Controlling Nanorod Oligomer Aggregation in Solutions - The Journal

Subscriber access provided by University of Sussex Library

Article

Controlling Nanorod Oligomer Aggregation in Solutions Houyang Chen, and Eli Ruckenstein J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02566 • Publication Date (Web): 05 Jul 2016 Downloaded from http://pubs.acs.org on July 11, 2016

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.

The Journal of Physical Chemistry C 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 27

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

The Journal of Physical Chemistry

Controlling Nanorod Oligomer Aggregation in Solutions

Houyang Chen*, Eli Ruckenstein* Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4200, USA

1

ACS Paragon Plus Environment


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 2 of 27

Abstract: Controlling the size of ordered nanorod aggregates in colloidal dispersions is a challenge. Here, we employ Brownian dynamics to explore the dependence of nanorod aggregate size and structure on the molecular weight of a polyelectrolyte attached to one end of the nanorod and on the nature of the solvent. Upon increasing the polyelectrolyte molecular weight (the length of polyelectrolyte), the size of the aggregates decreases because of increasing electrostatic repulsion. The critical van der Waals interaction strength for transition from individual nanorods to nanorod dimers/trimers+ (trimers and larger aggregates) increases with increasing polyelectrolyte molecular weight. In a medium with a dielectric constant of 1.0, upon increasing the van der Waals interaction between nanorods, the individual nanorods aggregate as dimers and trimers+, with approximately 50% of individual nanorods forming dimers. In a solvent with a sufficiently large dielectric constant (e.g. ≥10.0), upon increasing the van der Waals interaction between nanorods, most nanorods aggregate into trimers or larger aggregates; few dimers are generated. Lower solvent dielectric constant and higher polyelectrolyte molecular weight favor formation of more uniform aggregates. As the charge of the segments of the polyelectrolyte increases, the fraction of nanorod dimers increases and the fraction of nanorod trimers+ decreases. In media with the dielectric constant of water, aggregation was insensitive to temperature. In low dielectric constant media, aggregate formation was sensitive to the temperature for high molecular weight polyelectrolytes, but insensitive to the temperature for low molecular weight polyelectrolytes.

2


Page 3 of 27

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


1.Introduction The assembly of nanorods has attracted great interest1,2,3,4,5,6,7,8,9,10, 11, 12,13,14,15. The size and shape of nanorod aggregates affect their properties16 and play central roles in their optical and biomedical applications. Many contributions have focused on superstructures assembled from nanorods. For example, by attaching oxidized polypyrrole to gold nanorods, Park et al.1 produced several two dimensional and three dimensional structures (e.g. bundles, tubes, and sheets). Needle-like superparticles were assembled from cadmium selenide-cadmium sulfide (CdSe-CdS) core-shell nanorods2. The dependence of CdSe/Cds nanorod aggregate formation on addition of oleic acid or poly(ethylene glycol) methacrylate was investigated by Baranov et al.3 They found that additives (polymers) generate attractive depletion between nanorods. Binary superlattice structures formed by nanorods and nanospheres were obtained and studied by combined experimental and simulation methods.11 Brownian dynamics simulations predicted microphase separation of polymer grafted rods and identified the phases formed.12,15 Examples and understanding of nanorod dimers and small nanorod aggregates, which have applications in antigen detection17 and as optical materials18, are still limited. Gold rod heterodimers, which possess plasmon-induced transparency at visible wavelengths, were assembled by Biswas et al19. Coupled plasmon resonances of gold nanorod dimers18,20, 21,22 and trimers23 were investigated by a combination of experiments and numerical calculations. Another important problem which constitutes a challenge is the control of the size of ordered nanorod aggregates. This paper employs Brownian dynamics simulations to investigate the size of nanorod aggregates produced in varied solvent environments by attaching a polyelectrolyte to one end of the nanorods.

3



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 4 of 27

2.Simulation details The motion of each bead in Brownian dynamics (BD) simulations24,25 ,26,27 follows the Langevin equation

[

]

mi&r&i (t ) = −∇ ∑ E ij (rij ) + E b (rij ) + E a + E c − mi ζ r&i (t ) + Fi r (t )

(1)

j

where ζ , ri , and mi are the friction coefficient, position vector, and mass of bead i, respectively.

