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From the perspective of materials science—and perhaps with the exception of semiconductors—the 20th century was in many ways the century of polymers. The rapid development of industrial plastics such as polystyrene and polyethylene literally revolutionized the role of materials in industry and commerce, to the point where we now have to reexamine our approach to concepts such as recycling and degradability. From that same view, the 21st century is undoubtedly dawning as the age of nanotechnology. To anyone with a background in polymer science, there is an element of irony in this, because polymers are in many ways the original “nanotechnology”. Indeed, the rather primitive view first espoused by Thomas Graham—that macromolecules are merely colloids of “associated” atoms and molecules—has much in common with many aspects of what we now think of as modern nanotechnology. At the same time, biological polymers, conjugated polymers, and block copolymers are playing increasingly important roles in nanoscale science and engineering.
If we momentarily step back from our well-informed perspective of macromolecules as long chains of atoms held together by covalent bonds, there are in fact a number of analogies that can be made between nanoparticles and polymers on a level that is more than just academic. The most obvious is size. Polymer radius of gyration, Rg, typically lies in the range of 1–100 nm, which also coincides with currently accepted definitions of nanoscale.  There are less trivial similarities too, however. Consider, for example, one of the cornerstones of polymer science; the concept of solubility. The idea that nanoparticles might be intrinsically dispersed in a solvent without any surfactant or ligand has considerable appeal in the context of applications that demand both purity and ease of processing. Recent examples include quantum dots  and graphene  with a degree of solubility in organic solvents, and single-wall carbon nanotubes (SWCNTs) with intrinsic solubility in both organic solvents  and strong acids.  The ability to use liquid processing without the constraint of having to remove residual dispersant or surfactant is technologically empowering on a level that can only find analogy in the field of polymer science.
Here, we examine this paradigm in detail, focusing on recent trends in the dispersion, purification, and self-assembly of colloidal nanoparticles with clear analogies in polymer science. We offer the argument that several of the key ideas that form the well-established pillars of polymer physics, including polydispersity, fractionation, phase ordering, and viscoelasticity, have begun to take on unique significance in the domain of nanotechnology, and that this progression will have profound implications for a number of emerging applications. Starting from the common platform of an individual nanoparticle dispersed in a fluid, we review some of the liquid-based routes to nanoparticle purification—including separation by size, shape, and band structure—that have obvious connections to the realm of polymer science. We then examine the role of miscibility, phase behavior, and phase ordering in such systems, paying particular attention to the influence of nanoparticle purity, shape, and the familiar concept of “blending”. Finally, we look at the collective mechanical response through the perspectives of rheology, viscoelasticity, and plasticity before concluding with a discussion of how all of these ideas are already impacting the implementation of nanotechnology in contemporary applications.
Liquid Dispersion and Purification
The central tenet of the entire discussion is the concept of ideal or near-ideal nanoparticle dispersion. This is not a general constraint on the potential applications of nanoparticles in polymer science, as there are several well-established examples of how poor or incomplete nanoparticle dispersion are of considerable importance to the field of polymer nanocomposites, most notably in the context of mechanical and electrical percolation. [6, 7] Typically, minimally processed nanoparticle “powder” is melt-mixed with a commercial polymer resin in an effort to impart enhanced physical characteristics at minimal particle volume fraction. Although this is of profound technological importance, it is not the path of interest here, even though some of the applications we consider ultimately use nanoparticulates in an irreversibly agglomerated state.
With a few unique exceptions, the most common route to nanoparticle dispersion involves some type of surfactant or surface treatment. SWCNTs are probably one of the most well-studied nanomaterials in this regard,  and there are notable examples where the nature of the dispersion scheme can influence the dispersion state through surfactant-mediated attractive interactions. [9, 10] The most effective small-molecule surfactants for SWCNTs are sodium dodecylbenzenesulfonate,  sodium cholate, and sodium deoxycholate,  although sodium dodecyl sulfate (SDS) has been demonstrated to have utility as well. [13, 14] Block copolymers, including pluronics, have also been used with some success.  Wrapping polymers such as single-stranded DNA [16, 17] and certain aromatic polymers  can also be effective dispersants, and SWCNTs have recently been stably sequestered in self-assembled aqueous nanopores.  Chemical functionalization is an alternative route to dispersion,  although disruption of the pristine graphene lattice with what amounts to a chemical defect can have a significant effect on the optical and electronic properties of the nanotubes.  A variety of techniques are available to quantify SWCNT dispersion. 
