates, 10 such as surfactant
6
micelles, 11 block copolymers, 12–14 proteins, 15 etc., are used to modulate the interparticle
7
interactions externally.
8
Gupta et. al. 16 recently demonstrated the use of wormlike micelles (WLMs) as a template
9
for promoting anisotropic assembly of AgBr or AgCl nanospheres to form the corresponding
10
nanorods. In their experiments, nanospheres of AgX were prepared by reacting silver nitrate
11
(AgNO3 ) with surfactant counter ions X– , while the WLMs were formed by mixing sodium
12
salicylate (NaSal) and cetyltrimethyl ammonium halide (CTA-X). The resultant solution
13
was aged for 24 h under continuous stirring at 30 ± 2 , to yield nanorods. Most significant
14
observations in their work are wormlike micelles are necessary for the nanorods to form, and
15
the nanorod formation is always preceded by spherical particles (either prepared in-situ or
16
externally added). Further, even if particles lacked inherent tendency to form anisotropic
17
structures, the presence of WLMs facilitated the formation of nanorods. The main drawbacks
18
in their method were that the yield of nanorods was very poor and the variation in particle
19
dimensions was very large.
20
In this communication we focus on understanding the mechanism of formation of nanorods
21
in wormlike micellar templates using a mix of experimental and theoretical analysis. On the
22
experimental front, we investigate the role of controlled shear, precursor concentration, and
23
volume fraction of WLMs on the morphology and yield of nanorods. These experiments also
2 ACS Paragon Plus Environment
Page 2 of 34
Page 3 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
24
help us to address the issues of large variations and low yields encountered in the previous
25
study. 16 We use a simple lattice model for WLMs for simulating the proposed mechanism
26
and try to identify the principle factors behind formation of the nanorods. The main inputs
27
for our model are the physics of reptation of wormlike micelles and a set of rules that define
28
the interactions of spherical nanoparticles in the presence of WLMs. Understanding the
29
mechanism of nanorod formation is important from the theoretical perspective, obtaining
30
better yields, and gaining a better control over the morphology of nanorods. The method
31
then can easily be extended to other systems.
32
Wormlike micelles (WLMs) are self-assembled structures of surfactant molecules that
33
have morphology similar to the linear polymers. Beyond a critical concentration (c∗ ) they
34
entangle into a dynamic network and exhibit remarkable viscoelastic properties. 17–19 Sim-
35
ulations of wormlike micelles may be performed on many different length and time scales,
36
ranging from the atomistic to the mesoscopic. 18,20 At the smallest scale, molecular dynamic
37
simulations can capture the influence of the surfactant chemistry. At this level of detail, it
38
is difficult to simulate more than a small section of one WLM. Coarse-graining of the model
39
for WLMs provides a way forward, in which the micelles are represented as flexible chains
40
of relatively hard spheres (generic FENE–C, models). Unfortunately, all the bead-based
41
models are very CPU-intensive because many beads will be required to represent one en-
42
tanglement length of a realistic WLM. In yet another approach, WLMs are modeled on the
43
mesoscopic length scales for which the smallest unit of a WLM is one persistence length. 20,21
44
The typical time scale used in these studies is ≈ 10−9 s. For studying the phenomena of
45
directional aggregation in wormlike micellar media, which happens over the time span of 24
46
h a time step of 10−9 s is still a very fine one. To tackle this issue, we go ahead with the
47
simple representation of a WLM. We model a WLM by a string of thin rods, with each rod
48
measuring to a single Kuhn length much like as for a polymer chain. In this model, the
49
micelles have uniform contour length and are confined on to a cubic lattice.
50
In the next section, we describe, briefly, the synthesis protocol and the characterizations
3 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
51
for the case of maghemite nanorods in WLMs. In the following section, we propose a detailed
52
mechanism for the formation of nanorods and describe our minimalist lattice model. Then
53
we present our results and compare them with the experimental observations. With the
54
discussion on the future perspective, we then conclude in the last section.