(

The coefficient ζ =1.0 τ −1 ( τ = m0σ 02 / ε 0

)

12

) and mi = m0 . The random force Fi r (t ) satisfies

Fi r ( t ) ⋅ Fjr ( t / ) = 6kBTmζδ ijδ ( t − t / ) ( k B is the Boltzmann constant, T is the temperature, and

δ is the Dirac delta function). The quantities σ 0 , ε 0 and m0 are the units of length, energy, and mass, respectively. The Lennard-Jones (LJ) potential is employed for the interactions between beads (segments of polyelectrolyte or nanospheres of nanorods or counterions):

  σ 4ε ij  ij E ij =   rij   

12 6   σ ij    −     rij       0

rij ≤ rc ,ij

(2)

rij > rc ,ij

where rc,ij and rij are the cutoff distance and the distance between the centers of two beads, respectively. ε ij is the interaction strength between beads i and j. The LJ potential parameters involved in the pair interactions between beads are listed in Table 1. The LJ potential is shifted to zero at the cutoff distance. The harmonic potential Eb =

1 K b (rij − r0 ) 2 is used for the interactions between two 2

successive beads, with the equilibrium bond distance r0 =1.2 σ 0 and the spring coefficient K b =1500 ε 0 / σ 0 . The angle for three successive nanoparticles in nanorods is subject to the 2

4


Page 5 of 27

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


potential E a =

1 K a (θ − θ 0 ) 2 , with the equilibrium angle θ0=180° and the coefficient 2

K a =200 ε 0 / rad 2 . The electrostatic interactions between point charge pair (segments in polyelectrolyte and counterions of polyelectrolyte ) are given by E c =

1

qi q j

4π ∈ rij

, where qi and

q j are the charge in beads i and j, and ϵ is the dielectric constant. Nanorods were constructed from nanoparticles28. According to the previous experimental 1

and simulation12,29 works, we consider nanorods with one end-decorated with a polyelectrolyte,

denoted as R10Pn (R10 indicates a nanorod made up of 10 nanoparticles, and Pn is the polyelectrolyte, with n indicating the molecular weight, i.e. the length of the polyelectrolyte). Counterions are employed to balance the charges on the polyelectrolyte. The number density of the nanorods is 9.2593×10-5 (σ 0 ) . The charge q of a segment of −3

the polyelectrolyte varies from -0.1e to -3e, and the charge of a counterion is +1e. In this paper, an implicit solvent model is employed. To emphasize the solvent effects, dielectric constants are varied to mimic different solvents. By using the Large Atomic/Molecular Massively Parallel Simulator (LAMMPS) package26, all simulations were carried out in a system of size

(120σ 0 )3 for 107 BD steps. The time step is 0.005 τ .

3. Results and Discussions Figure 1 shows that the fractions of individual nanorods, nanorod dimers, and trimers+ (containing three and/or more nanorods) as functions of the van der Waals interaction

ε RR between nanorods in a solvent with a dielectric constant ϵ = 1.0. For small ε RR (e.g. ε RR / ε0 < 0.8), the fraction f1 (the number of individual nanorods over the total number of nanorods) 5



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 6 of 27

remains constant and close to 100%, indicating that most nanorods are present in the solvent as individual nanorods. This occurs because a small ε RR cannot overcome the entropy decrease when the nanorods aggregate. When ε RR increases to a moderate value, the fraction f1 decreases sharply, while the fractions f 2 (the number of nanorods in dimers over the number of total nanorods) and f 3+ (the number of nanorods in trimers+ over the number of total nanorods) increases sharply. In this range, the individual nanorods, nanorod dimers and nanorod trimers+ coexist. When ε RR becomes large, f 1 decreases to a constant which is close to 0, whereas f 2 and

