Assembling colloidal devices by controlling interparticle forces

Assembling colloidal devices by controlling interparticle forces

Darrell Velegol Department of Chemical Engineering, The Pennsylvania State University, University Park,

PA 16802, USA [email protected]

Abstract. In recent years the concept of “colloidal devices” has emerged. These include colloidal crystals with photonics properties, as well as displays, machines, and other assemblies having a particular purpose. The assembly of colloidal devices, or even simpler assemblies, can proceed with top-down approaches, applied fields, bottom-up approaches, or combinations of these. Bottom-up assembly, in which the particles have “colloidal force information” encoded chemically on their surfaces and interiors, appears to be especially suited for larger-scale production. The encoded information directs how the particles assemble and function, and a simple example is a colloidal crystal that has purely repulsive forces between all the particles. A richer assembly process can occur with site-specific chemistry, which sometimes occurs naturally on particles, such as when a particle has two different crystal faces. And in recent years, researchers have developed techniques for intentionally placing site-specific chemistry on particles, enabling assembly to proceed through localized electrostatic, van der Waals, depletion, hydrophobic, and receptor-ligand forces. Site-specific colloidal forces are useful in effecting colloidal and nanocolloidal assembly for state-of-the-art and future structures and devices.

Keywords: colloidal assembly, bottom-up assembly, colloidal forces, asymmetric forces, site-specific forces, colloidal molecules.

1 INTRODUCTION

1.1 Colloidal devices are mostly a recent conception

Colloidal particles have been used in traditional applications like coatings, glue, paper, ceramics, and inks for centuries [1]. A wealth of predictive and sophisticated theoretical techniques have been developed to engineer these applications [2], but these uses have not required a sophisticated “assembly” of particles. Rather, these applications require primarily that particles remain stable when desired (e.g., in a green body, or in a can of paint), and that they fuse or sinter when desired (e.g., when the green body is fired, or when the paint is applied). Recently, the concept of “colloidal devices” has emerged. Colloidal devices are single particles or assemblies of particles that have a particular function. Some of the first colloidal devices were conceived in the 1970s by Yablonovitch [3] and John [4,5] for photonic applications [6,7], which critically affect the propagation of light. Working from the earlier concept of Anderson localization [8], these researchers evaluated how materials with periodic dielectric properties could give a localization of photons, or a photonic band gap. Materials with a photonic band gap could, for instance, pass one wavelength of light, but block another. In the 30 years since the seminal articles by Yablonovitch and John, thousands of articles have appeared on “colloidal crystals” and “photonics” [9].

Real examples of colloidal crystals with photonic properties have been known for centuries in the form of natural opals. Precious opals have ordered arrays of 150-300 nm silica colloids that produce a beautiful “play of colors” based on Bragg diffraction [10,11].

Journal of Nanophotonics, Vol. 1, 012502 (25 June 2007)

© 2007 Society of Photo-Optical Instrumentation Engineers [DOI: 10.1117/1.2759184]Received 1 May 2007; accepted 18 Jun 2007; published 25 Jun 2007 [CCC: 19342608/2007/$25.00]Journal of Nanophotonics, Vol. 1, 012502 (2007) Page 1

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Journal of Nanophotonics, Vol. 1, 012502 (2007) Page 2

The first artificial device for using colloidal crystals as a photonic manipulator was patented by Sandy Asher. He used colloidal particles to control the propagation of photons [12], using polystyrene particles to filter narrowband radiation. Unlike traditional applications, colloidal crystals require a simple but precise ordering of particles, which is usually given by repulsive forces between them. Since Asher’s invention 25 years ago, many advances have been made, notably the “champion” diamond photonic-bandgap structure [13,14,15], cloaking [16], and negatively-refracting metamaterials [17].

1.2 Bottom-up assembly provides an inexpensive route to building devices

An important reason for using colloidal structures as photonic devices – or any of a variety of devices – is the expectation that they can be fabricated inexpensively, once the techniques are well-developed. Colloidal assembly can proceed by “top-down assembly”, “field-assisted assembly”, “bottom-up assembly”, or a combination of these. Top-down assembly involves an external apparatus that builds the colloidal structure, such as the placement of particles with an atomic force microscope [18]. Field-assisted assembly involves the use of external fields, such as magnetic [19], electric (either electrophoretic [20,21,22] or dielectrophoretic [23]), light [24, 25], flow [26], or combinations of these [27].

Bottom-up assembly, on the other hand, requires that the particles contain enough chemical information that they are able to assemble themselves. For example, in most colloidal crystals in solution, the particles have a repulsive force that packs the particles into a 3-dimensional array [28,29,30,31]. However, for this simple example, the only information that is required is a repulsive force as a function of distance between particles. Even simple information can yield fairly complex assemblies [32], but having more chemical information (e.g., using mixtures of particles) has produced nanoparticles crystals with a diamond-like (sphalerite) lattice [33,34].

Some assemblies involve both top-down assembly and bottom-up assembly. For example, electron-beam lithography has been combined with the subsequent evaporation of metal (gold or titanium) to produce nanometers-spaced mercaptoalkanoic acid lines [35]. Also, whether template-assistance is top-down or bottom up can be a debatable question [36]. For example, in one assembly of photonic crystals [37], template-assisted assembly guided particles in assembling in a precise manner. Current and future devices for photonics, energy, environmental [38], and other applications will require even more sophisticated assemblies. How will these devices be fabricated at a commercial scale?