55
Synthesis Protocol and Characterizations
Figure 1: (a) Schematic of the protocol for Fe2 O3 nanorods synthesis. (b and c) TEM and SEM micrographs of the Fe2 O3 nanorods, respectively. (d) Rheology of solution a-iii shows a single crossover between storage and loss moduli confirming the formation of wormlike micellar phase after addition of the precursors.
56
Figure 1a shows schematic of the protocol for preparation of iron oxide nanorods by as-
57
sembling nanospheres in the wormlike micellar medium. Nanospheres of Iron oxide (Fe2 O3 )
58
were synthesized by the reaction between FeCl3 and NH4 OH in the presence of aqueous
59
solution of cetyl-trimethylammonium chloride (CTAC). The wormlike micellar phase was
60
prepared by adding sodium salicylate (NaSal) after the formation of Fe2 O3 nanoparticles.
61
Rheological measurements were used to confirm the formation of wormlike micellar phase. 4 ACS Paragon Plus Environment
Page 4 of 34
Page 5 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
62
The system was then allowed to age for 24 h under controlled shear in a parallel plate
63
shear cell (Linkam Shear Cell CSS–450). Details of chemicals and characterization methods
64
are given in supporting information SI-1 and SI-2, respectively. In Fig. 1b and Fig. 1c
65
we report micrographs of Fe2 O3 nanorods obtained from transmission electron microscopy
66
(TEM) and scanning electron microscopy (SEM), respectively. The length and diameter of
67
these nanorods typically range from 40 to 120 nm and from 5 to 25 nm, respectively. The
68
energy dispersive X-ray spectroscopy (EDS) pattern of the same batch of the sample (Fig.
69
SI-1, in supporting information SI-3) confirms the presence of iron and oxygen. Further, the
70
formation of γ−Fe2 O3 nanocrystals was confirmed using X-ray diffractometry, X-ray photo-
71
electron spectroscopy and High Resolution TEM analysis (refer supporting information SI-3).
72
73
Rheology of wormlike micelles is best described by the Maxwellian model, which consists
74
of an elastic spring with a Hookean constant G0 in series with a dashpot of viscosity η0 . 17,22,23
75
The expressions of storage and loss moduli, G0 and G00 respectively, are given by Eq. 1,
ω 2 τR2 G0 1 + ω 2 τR2 ωτR G0 G00 (ω) = 1 + ω 2 τR2 G0 (ω) =
(1)
76
where G0 is the elastic modulus extrapolated to t → 0 (i.e., infinite frequency) and τR , the
77
relaxation time. The plateau modulus G0 is related to the number density of the entan-
78
glement points (ν), hydrodynamic correlation length ζ (or the mesh size) of the micellar
79
network and zero-shear viscosity (η0 ) at a given temperature, by:
5 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
G0 = νkT 1/3 kT ζ= G0
Page 6 of 34
(2)
η0 = G0 τR 80
Figure 1d shows the plot of storage and loss moduli (G0 , G00 ) verses frequency (ω) mea-
81
sured after introduction of nanospheres in the wormlike micellar system, in which the in-
82
gradient concentrations were: [CTAC]=100 mM , [NaSal]=160 mM , [FeCl3 ]=10 mM and
83
[NH4 OH]=30 mM . The fitting of rheological data to the Maxwell model (Eq. 1) yields the
84
plateau modulus G0 = 47.92 P a and the single relaxation time τR = 0.34 s. Using Eq.
85
2, the density of entanglement and the mesh size of micellar network are estimated to be
86
ν = 1.15 × 1022 m−3 and ζ = 44.2 nm, respectively.