Graphene, a single-atomic sheet of sp2-bonded carbon arranged in a honeycomb crystal lattice, can be similarly dispersed using surfactants, where the most notable examples are the facial amphiphile sodium cholate  and select pyrene derivatives that work efficiently through π-π stacking.  By far, however, the most popular approach for imparting colloidal stability to graphene has been its chemical modification into graphene oxide (GO),  which renders the carbon nanosheets soluble in water. To a large extent, however, this aqueous solubility occurs at the expense of the intrinsic electronic properties of interest.  A partial recovery of the desired transport characteristics has been achieved through additional post processing of GO flakes. [27-29]
Semiconductor nanocrystals and metallic nanoparticles, in contrast, are typically solubilized in organic liquids using small-molecule “ligands” covalently bound or adsorbed onto the nanoparticle surface. The field is well-established and diverse, with a wide variety of surface chemistries to choose from. [30, 31] Polymer adsorption, chemical surface modification, and block copolymer encapsulation are also starting to emerge as potentially powerful techniques. [32, 33] One of the most effective and useful schemes for then rendering such hydrophobic ligand-capped nanoparticles hydrophilic, particularly for biomedical applications, is the heterofunctional PEGylation of a phospholipid molecule.  The polyethylene glycol (PEG) “corona” forms a swollen polymer micelle around the ligand-covered surface of the nanoparticle through the hydrophobicity of the phospholipid hydrocarbon tail, providing a biochemical “handle” for a range of specific functionalities. Beyond providing excellent water solubility, covalent attachment of a protein or biopharmaceutical to PEG can reduce immunogenicity and antigenicity, as well as limit renal clearance by increasing the effective hydrodynamic radius of the nanoparticle. 
As noted in the introduction, exceptional circumstances exist for the “neat” solubility of specific types of nanoparticles in certain classes of solvents. The appeal of this can be seen, for example, in the influence of interfacial stabilizer on charge transport in carbon nanotube polymer composites; at comparable loading, neat melt composites have resistivities five orders of magnitude smaller than those containing dispersant.  The concept of intrinsic nanoparticle solubility emerged from studies on carbon nanotubes, [36, 37] where classical solubility theory has had mixed success. Similar ideas have the potential to be applied to graphene,  as well as to entirely new classes of layered materials such as the transition metal dichalcogenides.  One solvent with demonstrated success at effectively dispersing graphitic materials is chlorosulfonic acid.  Although such strong acids can temporarily alter the optical and electronic properties dictated by the pristine carbon lattice, there are certain instances when this can be beneficial, as it serves as way to preferentially “dope” the material. A notable example is the influence of thionyl chloride (SOCl2) on the electronic properties of graphene and carbon nanotubes, where it has been shown to boost the number of p-type electronic carriers.  By comparison, the search for intrinsic solvents to disperse semiconductor nanocrystals is relatively young, with one recent study suggesting that bare germanium nanocrystals can be solubilized in benzonitrile through electrostatic interactions. 
Just as chain conformation and branching influence the structural properties of polymer melts and solutions, nanoparticle shape presents a rich and emerging variable for controlling structure and performance at the nanoscale. Beyond the familiar examples of rods, tubules, sheets, and spheres, more complex shapes such as polyedra, nonpolyhedra, and even branched structures can now be synthesized through controlled nucleation and growth at the atomic level for both metallic  and semiconducting nanocrystals.  The self-assembly and packing characteristics of such intricate and complex nanoparticle shapes represent intriguing new problems in materials science and engineering.  Nanoparticle stiffness likewise represents an important structural parameter. The concept of persistence length (defined as where κ is the bending stiffness) has its roots in polymer physics, where it was originally derived as a way to quantify the stiffness of semiflexible polymer chains. This same concept is now widely used to describe the flexure of nanotubes,  and it has recently been used to model the conformation of graphene nanoribbons. 