1.3 This review has three primary purposes

This review focuses mainly on bottom-up assembly, and it has three purposes. 1) Bottom-up assembly is described in terms of colloidal forces, which ultimately control the assembly process, and especially in terms of either symmetric forces, time-dependent forces, or spatially-dependent (asymmetric) forces. 2) Starting points are provided for synthesizing “colloidal atoms” (particles of various materials, shapes, sizes, patterning). 3) Selected triumphs in colloidal assembly are highlighted, and promising methods are shown from the literature in colloidal assembly that might lead to devices. In a discussion of this final purpose, research challenges and future directions are given.

2 COLLOIDAL ATOMS

2.1 Recipes exist for many types of individual particles

Colloids are loosely defined as particles from 1 to 1000 nm in dimension suspended in a fluid. Thus, colloidal particles are generally (but not always) larger than molecules. It can be insightful to provide a criterion for the upper size range. Two definitions give the same



scaling for the colloidal size: i) equating the average time required for the particle to settle by gravity one particle radius (a) and the time required to diffuse by Brownian motion a distance (a), or ii) finding the radius (a) required for the particle’s gravitational energy at a height (a)to equal kT (the thermal energy, where k = 1.38 10-23 J/K and T is the absolute temperature).

One finds that 4/14/3 gkTa , where is the density of the particle minus the density

of the suspending fluid and g is the gravitational constant. For polystyrene particles suspended at T = 298 K in a 1.0 g gravitational field, this radius a = 1.38 m. For silica under the same conditions, a = 0.67 m. Another definition of “colloidal” uses the wavelength of light (~500 nm). For nanocolloids, one might choose an upper size limit where a property such as the dielectric constant is within 10% of the bulk value.

Colloidal particles come in many materials, sizes (roughly 1 to 5000 nm), and shapes (spheres, cubes, peanuts, rods, spheroids, pyramids, and others). In fabricating colloidal assemblies, the first step is to synthesize a base set of particles (or “colloidal atoms” [39]). Table 1 provides an entry point for synthesizing seven common classes of materials (metals, oxides, semiconductors, polymers, waxes/oils, aggregate particles, and biocolloids).

Table 1. The synthesis of representative colloidal atoms. These particles act as the building blocks for colloidal structures and devices. The references serve as starting points for synthesizing seven common classes of particles. material class material references for size, shape, class

metal silver, gold

cobaltcarbon nanotubes chromium

5-50 nm [40], 500-5000 nm [41], rods [42,43], striped [44], hollow [45] magnetic nanoparticles [46] [47,48] pyramids about 100 nm in size [49]

oxides silica (SiO2)titania (TiO2)zinc oxide (ZnO) hematite Au core, SiO2 shell

classic Stober silica [50,51], silver core/silica shell [52] rutile [53,54] and anatase [54,55] nanoparticles [56] pseudo-cubes, spheroids, peanuts [57] [58]

semiconductors silicon GaAsCdTecarbon nanotubes

[59,60] [61,62] [63] [47,48]

polymers general polystyrene PMMAPVAcspheroidsSU-8 epoxy

emulsion polymerization [64,65,66,67] spheres [68,69], spheroids [70], >3 m [71] fluorescent [72], particles and rods [73] [74] [73,75] rods [76]

waxes / oils ferrofluid droplets wax particles

magnetic droplets [77,78] [79]

complex particles

liposomescolloidosomesJanus particles patterned particles

stabilized by nanoparticles [80] [81] [82,83,84,85,86,87,88,89,90] coated [91], metal [92,93], gold nanodots [94,95], polymer particles [96,97], Fibonacci coating [98], raspberry coating [99], modeling [100], various complex coatings [101]

biocolloids bacteria

viruses yeast

100 nm (Mycoplasma) to 600 m (Epulopiscium fishelsoni),includes many E. coli for instance [102] tobacco mosaic virus PV-135 [102] Saccharomyces cerevisiae [102]



2.2 Colloidal forces are critical when designing colloidal atoms for assembly

In the language of actual atomic and molecular chemistry, it is of course common to speak of controlling forces and energies. Whenever we mention s or p atomic orbitals, or and molecular orbitals, we are focusing on probability distributions of electrons that dictate strengths of bonds (e.g., covalent, electrostatic, van der Waals, hydrogen bonds) [103,104]. With the bonding of atoms into molecules, the bond strengths, bond angles, and structures (e.g., tetrahedral or linear molecules) are already determined naturally; we are not in general able to adjust the quantum mechanical features of an atom. For colloidal assembly such control is now being developed over the bonding. Rather than being limited to particular bond strengths or particular bond lengths, researchers are developing the ability to place bonding regions at site-specific locations on particles, and to adjust the strength of those bonds [94]. Researchers have used the naturally-existing orientation-dependent forces – including asymmetric hydrophobic interactions between CdTe nanoparticles – to assemble the particles into free-floating sheets as large as 50 m 30 m[105]. Other researchers (including our own group) have begun to intentionally place site-specific bonding regions on particles in order to control their assembly. This is the new “chemistry” of colloidal atoms and molecules that is referred to a number of times in this review. The word “colloidal molecules” was coined in 2003 by van Blaaderen [106], and the term aptly describes the assembly process. Most controlled assembly processes take place in suspension, where there are several interparticle forces: van der Waals, electrostatic, depletion, biological, solvophobic (in which hydrophobic is an example), solvation, and steric. The total potential energy from all these forces is usually written as

stericsolvcsolvophobibiodepesvdw(1)

