Mechanism of Nanorod Formation by Wormlike Micelle-Assisted

Sep 8, 2015 - Mechanism of Nanorod Formation by Wormlike Micelle-Assisted Assembly of Nanospheres. Advait Chhatre, Suvajeet Duttagupta, Rochish Thaoka...
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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

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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 †

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of the nanorods obtained experimentally. The protocol has considerable potential for producing nanorods of several materials simply by changing the precursors.

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Introduction

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Studies on hierarchical nanostructures, formed by self-assembly or directed self-assembly of

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nanoparticles, have experienced tremendous growth in the past decade. 1–8 In self-assembly,

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the building blocks 4,5,9 get organized into ordered structures through either interparticle

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interactions or externally modulated interactions. Often templates, 10 such as surfactant

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micelles, 11 block copolymers, 12–14 proteins, 15 etc., are used to modulate the interparticle

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interactions externally.

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Gupta et. al. 16 recently demonstrated the use of wormlike micelles (WLMs) as a template

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for promoting anisotropic assembly of AgBr or AgCl nanospheres to form the corresponding

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nanorods. In their experiments, nanospheres of AgX were prepared by reacting silver nitrate

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(AgNO3 ) with surfactant counter ions X– , while the WLMs were formed by mixing sodium

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salicylate (NaSal) and cetyltrimethyl ammonium halide (CTA-X). The resultant solution

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was aged for 24 h under continuous stirring at 30 ± 2 ‰, to yield nanorods. Most significant

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observations in their work are wormlike micelles are necessary for the nanorods to form, and

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the nanorod formation is always preceded by spherical particles (either prepared in-situ or

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externally added). Further, even if particles lacked inherent tendency to form anisotropic

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structures, the presence of WLMs facilitated the formation of nanorods. The main drawbacks

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in their method were that the yield of nanorods was very poor and the variation in particle

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dimensions was very large.

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In this communication we focus on understanding the mechanism of formation of nanorods

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in wormlike micellar templates using a mix of experimental and theoretical analysis. On the

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experimental front, we investigate the role of controlled shear, precursor concentration, and

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volume fraction of WLMs on the morphology and yield of nanorods. These experiments also

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help us to address the issues of large variations and low yields encountered in the previous

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study. 16 We use a simple lattice model for WLMs for simulating the proposed mechanism

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and try to identify the principle factors behind formation of the nanorods. The main inputs

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for our model are the physics of reptation of wormlike micelles and a set of rules that define

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the interactions of spherical nanoparticles in the presence of WLMs. Understanding the

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mechanism of nanorod formation is important from the theoretical perspective, obtaining

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better yields, and gaining a better control over the morphology of nanorods. The method

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then can easily be extended to other systems.

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Wormlike micelles (WLMs) are self-assembled structures of surfactant molecules that

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have morphology similar to the linear polymers. Beyond a critical concentration (c∗ ) they

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entangle into a dynamic network and exhibit remarkable viscoelastic properties. 17–19 Sim-

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ulations of wormlike micelles may be performed on many different length and time scales,

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ranging from the atomistic to the mesoscopic. 18,20 At the smallest scale, molecular dynamic

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simulations can capture the influence of the surfactant chemistry. At this level of detail, it

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is difficult to simulate more than a small section of one WLM. Coarse-graining of the model

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for WLMs provides a way forward, in which the micelles are represented as flexible chains

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of relatively hard spheres (generic FENE–C, models). Unfortunately, all the bead-based

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models are very CPU-intensive because many beads will be required to represent one en-

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tanglement length of a realistic WLM. In yet another approach, WLMs are modeled on the

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mesoscopic length scales for which the smallest unit of a WLM is one persistence length. 20,21

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The typical time scale used in these studies is ≈ 10−9 s. For studying the phenomena of

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directional aggregation in wormlike micellar media, which happens over the time span of 24

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h a time step of 10−9 s is still a very fine one. To tackle this issue, we go ahead with the

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simple representation of a WLM. We model a WLM by a string of thin rods, with each rod

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measuring to a single Kuhn length much like as for a polymer chain. In this model, the

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micelles have uniform contour length and are confined on to a cubic lattice.