As a characterization tool, electron microscopy has been essential for exploring the microstructure of polymer systems. Because of the high intrinsic electron density typically encountered in metallic and semiconductor nanoparticles, however, it represents an even more powerful method for examining size, shape, and structure at the nanoscale. The high mechanical modulus typical of nanoparticles makes atomic force microscopy (AFM) an indispensable tool as well. Not surprisingly, the comparable scales of length encountered in both polymer science and nanotechnology (1–100 nm) implies that scattering methods are also highly effective. Techniques such as small-angle neutron scattering (SANS) and small-angle x-ray scattering can directly probe two-point correlations in 2H/H or electron density, respectively, which allows such methods to distinguish the “form” scattering of an individual nanoparticle from the structural scattering of a dense fluid, aggregate or ordered assembly. An example of this in the context of DNA-wrapped SWCNTs dispersed in polyacrylic acid (PAA) is shown in Figure 1.  When used in concert, high-resolution microscopy and small-angle scattering can provide a tremendous amount of quantitative information about nanoparticle size, shape, and dispersion state.
Purification by Size
Once the nanoparticles have been effectively dispersed in a fluid or polymer to the level of individuals, the attention turns to the distribution of size and shape. The concept of size “polydispersity” actually has its roots in polymer science, being defined as the ratio of weight-averaged to number-averaged molecular mass. A perfectly uniform size distribution thus has a “polydispersity index” of 1. The concept also plays a central role in colloidal science, where it has direct bearing on the tendency for a “hard-sphere” suspension to nucleate an entropic crystal. Recently, the idea of polydispersity has taken on an entirely new and unique significance in the realm of nanotechnology, and the methods for controlling it are all being drawn from polymer science.
The simplest form of polydispersity encountered in nanotechnology is associated with size, and one of the simplest approaches for dealing with it is density-gradient ultracentrifugation (DGU), which has its roots in the purification of biomacromolecules.  The method exploits the dependence of nanoparticle sedimentation rate on size and shape, being intimately linked to viscous hydrodynamics. Because of differences in the sedimentation flux in response to an applied centrifugal force, a transient separation by size or shape occurs down (or up, depending on the density of the nanoparticle/surfactant complex with respect to that of the solvent gradient) the centrifuge tube. The method has been successfully used to size-purify metallic nanoparticles and quantum dots, [48, 49] plasma-synthesized silicon nanocrystals in organic solvents, [50, 51] surfactant-coated SWCNTs, [52-54] and chemically modified graphene sheets,  to name just a few specific examples. The recent literature contains a number of studies that use DGU to purify nanoparticles by shape and size, and an example of DGU applied to plasma-synthesized silicon nanocrystals is shown in Figure 2, where the trends of quantum confinement with size are clearly evident in the photoluminescence (PL) spectra and, equivalently, the magnitude of the bandgap. [50, 51]
Other more elaborate approaches to nanoparticle size purification, such as size-exclusion chromatography (SEC), have also been adapted from polymer science. Figure 3 shows a schematic of how SEC can be used to fractionate DNA-wrapped SWCNTs by length.  Just as for polymers, the longer SWCNTs elute faster because they interact less strongly with the porous packing column. SEC has also been successfully applied to other nanoparticles, including gold nanospheres  and zwitterion-functionalized SWCNTs,  and gel electrophoresis, one of the classic methods for separating biological macromolecules and their fragments based on size and charge, has been used to separate metallic nanoparticles according to size and shape by coating the particles with a charged polymer layer.  Electrophoretic techniques in general represent inexpensive and efficient tools for quality control in nanotechnology.  Fractionation by precipitation, a traditional approach commonly used in polymer science, can also be readily applied to the separation of nanoparticles by size, both in conventional [61, 62] and gas-expanded solvents.  Finally, field-flow fractionation, a relatively modern technique for macromolecular separation that avoids some of the complications associated with a separation medium,  has been successfully used to fractionate metallic nanoparticles,  magnetic nanoparticles,  cellulose nanocrystals,  and SWCNTs. [68, 69]
Size homogeneity is critical to many aspects of nanotechnology, such as nanoparticle self-assembly and cellular uptake. Monte Carlo simulations of colloidal crystallization, for example, suggest that the free energy of the solid-liquid interface increases strongly with supersaturation in polydisperse suspensions, and the standard deviation in particle size must be less than 12 % of the mean (corresponding to a critical polydispersity index of 1.02) for entropic crystallization to occur in a “hard-sphere” suspension.  Once they have been purified by size, however, nanocrystals as small as 3 nm in diameter can be easily processed to exhibit ordered-close-packing tendencies.  Nanoparticle size is also a critical parameter for the cellular uptake of individual nanoparticles, with experimental studies of SEC-purified DNA-wrapped SWCNTs incubated in the presence of living IMR90 cells suggesting a critical length scale of around 50 nm for efficient endocytosis. 
