ARTICLE IN PRESS

www.elsevier.com/locate/cocis

+ model

Current Opinion in Colloid & Interface S

Self-assembly of anisotropic tethered nanoparticle shape amphiphiles

Sharon C. Glotzer a,b,*, Mark A. Horsch a, Christopher R. Iacovella a, Zhenli Zhang a,

Elaine R. Chan a, Xi Zhang b

a Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, 48109-2136, United Statesb Department of Materials Science & Engineering, University of Michigan, Ann Arbor, MI, 48109-2136, United States

Abstract

The varied and exotic shapes of new nanoscale organic and inorganic building blocks provide new opportunities to engineer materials

possessing specific functionality and physical properties dictated by the unique packings of these particles. We briefly review some of the current

strategies for inducing the self-assembly of these building blocks focusing on one strategy in particular—the attachment of tethers to the building

blocks at precise locations to create tethered nanoparticle ‘‘shape amphiphiles’’. We use computer simulation to demonstrate that the resulting

anisotropy imparted to nanocrystals or nanocolloids by the tethers can be used to encode simple design rules into the building blocks that

ultimately result in a unique self-assembled structure. We present a general classification scheme for tethered nanoparticles wherein the anisotropy

of a shape amphiphile is described by a vector comprised of one or more axes each describing a measure of anisotropy.

D 2005 Elsevier Ltd. All rights reserved.

1. Introduction

The science of colloids is enjoying an exciting revolution as

particle sizes reach down to nanometer scales. Over the past two

decades, advances in the synthesis of particles have resulted in

an impressive library of nanocrystalline particles and nanocol-

loids of various sizes, geometries, and compositions [1–5&,6–

10&&,11–13]. One of the current challenges in exploiting the

immense potential of these nanometer size building blocks is to

organize them into specific precursor structures for constructing

functional materials and devices. Historically, top down

approaches such as casting have been used to manufacture

materials, and photo-, X-ray and electron beam lithography have

been used to modify bulk materials on nanometer scales to

induce a specific functionality into the material. For example,

electron beam lithography is capable of etching patterns into a

material with feature sizes less than 100 nm [14]. The advent of

nanometer size building blocks opens the door to self-assembly,

a ‘‘bottom-up’’ approach that may provide unique opportunities

to arrange nanoscale building blocks (NBBs) into useful

structures by utilizing the interactions between the NBBs as

1359-0294/$ - see front matter D 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.cocis.2005.09.011

* Corresponding author. Department of Chemical Engineering, University of

Michigan, Ann Arbor, MI, 48109-2136, United States.

E-mail address: sglotzer@umich.edu (S.C. Glotzer).

the driving mechanism for the assembly process. The bottom-up

approach is motivated by self-assembly in natural systems

[15,16] as well as synthetic systems [17–20] such as liquid

crystals, surfactants and block copolymers. Self-assembly

provides several key advantages as compared to top-down

approaches: (1) large numbers of NBBs can be arranged

simultaneously, (2) self-assembled structures may be thermo-

dynamically stable and hence will tend toward the equilibrium

state if perturbed, thereby rendering these structures with self-

healing characteristics [21&&], and (3) highly complex structures

may be formed as a result of the structure being assembled on

nanometer length scales [21&&]. A prerequisite to exploiting these

NBBs as a viable means of engineering devices or materials is to

develop techniques that induce the NBBs to self-assemble into

target structures possessing the necessary properties or func-

tionalities. To date there have been several successful demon-

strations of techniques that induce self-assembly of NBBs, e.g.

magnetic fields [22], shear stress [23], solvent evaporation

[22,24], the use of soft-matter templates such as diblock

copolymers, or the use of soft-matter to coat nanoparticles with

synthetic polymers or oligonucleotides [10&&,12,25,26&,27–

32&&]. These demonstrations have resulted in structures resem-

bling chains [33] and wires, hexagonally arranged particles [22],

worm-like and labyrinth-like structures [22], precise clusters

[22,24], nanowires [34], and onion-like vesicles [23], as well as

aggregates with little or no order. In contrast to these techniques,

cience xx (2005) xxx – xxx

COCIS-00431; No of Pages 9

ARTICLE IN PRESSS.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx2

natural self-assembly processes may utilize design rules encoded

into the building blocks themselves or provided to the building

blocks by other particles to guide their assembly [35] into highly

complex and functional structures. For example, viruses are well

known to assemble into a variety of uniquely shaped capsids

such as icosahedra, tubes, helices, and sheets [36–41] and

diatoms, small unicellular algae with cell walls that are

impregnated with silica, assemble into complicated hierarchical

structures[42,43]. However, the self-assembly of these natural

building blocks is far from understood, and their intricate and

precise structures are unmatched by modern science.

An emerging strategy to encode design rules into synthetic

NBBs is to introduce anisotropy to the building blocks by

functionalizing the nanoparticles with a small number of tethers

[44&&] attached at specific locations on the surface of the particle.

Before turning our discussion to tethered nanoparticles it is

useful to briefly discuss a fairly well understood self-assembling

system, block copolymers (BCPs). BCPs provide an elegant

example of how anisotropy can influence the self-assembled

structure. By simply changing the degree of polymerization of

one block relative to the other block, the structures formed by

the BCP can be manipulated in a predictable manner. In the case

of diblock copolymer melts, varying the relative block fraction

results in four types of possible ordered structures: body-

centered cubic micelles, hexagonally packed cylinders, a

bicontinuous gyroid morphology, and lamellae [45]. Changing

the degree of polymerization of both blocks simultaneously can

be used to control the length scale of the domains of each

morphology from several nanometers to greater than 100 nm.