87
Theoretical considerations
88
Mechanism of nanorod formation
89
We hypothesize that the nanospheres present in the system adsorb on the backbones of
90
wormlike micelles (WLMs) and move along with them. The hypothesis is based on the
91
following attributes:
92
In wormlike micellar phase, a network of elongated micelles exists. This creates topo-
93
logical restrictions for diffusion of particles. 24 The hydrodynamic correlation length ζ
94
(or the mesh size) of the micellar network of WLMs can be estimated from Eq. 2. This
95
length is a measure of average cage size created by micellar strands and is estimated
96
to be 44.2 nm in the present case, i.e., ≈ 4 particle diameters (dp ) for dp = 10 nm.
97
A particle confined to such a cage will experience a water like viscosity. In such a
98
case, the time taken by a localized particle in the cage to hit a micellar strand may be 6 ACS Paragon Plus Environment
Page 7 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
99
100
Langmuir
estimated by equating mean square displacement (MSD) of particle to the mesh size ζ of micellar network: M SD = ζ 2 = 6Dcage τ
(3)
101
Setting ζ = 4dp and using Stokes-Einstein equation for diffusion coefficient of spherical
102
particles in Eq. 3 we get: 6
kT 3πηw dp
τ = (4dp )2
(4)
103
where, ηw is viscosity experienced by particle within the cage. On substituting the
104
typical values in Eq. 4 (i.e. dp = 10−8 m, T = 300 K, ηw = 10−3 P a · s) one gets
105
an estimate of τ as 6 µs. Depending upon the time scale of interest (τi ), the particle
106
diffusivity in a complex fluid like WLMs may vary over a range of magnitudes. If
107
τi ≈ τ , the diffusion coefficient within the micellar cage (Dcage = 4.4 × 10−12 m2 s−1 )
108
becomes important, whereas, if τi τ then the diffusion coefficient estimated by bulk
109
viscosity (η0 = 16.3 P a · s, Dbulk = 2.7 × 10−16 m2 s−1 ) becomes important. As the
110
experimental time scale of hours is τ , a single diffusion coefficient of particles based
111
on the bulk viscosity of WLMs (Dbulk ) is an appropriate diffusion coefficient to be used
112
in the further analysis.
113
Collision frequency between the particles 25 separated by a distance greater than the
114
mesh size of the WLMs (ζ) is dictated by the bulk diffusivity of particles in WLMs
115
(Dbulk ). The bulk diffusivity is negligible compared to Dcage which is same as the
116
particle diffusivity in the absence of WLMs (Dbulk /Dcage ≈ 6.1 × 10−5 ). Therefore the
117
presence of WLMs arrests spontaneous aggregation of the particles.
118
The number density of entanglement points in the wormlike micellar solution is ν =
119
1.15 × 1022 m−3 (using Eq. 2). The number density of the nanospheres (n), calculated
120
on the basis of 10 mM as precursor concentration and 10 nm as the diameter (as
121
obtained in experiments), is 2.91 × 1020 m−3 . The ratio of ν to n being much greater
122
than 1 ( nν ≈ 40) signifies that the probability of a particle being found in the vicinity 7 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
123
of a wormlike micellar strand is higher than that of the particle being located near
124
another particle.
125
Strength of the van der Waal’s interaction between particles and WLMs, mediated
126
through water, is of the order of AP −H2 O−W LM (Hamaker constant) = −5.2 kT (re-
127
fer supporting information SI-4 for details). An electrostatic interaction between the
128
particles and the WLMs may either assist or resist the adsorption of particles on the
129
WLMs. Experimental measurements show that the zeta potential of the particles is
130
-24.7 mV . The zeta potential of the WLMs varies with the molar ratio of the salt
131
(NaSal) to surfactant (CTAC). 26 For the present case of NaSal:CTAC=1.6, the zeta
132
potential of WLMs is of the order of +10mV. 26 Because, particles and WLMs carry
133
opposite charge and the net charge is still negative, the electrostatic attraction be-
134
tween them will therefore assist the adsorption of particles on the wormlike micellar
135
backbone.