Purification by Optical and Electronic Properties
Although the above examples of size purification have clear and obvious analogies in polymer science, the concept of band-structure “polydispersity” is unique to nanotechnology, and the purification of nanomaterials by optical and electronic properties is one of the most exciting trends to emerge in recent years. For many nanoscale systems, an outstanding challenge is the synthesis of broadly homogeneous particles with identical characteristics. There are, of course, well-known examples where this has already been achieved, most notably in the solution synthesis of metal-chalcogenide quantum dots.  Additionally, the nature of quantum confinement implies that size purification applied to semiconductor nanocrystals naturally results in a purification by bandgap.  There are exceptions to this rule, however, and at the other extreme (most notably for nanomaterials synthesized using gas-phase methods), there are equally well-known examples where band-structure purification requires an additional step. Again, the solutions to this unique polydispersity problem are being borrowed from the field of polymer science.
The most notable and important materials in this regard are the SWCNTs, which bear a striking resemblance to polymers just by the nature of their tubular shape.  SWCNTs can be visualized as a derivative of graphene, which exhibits the electronic characteristics of both a metal and a semiconductor (a “semi-metal”).  Near the six corners of the two-dimensional (2D) hexagonal Brillouin zone—the so-called “Dirac points”—the valence and conduction bands touch with linear energy-momentum dispersion, giving rise to many of the outstanding electronic properties of graphene.  With respect to the symmetry of the 2D lattice, there are virtually an infinite number of possible ways a graphene sheet can be conceptually rolled into a tube to create a SWCNT. As a consequence, SWCNTs prepared from any given synthetic scheme typically contain a distribution of distinct nanotube species, each characterized by a chiral index (n, m), where the vector na1 + ma2 describes how the sheet “rolls up” into a tube, and a1 and a2 are the real-space basis vectors of the graphene lattice. The chiral index (n, m) dictates SWCNT diameter through
where a = 0.246 nm is the width of the graphene unit cell.  Because of the semi-metal nature of graphene, the index (n, m) also dictates band structure. When n - m is an integer multiple of 3, the SWCNT is metallic; otherwise, it is semiconducting. 
Just as for length, ultracentrifugation provides an efficient means to sort SWCNTs by electronic type, and this was in fact the first DGU purification scheme ever established for nanotubes.  In contrast to transient DGU separation by size, however, the method relies on finding an isopycnic balance between the density-gradient medium and a solvated nanotube/surfactant complex,  as depicted in Figure 4(a). Using a nonlinear density gradient to enhance the buoyant contrast between the nanotube micelle and the suspending fluid, the DGU approach can also be used to separate semiconducting SWCNTs by chiral index, as shown in Figure 4(b).  The method can be further used to separate metallic “armchair” (n = m) SWCNTs by diameter,  as shown in Figure 4(c). The striking colors arise from the high purity of the colloidal suspensions combined with the unique interband absorption resonances associated with specific chirality and electronic type. A variation of the same isopycnic DGU scheme has recently been used to separate double-wall carbon nanotubes by diameter  and graphene platelets by the number of layers,  although the simpler transient DGU approach can be used to separate the zinc-blend and wurtzite phases of CdS nanorods in organic density gradients. 
Another entirely different method of separating SWCNTs by electronic type uses a unique freeze/thaw/compression cycle for nanotubes embedded in an agarose gel, which results in a solution containing 70 % metallic SWCNTs and a gel containing 95 % semiconducting SWCNTs,  and they can also be type-separated via column chromatography to a 95 % semiconductor and 90 % metallic yield.  In somewhat the same manner that SEC can be used to purify nanotubes by length, diameter separation of ssDNA-SWCNT suspensions has been achieved using ion-exchange chromatography (IEC),  and purification of individual SWCNT chiralities has also been successfully demonstrated quite recently through IEC,  where single chiralities have been isolated at levels ranging from 70 % purity for (8,3) and (9,5) up to 90 % purity for (6,5), (7,5), and (10,5).  Purification of SWCNTs by band structure has significant implications for electronic device technologies that rely on the unique polymer-like morphology of nanotubes,  particularly for the next-generation assembly schemes being directed at efficient high-speed logic applications,  a point we consider again at the conclusion of the article.