f3+ increase to constant values. Under these conditions, nanorod dimers and trimers+ coexist in the solvent. In this range, the attractive van der Waals interaction is sufficiently strong to overcome the entropy decrease. From Figure 1, a critical interaction ε RR,C for the transition from individual nanorods to nanorod dimers/trimers+ is identified. For pure nanorods, the critical interaction ε RR,C / ε 0 = 0.8. With increasing length of the polyelectrolyte, the critical interaction increases. In fact, for aggregation of the polyelectrolyte decorated nanorods to occur, the interaction ε RR between nanorods must be sufficiently strong to overcome the decrease of entropy generated through aggregation and the electrostatic interactions between polyelectrolytes. Hence, for polyelectrolyte end-decorated nanorods, ε RR,C is larger than that for pure nanorods, and ε RR,C increases with increasing polyelectrolyte molecular weight. For a selected ε RR > ε RR,C , we found that, by increasing the polyelectrolyte molecular weight, the fraction f 3+ decreases, whereas the fraction f 2 increases. In conclusion, the nanorod dimers and trimers+ can be controlled by the polyelectrolyte molecular weight. Figure 2 presents the average size of nanorod oligomer aggregates S3+ as a function of the interactions ε RR between nanorods in a solvent with a dielectric constant ϵ = 1.0. The average 6


Page 7 of 27

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


size of the aggregates generated from pure nanorods is between 12 and 26 nanorods when

ε RR >= ε RR,C ≡ 0.8 ε 0 . For an attractive interaction ε RR between nanorods, the nanorods selfassemble side-by-side when ε RR > ε RR,C . It should be noted that the angles between nanorods in dimers and/or in trimers+ aggregates are between 5 and 13°, but not equal to 0 (See Figure S1 in the supporting information), which are in agreement with the experimentally determined gold nanorod dimers22. The presence of an angle between nanorods in dimers and/or trimers+ reduces the repulsive interaction between nanorods. As two nanorods approach, the conformational entropy (of the two nanorods) decreases, and the free energy increases. This increase in free energy with decreasing distance constitutes a repulsive interaction between the two nanorods. The non-zero average angle between the two nanorods balances the above-mentioned repulsion, which is entropic in origin, and the attraction between the two nanorods. According to Ma’s study22, the angle in nanorod dimers plays a central role in the intensity and position of the absorption bands, and the nonzero angles between the nanorods result in electromagnetic coupling of dimers. The average size of aggregates from pure nanorods exhibits large fluctuations. For polyelectrolyte decorated nanorods, the average size of the aggregates decreases to 7 or less, and the average size decreases with increasing polyelectrolyte molecular weight, indicating that by decorating the nanorod with polyelectrolyte, one can control the average size of the aggregates. Further, the average size of the aggregates generated from polyelectrolyte decorated nanorods exhibits low fluctuations, indicating that the nanorod aggregates have a narrow polydispersity. In order to examine the size distribution of aggregates, the percentages of nanorod aggregates as functions of their size are presented in Figure 3. For the aggregates generated from pure nanorods (R10), the polydispersity of aggregates is large and the size distribution is from 3 7



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 8 of 27

to 20. For a short polyelectrolyte (the length of polyelectrolyte is 2), the polydispersity of the aggregates is reduced. The size distribution is from 3 to 11, and approximately 40% of the nanorod aggregates consist of 8 nanorods. By increasing the length of polyelectrolyte to 10 units, the size distribution becomes narrower (from 2 to 6), and most nanorod aggregates contain 3 and 4 nanorods (i.e. trimers and tetramers). Compared to the nanorod aggregates formed from pure nanorods, the aggregates from polyelectrolyte decorated nanorods possess small dispersity, indicating that more uniform nanorod aggregates would be generated from polyelectrolyte decorated nanorods in an organic solvent with a dielectric constant ϵ =1.0. Furthermore, the dispersity becomes smaller for larger polyelectrolyte molecular weight. From the snapshots of aggregates in insets of Figures 3 and S2, generally, polyelectrolytes are located at both ends of the aggregate. Previous investigation confirmed that the properties of nanorod aggregates depend on their size and shape16. From Figures 1 and 2, the average size of aggregates and their transition from individual nanorods to nanorod dimers/trimers+ can be controlled by the polyelectrolyte via electrostatic interactions, indicating that the polyelectrolyte plays a significant role in the formation of nanorod aggregates. One can also conclude that the polydispersity, which is still a challenge to control in experiments3, can be well controlled by the solvent and by the polyelectrolyte. Figure 4 shows that the fractions of individual nanorods f 1, nanorod dimers f 2 , and nanorod aggregates f 3+ of R10P10 as functions of the interaction ε RR between nanorods. By increasing ε RR , a transition from individual nanorods to nanorod dimers/trimers+ occurs. The critical interaction ε RR,C for the transition from individual nanorods to nanorod dimers/trimers+ decreases as the dielectric constant increases. For a selected ε RR and ε RR > ε RR,C , when the 8