136
On applying shear, the wormlike micelles slide over each other through a phenomenon
137
called as reptation. Reptation is a snakelike motion in which the stored length of a micellar
138
chain travels back and forth along the chain, and can be created and annealed only at the
139
ends. 27 While reptating, the particle-laden and highly entangled micelles (Fig. 2a, tile 1)
140
bring the adsorbed particles near each other (Fig. 2a, tile 2). Thus the relative motion of
141
the micelles holding these particles, regulate the frequency of interaction between the parti-
142
cles adsorbed on the adjoining micellar chains. The strength of van der Waal’s interaction
143
between the particles is an order of magnitude higher as compared to that between particles
144
and WLMs. Hamaker constant for particle-particle interactions mediated through water is
145
AP −H2 O−P = 66.4 kT (refer supporting information SI-4 for details). The AP −H2 O−P being
146
much grater than AP −H2 O−W LM the particles tend to aggregate by hopping from one micelle
147
to the other (Fig. 2a, tile 3-5), referred to as the inter-micellar particle exchange. Over the
148
time, these exchanges lead to the formation of chains of spherical nanoparticles lined along
149
the micellar backbone. The particle chains then consolidate into nanorods (Fig. 2a, tile 6). 8 ACS Paragon Plus Environment
Page 8 of 34
Page 9 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
150
The signature of intermicellar particle exchange was observed experimentally in cryo-
151
TEM analysis (Fig. 2b and Fig. 2c). In the early stages of aging (2 h), the particles get
152
lined up along the contours of wormlike micelles. They are still well separated from each
153
other and do not show any aggregation. At a later point in aging (12 h), the particles have
154
undergone directional aggregation and depict a morphology similar to chain of spherical
155
beads. These chains are loose aggregates of nanospheres that have not fused to form rod
156
shaped particles yet. Initially (Fig. 2b), the nanospheres are evenly distributed amongst the
157
wormlike micelles, whereas at a later stage most of the micelles are not associated with any
158
particles (Fig. 2c).
159
The mechanism of nanorod formation that we have proposed here is distinctly differ-
160
ent from the well studied mechanism of ‘nanorod growth via seed mediated approach’, 28,29
161
wherein twinned seeds grow along a preferred direction via molecular addition of precursors
162
from the solution. Whereas, in our mechanism the wormlike micellar template promotes the
163
growth of nanorods by directed self assembly of the seed particles.
164
Simulation framework
165
Representation of WormLike Micelles:
166
model for polymers. 30 In this model, a polymer chain is represented by a self-avoiding walk
167
(SAW) on a simple cubic lattice. The length between the successive bends in SAW phys-
168
ically corresponds to a “Kuhn segment” formed by several successive chemical monomers.
169
The Kuhn segment is a length over which the polymer chain (or micelle) is stiff. The chains
170
in this model of polymers have fixed bond length, and allowable values of bond angles are
171
only ±180◦ and ±90◦ . For further simplification we assume that the WLMs have uniform
172
contour length, implying that they do not break and reform during the simulation run. This
173
assumption introduces a further level of coarse-graining and results in WLMs having a sin-
174
gle relaxation mode, i.e., the reptation as opposed to reptation and breakage as relaxation
175
modes.
We represent WLMs by the Verdier-Stockmayer
9 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 34
Si gnat ur eof Cons ol i dat i on
Figure 2: (a) Schematic of the proposed mechanism for nanorod formation in wormlike micellar phase. (b and c) Cryo-TEM micrographs captured at 2 h and 12 h, respectively. 176
Kuhn segment of WLMs typically have length (Lk ) in the range of 20 - 250 nm, 17 while
177
the spherical particles in the system have typical diameter in the range of 8 - 14 nm. To
178
account for the relative length of WLMs and primary nanospheres we have used a multiscale
179
lattice (Fig. 3a). In the multiscale lattice, there are two length scales: one for the motion
180
of particles and the other for the motion of WLMs. The length scale for the dynamics
181
of nanoparticles is unit lattice distance, which is equal to the diameter of nanoparticles.