Not surprisingly, the nanoparticle purification schemes described above have profound implications for the self-assembly of nanoparticle ensembles into ordered structures. One example of this, colloidal crystallization, has already been noted; size-uniformity is critical for the fabrication of quantum-dot superlattices with long-range crystalline order.  Because the attractive van der Waals interactions between nanoparticles can be significantly influenced by their band structure,  homogeneity of optical/electronic properties can be a critical factor as well. For polymeric systems, miscibility, phase separation, and crystallization are established concepts deeply rooted in the broader topics of phase transitions and critical phenomena, and recent analogies and contrasts have even been drawn between polymer and colloid crystallization.  Because of the similar scales of size, the same ideas can be directly applied to nanoparticles, which we now review in the natural progression of increasing complexity.
Miscibility and Phase Separation
The first topic we addressed was dispersion—a critical requirement for all of the fractionation schemes described above. A closely related issue is miscibility. For polymer solutions and blends, the central concept underlying miscibility is the Flory–Huggins free energy of mixing, which balances the competing effects of entropy and enthalpy. Polymer solutions require the correct balance of chain entropy, segment excluded volume, and favorable monomer–solvent interactions to be stable, and in most polymer blends, the entropy of mixing is overcome by unfavorable segment–segment interactions and the mixture-phase separates.  Similar ideas can be applied to nanoparticle/polymer mixtures, [94-96] and more recently they have also been applied to mixtures of different nanoparticles. [97, 98]
A simple example of the similarity of nanocrystal and polymer phase behavior is shown in Figure 5. Figure 5(a) shows phase separation that occurs when a nanocrystal-ligand suspension is slowly dried in a solvent-rich atmosphere, where excess unbound ligand segregates into a nanocrystal-poor fluid phase [Fig. 5(a), right]. This can be seen at much smaller length scales when the unpurified suspension is dried as a monolayer on top of water [Fig. 5(b), left], but once the suspension has been size-purified through DGU (also removing unbound ligand), the monolayer becomes uniform and there is a tendency for ordered close packing [Fig. 5(b), right].  Figure 5(c) shows the complex pattern that emerges when a polystyrene/nanocrystal solution is quickly dried on a clean glass surface, where the radius of gyration of the polymer is comparable to the diameter of the nanocrystal.  The optical image is a false-color superposition of bandgap fluorescence from the nanocrystal (red) and phase contrast highlighting the polymer (blue). Two nonequilibrium effects are present in the image; a drying instability that leads to the deposition of nanocrystal at the edge of the droplet  and a pattern associated with the phase separation of a colloid/polymer mixture. 
Purity is thus essential to the establishment of long-range order in colloidal nanocrystal ensembles.  In comparison to the familiar and related example of entropic crystallization in “hard-sphere” colloids, nanocrystal superlattice structures bear a more striking resemblance to a true “atomistic” solid. Although characteristics of hard-sphere suspensions are observed for nanocrystal superlattices, the details of the pair-potential can be important.  The cohesive force—or binding energy—depends on both the nature of the core material, which defines the magnitude of van der Waals attraction in the lattice, and the length and density of the capping ligand, which provides steric stabilization in a good solvent. Nanocolloids typically have an attractive potential well on the order of a few in solvated suspensions, [102, 103] but this is much deeper in the absence of a solvent.  Schemes for superlattice formation are intimately linked to ideas borrowed from polymer science, such as the addition of a bad solvent,  drying on a solid surface of controlled wettability,  drying on the surface of an immiscible liquid,  and the application of shearing forces.  Small ordered domains of 4 nm silicon nanocrystals have recently been formed from monodisperse suspensions through drying, both on a treated substrate and on the surface of an immiscible fluid.  The different facets of an ordered superlattice of large indium nanocrystals are shown in Figure 6a.  Ordered binary superlattices can also nucleate from suspensions of nanocrystals of varied size under the appropriate conditions, but drying is more effective than the addition of a bad solvent because of the stronger influence of entropic effects. 
Like the liquid-crystalline structures exhibited by rigid-rod polymers and colloids,  suspensions of anisotropic nanoparticles with appropriately tuned interaction potentials can be anticipated to exhibit anisotropic ordered phases, but the rich diversity of nanoparticle shapes—including plates, sheets, disks, and rods—allows for a greater diversity of potential structures. A transmission electron microscope (TEM) image of monodisperse ZnTe nanorods, for example, shows hints of nematic and smectic packing [Fig. 6(b)],  whereas similar packing tendencies can be seen in CdSe nanoplatelets,  but with more potential complexity due to the higher degree of particle anisotropy [Fig. 6(c)]. Nanotubes stabilized against van der Waals aggregation in water by wrapping with single-stranded DNA can exhibit cholesteric liquid-crystalline order [Fig. 7(a)],  and liquid-crystalline phases have been observed for SWCNTs and graphene platelets dispersed in strong acids. [5, 40] The use of surfactants with intrinsic liquid-crystalline order, such as the bile-salt sodium deoxycholate, also offers novel routes to nanoparticle self-assembly, and SWCNTs purified by length through DGU have recently been assembled into 1D crystalline nanocomposite “wires” using this approach. 