Page 9 of 27

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


dielectric constant ϵ increases from 1.0 to 10.0 (or larger), the fraction f 2 decreases sharply, whereas f 3+ increases sharply, indicating that most nanorods are present as trimers+ in solvents with a large dielectric constant ϵ. Figure 5 presents the average size of aggregates S3+ of nanorod R10P10 as a function of the interaction ε RR between nanorods. As the dielectric constant ϵ increases, the size of aggregates increases. The error bars of the size in a solvent with a large dielectric constant are larger than for those with a small dielectric constant, indicating that more uniform aggregates are formed in an organic solvent with a small dielectric constant. Percentages of nanorod aggregates as a function of their size for R10P10 in aqueous solutions (dielectric constant ε = 78.0) are presented in Figure 6. By comparing Figures 6 and 3c, one can conclude that the dispersity of the size of the aggregates is smaller (size distribution narrower) for ϵ =1.0 than for ϵ =78.0, indicating that the organic solvents (ϵ = 1.0) provide more uniform nanorod aggregates than the aqueous solutions. This indicates that, for nanorod assembly, an organic solvent with low dielectric constant is a better candidate than an aqueous environment. Actually, numerous experiments regarding nanorod synthesis and self-assembly involved organic solvents3. Figure 7 shows the fraction of individual nanorods, nanorod dimers, and trimers+ as functions of the charge on the segments of the polymers in an organic solvent with a dielectric constant ϵ = 1.0 and interaction between nanorods εRR=2.2ε0. One can see that most nanorods aggregate and less than 6% of the nanorods remain nonaggregated (Fig. 7a). With decreasing charge from -3e to -0.1e, the fraction of nanorod dimers decreases and the fraction of nanorod trimers+ increases.

9



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 27

Figure 8 shows the average size of aggregates S3+ as a function of the charge of the segments of the polyelectrolyte in an organic solvent with a dielectric constant ϵ = 1.0 and interaction between nanorods εRR=2.2ε0. As the charge increases, the average size of aggregates decreases because the electrostatic repulsive interaction increases. When the charge is -3e, the sizes of aggregates are smaller than 4. Combining Figures 7 with 8, one can conclude that when the charge per segment of the polyelectrolyte is -3e (no matter how long the polyelectrolyte grafted on the nanorod), most nanorods are present as nanorod dimers and nanorod trimers+. It is worth mentioning that when the length of the polymer is larger than 4 segments, most nanorods are present as nanorod dimers and nanorod trimers+ with the charge -1e or larger. Figure 8 also shows that, for a selected charge, the average size of the aggregates decreases with increasing molecular weight of the polyelectrolyte. Figure 9 presents the effect of temperature on the aggregation of nanorods. In aqueous solutions (dielectric constant ϵ = 78.0), the nanorods are present as nanorod aggregates and the fractions f1, f2, and f3+ are insensitive to temperature. In an organic solvent with a dielectric constant ϵ = 1, the above fractions are insensitive to temperature for small molecular weight (i.e. length 2 segments), whereas the fractions depend on temperature for large molecular weight (i.e. length 10 segments). Figure 10 shows the effect of temperature on the size of nanorod aggregates. Generally speaking, the size of nanorod aggregates is insensitive to temperature. Combining Figures 9 and 10, one can conclude that in aqueous solutions, both the fractions and size of aggregates are insensitive to temperature. For a solvent with a dielectric constant ϵ = 1, aggregate formation was sensitive to the temperature for high molecular weight polyelectrolytes.

