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Ahuja, P. & Sharma, P. (2006). Colloidal Crystals and superlattices. PHILICA.COM Article number 68.

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Colloidal Crystals and superlattices

Prerit Ahujaunconfirmed user (Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai)
Prithu Sharmaunconfirmed user (Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai)

Published in chemo.philica.com

Abstract
Colloidal crystals and superlattices have potential to be engineered to synthesize novel architectured materials. Self organization of colloidal particles takes place when assisted by various techniques form single crystals similar to metals. Being a novel class of materials, crystallization of colloidal particles provide an insight into statistical systems and phase transitions. Here we review various synthesis techniques along with optical and electronic applications. The importance of colloidal photonic superlattices in photonics has also been reviewed.

Article body

Introduction:

 

Colloid or colloidal dispersion is a substance with components of one or two phases, a type of mixture intermediate between a homogeneous mixture (also called a solution) and a heterogeneous mixture with properties also intermediate between the two.

 

Colloidal crystals, the periodic distributions of colloidal particles in suspensions of aqueous and organic solvents, have been attracting attention recently. Many researchers have studied interparticle interaction, lattice structure, morphology of single crystals, phase transitions, crystallization kinetics of nucleation and crystal growth, physicochemical properties (rigidity, viscosity, etc.), and structural changes induced by external forces such as gravity, centrifugal and electric fields and shearing forces.

 

Two groups of colloidal crystals have been studied by several researchers: those in 1) diluted and deionized aqueous suspensions and 2) concentrated suspensions in refractive-index-matched organic solvents.

 

Generally speaking most colloidal particles get negative charges on their surfaces by two mechanisms: by the dissociation of ionizable groups and by the preferential adsorption of ions from suspension. These ionic groups leave their counterions, and these excess charges accumulate near the surface, forming an electrical double layer. The counterions in the diffuse region are distributed according to a balance between the thermal diffusive force and the forces of electrical attraction with colloidal particles. The importance of electrical double layers in the formation of the colloidal crystals has been clarified by many researchers. Giant single crystals have been formed in the exhaustively deionized and diluted suspension of colloidal species of polystyrene and silica. Colloidal crystals are very beautiful and fantastic; the interparticle distance is just within the range of wavelength of light in different colours by Bragg diffraction.


 

  

 

  Figure 1: SEM picture of fluorescent core-silica shell particle used for confocal microscopy.

 

Driving force:

 

Colloidal crystallization of soft sphere systems takes place for monodispersed colloidal particles in suspension. Many researchers have clarified that the colloidal crystals are formed by Brownian movement of colloidal size of particles resulting in interparticle repulsion by minimizing the dead space which is not occupied by the particles. In other words, each system forms a crystal-like distribution automatically with the help of Brownian movement of each particle in order to maximize the packing density. Thus, colloidal crystallization is one of the typical systems of three-dimensional auto-organization.

 

When the extra repulsive interaction, like electrostatic repulsion, is effective among colloidal particles in addition to the repulsion forces from their Brownian movement, colloidal crystallization takes place easily even at very low particle concentrations. Most colloidal particles get negative charges on their surfaces in polar solvents like water. The ionic groups leave their counterions and these excess charges accumulate near the surface forming an electrical double layer. The counterions in the diffuse region are distributed according to a balance between the thermal diffusion forces (“repulsive'') and the forces of electrical attraction with colloidal particles. The thickness of the electrical double layers is estimated approximately by the Debye screening length, Dl, given by Eq. (1). The Debye length corresponds to the distance from the colloidal surface, where the electrostatic potential decreases to 1/2.7 compared to that at the slipping zone.

 

                                                                                               (1)

 

Here, e is the electronic charge and ε is the dielectric constant of the solvent; n is the concentration of “diffusible” or “free-state” cations and anions in suspension. Thus, n is the sum of the concentrations of diffusible counterions, foreign salt, and both H+ and OH- from the dissociation of water. The maximum value of Dl in water is about 1 μm, which is estimated from Eq. (1) by taking n = 2 x 10-7 (mol/dm3) x NA x 10-3 cm-3, where NA is Avogadro number. It should be noted that the electrical double layers are always formed in solid in polar liquid.

 

In the deionized state, the electrical double layer is very thick, and the interparticle repulsive forces prevail to a long distance, as long as micrometers, though the forces become to be very weak. Formation of the crystal-like ordering is explained nicely with the effective soft- sphere model. The effective diameter, deff, of spheres includes the Debye screening length and is given by the diameter plus twice the Debye length. When deff is shorter than the observed intersphere distance, D, a gaslike distribution is observed.  When deff is comparable to or a bit shorter than the intersphere distance, the distribution of spheres is usually liquid-like. When the effective diameter is close to or larger than the observed intersphere distance, crystal-like ordering occurs. The effective soft-sphere model has been shown to be good by many researchers from the systematic comparison between deff and D values. The figure given below shows the SEM of a colloidal crystal.