182
Whereas the dynamics of the WLMs takes place over the length scale of a Kuhn segment,
183
which spans over multiple lattice points of the raw particle grid.
184
Reptation of WLM under shear:
185
by the ‘slithering snake algorithm’ in which the Kuhn monomers move collectively along
186
the chain mimicking the motion of a slithering snake. Computationally, this turns out to
187
removing a monomer from the trailing end of the chain and connecting it to the leading
Reptation of a wormlike micelle is implemented
10 ACS Paragon Plus Environment
Page 11 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
188
end of the chain leaving the middle section of the chain unchanged 31 (refer Fig. 3a). Shear
189
is implemented by introducing a pseudopotential (∆Us ) to describe the flow field, 32,33 such
190
that when a chain slithers in the direction of the shear field ∆Us < 0 and when it moves
191
opposite to the shear field ∆Us > 0. This pseudopotential is then used to determine the
192
metropolis acceptance 34 of a slithering move. It is accepted with probability one if ∆Us ≤ 0
193
and with probability p = exp(−∆Us /kT ), p ∈ (0, 1) if ∆Us > 0. A more detailed discussion
194
on implementation of shear is included in the supporting information SI-5.
195
Intermicellar particle exchange:
196
least one particle then the rule-based inter-micellar particle transfers are executed for that
197
micelle. For deciding the direction of inter-micellar particle transfers, particle populations
198
of adjacent Kuhn segments are compared, and particles are allowed to hop from the Kuhn
199
segments holding lower number of particles to the one with the higher population. Figure
200
3b illustrates the rules of inter-micellar particle transfers schematically for a case of square
201
lattice. Supporting information SI-6 provide a detailed list of the rules used for executing
202
intermicellar particle exchange in the simulations.
If the micelle that has undergone slithering holds at
203
204
A typical MC move
The events tracked in the simulation are: reptation of WLMs and
205
inter-micellar particle exchanges. The formation of primary spherical nanoparticles and their
206
adsorption on wormlike micellar backbone are assumed to be instantaneous, and particle-
207
laden WLMs are considered as initial conditions for the simulations. In a typical MC move,
208
a WLM is chosen at random for slithering and is allowed to slither subject to the metropolis
209
acceptance. If the micelle that has undergone slithering holds at least one particle then we
210
execute the rules of inter-micellar particle transfers for that micelle. If the chosen micelle is
211
empty it only undergoes reptation. Even though reptation alone is an unfruitful event for
212
the growth of nanorods, it is still a necessary event for the dynamics of wormlike micellar
213
chains under shear. Monte Carlo moves are made until frequency of inter-micellar particle 11 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
214
exchange falls below a critical value of 10−4 per unit Monte Carlo move.
Figure 3: Simulation scheme: (a) A multiscale lattice to take into account the relative length of (WLMs) and nanospheres. (b) Rules for inter-micellar particle exchange (IPE): Populations of adjacent Kuhn segments are compared, and particles hop from the Kuhn segment holding lower number of particles to the one with higher particle population. (WLMP : micelle that has undergone slithering; WLMN : strand of a neighboring micelle.)
215
Results and discussion
216
The simulations reveal that the particles begin accumulating on few of the micellar backbones
217
in the form of chains. Towards the end of the simulation, the total number of particles (i.e.,
218
the isolated particles and the chains) left on the lattice reduces to less than 5% of the
219
initial particle count, which is a behavior observed in coagulation processes. Representative
220
parameters of a simulation run is provided in Table 1.
221
12 ACS Paragon Plus Environment
Page 12 of 34
Page 13 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Table 1: Summary of simulation inputs Sr. No.