An excellent review of these forces appears in the book by Israelachvili [107]. The physical origins of these various forces are well-established from electrostatics and quantum mechanics. Table 2 lists simplified, quantitative, analytical models for a few of the forces; the value of these simple analytical models is not that they provide the most accurate calculations (see the references listed in Table 2), but rather that we can use them in thinking about and guiding the engineering of interparticle forces.

Figure 1 then gives a typical calculation using these equations for an aqueous system, showing the primary features that result from van der Waals, electrostatic, and depletion forces. At large separation, the interaction energy between the particles is nearly zero, by definition (since energies can be defined only up to a constant). As the particles approach each other, typically at 5 to 8 “Debye lengths” (defined later), the particles enter a shallow “secondary energy minimum” (~1-5 kT deep). As the particles approach even closer, they must climb the electrostatic energy barrier, and then they can fall into an essentially irreversible “primary energy minimum”. The actual separation distance for this minimum might be one atomic distance, or roughly 0.3 nm.

2.3 van der Waals forces always exist, and are almost always attractive

van der Waals dispersion forces (i.e., not Keesom or other permanent dipole forces [107]) arise due to the quantum mechanical dance of the electrons in the particles. At any instant, the instantaneous positions of the electrons within the particle give it a small dipole. This dipole, on average, will induce a dipole in a neighboring particle. These dipoles face each other such that the positive and negative parts are closest, making the van der Waals forces attractive in nature. They always exist between particles, although they can be greatly reduced by “index matching” (i.e., making the refractive index of the suspending fluid equal to that of the particle) [108]. If the relative permittivity (especially at ultraviolet wavelengths)



of one particle is greater than that of the surrounding medium, while the other particle’s is less, then the van der Waals forces in fact become repulsive [107]. While van der Waals forces have been tested to work well for micron-size particles [109], the phenomenon is less predictable for nanocolloids [110,111]. There are two key reasons for this: a) The discrete atomic nature of the particles becomes important. Continuum solutions assume geometric shapes like spheres, cylinders, or flat bodies, and thus miss the discrete atoms. b) Continuum solutions are usually put in terms of a relative permittivity, rather than in terms of atomic polarizabilities. At the macroscale these two are often interchangeable by the Clausius-Mossotti equation [107], but near to surfaces or at the nanoscale, the relative permittivity can change significantly, causing the van der Waals forces to change significantly. Our recent research on the “coupled dipole method” [110,111] predicts nanoscale van der Waals forces, accounting for all n-body interactions. Such methods enable the van der Waals forces to be accounted for in difficult geometries (e.g., roughness, odd shapes) and with greater accuracy in the non-retarded regime. Retardation of van der Waals forces occurs due to the finite speed of light; by the time the dipole electric fields reach another atom, the electron density of the first atom has already changed at least somewhat. Current research is being done into examining retardation effects for the van der Waals forces using the coupled dipole method.

Table 2. Colloidal forces between two nearly-touching particles in suspension. The variables: sphere radii (a1 and a2, in meters); gap between spheres ( , in meter); temperature (T, in Kelvins); Boltzmann constant (k = 1.38 10-23 J/K); Hamaker constant (A in Joule), which characterizes the van der Waals dispersion forces; the electrostatic screening length ( -1, in meters); the ion valence for a Z:Z electrolyte (e.g., for NaCl, Z=1); the bulk ion concentration (n , in #/m3, not molar or molal); the proton charge (e = 1.6 10-19 C); the fluid permittivity ( = 0 r, where 0 = 8.85 10-

12 C2/N-m2 and for water r = 80 at room temperature); the surface potentials ( 1 and 2, in volts); the depletant radius (R, in meter); the depletant concentration (n0, in #/m3).

colloidal interaction energies in aqueous solution limitations, more exact calculations van der Waals

21

21

6 aa

aaAvdw

primary limits: neglects retardation [112], neglects nanoscale effects [111]

more exact: Section L2.2 of Ref [112], coupled dipole method in [111]

electrostatic

eaa

aaes 21

21

214

kT

eZn 222 2

for Z:Z electrolyte

primary limits: valid for magnitude of surface potentials <50 mV, nearly-touching particles, ignores well-known image charge attraction term

more exact: Eq. 19 of [113]

depletion

R

RRRakTn

dep

20

202

122

0

220

primary limits: neglects long-distance interactions between depletants and particles, neglects non-dilute depletant effects (depletion repulsion)

Eqs. 8 and 9 of [114]

2.3 Electrostatic forces are known for aqueous systems, less so for non-aqueous

Electrostatic forces between particles are usually more complex than simple Coulomb interactions between particles, although the heuristic remains essentially true that



like-charged surfaces repel and oppositely-charged surfaces attract [115]. I here briefly describe aqueous phase electrostatic forces. Ref [115] gives a more proper review. When particles reside in aqueous media (and sometimes even organic media), their surfaces take on a charge by any of a variety of mechanisms. For example, polymer colloids are usually synthesized with surface groups that readily dissociate like salt in water. If sulfate groups are synthesized onto the surface of polymer colloids and dissociate to leave SO4

-2 groups, the surface takes on a negative charge. Another example is silica particles; here a surface reaction with water leaves dissociable silanol groups, giving a negative surface. Surfaces can become charged by dissociating groups, metal ion substitution, or adsorption.