 

 

Morphology and Structure:

 

It is interesting to note that the formation of the single crystals is quite similar to metals. Most metal crystals are composed of single crystals surrounded by grain boundaries. The lattice spacing (i.e., interparticle distance between the colloidal crystals) is very long – several thousand times greater compared with that of metals – and just in the range of wavelength of light.

 

The size of single crystals increases when sphere concentration is decreases in the exhaustively deionized suspensions. This observation is quite understandable because crystal size should increase with decreasing nucleation rate and also with decreasing number of nuclei. Nucleation rate, of course, decreases as sphere concentration decreases. When the sphere concentration is comparatively higher, the size of colloidal crystals is very small, and single crystals can not be observed with the naked eye at all.

 

Generally speaking, crystal structures are face-centered cubic (FCC) or body-centered cubic (bcc) lattices. Square-ordered structures however were observed when two plates of a cell were oriented in wedge geometry. From much data on the colloidal lattice structures, it is concluded that the fcc lattice are more stable and they transform in to bcc lattices when 1) particle concentration is highly diluted, 2) a small amount of salt is added, 3) the suspension temperature is raised, 4) the charge density of particles is high, or 5) high pressure is applied between the subphases of fcc and bcc crystal lattices is highly related to the increased free space for particles forming lattice structures, i.e., the fcc form is more dense than bcc. The FCC and bcc structures are observable visually by a metallurgical microscope especially in sedimentation equilibrium, and the interparticle distances can be determined from microscopic observation.

 

Amorphous-solid (or glass) structured are observed for highly polydispersed colloids, especially in rather concentrated suspensions. Several types of asymmetrical colloidal crystals have been studied, especially in sedimentation equilibrium in deionized suspensions of anisotropic-shaped particles. Cylindrical colloids of nickel dimethylglyoxime (length 9.6 mm, diameter 0.12 mm) were ordered in a hexagonal array. It is clear that the particles are oriented to reduce the dead space as effectively as possible. Interestingly these particles included spheres of various sizes in their cavities. Both the host and guest particles were not in direct contact, but were kept apart from each other by the electrical double layers formed around the particles. The transformation of the particle distribution of ellipsoidal poly(tetrafluoroethylene) from unsymmetrical to symmetrical crystals has been observed with dilution accompanied by the thickening of the electrical double layers. Asymmetrically ordered structures, similar to paved bricks, have been formed in rectangular tungstic acid colloids.

 

Alloy structures of colloids are especially important because most of the structures of metal alloy also appear in colloidal suspensions of binary mixtures of spheres of different sizes. The superlattice structures observed hitherto in colloidal systems are of the AlB2, NaZn13, CaCu5, MgCu2, NaCl and AB4 types.

 

Self-organization of colloidal particles:

 

There are two approaches for the building up of nanoscopic features: they are the 1) top-down method and 2) bottom-up method.  In the top down methods, the features are written directly onto a substrate, for example, by electron beams, and then by applying appropriate etching and deposition processes, the nanoscopic features are engraved. In the bottom up method, nano components are made from precursors in the liquid, solid, or gas phase employing either chemical or physical deposition processes that are integrated into building blocks within the final material structure. Colloidal nano particles are usually prepared by bottom up approach.

 

The formation of superlattice involves two processes. They are the self assembly process and the self organization processes. The Self assembly is an assembly process in which only the constituents of the final structure take part, that is, it gets incorporated into the resulting structure .Self-assembly process involves molecular interactions like hydrophobic versus hydrophilic components, gravitational, Van der Waals or Coulombic interactions.

 

The self assembly process is for the control of the size of the colloidal nano particle. This is generally achieved with the help of capping agents or ligands. The capping agents self assemble on the nano particle in the 3-D and this is referred to as 3-D self-assembly .This self assembly process helps in preventing the particles to agglomerate, thus acting as a barrier called the steric barrier. The steric stabilization is brought by 2 effects which are the volume restriction and the other being the osmotic pressure.

 

The Another method to prevent the agglomeration is by electrostatic stabilization which involves charging the surface by the adsorption of suitable ions, thus involving the formation of an electrical double layer.This introduces an electric potential and if that is high, it leads to the coulombic forces sufficing to prevent agglomeration. These barriers are necessary so as to prevent the agglomeration which is because of the van der Waal interactions which are stong in the nano particle region.

 

When ever self assembly takes a role in organizing, the arrangement is going to be periodic. When self-assembly is used to organize nanomaterial periodically, irrespective of whether the structures so formed are points, lines, layers, or composites, since such arrangements minimize the free energy of the systems. Nanoscale self-assembly is a concept that nature has been making use of since the beginning of life.

 

 

Self-Organization:

 

The self organization involves the formation of 2-D or 3-D arrays from the individual nano particles on to a substrate. 2-d films are formed from the smaller nano particles. For larger particles it aggregates into 3-D arrays due to the rapid increase in the van der Waal forces with size.

 

The different methods of self-organization are:

1) Self –organization through capillary forces

In this process the particles are electro statically charged and are deposited on an unpatterned polar silica surface. When a droplet of colloidal suspension is dried slowly on the substrate, the particles aggregate at the rim of the water droplet because of attractive capillary forces between the particles which comes into effect when the thickness of the liquid is equal to the diameter of the particle.