10


Page 11 of 27

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


4.Conclusions In conclusion, Brownian dynamics simulations suggest that one can control the size of nanorod aggregates by decorating the nanorod with a polyelectrolyte and/or by using a suitable solvent. Our results reveal that by increasing the length of the polyelectrolyte, the size of the aggregates decreases, whereas the critical interaction for the transition from individual nanorods to nanorod dimers/trimers+ increases. We found that when the dielectric constant of the solvent is 1.0, with the interaction between nanorods increases, the individual nanorods aggregate to both nanorod dimers and trimer+. However, when the dielectric constant becomes large (e.g. larger than 10.0), by increasing the interaction between nanorods, most individual nanorods aggregate into nanorod trimers+, and few nanorod dimers are generated. Our results also show that, compared to aqueous solutions, more uniform nanorod aggregates are formed in an organic solvent. The nanorod aggregates will be more uniform in organic solvents with lower dielectric constants than with higher dielectric constants. As the charge of the segments of the polyelectrolyte increases, the fraction of nanorod dimers increases and the fraction of nanorod trimers+ decreases. The results indicate that both the fractions and sizes of nanorod aggregates are insensitive to the temperature of aqueous solutions. However, for nanorods decorated with high molecular weight polyelectrolyte, the fractions and sizes of nanorod aggregates are sensitive to the temperature for solvents with a low dielectric constant.

AUTHOR INFORMATION Corresponding Authors. * Email: [email protected] (H. C.); [email protected] (E.R.). Phone : (+1)716-645-1179

Notes: The authors declare no competing financial interest. 11



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 12 of 27

ACKNOWLEDGMENTS We thank the Center for Computational Research at the University at Buffalo (SUNY) for providing computational resources to carry out this study. H.C. is also grateful for the financial supports from the National Natural Science Foundation of China (No. 21206049).

References 1.

Park, S.; Lim, J.-H.; Chung, S.-W.; Mirkin, C. A., Self-assembly of mesoscopic metal-

polymer amphiphiles. Science 2004, 303, 348-351. 2.

Wang, T.; Zhuang, J.; Lynch, J.; Chen, O.; Wang, Z.; Wang, X.; LaMontagne, D.; Wu,

H.; Wang, Z.; Cao, Y. C., Self-Assembled Colloidal Superparticles from Nanorods. Science 2012,

338 , 358-363. 3.

Baranov, D.; Fiore, A.; van Huis, M.; Giannini, C.; Falqui, A.; Lafont, U.; Zandbergen,

H.; Zanella, M.; Cingolani, R.; Manna, L., Assembly of Colloidal Semiconductor Nanorods in Solution by Depletion Attraction. Nano Lett. 2010, 10 , 743-749. 4.

Salant, A.; Amitay-Sadovsky, E.; Banin, U., Directed Self-Assembly of Gold-Tipped

CdSe Nanorods. J. Am. Chem. Soc. 2006, 128 , 10006-10007. 5.

Widmer-Cooper, A.; Geissler, P., Orientational Ordering of Passivating Ligands on CdS

Nanorods in Solution Generates Strong Rod–Rod Interactions. Nano Lett. 2014, 14, 57-65. 6.

Paik, T.; Diroll, B. T.; Kagan, C. R.; Murray, C. B., Binary and Ternary Superlattices

Self-Assembled from Colloidal Nanodisks and Nanorods. J. Am. Chem.Soc.2015, 137 , 66626669.

12


Page 13 of 27

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


7.

Cavallaro, M.; Botto, L.; Lewandowski, E. P.; Wang, M.; Stebe, K. J., Curvature-driven

capillary migration and assembly of rod-like particles. Proc. Natl. Acad. Sci. USA 2011, 108, 20923-20928. 8.

Yeom, B.; Kotov, N. A., Nanoparticle self-assembly: A loop of two rods. Nat Mater 2014,

13, 228-229. 9.

Kuemin, C.; Nowack, L.; Bozano, L.; Spencer, N. D.; Wolf, H., Oriented Assembly of

Gold Nanorods on the Single-Particle Level. Adv.Functional Mater. 2012, 22, 702-708. 10.

Vigderman, L.; Khanal, B. P.; Zubarev, E. R., Functional Gold Nanorods: Synthesis,

Self-Assembly, and Sensing Applications. Adv. Mater.2012, 24, 4811-4841. 11.

Ye, X.; Millan, J. A.; Engel, M.; Chen, J.; Diroll, B. T.; Glotzer, S. C.; Murray, C. B.,

Shape Alloys of Nanorods and Nanospheres from Self-Assembly. Nano Lett. 2013, 13, 49804988. 12.

Horsch, M. A.; Zhang, Z.; Glotzer, S. C., Self-Assembly of Polymer-Tethered Nanorods.

Phys. Rev. Lett. 2005, 95, 056105. 13.