Finally, hybrid schemes involving nanoparticles stabilized by block copolymers that exploit the tendency for polymer microphase separation as a way to manipulate nanocrystalline materials into ordered mesophases have just started to emerge. [97, 115] Figure 7(b) shows a high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) image of microphase-separated structures in PS-b-PAA-b-PMAA-coated CdSe nanocrystals self-assembled in water, and Figure 7(c) shows a TEM image of a microtomed section of such an assembly. The smectic-like arrangement of nanoparticle and polymer layers is highly reminiscent of the lamellar phases exhibited by diblock copolymers,  but adding just a small amount of salt to the system changes the structure of the hydrophilic block, leading to the formation of bilayer vesicles as shown in Figure 7(d). The utilization of block copolymers instead of ligands to stabilize nanoparticles is potentially attractive, as it could offer novel ways to more efficiently “tune” the large-scale arrangement of nanoparticle ensembles through easily controlled external variables such as temperature, strain, and composition.
Processing and Performance
The ultimate test of the utility of a large collection of nanoparticles resides in both how the ensemble responds to processing and how the material performs in the final application. An ever-strengthening paradigm in modern nanotechnology is the concept of solution processing, which has obvious analogies to polymer science and engineering. In the context of fluid processing, a critical aspect of such systems is rheology, and there are a number of striking similarities between the collective mechanical behavior exhibited by nanoparticle suspensions and the behavior exhibited by polymer solutions and melts. What truly makes “high-end” nanomaterials unique, however, is how they perform in niche applications, which can be strongly influenced by purity, phase behavior, and structure. In this last section, we examine the collective nanoparticle response, first from the perspective of flow processing and polymer rheology, and finally from the perspective of performance.
Rheology and Deformation
Despite significant potential importance in the context of liquid processing, the application of rheological concepts to nanoparticle suspensions is a relatively young and undeveloped subject. A notable recent exception is the rheology of carbon nanotube suspensions, [116-118] where a number of analogies exist with rigid-rod polymers and colloids. The subject has great potential relevance to both the engineering of epoxide carbon-nanotube composites [119, 120] and the fabrication of thin SWCNT films,  and the underlying physics has recently been clarified through simulations. [122-124] In contrast, only a handful of rheological studies on GO suspensions have appeared, [125-128] although extensive reviews of the rheology of polymer-clay nanocomposites can be found in the literature. [129, 130] Regardless of shape, colloidal suspensions of anisotropic nanoparticles can be delineated into three distinct regimes of concentration; dilute, semidilute, and concentrated. Just as for semiflexible polymers, the demarkation between “dilute” and “semidilute” occurs when the rotation volume of individual particles begins to overlap, and the boundary between “semidilute” and “concentrated” is marked by the onset of entropic and enthalpic interactions. 
Semidilute to concentrated suspensions of anisotropic nanoparticles can exhibit a number of rheological similarities to polymer melts and solutions, such as shear thinning, a strong increase in zero-shear viscosity with increasing concentration, yield-strain behavior, and viscoelasticity. Examples of this are shown in Figure 8(a) for GO nanoplates suspended in low-molecular-weight polydimethylsiloxane (PDMS),  and in Figure 8(b) for self-assembled amphiphilic block copolymer nanofibers in water.  The emergence of a low-frequency elastic plateau with increasing nanoparticle concentration can be interpreted through nanoparticle network formation,  where the percolation threshold can become quite small for very high-aspect-ratio tubes and rods.  Fruitful analogies can also be made with liquid-crystalline polymers. [74, 116, 117, 121] Although suspensions of anisotropic nanoparticles can exhibit remarkably similar rheology independent of shape, rheological studies of spherical nanocrystal suspensions are less common because such materials are typically not processed at sufficiently high concentration. Exceptions exist, however, such as the emerging importance of nanocrystal slurries in the solution processing of thin-film photovoltaics. [133, 134] Although these suspensions can be anticipated to have intriguing rheological properties, the use of hydrazine as a solvent presents a significant barrier to such studies.