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solvation /solvophobicsolvation /

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electrostericelectrosteric

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a b

Figure 1. Colloidal forces between two particles. a) Many types of forces exist. All of these are available for designing colloidal fabrication, especially when the forces are made to be site-specific over the surface of the particle. b) The force profile considers only the three forces given in Table 2 (electrostatics, van der Waals, depletion), using the simple equations given. The conditions are that the sphere diameters 2a = 100 nm, the ionic strength is 100 mM, the particle surface potentials are -50 mV, the particle Hamaker constants are 3.4 kT, the temperature T = 298 K, the depletion concentration is 0.5 mM, and the depletant radius of gyration is 10 nm. Roughly speaking, the energies and forces scale linearly with particle radius, until rather small radii (a < 25 nm) are obtained. The maximum potential barrier ( max/kT) extends from the bottom of the secondary energy minimum near = 5 to the top of the energy barrier near = 0.6.

Nature does not like to allow those charged groups to remain at the surface, and so oppositely-charged counter-ions are drawn from the solution toward the surface. For example, for a negatively-charged silica surface, positive ions (e.g., H+, Na+) from the bulk solution are pulled toward the surface. The counter-ions do not stick to the surface, since they are solvated by water, much the same way that Na+ and Cl- ions remain separate when table salt dissolves in water. The combination of these two layers – the permanent charge layer on the particle surface and the layer of mostly counter-ions near to the surface but actually in solution – are called the “electrical double layer” (EDL). The thickness of the EDL is an important parameter for electrostatic energies. As the counter-ions are pulled toward the surface, and the co-ions are pushed away, small concentration gradients develop. As a result, the high concentration of counter-ions diffuses away from the surface, while the co-ions diffuse toward the surface. This balance between counter-ions being pulled inward by the charged particle surface, but transporting outward due to diffusion, gives an equilibrium thickness of the EDL called the “Debye length” or the “electrostatic screening length” ( -1). An equation for 2 is given in Table 2. As an example, for 0.10 M NaCl (0.10 moles per liter) at T = 298 K, where the bulk ion concentration n = 6.02 1025 /m3, Z = 1, and the other constants are given in the Table 2 caption, one finds that -

1 = 0.97 nm. As the electrostatic equation in Table 2 shows, the electrostatic forces decay



exponentially with distance, with a length scale of the Debye length. Thus, by the time the particles are separated by 8 -1 to 10 -1, the electrostatic forces are small; they have been “screened out” by the ionic strength. Electrostatic screening is very important for asymmetric electrostatic forces, since the forces are often localized to regions on the particle surfaces (by changing the chemistry) of dimension roughly 10 -1. For non-aqueous systems, the electrostatic forces are much less well understood, although they are often just as important. A first thought might be that since nonaqueous media support very few charges relative to aqueous media [116], that electrostatics must not play a role in non-aqueous systems; however, because there are so few charges, these act with a long-range Coulomb mechanism, rather than the usual screened mechanism when a higher ionic strength exists. The Debye length for a solution that is 1 picomolar ionic strength is more than 300 m, and the average spacing between charges in solution is more than 10 m. One often uses the same Poisson-Boltzmann formalism to describe electrostatic forces in aqueous or non-aqueous media [116]; however, with so few charges in non-aqueous systems (either on a particle or in solution), using the continuum equations is often not appropriate. Furthermore, the charges can actually be removed from particles, especially during particle transport relative to the fluid. Experimentally, stability measurements of TiO2 have supported the use of Derjaguin-Landau-Verwey-Overbeek (DLVO) force theory in describing forces in non-aqueous media [117], but direct force measurements in non-aqueous systems have been taken for only about 5 years [118], and researchers have found inconsistencies with forces in non-aqueous media [119]. In the end, the use of electrostatic forces in non-aqueous media has a clear difference from that in aqueous media. Since the Debye length in non-aqueous media is usually much larger than the particle radius, site-specific assembly in non-aqueous media is difficult. After all, the particles are often held far enough apart that they appear as points. That said, there are advantages to working in non-aqueous media. The company E Ink has exploited non-aqueous electrostatics/electrokinetics to transport particles using large electric fields with small current [120].

2.4 Depletion forces result from the surrounding solution

Depletion forces result from differences in osmotic pressure. Osmotic pressure results from the thermal motion of species within a solution. Since all molecules and colloids have an energy of kT/2 due to movement in each direction (x-y-z), and in solution that energy means that kT/2 = <mv2/2>, where m is the mass of the species and v is its speed, one sees that the molecules are “beating on the particle” from all sides. In addition, when molecules diffuse into the gap region (but not all the way in, since they are excluded), they enter force free by diffusion; however, they are then pushed out by forces (e.g., electrostatic, Born repulsion), carrying fluid with them and decreasing the gap.