Rasin, B.; Chao, H.; Jiang, G.; Wang, D.; Riggleman, R. A.; Composto, R. J., Dispersion

and alignment of nanorods in cylindrical block copolymer thin films. Soft Matter 2016, 12, 21772185. 14.

Ferrier, R. C.; Koski, J.; Riggleman, R. A.; Composto, R. J., Engineering the Assembly

of Gold Nanorods in Polymer Matrices. Macromolecules 2016, 49, 1002-1015. 15.

Horsch, M. A.; Zhang, Z.; Glotzer, S. C., Self-Assembly of Laterally-Tethered Nanorods.

Nano Lett. 2006, 6, 2406-2413.

13



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

16.

Page 14 of 27

Daniel, M.-C.; Astruc, D., Gold Nanoparticles: Assembly, Supramolecular Chemistry,

Quantum-Size-Related Properties, and Applications toward Biology, Catalysis, and Nanotechnology. Chem. Rev.2004, 104, 293-346. 17.

Tang, L.; Li, S.; Xu, L.; Ma, W.; Kuang, H.; Wang, L.; Xu, C., Chirality-based Au@Ag

Nanorod Dimers Sensor for Ultrasensitive PSA Detection. ACS Appl. Mater. Interf. 2015, 7, 12708-12712. 18.

Wang, L.-Y.; Smith, K. W.; Dominguez-Medina, S.; Moody, N.; Olson, J. M.; Zhang, H.;

Chang, W.-S.; Kotov, N.; Link, S., Circular Differential Scattering of Single Chiral SelfAssembled Gold Nanorod Dimers. ACS Photonics 2015, 2, 1602-1610. 19.

Biswas, S.; Duan, J.; Nepal, D.; Park, K.; Pachter, R.; Vaia, R. A., Plasmon-Induced

Transparency in the Visible Region via Self-Assembled Gold Nanorod Heterodimers. Nano Lett.

2013, 13, 6287-6291. 20.

Shao, L.; Woo, K. C.; Chen, H.; Jin, Z.; Wang, J.; Lin, H.-Q., Angle- and Energy-

Resolved Plasmon Coupling in Gold Nanorod Dimers. ACS Nano 2010, 4, 3053-3062. 21.

Slaughter, L. S.; Wu, Y.; Willingham, B. A.; Nordlander, P.; Link, S., Effects of

Symmetry Breaking and Conductive Contact on the Plasmon Coupling in Gold Nanorod Dimers.

ACS Nano 2010, 4, 4657-4666. 22.

Ma, W.; Kuang, H.; Wang, L.; Xu, L.; Chang, W.-S.; Zhang, H.; Sun, M.; Zhu, Y.; Zhao,

Y.; Liu, L.; Xu, C.; Link, S.; Kotov, N. A., Chiral plasmonics of self-assembled nanorod dimers.

Sci. Rep. 2013, 3, 1934. 23.

Osberg, K. D.; Harris, N.; Ozel, T.; Ku, J. C.; Schatz, G. C.; Mirkin, C. A., Systematic

Study of Antibonding Modes in Gold Nanorod Dimers and Trimers. Nano Lett. 2014, 14, 69496954. 14


Page 15 of 27

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


24.

Schneider, T.; Stoll, E., Molecular-dynamics study of a three-dimensional one-

component model for distortive phase transitions. Phys. Rev. B 1978, 17, 1302-1322. 25.

DÜNWEG, B.; PAUL, W., BROWNIAN DYNAMICS SIMULATIONS WITHOUT

GAUSSIAN RANDOM NUMBERS. Internat. J. Modern Phys. C 1991, 02, 817-827. 26.

Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of

Computational Phys. 1995, 117, 1-19. 27.

Feng, J.; Liu, H.; Hu, Y., Molecular dynamics simulations of polyampholytes inside a slit.

Molecular Simulation 2005, 31 , 731-738. 28.

Kuijk, A.; van Blaaderen, A.; Imhof, A., Synthesis of Monodisperse, Rodlike Silica

Colloids with Tunable Aspect Ratio. J. Am. Chem. Soc. 2011, 133, 2346-2349. 29.

Zhang; Horsch, M. A.; Lamm, M. H.; Glotzer, S. C., Tethered Nano Building Blocks:

Toward a Conceptual Framework for Nanoparticle Self-Assembly. Nano Lett. 2003, 3, 13411346.