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In the next section, we describe, briefly, the synthesis protocol and the characterizations

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for the case of maghemite nanorods in WLMs. In the following section, we propose a detailed

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mechanism for the formation of nanorods and describe our minimalist lattice model. Then

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we present our results and compare them with the experimental observations. With the

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discussion on the future perspective, we then conclude in the last section.

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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.

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Figure 1a shows schematic of the protocol for preparation of iron oxide nanorods by as-

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sembling nanospheres in the wormlike micellar medium. Nanospheres of Iron oxide (Fe2 O3 )

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were synthesized by the reaction between FeCl3 and NH4 OH in the presence of aqueous

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solution of cetyl-trimethylammonium chloride (CTAC). The wormlike micellar phase was

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prepared by adding sodium salicylate (NaSal) after the formation of Fe2 O3 nanoparticles.

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Rheological measurements were used to confirm the formation of wormlike micellar phase. 4 ACS Paragon Plus Environment

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The system was then allowed to age for 24 h under controlled shear in a parallel plate

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shear cell (Linkam Shear Cell CSS–450). Details of chemicals and characterization methods

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are given in supporting information SI-1 and SI-2, respectively. In Fig. 1b and Fig. 1c

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we report micrographs of Fe2 O3 nanorods obtained from transmission electron microscopy

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(TEM) and scanning electron microscopy (SEM), respectively. The length and diameter of

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these nanorods typically range from 40 to 120 nm and from 5 to 25 nm, respectively. The

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energy dispersive X-ray spectroscopy (EDS) pattern of the same batch of the sample (Fig.

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SI-1, in supporting information SI-3) confirms the presence of iron and oxygen. Further, the

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formation of γ−Fe2 O3 nanocrystals was confirmed using X-ray diffractometry, X-ray photo-

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electron spectroscopy and High Resolution TEM analysis (refer supporting information SI-3).

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Rheology of wormlike micelles is best described by the Maxwellian model, which consists

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of an elastic spring with a Hookean constant G0 in series with a dashpot of viscosity η0 . 17,22,23

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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)

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where G0 is the elastic modulus extrapolated to t → 0 (i.e., infinite frequency) and τR , the

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relaxation time. The plateau modulus G0 is related to the number density of the entan-

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glement points (ν), hydrodynamic correlation length ζ (or the mesh size) of the micellar

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network and zero-shear viscosity (η0 ) at a given temperature, by:

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G0 = νkT  1/3 kT ζ= G0

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(2)

η0 = G0 τR 80

Figure 1d shows the plot of storage and loss moduli (G0 , G00 ) verses frequency (ω) mea-

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sured after introduction of nanospheres in the wormlike micellar system, in which the in-

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gradient concentrations were: [CTAC]=100 mM , [NaSal]=160 mM , [FeCl3 ]=10 mM and

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[NH4 OH]=30 mM . The fitting of rheological data to the Maxwell model (Eq. 1) yields the

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plateau modulus G0 = 47.92 P a and the single relaxation time τR = 0.34 s. Using Eq.

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2, the density of entanglement and the mesh size of micellar network are estimated to be

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ν = 1.15 × 1022 m−3 and ζ = 44.2 nm, respectively.

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Theoretical considerations

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Mechanism of nanorod formation

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We hypothesize that the nanospheres present in the system adsorb on the backbones of

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wormlike micelles (WLMs) and move along with them. The hypothesis is based on the

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following attributes:

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ˆ In wormlike micellar phase, a network of elongated micelles exists. This creates topo-

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logical restrictions for diffusion of particles. 24 The hydrodynamic correlation length ζ

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(or the mesh size) of the micellar network of WLMs can be estimated from Eq. 2. This

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length is a measure of average cage size created by micellar strands and is estimated

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to be 44.2 nm in the present case, i.e., ≈ 4 particle diameters (dp ) for dp = 10 nm.