Parameter
1 2 3 4 5 6 7 8
Lattice size Number of WLM Kuhn Length of WLM Number of Kuhn monomers in WLM Volume fraction of WLMs Diameter of primary nanospheres Mean Particle loading on WLM Distribution of particles on WLMs
Value 145 × 145 × 145 2500 70 nm 15 0.078 10 nm 1.5 Poissonion
Figure 4: TEM micrographs of particles captured after 24 h under various modes of shearing. (a) zero shear (b) mechanical stirring or uncontrolled shear (c) controlled shear applied using a shear cell (shear rate of 12 s−1 ). 222
Effect of shear
223
We investigated how the mode of shearing system affects nanorod formation by studying
224
the system under zero shear, uncontrolled shear, and controlled shear in a shear cell. Figure
225
4 shows a comparison of micrographs captured at the end of 24 h in each of the modes of
226
shearing the system. Experiments indicate that the application of shear, whether random or
227
controlled is essential for the nanorods to form. If the solution of wormlike micelles containing
228
nanospheres is left as such without shearing (i.e. γ˙ = 0 s−1 ) the nanorods do not form. In
229
the case of uncontrolled shear (i.e., mechanical stirring), nanorods are formed but with a low
230
yield and a wide distribution in size and shapes (Fig. 4b). A mechanical stirring does not
231
provide uniform mixing and results in formation of pockets that have a high mixing and the
232
ones with no or less mixing. The effect of nonuniform mixing gets amplified in viscoelastic 13 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
233
systems such as WLMs and inherently results in large variations in nanorod dimensions.
234
The system under controlled shear produced a crop of nanorods that was uniform in shape
235
as well as in dimensions and had a much improved yield as compared the other two modes
236
(Fig. 4).
237
Further we studied the formation of nanorods under controlled shear of varying magni-
238
tudes (2 − 32 s−1 , both experimentally and theoretically. At a shear rate of 2s−1 , we observe
239
formation of nanorods with a high aspect ratio and a large distribution. With increase
240
in the shear rate, nanorod length decreases appreciably and doesn’t show any perceptible
241
trend in the length or diameter (Fig. 5 b-f). The corresponding results of experiments and
242
simulations are plotted in Fig. 5g. Typically 100-150 particles were analyzed for getting
243
experimental size distribution in each case. A typical distribution for the case of γ˙ = 16 s−1
244
is reported in supporting information SI-8.
245
For simulating effect of shear the P´eclet number for WLMs in the simulations is matched
246
with that estimated for the experiments. P´eclet number (P e) is the ratio of rate of convective
247
transport to the molecular transports of a species in flowing fluids. For this system we
248
estimate P eexp for the basis unit of the wormlike micelles (WLMs), i.e. the Kuhn segments
249
for which L = Lk (70 nm) (refer supporting information SI-7 for details). Simulations
250
predict a constant length and diameter with an increase in the shear. The length and
251
diameter predicted by the simulations are comparable to the typical experimental sizes of
252
the nanorods. In spite of having a minimalist model for WLMs, the typical dimensions of
253
the nanorods are predicted well by simulations. It should be noted though, that the size of
254
primary nanospheres and the typical Kuhn length are taken from the experimental data and
255
the literature, 17 respectively.
256
Effect of precursor concentration
257
Figure 6 shows the effect of precursor concentration ([FeCl3 ]) on the dimensions of nanorods.
258
For FeCl3 concentrations less than 5 mM neither experiments nor simulations yield any 14 ACS Paragon Plus Environment
Page 14 of 34
Page 15 of 34
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Figure 5: Comparison of experiments and simulation showing effect of controlled shear: In the absence of shear, no nanorods were observed (see a). Experiments depict an imperceptible trend in the length as well as in the diameter of the nanorods (see c-f). The simulations predict constant length and diameter with an increase in the shear rate (see g).
15 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
259
nanorods. At these concentrations, the system of particles is too dilute for wormlike mi-
260
celles to bring the particles close to each other. At intermediate concentrations i.e., 5