These controllable features in BCPs may provide insight into

how tethered NBBs will self-assemble.

Many examples of ‘‘tethered’’ nanoparticles have recently

been reported in the literature. For example, Song et al. [31]

synthesized Buckyballs with poly(ethylene oxide) (PEO)

tethers attached. They studied the effect of miscibility and

C60 concentration on the aggregation behavior of the PEO-

tethered fullerenes. Alivisatos’ group demonstrated the ability

to attach one, two, three, or more tethers to the surface of

spherical Au nanoparticles [5&]. Stellaci’s group developed a

technique whereby spherical Au nanoparticles are coated with

surfactant molecules (octanethiol and mercaptopropionic acid)

that phase separate into rings on the particle surface [46&&].

Westenhoff and Kotov [47] created a network of CdTe quantum

dots tethered to a polyelectrolyte film via anionic polyethylene

glycol (PEG) tethers. They demonstrated that the distance

between the nanoparticles and the film can be controlled by the

solvent quality, resulting in a change in the luminescence of the

particles. Coughlin’s group attached a single polystyrene tether

to nanometer-sized cubic silsesquioxanes [48], and Mather’s

group synthesized amphiphilic telechelic cubic silsesquioxanes

where the cubes are linked together by a PEG tether [49].

Demonstrations of tethered rods include rod-like molecules

with tethers attached at one end of the rod [50], the middle of the

rod [51], and at both ends of the rod [52].

The above examples illustrate significant advances in the

ability to synthesize anisotropic nanometer size building blocks

with specific geometries and topologies and serve as proof-of-

concept for the synthesis of tethered nano building blocks in

particular. However, little is known about the self-assembled

structures formed by these building blocks. In general, no

theory exists that can predict the self-assembly behavior of

tethered NBBs and it is here where simulation of model NBBs

can play an important role in helping to identify the parameters

relevant to the self-assembly process and how they influence

the formation of target structures. By systematically varying

the type and degree of anisotropy in model NBBs, we can

extract information that is useful for developing a general

framework to aid in the design of NBBs that can self-assemble

into specific structures. Here we focus on self-assembly of

amphiphilic tethered NBBs and make direct comparisons with

self-assembling block copolymers, surfactants and liquid

crystals.

2. NBB anisotropy

A first and important step towards understanding the self-

assembly behavior of anisotropic, NBBs is to classify the degree

and type of the anisotropy and then to determine the effect of the

anisotropy on the final structure formed by the NBBs. We begin

by classifying tethered nanoparticles according to independent

measures of their anisotropy, using a classification scheme

developed by Solomon and Glotzer [53] whereby the anisotropy

of a given building block is described by a vector formed by

combining multiple axes. Fig. 1 demonstrates a few of the

possible ways in which the anisotropy of tethered particles can

be manipulated. For example, the A and B axes denote the

number and length of tethers, respectively, where these

parameters can be varied independently. Axis C refers to

nanoparticle anisometry arising from the number of vertices on

the nanoparticle [53]. The geometry of a nanoparticle may

strongly impact the local arrangement of particles and has been

shown to induce liquid crystalline ordering in various systems

[44&&,54]. The D axis denotes variation in the relative placement

of tethers where the ‘‘geometry’’ of the building block is altered

moving along the axis. The NBB geometry is expected to

critically affect the self-assembled structures possible. For

example, a particle with two diametrically opposed tethers

may self-assemble into vastly different structures compared to

particles with the tethers attached at a 10- angle of separation.The degree of specificity of the tethers may also be altered (Fig.

1 axis E), with the limiting cases being that of a homopolymer

(low degree of specificity) and a DNA oligonucleotide (high

degree of specificity). Between these extremes exists varying

degrees of specificity, including diblock, triblock, and multi-

block copolymer tethers, polyelectrolyte tethers, etc. Fig. 1

illustrates only a few anisotropy dimensions that can be

manipulated in tethered nanoparticles. Understanding how each

of these anisotropies influences the types of structures these

NBBs self-assemble into is paramount in developing a

theoretical framework for predictably and rationally designing

future materials and devices, and this is the focus of the work

discussed in this review. Specifically, we concentrate here on

understanding the effect of anisotropies in shape, tethered NBB

topology and geometry, and solvent selectivity on the equilib-

ARTICLE IN PRESS

Fig. 1. Classification of tethered nanoparticle ‘‘shape amphiphile’’ anisotropy, following scheme developed by Glotzer and Solomon [53]. Various building blocks are

classified in homologous series according to particular measures of anisotropy: (a) Number of tethers, (b) Length of tether, (c) Number of nanoparticle vertices, (d)

Relative location of tethers, (e) Tether specificity. Many additional anisotropy dimensions are not shown. More complex anisotropies can be described as

combinations of these dimensions.

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx 3

rium structures formed by amphiphilic tethered nanoparticles

that interact via weak nonspecific interactions.

3. Model and method

As discussed in the following sections, the complex

phase behavior exhibited by model amphiphilic tethered

nanoparticles arises from the coupling between the amphi-

philic nature of the model NBBs and the local packing of

the rigid nanoparticles. We developed a coarse-grained

particle-based model to study this coupling for a diverse

array of nanoparticle shapes and tethered NBB topologies.