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A particle confined to such a cage will experience a water like viscosity. In such a

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case, the time taken by a localized particle in the cage to hit a micellar strand may be 6 ACS Paragon Plus Environment

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estimated by equating mean square displacement (MSD) of particle to the mesh size ζ of micellar network: M SD = ζ 2 = 6Dcage τ

(3)

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Setting ζ = 4dp and using Stokes-Einstein equation for diffusion coefficient of spherical

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particles in Eq. 3 we get:  6

kT 3πηw dp



τ = (4dp )2

(4)

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where, ηw is viscosity experienced by particle within the cage. On substituting the

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typical values in Eq. 4 (i.e. dp = 10−8 m, T = 300 K, ηw = 10−3 P a · s) one gets

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an estimate of τ as 6 µs. Depending upon the time scale of interest (τi ), the particle

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diffusivity in a complex fluid like WLMs may vary over a range of magnitudes. If

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τi ≈ τ , the diffusion coefficient within the micellar cage (Dcage = 4.4 × 10−12 m2 s−1 )

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becomes important, whereas, if τi  τ then the diffusion coefficient estimated by bulk

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viscosity (η0 = 16.3 P a · s, Dbulk = 2.7 × 10−16 m2 s−1 ) becomes important. As the

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experimental time scale of hours is  τ , a single diffusion coefficient of particles based

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on the bulk viscosity of WLMs (Dbulk ) is an appropriate diffusion coefficient to be used

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in the further analysis.

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ˆ Collision frequency between the particles 25 separated by a distance greater than the

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mesh size of the WLMs (ζ) is dictated by the bulk diffusivity of particles in WLMs

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(Dbulk ). The bulk diffusivity is negligible compared to Dcage which is same as the

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particle diffusivity in the absence of WLMs (Dbulk /Dcage ≈ 6.1 × 10−5 ). Therefore the

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presence of WLMs arrests spontaneous aggregation of the particles.

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ˆ The number density of entanglement points in the wormlike micellar solution is ν =

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1.15 × 1022 m−3 (using Eq. 2). The number density of the nanospheres (n), calculated

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on the basis of 10 mM as precursor concentration and 10 nm as the diameter (as

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obtained in experiments), is 2.91 × 1020 m−3 . The ratio of ν to n being much greater

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than 1 ( nν ≈ 40) signifies that the probability of a particle being found in the vicinity 7 ACS Paragon Plus Environment

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of a wormlike micellar strand is higher than that of the particle being located near

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another particle.

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ˆ Strength of the van der Waal’s interaction between particles and WLMs, mediated

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through water, is of the order of AP −H2 O−W LM (Hamaker constant) = −5.2 kT (re-

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fer supporting information SI-4 for details). An electrostatic interaction between the

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particles and the WLMs may either assist or resist the adsorption of particles on the

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WLMs. Experimental measurements show that the zeta potential of the particles is

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-24.7 mV . The zeta potential of the WLMs varies with the molar ratio of the salt

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(NaSal) to surfactant (CTAC). 26 For the present case of NaSal:CTAC=1.6, the zeta

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potential of WLMs is of the order of +10mV. 26 Because, particles and WLMs carry

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opposite charge and the net charge is still negative, the electrostatic attraction be-

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tween them will therefore assist the adsorption of particles on the wormlike micellar

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backbone.

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On applying shear, the wormlike micelles slide over each other through a phenomenon

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called as reptation. Reptation is a snakelike motion in which the stored length of a micellar

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chain travels back and forth along the chain, and can be created and annealed only at the

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ends. 27 While reptating, the particle-laden and highly entangled micelles (Fig. 2a, tile 1)

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bring the adsorbed particles near each other (Fig. 2a, tile 2). Thus the relative motion of

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the micelles holding these particles, regulate the frequency of interaction between the parti-

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cles adsorbed on the adjoining micellar chains. The strength of van der Waal’s interaction

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between the particles is an order of magnitude higher as compared to that between particles

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and WLMs. Hamaker constant for particle-particle interactions mediated through water is

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AP −H2 O−P = 66.4 kT (refer supporting information SI-4 for details). The AP −H2 O−P being

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much grater than AP −H2 O−W LM the particles tend to aggregate by hopping from one micelle

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to the other (Fig. 2a, tile 3-5), referred to as the inter-micellar particle exchange. Over the

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time, these exchanges lead to the formation of chains of spherical nanoparticles lined along