15



Figure 1. Fractions of individual nanorods f1 (a), nanorod dimers f2 (b), and nanorod trimers+ f3+ (c) as functions of the interaction εRR between nanorods in an organic solvent for ϵ = 1.0, q = -1e and T * = 1.0 . Dashed lines : R10; black solid lines: R10P2; blue solid lines: R10P4; red solid lines:R10P6; dark green solid lines: R10P8; pink solid lines: R10P10. The polyelectrolyte molecular weight Pn (n=0, 2,..10) increases along the direction of the arrow.

0.4

(a)

fraction f2

fraction f1

1.0 0.8 0.6 0.4 0.2

(b)

0.3 0.2 0.1 0.0

0.0 -0.1

0.0

1.0

2.0

3.0

4.0

0.0

1.0

εRR/ε0

2.0

3.0

4.0

εRR/ε0

1.0

fraction f3+

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 16 of 27

0.8 0.6 0.4 0.2

(c)

0.0 0.0

1.0

2.0

3.0

4.0

εRR/ε0

16


Page 17 of 27

Figure 2. Average size of aggregates S3+ as functions of interactions between nanorods in an organic solvent for ϵ = 1.0, q = -1e and T * = 1.0 . Line: R10; circle ( ): R10P2; square ( ): R10P4; triangle up ( ): R10P6; triangle down ( ): R10P8; diamond ( ): R10P10.

25 20

S3+

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


15 10 5 0 0.0

1.0

2.0

3.0

4.0

εRR/ε0

17



Fig 3. Percentages of nanorod aggregates as functions of their sizes in an organic solvent for ϵ =1.0, q= -1e, εRR=2.2ε0 and T * = 1.0 . (a) R10; (b)R10P2; (c)R10P10. Insets: snapshots of aggregates.

50

50

40

(b)R10P2

40

percentage (%)

percentage (%)

(a)R10 30 20 10 0

30 20 10 0

0.0

5.0

10.0 15.0 20.0

size of aggregates S

0.0

5.0

10.0 15.0 20.0


50

(c)R10P10

40

percentage (%)

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 18 of 27

30 20 10 0 0.0

5.0

10.0 15.0 20.0


18


Page 19 of 27

Fig 4. Fractions of individual nanorods f1 (a), nanorod dimers f2 (b), and nanorod trimers+ f3+ (c) of R10P10 as functions of interaction εRR between nanorods in solutions with various dielectric constants, q= -1e and T * = 1.0 . Black solid lines: dielectric constant ϵ = 1.0; blue solid lines: ϵ = 10.0; red solid lines: ϵ = 20.0; dark green solid lines: ϵ = 78.0; pink solid lines: ϵ = 100.0. The dielectric constant increases along the direction of the arrow.

(a)

(b)

0.3

fraction f2

fraction f1

1.0 0.8 0.6 0.4 0.2

0.2 0.1 0.0

0.0 0.0

1.0

2.0

3.0

4.0

0.0

1.0

εRR/ε0

2.0

3.0

4.0

εRR/ε0

1.0

fraction f3+

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


0.8 0.6 0.4 0.2

(c)

0.0 0.0

1.0

2.0

3.0

4.0

εRR/ε0

19



Fig. 5 Average size of aggregates S3+ of nanorod R10P10 as functions of interactions between nanorods in solutions with various dielectric constants, q= -1e and T * = 1.0 . circle( ): dielectric constant ϵ = 1.0; square( ): ϵ = 10.0; triangle up( ): ϵ = 20.0; triangle down( ): ϵ = 78.0; diamond( ): ϵ = 100.0.

10 8

S3+

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 20 of 27

6 4 2 0 0.0

1.0

2.0

εRR/ε0

3.0

4.0

20


Page 21 of 27

Fig 6. Percentages of nanorod aggregates as functions of their sizes with R10P10 in aqueous solutions (i.e. dielectric constant ϵ =78.0) for the charge of a segment of the polyelectrolyte q = 1e and εRR=2.2ε0 at T * = 1.0 . .