 

The mechanism is a 3-step one which involves 1) the positioning and adhesion are controlled by charge and polar interactions between the substrate and the charged particles. A sub monolayer is formed on the surface due to electrostatic adsorption of the particles on the surface and the coulomb forces of the like charged particles restrict the very dense packing of the particles on the surface and the sub monolayer is formed in its shape.

 

In the 2nd step as the evaporation of the liquid drop takes place, the liquid drop moves very slowly on the adsorbed layer and a thin meniscus remains on the particle assembly which generates capillary forces between the particles. These capillary forces between the particles and the surface displace the particles laterally during drying. In the 3rd step, a complete evaporation takes place and an irreversible reorganization of the particles occurs. This layer formed is permanent and does not covert back to suspension if immersed in the liquid again.

 

As the evaporation of the liquid occurs, the multilayers are also formed in conjugation. when the droplet front slowly moves ,the particles move towards the liquid front .There the thickness of the water layer above the 1st layer is equal to  diameter of the particle , then the capillary forces come into play and the  get deposited on the top of the colloidal assembly . Thus a multilayer is formed which is an ordered structure. The ordered structure is brought about by the interaction between the capillary forces and the columbic repulsive forces.

 

2) Template assisted:

In this process, a template which has the structure that is intended to be transferred on to the colloidal cystal is used .Those are fabricated using the methods such as photolithography techniques. The advantage of this method is that the no of particles in each template hole can be designed by us by varying the template size and shape .The desired crystalline ordering and orientation can be achieved in the colloidal crystal.

 

3) Optically Directed Self-organization:

An optical standing wave pattern having a regular array of intensity antinodes is created. The colloidal spheres are then driven to the antinodes maximum by the optical forces. Depending on the no of laser beams used, more and more complex colloidal crystal structures can be obtained.

 

 

 

4) Electric or Magnetic Field –assisted:

In this process a layer by layer control of the deposition of colloidal nano particles is possible .The speed of the colloidal crystal growth can be controlled by varying the electrodeposition parameters like voltage, time and electrophoretic mobility. The particles get into ordered phase upon reaching the electrode, which is attributed to the reorganization of the micorspheres in the grooves by squeezing the newly arriving sphere in the already deposited particles. Then they undergo a rearrangement and large scale ordering takes place .In this method the colloidal particles are only weakly adsorbed on to the surface of the substrate and are fairly mobile. The fixing of the colloidal film occurs only after the application of high electric field.

 

5) Combination of the template assisted and the electrophoresis:

In this method, the colloidal particles are charged, so they come to the oppositely charged electrode and deposit. The electrode can be made of a special pattern, so the capillary forces, electrical forces with the help of pattern help in the colloidal crystallization. The pattern has well defined sites to get deposited, so the first layer adjacent to the substrate is formed accordingly. Now this layer acts as a template for the formation of the next layer.

 

 

                    

Figure 2: The formation of the closed packed 2-d crystal layer on different patterns.

 

Formation of Superlattices:

When two colloidal crystals of different sizes are taken, which is told by the factor α=Rs/Rl, then the crystallization occurs and the formation of the superlattice is found to occur at the values of α =0.58 or so. Two kinds of superlattices formed which are the AB2 and AB13 type structures.

 

Ordered AB13 structure:

In the AB13 structure the large particles form a simple cubic lattice; each cubic subcell contains thirteen small particles, one at the body center and the remaining twelve on the vertices of an icosahedron surrounding the central particle. The icosahedra are rotated by 90° between adjacent subcells so that the full unit cell contains eight subcells and a total of 112 particles. The AB13 crystal has been seen in colloidal hard-sphere mixtures at α=0.58 and 0.62

 

Ordered AB2 structure: This crystal, which is isostructural with the alloy AlB2, consists of a simple hexagonal crystal of large spheres with smaller particles filling all the trigonal cavities between the A layers. The structure has been observed in mixtures of colloids with α=0.58

 

Relating with the entropy concepts for the superlattice:

To Minimize the free energy F=U-TS is to maximize the entropy the stability of a binary crystal, AmBn, depends on 3 variables, namely the (a) size ratio a, (b) the total packing fraction f=fs+fl, and (c) the relative numbers of small and large spheres Ns/Nl. The total entropy is made of two parts, degree of spatial ordering which is the ‘‘configurational’’ entropy and that associated with the space available to each particle for local motions, the ‘‘free volume’’ entropy.

 

The configurational entropy decrease as it is confined in a unit cell than that of liquid in which it is free. The superlattice has more free volume, so free entropy is more provided the superlattice fills space more efficiently than the fluid. At low concentrations, the configurational entropy dominates and the fluid is stable but with increasing concentration, the gain in free volume entropy on superlattice formation more than compensates for the loss of configurational entropy, and a stable superlattice is formed. For a Given the size ratio, in particular, if a crystal structure has a high close-packed density (fcp), then, at the lower densities where freezing occurs, the constituent particles will have a large volume in which to move and a correspondingly higher free volume contribution to the entropy. On this basis, the entropy of each structure AmBn should mirror the maximum packing curve fcp (α). Superlattice will form only if its maximum packing fraction exceeds that for the pure one-component phase-separated crystals (=0.74).