The model NBBs are treated as a group of small spherical

subunits frozen into a specific geometry (Fig. 2), where the

subunits interact with empirical pair potentials, e.g., Len-

nard–Jones (LJ) or Weeks–Chandler–Andersen (WCA)

potentials (Fig. 3). For solvophilic species, the interactions

are treated with a purely repulsive WCA potential to prevent

aggregation of the species, incorporate excluded volume, and

induce swelling of the tethers. Interactions between solvo-

phobic species are treated with a LJ potential to account for

excluded volume effects and to induce aggregation at low

temperature. This model, while crude, allows for the study

of nanoparticles with a variety of different geometries

without the development of complicated force fields for

each of the specific geometries studied. Polymer tethers are

modeled as linear bead-spring chains where the connectivity

of the beads is modeled by a finitely extensible non-linear

elastic (FENE) spring [55]. To prevent unphysical chain

crossing, the dimensionless spring constant is taken to be 30

and the maximum extendable length of the FENE spring is

1.5r, where r is the diameter of a bead. An advantage of

this model is that the complex coupling between the

enthalpic and entropic interactions arises naturally.

The time evolution of the model NBBs is tracked using

Brownian dynamics (BD), a subset of Langevin dynamics,

wherein particle trajectories are governed by the Langevin

equation.

mi

dmi tð Þdt

¼ � cimi tð Þ þ Fi x tð Þf g þ Ri tð Þ ð1Þ

The left hand side of Eq. (1) is the force felt by particle

i at time t. The first term on the right hand side is the non-

conservative drag force, Fi is the deterministic force

obtained from differentiation of the conservative potential

field, and Ri is the stochastic force, which satisfies the

fluctuation dissipation theorem. ci is the friction coefficient

and is related to particle diffusion by the Einstein

relationship,

ci ¼ kBT=D; ð2Þ

where kB is Boltzmann’s constant, T is the temperature, and

D is the diffusion coefficient. In BD, solvent molecules are

treated implicitly in a statistical manner, significantly

reducing the number of force calculations required. When

solvent molecules are considerably smaller than the NBBs,

implicit treatment of the solvent also avoids resolving the

time scale necessary to consider their fast degrees of

freedom. Additionally, the dissipative forces in the BD

ARTICLE IN PRESS

Fig. 2. Model building blocks. Blue spheres represent soft matter and collections of red spheres represent rigid nanoparticles. (a) Representative model of mono-

tethered sphere illustrated in Fig. 4(a). (b) Representative model of tri-tethered triangle plate illustrated in Fig. 4(i). (c) Representative model of end-tethered rod

particle illustrated in Fig. 4(c). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx4

method increase the size of the allowable time steps for

integrating the equations of motion.

4. Self-assembly of tethered nanoparticles

Using this model and method we have investigated several

important geometries and topologies (see Fig. 4) relevant to

amphiphilic tethered NBBs and their subsequent roles in the

self-assembly process. Specifically, we discuss mono- and di-

tethered spheres, mono- and tetra-tethered cubes, several plate-

like geometries, and mono-tethered rods.

4.1. Mono- and di-tethered spheres

We begin by discussing the impact of nanoparticle diameter

on the overall phase behavior of mono-tethered spheres (Fig.

4(a)), where the nanoparticles are solvophilic and the tethers

are solvophobic. We conducted a series of simulations for

several different nanoparticle diameters and a fixed tether

length [56]. Simulations were performed for a tether length of

8r and nanoparticle diameters of d =1.5r, 2.0r, 2.5r, and3.0r. We predicted the existence of three distinct regimes in

the phase behavior of tethered nanospheres (TNS) depending

on the ratio Fv [56] of the nanoparticle volume to tether

volume.

The first regime studied is where the head group volume is

small compared to the tether volume, and predominantly

Fig. 4. Cartoon schematics of models studied: (a) mono-tethered sphere, (b) di-

tethered sphere, (c) end-tethered rod, (d) side-tethered rod, (e) mono-tethered

cube, (f) tetra-tethered cube, (g) edge-tethered hexagonal plate, (h) face tethered

Fig. 3. Diagram of the range and shape of the Weeks–Chandler–Andersen

(WCA) potential and the Lennard–Jones (LJ) potential used to model the

amphiphilic and packing interactions between the nanoscale building blocks

such as those illustrated in Figs. 2 and 4.

,

lamellar phases result. For a nanoparticle diameter d =1.5r and a

fully extended tether length of 8r we predicted the formation of

a lamellar (L) phase and a perforated lamellar phase (PLH) [56].

In the perforated lamellar phase the perforations exist in the

layers formed by the head groups, which contrasts with what is

typically observed for surfactants [57,58] where the perforations

are restricted to the layers formed by the tail group ‘‘tethers’’

(PLT).

The second regime investigated is where head group and

tether volumes are similar, and this set of parameters results in a

rich combination of phases. For a nanoparticle with diameter

d =2.0r connected to a tether with a fully extended length of 8r,we predicted the formation of hexagonally packed cylinders (H),

lamellae (L), and perforated lamellae (PLT) where the perfora-

tions are through the tether layers (Fig. 5(a)). These results are

similar to those observed by Larson [59,60] in lattice Monte

Carlo simulations of surfactants modeled as two flexible chains

(head and tail chains) bound together.