Let us look at the case when, say, particles of type A (diameter 1000 nm) are in suspension with particles of type B (smaller particles of diameter 30 nm). If two A particles get closer than 30 nm, then no B particle can enter the gap between the two A particles. Thus, the osmotic pressure between the A particles is lower than outside the gap, and the A particles are pushed together by the thermal motion of the B particles. The net attractive force is predicted (for low volume fractions of the smaller particles) by the Asakura-Oosawa depletion potential given in Table 2.

Depletion forces for particles of radius 100s of nanometers are well-understood, both theoretically [114,121] and experimentally [122,123,124]. A more challenging topic with depletion forces arises when the depletant molecule (or nanocolloid) is of a comparable size to the particles on which they are applying a force. Schweizer, Zukoski, and co-workers have developed the PRISM model for predicting depletion forces when the surrounding polymer is



comparable or larger in size than the nanocolloids [125], and the experiments have generally supported the theory [126].

Researchers have localized depletion forces using surface topography to effect directed adherence to particular regions of a surface [127]. Mason has used depletion forces for disk-shaped particles to direct the assembly of stacks of clay disks [128], and Stroock and co-workers have similarly used depletion forces to assemble short cylinders with flat ends [129]. An advantage in using depletion forces for assembly is that the interaction potentials are easily controlled in the weak-attraction regime (1 to 5 kT).

2.5 Other forces especially important for nanocolloids are known

Whereas depletion forces result from non-adsorbing depletant molecules (or particles), solvation and solvophobic forces result from solvent-surface and solvent-solvent interactions [130]. Simple analytical expressions have been obtained to predict these forces, based on experimental data [107], and the distances scale with solvent-molecule diameter; however, molecular dynamics modeling gives the best predictions to date [130]. In general, solvation forces stabilize particles, because solvent molecules attach weakly to the surface and provide a barrier layer between the particles. The phenomenon occurs even for hard-sphere interactions due to entropy. An analogy would be to place marbles (like solvent) on a hardwood floor (like a particle), and then to place a piece of plywood on top (other particle). The plywood would never touch the floor, only the marbles.

In general, the stabilizing solvation forces result when the solvent is attracted to the particle more than itself (i.e., the van der Waals attraction between the solvent molecules and particle surface is stronger than between two solvent molecules), while attractive solvophobic forces result when the solvent is attracted to itself more than to the particle. Solvophobic forces have been localized on particles, and by alternating the pH to create local regions of solvophobic and solvophilic forces, assemblies have been created [131,132]. Anisotropic solvophobic (hydrophobic) forces have also driven the assembly of CdTe sheets [105]. A much more common use for solvophobic forces in assembly is in the exploitation of surface tension, which is an extremely strong macroscopic force that drives colloidal assembly in many cases. Indeed, the use of surface tension, often during a drying process, is currently the most common force used in particle assembly. The magnitudes of both solvation and solvophobic forces can be quite strong, even dominant; however, their prediction is seldom simple. Steric forces result when particles are coated with a polymer layer [133], such that compression of the layer is energetically unfavorable. Furthermore, since the polymer layer is not a dense layer, the van der Waals forces are also reduced in most cases [134]. Biological forces tend to be quite specific, resulting from pockets of receptors and ligands which collectively have a very strong interaction. The PDBbind database contains a list of many receptor-ligand interaction strengths [135].

2.6 The colloidal aggregation rate is known in terms of interparticle energies

Individual particles are typically made to be stable in suspension, meaning that they usually do not aggregate on time scales of months or even years. Sometimes stability occurs naturally, such as when silica particles in aqueous solutions have a negative surface charge that makes them mutually repulsive. However, at high ionic strengths (e.g., 1.0 M NaCl), the electrostatic forces between particles are greatly decreased, and the attractive van der Waals forces causes particles to aggregate. This phenomenon is readily seen at the delta to a river; when particles that are well-suspended in the fresh water of the river (i.e., low ionic strength, often 2 or 3 mM) hit the higher ionic strength of the ocean (i.e., roughly 150 mM), they aggregate and settle quickly out of suspension.



The usual route to understanding the rate of colloidal aggregation is the Smoluchowski rapid-flocculation approach. The essence is to examine how quickly particles diffuse toward each other by Brownian motion, and assuming no interparticle forces, to find how quickly half of the original singlet particles will form doublets. The characteristic time is

found to be kTa 2/3 . Thus, for 2a = 100 nm diameter spherical colloids in water at T

= 298 K (viscosity = 0.00089 Pa-s) at a volume fraction 1.0%, the characteristic time = 4.2 ms. Results are also well-known for shear-induced flocculation [2].