 

Guided by maximum packing arguments, the following different crystals are as possible equilibrium structures in mixtures of hard spheres Ordered AB2 structure, Ordered AB13 structure, Ordered NaCl or NiAs structures stiochiometry AB. For α=0.58, the AB2 and AB13 type structures are formed.

 

Example of the formation of the superlattice in gold nano particles:

 

Gold particles prepared as hydrosols were capped with alkane thiols to render them soluble in a non-polar solvent. The particles were then deposited electrophoretically. The solution consisted of Gold colloidal particles of nearly 4.5 and nearly 7.8 nms. This resulted in the formation of the Bimodal AB2 type of superlattice.

 


 

 
Figure 3: TEM micrograph of an AB2 (AlB2-type) superlattice of gold nanoparticles stabilised by decanethiol having a bimodal size distribution.

 

Fabrication of metal colloidal crystals:

The metal colloidal super lattice crystals formed from monodisperse solution of metal nanoparticles show some interesting novel properties that are not shown in isolated nanoparticles.  The fabrication of these enables us to produce nano-optical devices like surface enhanced Raman scattering (SERS) films, optical grating, antireflective surface coating, selective solar absorbers, and data storage devices. The monodisperse metal nanoparticles can also be used as building blocks for nanoelectronic devices also. The formation of metal super lattice structures is done in 2 ways, one is by self-assemble, and other is to use external forces.

 

One-Dimensional Superlattices:

The fabrication of 1D superlattices is the most challenging subject because it is quite difficult to self assemble metal nanoparticles in low symmetry. Template methods are generally used to align the nanoparticles in 1D lattice.

 


 

 
Figure 4: Alumina membrane

 

1-D lattice of 1.4-nm Au nanoparticles can be fabricated by electrophoresis of porous alumina membrane. The pores of these membranes are packed in a parallel hexagonal array formed by an electrochemical anodic process, and the pore diameter is controlled by regulation of anodic potential. By applying electric field strength Au particles can be arranged in 1-D lattice along the length of the pore channel. 

 

Au particles can be arranged in 1-D lattice on amorphous carbon films using the adhesive force at the step edge of carbon films. They can also be arranged on a DNA or biopolymer template, deposited between metal electrodes on an insulating substrate.

 


 

Figure 5: Ridge and valley carbon structure

A novel method is developed to fabricate planar array of 1D chains of Au nanoparticles by the heat treatment in the solid state in combination with another technique to produce nanoscale ridge and valley structured substrates using a vacuum process. Using this method chains of Au nanoparticles are formed on a few square millimeters of carbon substrate.                                             

 

Two-dimensional Superlattices:   

                                   

The fabrication of 2D superlattices mainly involves self-assembly of organic ligand protected metal nanoparticles larger than 2-nm. They easily self-assemble in a hexagonal packing on various substrates due to the capillary force between the nanoparticles during solvent evaporation. But precise control of particle size and shape is necessary to fabricate perfect superlattices.

 


 

Figure 6: Figure illustrating the change in mean diameter with heat treatment.

 

 

A simple and useful method is developed to manipulate the size of Au nanoparticles. By using the heat-treatment of small Au nano-particles in the solid state but not in solution size of Au nanoparticles can be varied. The Au nanoparticles prepared by heat treatment at 150, 190 and 2300C leads to the particle sizes becoming 3.4, 5.4, and 6.8 nm respectively with a variation of 0.5 nm. The 2D superlattice thus formed on the flat carbon-coated copper grids is completely. The thickness of alkanethiol ligand layer which surrounds the metal atoms was found to be 1.25 nm, which is smaller than ligand length (1.8 nm). This shows that ligands interpenetrate each other in 2D superlattices of nanoparticles. It was found that it is possible to control the interparticle spacing of superlattices by changing the alkanethiol ligand. The particle gap increases at the rate of 1.2 A per increase in the carbon atom of the alkanethiol. The control of the particle spacings is important to some potential applications like single-electron tunneling devices etc.

 

 

 


 

 
Figure 7: Figure illustrating the variation of particle spacing with thiol chain length.

 

The 2D superlattices are fabricated not only from the monodisperse nanoparticles of Au, but also from Ag, Pt & other 3d-transition metals. There is an interesting difference between Platinum and others in that platinum frequently forms square lattices while others form hexagonal.

 

There is an interesting feature in the self-assembly of Au nanoparticles of different and well defined sizes. When a 2D superlattice is formed from Au nanoparticles with diameter of less than 10nm and well defined 2 different particle sizes, then the structure depends on the number ratio & size ratio of the particles.

 

Two chemically different metals like Au and Ag nanoparticles can also spontaneously self-assemble to form true nanoscale colloidal alloy superlattices.