The third regime probed is where the head group volume is

larger than the tether volume and predominantly phases with

curved interfaces result. For a nanoparticle with diameter

d =2.5r connected to a tether with a fully extended length of

8r, we predicted the formation of cubic ordered micelles (C),

hexagonally packed cylinders (H) (Fig. 5(b)), lamellae (L), and

perforated lamellae (PLT) where the perforations are through

the tether layers [56]. For a nanoparticle with diameter d =3.0r,

hexagonal plate, (i) tri-tethered triangle plate.

ARTICLE IN PRESS

Fig. 5. (a) Perforated lamellae through the tethers (PLT) for d =2.5r, / =0.525, T*=1.5. Inset: a single perforated sheet. (b) Hexagonally packed cylinders (H) for

d =2.0r, / =0.3, T*=1.0. Inset: a single cylinder. (c) Cubic ordered micelles for d =3.0r, / =0.3, T*=0.25. Inset: a single micelle. (d) Lamellar bilayers (L) for

d =3.0r, / =0.3, T*=0.25. Inset: hexagonal order within each bilayer. (a) and (b) are re-rendered using data from Ref. [56], and (c) and (d) are re-rendered using

data from Ref. [44].

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx 5

we also observed the formation of micelles for intermediate

volume fractions (/ =0.3) of the mono-tethered sphere (Fig.

5(c)). However, if the solvent conditions are changed such that

the nanoparticles are solvophobic and the tethers are solvo-

philic we observed the formation of bilayer sheets instead of

cubic ordered micelles (Fig. 5(d)) at the same value of /.

In all cases of nanoparticle size, we observed an increase in

the ordering of the nanoparticles with an increase in concen-

tration of the system. Furthermore, as the volume of the

nanoparticle is increased for a fixed tether length, the dominant

structures shift from sheet-like structures for small Fv to curved

structures for large Fv.

In the study of di-tethered spheres with diametrically

opposing tethers (Fig. 4(b)), one tether and the nanoparticle

are chosen to be solvophobic and the other tether is solvophilic.

The diameter of the nanoparticle is d =2.0r and the tethers each

have length 5r. For this system, the nanoparticles self-

assembled into core-shell cylinders and spherical micelles and

mono-layered sheets depending on the NBB concentration and

system temperature (Fig. 6). These di-tethered spheres are to

some extent analogous to short linear triblock copolymers,

where the middle ‘‘block’’ is a nanoparticle. Triblock copoly-

mers have been demonstrated to self-assemble into structures

considerably more complicated than those observed for diblock

copolymers [61–64], e.g. interpenetrating tetragonally arranged

cylinders, lamellae with spherical micelles inside, etc. have been

observed. To date, the bulk phases we predicted for the di-

tethered spheres are similar—on the mesoscale—to those

observed for simple mono-tethered spheres; however, the local

ordering is different. A comparison between the cylindrical

phases formed by the mono-tethered spheres and those formed

by the di-tethered spheres reveals that the latter assembles into

core-shell cylinders that are separated by a polymer matrix (Fig.

6(b)). We also found that the lamellar structures formed by di-

tethered spherical NBBs are mono-layered sheets comprised of

nanoparticles while bilayer sheets formed in the mono-tethered

sphere systems (Fig. 6(a)).

4.2. Mono- and tetra-tethered cubes

To investigate the role of nanoparticle shape (e.g. moving

along the C-axis in Fig. 1) we studied systems of mono- and

tetra-tethered nanocubes (Fig. 4(e)). In this study, the tethers are

attached at the corners of the cubes akin to the functionalization

of polyhedral oligomeric silsesquioxane cubes [65,66]. In one

case, the cubes are solvophobic and the tethers are solvophilic.

The length of one side of the cube is d =2r. For the systems

composed of mono-tethered cubes at low volume fractions /¨0.3, we predicted the formation of bilayer sheets (Fig. 7(a))

[67]. Furthermore, we investigated the role of relative volume

fraction fA of the tether and predicted that for fA=0.3–0.6 the

stable structure is bilayer sheets, rather than cylindrical or

spherical micelles as would be expected for self-assembling

asymmetric BCPs or surfactants.

ARTICLE IN PRESS

Fig. 6. (a) Monolayer sheets formed from di-tethered spheres for d =3.0r, / =0.57, T*=1.0. Inset: hexagonal ordering within a nanoparticle layer. (b) Hexagonally

arranged cylindrical shells formed from di-tethered spheres for d =3.0r, / =0.25, T*=2.0. Inset: a single cylinder. Re-rendered using data from Ref. [44&&].

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx6

For the tetra-tethered cubes (Fig. 4(f)), the tethers are attached

at the corners on the same side of the cube. Relative volume

fractions of fA=0.5 and fA=0.67 were studied. In contrast to the

mono-tethered cubes with fA=0.5, we predicted that only

structures with curved interfaces are formed [68]. Specifically,

we predicted the formation of disordered spherical micelles,

FCCmicelles, and hexagonally packed cylinders (Fig. 7(b)). For

an overall volume fraction of / =0.3, cylinders or FCC micelles

were formed for fA=0.5 and fA=0.67, respectively. Thus,

attaching multiple tethers to the same face of the cube results

in the stabilization of ‘‘curved’’ structures instead of sheet-like

structures. In all cases, the cubic nature of the building block

induces the formation of structures with distinctly ‘‘square’’

cross-sections.

4.3. Multi-tethered planar geometries

Planar nanoparticle geometries were also investigated. We

studied circular and hexagonal disks with tethers attached

either on the edges or on the faces, and triangular plates with

tethers attached at the vertices (Fig. 4(g)–(i)) [44&&].