The deformation mechanics of nanoparticle films is also relevant, with a broad range of practical implications. Thin films engineered from carbon nanotubes,  graphene,  and semiconductor nanocrystals  have significant potential importance for a number of emerging technologies. Again, such systems exhibit a number of striking similarities to the mechanical behavior of thin polymer films, which is particularly palpable in the case of nanotubes. One of the most promising applications for such materials is flexible electronics, [138, 139] and the performance of such devices is intimately linked to how the films respond to cyclic compression and strain. The novel approaches recently developed for thin polymer films [140, 141] have potential relevance to nanoparticle films as well, and in the case of SWCNTs, recent studies suggest that purification by length [142, 143] and electronic type  have significant ramifications for film durability and device performance.
An example of the ubiquity of the response is shown in Figure 9, which compares the morphology of compressed polystyrene on PDMS,  compressed nanotubes on PDMS, [142, 143] and compressed GO on water.  In Figure 9(a), the deviation from the usual sinusoidal wrinkling pattern commonly exhibited by strained polymer films [140, 141] is associated with stress localization, which has recently been linked to disorder and wavelength doubling.  Although the specific scales of length vary from system to system (being intimately linked to film thickness and modulus),  the pattern itself is ubiquitous, as evidenced by the digital power spectra shown as insets in Figure 9. This similarity supports the notion that thin nanoparticle films can be modeled using the same continuum tools developed for thin polymer films, although there are again important differences related to the nature of nanoparticle percolation. Most notably, recent studies of polymer-supported SWCNTs that have been purified by length [142, 143] or electronic type  suggest strongly “plastic” behavior. Length-purified films exhibit plateau moduli consistent with the TPa modulus of individual SWCNTs but with remarkably small yield strains, [142, 143] whereas the electronic response of type-purifed films suggest significant differences in the electronic durability of metallic and semiconducting SWCNT networks. 
The deformation mechanics of nanocrystal films has also recently been investigated by applying AFM to monolayer films draped over holes in TEM grids. [146-148] Results for free-standing nanocrystal films with a variety of core materials, varied core sizes, and different capping ligands suggest that drying-mediated self-assembly can create close-packed monolayer membranes spanning several micrometers in diameter with promising mechanical properties. The membranes are remarkably elastic, and the moduli are determined by how tightly the ligands bind to the particle cores and by the corresponding ligand–ligand interactions. [146-148] The ligand is critical, as ligand interdigitation plays a role that is qualitatively analogous to polymer entanglement. This stands in stark contrast to the flexible nanotube films described above,  which are porous, contain no interfacial stabilizer, and exhibit small-strain plastic behavior. Stabilizers that also act as conductive “bridges” or electronic “dopant” could be particularly promising in this regard, [149, 150] because they might offer a way to optimize both the mechanical and electronic properties of SWCNT films.
The physical characteristics of free-standing graphene have likewise been studied in detail, and such films show significant promise for a range of potential applications. [151-153] In terms of deformation mechanics, however, graphene—a 2D sheet formed from a single layer of atomic carbon—represents an intriguing and important exception to the previous two examples of nanotubes and nanocrystals. Although polymer melts and solutions are classical systems that in almost all situations can be modeled effectively using statistical and continuum mechanics, these methods can be anticipated to break down at sufficiently small length scales, where quantum mechanical effects will start to emerge.  Indeed, it has recently been demonstrated that graphene does not conform to the continuum approaches commonly used to model the mechanics of a variety of thin-film materials. 
Nanomaterials as Soft Matter
There are numerous recent examples of how the above themes can impact material performance. The concept of “blend” morphology, for example, is familiar to the polymer physics community,  but it also has important ramifications for the performance of photovoltaic devices, [157-159] where it can influence device efficiency through the interplay of exciton diffusion length and the scales of interfacial separation. Similarly, entropic crystallization is a familiar concept in polymer and colloid science,  but the establishment of long-range crystalline order in nanocrystal superlattices can also have important implications for tunable magnetoresistance,  modified charge transport in self-assembled binary superlattice structures,  and the efficient photovoltaic conversion of visible and near-infrared solar radiation. [163, 164] SWCNTs purified by electronic type are particularly important for thin-film optical and electronics applications,  but they can also be used as “nanoparticle surfactant” in polymer mixtures, where they can lower the percolation threshold for charge transport in nanocomposites by more than an order of magnitude. 