 

Although the fabrication of 2D superlattices of metal nanoparticles through self-assembly is convenient, it is difficult to enlarge the assembly area. So a large-scale 2D assembly is formed by using methods (external forces) like electrophoretic deposition and Langmuir-Blodgett technique.

 

Electrophoretic deposition is a useful technique for achieving the 2D assembly of metal nanoparticles of various sizes onto a carbon-coated grid. In this method, the electrophoretic deposition is carried out by immersing the copper sheath carbon (anode) grid and aluminium foil (cathode) into the solution with the electrode spacing of the order of 0.2 cm. A conventional dc power supply is used to generate the applied voltage. Deposition of metal nanoparticles starts occurring due to polarization. The deposition of nanoparticles depends on the time of polarization and gradually increases with time.

 

The Langmuir-Blodgett technique is used for large-scale formation of metal nanoparticle superlattices. This technique can be used for any hydrophobic ligand protected nanoparticles and the assembly area can be expanded to a few hundred square centimeters. In this method the nanoparticle solution is finely spread out on pure water surface and the nanoparticles are slowly compressed to form a layer. The LB film obtained can be transferred onto various solid substrates by the dipping-withdrawing method.

 

Three-dimensional Superlattices:

 

Three-dimensional superlattices of metal nanoparticles consist for nanometer to micrometer sized crystals of close-packed metal nanoparticles. Multilayer deposition of metal nanoparticles can be achieved by 2 ways: one is to use self-assembly technique and another is multilayer assemblies of 2-D particle arrays.

 

Fast evaporation of the solvent from a concentrated metal nanoparticle solution results in the formation of well shaped crystals in the size range of hundreds of nanometers upto a few micrometers. Depending on the particle size & conditions of solvent evaporation, several kinds of superlattices are observed. For example, the superlattice formed from fast evaporation of Au nanoparticle solution corresponds to a hexagonal close packing, while that of CoPt3 nanoparticles had a cubic close packing.

 

 

 

 

 

 

 


 

 

 
Figure 8: Multilayer assembly of 3D superlattices.

 

Multilayer assemblies are achieved by sequential adsorption of dithiol molecules and metal nanoparticles of desired size. A dithiol covered substrate is immersed into the solution of metal nanoparticles with intermediate steps like washing the substrate with toluene and drying it. These steps are repeated to obtain 3D superlattice crystals. Several monometal, bimetal and metal-semiconductor 3D superlattices can be prepared by this method.

Crystallization of colloids to provide insights into phase transitions:

Colloidal crystallization can be used to model the process of general crystallization, and is capable of giving us information about the phase transitions. Unlike the regular metallic crystallization, these transformations involve much larger time scale as well as the length scale. A confocal microscopy can be used to record the process of crystallization.

 

Hard-sphere colloids suspended in a solvent provide an excellent Illustration of the difficulties involved in understanding the equilibrium states and the mechanisms by which systems evolve.

 

Consider a two phase system, a crystal and a fluid. This itself offers a lot of interesting behaviour and indeed has revealed certain intricacies of crystallization. The following may be seen as some of them:

1.      Fluids try to crystallize in the close packed structures, say FCC. In achieving this they pass through many meta-stable states (hcp has been observed as hcp-fcc transition was slow) thus proving the proposed Ostwald rule.

2.      During the nucleation process, not always should the nuclei be spherical. Elliptical nuclei have been observed using confocal microscopy.

3.      But this had its share of controversies even. The effect of gravity is too pronounced on the kinetics of these crystals that systems shown to undergo glass transition and never crystallize on earth, crystallized in a time span of seven days in the gravity free space, which may not be the case with metallic crystallization.

A three-phase system offered a more interesting behaviour for study. The fluid-solid transition can be complicated, but transitions involving three-phase equilibria or metastable states, as found in more familiar atomic and molecular systems, can be even more tortuous, as can be inferred from the increased complexity of the phase diagrams. An analogous situation can be produced in colloidal systems where the addition of polymer is used to produce a short-range attraction between the particles. Depending on the relative sizes of the polymer and the colloid, such systems not only show the gas-crystal coexistence described above, but also gas, liquid and crystal coexistence, leading to remarkable phase behaviour.

 (Note: In this discussion we use the hard sphere model of colloids. Their long-range interaction is termed as solid phase, short-range as liquid, and no interaction as gas.)

 

 The free energy- temperature curves give an idea of the deviation of the system from equilibrium and thus can roughly predict the kinetics of crystallization. Concept of spinodal decomposition vs nucleation and growth is best explained using colloidal systems. The aggregation behaviour seen in colloids is the so-called spinodal decomposition. Similar kinetics has been reported for both the processes. Aggregation can be modeled as particles diffusing and then sticking to each other. So, modeling the spinodal decomposition is now reduced to the problem of diffusion and subsequent sticking reaction (depending on which is the rate-determining step.)

 

Thus phase transitions present us with a variety of bewildering pathways to phase separation, and although many are beginning to be well understood it is perhaps in those routes which lead to the non-equilibrium states-glasses or gels where future surprises

may be found.