Fig. 7. (a) Lamellae formed from mono-tethered cubes for / =0.3, and fA=0.6 (c

Cylinders formed from tetra-tethered cubes for / =0.3, and fA=0.5 (tethers removed

cubes. Re-rendered using data from Ref. [68]. (For interpretation of the references

article.)

In the study of tethered disks, we observed that for certain

temperature ranges the disks form hexagonally packed colum-

nar structures when the tethers are bonded equatorially to the

disks (Fig. 8(a)), and form sheets within which the disks pack

hexagonally when the tethers are attached on opposite faces of

the disk (Fig. 8(b)) for overall volume fractions of / =0.42 and

/ =0.31, respectively. This is in contrast to BCPs where we

expect sheet-like structures for / =0.42 and column-like

structures for / =0.3. For the triangular plates, we found that

at an overall volume fraction / =0.31 hexagonally arranged

columnar structures formed (Fig. 8(c)). In the case of the

triangular plate, where / =0.31 and fA=0.36, analogies with

surfactants and BCPs would predict the formation of sheet-like

structures. For these systems, the placement of the tethers

ultimately determines the structures that form.

4.4. Mono-tethered rods

Amphiphilic tethered nanorods can be regarded as geomet-

rically similar to short, amphiphilic, rod-coil block copolymers.

In contrast to amphiphiles consisting of two flexible chains,

ubes are blue and tethers are red). Re-rendered using data from Ref. [67]. (b)

for clarity). Note the cubic cross-section induced by the face-to-face packing of

to colour in this figure legend, the reader is referred to the web version of this

ARTICLE IN PRESS

Fig. 8. (a) Hexagonal columnar (cylinder) phase formed from edge-tethered disks (see Fig. 4(g)) for / =0.42, fA=0.28, and T*=1.0. The disks are tilted with respect

to the interfacial normal. (b) Lamellar phase formed from face-tethered hexagonal disks (see Fig. 4(h)) for / =0.31, fA=0.5, and T*=1.0. The disks pack

hexagonally within the sheet. (c) Hexagonal columnar phase formed where tethers are attached to the three vertices of a triangular plate (see Fig. 4(i)) for / =0.31,

fA=0.35, and T*=0.83. The triangles form a twist about the cylindrical axis. Re-rendered using data from Ref. [44&&].

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx 7

theories for amphiphiles with a rod-like block are less

developed. Although the principles governing self-assembly

into microphases are similar, the entropic interactions for

tethered rods are more complicated due to the asymmetry

between the rod and the tether and the tendency of the rigid

block to orient itself with respect to other rigid blocks (i.e.

exhibit liquid crystalline ordering). This asymmetry leads to the

formation of self-assembled mesoscale structures that are

locally more ordered than those observed for amphiphiles

consisting of two flexible blocks. We briefly review our

findings for two different classes of tethered nanorods (Fig.

4(c,d)). For both classes, the nanorod is solvophobic and the

tether is solvophilic. We first discuss end-tethered nanorods

with a rod aspect ratio of 5 :1 and equal relative volume

fractions of rod and tether (R5ET5).

We observed that at low volume fractions / =0.3 and at

relative block fractions of fA=0.5 the end-tethered rods self-

assembled into a hexagonally packed cylindrical arrangement

[54]. For the systems of end-tethered rods, we predicted that at

fA=0.5 lamellar structures, e.g. a smectic C phase (Fig. 9(a)),

will only form at higher overall volume fractions of / >0.35.

Additional liquid crystalline phases observed include tetrago-

nally perforated lamellae, honeycomb, hexagonal chiral cylin-

ders, and cubic micelles [54].

For side-tethered rods with a rod aspect ratio of 5 :1, equal

relative block fractions fA=0.5 of rod and tether (R5ST5),

and overall volume fraction / =0.3, we predicted the

formation of a lamellar structure (Fig. 9(b)) at the same

values of fA and / as those discussed for the end-tethered

rods. This morphology contrasts with that observed for the

end-tethered rods where a cylindrical or curved structure is

the stable structure [69].

5. Conclusions

In this paper, we have attempted to provide a brief

background of the types of structures relatively simple

tethered nanoparticle shape amphiphiles will form due to

self-assembly. In particular, we discussed how the placement

of tethers at specific locations on the nanoparticles can

introduce further building block anisotropy to the particle.

We provided a rudimentary classification scheme of the

types of anisotropy that can potentially be imparted to

nanoparticles through the use of tethers. Furthermore, we

demonstrated through simulation how a specific tethered

NBB anisotropy results in their self-assembly into a specific

structure. For example, by attaching tethers to the four

corners on the same side of a cubic particle at relatively high

volume fractions, cubes can be induced to self-assemble into

hexagonally ordered cylindrical structures with square cross-

sections. Thus, the four tethers— when combined with the

correct conditions—provide a set of rules that dictate the

type of structure formed by the NBB. In addition to

demonstrating how anisotropy can be used we observed

three other salient features of amphiphilic, tethered nanopar-

ticles: (1) for the model NBBs discussed here the meso-

phases formed are largely limited to those commonly

observed in BCP, surfactant, or liquid crystal systems, but

with shifts in phase boundaries and significant modifications

to local packing; (2) the local ordering of the nanoparticles

within the mesophases is a strong function of the geometry

of the nanoparticle, and (3) BCPs, surfactants and liquid

crystals can be used as a rough guide to understanding the

structures formed by the NBBs.