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the micellar backbone. The particle chains then consolidate into nanorods (Fig. 2a, tile 6). 8 ACS Paragon Plus Environment

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The signature of intermicellar particle exchange was observed experimentally in cryo-

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TEM analysis (Fig. 2b and Fig. 2c). In the early stages of aging (2 h), the particles get

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lined up along the contours of wormlike micelles. They are still well separated from each

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other and do not show any aggregation. At a later point in aging (12 h), the particles have

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undergone directional aggregation and depict a morphology similar to chain of spherical

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beads. These chains are loose aggregates of nanospheres that have not fused to form rod

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shaped particles yet. Initially (Fig. 2b), the nanospheres are evenly distributed amongst the

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wormlike micelles, whereas at a later stage most of the micelles are not associated with any

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particles (Fig. 2c).

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The mechanism of nanorod formation that we have proposed here is distinctly differ-

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ent from the well studied mechanism of ‘nanorod growth via seed mediated approach’, 28,29

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wherein twinned seeds grow along a preferred direction via molecular addition of precursors

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from the solution. Whereas, in our mechanism the wormlike micellar template promotes the

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growth of nanorods by directed self assembly of the seed particles.

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Simulation framework

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Representation of WormLike Micelles:

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model for polymers. 30 In this model, a polymer chain is represented by a self-avoiding walk

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(SAW) on a simple cubic lattice. The length between the successive bends in SAW phys-

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ically corresponds to a “Kuhn segment” formed by several successive chemical monomers.

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The Kuhn segment is a length over which the polymer chain (or micelle) is stiff. The chains

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in this model of polymers have fixed bond length, and allowable values of bond angles are

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only ±180◦ and ±90◦ . For further simplification we assume that the WLMs have uniform

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contour length, implying that they do not break and reform during the simulation run. This

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assumption introduces a further level of coarse-graining and results in WLMs having a sin-

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gle relaxation mode, i.e., the reptation as opposed to reptation and breakage as relaxation

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modes.

We represent WLMs by the Verdier-Stockmayer

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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

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the spherical particles in the system have typical diameter in the range of 8 - 14 nm. To

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account for the relative length of WLMs and primary nanospheres we have used a multiscale

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lattice (Fig. 3a). In the multiscale lattice, there are two length scales: one for the motion

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of particles and the other for the motion of WLMs. The length scale for the dynamics

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of nanoparticles is unit lattice distance, which is equal to the diameter of nanoparticles.

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Whereas the dynamics of the WLMs takes place over the length scale of a Kuhn segment,

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which spans over multiple lattice points of the raw particle grid.

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Reptation of WLM under shear:

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by the ‘slithering snake algorithm’ in which the Kuhn monomers move collectively along

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the chain mimicking the motion of a slithering snake. Computationally, this turns out to

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removing a monomer from the trailing end of the chain and connecting it to the leading

Reptation of a wormlike micelle is implemented

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end of the chain leaving the middle section of the chain unchanged 31 (refer Fig. 3a). Shear

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is implemented by introducing a pseudopotential (∆Us ) to describe the flow field, 32,33 such

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that when a chain slithers in the direction of the shear field ∆Us < 0 and when it moves

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opposite to the shear field ∆Us > 0. This pseudopotential is then used to determine the

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metropolis acceptance 34 of a slithering move. It is accepted with probability one if ∆Us ≤ 0

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and with probability p = exp(−∆Us /kT ), p ∈ (0, 1) if ∆Us > 0. A more detailed discussion

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on implementation of shear is included in the supporting information SI-5.

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Intermicellar particle exchange:

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least one particle then the rule-based inter-micellar particle transfers are executed for that

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micelle. For deciding the direction of inter-micellar particle transfers, particle populations

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of adjacent Kuhn segments are compared, and particles are allowed to hop from the Kuhn

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segments holding lower number of particles to the one with the higher population. Figure

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3b illustrates the rules of inter-micellar particle transfers schematically for a case of square

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lattice. Supporting information SI-6 provide a detailed list of the rules used for executing

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intermicellar particle exchange in the simulations.