 


 

 Figure 9: a. A traditional picture of a crystal nucleating and growing in the original fluid is shown. In order to get reasonable nucleation rates the initial concentration may have to be quite high, resulting in rapidly growing (owing to the large thermodynamic driving force) and thus more-disordered crystals, or aggregates. b, A two-step mechanism is suggested to occur around the metastable critical point. In this case, the initial step is the formation of a fluid droplet, either through phase separation or the presence of critical fluctuations. The high density of this droplet increases the nucleation rate. As the crystal grows, a covering film of fluid acts like a buffer between the original fluid and the growing crystal.


 

  Figure 10: Confocal microscope images of crystallization.

 

Colloidal crystals as electronic and optical materials

 

Finite size effects in superlattices of colloidal nanocrystals results in novel electronic, magnetic, optical, and structural properties of the material. Scaling limits of magnetic storage and microelectronics made out of magnetic [16-20] and semiconductor [21-24] materials play a key role in information technology. Uniformity in composition, size, shape, internal structure, and surface chemistry is very important for desired size-dependent properties of materials. Such uniformities can be obtained by various preparation techniques already investigated for metals [20, 25] and semiconductors [24, 26].


 

 

 Figure 11: Schematic representation of the synthetic procedures of nanocrystals.

 

Monodisperse nanocrystals can be obtained by high temperature solution phase synthesis [26] by adding reagents at hot temperature to achieve nucleation and growth as shown in the figure.

An alternative synthesis approach involves supersaturation at low temperature which finally bursts with nucleation. The time interval between the formations of nuclei and ratio of the concentration of reagents to that of surfactants provides a control to the size distribution of nanocrystals. Surfactants that bind more tightly to the NC surface or larger molecules providing greater steric hindrance (bulkier trioctylphosphines as compared to more compact tributylphosphines) slow the rate of materials addition to the NC, resulting in smaller average NC size. These nanocrystals are collected in powder form by flocculation caused by non-solvents; these powdered nanocrystals can be redispersed in variety of solvents.

 

Quantum Dots

The quantum confinement of nanocrystals of PbSe collapses the continuous density of states of the bulk solid into the discrete electronic states of the nanocrystals. Optical absorption spectra prove the expected size-dependent effects of quantum confinement [27]. These size controlled nanocrystals, obtained by temperature arrestment are shown in the TEM images given below. Such 3D quantum confinements are called Quantum Dots.

 

 

Figure 12: (a) High-resolution TEM image of 7-nm HCP Co nanocrystals revealing subtle lattice imaging of the nanocrystals. (b) Lower-resolution TEM images of an ensemble of 10-nm HCP Co nanocrystals.

 

Fabry-Perot Etalons

Fabry-Perot Etalons are widely used for measuring and controlling wavelength of light in telecommunications, lasers and spectroscopy. Recent advances in fabrication with colloidal crystals have enables the creation of very precise tunable Fabry-Pérot interferometers. In one such research work, colloidal photonic crystals were optimized to yield high reflectance and low loss [28].

 

 

 

Single Electron Transistors

Single-electron transistors and memory cells [29] with Au colloidal islands linked by C60 derivatives when fabricated by hybridization of top–down advanced electron-beam lithography and bottom–up nano-phased material synthesis techniques exhibit clear Coulomb-blockade-type current–voltage characteristics and hysteretic-type gate modulated current.

 

Light Emitting Diodes

SiO2 nanoparticles (~10nm) when spin coated onto silicon substrates and fabricated into large area IR LED, near lasing phenomena can be observed. They are useful for silicon based optical communication system [15]. II-VI semiconductors such as CdS nanoparticles (~5nm) and CdSe (~5nm) have been spin coated onto different substrates and fabricated into flexible green light LED (FLED) [31,32] and orange light LED[33] respectively.

 

Photonic Crystals

Luminescence properties of colloidal nanoparticles can be manipulated by self-assembled photonic crystals. When the emitting wavelength of nanoparticles matches the stop band of photonic crystal, the photoluminescence of the colloidal nanoparticles can be greatly enhanced by up to 5 times. By changing the collection angle of photoluminescence measurements, the photoluminescence intensity of colloidal nanoparticles embedded in photonic crystal can also be controlled.

 

Photovoltaic devices

The photovoltaic devices fabricated from CdS nanoparticles /conducting polymer MEHPPV hybrid exhibits a 64 times increase in power efficiency as compared with pure polymer. If the angle of photoluminescence collection is controlled, the total inhibition of CdSe photo-luminescence can be possible.

 

Colloidal Photonic Crystals

 If the 20th century can be called as the ‘Electronic century’, the 21st will belong to ‘Photonics’. Progress in photonics is closely connected to the development of optical materials, which allow new ways for controlling the dynamics of photons. The fabrication of photonic crystals and periodically modifying them shows the commitment towards achieving these ends.

 

Photonic crystals are periodic arrangement of entities with a periodic variation in the ‘di-electric function.’ Di-electric function (e) is borrowed from the literature of solid-state physics (B1) and for the discussion that follows can be seen as a scalar connecting the electric field (E) and polarization (P). These are typically modeled as ‘patterned di-electric structures.’