The future of self-assembled materials lies in the

purposeful engineering of building blocks to achieve a given

target structure. As our ability to pattern and functionalize

particles with nanometer scale precision grows, so too will

our ability to fabricate self-assembled materials and struc-

tures with great complexity and sophistication, eventually

rivaling the intricate structures of the biological world.

Systematic investigation of the various anisotropy dimen-

sions available to nanocolloidal building blocks such as

those shown in Fig. 1 will provide critical insight into the

ARTICLE IN PRESS

Fig. 9. (a) Smectic C phase formed from end-tethered nanorods (see Fig. 4(c)) for / =0.35, fA=0.5, and T*=4.0. Re-rendered using data from Ref. [54]. (b) Lamellar

phase formed from side-tethered nanorods (see Fig. 4(d)) for / =0.4, fA=0.5, and T*=1.3. Re-rendered using data from Ref. [69].

S.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx8

design rules that will make such engineered structures

feasible.

Acknowledgements

Financial support for this work has been provided by the

National Science Foundation under Grant DMR-0103399 and

the U.S. Department of Energy under Grant DE-FG02-

02ER46000.

References and recommended readings

[1] Busbee BD, Obare SO, Murphy CJ. An improved synthesis of high-

aspect-ratio gold nanorods. Adv Mater 2003;15(5):414–6.

[2] Im SH, Lee YT, Wiley B, Xia Y. Large-scale synthesis of silver

nanocubes: the role of HCl in promoting cube perfection and mono-

dispersity. Angew Chem Int Ed 2005;44(14):2154–7.

[3] Jana NR, Gearheart L, Murphy CJ. Wet chemical synthesis of silver

nanorods and nanowires of controllable aspect ratio. Chem Commun

2001;7:617–8.

[4] Kabashin AV, Meunier M, Kingston C, Luong JHT. Fabrication and

characterization of gold nanoparticles by femtosecond laser ablation

in an aqueous solution of cyclodextrins. J Phys Chem, B 2003;

107:4527–31.

[5]&

Manna L, Milliron DJ, Meisel A, Scher EC, Alivisatos AP. Controlled growth

of tetrapod branched inorganic nanocrystals. Nat Mater 2003;2(6):382–5.

This paper presents a high yield method for producing monodisperse nano

tetrapods.

[6] Murphy CJ. Nanocubes and nanoboxes. Science 2002;298:2139.

[7] Ohno T, Yatsuya S. Growth of fullerene nanoparticles prepared by the gas-

evaporation technique. J Mater Sci 1998;33(24):5843–7.

[8] Peng X, Manna L, Yang W, Wickham J, Scher E, Kadavanich A,

Alivisatos PA. Shape control of CdSe nanocrystals. Nature 1998;396:444.

[9] Pinna N, Weiss K, Urban J, Pileni MP. Triangular CdS nanocrystals:

structural and optical studies. Adv Mater 2001;13:261.

[10]&&

Puntes VF, Krishnan KM, Alivisatos PA. Colloidal nanocrystal shape and

size control: the case of cobalt. Science 2001;291:2115.

This paper presents evidence that a unified set of synthetic strategies is

applicable for different nanoparticle systems. The authors demonstrate

that principles used for cadmium selenide can be used to control the size

and shape of cobalt nanoparticles. They show that by using a mixture of

surfactants they can control the growth rate of different faces on the

nanocrystal, thereby controlling shape.

& of special interest.&& of outstanding interest.

[11] Sun YG, Xia YN. Shape-controlled synthesis of gold and silver

nanoparticles. Science 2002;298:2176–9.

[12] Viau G, Brayner R, Poul L, Charoune N, Lacaze E, Fievet-Vincent F, et al.

Ruthenium nanoparticles: size, shape, and self-assemblies. Chem Mater

2003;15:486–94.

[13] Zhao HY, Douglas EP, Harrison BS, Schanze KS. Preparation of CdS

nanoparticles in salt-induced block copolymer micelles. Langmuir

2001;17(26):8428–33.

[14] Hess HF, Pettibone D, Adler D, Bertsche K, Nordquist KJ, Mancini DP, et

al. Inspection of templates for imprint lithography. J Vac Sci Technol, B

2004;22(6):3300–5.

[15] Jones MN, Chapman D. Micelles, monolayers, and biomembranes. . New

York’ Wiley-Liss; 1995.

[16] Grantcharova V, Alm EJ, Baker D, Horwich AL. Mechanisms of protein

folding. Curr Opin Struct Biol 2001;11(1):70–82.

[17] Desiraju GR. Crystal engineering: the design of organic solids. . New

York’ Elsevier; 1989.

[18] Evans DF, Wennerstrom H. The colloidal domain: where physics,

chemistry, biology, and technology meet. . New York’ Wiley; 1999.

[19] Thomas EL. Materials science—the abcs of self-assembly. Science

1999;286(5443):1307.

[20] Kumar A, Abbott NL, Kim E, Biebuyck HA, Whitesides GM. Patterned self-

assembled monolayers and mesoscale phenomena. Acc Chem Res

1995;28(5):219–26.

[21]&&

Whitesides GM, Boncheva M. Beyond molecules: self-assembly of

mesoscopic and macroscopic components. Proc Natl Acad Sci USA

2002;99(8):4769–74.

This paper provides an excellent general discussion of self-assembly on

different size scales.

[22] Pileni MP. Nanocrystal self-assemblies: fabrication and collective proper-

ties. J Phys Chem, B 2001;105:3358–71.