If the micelle that has undergone slithering holds at

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A typical MC move

The events tracked in the simulation are: reptation of WLMs and

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inter-micellar particle exchanges. The formation of primary spherical nanoparticles and their

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adsorption on wormlike micellar backbone are assumed to be instantaneous, and particle-

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laden WLMs are considered as initial conditions for the simulations. In a typical MC move,

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a WLM is chosen at random for slithering and is allowed to slither subject to the metropolis

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acceptance. If the micelle that has undergone slithering holds at least one particle then we

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execute the rules of inter-micellar particle transfers for that micelle. If the chosen micelle is

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empty it only undergoes reptation. Even though reptation alone is an unfruitful event for

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the growth of nanorods, it is still a necessary event for the dynamics of wormlike micellar

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chains under shear. Monte Carlo moves are made until frequency of inter-micellar particle 11 ACS Paragon Plus Environment

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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.)

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Results and discussion

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The simulations reveal that the particles begin accumulating on few of the micellar backbones

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in the form of chains. Towards the end of the simulation, the total number of particles (i.e.,

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the isolated particles and the chains) left on the lattice reduces to less than 5% of the

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initial particle count, which is a behavior observed in coagulation processes. Representative

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parameters of a simulation run is provided in Table 1.

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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

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We investigated how the mode of shearing system affects nanorod formation by studying

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the system under zero shear, uncontrolled shear, and controlled shear in a shear cell. Figure

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4 shows a comparison of micrographs captured at the end of 24 h in each of the modes of

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shearing the system. Experiments indicate that the application of shear, whether random or

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controlled is essential for the nanorods to form. If the solution of wormlike micelles containing

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nanospheres is left as such without shearing (i.e. γ˙ = 0 s−1 ) the nanorods do not form. In

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the case of uncontrolled shear (i.e., mechanical stirring), nanorods are formed but with a low

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yield and a wide distribution in size and shapes (Fig. 4b). A mechanical stirring does not

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provide uniform mixing and results in formation of pockets that have a high mixing and the

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ones with no or less mixing. The effect of nonuniform mixing gets amplified in viscoelastic 13 ACS Paragon Plus Environment

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systems such as WLMs and inherently results in large variations in nanorod dimensions.

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The system under controlled shear produced a crop of nanorods that was uniform in shape

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as well as in dimensions and had a much improved yield as compared the other two modes

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(Fig. 4).

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Further we studied the formation of nanorods under controlled shear of varying magni-

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tudes (2 − 32 s−1 , both experimentally and theoretically. At a shear rate of 2s−1 , we observe

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formation of nanorods with a high aspect ratio and a large distribution. With increase

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in the shear rate, nanorod length decreases appreciably and doesn’t show any perceptible

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trend in the length or diameter (Fig. 5 b-f). The corresponding results of experiments and

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simulations are plotted in Fig. 5g. Typically 100-150 particles were analyzed for getting

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experimental size distribution in each case. A typical distribution for the case of γ˙ = 16 s−1

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is reported in supporting information SI-8.

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For simulating effect of shear the P´eclet number for WLMs in the simulations is matched

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with that estimated for the experiments. P´eclet number (P e) is the ratio of rate of convective

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transport to the molecular transports of a species in flowing fluids. For this system we

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estimate P eexp for the basis unit of the wormlike micelles (WLMs), i.e. the Kuhn segments

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for which L = Lk (70 nm) (refer supporting information SI-7 for details). Simulations

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predict a constant length and diameter with an increase in the shear. The length and

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diameter predicted by the simulations are comparable to the typical experimental sizes of

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the nanorods. In spite of having a minimalist model for WLMs, the typical dimensions of

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the nanorods are predicted well by simulations. It should be noted though, that the size of

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primary nanospheres and the typical Kuhn length are taken from the experimental data and

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the literature, 17 respectively.

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Effect of precursor concentration

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Figure 6 shows the effect of precursor concentration ([FeCl3 ]) on the dimensions of nanorods.

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For FeCl3 concentrations less than 5 mM neither experiments nor simulations yield any 14 ACS Paragon Plus Environment

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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).

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Langmuir

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nanorods. At these concentrations, the system of particles is too dilute for wormlike mi-

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celles to bring the particles close to each other. At intermediate concentrations i.e., 5