   

Photonic crystals exhibit a band structure based on the energies of the photons just as the semiconductors exhibit an electronic band structure. Semiconductors show electronic band structure due to periodic variation of potential, photonic crystals due to periodic variation of e. We are interested in the band-gaps in visible spectrum for it gives the so-called novel properties of photonic crystals. This is where fabrication of photonic crystals plays an important role. We shall get back to the fabrication and aspects relating to it in a while.

 

Speaking in analogous terminology of semiconductors, existence of lattice defects may reduce the photonic band gaps and make the photonic travel easier. This is the principle used in making of ‘resonance cavities’ and ‘wave guides.’ This makes the engineering of the existing Photonic crystals all the more important.

 

Band structure can be obtained by solving the Maxwell’s equations (with necessary assumptions) coupled with the Bloch theorem for periodic crystals. Solutions become complicated often. We take the help of numerical methods like FTD, Plane wave expansion etc to simulate the band structure, and subsequently engineer it.

 

Fabrication of photonic crystals

Artificially engineered photonic crystals need to have its band gap in visible spectrum. A general micron technology (as in semi-conductor industry), would give results way away from the requirements. Due to these extreme demands on miniaturization, substantial progress in nanotechnology has allowed one only recently to consider the artificial manufacturing of Photonic Crystals for optical frequencies in a controlled way.

  

Broadly, the methods of fabrication may be divided into two types:

  1. Top-down approach-Lithographic techniques are used to generate a di-electric modulation within a substrate.
  2. Bottom-up approach- Tendency of the sub-micron sized particles to self-organize themselves into ordered arrays is exploited.

In the discussion that follows we talk about ‘b’

  

Colloidal crystals show a dielectric contrast between the matrix (interstitials) and the lattice points.  If the contrast is significant, the crystals present themselves as photonic crystals. So, a photonic crystal fabrication is equivalent to a colloidal crystal self-organization under controlled conditions. As mentioned earlier, significant progress has been achieved recently in the fabrication of close-packed colloidal arrays. It is now possible to grow crystals in planar geometries with precise thickness control. These samples exhibit high crystalline quality and can be designed to contain anywhere from a few to hundreds of crystalline layers. These materials so formed will be single crystals. To evaluate the band structure of these materials, the formation of stop bands, etc there is an inherent necessity of proposing a theoretical model.

     

Two of the simple models proposed to describe a colloidal photonic crystal are:

a.       Scalar Wave Approximation. (SWA)

b.      Dynamical Diffraction Theory (DDT)

 

These models would enable us to control the conditions of colloidal crystallization in the necessary manner. A comparison between both the approaches and the experimental results is available in literature.

 

Both the models assume di-electric variation to be of the form:

     e(r)= e0 + SU (G) exp (i(k-G).r); U(G) being a Fourier exponent U(G)

is calculated to be, a function of the dielectric contrast and the volume fraction and of course the reciprocal lattice vector G. This is what was meant when one says, periodic variation of the dielectric.

 

In SWA, the electric field is assumed to be a scalar quantity, thus obviously limiting our analysis to a single direction. Both DDT and SWA assume that, the scattering of light is predominantly along one set of planes, which can be a specific experimental condition.  Using these, reasonable values of the wave vectors have been predicted and stop bands well estimated.

 

The modeling has given an idea of using the ‘inverse closed pack’ structure, which involves material of a lower dielectric as the lattice colloids (typically air) and continuous matrix as a material of higher dielectric. This alters the stop bands. One can also play around with the continuous matrix. Changing it so as to give a greater dielectric contrast may yield a high frequency band-gap.

 

The open pore in an interconnected dielectric matrix is obtained in a three-step process. First, a colloidal crystal of latex or silica spheres is self-assembled to generate a template.

Next, the interstitial regions are infiltrated with ceramic (using a sol-gel process) or other materials followed by the removal of template materials by calcinations or etching.

 

Very recently, a faster method to make inverse structures came into light in which we start with commercially available monodisperse polystyrene spheres and nano-crystalline Titania and make a suspension of the titania and polystyrene spheres. A few drops of this suspension is spread on a glass substrate and allowed to dry slowly over a period of 24 h in a humidity chamber. A humidity of 90–95% has maintained at the room temperature of 25o C. As the suspension dries, regions of the film show characteristic colour indicating spontaneous ordering of the spheres.

   

Reason for colour is obviously the huge reflectance at the band gap wavelengths. Hence we see the white light minus the reflected light. This is size dependent and of course orientation dependent i.e. it depends upon which plane is involved in Bragg reflection.

 

  

 

Figure 13: The change in band gap wavelengths with size

 

The band gaps in photonic crystals are characterized by the optical density (absorbance) vs wavelength curves, which are accomplished through a UV-Vis spectrometer.