When colloidal forces are involved, they can slow the rapid-flocculation rate down by a factor W, which is usually called the stability ratio (ratio of actual flocculation time to rapid flocculation time). The stability ratio gives the ratio of the number of collisions required between colloids before an adhesion occurs. Estimates of W as a function of energy barrier have been found to follow a Boltzmann expression [2,136]:

125.01 /max kTeW (2)

max is shown schematically in Figure 1. If max = 10 kT, then W = 5507. Thus, in our previous example, the new = 4.2 msec 5507 = 23 seconds, still a very short shelf-life. On the other hand, if max = 25 kT, then W = 1.8 1010, and = 4.2 ms 5507 = 2.4 yrs. Even if Eq 2 is not identically correct for all circumstances, we expect the exponential relation between max and W. Armed with simple expressions for colloidal forces and aggregation rates – even if one does not use the most rigorous equations – one can see qualitatively that colloidal stability is rather sensitive to solution conditions, as described above for the river delta example. Changing from 10 mM to 100 mM NaCl solution can sometimes change max from greater than 25 kT to 10 kT, and since W depends exponentially on max, the resulting aggregation time can be reduced from years to seconds. Indeed sometimes even small changes in ionic strength (or pH, or other solution conditions) can change a suspension of particles from “stable” to “unstable”. However, the aggregation that results for “unstable” particles is a random aggregation. Bottom-up assembly usually requires that particles have a controlled aggregation. How can we have aggregation of the particles on the one hand, but controlled aggregation on the other? The answer lies in producing asymmetries of colloidal forces over various parts of the colloidal particles.

2.7 Asymmetries in colloidal forces allowed directional bonding of particles

The forces between colloidal particles can be made asymmetric, if the chemistry on a particle’s surface is spatially site-specific. An example is shown in Figure 2. Asymmetric colloidal forces become a bit more complex to consider, however. In the schematic, particle B (blue is negatively-charged) wants to interact with the small green region (positively-charged) on particle A. If particle B approaches the negative (blue) part of A, then the particles repel as expected.

On the other hand, if B approaches the green part, the situation becomes a balancing act. The electrostatic forces around a particle decay with distance on a length scale of the Debye length. If the Debye layer is thick (Figure 2a), then particle B feels not only the attraction due to the oppositely-charged green region on particle A, but also the repulsion due to the blue region surrounding the green region. Thick double layers occur in either non-aqueous fluids (where they can be m’s thick) or in aqueous solutions at low ionic strength (in practice, due to equilibration of CO2 from the air into the water, ~180 nm). In Figure 2b,where the double layer is thinner, particle B would not be subject to as much repulsion from the blue regions of particle A, and the particles can aggregate there. Furthermore, at a well-adjusted ionic strength, particle B will “funnel” in toward the center of the green region on particle A [137].



Natural particles can have variations in van der Waals or electrostatic forces for various crystal planes. With van der Waals forces, variations due to different crystal planes can give anisotropic dielectric functions, which produce torques due to van der Waals forces [112]. For electrostatic forces, the surface charge groups will in general be different or dissociated differently for two different crystal faces. This is described by the multi-site complexation (MUSIC) model [138], and it is well-known to occur for clay particles [139]. I distinguish this known variation in surface charge or potential over a particle surface from the random surface charge that occurs on some colloids [140,141].

a b

A BA B

a b

A BA B

Figure 2. Spatially nonuniform colloidal forces between two particles. a) A thick electrical double layer, which does not allow the small blue particle to cross the energy barrier to reach the oppositely-charged green region. The black dotted line outside the particles is for example a 10 kT electrostatic energy barrier. b) A well-adjusted electrical double layer, which allows the small blue particle to access the green region. If the ionic strength is increased much higher, all the particles will aggregate randomly.

The modeling of colloidal assembly has proceeded along several paths. One is the modeling of the fundamental forces, as described previously. Another route is to ask, “What is the final assembly structure, given a mixture of particles with known orientation-dependent forces?” Glotzer and co-workers have done considerable work in this area [142,143,144,145]. They use molecular simulations (e.g., Brownian dynamics) to deduce expected shapes, and they have used their techniques for instance to propose methods for fabricating diamond structure colloidal crystals [146]. Their outcomes have analogy to using quantum density functional theory to determine equilibrium structures of molecules [147]. Another group has done similar work for the onset of crystallization [148]. A third type of question to ask is, “What structure must I obtain in order to obtain certain properties, such as a 3-D photonic bandgap?” One group has answered this question, finding that the diamond or pyrochlore structures give the desired result [149].

2.8 The particle lithography technique provides site-specific chemistry

In the past 10 years, several researchers have developed methods for placing site-specific chemistry on particles. The first was the Whitesides group [92], who patterned metallic regions, followed by the Halas group [93], who worked on a similar problem. Later, the Mohwald group created site-specific gold regions on particles using a vapor deposition technique [94]. Our lab group developed the particle lithography technique at about the same time [94]. This last technique provides a general way to pattern polymer, oxide, metallic,



semiconductor, or biological particles. By placing chemistry at site-specific locations on a particle, one can control orientation-dependent interparticle forces and bonding. We have used electrostatic, van der Waals, receptor-ligand, and other interactions site-specifically.

Figure 3. Particle lithography method for placing site-specific chemistry on individual particles [96]. a) Amidine particles (positively-charged in the figure) adhere to a negatively-charged glass slide in water. b) Negatively-charged PSS polyelectrolyte (Rg ~ 10 nm) is introduced, which covers the amidine particles except in the “lithographed” region near the plate where the PSS cannot access. c) The particles are sonicated off the glass slide, exposing the nanoscale positively-charged region. d) Negative particles (e.g., silica, sulfated latex) are introduced, which adhere selectively to the positively-charged region on the amidine PSL particles. Figure originally published in Ref. 96. Also see Refs. 150 and 151.