[23] Gauffre F, Roux D. Studying a new type of surfactant aggregate (‘‘spher-

ulites’’) as chemical microreactors. A first example: copper ion entrapping and

particle synthesis. Langmuir 1999;15:3738–47.

[24] Manoharan VN, Elsesser MT, Pine DJ. Dense packing and symmetry in

small clusters of microspheres. Science 2003;301(5632):483–7.

[25] Boal AK, Ilhan F, DeRouchey JE, Thurn-Albrecht T, Russell TP, Rotello

VM. Self-assembly of nanoparticles into structured spherical and network

aggregates. Nature 2000;404:746–8.

[26]&

Carroll JB, Frankamp BL, Rotello VM. Self-assembly of gold nanoparticles

through tandem hydrogen bonding and polyoligosilsequioxane (poss)-poss

recognition processes. Chem Commun 2002;17:1892–93.

This paper demonstrates the self-assembly of tethered gold nanoparticles

into well-defined spherical domains. The nanoparticles are functionalized

with polyhedral oligomeric silsequioxanes which induce the aggregation of

the functionalized nanoparticle.

[27] Saini RK, Chiang IW, Peng HQ, Smalley RE, Billups WE, Hauge RH, et

al. Covalent sidewall functionalization of single wall carbon nanotubes. J

Am Chem Soc 2003;125(12):3617–21.

ARTICLE IN PRESSS.C. Glotzer et al. / Current Opinion in Colloid & Interface Science xx (2005) xxx–xxx 9

[28] Korgel BA, Fitzmaurice D. Self-assembly of silver nanocrystals into two-

dimensional nanowire arrays. Adv Mater 1998;10(9):661–5.

[29] Riggs JE, Guo Z, Carroll DL, Sun YP. Strong luminescence of solubilized

carbon nanotubes. J Am Chem Soc 2000;122:5879–80.

[30] Song T, Dai S, Tam KC, Lee SY, Goh SH. Aggregation behavior of

two-arm fullerene-containing poly(ethylene oxide). Polymer 2003;

44(8):2529–36.

[31] Song T, Dai S, Tam KC, Lee SY, Goh SH. Aggregation behavior of C-60-

end-capped poly(ethylene oxide)s. Langmuir 2003;19(11):4798–803.

[32]&&

Mirkin CA, Letsinger RL, Mucic RC, Storhoff JJ. A DNA-based method

for rationally assembling nanoparticles into macroscopic materials. Nature

1996;382(6592):607–9.

This pioneering paper discusses the use of DNA as a means to rationally

assemble spherical gold nanoparticles into ordered arrays. In this scheme

gold nanoparticles are coated with one of two types of DNA and are then

mixed with a solution of oligonucleotides where each end of the

oligonucleotide has a complementary sequence to one of the two types

of DNA used to coat the nanoparticles. The oligonucleotide ‘‘linkers’’

bind the nanoparticles together to form simple ordered aggregates.

[33] Caruso F, Susha AS, Giersig M, Mohwald H. Magnetic core-shell

particles: preparation of magnetite multilayers on polymer latex micro-

spheres. Adv Mater 1999;11:950.

[34] Lopes WA, Jaeger HM. Hierarchical self-assembly of metal nanostruc-

tures on diblock copolymer scaffolds. Nature 2001;414(6865):735–8.

[35] Frydman J. Folding of newly translated proteins in vivo: the role of

molecular chaperones. Annu Rev Biochem 2001;70:603–47.

[36] Kaper JM. The chemical basis of virus structure, dissociation and

reassembly. . Amsterdam’ North Holland Pub. Co.; 1975.

[37] Johnson JE, Argos P. In: Francki RIB, editor. Virus particle stability and

structureR The plant virusesR Polyhedral virions with tripartite genomes,

vol. 1. London’ Plenum Press; 1985.

[38] Pfeiffer P, Herzog M, Hirth L. Stabilization of brome mosaic-virus. Philos

Trans R Soc London, Ser B 1976;276(943):99–107.

[39] Pfeiffer P, Hirth L. Aggregation states of brome mosaic-virus protein.

Virology 1974;61(1):160–7.

[40] Krol MA, Olson NH, Tate J, Johnson JE, Baker TS, Ahlquist P. Rna-

controlled polymorphism in the in vivo assembly of 180-subunit and 120-

subunit virions from a single capsid protein. Proc Natl Acad Sci USA

1999;96(24):13650–5.

[41] Bancroft J, Hills G, Markham R. A study of self-assembly process in a

small spherical virus—formation of organized structures from protein

subunits in vitro. Virology 1967;31(2):354-&.

[42] Pappas JL. Geometry and topology of diatom shape and surface

morphogenesis for use in applications of nanotechnology. J Nanosci

Nanotechnol 2005;5(1):120–30.

[43] Hemsley AR, Griffiths PC. Architecture in the microcosm: biocolloids,

self-assembly and pattern formation. Philos Trans R Soc London, Ser A

2000;358(1766):547–64.

[44]&&

Zhang ZL, Horsch MA, Lamm MH, Glotzer SC. Tethered nano building

blocks: toward a conceptual framework for nanoparticle self-assembly.

Nano Lett 2003;3(10):1341–6.

This paper presents the first computational study of tethered nanoparticle

‘‘shape amphiphiles’’ of various geometries.

[45] Matsen MW, Bates FS. Origins of complex self-assembly in block

copolymers. Macromolecules 1996;29(23):7641–4.