 

Colloidal photonic superlattices:

One issue, which has not yet been addressed in the fabrication of colloidal photonic crystals, is that of engineered defects. There has been much work on the incorporation of specific types of structural defects into both two-dimensional and three-dimensional crystals. When photonic crystals are formed via lithographic or micromachining methods, both point and extended defects can naturally be built into the structure during the fabrication process. Such defects give rise to propagating modes lying within the forbidden gap in the photonic density of states. However, in the case of self organized crystals, the fabrication of specific types of defects in specific locations within the periodic dielectric lattice is not so straightforward. As a result, the formation of midgap, propagating modes in colloidal crystals is problematic. Another approach to the controlled formation of states within the forbidden gap is to use an extended periodicity, in the form of an optical superlattice. As in electronic superlattice structures, the properties of such systems are dictated by the interplay between the two superimposed periodicities, one corresponding to that of the underlying lattice with lattice parameter a and the second arising from an engineered multilayer structure, typically with a much longer length scale L. This longer periodicity introduces folding in the Brillouin zone and induces the formation of a series of minibands and corresponding midgap states. One added advantage is that we don’t require the L/a ratios to be high in case of colloidal crystals, as even small L/a can induce significant contrast in dielectric constant (thus refractive index) and thus can help in folding of the Brillouin zone. The superlattice structure is formed by the sequential deposition of colloidal photonic crystals using two alternating sizes of silica colloids. Structures fabricated in this fashion offer all of the advantages of colloidal crystals, including simple and inexpensive fabrication from a wide range of materials, precise thickness control, planar thin-film formats, and long-range three-dimensional order with no grain boundaries.

  

The optical density vs wavelength curves as a function of number of layers shows the spring up of mini bands experimentally.

 

It is not an exaggeration to state that the realization of photonic crystals using colloids and their subsequent modification using superlattice structures is a first step in revolutionizing the photonics industry which inturn is going to revolutionise the world.


 

 Figure 14: Band structure illustrating the formation of mid-bands. A is one kind of lattice, B another. It is a sequential deposition of B over A and vice versa, until some 6 layers.

 

Conclusion

The development of synthesis techniques for colloidal crystals and superlattices has dramatically changed the demand, stability and reliability scenario of electronic materials by superbly outperforming the conventional materials. The formation of the single crystals is quite similar to metals. Their synthesis in 1D, 2D, or 3D architecture caters in the form of electronic materials to photonic crystals. Colloidal crystals' self organization has even provided an insight into the phase transitions and study of statistical systems.

 

Artificially engineered photonic crystals hold a firm promise as excellent optical materials. 1D photonic crystals have already been brought to use in the form of thin-film optics for reflection coatings on lenses or mirrors and color changing paints or inks.

 

Establishments such as IBM are doing an excellent job in promoting this field among young scientists. Thus photonics, holds a similar promise to revolutionize the electronics world in the coming years.

 

 

References:

 

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Book Reference:

1. Thermodynamics of materials, David R.Gaskell, Third edition, Taylor and Francis

2. Introduction to Solid State Physics, Charles Kittel, John Wiley and sons.

3. Colloidal crystals grown on patterned surface by Mathieu Allard, Edward H. Sargant.

 

Chapter in edited book:

1. Joydeep Dutta and Heinrich Hofmann. (2004). Self-Organization of Colloidal Nanoparticles. Encyclopedia of Nanoscience and Nanotechnology, Volume 6.

2. Toshiharu Teranishi and Mikio Miyake. (2004). Metal nanoparticle superlattices. Encyclopedia of Nanoscience and Nanotechnology, Volume 5.

 

Conference presentation:

1. W. F. Su, T. W. Tseng, L. Y. Wang and C. A. Dai. (2004). High Efficiency Photovoltaic Devices Fabricated from Nanoparticle-Polymer Hybrids. US Airforce Nanomaterial Symposium.

 





Information about this Article
Peer-review ratings (from 2 reviews, where a score of 100 represents the ‘average’ level):
Originality = 125.00, importance = 175.00, overall quality = 162.50
This Article was published on 20th December, 2006 at 13:23:55 and has been viewed 24711 times.

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The full citation for this Article is:
Ahuja, P. & Sharma, P. (2006). Colloidal Crystals and superlattices. PHILICA.COM Article number 68.


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1 Peer review [reviewer #96352unconfirmed user] added 23rd December, 2006 at 06:58:43

The article is an excellent overview of the subject and touches all the related fields in way that has never been cited before.

The brief explanation of each and every sub topic makes it a very original piece of work and the authors seem to have a good view of the field.

Originality: 7, Importance: 7, Overall quality: 7


2 Peer review [reviewer #47336unconfirmed user] added 20th August, 2011 at 20:48:04

A well presented and interesting overview. It would benefit from a more fundamental, quantum physics and crystallographic approach to
superlattices, currently available on Nature Proceeds. Thus, colloidal quasi-crystals, paracrystals and superlattices can be viewed as represented by quantum groupoids. The preprint largely ignored the Hosemann’s theory of paracrystals and the fruitful convolution approach to a proper/ adequate treatment of such interesting systems. Moreover, experimental approaches and techniques are not considered sufficiently in the preprint, and recent work on graphene, quantum superlattices is not mentioned, although it is pertinent to the subject discussed in this interesting article.

Originality: 3, Importance: 7, Overall quality: 6




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