3 COLLOIDAL MOLECULES

3.1 Lab-scale examples of “colloidal molecules” abound in the literature

The literature of the past 10 years contains many examples of colloidal assemblies; Table 3 lists a few. The focus of Table 3 is on “colloidal molecules” assembled either entirely from the bottom-up, or using a templated assist. No field-induced-only assemblies are shown [20,21,22,152,153,], although these can be very important for certain types of monolayers and crystals; these methods do not rely significantly on interparticle colloidal forces. Table 3 also shows the interparticle force used for the assembly process. The most common force exploited is surface tension, which is usually caused during the drying process resulting from hydrophobic forces (which in turn are usually due to van der Waals and hydrogen bond forces).

3.2 Assembly time for particles with site-specific chemistry (“reaction”)

The usual description of particle aggregation follows a diffusion model. All particles are undergoing Brownian motion, and as the particles conduct their “Brownian dance”, some of the particles will approach each other. If two spheres (radius a) adhere to form a doublet, we say that they aggregate. Using the usual diffusion model, we obtain the Smoluchowski rapid flocculation time ( ) given earlier. However, for aggregation of particles with site-specific chemistries, the result is a bit more involved. The “reaction” scheme of particles A and B is comparable to before. Because a number of combinations are possible in general (A-



A, A-B, and B-B), we take the simple case when particle B is in great excess, so that its concentration is not changed significantly upon aggregation.

Table 3. Examples of bottom-up assembled colloidal structures and “molecules”. Most of these are still relatively simple, and the most commonly-produced assembly is the doublet. The force most commonly employed is surface tension, caused by solvophobic forces.

structure force used for assembly crystals sedimentation and surface tension [37], electrostatic [33,33] doublets surface tension [154], electrostatic [96], van der Waals [155], thiol binding

[156], shear-induced aggregation plus van der Waals [157] “water” surface tension [154] T-shapes modeling only [158] tetramers surface tension [154, 159] grape-like clusters surface tension [159] rings of spheres by surface tension [160], of rods by hydrophobic forces [161] lines surface tension [162], surface tension zig-zag [160] and chiral zig-zag [160],

chains of divalent-nanoparticles [163]

The reaction thus proceeds according to BAAB nkndtdn / . Initially we have nA0

concentration of A and nB0 of B. Since B is in excess it remains relatively constant. We examine the case of heteroaggregation of two particles, in which a fraction fA of particle A and fB of particle B are able to bind. For example, if particle A has one small positive region covering 2% of the particle, fA might be 0.02 (or a bit less). If particle 2 is entirely negative, then fB = 1.00. On the other hand, if particle A has a biotin patch covering 3% of the particle, while particle B has an avidin patch covering 4% of the particle, then fA = 0.03 and fB = 0.04. Using a similar analysis to that discussed earlier, for diffusion-limited aggregation, one finds

BAABBBA

BABAAB

BA

BAAB

ffaakT

aaff

aa

aakTk

2

42 66.0,

3

2(3)

For example, say we have particle A with diameter 1000 nm and particle B with diameter 500 nm. They co-exist in water at T = 293 K. Material B is at a volume fraction of 0.01, and it is “hot” all over. Particle A has only 1% of its area “hot”. Then the time for formation is 5.67 sec. One sees that in most cases, the controlling factor for aggregation time is not the diffusion limited aggregation, but the stability that results from interparticle forces.

a1

s1

a2

2s2

a1

s1

a2

2s2

Figure 4. Heteroaggregation of particles with regions of site-specific chemistry. The schematic shows particles whose red regions are repulsive, while their green regions are attractive to the red. Not only must the particle diffuse toward each other by Brownian translation, but their green patches must align by Brownian rotation. Each particle (i = 1 or 2) has roughly a fraction fi = si

2 / 4ai2 of

attractive region for small patches.



3.3 Separations are currently difficult for commercial quantities

In ordinary molecular chemistries, a chemical reaction often takes place, and the products must be separated. Separations must also occur at the colloidal level. If one starts with colloidal atoms and produces colloidal molecules along with some by-products, then these must be separated. There are a number of techniques for separating colloidal particles (Table 4). The challenge is that most of the techniques produce volumes at the analytical scale (<1 mL of particles). Centrifugation is the technique currently best suited to producing larger volumes; however, it is important to note that under most circumstances, a density gradient is required to obtain a successful separation of two or more types of particles [164]. Without the gradient, swirling appears to be inevitable since different parts of the fluid have slightly different effective densities [165,166].

Table 4. Methods for separating colloidal particles. Most of these methods are used for small quantities, as in analytical operations. The only one that is used for particles for larger separation operations is density gradient centrifugation. Ref. 164 is a good general reference book for many of the separations techniques below.

technique separation driving forces plus and minus centrifugation particle densities and sizes + simple

- instability of separation density-gradient centrifugation

particle densities and sizes + fairly simple, some volume - setting up gradients

hydrodynamic chromatography (HDC)

sizes (exclusion from tube wall) + high purity separations - very low (analytical) volume

field-flow fractionation (FFF)

particle size, density, magnetic susceptibility, electrostatic charge, etc.