The implications of the novel aspects of reduced “band polydispersity” also spill over into the world of soft materials. As noted above, the purification of plasma-synthesized silicon nanocrystals by size promotes localized tendencies for crystalline order in dried solutions, but it also improves “band alignment”, whereby the optical and electronic properties of the ensemble become broadly homogeneous.  Such assemblies exhibit PL brightening associated with an enhanced quantum yield, and nanocrystal interactions have been implicated as a possible explanation; photoelectrons moving through the ensemble passivate “dark” surface trap states, thereby promoting radiative recombination. Ensemble microstructure may play an important role as well, as disordered nanocrystal clusters formed through phase separation with a nonadsorbing polymer exhibit a suppression of the brightening effect.  Enhanced performance associated with nanocrystal size purification has also recently been observed in solution processed light-emitting diodes, where the morphology of the nanocrystal phase has been cited as an important factor. 
In the case of nanotubes, an interesting example of how all the topics in this review converge in a single platform is the recent demonstration by researchers at IBM that chemical self-assembly can be used to integrate purified semiconducting SWCNTs into device arrays at densities as high as 109 nanotubes per square centimeter.  The simple and common surfactant SDS was used to disperse the nanotubes, and DGU in a step-gradient of the water-soluble polymer iodixanol was used to remove impurities.  Type purification was then performed with a simple SEC procedure,  whereby a blue metallic fraction first emerges from the column, followed by red semiconducting fractions. The semiconducting SWCNTs were collected, dialyzed, and deposited in trenches on doped silicon substrates through the ionic exchange of a surface-deposited iodide anion and the sodium cation of the SDS.  In this manner, the authors were able to assemble high-density nanotube transistors on a conventional semiconductor fabrication line and electrically test 10,000 devices on a single chip. The technique is particularly relevant to the topics of interest here, as it opens up a potentially viable route to commercial circuit fabrication through the manipulation of purified colloidal SWCNTs. 
We have reviewed a number of contemporary examples of how ideas from polymer science are being used to enable nanotechnology, most notably through the application of solution processing, liquid-phase nanoparticle purification, and fluid-based self-assembly. All three of these themes are ultimately interrelated, and they are all thus equally critical to successful commercialization. To see the potential paths forward, we focus once again on SWCNTs, the nanoparticles that have the most obvious similarity to polymers. The biggest hurdle that remains is purity, and there are two possible remedies; the synthesis of tightly homogeneous materials and large-scale purification applied to established synthetic techniques. In reality, it is likely that both of these will be used in concert, and it is conceivable that solution-based methods for rapidly generating large-scale quantitates of single-chirality SWCNTs will be realized in the very near future. The implications of this can perhaps be best taken from a recent article in the New York Times that highlights the work being done at IBM on the solution processing of nanotube transistors,  as described above. The integration of semiconducting SWCNTs into computer chips has the potential, sometime after the end of this decade, to both sharply increase the speed of chips and sharply increase the density of transistors in a manner that will allow us to continue to realize Moore's law. To do so, however, will require semiconducting SWCNT fractions with a metallic content of 10−4 or less. Although this is clearly a challenge, it is particularly exciting that ideas and methods acquired from polymer science could very well be what ultimately make this possible.
The authors gratefully acknowledge the support of the National Science Foundation (NSF) through CBET-1133135 and CMMI-0969155.
Joseph B. Miller received the B.S. degree in physics from North Dakota State University in 2010, where he is currently working toward a Ph.D. in the Materials and Nanotechnology Program. His research is directed at the purification, characterization and self-assembly of silicon nanocrystals for applications in solid-state lighting, photovoltaics and biomedical sensing.
Erik Hobbie received his Ph.D. from the University of Minnesota and was a National Research Council Postdoctoral Fellow in Polymer Science at the National Institute of Standards and Technology (NIST) in Gaithersburg Maryland. He was a Senior Research Scientist in the Polymers Division at NIST for several years before joining the faculty at NDSU in the fall of 2009, where he is a Professor in the Department of Physics and the Department of Coatings and Polymeric Materials. He directs the Graduate Program in Materials and Nanotechnology at NDSU. His research interests lie at the interface between soft materials, condensed matter physics, and nanotechnology, with an emphasis on engineering new materials from polymers and nanoparticles.