50 40

percentage (%)

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


30 20 10 0 0.0

5.0

10.0 15.0 20.0


21



Fig 7. Fractions of individual nanorods f1 (a), nanorod dimers f2 (b), and nanorod aggregates f3+ (c) as functions of the charge q of the polymer in an organic solvent with a dielectric constant ϵ = 1.0 and interaction between nanorods εRR=2.2ε0 for T * = 1.0 . Circle( ): R10P2; square( ): R10P4; triangle up( ): R10P6; triangle down( ): R10P8; diamond(

): R10P10.

0.5

(a)

0.08

fraction f2

fraction f1

0.10

0.06 0.04 0.02 0.00 -0.02

(b)

0.4 0.3 0.2 0.1 0.0

-3.0

-2.0

-1.0

0.0

-3.0

-2.0

-1.0

0.0

charge q

charge q

fraction f3+

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 22 of 27

1.0 0.8 0.6

(c)

0.4 -3.0

-2.0

-1.0

0.0

charge q

22


Page 23 of 27

Fig.8. Average size of aggregates S3+ as functions of the charge q of the polymer in an organic solvent with a dielectric constant ϵ = 1.0 and interaction between nanorods εRR=2.2ε0 for T * = 1.0 . Circle( ): R10P2; square( ): R10P4; triangle up( ): R10P6; triangle down( ): R10P8; diamond( ): R10P10.

14 12

S3+

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


10 8 6 4 2 -3.0

-2.0

-1.0

0.0

charge q

23



Fig 9. Fractions of individual nanorods f1 (a), nanorod dimers f2 (b), and nanorod aggregates f3+ (c) as functions of temperature in various solutions with the interaction between nanorods εRR=2.2ε0 and the charge of a segment of the polyelectrolyte q = -1e. Circle( ): R10P2 and dielectric constant ϵ = 1.0; square( ): R10P10 and dielectric constant ϵ = 1.0; triangle up( ): R10P2 and dielectric constant ϵ = 78.0; triangle down( ): R10P10 and dielectric constant ϵ = 78.0.

(a)

0.10 0.05 0.00 -0.05

(b)

0.4

fraction f2

fraction f1

0.15

0.3 0.2 0.1 0.0

-0.10 0.6

0.9

1.2

1.5

0.6

T*

0.9

1.2

1.5

T*

1.0

fraction f3+

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 24 of 27

0.9 0.8 0.7 0.6

(c)

0.5 0.4 0.6

0.9

1.2

1.5

T*

24


Page 25 of 27

Fig 10. Size of aggregates S3+ as functions of temperature in various solutions with the interaction between nanorods εRR=2.2ε0 and the charge of a segment of polyelectrolyte q = -1e. Circle( ): R10P2 and dielectric constant ϵ = 1.0; square( ): R10P10 and dielectric constant ϵ = 1.0; triangle up( ): R10P2 and dielectric constant ϵ = 78.0; triangle down( ): R10P10 and dielectric constant ϵ = 78.0.

14 12

S3+

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


10 8 6 4 2 0.6

0.9

1.2

T*

1.5

25



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 26 of 27

Table 1. Lennard-Jones Potential parameters in the simulations

Cutoff Interaction pairs

Energy ( ε 0 )

Size ( σ 0 )

R-R (nanosphere-nanosphere in

ε RR

σ RR = σ 0

2.5 σ RR

ε PR =1.0

σ PR = σ 0

21 6 σ PR

ε RI =1.0

σ RI = σ 0

21 6 σ RI

ε PP =1.0

σ PP = σ 0

21 6 σ PP

ε PI =1.0

σ PI = σ 0

21 6 σ PI

ε II =1.0

σ II = σ 0

21 6 σ II

distance( σ 0 )

nanorods)

P-R (segments in polyelectrolyte – nanosphere in nanorods)

R-I (nanospheres in nanorodscounterions of polyelectrolyte)

P-P (segments in polyelectrolyte – segments in polyelectrolyte)

P-I (segments in polyelectrolytescounterions of polyelectrolytes)

I-I (counterions of polyelectrolytes-counterions of polyelectrolytes)

26


Page 27 of 27

TOC

Polyelectrolyte

+

50

(a)R10 40

50

(c)R10P10

40

percentage (%)

percentage (%)

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


30 20 10 0

30 20 10 0

0.0

5.0

10.0 15.0 20.0


0.0

5.0

10.0 15.0

20.0


27


Controlling Nanorod Oligomer Aggregation in Solutions - The Journal

Recommend Documents