+ high purity separations - very low (analytical) volume

cell sorter optical characteristics + high purity separations - very low (analytical) volume

column separation [167,168,169]

HDC, FFF effects + good separation, volume - no working prototype!

microfluidics [170] deterministic flow bifurcations based on particle size

+ very accurate separations - low (analytical) volume

3.4 Storage of precursor particles is often straightforward

The storage of precursor particles follows many of the same heuristics that are used to store particles without site-specific chemistry. Low ionic strength is often conducive to storage, and when a “reaction” is desired between particles, the ionic strength is raised slightly. If the ionic strength is raised too much, rapid aggregation can occur at all angles, thereby ruining the controlled aggregation that is sought. Storage of precursors is applicable when the particles have site-specific chemistry placed on their surfaces, as opposed to the formation by surface tension techniques.

4 COLLOIDAL DEVICES

4.1 Some colloidal devices exist already

Currently, colloidal assemblies are at an elementary level; however, it is probable that much more complex colloidal assemblies are coming in the next 10 years, to the point that the engineering of devices will become more common. These will be low power, small devices, some of which cover applications not possible with current technology. Areas of application will include photonics, displays, energy, environmental, and drug carriers.



That said, colloidal devices are not merely a “thing of the future”. Table 5 lists a number of devices that have been fabricated and described in the literature. One current commercial application includes the particle capsules used by E Ink for its display technology, in which small colloids (either white or black) are moved electrically in a capsule of roughly 100 m in diameter. Such displays are currently used for Sony E Books, and are expected to be important in a variety of applications. A research application includes microfluidic applications, in which pumps, valves, and other microfluidic components have been made of colloidal particles, and controlled by laser traps [25].

Table 5. Examples of colloidal devices in the literature. device use or potential use

wavelength filtering device [12] Filtering particular wavelengths of radiation. electrophoretic ink [120] Flexible display with very fine resolution; currently

commercialized by Sony and others. colloidal separator [171] Separation or sorting of microscale particles (e.g., colloids,

bacteria) with a microfluidic system. pumps and valves [25,172] Pumps and valves made of particles, used in microfluidic devices. display [173] Flexible display self-assembled from small electronic components

(>100 m parts) barcode identification tags Small identification tags for information or sensing [174,175]sensor [176] Detection of particles with over a million unique identifications.

4.2 What devices might we expect in the future?

Colloidal device research is progressing at a rapid pace. It is expected that devices will arise in the coming years for photonic applications (e.g., switching), conformal communication systems, rapid DNA sequencing and genetic screening, microscale robotics, energy production/storage, environmental remediation, drug delivery, and other applications.

5 CONCLUSIONS AND FUTURE DIRECTIONS

In comparing colloidal fabrication and molecular synthesis, we are as a research community still studying how to design and produce “colloidal atoms”, and we have begun to fabricate simple “colloidal molecules”. We are not yet near to the enormous complexity of a protein at the colloidal scale, such as Linus Pauling would have appreciated in the molecular regime. However, it is possible that there will one day be a comparable complexity to colloidal assemblies and devices. Current experimental research directions include improving methods for placing chemistry site-specifically on particles. This enables the controlled colloidal bonding that allows for controlled fabrication of particles into devices. Such site-specific placement will likely require a suite of clever techniques developed by many researchers. More fundamentally, experimental research into localized van der Waals forces, localized electrostatic forces, and other localized forces (depletion, receptor-ligand) is underway; the study of these fundamental physical phenomena require detailed analysis and experiments. A third important area of experimental research is placing weak colloidal forces site-specifically on particles, which will require both clever techniques and fundamental research. From a modeling standpoint, the current drives are to learn what structures will result from various orientation-dependent forces – and the inverse problem of designing the colloidal atoms to give a desired colloidal molecules – as well as to study what structures are required to obtain desired material properties. The devices that one can conceive for colloidal assemblies will not only displace some current macroscale technologies, but some devices are likely to be entirely new due to



the new size regimes (colloidal, nanocolloidal) available for fabrication. These devices will be low-power, portable (e.g., to the human body for wearing), conformal (e.g., to a curved airplane body surface, or to a human body), and sometimes of a stealth nature. A few devices have already been fabricated or even commercialized. Applications in photonics, communications, electronics, the environment, drug delivery, and energy are likely on the horizon.

ACKNOWLEDGMENTS

I acknowledge many excellent PhD students who have contributed to our assembly and device work, especially Jason D. Feick, Allison M. Yake, and Charles E. Snyder. I also thank many organizations for funding various parts of this work, including the National Science Foundation (CAREER, NIRT, NER, MRSEC, CBET), the Petroleum Research Fund, the Ben Franklin Technology Partners of Pennsylvania, and the Environmental Protection Agency. Finally, I thank a number of excellent collaborators at Penn State University, especially Milton Cole, James Adair, Ayusman Sen, Tom Mallouk, Christine Keating, Kristen Fichthorn, and Theresa Mayer.

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Darrell Velegol is an associate professor at The Pennsylvania State University. He received his BS degree in chemical engineering from West Virginia University in 1992, and his PhD degree in chemical engineering from Carnegie Mellon University in 1997. He is the author of more than 45 journal papers and book chapters. His current research interests include colloidal and nanocolloidal forces and fabrication.


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Assembling colloidal devices by controlling interparticle forces