[46]&&

Jackson AM, Myerson JW, Stellacci F. Spontaneous assembly of subnano-

metre-ordered domains in the ligands shell of monolayer-protected nanopar-

ticles. Nat Mater 2004;3(5):330–6.

This paper describes the self-assembly of amixture of ligands on the surface of

a spherical gold nanoparticle. The ligands phase separate into ordered domains

on length scales as small as 0.5 nm. The work demonstrates that the domain

size and shape are dependent on the ligand concentration and the size of the

nanoparticle and shows a new way to pattern nanoparticles.

[47] Westenhoff S, Kotov NA. Quantum dot on a rope. J Am Chem Soc

2002;124(11):2448–9.

[48] Cardoen G, Coughlin EB. Hemi-telechelic polystyrene-poss copolymers as

model systems for the study of well-defined inorganic/organic hybrid

materials. Macromolecules 2004;37(13):5123–6.

[49] Kim BS, Mather PT. Amphiphilic telechelics incorporating polyhedral

oligosilsesquioxane: 1. Synthesis and characterization. Macromolecules

2002;35(22):8378–84.

[50] Lee M, Cho BK, Jang YG, Zin WC. Spontaneous organization of

supramolecular rod-bundles into a body-centered tetragonal assembly in

coil – rod–coil molecules. J Am Chem Soc 2000;122(31):7449–55.

[51] Hildebrandt F, Schroter JA, Tschierske C, Festag R, Wittenberg M,

Wendorff JH. Formation of columnar mesophases by rod-like molecules:

facial amphiphilic p-terphenyl derivatives. Adv Mater 1997;9(7):564-&.

[52] Lee M, Lee DW, Cho BK, Yoon JY, Zin WC. Supramolecular cylinder

and sphere generating thermotropic hexagonal columnar and spherical

micellar liquid crystalline assemblies in coil – rod–coil block molecules. J

Am Chem Soc 1998;120(50):13258–9.

[53] Glotzer SC, Solomon MJ. To be submitted for publication.

[54] Horsch MA, Zhang ZL, Glotzer SC. Self-assembly of polymer-tethered

nanorods. Phys Rev Lett 2005;95(5):056105-1–4.

[55] Warner HR. Kinetic-theory and rheology of dilute suspensions of finitely

extendible dumbbells. Ind Eng Chem Fundam 1972;11(3):379.

[56] Iacovella CR, Horsch MA, Zhang ZL, Glotzer SC. Phase diagrams of self-

assembled mono-tethered nanospheres from molecular simulation and

comparison to surfactants. Langmuir 2005;21(21):9488–94.

[57] Schulz MF, Khandpur AK, Bates FS, Almdal K, Mortensen K, Hajduk

DA, et al. Phase behavior of polystyrene-poly(2-vinylpyridine) diblock

copolymers. Macromolecules 1996;29(8):2857–67.

[58] ImaiM,Kawaguchi A, Saeki A, NakayaK, Kato T, ItoK, et al. Fluctuations of

lamellar structure prior to a lamellarYgyroid transition in a nonionic

surfactant system. Phys Rev, E 2000;62(5):6865–74.

[59] Larson RG. Monte Carlo simulations of the phase behavior of surfactant

solutions. J Phys II France 1996;6:1441–63.

[60] Larson RG. Molecular simulation of ordered amphiphilic phases. Chem

Eng Sci 1994;49(17):2833–50.

[61] Shefelbine TA, Vigild ME, Matsen MW, Hajduk DA, Hillmyer MA,

Cussler EL, et al. Core-shell gyroid morphology in a poly(isoprene-block-

styrene-block-dimethylsiloxane) triblock copolymer. J Am Chem Soc

1999;121(37):8457–65.

[62] Bates F, Fredrickson G. Block copolymers—designer soft materials. Phys

Today 1999;52(2):32–8.

[63] Beckmann J, Auschra C, Stadler R. Ball at the wall—a new lamellar

multiphase morphology in a polystyrene-block-polybutadiene-block-poly(-

methyl methacrylate) triblock copolymer. Macromol Rapid Commun

1994;15(1):67–72.

[64] Mogi Y, Kotsuji H, Kaneko Y, Mori K, Matsushita Y, Noda I. Preparation

and morphology of triblock copolymers of the abc type. Macromolecules

1992;25(20):5408–11.

[65] Zhang CX, Bunning TJ, Laine RM. Synthesis and characterization of

liquid crystalline silsesquioxanes. Chem Mater 2001;13(10):3653–62.

[66] Sellinger A, Laine RM, Chu V, Viney C. Palladium-catalyzed and

platinum-catalyzed coupling reactions of allyloxy aromatics with hydri-

dosilanes and hydridosiloxanes-novel liquid-crystalline organosilane

materials. J Polym Sci, Part A: Polym Chem 1994;32(16):3069–89.

[67] Zhang X., Chan ER, Glotzer SC. Self-assembled mophologies of mono-

tethered polyhedral oligomeric silsesquioxane nanocubes from computer

simulation. J. Chem. Phys.; in press.

[68] Chan ER, Zhang X, Lee CY, Neurock M, Glotzer SC. Simulations of tetra-

tethered organic/inorganic nanocube-polymer assemblies. Macromole-

cules 2005;38(14):6168–80.

[69] Horsch MA, Zhenli ZL, Glotzer SC. Self-assembly of polymer-tethered

nanorods: the role of tether placement. To be submitted for publication.